BUSINESS CASES FOR MICROGRIDS IN AFRICA: An application ...

BUSINESS CASES FOR

MICROGRIDS IN AFRICA:

An application study for Rukara,

Rwanda.

JULIO 2016

PATRICIA CONDE PEÑA

DIRECTOR DEL TRABAJO FIN DE MASTER:

Vanesa Valiño López

Pa

tric

ia C

on

de

Pe

ña

TRABAJO FIN DE MASTER

PARA LA OBTENCIÓN DEL

TÍTULO DE MASTER EN

INGENIERÍA de la ENERGÍA

1

Business cases for microgrids in Africa:

An application study for Rukara, Rwanda

Master en Ingeniería

de la Energía

Contenido

1. Resumen ........................................................................................................................................ 2

2. Introducción .................................................................................................................................. 4

2.1. Reto de Mil Colinas. Condiciones de partida ......................................................................... 4

2.2. Ruanda ................................................................................................................................... 4

2.3. Panorama energético en Ruanda. ......................................................................................... 5

3. Objetivos ....................................................................................................................................... 7

4. Solución técnica. ............................................................................................................................ 8

4.1. Descripción de la idea ........................................................................................................... 8

4.2. Determinación del consumo eléctrico .................................................................................. 8

4.3. Producción eléctrica .............................................................................................................. 9

Datos climatológicos. .................................................................................................................... 9

Suposiciones climatológicas .......................................................................................................... 9

Elección de los componentes de la instalación. .......................................................................... 11

Estado de carga de las baterías ................................................................................................... 12

4.4. Plan económico-financiero .................................................................................................. 17

5. Conclusiones ................................................................................................................................ 19

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de la Energía

1. Resumen

El presente trabajo de fin de máster se centra en el diseño de una microgrid con una

instalación fotovoltaica off-grid para dotar de electricidad a una futura escuela para la asociación

Mil Colinas.

Mil Colinas es una ONG de cooperación internacional fundada en 2011 para luchar contra

las desigualdades sociales entre los países norte-sur. Mil Colinas lleva a cabo un proyecto

educativo en Rukara, Ruanda, que cuenta con tres educadores nativos y casi 200 niños y jóvenes

y sus respectivas familias. El proyecto ha crecido muy rápido y se prevé su continuo aumento en

un futuro próximo, por lo surge la necesidad de tener una escuela propia en la que se pueda

garantizar una educación de calidad.

El pasado verano (2015), se acudió a Rukara para la toma de medidas in-situ así como la

compra del terreno de la futura escuela. El presente proyecto plantea el uso de la energía solar

fotovoltaica como única fuente de alimentación eléctrica a la escuela.

Durante ese período, varias instalaciones fueron visitadas (principalmente escuelas

ruandesas y el centro de salud del pueblo de Rukara). Algunas de estas instalaciones ya cuentan

con suministro eléctrico proveniente de paneles fotovoltaicos. También se tuvieron reuniones

con empresas claves en el sector de las energías renovables en África Central, como Mobisol así

como con instaladores de paneles fotovoltaicos en Ruanda. Además, se estuvo en contacto

directo tanto con los educadores como con los niños y jóvenes que forman parte de Mil Colinas

para conocer sus deseos y necesidades para la futura escuela.

Una vez recogidos los datos pertinentes de este país africano, es necesario comenzar el

dimensionamiento de una microgrid (off-grid) para abastecer de energía eléctrica el proyecto.

Esta red proporcionará la energía necesaria para el alumbrado y la conexión de los ordenadores

principalmente además de dispositivos eventuales como proyectores e impresora.

Todos los componentes que forman parte de la instalación fotovoltaica, se escogen

cuidadosamente teniendo en cuenta factores como la disponibilidad en la zona, fiabilidad del

producto, coste del mismo y vida útil.

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Inicialmente es necesario realizar una estimación del consumo energético diario para

realizar diversas hipótesis acerca de la radiación solar de la zona. Existen datos históricos sobre

la radiación solar media mensual en esta área, pero se necesitan datos más precisos ya que no

todos los días son climatológicamente idénticos.

A raíz de estas hipótesis, es posible realizar diversas simulaciones con ayuda del software

Python con el fin de mostrar el nivel de carga de las baterías en un intervalo de tiempo de una

hora durante un año completo. Con estas simulaciones es posible visualizar de manera gráfica

las carencias energéticas en la red así como analizar el número de ciclos a los que estarían

sometidas las baterías para evitar su acelerado deterioro.

Se realiza una optimización del precio de la instalación. Para ello, se tiene también en

cuenta un precio hipotético de penalización para la demanda energética no cubierta en caso de

que hubiera varios días con muy baja irradiación solar. En función a este precio de sanción y con

ayuda de la herramienta Solver en Excel, es posible optimizar el precio de la instalación

resultante.

Como resultado de este proyecto, se obtiene una instalación que trabajará en 48 V antes

del inversor y con 230 V aguas arriba. El proyecto necesitará 10 paneles fotovoltaicos de 295 W

cada uno y 12 baterías de 200 Ah de capacidad cada unidad.

Estos dispositivos junto con el inversor y el controlador además de los cables y otros

accesorios, el coste de la instalación alcanza un valor de $12,257.67 pero sería necesario contar

con un presupuesto de $19,800.89 en total para asegurar el correcto funcionamiento de la

instalación durante al menos 24 años de vida útil.

Se han realizado varios planos de la instalación con AutoCAD que se adjuntan en el

proyecto y una maqueta 3D realizada con la herramienta Sweet Home 3D.

* Se aconseja consultar la versión en inglés ya que posee toda la información detallada del proyecto.

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2. Introducción

2.1. Reto de Mil Colinas. Condiciones de partida

Uno de los principios de Mil Colinas es contribuir con el desarrollo sostenible ya que es

importante satisfacer las necesidades actuales sin poner en peligro las necesidades futuras. Mil

Colinas quiere ser respetuosa con el medioambiente y contribuir con las políticas energéticas en

Ruanda, las cuales están promoviendo las energías renovables, sobre todo la energía solar

fotovoltaica.

También es importante respetar la cultura y las tradiciones ruandesas así como los valores

éticos de la zona. Es fundamental tener en cuenta que la cooperación implica el intercambio de

valores y no la imposición de los mismos. Por esta razón, Mil Colinas quiere que el trabajo sea llevado

a cabo por gente nativa para potenciar la economía local.

Es evidente que hay una carencia energética en el área y en aquellas zonas en las que hay red

eléctrica, los cortes de suministro son muy frecuentes. Mil Colinas cree que para el desarrollo de un

país hay que potenciar la educación y para conseguir este objetivo, es necesario tener un sistema

eléctrico fiable. Mil Colinas quiere garantizar la existencia de un lugar en el cual los niños y jóvenes

puedan estudiar y llevar las actividades diarias para su desarrollo personal y profesional.

El último requerimiento para este proyecto, es la optimización del sistema eléctrico. Es

primordial prestar atención al aspecto económico garantizando una calidad en el sistema eléctrico.

Mil Colinas establece una inversión inicial máxima de $12,000 para la construcción y puesta en

marcha de la instalación, y $8,000 para el posterior mantenimiento y garantizar una vida útil de la

instalación de al menos 24 años.

2.2. Ruanda

Ruanda es un país interior situado en África Central con frontera con Uganda en el norte,

Tanzania en el este, Burundi al sur y la República Democrática del Congo al oeste, junto con el lago

Kivu.

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Tiene un área de 26.388 km2 y el país entero está situado a una gran altura estando por

encima de los 1000 metros sobre el nivel del mar en los puntos más bajos. La capital del país es Kigali

que está situada en el centro de Ruanda.

El país tiene un clima tropical templado debido a su altitud y tiene temperaturas más bajas

en comparación con los países ecuatoriales. La media se sitúa entre 16 y 26 °C.

Respecto a la población, Ruanda tiene una estimación de 11,6 millones de habitantes al

comienzo de 2016, con una esperanza de vida de 63,9 años.

Ruanda tiene una de las densidades de población más altas del mundo (460 habitantes por

m2) y hay un doctor por cada 16.000 habitantes.

En los últimos años, el gobierno se ha centrado en promover la educación para los jóvenes.

Actualmente el 29% de la población es analfabeta sin embargo el 95% de los niños están matriculados

en estudios de educación primaria.

Ruanda es un país trilingüe, las lenguas oficiales son inglés, francés y kinyaruanda.

La moneda nacional es el franco ruandés (RWF). Ruanda tiene una economía de subsistencia

que representa el 90% y las exportaciones principales son de té y café.

2.3. Panorama energético en Ruanda.

Se estima que solamente el 23% de la población tiene acceso a la electricidad. Este hecho

afecta fuertemente a la situación del país y a su desarrollo, convirtiéndolo en un país débil y

vulnerable. Los balances energéticos del país muestran que el 84% de la energía consumida viene de

la biomasa por el alto uso de madera y carbón para cocinar. El petróleo cubre solamente el 12% de

la demanda energética actual.

La electricidad en Ruanda es un producto de lujo. En septiembre de 2015, su precio aumentó

un 35% alcanzando un coste aproximado de 0,28 $.

Ruanda es un país con varias fuentes de energías renovables: la energía hidroeléctrica es muy

recurrida debido a la orografía del país, hay reservas de metano en el lago Kivu pero la falta de

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tecnología hace que no se hayan explotado por el momento. La nueva tendencia en Ruanda es la

energía solar y el mercado de la energía fotovoltaica está en pleno auge.

Actualmente, Ruanda tiene una de las plantas fotovoltaicas más importantes en África.

Rwamagana Solar Power Station funciona desde septiembre de 2014 y es una instalación conectada

a red que supone más del 6% de la energía nacional actual.

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3. Objetivos

El principal objetivo de este proyecto es el estudio y diseño de una red de suministro eléctrico

para una escuela en Rukara, Ruanda. Objetivos secundarios se describen a continuación:

- Dimensionamiento de la instalación eléctrica acorde a las necesidades existentes en la

actualidad.

o Estimación del consumo energético diario así como la tendencia de la irradiación

solar en el área.

o Elección de los equipos apropiados para la instalación fotovoltaica: paneles

fotovoltaicos, acumuladores y otros dispositivos electrónicos necesarios.

o Optimización tecno-económica de los paneles fotovoltaicos y las baterías con el

software Python.

- Estudio de viabilidad del proyecto el Ruanda adaptado a las condiciones locales.

- Estudio económico.

o Presupuesto del proyecto

o Comparación entre sistema conectado a red e aislado: ventajas e inconvenientes

o Mantenimiento de la instalación después de la puesta en marcha.

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4. Solución técnica.

4.1. Descripción de la idea

Se pretende construir una escuela en Rukara, Ruanda. El alcance de este proyecto es el

dimensionamiento del sistema eléctrico. El terreno dónde se construirá la futura escuela tiene las

siguientes coordenadas: latitud: -1.800, longitud: 30.504.

4.2. Determinación del consumo eléctrico

En la siguiente Tabla se muestra la previsión del consumo energético.

Tabla 1. Estimación del consumo energético de lunes a viernes.

Devices Power

(W) Quantity

Total

Power (W)

Maximum time

per day (h)

Daily energetic

consumption (Wh)

Laptops 50 23 1150 3 3450

50 2 100 10 1000

Speakers 20 1 20 4 80

Printer 600 1 600 1 600

Lights 4x classroom (15x6m) 11 56 616 3 1848

Lights office (6x6m) 5 4 20 4 80

Lights big room (18x12m) 11 40 440 3 1320

Outside lights 11 7 77 13 1001

Projector 190 1 190 5 950

Charge Mobiles & other things 5 10 50 6 300

3263 10629

Es posible observar que se requiere un suministro de 10629 Wh de lunes a viernes, el

consumo eléctrico durante los sábados y domingos será inferior.

Todos estos valores se muestran de forma detallada en el proyecto en la versión en inglés

dónde también se pueden ver los consumos energéticos por hora.

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de la Energía

4.3. Producción eléctrica

Datos climatológicos.

Una vez conocidos los datos de la previsión de consumo, es necesario cuantificar la energía

solar disponible en la zona. Los meses con menor irradiación solar corresponden con noviembre y

diciembre, teniendo unos valores de 4,54 y 4,57 kWh/m2/día respectivamente.

Figura 1. Radiación solar en Rukara

La microgrid será dimensionada a partir de los datos de los dos últimos meses del año. Es una

manera de cerciorarse que los meses en los que el sol brille más, no habrá carencia energética si la

instalación está bien dimensionada.

En otro lugar, es necesario conocer la hora del amanecer que es a las 6 de la mañana y la

puesta de sol a las 18 horas, el pico de radiación solar es a las 12 am.

Suposiciones climatológicas

Para comenzar, se construye la curva porcentual de la radiación solar recibida. Para poder

trabajar con el área bajo la curva, se crea el gráfico mostrado en la Figura 2 en el que cada barra

vertical representa la radiación solar recibida por un intervalo de tiempo de una hora en Wh.

4

4,2

4,4

4,6

4,8

5

5,2

5,4

kWh

/m2 /

día

Radiación solar

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Figura 2. Gráfica porcentual de radiación solar.

Se han realizado varias suposiciones climatológicas asumiendo 0%, 10%, 25% y 50% de días

sin radiación solar. Interpolando posteriormente todos los resultados, se concluye que si se

considerasen simplemente dos tipos de días, soleado y nublado, tomando como valores de

irradiación solar para cada uno de ellos 100 y 0%, en la población de Rukara habría una media de 19

días soleados y 11 nublados en los meses como noviembre y diciembre.

Asumir que haya un 100% o un 0% de sol, es una suposición muy poco precisa ya que, en la

realidad esto no ocurre prácticamente ningún día.

Acorde con la zona en la que se está realizando el estudio, se considera adecuado seguir tres

diferentes patrones para la radiación solar recibida. Los establecidos “Sunny days” implicarán el

máximo valor posible de radiación solar a las 12 (hora del pico solar) 1.00 kW/m2, los llamados

“Normal day” suponen el 70% de energía respecto a los descritos previamente. Por último, el tercer

patrón a seguir es el conocido como “Cloudy day”, en el que la energía recibida será de 0.250 kW/m2

en el momento del día que en el que los rayos del sol brillen con más fuerza. De nuevo, en la versión

en inglés es posible ver el desarrollo detallado de la obtención de estos resultados.

0%

20%

40%

60%

80%

100%

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Hour

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Elección de los componentes de la instalación.

En este apartado se van a describir las principales características de los componentes elegidos

para la instalación fotovoltaica. En primer lugar, cabe mencionar que la red trabajará en 48 V en

corriente continua antes del inversor y en 230 V y alterna después de éste.

Paneles fotovoltaicos.

Son paneles monocristalinos de la marca African Energy. Cada panel tiene una potencia pico

de 295 W y su eficiencia modular es superior al 15% con un área de 2 m2.

Baterías

Los acumuladores seleccionados son de la marca Sun Light y el modelo es VRLA Battery SPB

12-200. Se trata de baterías de plomo-ácido con una capacidad de 200 Ah cada unidad, que

corresponde con 2,4 kWh de energía. La vida útil es de 12 años pero hay que prestar especial atención

al número de ciclos a los que serán sometidas las baterías para no dañarlas antes de lo previsto.

Inversor

El inversor es el encargado de convertir la corriente continua de 48V en alterna a 230 V. Se

ha escogido la marca Victron Energy y el modelo es Quattro inverter 48/5000/70-100/100 230V

debido a que, a parte de ser una de las marcas más fiables del mercado, este modelo tiene la potencia

que se estaba buscando (5000 W).

En teoría, con sólo 3,2 kW sería suficiente, pero se prevé el crecimiento de la escuela. De este

modo, sólo sería necesario añadir paneles y baterías no teniendo que cambiar este aparato ya que

tiene un coste elevado.

Controlador

El modelo elegido es FLEXmax 80 (FM80-150VDC). Se caracteriza por su elevada eficiencia

(97.5%) y puede trabajar en 48 V que es el voltaje de la migrogrid.

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Estado de carga de las baterías

El objetivo de este apartado es mostrar el estado de carga de las baterías para poder

optimizar el número de paneles fotovoltaicos y baterías en la instalación.

Se han corrido varias simulaciones en Python, el código y las variables detalladamente

explicadas se encuentran en la versión en inglés.

Se han hecho simulaciones con 8 y 12 baterías, ya que tienen que estar distribuidas en ramas

de cuatro unidades para alcanzar el voltaje requerido (cada batería trabaja a 12 V). Referente a los

paneles fotovoltaicos, se han corrido simulaciones con 8, 10 y 12 unidades (cada rama en serie debe

contar con dos unidades).

Se han establecido también varias restricciones, como por ejemplo, que las baterías no se

descarguen por un nivel inferior al 30% para evitar su deterioro prematuro.

A continuación se van a mostrar los resultados obtenidos para cada caso.

Distribución aleatoria

En este caso se asignan de manera aleatoria los diferentes patrones climatológicos

previamente explicados (Sunny, Normal y Cloudy day) respetando los valores de los datos

estadísticos de radiación recibida mensualmente. Por ejemplo, para noviembre y diciembre,

habrá un 33,3% de días de cada patrón y para los meses más soleados, como pueden ser julio

agosto y septiembre, se asume que el 40% de los días seguirán el patrón “Sunny”, otro 40%

el patrón “Normal” y tan sólo el 20% de ellos serán “Cloudy days”.

En la primera simulación se han tenido cuenta los datos para un año entero en un intervalo

de tiempo de 1 hora.

En las Figuras 3 y 4 se muestran las gráficas de las simulaciones usando 10 paneles

fotovoltaicos y 8 y 12 baterías respectivamente.

