Optimized management of lighting conditions in spaceswith multiple users

João Pedro Pires Martins

Thesis to obtain the Master of Science Degree in

Engineering Physics

Supervisors: Prof. Carlos Augusto Santos SilvaProf. Luís Filipe Moreira Mendes

Examination Committee

Chairperson: Prof.a Maria Joana Patrício Gonçalves de SáSupervisor: Prof. Carlos Augusto Santos Silva

Member of the Committee: Prof. João Carlos Carvalho de Sá Seixas

June 2017

ii

Acknowledgments

Em primeiro lugar gostaria de agradecer ao Professor Carlos Silva, pelas ideias, orientação e dis-

cussões que tivemos. Serviços de Energia foi a cadeira que tive que me motivou para explorar esta área

de conhecimento, pois foi das cadeiras que mais apreciei ao longo deste percurso académico. Sempre

teve disponibilidade para me ajudar neste projecto.

Quero também agradecer aos meus amigos e colegas, em especial o Rúben, o Zé, o João Vargas,

o Daniel, o Jorge, pelas parvoíces e conversas que tivemos. Pelos testes e exames partilhados, pelas

frustrações comuns, por terem tornado este percurso académico mais fácil. Obrigado pelo apoio e

motivação.

Quero agradecer à Ana, pela paciência que tem tido para comigo, pela força que me deu quando

mais precisei, por ter estado sempre ao meu lado.

Por fim, à minha família, pelo apoio incondicional que me deram.

iii

iv

Resumo

O consumo energético tem um peso cada vez maior na sociedade. Utilizar de forma responsável é

uma preocupação devido ao consumo de energias fósseis. O maior consumo energético na sociedade

provém de edifícios, e dentro destes, uma parte significativa provém da iluminação. Como tal, um passo

para reduzir o consumo energético é aproveitar a luz solar. Além de providenciar iluminação, permite

também reduzir o consumo de sistemas de ar condicionado, pois há menos calor gerado devido aos

ganhos internos das lâmpadas durante o verão; no inverno, a luz solar permite o aquecimento das

divisões, diminuindo igualmente o consumo de sistemas de ar condicionado e consequentemente o

consumo eléctrico. Um espaço de trabalho bem iluminado pode aumentar a produtividade dos diversos

utilizadores que estejam no espaço a trabalhar, contudo, é necessário ter em atenção a incidência

directa de luz solar, causando desconforto e encadeamento. Assim surge o desafio de utilizar a luz

solar de forma a criar condições favoráveis ao trabalho, sem causar encadeamento.

Este trabalho passa então por conseguir medir eficazmente a iluminação e conseguir gerir o controlo

de persianas e iluminação eléctrica para fornecer um ambiente propício para bom rendimento dos

utilizadores. Foi também feito um estudo sobre a iluminância ao longo do dia para compreender o seu

comportamento e distribuição. Por fim, após a medição de iluminância determina-se se é necessário

utilizar as persianas para diminuir ou subir a iluminância ao longo da sala, ou utilizar a iluminação

eléctrica caso a iluminância seja demasiado baixa.

Palavras-chave: Controlo automático, consumo energético, modelo de iluminância, opti-

mização de iluminância.

v

vi

Abstract

Electrical consumption has an increasing weight in society. Using responsibly is a concern due to

consumption of fossil fuels. The biggest energetic consumption derives from buildings, and from these, a

significant consumption is from electrical lighting. As such, a step to reduce electrical consumption is to

use sunlight. Besides providing illumination to the room in question, it also allows the reduction of use of

cooling systems, as there is less heat generated through electrical lighting due to heat gains in summer;

in winter, the sunlight heats the surrounding space, reducing likewise the use of cooling systems and

therefore the electrical consumption. Having a space well lit can increase the productivity of several

users that are working in the space, however, it is necessary to take into account direct sunlight hitting

the users, causing discomfort and glare. Rises then a problem, in which is necessary to use sunlight,

whenever possible, that provides favorable conditions to work, without glare.

This work has to measure efficiently the illumination and manage the control of the blinds and elec-

trical lighting to provide a good working environment for the users. It was also made a study about the

illuminance throughout the day to understand it’s behavior and distribution. Finally, after the measure

of illuminance, it is determined if it is necessary the use of the blinds to lower or rise the illuminance

through the room, or use the electrical lighting in case the illuminance is not high enough.