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Figura 3. Estado de carga de las baterías. 8 baterías y 10 paneles fotovoltaicos.

Figura 4. Estado de carga de las baterías. 12 baterías y 10 paneles fotovoltaicos.

En ambas Figuras, es posible apreciar que la demanda eléctrica es cubierta en todo momento

y que en ninguna de las dos simulaciones mostradas el nivel de las baterías llega al 30%. Si se

realiza una instalación con 12 baterías, se asegura que las baterías no van a sufrir con la carga

y descarga de las mismas.

En esta simulación con distribución aleatoria, no se ha permitido la existencia de dos “cloudy

day” consecutivos, las siguientes simulaciones trataran escenarios climatológicos más severos. A

partir de ahora, las simulaciones serán realizadas solamente para noviembre y diciembre porque si

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no hay carencias energéticas para estos meses, no las habrá para el resto del año dónde la radiación

solar es mayor.

S-N-C

Este segundo escenario sigue un patrón de un día de cada tipo. Con otras palabras, se realizan

series de “Sunny”, “Normal” y “Cloudy day”. En la Figura 5 se muestra la gráfica comparativa

para 8 y 12 baterías, usando 10 paneles fotovoltaicos.

Figura 5. Estado de carga de las baterías.8 y 12 baterías y 10 paneles fotovoltaicos. SNC

Cómo se aprecia en la Figura 5, en ninguno de los dos casos, el nivel de carga de las baterías

es inferior al 40%. A continuación otra simulación más estricta se lleva a cabo.

S-S-N-C-N-C

En este escenario, se presentan dos días soleados consecutivos y normal y nublados

intercalados entre ellos. Los resultados se muestran a continuación en la Figura 6.

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8 batteries 12 batteries

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Figura 6. Estado de carga de las baterías.8 y 12 baterías y 10 paneles fotovoltaicos. SSNCNC

En el caso de la implementación de 8 baterías, habría carencias energéticas de 2.41 kWh

durante estos dos meses de simulación.

S-S-N-N-C-C

Aquí se plantea la primera simulación hasta el momento que reúne dos días consecutivos con

baja irradiación solar. Los resultados se muestran en la Figura 7.

Figura 7. Estado de carga de las baterías.8 y 12 baterías y 10 paneles fotovoltaicos. SSNNCC

En la Figura 7 es posible observar que existen puntos en los que la demanda energética no es

cubierta cuando la instalación tiene 8 baterías.

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S-S-S-N-N-N-C-C-C

Este escenario es el más severo de todos los propuestos. Consiste en tres días soleados, tres

días normales y tres días nublados. Es extremadamente raro que esta distribución pueda

tener lugar en un país como Ruanda, pero se considera importante realizar la simulación para

hacer mejor las previsiones y no tener cortes de suministro en la red eléctrica de la futura

escuela.

En la Figura 8 es posible, al igual que en los apartados anteriores, observar la comparación

del estado de carga de las baterías en el caso de utilizar 8 o 12 baterías. La simulación es

realizada asumiendo que serán instalados 10 paneles fotovoltaicos.

Figura 8. Estado de carga de las baterías.8 y 12 baterías y 10 paneles fotovoltaicos. SSSNNNCCC

En este caso, hay una carencia energética en ambos casos (2 y 3 ramas de baterías). Esto se

observa ya que hay varios puntos en los que el nivel de carga de las baterías alcanza el 30%

(ya que es el valor mínimo establecido).

Se concreta un precio hipotético de penalización para esta demanda no cubierta (13,92$ por

kWh no cubierto) y se concluye que, optimizando el precio de los componentes de la instalación y

teniendo en cuenta esta sanción económica ficticia, la mejor configuración es la instalación de 10

paneles fotovoltaicos y 12 baterías.

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También se ha calculado la sección de los cables así como su longitud. La Tabla 2 recoge estos

datos.

Tabla 2. Sección de los cables.

Sección Sección de los cables

(mm2)

1. Paneles fotovoltaicos - Controlador 16

2. Controlador – Baterías 35

3. Controlador - Inversor 10

4. Inversor – Cuadro eléctrico 4

4.4. Plan económico-financiero

Una vez que se ha determinado el número de equipos necesarios, es posible saber el coste

de la instalación completa. A continuación, en la Tabla 3, se observan los precios de los diferentes

equipos para la instalación así como para su correcto funcionamiento para los primeros 24 años de

vida útil.

Tabla 3. Coste de la instalación.

Vida útil (años)

Cantidad Item Precio por unidad ($)

Dto Precio

total ($)

Precio por año

($)

Precio para 24 años ($)

12 12 Batería (200Ah) 343.75 5% 3918.75 326.56 7837.50

30 10 Panel

fotovoltaico (295W)

375.00 5% 3562.50 118.75 3562.50

12 1 Controlador 781.25 5% 742.19 61.85 1484.38

15 1 Inversor 2656.25 5% 2523.44 168.23 4205.73

25 1 Materiales

varios 1000.00 - 1000.00 40.00 1000.00

25 1 Instalación &

transporte 390.79 - 390.79 15.63 390.79

2 1 Mantenimiento 120.00 - 120.00 60.00 1320.00

12257.67 791.02 19800.89

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de la Energía

El precio total para la puesta en marcha es de 12257,67 $, pero será necesario contar con un

presupuesto de 20000 $ para asegurar la continuidad de esta instalación durante al menos 24 años.

Para finalizar, se ha realizado una comparación del precio de la electricidad en Ruanda

proveniente de la red eléctrica nacional con el precio de la electricidad de la microgrid ya diseñada.

La electricidad en Ruanda es de prepago. El coste de cada kWh es de 215.3 RWF que equivale

a 0,278 $, sin embargo el precio del kWh proporcionado con la microgrid diseñada tendrá un coste

de 0,264 $.

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de la Energía

5. Conclusiones

El desarrollo de un proyecto como este, no utiliza una tecnología novedosa, sin embargo es

necesario señalar que en África, este tipo de tecnología no ha sido implementada tanto como en el

mundo occidental. Un diseño sostenible que usa energía solar fotovoltaica, no satisface solamente

las necesidades energéticas, sino que permite el crecimiento económico de este continente.

El uso de softwares como Python, permite mejorar y optimizar los diseños. Por ejemplo, el

código creado, permite mostrar el nivel de carga de las baterías en un intervalo de tiempo de una

hora durante un año entero. Esta herramienta es altamente útil ya que ha permitido optimizar

exitosamente el número de paneles fotovoltaicos y baterías para el correcto funcionamiento de la

instalación. Es importante hacer hincapié en este aspecto ya que todo el dinero ahorrado en la puesta

en marcha y mantenimiento de la instalación, es dinero que se invertirá en la educación de más niños

y jóvenes en un área tan pobre y vulnerable como Rukara.

Las principales conclusiones de este proyecto son brevemente discutidas a continuación:

- La primera de ellas, es señalar la importancia del uso de tecnologías renovables en

conexiones aisladas. Esto reduce el precio de la factura eléctrica, reembolsando el dinero

invertido en la instalación. Actualmente, la red eléctrica de Ruanda sufre numerosos cortes

de suministro y con el diseño de la micro-grid, este problema estaría resuelto. No es posible

asegurar una educación de calidad si hay frecuentes cortes eléctricos.

- Es necesario tener un adecuado mantenimiento y vigilancia de la instalación. Por ejemplo,

una falta de limpieza de los paneles fotovoltaicos puede reducir la energía producida no

llegando a cubrir las expectativas energéticas previstas.

- La simulación realizada con Python muestra que la mejor configuración es de 12 baterías de

200 Ah cada unidad, distribuidas en ramas de 4 unidades cada una. Respecto a los paneles

fotovoltaicos, se necesitan 10 unidades de 295 W pico cada uno, conectados de dos en dos

para alcanzar el voltaje de 48 V. Esta cantidad ha sido determinada teniendo en cuenta el

precio de cada equipo así como el precio hipotético de penalización que es de 13,92 $ por

kWh no cubierto.

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de la Energía

- El presupuesto necesario para la instalación es de 12257,67 $, pero se requieren 7543,23 $

extras para asegurar el correcto mantenimiento durante al menos 24 años de vida.

Para concluir esta sección, es importante enfatizar en la importancia de este proyecto ya que

muy pronto pasará de ser una idea a un hecho. La electricidad tendrá un coste de 0,264 $ por kWh

consumido proveniente de la diseñada microgrid. El precio de la electricidad en Ruanda es

actualmente de 0,278 $ por kWh. Es un proyecto viable y que merece la pena por todos los puntos

comentados previamente.

-



Energy Engineering

Master’s Degree

Faculty of Applied Sciences

Energy Engineering Master’s Degree

Final Master’s Thesis

BUSINESS CASES FOR MICROGRIDS IN AFRICA


Patricia Conde Peña Academic year 15/16



Energy Engineering

Master’s Degree

Energy Engineering Master’s Degree

Master’s thesis

The present work, below the name “BUSINESS CASES FOR

MICROGRIDS IN AFRICA: An application study for Rukara, Rwanda”,

constitutes the memory which belongs to the subject Final Masters

Thesis and it is presented by PATRICIA CONDE PEÑA as a part of her

formation to aspirate to the title Master’s Degree in Energy

Engineering. The current work has been made in Liège University in

the applied sciences department.

Liège, 8 June 2016.



Energy Engineering

Master’s Degree

Je souhaiterais dédier une petite place dans le présent travail de fin d’études (TFE) à ces personnes

qui m’ont aidée à sa réalisation et qui m’ont accompagnée tout au long de mon Master à Madrid ou à

Liège. J’ai rédigé celui-ci en français pour laisser une petite trace de la région où j’ai habité ces derniers

mois et où j’ai réalisé mon TFE.

Je tiens à remercier en premier lieu mon coordinateur, Monsieur Damien Ernst pour son initiative

de s’être disposé pour suivre les travaux d’étudiants Erasmus, ainsi que la motivation et la confiance qu’il

m’apporté pour le réaliser. En outre, je souhaite remercier Vincent François, ainsi que Samy Aittahar, pour

le temps qu’ils m’ont accordé pour encadrer le TFE.

Ensuite, j’aimerais mentionner mes collègues de l’université de Madrid pour avoir été des piliers

fondamentaux lorsque j’ai traversé cette étape. Parmi eux, je remercie tout particulièrement Pablo, pour

sa connaissance par coïncidence la première semaine de cours et son expérience dans le domaine de

l’éxergie, Rubén pour sa maîtrise des Diagrammes de Bode, ainsi que de Juan que nous avions rencontré

par correspondance et qui est devenu un véritable ami. En outre, mon amie Sara avec qui j’ai réalisé mes

études et partage de nombreux souvenirs dans les domaines scolaires, professionnels et du voyage. Je ne

peux pas oublier de mentionner Héctor et Álvaro qui ont résolu des doutes en ce qui concernent la partie

plus technique du projet avec plaisir.

De plus, je souhaiterais mentionner tous les liens d’amitié créés à Liège, dans un pays où la culture

est différente de la mienne. Entre eux, Giulio, Mireia et Riccardo pour avoir formé la meilleure équipe

Erasmus à Liège. Marina pour être mon âme sœur lors de ces derniers mois, ainsi que Laura, sans laquelle

je ne serais pas parvenue à réaliser un tel projet.

A présent, je voudrais remercier de tout cœur Mil Colinas, une organisation qui me permet de

réaliser mes rêves. En effet, je voudrais parler des jeunes, ainsi que des éducateurs Rwandais qui

collaborent pour que l’éducation soit possible pour tous, et spécialement Tharcisse. Tout particulièrement

María, responsable de cette magnifique organisation de coopération qui se bat pour un monde un petit

peu plus juste, et qui a m’a toujours aidée lors de la conception de ce TFE.

Pour conclure, je dédie ces quelques lignes à ma famille, en reconnaissant l’effort économique

qu’ils ont dû réaliser pour me permettre d’étudier à l’étranger. Mes grands-parents pour leurs

encouragements, ainsi que ma mère qui a suivi mon séjour avec le plus beau de ses sourires.



Energy Engineering

Master’s Degree

INDEX

1. SUMMARY ..................................................................................................................................... 1

2. INTRODUCTION ............................................................................................................................. 1

2.1. Mil Colinas ..................................................................................................................................... 2

2.1.1. Mil Colinas’ challenge ............................................................................................................. 2

2.1.1.1. Starting conditions .......................................................................................................... 2

2.2 Rwanda ........................................................................................................................................... 3

2.2.1. Geography and climate .......................................................................................................... 3

2.2.2. Demographics and social statistics ........................................................................................ 4

2.2.3. Economy ................................................................................................................................. 5

2.3. Global current energetic outlook .................................................................................................. 6

2.3.1 In Africa .................................................................................................................................... 7

2.3.2 In Rwanda ................................................................................................................................ 8

2.4. Solar energy in Rwanda ................................................................................................................. 9

3. OBJECTIVES .................................................................................................................................... 2

4. TECHNICAL ASPECTS ...................................................................................................................... 2

4.1. Microgrids .................................................................................................................................... 12

4.1.1. Photovoltaic system ............................................................................................................. 12

4.1.1.1. Photovoltaic generator ................................................................................................. 13

4.1.1.2. Batteries ........................................................................................................................ 14

4.1.1.3. Inverter .......................................................................................................................... 15

4.1.1.4. Controller ....................................................................................................................... 16

5. TECHNICAL SOLUTION ................................................................................................................. 17

5.1. Description of the idea. ............................................................................................................... 18

5.2. Determination of the electrical consumption. ........................................................................... 19



Energy Engineering

Master’s Degree

5.3. Electrical production ................................................................................................................... 20

5.3.1. Climatological datum. .......................................................................................................... 20

5.3.2. Weather assumptions. ......................................................................................................... 21

5.3.2.1. Types of daily climates. ................................................................................................. 23

5.3.2.2. Climatological days distribution ................................................................................... 28

5.3.3. Devices characteristics ......................................................................................................... 29

5.3.3.2. Batteries ........................................................................................................................ 31

5.3.3.3. Inverter .......................................................................................................................... 33

5.3.3.4 Controller ........................................................................................................................ 34

5.3.4 Python simulations. ............................................................................................................... 35

5.3.4.1. Definition of the variables. ........................................................................................... 35

5.3.4.2. Python program............................................................................................................. 36

5.3.4.3. Python results ................................................................................................................ 37

5.3.5. Microgrid measuring ............................................................................................................ 47

5.3.6. Buildings distribution. .......................................................................................................... 50

5.3.7. Economical plan. .................................................................................................................. 51

6. CONCLUSIONS ............................................................................................................................. 17

7. BIBLIOGRAPHY ............................................................................................................................. 52

8. APPENDICES ................................................................................................................................ 56

Appendix 1. Relevant data. ................................................................................................................ 56

Appendix 2. Python code. .................................................................................................................. 68

Appendix 2.1. Demand values for Random Distribution. ............................................................. 72

Appendix 3. Results ............................................................................................................................ 93

Appendix 4. School Plans ................................................................................................................... 94

Appendix 5. Brochures……………………………………………………………..………………………………………………. 96



Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

1. SUMMARY

1



Energy Engineering

Master’s Degree

Mil Colinas is a NGO founded in 2011 in order to contribute to the battle against inequality.

Mil Colinas mediates between northern and southern countries in order to further social

development. It is an educative project which started with 30 children and has grown to almost 200

people in addition to three Rwandese educators. Due to the fact that the current room is too small

to carry out the activities, there is a clear necessity for the association to have its own space.

Last summer (2015), I went to Rukara, the Rwandese village in which Mil Colinas operates. I

began taking its measurement and shortly after the land was purchased. The current project plan is

to utilize solar energy for the school's main source of power.

During the period in which I was there, several facilities were visited (mainly schools and the

health centre of Rukara) and some of them are already working with photovoltaic energy. Meetings

took place around the country with key energy businesses in East Africa, such as Mobisol. Also the

educators and children who are involved in Mil Colinas were directly contacted in order to understand

and record the needs and desires they have for the new school.

With all the necessary data from this African country, an off-micro grid has to be designed for

the current project. This grid provides the required energy (mainly for lights and laptops) through a

photovoltaic system and accumulators.

Initially, it was necessary to measure the consumption as well as the solar irradiation in the

area. Several hypothesis were created; taking into account different weather and other assumptions.

Following the hypothesis, some simulations were run in Python in order to plot the charge

level of the batteries per hour throughout the whole year. Having these results, some decisions could

be taken in account in relation to the quantity of the photovoltaic panels and the batteries with the

help of the tool Solver in Excel. The wiring was also calculated as well as the optimum angle for the

electrical generators. The system is optimized regarding the economical plan. Several plans were

made with AutoCAD are attached as well as the 3D views of the school made with SweetHome3D.

As result of this project, there is an installation which will work in 48 V before the inverter

and in 230 V upstream; 10 photovoltaic panels of 295 W each and 12 batteries of 200 Ah of capacity.

Each unit is part of the installation along with the inverter and the controller. Initial investment

reaches $12,257.67 but it is necessary to have a budget of $19,800.89 in total to assure the proper

function during at least 24 years.



Energy Engineering

Master’s Degree

2. INTRODUCTION

2



Energy Engineering

Master’s Degree

2.1. Mil Colinas

Mil Colinas is an association that takes its name from the Rwandese orography. Mil Colinas

was founded in 2011 by a group of volunteers from different professions. They are aware of the

reality of the Rwandese people. They think that, together, it is possible to build a fairer and more

human society. Their mission is to raise awareness about the fact the poverty levels in the country

and to collaborate with the Rwandese people to tackle this problem.

2.1.1. Mil Colinas’ challenge

When Mil Colinas was founded, 30 young people were part of it. Now, in 2016, 200 children

young people, along with their families, are part of the association. The current problem is that the

place they use for their activities is still the same one. It is not possible to rent a bigger place because

in this rural area it is very difficult to find a space that can cover their needs. Therefore, building one

is a priority for Mil Colinas in order to ensure they can continue providing good quality education.

During the summer of 2015, the land was bought and now there are several fundraising

campaigns ongoing which will provide enough money to start building the new school as soon as

possible.

The goal of this project is to design the electrical system of the aforementioned future school.

Some requirements are mentioned below.

2.1.1.1. Starting conditions

Mil Colinas aims to contribute to sustainable development. It is important to satisfy the

current needs without putting future needs in danger. Mil Colinas wants to be environmentally

friendly and side with the energetic policies in Rwanda, which are promoting renewable energies such

as solar energy.

It is also necessary to preserve the culture and traditions as well as the ethical values of this

area. It is important to realise that it is a cooperation work in which some values are interchanged

and not imposed. For this reason, Mil Colinas wants the work to be carried out by as many native

people as possible in order to promote the local economy.

There is a lack of unreliability in the energy supply in this area. Power cuts are very frequent.

Mil Colinas believes that in order to achieve progress in the development of a country, it is necessary

3



Energy Engineering

Master’s Degree

to promote education and, to achieve this goal, it is vital to have a reliable energy system in the

school. Mil Colinas wants to guarantee they have a place in which children and young people can

study and carry out several daily activities.

The last requirement is to optimize the electrical system. It is important to pay attention to

the quality as well as to the economic aspect. Mil Colinas has established a maximum budget as initial

investment around $12,000 to build it and $8,000 to maintain the whole system, which must have a

lifespan of at least twenty-four years.

2.2 Rwanda

2.2.1. Geography and climate

Rwanda is a landlocked country located in central Africa. It is known as the “Land of the

Thousand Hills” due to its orography. Rwanda has five volcanoes, many lakes and thousands of rivers.

[1]

Rwanda is bordered by Uganda to the north, Tanzania to the east, Burundi to the south and

the Democratic Republic of Congo to the west with the Kivu Lake.

Rwanda occupies an area of 26,338 km2. It is the fourth smallest country in Africa. The entire

country is at a high altitude, having the lowest points at 1,000 meters above sea level. The capital of

the country is Kigali and it is located near the centre of Rwanda. [1]

Figure 1. Rwanda map. [2]

4



Energy Engineering

Master’s Degree

Rwanda has a mild tropical climate due to its altitude. It has lower temperatures in

comparison to equatorial countries. The average temperature is between 16 °C and 26 °C with little

variation throughout the year but there are strong variations depending on the area and the altitude.

There are two rainy seasons during the year. The first one is from February to June and the second

one from September to December. There are also two dry seasons between the rainy ones. [3].

During the last years, rainfalls have changed due to the global warming. The number of rainy days is

smaller but there is an increased number of torrential rains. These changes are harming the farmers,

decreasing their productivity. [4]

2.2.2. Demographics and social statistics

At the beginning of 2016, Rwanda´s population amounted to an estimated 11,553,446

habitants with a life expectancy at birth of 63.9 years. [5] [6]. 5.2% of the population do not live in

rural areas and 4.8% of the Rwandese people are 60 or above. [7]

Figure 2. Rwandese population from 1960 to 2015. [8]

In Figure 2 it is possible to appreciate the evolution of the number of habitants, with a

significant drop from 1992 to 1995 due to the genocide suffered in the country.

Rwanda has one of the highest population densities in the world, with 460 inhabitants per

square metre. 87% of the population has access to the health service but there is just one doctor for

every 16,000 people [6]. The two most common health problems nowadays are malaria and AIDS and

both are the main cause of death in the country. [9]

2

3

4

5

6

7

8

9

10

11

12

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Mill

ion

s o

f h

abit

ants

Year

5



Energy Engineering

Master’s Degree

In the last years, the government is focusing on providing education for every young person.

71% of the population is literated. 95% of children are signed up to primary school and it is important

to note that primary education and the first three courses of secondary education are free. However,

some students cannot go to school in spite of being signed up due to the cost of the school uniform

and supplies. There is an average of 65 children per teacher. [6]

Rwanda is a trilingual country. Kinyarwanda, English and French are the official languages.

Kinyarwanda is the language of the government and English the language taught in primary school.

There some rural areas where Swahili is spoken. [10]

2.2.3. Economy

The economy is managed by the National Bank of Rwanda and their currency is the Rwandan

franc (RWF). It is possible to see the evolution of this currency in Figure 3.

Figure 3. Evolution of the value of USD and RWF currencies.

Rwanda´s economy is based on a subsistence economy in 90% of the country. The country

lacks natural resources, including minerals (it just has a certain amount of coltan in Kivu lake) [11]

[12] Rwanda has a scanty technological development and droughts are frequent.

Rural population survive with subsistence crops. The most common crop is matoke (green

bananas used for cooking), which make up around 35% of all Rwandese crops. Other farmings are

potatoes, beans and maize. The main exportations are coffee and tea. [13]

6



Energy Engineering

Master’s Degree

Animals raised in Rwanda are mainly cows, goats, chicken and rabbits. However, it is difficult

for rural families to keep animals due to the lack of land and water. They are usually not well fed and

recurrently have diseases. It is not easy to find fish in Rwanda. [14]

The tourism is the most significant source for the country´s GDP. Tourist are attracted by the

Volcanoes National Park, where it is possible to safely see gorillas. They are also attracted by Akagera

park, close to the Tanzania border, and by Kivu lake, which is located near Congo’s border. [15]

GPD per capita was 769 USD per capita in 2015 [16]. That year, Rwanda thus ranked 141 out

of 194 countries. The Human Development Index (IDH) places Rwanda in the 151st position, with a

value of 0.506 in 2014. Rwanda is a country with low salaries but it has achieved one of the highest

values in its speed of economic growth in the continent. [17]

2.3. Global current energetic outlook

The current energetic panorama is characterized by high energy consumption. Energy is the

engine of the world and the key to economic and technical development.

To promote economic growth it is important that access to the energy is provided in a

feasible, reliable and sustainable way. It is important in the context of fighting extremely poverty,

considering that there are around 1,100 million inhabitants (15% of the population) who do not have

electricity. [18]

In Figure 4 it is possible to see the main energy sources used in Rwanda to produce electricity.

In appendix 1, the electrical generation expressed in TWh is shown in Table A.

Figure 4. Distribution of different sources to produce electricity. [19]

Coal40%

Oil4%

Gas22%

Nuclear11%

Hydro16%

Bioenergy2%

Renewable5%

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Energy Engineering

Master’s Degree

Figure 4 shows that the main source to produce electricity is coal, with 9,576 TWh in 2015.

Another significant source to produce electricity is gas (22%). Hydro electrical centrals produce 16%

of it. Other renewable energies represent just the 5% of the global production. This 5% is divided

between wind energy (845 TWh) and photovoltaic energy (246 TWh). Other sources included in this

group are concentric solar power, marine and geothermal, but they are less representative.

Modern energy services improve the quality of life of millions of people all over the world

and they support progress in every field of development.

2.3.1 In Africa

Energy sector in Africa is important for its future development however, it is one of the

regions less kept in mind in the global energetic system. It is a gigantic continent and it has more than

enough energy resources to satisfy the domestic needs. However, more than two thirds of the African

population has no access to the “modern energy” - defined as the access households need to have a

minimum level of electricity. Furthermore, people with access to energy are paying high prices, the

electricity is of bad quality and the system is underdeveloped and unable to meet the needs. [20].

Figure 5. Africa map of the population without access to the electricity.

8



Energy Engineering

Master’s Degree

Access to modern energy is important considering that it is the key to economic and social

development for the continent. There are some issues referred to the quality and the supply of the

energy, such as technical availability, adequacy, reliability, convenience, safety and affordability.

In the above Figure (Figure 5) is possible to take a look at the energy situation in Africa, having

four different areas well distinguished based on the percentage of population which has no access to

electricity. In yellow is possible to see the millions of population whose basic needs are not covered.

2.3.2 In Rwanda

It is estimated that in Rwanda only 23% of the population has access to modern electricity

compared to 100% of population who has access to the electricity in every European country [21].

This fact strongly affects the situation of the country and its development. It makes Rwanda a

vulnerable country. However, the government expects that, in 2020, at least 60% of the houses have

access to the electricity. [22]

Energetic balance of Rwanda shows that 84% of the energy consumed comes from biomass.

This is due to the high use of wood to cook and the lack of modern energy in the country. The use of

petroleum covers 12% of the energetic need of the country. The oil is mainly used to produce

electricity.

Before 2004, Rwanda did not generate any electricity from fossil fuels, only from

hydroelectrical sources, whose supply is very poor due to its losses. In that moment, the government

set in motion an energy project which was supposed to increase electricity prices but guarantee a

minimum of quality (just in the urban areas). In the period 2004-2006 the price increased from 0.12

$/kWh to 0.21 $/kWh. Thanks to that, Rwanda started experiencing rapid economic growth in

comparison to the neighbouring countries, with an increase of its GDP of 7% yearly (until 2010) and

more than 11% in 2011. [23] [24] [25]

In September 2015, the government increased the electricity price by 35%, which made it

even more difficult for citizens to afford it. Nowadays, the price of the electricity changed from 134

RWF to 158 RWF per kWh (plus the 18% of taxes). 215.3 RWF is the exact price that an inhabitant

has to pay for each kWh consumed. This value is aproximatedly $0.27-0.28 per kWh. [21] [26]

9



Energy Engineering

Master’s Degree

As of today, Rwanda’s government is making an effort to develop the energy system in rural

areas, which make up the majority of the country. Their first priority in 2013 (as outlined in their

Poverty Reduction Strategy “EDPRS”) was: Increase the domestic interconnectivity of the Rwandan

economy through investments in hard and soft infrastructure by meeting the energy demand of the

private sector; increasing access to public goods and resources in priority sectors of the economy; and

deepening the integration of key value chains. [27] [28] [29]

2.4. Solar energy in Rwanda

The sun is a free renewable energy source, which can help modern society to build a

sustainable development model of life.

Rwanda is a country with several renewable energy sources: hydroelectrical (already in use

since the last 2-3 decades). There are also big quantities of methane practically hidden in Kivu lake

[30] but the lack of technology and agreements with some private business mean that it is not being

taken full advantage of. Using wind resources is starting to be studied. Solar energy is the newest

trend in this African country.

Given its location, Rwanda is an excellent country in which to use solar energy. Temperatures

are not too high due to its altitude and the solar irradiation has a constant value during the whole

year.

The photovoltaic market is emerging and dominated by the government and promoted by

the health and education services. The lack of financing as well as the lack of knowledge led to some

technical problems, including the incorrect sanctioning of the batteries and defective wiring.

Some business recently became aware of this Rwandese treasure and they have already

started taking advantage of this renewable source.

Nowadays, Rwanda has one of the biggest solar energy plants in East Africa. Rwamagana

Solar Power Station (managed by the Dutch business Gigawatt Global), is a project which began

functioning in September 2014. This photovoltaic plant connected to the grid increased in 6% the

national energy capacity. [31] [32] [33]

Mobisol is a German company with a strong presence in Rwanda and Tanzania. It started in

the country of the thousand hills in May 2014 and in two years, the solar company has installed almost

10



Energy Engineering

Master’s Degree

46,000 solar home systems (SHS). This business gives the facility to rent-to-own, which means to pay

12,000 RWF per month during 3 years. It costs around $600 but it is also possible to acquire the

system for $500 if it is paid upfront. The SHS consists in the photovoltaic installation with a panel of

100 Wp and the devices needed, such as batteries, three light sets, one mobile charger and a torch.

[34]

These are just the most well-known examples in the country but tens of entrepreneurs have

also become aware of Rwanda’s solar source and are starting their business there.

Aside from the photovoltaic installations from the government, solar heating of the water is

gaining importance to substitute the high consumption of biomass as a way of heating water. [20]



Energy Engineering

Master’s Degree

3. OBJECTIVES

11



Energy Engineering

Master’s Degree

The objective of this master’s thesis is the study and design of a photovoltaic power

supply system for a new school in Rukara (Rwanda). Some of the main goals are established

below:

- The measurement of the electrical installation according to the needs they actually

have. The secondary goals are the following:

The estimation of the average energy consumption in the building per day,

taking in account different environmental conditions. Study of the

atmosphere conditions and solar irradiation trends.

Choice of the appropriate devices required for this project: photovoltaic solar

panels, batteries, power electronic devices and connections.

Techno-economical optimization of panels and batteries with Python

programming.

- Study of the feasibility of the Project in the Rwandese area adapting the design with

local conditions. Scalability over time.

- Economic study:

Calculation the budget of the project.

Comparison between off-grid and power grid supply: advantages and

drawbacks of stand-alone power system.

Maintenance plan and performance of the facilities after start-up.



Energy Engineering

Master’s Degree

4. TECHNICAL ASPECTS

12



Energy Engineering

Master’s Degree

4.1. Microgrids

A microgrid is a small energy system capable of balancing captive supply and demand

resources to maintain stable service within a defined boundary. They are important because they

offer more reliability, especially in emergency situations. They are able to the diversification of energy

sources and reduction of the cost. [35] [36]

4.1.1. Photovoltaic system

The process which takes place in a photovoltaic systems is the following: The solar irradiation

arrives on the photovoltaic panels where is converted to electrical energy in DC supply. After, the

electricity is driven to the controller. The controller should send all the energy (or a part of it) to the

batteries, where is going to be accumulated. This stored energy is used to provide the charges when

there is no sun.

Before the supply of energy to the loads, it is necessary for it to go through an inverter to

change from DC to AC.

The most common devices are the photovoltaic panels, the batteries, the inverter and the

controller. [37]

Figure 6. Solar system Off-grid.

13



Energy Engineering

Master’s Degree

4.1.1.1. Photovoltaic generator

A photovoltaic power generator employs solar panels. These panels are composed of solar

electrical cells containing a photovoltaic material. Its function is to transform the solar light into

electrical in direct current.

Their functioning is based on the photovoltaic effect. It is known as a method to generate

electric power by using solar cells to convert energy from the sun into a flow of electrons.

There are different types of panels available in the market.

- Mono-crystalline silicon module: they are blue in a uniform way. They are characterized by

having the highest yields (maximum of 16%).

- Poly-crystalline silicon module: they are also blue but not uniform. They are easy to recognise

because their surface has a grainy aspect. The yield reaches a maximum of 14%. Their Price

is also lower than mono-crystalline ones.

- Amorphous silicon module: they are also made of silicon, but, contrary to the previous types,

they do not have a crystalline structure. They are considerably cheaper than the crystalline

ones and their maximum efficiency is 8%.

The main parameters of the photovoltaic panels are the following:

- Short-circuit current, Isc: the maximum current that the panel can provide. It takes the same

value as the current received when the two terminals are connected. (The value of Isc is

around 3A)

- Open circuit voltage, Voc: maximum voltage that the panel provides when the terminals are

not connected.

- Maximum power point, Pmax: it follows the equation (1). For this point, the delivered power

is maximum. This value is expressed in Watts.

𝑃𝑚𝑎𝑥 = 𝐼𝑝𝑚𝑎𝑥 · 𝑉𝑝𝑚𝑎𝑥 (1)

- Efficiency, ŋ: it is the quotient between the maximum electrical power that the panel can

delivery to the load and the power of the solar irradiation.

All of these values are given by the manufacturer referred to some determined conditions.

The most important are the irradiance (1 kW/m2) and the temperature of the cells (25 °C).

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Photovoltaic panels can be interconnected. It is done to reach the required values. The first

connection has to be in series until there is the required voltage and then, the parallel connexion for

the electrical current. All the connected panels have to be identical, that is, they have to be of the

same brand and the same technical characteristics.

4.1.1.2. Batteries

The solar energy received in the photovoltaic panels is not uniform. Sometimes it is

predictable as the length of the day and the night and the seasons. There other causes which happen

in a random way and make it difficult to predict the solar energy received. For example, it is difficult

to estimate how many cloudy days there are going to be in a given year.

To solve this problem, batteries are used. They transform electrical energy in chemical energy

and later in electrical energy once again.

Electrical Energy Chemical Energy Electrical Energy

(Generation) (Storage) (Consumption)

The batteries have three relevant missions:

- Store energy during a certain number of days.

- Be able to give a big quantity of instantaneous power.

- Determine the voltage of work.

The most important parameter when choosing a battery is its capacity. The capacity is the

maximum electricity available in a complete cycle of discharge, starting with a full battery. The unit

of measure is Ah.

Aside from the capacity, it is also important to take in account other parameters:

- Efficiency of charge: Relation between the energy used to refill the battery and the real

quantity of storage energy. It would be recommendable to select one model with a high value

in order not to have too many losses.

- Autodischarge: Chemical energy lost not being used, only accumulated.

- Maximum depth of discharge: percentage of energy obtained in a cycle. It is highly linked

with its lifetime.

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Other aspects to keep in mind are good resistance to cycles and low maintenance.

There are different types of batteries. In Table 1 is possible to see their basic characteristics.

Table 1: Batteries characteristics.