Keywords: Automatic control, electrical consumption, illuminance model, illuminance optimiza-

tion.

vii

viii

Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Energy demand overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4.1 Visible light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4.2 Properties of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4.3 Solar Angles and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.4 Interior Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 State-of-art 11

2.1 Daylight impact on illuminance in a room . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Sun radiation impact on illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Automatic control systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Visual comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Methodology 23

3.1 Sun radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.1 Horizontal data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.2 Pèrez Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Windows transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Calibration of sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.4 Daylight control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.1 Blinds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

ix

3.4.2 Electrical lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4 Results 31

4.1 Radiation to lux conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2 Window’s transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Natural lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4 Artificial lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.5 Prediction of the illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Conclusions 47

5.1 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Bibliography 49

x

List of Tables

2.1 Brightness coefficients for Perez anisotropic sky . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Best sun radiation models to different sky conditions . . . . . . . . . . . . . . . . . . . . . 15

2.3 Effects of different setting for various sensor types . . . . . . . . . . . . . . . . . . . . . . 17

2.4 Reference illuminance values for a classroom . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 Parameters obtained for the fit between sensors . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Relation between radiation and illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Prediction using different ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.3 Prediction of illuminance for blinds completely open during morning . . . . . . . . . . . . 41

4.4 Summary table for the values measured . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

xi

xii

List of Figures

1.1 Energy consumption in Portugal and EU-28 in 2014 . . . . . . . . . . . . . . . . . . . . . 2

1.2 Energy prediction in buildings in USA for 2015 . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Electromagnetic spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Representation of law of reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Representation of light transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6 Representation of Snell’s law of reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.7 Representation of one steradian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.8 Generic luminous intensity over one steradian . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.9 Generic luminous flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.10 Representation of illuminance and luminance . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1 Horizontal and vertical illuminance measured during summer . . . . . . . . . . . . . . . . 11

2.2 Horizontal and vertical illuminance measured during winter . . . . . . . . . . . . . . . . . 12

2.3 Schematic of open and closed loop systems . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Illuminance measured with manual and automatic control . . . . . . . . . . . . . . . . . . 19

2.5 Illuminance frequency with manual and automatic control . . . . . . . . . . . . . . . . . . 19

3.1 Representation of algorithm proposed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Characteristic of the light meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Relation between sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4 Representation of interest points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.5 Illuminance measurements throughout the room . . . . . . . . . . . . . . . . . . . . . . . 28

3.6 Illuminance measurements throughout the room with log scale . . . . . . . . . . . . . . . 29

3.7 Representation of the algorithm for electrical lighting . . . . . . . . . . . . . . . . . . . . . 30

3.8 Representation of the position of the lamps . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.1 Comparison of the different ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2 Window’s transmittance expected in the classroom . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Transmittance setup in the classroom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4 Transmittance measured in the classroom . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.5 Distribution of illuminance provided by natural lighting . . . . . . . . . . . . . . . . . . . . 37

4.6 Distribution of illuminance provided by lamps . . . . . . . . . . . . . . . . . . . . . . . . . 38

xiii

4.7 Representation of the lamps using configurations “L4” and “L4+L2” . . . . . . . . . . . . . 38

4.8 Representation of the lamps using configurations “L4t+L3t” and “L4t+L2+L3t” . . . . . . . 39

4.9 Impact of each lamps and configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.10 Representation of the algorithm used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.11 Prediction of illuminance for blinds completely open during morning . . . . . . . . . . . . 41

4.12 Prediction of illuminance and it’s correction using blinds . . . . . . . . . . . . . . . . . . . 42

4.13 Prediction of illuminance and it’s correction using lamp L4 . . . . . . . . . . . . . . . . . . 43

4.14 Electrical consumption in the room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

xiv

Nomenclature

Greek symbols

αs Solar altitude angle [ ]

β Slope [ ]

δ Declination of the sun [ ]

γ Surface azimuth angle [ ]

Ω Solid angle [sr]

ω Hour angle [ ]

φ Latitude [ ]

φL Luminous flux [lm]

ρ Reflectance

τ Transmittance

θ1 Incident angle of a beam [ ]

θ′

1 Reflected angle of a beam [ ]

θ2 Refracted angle of a beam [ ]

θz Zenith angle [ ]

Roman symbols

F1 Circumsolar brightness coefficient

F2 Horizontal brightness coefficient

f[1,2],[1,2,3] Pèrez brightness coefficient

Fc-g View factor surface to ground

Fc-s View factor surface to sky

Ib Beam radiation

Id Diffuse radiation

IT Total radiation

Li Switch that controls lamp i

n Refractive index of the material

nday Number of day

c Speed of light in vacuum [m/s]

E Illuminance [lx]

I Luminous intensity [cd]

L Luminance [cd/m2]

v Speed of light in a material [m/s]

xv

xvi

Chapter 1

Introduction

1.1 Background

Interior lighting in space offices accounts for approximately 25 − 35% of electricity used in buildings.