Type of battery Time of

recharge (h)

Autodischarge

(%)

Number of

cycles

Capacity

(Wh/kg) Price

Lead-Acid 8-16 <5 Medium 30-50 Low

Nickel-Cadmium 1 20 High 50-80 Medium

Nickel-Metal hydride 2-4 20 Medium 60-120 Medium

Li ion 2-4 6 Low 110-160 High

It is possible to see that the cheapest ones are lead-acid batteries. They have the inconvenient

that they need a long time to be charged but, on the other side, their auto-discharge is small. Those

characteristics make them the best kind for certain photovoltaic installations. They can been charged

during the whole day and deliver energy during the night when there is no sun.

4.1.1.3. Inverter

The inverter converts DC into AC. Altern current usually has a voltage of 230 V and a frecuency

of 50Hz.

It is a key component in the installations connected to the power grid but it is going to be

used as well in the main part of the off-grid installations. The most important characteristics for an

inverter are the following:

- High efficiency: it is necessary that it works well for different power values.

- Low consumption in current vacuum.

- High reliability: it is important to supply large quantities of energy in the consumption peaks.

- Protection against short-circuits.

- Security

- Good voltage regulation and output voltage: It has to be compatible with the electrical grid.

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4.1.1.4. Controller

To ensure a good functioning of the installation it is necessary to install a regulator system

between the load of the photovoltaic panels and the batteries. The controller carries out this

function. Its mission is to avoid overloads to the batteries and to assure that the batteries do not

discharge more than the allowed level.

Manufacturers will provide technical characteristics as weight, size as well as the electrical

characteristics and safety regulations. The brochures show the type of regulation allowed (series or

parallel) as well as the kind of batteries that the controller admits.

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5. TECHNICAL

SOLUTION

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5.1. Description of the idea.

First of all, the goal is create a school based off design of the electrical system for a new school

in Rukara, Rwanda in which photovoltaic panels will provide the required energy. The land of this

future school is already bought and at the moment, it is being used to grow some vegetables.

This land has the following coordinates: latitude -1.800217015, longitude: 30.50431245. It is

important to know these coordinates because they will be used to calculate the irradiation data.

Figure 7. Land plan with 9937 m2.

The parcel in which the school will be built is marked 9200.

Mil Colinas is an association that will be responsible for carrying out this project. One hundred

sixty children and teenagers, divided in 5 groups, are part of this association which is projected to

grow quickly, therefore, the current area is not enough.

This project will include the detailed dimensions of the electrical system provided by

photovoltaic panels. The building architecture will be made by some professionals in this field but the

layout for the different classrooms and offices has already been decided upon.

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5.2. Determination of the electrical consumption.

The energy requirement is explained in Table 2.

Table 2. Estimation of the energy consumption per day from Monday to Friday.

Devices Power

(W) Quantity

Total Power

(W)

Maximum time per day (h)

Daily energetic consumption

(Wh)

Laptops 50 23 1150 3 3450

50 2 100 10 1000

Speakers 20 1 20 4 80

Printer 600 1 600 1 600

Lights 4x classroom (15x6m) 11 56 616 3 1848

Lights office (6x6m) 5 4 20 4 80

Lights big room (18x12m) 11 40 440 3 1320

Outside lights 11 7 77 13 1001

Projector 190 1 190 5 950

Charge Mobiles & other things 5 10 50 6 300

3263 10629

It is important to point out that in Table 2 the consumption from Monday to Friday is shown.

On Saturday, the school is not going to be open and on Sunday, it is going to be used only for the half

day. The daily and hourly consumption is outlined in appendix 1 in Tables B, C and D.

The devices described above which will require energy are the following: 25 laptops, 2 of

them will be used throughout the whole work day by the Rwandese educators. The other 23 laptops

will be placed in a computer room and all of them will be available for the students for computer

science subjects, which is planned for a maximum of 3 hours per day.

Other devices are the speakers, the printer, the projector and the current electricity to charge

small devices like mobile phones.

The lights for the rooms will be to be one LED bulb of 5 W (energy saver) placed every 2 m in

the main office (4 bulbs in total). The other rooms will have the same configuration but in that case

the power of the bulbs will be 11 W. Following this plan, the lights required will be 14 bulbs for each

normal classroom, 40 bulbs for the big room and 7 emergency lights located above the main door of

each room (the big room will have two entrances).

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The sketch of the light configuration is shown in appendix 1. They correspond with Figures A,

B and C.

The estimated consumption of each device is also shown in Table 2. It is an overestimation

in order to avoid the lack of electricity in the school.

5.3. Electrical production

5.3.1. Climatological datum.

The number of the hours of solar irradiation change depending on the location of the facility

and on the month of the year. Having the aforementioned coordinates and using the online software

PVgis [38], it is possible to determine how long the solar irradiation can be used. The information is

given in the following Table and in Figure 8.

Table 3. Solar irradiation average in Rukara per square meter.

Month Energy

(kWh/m2/d)

January 4.93

February 5.22

March 4.97

April 4.83

May 4.71

June 4.83

July 5.14

August 5.09

September 5.07

October 4.68

November 4.54

December 4.57

Average 4.88

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Figure 8. Daily solar irradiation in Rukara per square metre.

The microgrid needs to provide all the energy that will be consumed and it has to ensure that

the school will not have a blackout. For this reason, it is necessary to consider the month with the

lowest solar irradiation figures. In Rukara’s case, this month will be November.

It is necessary to configure the microgrid using the month with least irradiation to assure

success throughout the whole year. In this case, the worst solar month is November. It has an average

of 4.54 kWh/m2/day which would extrapolate to 136.2 kWh/m2 per month. From this monthly data

different hypothesis will be made. It is also important to know the time of the sunrise, sunset and the

solar peak in the studied area. The results are shown in Table 4:

Table 4.Time solar data

Sunrise Solar peak Sunset

5:56 11:59 18:03

The next step is to make a study about how much irradiation will be received each day by the

photovoltaic panels taking into account time of the sunrise, the solar peak and the sunset.

5.3.2. Weather assumptions.

Some weather assumptions should be made because it is not possible accurately predict the

exact solar irradiance, which will reach the surface of the land in Rukara every day.

4

4,2

4,4

4,6

4,8

5

5,2

5,4

kWh

/m2 /

day

Solar irradiance

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The first assumption to set is the time of the sunrise, the solar peak and the sunset, which are

going to be at 6:00, 12:00 and 18:00 respectively.

It is necessary to build the irradiation solar curves with the percentages shown in Table 5.

Hour % of irradiance

5:00 0%

6:00 6%

7:00 18%

8:00 37%

9:00 63%

10:00 84%

11:00 95%

12:00 100%

13:00 95%

14:00 84%

15:00 63%

16:00 37%

17:00 18%

18:00 6%

19:00 0%

Table 5. Percentages of solar irradiation

reference to the solar peak.

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0

Hour

Figure 9. Percentage solar curve

Figure 10. Percentage solar graphic.

0%

20%

40%

60%

80%

100%

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Hour

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Figure 9 shows the irradiance curve expressed in percentage but in it is not possible to

calculate the area under the curve. However, there is another graphic (Figure 10) which is created to

show the way to calculate the total energy per day.

𝐸𝑛𝑒𝑟𝑔𝑦 (𝑊ℎ) = 𝑃𝑜𝑤𝑒𝑟 (𝑊) · 𝑇𝑖𝑚𝑒 (ℎ) (2)

Every vertical bar represents 1 hour of solar irradiation so, based on Equation 2 is possible to

know the monthly energy received per square meter.

5.3.2.1. Types of daily climates. It is important to point out that the average of solar irradiation within the coordinates is

known, however, the distribution of solar irradiation lengthwise per month is not published. This

means it is not known how many “cloudy” days there will be.

A cloudy day refers in which no sun is reaches the surface of this piece of land. In reality,

weather does not work like that, because a cloudy day does not mean 0% of solar irradiation.

Based on this, some assumptions will be made from November solar data.

- No cloudy days.

The first, and easiest assumption, would be to suppose that there will not be cloudy days and

every day during the whole month are identical in terms of the amount of sun that hits the

land. Following the aforementioned percentages and knowing that the energy received will

be 5.54 Wh/m2 per day, which implies 136.2 Wh/m2 per month (following (2)). The data hour

per hour is available in appendix 1. Table E.

In Figure 11 is possible to see the curve obtained:

Figure 11. Solar curve assuming no cloudy days.

0

100

200

300

400

500

600

700

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

W/m2

Hours

643W/m2

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As it is already mentioned, it is unlikely to have the same weather every day.

- 10% cloudy days.

In this section the assumption will be that 10% of the days in the month will be cloudy and

that percentage will be distributed reasonably throughout the whole month.

In Table F in appendix 1, the energy received per square meter is shown; supposing that

there are only 3 days within the whole month that the sun is not going to shine. In the

following Figure it can be seen that the solar peak at 12:00 reaches a value of 715 W/m2.

Figure 12. Solar curve assuming 10% of cloudy days.

- 25% cloudy days.


0

100

200

300

400

500

600

700

800

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

W/m2

Hours

715W/m2

839W/m2

0

100

200

300

400

500

600

700

800

900

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

W/m2

Hours

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In this section it will be assumed that a quarter of the month is completely cloudy. This means

that the sun will shine only 23 days per month.

Furthermore, it is important to appreciate how this would affect the peak irradiation at 12:00.

It is plotted in Figure 13. Table G, in appendix 1, displays all the results from this section.

The maximum value of irradiation received is 839 W/m2.This is the best approach up until

now, having almost 6,000 Wh/m2 of energy every sunny day. However, other options need

to be explored.

- 50% of cloudy days.

In this case we will assume that one of out every two days is cloudy. The following Figure

shows the expected energy received. The Table along with the data of this section is shown

in Table H, located in appendix 1.


1286W/m2

0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

W/m2

Hours

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Looking at Table H and Figure 14, is easy to realise that it is not possible to carry on with this

assumption because the maximum irradiation is 1000 W/m2 and here it is shown that the

peak reaches 1,286 W/m2 which is 28% more compared to the real value.

For this reason, the average solar data of 4.54W/m2 per day is only valid with a maximum of

11 cloudy days per month distributed in a uniform way and 19 sunny days. Here there is a possibility

of 35% cloudy days describing a cloudy day as 0% sun received and the other days 65% clear having

an irradiation level of 1,000 W/m2 during the solar peak. Each sunny day supposes 7.06 kWh/m2/day.

7.06 · 19 = 134.14 kWh/m2/month

Thousands of combinations of solar percentages are possible but for the current project it

has been decided to assume three different types of climatological days. They are called sunny (S),

normal (N) and cloudy (C) days. The first one assumes that it is going to be a day with the maximum

amount of sun possible, which means 1,000 W/m2. The normal day will be the day in which the sun

is going to shine 70% in comparison to the sunny day and a cloudy day is when there will be just 25%

of the maximum.

It is possible to see the values obtained in Table 6.

Table 6. Different types of days.

Hour Sunny day (100%)

(kW/m2) Normal day (70%)

(kW/m2) Cloudy day (25%)

(kW/m2)

5:00 0.000 0.000 0.000

6:00 0.060 0.042 0.015

7:00 0.180 0.126 0.045

8:00 0.370 0.259 0.093

9:00 0.630 0.441 0.158

10:00 0.840 0.588 0.210

11:00 0.950 0.665 0.238

12:00 1.000 0.700 0.250

13:00 0.950 0.665 0.238

14:00 0.840 0.588 0.210

15:00 0.630 0.441 0.158

16:00 0.370 0.259 0.093

17:00 0.180 0.126 0.045

18:00 0.060 0.042 0.015

19:00 0.000 0.000 0.000

Total 7.060 4.942 1.765

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The option of having less than 25% of irradiation is not considered because of the location

of the land.

This distributions gets 137.67 kWh/m2/month. It is being accepted a margin of error around

2%.

Following Figure 8 and Table 6, some monthly data are going to be associated in different

groups in order to simplify the simulation.

- Group 1. This group includes the months with less solar irradiation. Those months are

November and December with 4.54 kW/m2/day and 4.57 kW/m2/day.

- Group 2. Two months are going to belong to this group. They are May and October with 4.71

kW/m2/day and 4.68 kW/m2/day.

- Group 3. January, March, April and June are part of the third group. Their values are 4.93

kW/m2/day for January, 4.97 kW/m2/day for March and 4.83 kW/m2/day for the last two

months in this group.

- Group 4. The last group of this monthly data is composed of February, July, August and

September. They are the months in which the sun shines the most. The average irradiance of

the comprised months is 5.22 kW/m2/day, 5.14 kW/m2/day, 5.09 kW/m2/day and 5.07

kW/m2/day.

In Table 7 the previous information is summarised.

Table 7. Summary of the weather assumptions.

Months Quantity of days Solar irradiation

(kW/m2/day) Sunny Cloudy Normal

Group 1 November, December 10 10 10 4.58

Group 2 May, October 11 10 9 4.76

Group 3 January, March, April, June 11 12 7 4.97

Group 4 February, July, August, September 12 12 6 5.15

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5.3.2.2. Climatological days distribution As explained above, the distribution of the different kinds of days (S,N,C) has already been

decided, as well as the different groups for each the months. The next step is to do the simulations,

taking different assumptions to study the charge level of the batteries in each case. (The critical

months are those which belong to group 1. This group is the one in which the study is going to be

focused).

These cases are proposed:

- Random distribution.

The first simulation will be composed of S, N and C days throughout the whole year in respect

to the criteria established in Table I in appendix 1. This is going to be the only case in which

the batteries’ level is going to be simulated for the whole year.

- S-N-C

In the second simulation, it is supposed that it is going to be one of each type of day shown

in Table 7. The distribution of them is the same as in the previous part. From this point

forward, the simulations with Python are going to be run just for the months included in

group 1.

- S-S-N-C-N-C

In this case, it is assumed that they are going to be two sunny days and after, a series of four

days of combing normal and cloudy days.

- S-S-N-N-C-C

In the fourth one, each type of day will appear the same number of times (33.3% of each type

throughout the whole month), but in this case, they are distributed by twos. This is a rare

combination in Rukara, a place in which almost every day is sunny, but it is going to be

simulated to consider what would happen in the worst case scenario.

- S-S-S-N-N-N-C-C-C

This last case consist of make a simulation supposing a series of the three types. This case is

very rare. It is possible it could happen in the North of the country where the climate is less

sunny than in the East of Rwanda. Nevertheless, this simulation will be run with the goal to

observe what would happen if this distribution arrives.

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The results are going to be shown later, when the simulation is run. First, it is necessary to

choose the appropriate devices which will best fulfil the energetic demand.

5.3.3. Devices characteristics

First of all, it is necessary to establish the voltage at which the system would work. The most

common options are 24V and 48V. In this case, 48V is selected due to fact that the system will be

cheaper and it would probably have less electronic problems between the two devices. The visited

facilities in the area also have this configuration. The most common devices sold in East Africa

(Inverter and Controllers) work in 48V. Due to their variety, the cost of acquisition of those devices

will be lower.

5.3.3.1. Photovoltaic panels

The photovoltaic panels chosen are “African Energy” brand. The model is AFR-295. Each panel

is 295W of peak power and it produces 24 Volts (parallelly connecting every two devices to reach 48V

per branch). The most relevant information is shown in Table 8. The brochure with all the technical

characteristics is attached in appendix 5.

Table 8. Photovoltaic panels characteristics.

Pmax (Wp) 295

Voltage at Pmax (V) 36.92

Current at Pmax (A) 8.00

Voc (V) 45.93

Isc (A) 8.63

Cell Efficiency (%) 17.60

Module Efficiency (%) 15.20

Dimensions (mm) 1956 x 992 x 50

These panels are chosen carefully after comparing them with several other types. They are

monocrystalline photovoltaic modules which increases their efficiency compared to polycrystalline

ones. Their efficiency is 17.60%, a good position in the competitive market, considering that the

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efficiency average of them range from 15 to 20%. They have a higher efficiency than the

polycrystalline ones, so they are space efficient.

African Energy brand gives 25 years of warrantee to its solar panels estimating a lifetime of

more than 30 years. These characteristics, together with their good tendency to create solar energy

in low-light conditions, is the reason why they were selected for this microgrid in Rwanda.

One disadvantage to mention is that if they are partially covered by snow, shade or dirt, the

entire circuit could break down. This case is not worrisome. In Rukara, there has never been snow.

Shade does not affect our case because the photovoltaic panels are going to be fixed on the roof at

the optimal inclination.

There are photovoltaic panels with higher efficiency and similar prices but their

inconvenience is the high transportation cost to move them as far as Rukara; due to the fact that

there are not manufacturers near the studied area.

From now, let it be known that the photovoltaic panels will work grouped in pairs to reach

48 V.

As it was before mentioned, the photovoltaic panels are going to be fixed on the roof and

they are not going to have the ability to move for two reasons. The first one is to reduce the price of

the installation and minimize the maintenance. A photovoltaic installation with movement in one or

two axis, needs more inspections and it presents some problems due to its moving parts. The second

reason is that in a country as Rwanda, the outcome is not going to vary in a notable way. Rwanda’s

latitude is -1.80° (it is near to the equator line).

The optimal tilt angle is the angle which collects the most solar irradiation. The optimal tilt

depends on the latitude of the site. There is a linear approximation to calculating the optimal tilt angle

[39] [40].

𝛽𝑜𝑝𝑡 = 3.7 + 0.69 · |𝜑| (3)

In Equation 3, 𝛽𝑜𝑝𝑡 is the optimal tilt and 𝜑 represents the latitude of the place in its absolute

value. The optimal tilt for the panels is 4.9° oriented to the north.

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5.3.3.2. Batteries The batteries are also key components for the installation because of the important role they

have in a solar installation off-grid. It is important to focus on them because they are the most

expensive element due to their short lifetime in comparison to the PV panels. Also, they are the most

sensitive components involved in the installation.