Using daylight could reduce electrical consumption, and may help creating a better indoor environment.

A higher indoor environment may increase visual comfort and rise the productivity of office users, and

may reduce the need to use cooling systems, because there are less heat generated through electric

lighting (usually called internal gains). All these factors help to reduce carbon footprint, which is a key

point in today’s society [1, 2].

However, in an office space, it is also important to take into account glare and direct sunlight, which

causes visual discomfort to the users. To avoid these issues, shading devices are a necessary solution.

These devices can block or allow direct sunlight, depending on the season and hour, block or enable

solar gains (during cooling season, it is necessary to block direct sunlight to reduce the load on cooling

systems, while in heating season, it is necessary to allow direct sunlight and thus to have solar gains,

which in turn reduce the load in heating systems), can diffuse direct sunlight from clear skies (not causing

visual discomfort) or transmit direct sunlight in overcast days [3, 4, 5]. There are two ways to control

these shading devices: with manual or automatic control. Automatic control is a more attractive option,

as it can monitor and control several devices at the same time, whatever is the space of the office, while

with manual control it is only possible to control one system at the time, and it may not be optimal.

When natural lighting is not enough to ensure visual comfort, it is necessary to use artificial lighting

systems. These can also be manually or automatically controlled. Automatic controlled lighting systems

can substantially reduce the energy consumption on an office space using different methods. These

systems are divided in three types: timers, daylight linked controls, and occupancy based controls. As

the name suggests, timers turn light on/off during a specific time. Daylight controls, besides controlling

on and off, can also regulate the dimming of lights, taking as input the illuminance of indoor lighting.

Occupancy based controls can control lights depending if occupancy sensors detect someone [2].

As such, knowing how to control shading devices and artificial lighting systems, and thus obtaining

energetic savings becomes of utmost importance. This document will provide an overview of how to

1

control lighting systems (shading, artificial, etc) and how it impacts the illuminance measured, and the

control made to guarantee that the illuminance in a given room is always within the comfort range for its

users.

1.2 Energy demand overview

When analyzing the energy consumption in 2014, for EU-28 [6], there are three categories that

amounted to 83.9% of all energy: transport, which used 353 Mtoe or 33.2%; industry, responsible for 275

Mtoe, meaning 25.9% of all energy; and households, using 264 Mtoe or 24.8%, as it is possible to see

from Fig. 1.1. MToe stands for million tonne of oil equivalent, which is a unit of energy and is equivalent

to the amount of energy released when burning a tonne of crude oil. One tonne of oil equivalent is equal

by convention to 11.3 ×109 kWh or 4.19 ×1010 MJ.

For Portugal, in regards to the same year [6], the distribution of electrical demand alone is slightly

different. From the figure it is possible to see that most of energy used is for industry, consuming

17.304 ×109 kWh, amounting a total of 34.47% of energy used, followed by the use in domestic (11.907

×109 kWh – 25.79%) and non-domestic (12.136 ×109 kWh – 26.28%). Typically, the use of energy in

buildings is mostly to electrical lighting, heating and cooling system (HVAC – heating, ventilation and air

conditioning), and other electrical equipment (as computers, printers, etc.).

(a) EU-28 (b) Portugal

Figure 1.1: Energy consumption in EU-28 and in Portugal in 2014 [6].

Analyzing the energy consumption in buildings located in United States, represented in Fig. 1.2,

over half of energy is used in heating/cooling systems, followed by equipment’s consumption and lastly

lighting. Lighting and HVAC systems can be both controlled in an integrated manner and it’s use dimin-

ished by using daylight. From [7], the energy for HVAC systems is 14.70 ×1015 Btu (4.31 ×1012 kWh),

for equipments is 9.21 ×1015 Btu (2.70 ×1012 kWh) and for lighting is 4.65 ×1015 Btu (1.363 ×1012

kWh). Therefore, the integrated control of lighting and climatization is important to reduce the worldwide

energetic consumption.

2

Figure 1.2: Energy prediction in 2015 for buildings located in USA [7].

1.3 Objectives

The objectives of this work are to develop, simulate and analyze lighting and climatization manage-

ment algorithms in spaces with multiple users. To do so, the following tasks are proposed to be done:

• Development of simplified models that estimate luminosity;

• Develop algorithms capable of managing lighting without intervention of users;

• Development of lighting management algorithms;

• Comparison of the different strategies based on energy consumption and user’s comfort.

1.4 Definitions

1.4.1 Visible light

Visible light is the electromagnetic radiation spectrum that lies between two wavelengths (from about

380 and 780 nanometers). This is the only type of electromagnetic radiation (from the whole spectrum)

that it is absorbed by the human eye, allowing humans to see. Below 380 nanometers is the infrared

radiation, which corresponds to radiation with longer wavelengths, and above 780 nanometers is the

ultraviolet radiation, which has shorter wavelengths, as it is shown in Fig. 1.3. We can define light by its

direction, its intensity, its polarity, and its wavelength (or frequency).

We can decompose visible light using an optical prism, and we can see it is a mixture of seven

different colors: violet, blue, cyan, green, yellow, orange, and red. This split of colors occurs because

each color has its own wavelength. When they are propagating in the optic prism, its refractive index

changes with wavelengths. This effects causes light to refract differently, separating the colors. The

overlap of these colors gives the white light.

When we observe a given object, the color which we see is due to the fact that it reflects the light

that gives that specific color, and absorbs the other ones. For example, when we observe a red object,

what happens in fact is the red color being reflected, while the others are being absorbed. This can be

extended to other colors. If an object is perceived as black, then it is because all colors are absorbed; in

the opposite direction, if the object is white, then all colors are reflected.

3

Figure 1.3: Electromagnetic spectrum (Credit: NASA’s Imagine the Universe) [8].

1.4.2 Properties of light

When light hits an object or surface, it can be reflected from or refracted through the surface into the

material beneath. Once it hits the material, it can be transmitted, absorbed or diffused.

Reflection. There are two types of reflection, which are specular and diffuse. In specular reflection the

light is reflected at the same angle as the incoming light’s angle, and the properties of the beam remain

the same (the beam maintains its form). This is characteristic of mirrors and polished surfaces. Diffuse

reflection occurs when light hits a non polished surface, causing the reflected beams to disperse. After

hitting the surface, light bounces through all directions, making it to be diffuse. Ideally, the luminance

should be the same for all directions.

Figure 1.4: Law of reflection.

The law of reflection can be shown by specular reflection. When the light hits an object, it has a

well defined angle (incidence angle), which is defined between the incident ray and a imaginary line that

is perpendicular to the surface (or plane of incidence), defined as normal, as it is possible to see from

Fig. 1.4. The angle between the reflected ray and the normal is called reflected angle.

4

Absorption. When light shines on an object, that same object can absorb part of the light. This

absorption is a ratio between the light that is absorbed and the light that hits the object. It can contribute

to the rise of internal temperature, can change the shape, and can also change the state of the object

that is absorbing. However, from the point of view of lighting, this factor isn’t relevant.

Transmission. This property represents the fraction of light that is capable of going through a medium

(different from the medium of propagation, which is typically the air) that is adjacent to the incidence

plane. Usually the adjacent medium has a different index of refraction, which is responsible for the

difference in the angles (angle of incidence and angle of refraction). There are two types of transmission:

direct and diffuse. Direct transmission is the case where the angle of exit of the beam is equal to the

angle of incidence, and diffuse transmission is the case where the light is diffused as it exits the second

medium. Both types of transmission are represented in Fig. 1.5.

Figure 1.5: Representation of light transmission [9].

Refraction. When light travels from one medium to a different one, it refracts (meaning it changes

it’s trajectory and velocity). This refraction depends on two factors: the refractive index of the material

(defined as the letter n), and the incidence angle of the beam. The index of the material is defined as

the ratio of the speed of light in vacuum (defined as c) over the speed of light in the material (defined as

v), as such:

n =speed of light in vacuum

speed of light in the material=c

v. (1.1)

The speed of light in air is almost the same as the speed of light in vacuum, so the index of refraction

for air is considered 1. Because the speed of light in other materials is lower than the speed of light in

the air, the index of refraction for these other materials is greater than the index of refraction for air, as it

is possible to see from expression 1.1.