The brand selected is Sun Light and the model is VRLA Battery SPB 12-200. This model is

selected because it is recommendable to use lead-acid batteries. AGM batteries are not selected for

the installation because even though the quality is very high, their price makes them unaffordable for

the project in question.

The main characteristics of the batteries selected are shown in the following Table,

nevertheless, it is possible to find the complete brochure in appendix 5.

Table 9. Batteries characteristics.

Lifetime (years) 12

Nominal Voltage (V) 12

Short-circuit current (A) 3300

Max Charging current (A) 60

Capacity (Ah) 200

Self-discharge per month (%) 3

This choice was made because Sun Light is a common brand in Rwanda, which makes it easier

to find it there. The main characteristics to justify the choice is the long lifetime of this model, as well

as, its capacity in comparison with other batteries sold in East Africa.

The lifetime of these devices is important. If the batteries receive the suitable use, their

lifetime can reach up to 12 years. This characteristic places these batteries as one of the most

attractive in a non-developed area such as Rwanda.

In addtion, their rated capacity at 10h per cycle is 200Ah. Following Equation 4, the capacity

of each storage device is 2.4 kWh.

𝐸𝑛𝑒𝑟𝑔𝑦 (𝑘𝑊ℎ) = 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (𝐴ℎ)·𝑉𝑜𝑙𝑡𝑎𝑔𝑒 (𝑉)

1000 (4)

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Those batteries will be connected in groups of fours to reach 48V, the voltage at which the

microgrid works before the inverter.

Another important characteristic of the selected batteries is to pay attention to the number

of cycles they can support. Figure 15 shows this information.

Figure 15. Battery lifetime due to the number of cycles.

In the horizontal axis the number of cycles that the battery can afford depending on its depth

is represented. According to Figure 15, some decisions are for the maximum quantity of cycles

admissible in the designed microgrid. They are shown in Table 10.

Table 10. Batteries lifetime depending on the cycles.

(%) DOD (%) SOC Cycles

30 70 2200

50 50 1000

80 20 400

The values taken from Figure 15 are the most pessimistic ones, to guarantee the good quality

throughout its lifetime. It also will be established that the battery cannot be at a power level ofless

than 30%. It is also recommendable not push the battery under 50% of its SOC level. All these

restrictions will be written in the software.

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5.3.3.3. Inverter

The inverter is the heart of a microgrid. It is responsible for converting direct current (DC),

which the photovoltaic panels produce, to AC current, which is going to be used in the buildings.

In Table 2 is shown that the total power is 3,263 W. The required inverter has to be, at least,

this value of power. In East Africa it is not easy to find an array of products with these characteristics.

Some 3kW and 5kW inverters were found. The option of having two of them (of 3kW each) connected

was discarded due to the high cost of this configuration.

The Inverter chosen is Victron energy brand and the model is Quattro inverter 48/5000/70-

100/100 230V. This model is chosen because it is the one with the best characteristics in the market

for solar applications. This high quality product guarantees proper function over the years.

The selected model can work in adverse weather conditions. The electronic components are

prepared to avoid corrosion as well as bad atmospheric conditions.

This model has the appropriate input voltage for the microgrid because it will be changeable

between 37.2 and 64.4 and the required value is 48V. The output voltage is 230 V ±2%. The frequency

is 50 Hz ±0.1%.

The main characteristics of it are shown in the Table 11:

Table 11. Inverter characteristics.

Wave type Sine curve

Total power (W) 5000

Output Voltage (V) 230

Input Voltage (V) 37.2 - 64.4

Frequency (Hz) 50

Efficiency (%) 95

It is also remarkable that this device has the highest efficiency in comparison with the

available models found in Rwanda.

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5.3.3.4 Controller The controller is responsible for avoiding power surges in the batteries. The vigilance is done

by this device, which protects the batteries against extreme situations to avoid their damage.

Its function consists in taking information from the state of charge of the system. It compares

this information with maximum and minimum levels of admissible charge and it impedes the excess

charge and discharge of the batteries.

In order to know the electrical characteristics, it is required to know the maximum value of

current in the photovoltaic panels and the current of the charges connected at the exit of the

controller.

The way to calculate the minimum input current needed follows Equation 5:

𝐼𝑐𝑖 = 𝑃𝑏 · 𝐼𝑠𝑐 · 𝐾𝑠 (5)

Where:

- 𝐼𝑐𝑖 is the minimum current value which the controller has to support in the entrance (A)

- 𝑃𝑏: Number of parallel branches in the photovoltaic panels.

- 𝐼𝑠𝑐: Short-circuit value from the photovoltaic panels (A).

- 𝐾𝑠: Security Coefficient. Typical value: 1.25

To establish the current that the controller should tolerate, it is necessary to follow

Equation 6.

𝐼𝑐𝑜 =𝑇𝑝

𝑛𝑖⁄

𝑉 (6)

Where:

- 𝐼𝑐𝑜 is the minimum value of current at the exit of the controller (A).

- 𝑇𝑝: Total power installed, in other words, the maximum power if all the loads work at the

same time (maximum of 3,800 W).

- 𝑛𝑖: inverter yield.

- 𝑉: Working voltage in the designed system (48 V).

Knowing these values, it is possible to choose a commercial controller.

The model chosen is FLEXmax 80 (FM80-150VDC). It has a high efficiency (97.5%). It allows

current up to 80 A and it is able to work in 48 V. Table 12 gathers this information.

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Table 12. Controller characteristics.

Nominal Batteries Voltage (V) 12, 24, 36, 48, 60

Maximum Output Current (A) 80

Power Conversion Efficiency (%) 97.5

The next sections will check if the selected model is still good for the designed microgrid.

5.3.4 Python simulations.

The software chosen to run the simulations is Python. It is fed with a programming language

called Python as well. The software is selected due to its intuitive and legible language. Python is

chosen for this project because of its free availability.

The simulation carried out shows the level of the group of batteries for each defined time.

5.3.4.1. Definition of the variables.

In this section, the different variables defined in Python are going to be explained:

- xbattery: the theoretical capacity of the batteries. If there are eight batteries, this value will

be 19.2kWh. If there are twelve units, this value will be 28.8 kWh.

- xmin: minimum value allowed for the battery charge. In this simulation 30% of the whole

battery capacity is the established minimum battery charge allowed for avoid the batteries

damage.

- stini: initial level of the battery for the time 0. It is supposed that the batteries starts with a

full charge.

- level: the level of the battery charge at each each time t. In time 0, it will have the value of

stini.

- rt: charge retention rate. In the studied case this value is 0.999958 due to it assumed 3% per

month.

- nc: controller’s efficiency which is 97.5%

- ni: inverter’s efficiency with a value of 95%.

- n: product of the battery yield and the controller’s efficiency.

- ed: discharge efficiency of the battery multiplied by the inverter’s efficiency.

- t: temporary step. In the present case, this step is 1 hour.

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- summ1: shows how many kWh are provided having less than 50% charge in the batteries.

- summ11: this counts how many times the charge level of the batteries is lower than 50%.

- summ2: shows how many kWh are provided having less than 70% charge in the batteries.

- summ21: this counts how many times the charge level of the battery is lower than 70%.

- summ3: shows how many kWh are not satisfied regarding the demand.

- summ31: this counts how many times the charge level of the batteries reach xmin level (30%).

- demand: list which shows the energetic demand per hour.

- i: each value of the list demand.

The code used for running the different simulations is written in Appendix 2.

5.3.4.2. Python program

At the beginning of the code, which can be seen in Appendix 2, the quote to import the library

to plot the functions and right after, all the variables are defined.

Once all the variables are defined, the whole demand is established which is calculated as the

difference between the consumption and the production.

When the result (i) is positive, it means that the energy not used is going to be stored in the

batteries unless the batteries are full. In this case, the excess energy is going to be wasted.

If the value of (i) is negative, this means that the energy produced from the sun is not enough

to cover the whole consumption, some energy will be delivered from the batteries.

In this section, several measures will be taken to be able to choose the appropriate quantity

of batteries.

There will be three summaries. The first of them shows how many kWh are going to be

supplied having the batteries with a charge level under 70% as well as the times that it happens. The

second summatory shows the same as the first one but with 50% of a charge level. The third

summatory counts how many times the batteries are at a charge level of 30% (minimum level

accepted to protect the batteries) as well as, how many kWh are not covered for the whole simulation

run.

It is programmed that if the production has the same level as the consumption, the charge

level of the battery should take the same value as the previous stage. [42]

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If i>0, energy is going to be stored in the batteries;

If i<0, energy will be delivered from the batteries;

Otherwise, the situation will not affect to the charge of the batteries.

5.3.4.3. Python results

As it was mentioned in section 5.3.2.2., five simulations will be run. These cases are proposed

in order to be able to evaluate what will happen along the different distribution of the types of

climatological days already selected. Some simulations are done assessing two possibilities:

a) Two branches of batteries (8 batteries)

b) Three branches of batteries (12 batteries)

Before deciding the quantity of batteries it is necessary to establish the quantity of

photovoltaic panels. Some tests were done with 8, 10 and 12 units.

It would be possible to design the microgrid with 8 panels but the quantity of batteries must

be increased notably if there are two consecutive cloudy days. The batteries are much more

expensive than photovoltaic panels due to its lifetime. For this reason, this option is discarded. The

tests with 10 and 12 photovoltaic units give back more similar results between each other. Installing

12 photovoltaic panels, a big quantity of energy is going to be wasted, the installation is going to be

more expensive and the batteries required are going to be the same for both studied cases.

In this section the results using 10 photovoltaic panels are going to be shown. The results

using 8 and 12 photovoltaic panels are shown in Table J at appendix 3. The 8760 values of the demand

which feed Python are shared in Appendix 2.

- Random distribution.

In this part was decided to simulate the level of the batteries for the whole year. The

climatological distribution of the days are shown in Table I in appendix 1, which affects the

electrical production from the photovoltaic panels. The consumption is assumed will be

uniform along the whole year. From Monday to Friday, the consumption will be the same

every day meanwhile the school is not going to be used on Saturday and on Sunday it is going

to be used just for the half day.

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The system is going to work in 48 V so the batteries should be connected in branches of four

batteries each.

8 batteries

Eight batteries in the current designed system means 19.8 kWh, following Equation

4 but is not possible to let the charge drop to more than the 30% of the whole

capacity according to the manufacturer; otherwise, their lifetime will be considerably

reduced. Their available use capacity is 13.86 kWh. In the following Figure are plotted

the results (obtained from Python) of the level of the batteries.

Figure 16. Simulation of the batteries level with 10 PV panels and 8 batteries for the whole year.

The software gives back the amount of kWh not used for the whole simulation. In

this case, the whole demand is satisfied. It is also possible to see it in Figure 16

because during all the simulation, all the values are over 30% battery charge level.

Python also returns the quantity of kWh supplied given that the battery has a level

under 50% or 70% of its entire capacity. It is important to not disregard this

30%

40%

50%

60%

70%

80%

90%

100%

Bat

teri

es le

vel (

kWh

)

Time (h)

Random distribution - 8 batteries

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information because the battery lifetime depends on the cycles depth and the

number of them as it was explained in section 5.3.3.2. For this reason it would be

interesting to pay attention to this value. The set of batteries would supplied 108.12

kWh being under 50% of its charge level (3.61% of the annual electrical consumption)

and this 108.12 kWh are comprised in 47 cycles each year. We will assume this will

happen in at least 564 cycles throughout its lifetime. The maximum number of

oscillations under 50% of SOC is around 1,000 cycles.

Regarding what happen to them at a 70% charge level it is clearly shown that 367.60

kWh will be supplied under this value. This amount of energy takes place in 103

cycles. The maximum quantity of cycles before the end of the batteries’ life at 70%

of SOC is 2,200 cycles. In this case, there will be 1,236 cycles in its 12 year lifetime.

The requires of the battery are fulfilled however, the battery suffers from this

functioning and it could be damaged.

This configuration will be possible assuming there is a homogeneous distribution of

the different type of days. Here, it was not considered having two cloudy days

following each other as Table I shows in appendix 1.

Another study will be done with a bank of 12 batteries in order to be able to compare

both studies.

12 batteries

In this section, the simulation will be run with a bank of 12 batteries. It would be

interested to also run a simulation with 10 batteries but for this project is not possible

due to the fact that the batteries should be associated in groups of four. They have

to be connected in series to reach the desired voltage.

As the simulation shows and as the software confirms, throughout the whole year,

the charge level of the batteries will be over 60%. The whole demand is covered and

the charge level of the batteries will be under 70% only 60 times per year, which

means 188.14 kWh in those 365 days. All these results are shown in Table J in

appendix 3.

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Figure 17. Simulation of the batteries level with 10 PV panels and 12 batteries for the whole year.

Reaching these charge levels of the batteries is the best way to guarantee good

production throughout their life making sure that the batteries are available to be

used the 12 years of their expected lifetime.

This is the only simulation done for the whole year. From now on, the results are going to be

shown for the months with less solar irradiation (months included in group 1 according to

Table 7). If the optimization of the microgrid is done well for November and December, it will

work appropriately for the whole year.

- S-N-C Distribution.

The series of a sunny day, normal day and a cloudy one during the last two months of the

year, gives the results shown In Figure 18.

50%

60%

70%

80%

90%

100%

Bat

teri

es le

vel

Time (h)

Random distribution - 12 batteries

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Figure 18. Simulation of the batteries level with SNC distribution.

Above, Figure 18 shows the comparison of the battery levels making different installations.

The grey line shows the level of charge when there are just eight batteries and the red one

when there are 12 batteries. In this case, again, the whole demand would be satisfied and in

the red case, the level of the batteries will be over 60%, which would guarantee a longer

lifetime of the energy accumulators.

In the following Table, the values given by the code programmed in Python are shown.

Table 13. Batteries’ cycles information with SNC distribution.

SOC (kWh) SOC (times)

30% 50% 70% 30% 50% 70%

8 batteries - 27.28 78.77 - 12 26

12 batteries - - 46.55 - - 12

In Table 13 is possible to appreciate with accuracy the idea given by Figure 18. The simulation

done for these two months follows the same scheme as the first simulation already

40%

50%

60%

70%

80%

90%

100%

Bat

teri

es le

vel

Time (h)

SNC Distribution


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explained, but the results are not comparable. For the previous analysis (Random

Distribution), making an installation of 12 batteries, 188.14 kWh will occur with the batteries

at its level lower than 70% of its maximum. If all the months were climatologically identical,

every month would supply 15.67 kWh under 70% of SOC (31.35 kWh is the sum of November

and December) and Table 13 shows that the value in this case is 46.55 kWh. The lack of sun

during these months cause an increase of 48.48% of the average value.

In the hypothetical situation of having this data throughout the whole year; the installation

of eight batteries will still be appropriate because for their 12 year lifetime would be 1,872

cycles until its 30% of DOD. According to the manufacturer, at least 2,200 cycles are allowed

if the rest of the conditions of operation are respected.

Nevertheless, this is a very optimistic case because in spite of Rukara being a sunny area,

some cloudy days can occur. More simulations are going to be shown.

- S-S-N-C-N-C Distribution.

Figure 19. Simulation of the batteries level with SSNCNC distribution.

20%

30%

40%

50%

60%

70%

80%

90%

100%

Bat

teri

es le

vel

Time (h)

SSNCNC Distribution


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This distribution is set out as an intermediate stage between SNC and the next one in in which

two cloudy days followed by each other will appear.

The results are plotted In Figure 19 in which is easy to see the notable difference between

using 8 batteries and 12 batteries. When 12 batteries are used, the whole demand is covered,

a fact that encourages us to do the installation with three branches of energy storage devices.

The numerical data is shown in Table 14.

Table 14. Batteries’ cycles information with SSNCNC distribution.


30% 50% 70% 30% 50% 70%

8 batteries 2.41 31.29 82.97 3 15 24

12 batteries - 6.48 60.72 - 3 14

The times the batteries have a charge level lower than 30%, 50% and 70% is very similar in

comparison to the SNC case. With respect to the kWh, it is possible to discover a new fact;

when the microgrid works with eight batteries at least 2.41 kWh these two winter months

will not be covered its demand. In the whole year, there would be more than 14 kWh of lack

of energy if this series of distribution days continues.

However, with the configuration of eight batteries, there will be 15 times every two months

(at the most, 90 times per year and 1080 in its entire lifetime) when the batteries will be

under 50% of their charge level. According to the manufacturer, 1000 cycles below 50% are

admissible. Maybe their lifetime would be reduced in some months, increasing the cost of

the installation because of the batteries suffering.

- S-S-N-N-C-C Distribution.

Further, the last simulation in this case that is going to be studied is what would happen when

two cloudy days follow each other. In Figure 20 the results obtained from Python are plotted.

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Figure 20. Simulation of the batteries level with SSNNNCC distribution.

As the previous Figures showed for the other simulations, the grey line represents the

batteries level if eight batteries are installed, where the red line represens the batteries

charge when 12 of them are used.

The red line never reaches the 30% strip. This means that the whole energetic demand will

be covered; something that does not occur using two batteries branches. The numerical data

is shown in the Table below.

Table 15. Batteries’ cycles information with SSNNCC distribution.


30% 50% 70% 30% 50% 70%

8 batteries 4.68 37.62 97.92 5 7 14

12 batteries - 15.68 65.99 - 5 10

Another more severe simulation will be done to assure that the microgrid works correctly if

a cloudy period arrives.