It is possible to show the relation between the incident angle and refractive angle using Snell’s law of

refraction, given by:

5

n1 sin θ1 = n2 sin θ2, (1.2)

where:

n1 - refractive index of medium 1;

n2 - refractive index of medium 2;

θ1 - incident angle;

θ2 - refracted angle;

θ′

1 - reflected angle.

In Fig. 1.6 is shown a representation of Snell’s law of refraction. The angles represented are all in

respect to the normal, as is depicted in the figure.

Figure 1.6: Snell’s law of refraction [10].

Using Snell’s law (expression (1.2)), when the incidence angle is 0 (meaning the light hits the

surface perpendicularly, as the normal representation), the light doesn’t change it’s trajectory in the new

medium, that is, θ2 as the same value as θ1, which is 0.

When, however, the light travels from different mediums, one of two cases can happen: if the first

medium has a lower index value (such as n1 < n2) than the second medium, the light, as it makes the

transition between mediums, bends towards the normal; the opposite effect occurs if the first medium

has a higher index value (as n1 > n2), and the light bends away from the normal.

Another phenomenon that can occur with reflection is the total internal reflection, and it happens

when light travels from one medium with higher index of refraction to another. If the light’s beam of

incidence bends further away from the normal, it will reach a critical point – called critical angle θc –

at which the light will be refracted along the boundary (not being reflect nor refracted). If the angle of

incidence increases, all the light will be reflected at the boundary and will stay in the medium. A common

application for this phenomenon is fiber optics, allowing to transport light along their length with little or

no losses.

6

1.4.3 Solar Angles and Definitions

Due to the movement of the Earth around the Sun, and as well it’s rotation along it’s axis, there are

some variables and angles which are important to define and are fundamental to this work [11]:

Latitude (φ). It is defined as the angle between the place in question and the equator, and is defined

as −90 ≤ φ ≤ 90 , where it is defined as positive the locations above the equator line (90 being the

North Pole).

Declination (δ). It is the angle the sun makes at solar noon, measured with the plane of the equator.

It can be calculated using the formula

δ = 23.45× sin

(360×

284 + nday

365

), (1.3)

where nday represents the number of the day of the year.

Slope (β). This represents the angle between the plane of the surface and the horizontal, and has

values between 0 ≤ β ≤ 180 (when β > 90 , then the slope is facing downward).

Angle of incidence (θ). Is the angle the light makes between a surface and it’s normal.

cos θ = sin δ sinφ cosβ − sin δ cosφ sinβ cos γ + cos δ cosφ cosβ cosω

+ cos δ sinφ sinβ cos γ cosω + cos δ sinβ sin γ sinω(1.4)

Surface azimuth angle (γ). Making a projection of the surface on a horizontal plane, it is the angle

between the projection and the normal of the surface. It has values between −180 < γ < 180 , where

if the surface is facing south, the value is 0, if facing east is negative (γ = −180 ), and positive if facing

west (γ = 180 ).

Solar time. This time is based on the rotation the earth does around the sun, giving the movement

the sun is moving across the sky. The time in which the sun crosses the meridian of the zone of the

observer is defined as the solar noon. It is possible to relate solar time with local time, with the use of

the expression

Solar time− Standard time = E + 4× (Lst − Lloc)− 60ST

E = 2.292(0.0075 + 0.1868 cos(B)− 3.2077 sin(B)− 1.4615 cos(2B)− 4.089 sin(2B)),(1.5)

where Lst is the standard meridian for the local timezone, Lloc is longitude of the local in which is the

calculus of the solar time, E is the equation of time, which is calculated in minutes, and ST is 1 if daylight

saving is being used and 0 if it is not. The value from equation (1.5) is given in minutes.

7

Hour angle (ω) . This value is due to the rotation the earth makes around the sun, giving a variation of

15 per hour to east or west of the local meridian. In the morning this value is negative, at noon is zero,

and at the afternoon the value is positive. This value can be calculated using the following expression

ω = 15× (ts − 12), (1.6)

where ts is the solar time.

Zenith angle (θz). This value measures the angle the line of the sun makes with the normal of a

horizontal surface (or the angle of incidence of the beam).

Solar altitude angle (αs). Is the angle between the surface and the line of the sun (it is complimentary

to the zenith angle).

1.4.4 Interior Lighting

To allow the quantification of light and to better understand it, it is necessary to define additional

concepts, such as:

Solid angle (Ω). A solid angle is a three-dimension representation of a two-dimension angle, and it’s

unit of measurement is steradian (sr). To define a solid angle, it is necessary a sphere with a radius r.

A steradian is a cone shaped section that has an area equal to r2. A visual representation is shown in

Fig. 1.7.

Figure 1.7: Sphere with a one sr removed and a solid angle measuring one sr [10].

A steradian can be defined with use of the expression

Ω =A

r2. [sr] (1.7)

Luminous intensity (I). This value corresponds to the light emitted by a light source in a specific

direction of a solid angle. The unit of this measurement is the candela (cd).

8

Figure 1.8: Generic luminous intensity over one steradian.

Luminous flux (φL). Having a light source, the amount of light emitted every second by a given solid

angle is defined as luminous flux, and is measured in lumens. A lumen is the flux generated in a solid

angle measuring one steradian by a light source with a luminous intensity of one candela.

Figure 1.9: Generic luminous flux.

Illuminance (E). This value is a ratio between the luminous flux (φL) and a surface of area A in which

the light hits, and is measured using lux (lx). This unit represents the measurement of the light’s intensity,

as perceived by the human eye. As such, illuminance can be computed using

E =φ

A. [lx] (1.8)

Luminance (L). This is the luminous flux reflected by a surface of reflectance ρ in a given direction.

This represents the perception the human eye has if the surface is well lit or not, and it’s unit is candela

by square meter [cd/m2]. In Fig. 1.10 is represented both illuminance and luminance.

Figure 1.10: Representation of illuminance and luminance.

9

1.5 Organization

This document has been divided in 6 chapters:

1. The first chapter (current one) will consist in the objectives proposed for this work, and the funda-

mental definitions regarding light;

2. The second chapter will describe some work and studies that were made in the area of interest,

which are relevant to this work;

3. The third chapter is described the methodology used for this work;

4. The fourth chapter presents the obtained results;

5. The final chapter will be the conclusions drawn from this work.

10

Chapter 2

State-of-art

2.1 Daylight impact on illuminance in a room

The sun emits electromagnetic radiation, which spawns from X-rays to radio waves. However, from

that range, the most that reaches the surface of the Earth is visible light. Direct light is the light that

shines directly on a surface, while diffuse light is light that is overall homogenous, due to the reflections

of light in other materials. The first type of light is characteristic of sunny days, and the second type is

characteristic of overcast days. Because the days are different between each other, the quantity and

type of light that reaches a specific place may vary. With a clear sky (generally with no clouds), and with

plenty of direct sunlight, the measured illuminance will be high; on the other hand, with an overcast day

(clouds covering the sky) and with diffuse sunlight, the illuminance measured will be much lower.

[12] has been studied the daylight illuminance measured in horizontal and vertical surfaces in a

region in Spain. The sensors were placed on a flat platform at a certain height, to avoid shading from

the vegetation. The measures were made on clear days, during one year. Some of the obtained results

are presented in Fig. 2.1 and Fig. 2.2.

Figure 2.1: Horizontal and vertical illuminance measured during summer (adapted from [12]).

11

Figure 2.2: Horizontal and vertical illuminance measured during winter (adapted from [12]).

From Fig. 2.1 and Fig. 2.2 it is possible to see some interesting aspects. For one, the illuminances

detected in North, East, South and West orientations are not equal throughout the day. For the sensors

turned to East, the peak of illuminance is measured in the morning, while the sensor oriented to West

has its peak in the afternoon, and this is verified all year long. For the rest of they day, the type of

radiation the sensors measure is diffuse sunlight.

Besides the illuminances being different throughout the day, they are also different throughout the

year. For the horizontal orientation, the illuminance measured increases steadily until the summer sol-

stice, where it is measured it’s maximum peak, and then decreases until the winter solstice, where it is

possible to measure it’s minimum. The solar angle also describes a behavior similar to the illuminance,

where it’s peak is measured in the summer solstice. The solar angle and illuminance are correlated,

as the higher the solar angle is, the more vertical the sun hits the surface, and the more illuminance is

measured [13].

It is possible to conclude that the orientation of a window plays an important role in how much the

sun light can be measured or how much can enter the room, and must be taken in consideration in the

type of algorithm one wishes to use daylight to control electrical consumption from indoor lighting and

heating/cooling systems [5]. Knowing that the room is turned to a specific direction, it is possible to use

it’s direct and diffuse sunlight to light the room, avoiding the use of electrical lighting (unless it doesn’t

achieve a pre-set lighting level), and use an algorithm coupled with automatic control to control the blinds

to adjust the brightness of the room.