20%

30%

40%

50%

60%

70%

80%

90%

100%

Bat

teri

es le

vel

Time (h)

SSNNCC Distribution


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- S-S-S-N-N-N-C-C-C Distribution

This is the last simulation and the least probable to occur. Nevertheless, the simulation was

run to foresee what would happened to in the microgrid if the proposed configuration takes

place. This case study shows the batteries level if a combination of three following days of

sunny, normal and cloudy days occurs.

Below is Figure 21 which corresponds to the previous description. And Table 16 which

summarise the results obtained from Python.

Figure 21. Simulation of the batteries level with SSSNNNCCC distribution.

Table 16. Batteries’ cycles information with SSNNCC distribution.


30% 50% 70% 30% 50% 70%

8 batteries 5.72 32.03 58.11 5 7 11

12 batteries 2.01 25.44 74.92 3 5 10

20%

30%

40%

50%

60%

70%

80%

90%

100%

Bat

teri

es le

vel

Time (h)

SSSNNNCCC Distribution


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In this case, there will be a lack of energy in both cases. It is a strict and not often distribution.

When 12 batteries are being used, the lack of energy during these two months will be just

2.01 kWh which represents 0.4% of the monthly required energy.

Those 2.01 kWh are for November and December. There is approximately 1 kWh per month

in group 1 which coincides with the required electricity for using two laptops for a whole day.

In the XX century is not admissible to design an electrical system for a school in which the

energy is in short supply even though the lack of energy value is actually low.

If the last configuration mentioned this will occur. The measure that would be carried out

would be to cancel the computer sciences course during this lack of energy but this situation should

be avoided, so that’s why a 12 batteries system is chosen. With two branches of batteries, the risk

run is even bigger taking a value of 5.72 kWh of lack of energy during these two months.

However, there is a way to check the maximum quantity of batteries to keep the electrical

price lower than the price from the power lines. It is shown in Equation 7.

𝐶𝑝𝑙 =𝑃𝑏·𝑛𝑏·𝐸𝑏

𝐷·𝑙𝑡 (7)

Where:

- 𝐶𝑝𝑙 is the price of the electricity from the power lines in the hypothetical case that the

conventional electricity reaches the area of the future school of Mil Colinas. This parameter

has the value of $0.278 taking in account the exchange currency of 20 April 2016 ($1 = 775.48

RWF).

- 𝑃𝑏 is the price of each battery. For this project, the cost is $326.56.

- 𝑛𝑏 is the number of batteries. In this case, this is the value to find.

- 𝐸𝑏 this parameter represent the capacity of each battery expressed in kWh. The chosen

batteries are 210 Ah or 2.4 kWh.

- 𝐷: Electrical demand for the whole year. The school will have an energy consumption of

2,994.65 kWh.

- 𝑙𝑡: this parameter is the lifetime of the storage device. The batteries selected have a lifetime

of 12 years.

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Solving Equation 7, 𝑛𝑏 has a value of 12.74 batteries. This means that if the microgrid requires

more than 12.74 batteries, maybe the installation would not be worthwhile economically.

In Python code there is a variable (LL) which has a value of $13.92. This price is calculated

being based on the educator’s salary. They earn an average of $6.96 per day (208.9 RWF). One kWh

not supplied corresponds to having no electricity for the two educators’ laptops throughout the

whole day. For this reason, the hypothetical cost for the lack of electricity will be the salary of two of

them. In the following Table is going to be shown the extra cost of each case for the not covered.

Table 17. Extra cost for the demand not covered with the designed system for with 10 photovoltaic panels.

Batteries

Demand not covered

(kWh)

Extra cost per month

($)

Extra cost per year

($)

SSNCNC 8 2.41 16.77 201.28

12 - - -

SSNNCC 8 4.68 32.57 390.87

12 - - -

SSSNNNCCC 8 5.72 39.81 477.73

12 2.01 13.99 167.88

In Table 17 it is possible to appreciate that having the system with 8 batteries, increase

notably the hypothetical price of the installation. This fact corroborate the importance of using 12

batteries.

5.3.5. Microgrid measuring

From this point, the measuring of the microgrid can be completed. The characteristics are

already known. There is going to be one inverter and one controller. Thanks to Python simulations,

the use of 10 photovoltaic panels is set up grouped in twos and 12 batteries grouped in three

branches as Figure 22 shows, made with AutoCAD.

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Figure 22. Installation sketch.

The next step is to make the best choice for the cables. The cables are responsible for carrying

the electricity from the photovoltaic panels to the different devices within the installation.

To find the appropriate dimensions of them it is necessary to follow Equation 8.

𝐴𝑚𝑖𝑛 =𝐾 · 𝐼 · 𝐷

δ · ∆V (8)

Where:

- 𝐴𝑚𝑖𝑛 minimum value required for the cable. There are some dimensions standardised, so it

will be necessary to choose the one which is directly above the value obtained.

- 𝐾: coefficient, which depends on the type of electrical supply. Its alternating current value is

2 due to the fact that the current should go into the device through one cable and come back

through another cable.

- 𝐼: current in the studied stretch (A).

- 𝐷: cables’ distance (m).

- δ: Cable’s conductivity. The cables will be made of cooper. Cooper conductivity takes a value

of 56 m/(Ω·mm2).

- ∆V: maximum drop in voltage admissible. It usually takes a value of 3%.

Next, the cables’ area is going to be calculated. There are different sections in the installation

which can have different size:

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- Photovoltaic panels – Controller

- Controller – Batteries

- Controller – Inverter

- Inverter – Electrical Board

1. Photovoltaic panels – Controller

The cables that stretch from the panels to the controller will have a maximum length of 12

meters. Their position is shown in Figure 22. The current in this section is 8 A in each branch.

There will be 40 A in the whole photovoltaic panel set. The voltage is 48 V. Following the

equation 8, the result is 11.90 mm2. The standardised size that will be used is 16 mm2. The

standardised dimensions are 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50 mm2.

2. Controller – Batteries

For this part of the installation the estimated cable's length is 6 m and the voltage is 48 V.

The maximum current among the 3 branches will be 180 A. Utilizing Equation 8, the obtained

value is 26.78 mm2. The required cables should have an area of 35mm2.

3. Controller – Inverter.

Again, the voltage is 48 V because this area is located before the inverter where the voltage

will be changed to 230 V. Here, the length will be less than 2 m and the maximum current

takes the same value as in the batteries section. Applying equation 8, the result obtained is

8.92 mm2. The cable of 10 mm2 of area will be selected for this case.

4. Inverter - Electrical Board

In this part of the installation, the voltage is 230 V and the maximum length of the cables will

be 5 m. The current allowed for the inverter is 100 A per branch (there are two). Using

Equation 8 again, a value of 2.58 mm2 is obtained. The commercial cable size chosen for this

stretch is 4mm2.

In the following Table the results obtained from the cables’ dimension for each section are

shown.

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Table 18. Area of the required cables.

Section Cables’ area

(mm2)

1. Photovoltaic panels – Controller 16

2. Controller – Batteries 35

3. Controller – Inverter 10

4. Inverter - Electrical Board 4

5.3.6. Buildings distribution.

In this section the distribution of the future school for Mil Colinas will be explained.

Figure 23. School’s distribution.

The buildings in which it is possible to see 1a and 1b is the office. Its area is 4x12 m. It is

divided into two parts. The teachers’ office will be 1a and 1b this is where the batteries as well as the

inverter and the controller are going to be placed. The area of 1a is 4x8 leaving 16m2 available for 1b.

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Building 2 is going to be the big room for the meetings and the activities which will require

more space. On its roof there is going to be 10 photovoltaic panels. This roof is chosen because it is

the closest to 1b room. The photovoltaic panels are going to be oriented at 88º in respect to the

vertical axis [41] to take advantage of solar irradiation during the months comprised in group 1

(November and December).

The buildings numbered 3 are the normal classrooms. Their area is 6x15 m

Buildings numbered 4 are not planned to be built in a near future. If in some years, more

space is required due to the school’s growth, they will be built and the electrical system could be

measured (adding some batteries and photovoltaic panels because the inverter has a capacity of up

to 5,000 W).

In appendix 4, in Figure D is it possible to see the screenshot from the mock-up designed for

the present project, done with the software Sweet Home 3D. Figure E in appendix 4, shows the

electrical drawing for the whole installation made with AutoCAD.

5.3.7. Economical plan.

In the following section the costs of the microgrid already measured in the previous sections

will be developed.

Table 19. Economical plan

Timelife (years)

Quantity Item Price per Unit ($)

Offer Total

price ($) price per year ($)

Price per 24 years ($)

12 12 Battery (200Ah)

343.75 5% 3918.75 326.56 7837.50

30 10 PV Panel (295W)

375.00 5% 3562.50 118.75 3562.50

12 1 Controller 781.25 5% 742.19 61.85 1484.38

15 1 Inverter 2656.25 5% 2523.44 168.23 4205.73

25 1 Frame Roof &

materials 1000.00 - 1000.00 40.00 1000.00

25 1 Installation & transport cost

390.79 - 390.79 15.63 390.79

2 1 Maintenance 120.00 - 120.00 60.00 1320.00

12257.67 791.02 19800.89

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Table 19 shows the price of the different devices selected. In the first column the expected

lifetime for the different products is shown. In the second one the required units of each device is

written. In the fourth column its price in the market is recorded and in the next column the discount

achieved. This offer is going to be made if all these devices are bought from the same business.

Several purchases offers were received from Rwanda and also from Uganda and Tanzania.

The first idea was to deal with a supplier near Rukara. After looking on the Internet and being

researching within the area, it was decided that a company from Uganda will be in charge of providing

the devices as well as doing the installation due to their price of the components required and their

experience in this sector because the reliability is an important factor to keep in mind.

Right after, there is another column where the price per year keeping in mind their lifetime

is shown.

In Table 20 the energetic consumption of the school throughout the whole year is

determined.

Table 20. Electrical consumption per year.

Type of day Energy per day (kWh)

Total energy (kWh)

261 Daily day 10.63 2774.17

52 Saturday 1.00 52.05

52 Sunday 3.24 168.43

2994.65

From Monday to Friday the energetic consumption is higher because there are more devices

connected. However, on Saturday the school is not going to be used and the consumption of 1.00

kWh belongs to the emergency lights. On Sundays, the school works just half of the day so the

consumption is notably lower. On Sundays the students’ computers are not expected to be used. In

any case, the distribution of the consumption based on different type of days is possible to see in

Tables B, C and D in appendix 1.

Total energy is calculated by the product between the required energy per day and the

number of days in the year with this consumption profile.

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From this point, it is possible to estimate the price of each kWh from the designed microgrid.

The value obtained from Table 20 for the annual consumption is 2,994.65 kWh and Table 20

shows the microgrid price per year ($791.02). Dividing both figures, the electricity price is $0.264 per

kWh.

Rwandese electrical price is 215.3 RWF. Its equivalence is approximately $0.278 per kWh with

a currency exchange of 775.48 RWF per $. It is possible to see the variety of the currency throughout

the time in Figure 3 in the introduction section.

The energy from the designed microgrid is 5.6% cheaper than the electricity from the ordinary

grid. In addition to that, in the area where the school is going to be built, there is no access to the grid

and the possibility of build it is far from the economical allowances of this association.

Figure 24. Electricity price in Rukara in 2016. Figure 25. Electricity price in Rukara in 2015.

Figure 24 shows two receipts from the Health Centre in Rukara. The receipts show the current

price is 215.3 RWF for each kWh. On the contrary, Figure 25 shows the price in 2015 was 35% lower;

158.2 RWF per kWh.

Nevertheless, if the village continues being developed and the power lines reach the area of

the future school for Mil Colinas in a few years, the current grid can be used combining the energy

from both sources.

If this occurs and the conventional grid is reliable (without that constant power cuts that

currently happens), another option would be to translate the designed microgrid to another rural

area where the power lines are weaker.



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6. CONCLUSIONS

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In the following section all the main contributions developed throughout this master’s thesis

about the work done in Rukara, Rwanda are presented. Apart from that, a collection of conclusions

is briefly discussed as well as future ideas to improve the design and operation of this power supply

design.

Nowadays, the design of a renewable project like the one we have already developed is not

an unheard of idea largely because of the spread of this technology over the past decades. However,

it is necessary to point out that in Africa this type of technology has not been utilized as much as in

the Developed World (Europe, America…). A sustainable design using solar energy can meet not only

the needs of energy, but also the economical growth of this continent.

It is also remarkable that we can use software like Python or Matlab to improve and optimize

the design. For example, the code designed in Python shows the level of the batteries per hour

throughout the whole year. This is extremely useful when optimizing the number of photovoltaic

panels and batteries needed. This is also helps lower the costs of our project. It is important that we

do not forget about money because in undeveloped countries, such as Rwanda, the budget of a

project is a vital pillar for its development.

We have seen that distributed generation in this country also return money saving during the

operation of the school. That money can be invested in the education of hundreds of children in an

undeveloped area such as Rukara, helping the poorest and most vulnerable population.

In summary, we can exhibit the following conclusions for this project:

The first conclusion is to point out the importance of using renewable off-grid technologies

in construction. It reduces the electricity bill while the system is working, paying back the

facilities’ investment in few years without being affected by the power grid's’ state and the

changes in electricity prices. By removing the current power cuts produced bye in the power

grid supply in Rwanda, we can improve the quality of the education.

Mathematical calculation software can help engineers throughout the design phase of the

project. Along with technical calculations (currents, power consumptions, electrical

protections…), this kind of software can improve the budget of the project and the

performance of the system. The design must supply the necessary energy even if there are

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the most adverse conditions, and the equipment chosen must assure the proper

performance. There will be enough electricity for the lights, as well as for the emergency

lights at night, computers and small devices even if there are some consecutive cloudy days.

A proper maintenance of the solar and electrical system is necessary to preserve the

properties of the equipment. A lack of panel cleanliness, for example, may reduce the power

given to the inverter producing a shortage of electricity within the school.

The simulations with Python show that 12 batteries distributed in three branches is the best

option to cover all the energy demands. Also the Excel calculations show that 10 photovoltaic

panels is the best quantity due to the economical comparison, establishing a lack of energy

price of $13.92. The price for the whole installation reaches $12,257.67 and it will be

necessary to have a budget of $7,543.23 for its proper functioning for at least 24 years.

To conclude this section, it is important to emphasise the importance of this project because

it is a real project whose construction will start as soon as possible. It will have a cost of $0.264 per

kWh in comparison to the price of to the electricity from the grid ($0.278 per kWh).



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7. BIBLIOGRAPHY

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[1] "Geography." Http://gov.rw/. N.p., n.d. Web.

[2] "Rwanda Political Map with Capital Kigali, National Borders, Important Cities, Rivers and Lakes.

English Labeling and Scaling." Shutterstock. N.p., n.d. Web. Jan.-Feb. 2016.

[3] "World Weather Information Service." World Weather Information Service. N.p., n.d. Web. Jan.-

Feb. 2016.

[4] "Farmers Wary as New Weather Patterns Threaten Production." The New Times Rwanda. N.p.,

n.d. Web. 01 June 2016.

[5] "National Institute Of Statistics Of Rwanda." Http://www.statistics.gov.rw/. N.p., n.d. Web. 01

June 2016.

[6] "Acceso a La Electricidad (% De Población)." Datos. N.p., n.d. Web. Mar.-Apr. 2016.

[7] “Fourth Population and Housing Census, Rwanda, 2012.” Datos. N.p., n.d. Web. Mar.-Apr. 2016

[8]"Indicadores Del Desarrollo Mundial| Banco De Datos Mundial." Indicadores Del Desarrollo

Mundial| Banco De Datos Mundial. N.p., n.d. Web. 25 Mar. 2016.

[9] "UNAIDS." Rwanda. N.p., n.d. Web. 01 June 2016.

[10] 9:191–215, Lang Policy (2010), and Doi 10.1007/s10993-010-9170. ISSN 1568-4555, Volume 9,

Number 3 (n.d.): n. pag. Web.

[11] "Special Report on Rwanda July 97." Special Report on Rwanda July 97. N.p., n.d. Web. 01 June

2016.

[12] "Tantalum-Niobium International Study Center (T.I.C.)." TIC. N.p., n.d. Web. Apr.-May 2016.

[13] "Climate & Agriculture." Our Africa. N.p., n.d. Web. 18 Apr. 2016.

[14] "Rwanda to Restock Water Bodies with Fisheries." The New Times Rwanda. N.p., n.d. Web. 01

June 2016.

[15] "Over a Million Tourists Help Rwanda's Tourism Revenue Cross US$ 300m, Reports KT

Press." Over a Million Tourists Help Rwanda’s Tourism Revenue Cross US$ 300m, Reports KT Press.

N.p., n.d. Web. Feb.-Mar. 2016.

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[16] "Report for Selected Countries and Subjects." Report for Selected Countries and Subjects. N.p.,

n.d. Web. Apr.-May 2016.

[17] "Economic Growth Pulls Rwandans out of Poverty." GlobalPost. N.p., 28 Mar. 2012. Web. 01

June 2016.

[18] "Energía: Panorama General." Energía: Panorama General. N.p., n.d. Web. Oct.-Nov. 2016.

[19] Redrawing the Energy-climate Map World Energy Outlook Special Report. Paris: OECD/IEA,

2013. Web.

[20] "Multimedia." IEA. N.p., n.d. Web. 23 Feb. 2016.

[21] "Rwanda: Power Tariffs Go up 35% Effective Tuesday." Rwanda: Power Tariffs Go up 35%

Effective Tuesday. N.p., n.d. Web. 03 May 2016.

[22] "Le Solaire Se Lève Au Rwanda." Libération.fr. N.p., 24 Nov. 2015. Web. 01 May 2016.