2.2 Sun radiation impact on illuminance

When it is only known the radiation on a horizontal surface, it raises a problem when one wishes to

compute the radiation in a sloped surface, like a window. First it is needed the direction of direct and

diffuse components of the beam that reach the surface in question. The direction of the direct component

12

is the incidence angle, but the direction of the diffuse component depends of the cloudiness of the sky

and the ground reflectance.

If it is assumed that the combination of diffuse and ground-reflected radiation to be isotropic (the

same for all directions), then the sum of both these factors is the same whatever the direction is. A model

was developed that took into account the beam component, the isotropic diffuse and the solar radiation

reflected from ground, also diffuse. A surface that is tilted with an angle β has a view factor to the sky

defined as Fc-s = (1+cos(β))/2, while it has a view factor to the ground defined as Fc-g = (1− cos(β))/2.

As such, the total solar radiation, defined as IT , on the tilted surface is

IT = IbRb + Id

(1 + cosβ

2

)+ Iρg

(1− cosβ

2

), (2.1)

where Ib is the beam radiation, or direct radiation, Rb is the ratio between the beam radiation on a

tilted surface and on a horizontal surface, Id is the diffuse radiation on an horizontal surface, I is the

sum of direct and diffuse radiation that it’s the ground and is reflected with the factor ρg [11].

This model is conservative, as it tends to underestimate IT . Most recent models have been devel-

oped to take into account the circumsolar diffuse, which is the diffuse radiation coming from all the sky,

and direct components on a tilted surface, as well with anisotropic sky. The Perez model for total irradi-

ance on a sloped surface is based on a more profound analysis of the diffuse components, as it is given

by:

Id,T = Id

[(1− F1)

(1 + cosβ

2

)+ F1

a

b+ F2 sinβ

], (2.2)

where F1 is the circumsolar brightness coefficient, F2 is the horizontal brightness coefficient, and a

and b are related to the angles of incidence of the cone of circumsolar radiation (radiation coming from

a point in the sun), which are given by

a = max(0, cos θ) (2.3a)

b = max(cos 85, cos θz). (2.3b)

The brightness coefficients F1 and F2 depend on three factors: the zenith angle θz; the clearness

index ε, which represents overcast skies for low values (1 ≤ ε ≤ 1.23) and clear skies for high values

(ε > 4.5) [14]; and ∆, the sky brightness index. ε on it’s turn is a function of Id – hour’s diffuse radiation

– and Ib,n – normal incidence beam radiation –,

ε =

Id+Ib,nId

+ 5.535× 10−6 · θ3z1 + 5.535× 10−6 · θ3z

. (2.4)

The brightness parameter is given by the following expression,

∆ = mIdIon

, (2.5)

where m is the air mass, and Ion is the normal incidence radiation measured outside the Earth’s

13

atmosphere. The coefficients F1 and F2 are defined as

F1 = max

[0,

(f11 + f12∆ +

πθz180

f13

)](2.6a)

F2 =

(f21 + f22∆ +

πθz180

f23

). (2.6b)

The values for brightness coefficient fij for the Perez model are shown in the table 2.1. Adding

the beam and ground-reflectance contributions to expression 2.2 and using the equations 2.3a- 2.6b,

it is possible to have the total radiation on a tilted surface, which includes five terms: the previous two,

isotropic diffuse, circumsolar diffuse, and diffuse from the horizon [11], making the final expression 2.7:

IT = Ibeam + Iisotropic diffuse + Icircumsolar diffuse + Idiffuse from horizon + Iground reflected

= IbRb + Id(1− F1)

(1 + cosβ

2

)+ IdF1

a

b+ IdF2 sinβ + Iρg

(1− cosβ

2

) (2.7)

Range of ε f11 f12 f13 f21 f22 f23

1.000–1.065 -0.008 0.588 -0.062 -0.060 0.072 -0.0221.065–1.230 0.130 0.683 -0.151 -0.019 0.066 -0.0291.230–1.500 0.330 0.487 -0.221 0.055 -0.064 -0.0261.500–1.950 0.568 0.187 -0.295 0.109 -0.152 0.0141.950–2.800 0.873 -0.392 -0.362 0.226 -0.462 0.0012.800–4.500 1.132 -1.237 -0.412 0.288 -0.823 0.0564.500–6.200 1.060 -1.600 -0.359 0.264 -1.127 0.1316.200–∞ 0.678 -0.327 -0.250 0.156 -1.377 0.251

Table 2.1: Brightness coefficients for Perez anisotropic sky [11].