[23] "PIB De Ruanda 2016." Datosmacro.com. N.p., n.d. Web. 01 June 2016.

[24] "The Solar Energy Market in Rwanda." “gtz%20.pdf”. N.p., n.d. Web.

[25] "ENERGY: The Opportunity in Rwanda. Web “http://www.rdb.rw/home.html” N.p., n.d.

[26] "Water, Electricity Tariffs to Increase." The New Times Rwanda. N.p., n.d. Web. 08 Jan. 2016.

[27] Rwanda: Poverty Reduction Strategy Paper. Rep. no. 13/360. N.p.: n.p., n.d. Pdf.

[28] Rwanda, Republic Of. THE EVOLUTION OF POVERTY IN RWANDA FROM 2000 T0 2011: (n.d.): n.

pag. Web.

[29] "Rwanda Energy Situation." Energypedia.info. N.p., n.d. Web. Mar.-Apr. 2016.

[30] "Rwanda Adds 25MW from KivuWatt, Symbion Signs Methane Deal."Rwanda Finally Taps

Electricity from Lake Kivu Methane Gas. N.p., n.d. Web. 01 June 2016.

[31] Smith, David. "How Africa's Fastest Solar Power Project Is Lighting up Rwanda." The Guardian.

Guardian News and Media, 23 Nov. 2015. Web. 01 June 2016.

[32] "Africa's Largest Solar (PV) Power Plant." Blue Energy Are Leading UK Developers of Renewable

Energy Infrastructure. N.p., n.d. Web. Apr.-May 2016.

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[33] "Rwamagana 8.5MW Solar Plant to Be Commissioned Today." The New Times Rwanda. N.p.,

n.d. Web. 01 June 2016.

[34] "Mobisol – Plug in the World!" Mobisol. N.p., n.d. Web. 01 June 2016.

[35] "About Microgrids." Microgrid Institute. N.p., n.d. Web. 01 June 2016.

[36] Vadillo, David Chinarro. OPTIMAGRIDAgenda (2011): n. pag. Web.

[37] I, Módulo. COMPONENTES DEL SISTEMA FOTOVOLTAICO (n.d.): n. pag. Web.

[38] "NASA Surface Meteorology and Solar Energy: RETScreen Data." NASA Surface Meteorology

and Solar Energy: RETScreen Data. N.p., n.d. Web. 01 June 2016.

[39] Handbook of Photovoltaic Science and Engineering. N.p.: n.p., 2010. Print.

[40] "Solar System Sizing." Open Electrical RSS. N.p., n.d. Web. 01 June 2016.

[41] "Solar Panel Tilt Calculator." - DIY Solar Kits. N.p., n.d. Web. 13 Jan. 2016.

[42] Lavet, Vincent François, Quentin Gemine, Damien Ernst, and Raphael Fonteneau. Towards the

Minimization of the Levelized Energy Costs of Microgrids Using Both Long-term and Short-term

Storage Devices. N.p, n.d. Pdf.

[43]Http://www.strategicforesight.com/publication_pdf/84153Blue%20Peace%20for%20the%20Nil

e.pdf. Web.

[44] King, David C. Rwanda. New York: Marshall Cavendish Benchmark, 2007. Print.

[45] "Rwanda." Gigawatt Global |. N.p., n.d. Web. Apr.-May 2016.



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8. APPENDICES

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Appendix 1. Relevant data.

Table A. Electrical generation in 2015. [19]

Electricity (TWh)

Coal 9576

Oil 1021

Gas 5279

Nuclear 2691

Hydro 3941

Bioenergy 531

Wind 845

Geothermal 85

Solar PV 246

Csp 16

marine 2

total 24233

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Table B. Electrical consumption from Monday to Friday.

Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Consumption (W)

Laptop children 1150.0 575.0 575.0 1150.0

Laptop teachers 50.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 50.0

Small speakers 7.3 7.3 7.3 7.3 7.3 7.3 7.3 7.3 7.3 7.3 7.3

Printer 46.2 46.2 46.2 46.2 46.2 46.2 46.2 46.2 46.2 46.2 46.2 46.2 46.2

Lights 4x normal classroom (15x6m)

352.0 352.0 352.0 704.0 352.0

Light office (6x6m) 10.0 10.0 10.0 20.0 20.0 10.0

Light big room (18x12m)

297.0 297.0 297.0

Outside light 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0

Projector 86.4 86.4 86.4 86.4 86.4 86.4 86.4 86.4 86.4 86.4 86.4

Charge Mobiles & other things

20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0

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Table C. Electrical consumption on Saturday.

Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Consumption (W)

Laptop children

Laptop teachers

Small speakers

Printer


Lights office (6x6m)

Lights big room (18x12m)

Outside lights 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0

Projector


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Table D. Electrical consumption on Sunday.

Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Consumption (W)

Laptop children

Laptop teachers 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

Small speakers 7.3 7.3 7.3 7.3 7.3 7.3 7.3 7.3 7.3

Printer 46.2 46.2 46.2 46.2 46.2 46.2 46.2 46.2 46.2


Lights office (6x6m)

Lights big room (18x12m)

Outside lights 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0 77.0

Projector 86.4 86.4 86.4 86.4 86.4 86.4 86.4 86.4 86.4


20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0

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Figure A. 4 x Normal rooms lights distribution.

Figure B. Office lights distribution.

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Figure C. Big room lights distribution.

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Table E. Solar irradiation supposing no cloudy days.

Hours Solar irradiation (kW/m2)

5:00 0.00

6:00 0.04

7:00 0.12

8:00 0.24

9:00 0.41

10:00 0.54

11:00 0.61

12:00 0.64

13:00 0.61

14:00 0.54

15:00 0.41

16:00 0.24

17:00 0.12

18:00 0.04

19:00 0.00

4.54

Table F. Solar irradiation supposing 10% days of no sun.


5:00 0.00

6:00 0.04

7:00 0.13

8:00 0.26

9:00 0.45

10:00 0.60

11:00 0.68

12:00 0.72

13:00 0.68

14:00 0.60

15:00 0.45

16:00 0.26

17:00 0.13

18:00 0.04

19:00 0.00

5.05

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Table G. Solar irradiation supposing 25% days of no sun.


5:00 0.00

6:00 0.05

7:00 0.15

8:00 0.31

9:00 0.53

10:00 0.70

11:00 0.80

12:00 0.84

13:00 0.80

14:00 0.70

15:00 0.53

16:00 0.31

17:00 0.15

18:00 0.05

19:00 0.00

5.92

Table H. Solar irradiation supposing 50% days of no sun.


5:00 0.00

6:00 0.08

7:00 0.23

8:00 0.48

9:00 0.81

10:00 1.08

11:00 1.22

12:00 1.29

13:00 1.22

14:00 1.08

15:00 0.81

16:00 0.48

17:00 0.23

18:00 0.08

19:00 0.00

9.08

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Table I. Distribution of different climatological days for Random Distribution.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

January N N S C S N N N S N C S N S S C N N C N S C S C N S N C S N S

February C S N N S N N S N S C S N S S N S C N N S N N C S N S C

March N S N S C N S C N S C N N S C S C S N N S C N S N S C N N S N

April S C S N N N S C S N S C S N C S N N N S C S N C N S N S C N

May S N C S N C S C N S C N S C N S N N S C N S N C S N C S N C S

June N S N C N S N N S C S S C N S N C S N N C S N C S N C S N S

July C S N C S N S N C N S S S N C N S N S N S N C N S N S C N S N

August C S N C S N S N C N S S S N C N S N S N S N C N S N S C N S N

September S C S N N S N C S N S S C N N S N C S N S C S N N S C N S N

October C N N S C S N S C S N N S C N N S C N S C N S C N S C N S C S

November S N C S N C S N C S N C S N C S N C S N C S N C S N C S N C

December S N C S N C S N C S N C S N C S N C S N C S N C S N C S N C S

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Appendix 2. Python code.

Created on Mon Apr 04 17:48:08 2016

@author: Patricia Conde

"""

import matplotlib.pyplot as plt #for calling the plot library

xbattery= BATTERIES CAPACITY #kWh batteries capacity

xmin=xbattery*0.3

stini=xbattery #kWh

level=stini

rt=0.999958

nc= 0.975 #controller eficiency

ni=0.95 #inverter eficiency

n=.90*nc #yield storage batt + controller

ed=0.90*ni #yield delivery batt + inverter

t=1 #hour

v=0

summ1=0

summ11=0

w=0

summ2=0

summ21=0

y=0

summ3=0

summ31=0

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ll=6.96*2 #$/kWh

demand=[]

for i in [ 8760 VALUES OF DEMAND ]:

if i>0: #storage,

st=min(rt*level+n*i*t,xbattery)

level=st

demand+=[round(level,3)]

elif i<0: #delivery

st=max(rt*level+(i*t)/ed,xmin)

if st<(xbattery*0.5): #kWh under 50% load level of the batteries

if st-level==0:

v=0

else:

v=level-st

summ1=summ1+v

else:

v=0

if st<level: #times under 50% load level of the batteries

if st<(xbattery*0.5):

if level>(xbattery*0.5):

b=1

summ11=summ11+b

else:

b=0

else:

b=0

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else:

b=0

if st<(xbattery*0.7): #kWh under 70% load level of the batteries

w=level-st

summ2=summ2+w

else:

w=0


if st<(xbattery*0.7):


c=1

summ21=summ21+c

else:

c=0

else:

c=0

else:

c=0

if st<=(xbattery*0.3): #kWh under 30% load level of the batteries

y=level-st

summ3=summ3+y

else:

y=0


if st==(xmin):


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d=1

summ31=summ31+d

else:

d=0

else:

d=0

else:

d=0

level=st


else: #production=consumption

st=level


print ("The battery level per hour is:", demand)

print ("por debajo del 70% de SOC:", summ2, "kWh",summ21,"veces")

print ("por debajo del 50% de SOC:", summ1, "kWh",summ11,"veces")

print ("se descarga hasta el 70%:", summ31, "veces")

print("demand not satisfied:",round(summ3,3), "KW")

if summ3<=0:

print("All the demand is satisfied")

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else:

cost1=llt*summ3

print("por lo que el coste es:",round(cost1,3), "$")

plt.plot(demand)

plt.show()

plt.plot(demand, linestyle='-', color='k', label = "Random Distribution") # Plot the function

plt.title("Battery level") # Title

plt.xlabel("Hour") # X axis title

plt.ylabel("kWh") # Y axis title

plt.legend(loc="lower left")

Appendix 2.1. Demand values for Random Distribution.

10 Photovoltaic Panels.

-0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224,

1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -

1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -

0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281,

0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941,

0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

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0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

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2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

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0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

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0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

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1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

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1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281,

0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941,

0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

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2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

74

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

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0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

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2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

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1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

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0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

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0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077,

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1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

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-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281,

0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941,

0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

75

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

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1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

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1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

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0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

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2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

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0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

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1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

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76

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

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0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

77

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

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2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

78

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

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1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

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-0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138,

0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

79

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059,

-0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -

0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138,

80

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

-0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -

0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

81

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138,

0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

82

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

-0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -

0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

-0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -

0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281,

83

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941,

0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

84

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059,

-0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -

0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059,

-0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -

0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

85

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

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0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

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1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059,

-0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -

0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059,

-0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -

0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

86

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

87

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

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2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

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0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

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0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

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0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

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1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

88

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

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1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

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1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

-0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -

0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077,

89

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

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0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

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2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

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0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

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1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138,

0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592,

1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

90

Energy Engineering

Master’s Degree



Energy Engineering

Master’s Degree

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

-0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -

0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138,

0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102,

0.530880307, 1.091253965, 1.858081075, 2.477441434, 2.801868288, 2.94933504, 2.801868288,

2.477441434, 1.858081075, 1.091253965, 0.530880307, 0.176960102, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974, 0.132720077, 0.113023281, 0.204730059, 0.359570149,

0.440676862, 0.47754355, 0.440676862, 0.359570149, 0.204730059, 0.013023281, 0.132720077, -

0.032759974, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543,

0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457, 0.504087566, -

0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483,

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2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -

0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281,

0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941,

0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

-0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -

0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928,

-0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592,

0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355,

0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.291127928, -0.012537631, 0.604087566,

1.090866543, 0.324418794, 1.126517592, 1.804744318, 1.701517592, 0.899418794, -0.109133457,

0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078,

2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.032759974,

0.132720077, 0.272813491, 0.464520269, 0.619360358, 0.700467072, 0.73733376, 0.700467072,

0.619360358, 0.464520269, 0.272813491, 0.132720077, 0.044240026, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072, 0.371616215, 0.604087566, 1.040866543, 1.474418794,

1.701517592, 1.804744318, 1.701517592, 1.474418794, 1.040866543, 0.504087566, 0.371616215,

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0.046872072, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898,

0.146726461, 0.931463755, 1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078,

1.642651224, 0.448290865, 0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059,

-0.790429851, -0.134323138, 0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -

0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.291127928, -0.012537631, 0.604087566, 1.090866543, 0.324418794, 1.126517592, 1.804744318,

1.701517592, 0.899418794, -0.109133457, 0.504087566, -0.646173995, -1.288918138, -0.961153846, -0.107,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755,

1.648290865, 1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865,

0.831463755, -0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.370759974, -0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138,

0.47754355, 0.440676862, -0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -

0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, 0.046872072,

0.371616215, 0.763877775, 1.300656753, 1.734209004, 1.961307802, 2.064534528, 1.961307802,

1.734209004, 1.300656753, 0.763877775, 0.371616215, 0.123872072, 0, -0.077, -0.077, -0.077, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, 0.099960102, 0.530880307, 0.931463755, 1.598290865, 2.217651224,

2.542078078, 2.68954483, 2.542078078, 2.217651224, 1.598290865, 0.831463755, 0.530880307,

0.099960102, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.370759974,

-0.251433769, 0.113023281, 0.254730059, -0.790429851, -0.134323138, 0.47754355, 0.440676862, -

0.215429851, -0.945269941, 0.013023281, -0.885070133, -1.368550184, -0.961153846, -0.107, -0.077, -0.077,

-0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.077, -0.238039898, 0.146726461, 0.931463755, 1.648290865,

1.067651224, 1.967078078, 2.68954483, 2.542078078, 1.642651224, 0.448290865, 0.831463755, -

0.486909903, -1.235830107, -0.961153846, -0.107, -0.077, -0.077, -0.077, -0.077

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Business cases for Microgrids is Africa


Energy Engineering

Master’s Degree

Appendix 3. Results

Table J. Recovery of results from Python.

Charge level of the batteries (SOC)

Weather configuration

Batteries Photovoltaic

Panels (kWh) (times)

30% 50% 70% 30% 50% 70%

Random Distribution

8

8 5.427 254.53 719.69 7 66 148

10 - 108.12 367.60 - 47 103

12 - 19.00 240.77 - 42 57

12

8 - 27.46 349.82 - 8 115

10 - - 188.14 - - 60

12 - - 106.84 - - 47

SNC Distribution 8

10 - 27.28 78.77 - 12 26

12 - - 46.55 - - 12

SSNCNC Distribution

8 10

2.41 31.29 82.97 3 15 24

12 - 6.48 60.72 - 3 14

SSNNCC Distribution

8 10

4.68 37.62 97.92 5 7 14

12 - 15.68 65.99 - 5 10

SSSNNNCCC Distribution

8

8 7.72 35.39 72.60 6 8 11

10 5.72 32.03 28.11 5 7 11

12 3.56 30.26 57.39 4 6 6

12

8 2.22 38.77 88.67 4 8 9

10 2.01 25.44 74.92 3 5 10

12 1.62 22.47 60.33 2 4 6

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Appendix 4. School Plans

Figure D. School’s mock-up

+ -

12v

+ -

12v

+ -

12v

+ -

12v

+ -

12v

+ -

12v

+ -

12v

+ -

12v

+ -

12v

+ -

12v

+ -

12v

+ -

12v

Output

Power (W)

Imax (A)

Un (V)

Computer room Office+Big room

Classrooms

Ext. Lighting

300 W

230 V

1,3 A

1200 W

230 V

5,21 A

2000 W

230 V

8,69 A

2000 W

230 V

8,69 A

2P

25 A

2P

25 A

30mA

2P

10 A

2P

10 A

2P

10 A

2P

6 A

2x4mm2 [Cu RV/K 0,6/1 kV]

INVERTER

Victron Energy

5000W / 48 V

+-

+-

DISTRIBUTION

BOARD

25A

FUSE Protections

BATTERY

CONTROLLER

Outback Brand

80A

2x10mm2 [Cu RV/K 0,6/1 kV]

2x35mm2 [Cu RV/K 0,6/1 kV]

2x50mm2 [Cu RV/K 0,6/1 kV]

2P

40 A

2P

40 A

2P

40 A

2P

40 A

2P

40 A

2x5 modules 24Vcc

10x295W

Interconnections

2x16mm2

2x10mm2 [Cu RV/K 0,6/1 kV]

BATTERY BANK

3x4 Sealed Batteries

200Ah/12V

295-Watt MonocrystallinePhotovoltaic Module

Africa’s Source for Renewable Energy TM

AFR-295

Copyright © 2014 African EnergyTel. (520) 720-9475 - Fax (520) 720-9527Box 664, St. David, Arizona, USA 85630 www.AfricanEnergy.com | [email protected]

African Energy modules are made by some of the world's most sophisticated module manufacturers and are designed for Africa's off-grid solar charging and water pumping needs. The modules include efficient crystalline cells set in a solid aluminium frame and feature TÜV and IEC certification. With a 25 year warranty, these modules can provide power for several generations - and the quality is assured by African Energy's decade of experience in the solar industry.

Nominal Output (Pmax) [Wp]

Current at Pmax (Imp) [A]Voltage at Pmax (Vmp) [V]

Open Circuit Voltage (Voc) [V]Short Circuit Current (Isc) [A]Power Tolerance +/- 3% (referenced to the Nominal Output) Maximum System VoltageCell Efficiency

29536.928.0045.938.63

DC 1000V >17.60%

ELECTRICAL CHARACTERISTICS at STC*

Module Efficiency >15.20%

MECHANICAL CHARACTERISTICSSolar CellsFront CoverBack CoverEncapsulantFrameDiodes

72 mono crystalline silicon solar cells 3.2 mm thick, tempered glass / AR coating glassTPT (Tedlar-PET-Tedlar)/BBFEVA (ethylene vinyl acetate)Double-layer anodized aluminum alloy6 bypass diodes serviceable

Junction Box IP65 RatedConnectorsCablesDimensionsWeightMax. Load

MC4 or compatible connectorsLength: 900 mm 1956 x 992 x 50mm 23 kg60m/s(200kg/sq.m)

NOCT**Temperature Coefficient of PmaxTemperature Coefficient of VocTemperature Coefficient of IscMaximum Series Fuse RatingOperating Temperature

45 +/-2 °C-(0.5+/-0.05) /°C

-(2.23+/-0.1) mv /°C0.065+/-0.015 %/°C

20 A from -40°C~+85 °C

TEMPERATURE CHARACTERISTICS

Storage Temperature from -40 to +85 °C

STC*: Irradiance of 1000W/m2, AM1.5 Spectrum and Cell Temperature of 25 . NOCT**: Irradiance of 800W/m2, ambient temperature 20 and wind speed 1 m/s

Nominal Voltage 12 V

Rated Capacity 20hr Rate (1,80V/cell) 10hr Rate (1,80V/cell) 5hr Rate (1,70V/cell) 1hr Rate (1,60V/cell)(25 °C) 210 Ah 200 Ah 181 Ah 126,6 Ah

Dimensions (mm) Length Width Height Overall Height Weight& Weight (kg) 522mm 238mm 218mm 223mm 65 kg

Number / Type of Terminals 2 / M8

VRLA Battery SPB 12-200

Technical CharacteristicsDesign Life at 200C 10-12 years

Eurobat Classification High Performance

Internal Resistance (Fully charged - 250C) 3,5 mΩ

Short-circuit current 3300 A

Max Charging Current 60 A

Min safe end Discharge Voltage 1,60 V/cell

Self discharge per month at 200C 3%

Recommended Charging Voltage at 200C Stand-by use (V/cell): 2,25 to 2,30

Cycle use (V/cell): 2,40 to 2,50

Container Material ABS-UL94 HB

Electrolyte Type Sulfuric Acid

Type of plates / Alloy Flat plates / Lead-Calcium-Tin alloy

Type of Separator Absorbant Glass Mat

Valve Type / Operational Pressure Rubber / 1-3 psi (70-200 mbar)

Operating Temperature Range -20 to + 50°C

Storage time at 200C 9 months

Specifications

SYSTEMS SUNLIGHT S.A.Headquarters23rd Km. N.R. Athens - Lamia,145 65 Agios Stefanos - Attica, GreeceTel.: +30 210 624 5400,Fax: +30 210 624 5409

Manufacturing PlantNeo Olvio67 200 Xanthi, GreeceTel.: +30 25410 48100,Fax: +30 25410 95446

www.sunlight.gr

www.victronenergy.com

xxx

Two AC inputs with integrated transfer switch

The Quattro can be connected to two independent AC sources, for example shore-side power and a generator, or two generators. The Quattro will automatically connect to the active source.

Two AC Outputs

The main output has no-break functionality. The Quattro takes over the supply to the connected loads in the event of a grid failure or when shore/generator power is disconnected. This happens so fast (less than 20 milliseconds) that computers and other electronic equipment will continue to operate without disruption. The second output is live only when AC is available on one of the inputs of the Quattro. Loads that should not discharge the battery, like a water heater for example, can be connected to this output.

Virtually unlimited power thanks to parallel operation

Up to 10 Quattro units can operate in parallel. Ten units 48/10000/140, for example, will provide 90kW / 100kVA output power and 1400 Amps charging capacity.

Three phase capability

Three units can be configured for three-phase output. But that’s not all: up to 10 sets of three units can be parallel connected to provide 270kW / 300kVA inverter power and more than 4000A charging capacity.

PowerControl – Dealing with limited generator, shore-side or grid power

The Quattro is a very powerful battery charger. It will therefore draw a lot of current from the generator or shore side supply (16A per 5kVA Quattro at 230VAC). A current limit can be set on each AC input. The Quattro will then take account of other AC loads and use whatever is spare for charging, thus preventing the generator or shore supply from being overloaded.

PowerAssist – Boosting shore or generator power

This feature takes the principle of PowerControl to a further dimension allowing the Quattro to supplement the capacity of the alternative source. Where peak power is so often required only for a limited period, the Quattro will make sure that insufficient shore or generator power is immediately compensated for by power from the battery. When the load reduces, the spare power is used to recharge the battery.

Solar energy: AC power available even during a grid failure

The Quattro can be used in off grid as well as grid connected PV and other alternative energy systems.

System configuring has never been easier

After installation, the Quattro is ready to go. If settings have to be changed, this can be done in a matter of minutes with a new DIP switch setting procedure. Even parallel and 3-phase operation can be programmed with DIP switches: no computer needed! Alternatively, VE.Net can be used instead of the DIP switches. And sophisticated software (VE.Bus Quick Configure and VE.Bus System Configurator) is available to configure several new, advanced, features.

Quattro

48/5000/70-100/100

Quattro

24/3000/70-50/30

Quattro inverter / charger 3kVA - 10kVA Lithium Ion battery compatible

Victron Energy B.V. | De Paal 35 | 1351 JG Almere | The Netherlands General phone: +31 (0)36 535 97 00 | Fax: +31 (0)36 535 97 40 E-mail: [email protected] | www.victronenergy.com

Quattro 12/3000/120-50/30 24/3000/70-50/30

12/5000/220-100/100 24/5000/120-100/100 48/5000/70-100/100

24/8000/200-100/100 48/8000/110-100/100

48/10000/140-100/100

PowerControl / PowerAssist Yes

Integrated Transfer switch Yes

AC inputs (2x) Input voltage range: 187-265 VAC Input frequency: 45 – 65 Hz Power factor: 1

Maximum feed through current (A) 50 / 30 2x100 2x100 2x100

INVERTER

Input voltage range (V DC) 9,5 – 17V 19 – 33V 38 – 66V

Output (1) Output voltage: 230 VAC ± 2% Frequency: 50 Hz ± 0,1%

Cont. output power at 25 °C (VA) (3) 3000 5000 8000 10000

Cont. output power at 25 °C (W) 2500 4500 7000 9000

Cont. output power at 40 °C (W) 2200 4000 6300 8000

Peak power (W) 6000 10000 16000 20000

Maximum efficiency (%) 93 / 94 94 / 94 / 95 94 / 96 96

Zero-load power (W) 15 / 15 25 / 25 / 25 30 / 35 35

Zero load power in AES mode (W) 10 / 10 20 / 20 / 20 25 / 30 30

Zero load power in Search mode (W) 4 / 5 5 / 5 / 6 8 / 10 10

CHARGER

Charge voltage 'absorption' (V DC) 14,4 / 28,8 14,4 / 28,8 / 57,6 28,8 / 57,6 57,6

Charge voltage 'float' (V DC) 13,8 / 27,6 13,8 / 27,6 / 55,2 27,6 / 55,2 55,2

Storage mode (V DC) 13,2 / 26,4 13,2 / 26,4 / 52,8 26,4 / 52,8 52,8

Charge current house battery (A) (4) 120 / 70 220 / 120 / 70 200 / 110 140

Charge current starter battery (A) 4 (12V and 24V models only)

Battery temperature sensor Yes

GENERAL

Auxiliary output (A) (5) 25 50 50 50

Programmable relay (6) 1x 3x 3x 3x

Protection (2) a-g

VE.Bus communication port For parallel and three phase operation, remote monitoring and system integration

General purpose com. port (7) 1x 2x 2x 2x

Remote on-off Yes

Common Characteristics Operating temp.: -40 to +50 ˚C Humidity (non condensing): max. 95%

ENCLOSURE

Common Characteristics Material & Colour: aluminium (blue RAL 5012) Protection category: IP 21

Battery-connection Four M8 bolts (2 plus and 2 minus connections)

230 V AC-connection Screw terminals 13 mm2 (6 AWG) Bolts M6 Bolts M6 Bolts M6

Weight (kg) 19 34 / 30 / 30 45/41 45

Dimensions (hxwxd in mm) 362 x 258 x 218 470 x 350 x 280 444 x 328 x 240 444 x 328 x 240

470 x 350 x 280 470 x 350 x 280

STANDARDS

Safety EN 60335-1, EN 60335-2-29

Emission, Immunity EN55014-1, EN 55014-2, EN 61000-3-3, EN 61000-6-3, EN 61000-6-2, EN 61000-6-1 1) Can be adjusted to 60 HZ; 120 V 60 Hz on request 2) Protection key: a) output short circuit b) overload c) battery voltage too high d) battery voltage too low e) temperature too high f) 230 VAC on inverter output g) input voltage ripple too high

3) Non linear load, crest factor 3:1 4) At 25 ˚C ambient 5) Switches off when no external AC source available 6) Programmable relay that can a. o. be set for general alarm, DC undervoltage or genset start/stop function

AC rating: 230V/4A DC rating: 4A up to 35VDC, 1A up to 60VDC

7) A. o. to communicate with a Lithium Ion battery BMS

Digital Multi Control Panel A convenient and low cost solution for remote monitoring, with a rotary knob to set Power Control and Power Assist levels.

Blue Power Panel Connects to a Multi or Quattro and all VE.Net devices, in particular the VE.Net Battery Controller. Graphic display of currents and voltages.

Computer controlled operation and monitoring Several interfaces are available:

- MK2.2 VE.Bus to RS232 converter

Connects to the RS232 port of a computer (see ‘A guide to VEConfigure’) - MK2-USB VE.Bus to USB converter

Connects to a USB port (see ‘A guide to VEConfigure’) - VE.Net to VE.Bus converter

Interface to VE.Net (see VE.Net documentation) - VE.Bus to NMEA 2000 converter

- Victron Global Remote

The Global Remote is a modem which sends alarms, warnings and system status reports to cellular phones via text messages (SMS). It can also log data from Victron Battery Monitors, Multi’s, Quattros and Inverters to a website through a GPRS connection. Access to this website is free of charge. - Victron Ethernet Remote

To connect to Ethernet.

BMV Battery Monitor The BMV Battery Monitor features an advanced microprocessor control system combined with high resolution measuring systems for battery voltage and charge/discharge current. Besides this, the software includes complex calculation algorithms, like Peukert’s formula, to exactly determine the state of charge of the battery. The BMV selectively displays battery voltage, current, consumed Ah or time to go. The monitor also stores a host of data regarding performance and use of the battery. Several models available (see battery monitor documentation).

OutBack reserves the right to make changes to the products and information contained in this document without notice.Copyright © 2013-2014 OutBack Power. All Rights Reserved. OutBack is a registered trademark of The Alpha Group.

FLEXmax™ SeriesContinuous Maximum Power Point Tracking (MPPT) Charge Controllers

The FLEXmax family of charge controllers is the industry leading innovation in Maximum Power Point (MPPT) charge controllers from OutBack Power.

The innovative FLEXmax MPPT software algorithm is both continuous and active, increasing your photovoltaic array power yield up to 30% compared to non-MPPT controllers. Thanks to active cooling and intelligent thermal management cooling, both FLEXmax charge controllers can operate at their full maximum current rating, 60 Amps or 80 Amps respectively, in ambient temperatures as high as 104°F (40°C).

Included in all the FLEXmax charge controllers are the revolutionary features first developed by OutBack Power, including support for a wide range of nominal battery voltages and the ability to step down a higher-voltage solar array to recharge a lower-voltage battery bank. A built-in, backlit 80 character display shows the current status and logged

system performance data for the last 128 days at the touch of a button. The integrated OutBack Power network communications allow FLEXmax series charge controllers to be remotely programmed and monitored using the MATE family of system displays and provide unrivaled complete system integration.

FLEXmax MPPT charge controllers are the only choice when you demand a high performance, efficient and versatile charge controller for your advanced power system.

Increases PV Array Output by up to 30%

Advanced Continuous Maximum Power Point Tracking

Full Power Output in Ambient Temperature up to 104°F (40°C)

Battery Voltages from 12 to 60 VDC

Fully OutBack Network Integrated and Programmable

Programmable Auxiliary Control Output

Built-in 128 Days of Data Logging

Standard 5-Year Warranty

FLEXmax 80 FLEXmax 60

Worldwide Corporate Offices

North America Tel: +1 360.435.6030 Fax: +1 360.435.6019

Europe Tel: +49 9122.79889.0 Fax: +49 9122.79889.21

Latin America Tel: +1 561.792.9651 Fax: +1 561.792.7157

Asia Pacific Tel: +852 2736.8663 Fax: +852 2199.7988

A v A i l A b l e F r o m

FLEXmax Series Specifications 06/2014

Models: FLEXmax 80 (FM80-150VDC) FLEXmax 60 (FM60-150VDC)Nominal Battery Voltages 12, 24, 36, 48, or 60VDC (Single model, selectable via field programming at start-up) 12, 24, 36, 48, or 60VDC (Single model, selectable via field programming at start-up)

Maximum Output Current 80A @ 104°F (40°C) with adjustable current limit 60A @ 104°F (40°C) with adjustable current limit

NEC Recommended Solar Maximum Array STC Nameplate

12VDC systems: 1000W / 24VDC systems: 2000W48VDC systems: 4000W / 60VDC systems: 5000W

12VDC systems: 750W / 24VDC systems: 1500W48VDC systems: 3000W / 60VDC systems: 3750W

PV Open Circuit Voltage (VOC) 150VDC absolute maximum coldest conditions / 145VDC start-up and operating maximum 150VDC absolute maximum coldest conditions / 145VDC start-up and operating maximum

Standby Power Consumption Less than 1W typical Less than 1W typical

Power Conversion Efficiency 97.5% @ 80 ADC in a 48VDC System (typical) 98.1% @ 60 ADC in a 48VDC System (typical)

Charging Regulation Five stages: bulk, absorption, float, silent and equalization Five stages: bulk, absorption, float, silent and equalization

Voltage Regulation Set points 13 to 80VDC user adjustable with password protection 13 to 80VDC user adjustable with password protection

Equalization Charging Programmable voltage setpoint and duration, automatic termination when completed Programmable voltage setpoint and duration, automatic termination when completed

Battery Temperature Compensation Automatic with optional RTS installed / 5.0 mV per °C per 2V battery cell Automatic with optional RTS installed / 5.0 mV per °C per 2V battery cell

Voltage Step-Down Capability Down convert from any acceptable array voltage to any battery voltage. Example: 72VDC array to 24VDC battery; 60VDC array to 48VDC battery

Programmable Auxiliary Control Output 12VDC output signal which can be programmed for different control applications (maximum of 0.2 ADC) 12VDC output signal which can be programmed for different control applications (maximum of 0.2 ADC)

Status Display 3.1” (8 cm) backlit LCD screen, 4 lines with 80 alphanumeric characters total 3.1” (8 cm) backlit LCD screen, 4 lines with 80 alphanumeric characters total

Remote Display and Controller Optional MATE3, MATE or MATE2 with RS232 serial communications port Optional MATE3, MATE or MATE2 with RS232 serial communications port

Network Cabling Proprietary network system using RJ-45 modular connectors with CAT5 cable (8 wires) Proprietary network system using RJ-45 modular connectors with CAT5 cable (8 wires)

Data Logging Last 128 days of operation: Amp Hours, Watt Hours, Time in Float, Peak Watts, Amps, Solar Array Voltage, Max. Battery Voltage, Min Battery Voltage and Absorb, Accumulated Amp Hours, and kW Hours of production

Operating Temperature Range -40 to 60°C (power automatically derated above 40°C) -40 to 60°C (power automatically derated above 40°C)

Environmental Rating Indoor Type 1 Indoor Type 1

Conduit Knockouts One 1” (35 mm) on the back; One 1” (35 mm) on the left side; Two 1” (35 mm) on the bottom One 1” (35 mm) on the back; One 1” (35 mm) on the left side; Two 1” (35 mm) on the bottom

Warranty Standard 5-year / Available 10-Year Standard 5-year / Available 10-Year

Weight (lb/kg) Unit: 12.20 / 5.56 Shipping: 15.5 / 7.3

Unit: 11.65 / 5.3 Shipping: 1490 / 6.7

Dimensions H x W x D (in/cm) Unit: 16.25 x 5.75 x 4.5 / 41.3 x 14.6 x 11.4 Shipping: 19 x 9.5 x 8.5 / 48.3 x 24.1 x 21.6

Unit: 13.75 x 5.75 x 4.5 / 35 x 14.6 x 11.4 Shipping: 17 x 9.5 x 8.5 / 43.2 x 24.1 x 21.6

Options Remote Temperature Sensor (RTS), HUB4, HUB10, MATE, MATE2, MATE3 Remote Temperature Sensor (RTS), HUB4, HUB10, MATE, MATE2, MATE3

Menu Languages English & Spanish English & Spanish

Certifications ETL Listed to UL1741, CSA C22.2 No. 107.1 ETL Listed to UL1741, CSA C22.2 No. 107.1

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