However, more models have been developed. In [14], the authors used nine models to calculate

the total irradiance, considering eight types of sky, in order to try to understand which model is more

consistent and the most reliable. The results are presented in table 2.1. Two models were developed

by the authors of the study: in the first one (M1), it was used a constant value for the diffuse luminous

efficacy, for each vertical surface (North, East, West, and South), while in the second one (M2) the value

used was constant, but different for each set of values of ε. Three models were variations of the pre-

viously described Perez’s model: the first model (P1), the coefficients fij were obtained and analyzed

considering cities in the United States; the second model (P2), the coefficients were calculated for the

location of the study, considering all four orientations together; the third model (P3), the orientations

were considered separately. A sixth model is defined by Muneer, Gul and Kubie (Mu), correlating diffuse

luminous efficacy to clearness index kt, which is defined as the ratio of the global irradiance over the

extraterrestrial irradiance, both measured on the horizontal plane. The final three models were devel-

oped by Robledo and Soler, where the first one (R1) correlates diffuse luminous efficacy and the ratio

between diffuse irradiance over the extraterrestrial irradiance, over the horizontal plane; the second one

(R2), the diffuse luminous efficacy is correlated to the sinus of the solar altitude; and the last one (R3)

14

is described the relation between diffuse luminous efficacy to the sky brightness index ∆. The last four

model were developed to horizontal surfaces and were applied to vertical ones.

The measurements were made for the different intervals of ε, each representing a type of sky. The

data was acquired every five minutes, and used to obtain the mean hourly values for illuminance and

irradiance. For each direction, the nine models were applied to every ε, in order to compute and then

determine the errors associated with each model. Having an average for all four directions and for all

types of sky (ε > 1), the model with the lowest error was the model developed by the authors, where it

was considered the luminous efficacy changes with ε – model M2. From table 2.2 it is possible to see

which model is best for each direction and for each interval of ε. If all directions are to be considered

together, all models behave in a similar way, with the exception of P1 model, being the models M2 and

Mu the ones who are the best.

Range of ε North East South West

1.000–1.065 M2 M2 M2 Mu1.065–1.230 M2 M2 P2 M21.230–1.500 M2 M2 P2 M21.500–1.950 M2 R1 R1 M21.950–2.800 Mu P3 P3 M12.800–4.500 P3 P3 M2 P34.500–6.200 P3 P3 M2 P26.200–∞ P3 P3 M2 P3

Table 2.2: Best models for each interval ε [14].

It is important to note that the model with the highest errors was the model considered as P1, as the

values were adjusted to the United States, which has a different climate and it is not in the same latitude.

Adjusting the models to the local climate is necessary to have good results, as well as considering the

four orientations separately, which is why the model M2 and P3 have low errors.

2.3 Automatic control systems

Energy consumption for lighting in office spaces depends greatly of the space in which the office

is located and also existence of automatic control systems. With simple automatic control systems (as

timers), there will be times of day where lights will be on, even though there is a possibility that there is no

one using the space. This will cause an unnecessary consumption of energy, and the opposite can occur,

where the lights turn off while there are users still in the space. On the other hand, with more robust

control systems (like occupancy-based controls), it is possible to have as little energy consumption as

possible, since when it detects a user, it turns on the lights; when the user leaves, the lights turn off.

This, however, raises a problem: the system may (or may not) detect a user, causing to turn the lights

on/off incorrectly. It is also possible to control the intensity of light bulbs using daylight control systems.

Using the daylight outside the office, these systems can dim the lights inside to adjust luminosity and

15

thus be in range for user’s visual comfort [2, 15].

A simple, on-off algorithm is described for occupancy-based and daylight-based sensors. For the

former, the sensors verifies if it detected someone or not. If it didn’t, then it starts a timer. If the timer is

over some defined threshold, then it sets the space as not occupied and turns off the lights. If, however,

detects someone before the timer is over, then it resets the timer and sets the space as occupied. For

the latter, its possible to have either a closed loop or an open loop algorithm, witch are represented in

Fig. 2.3. In a closed loop, the sensor is always measuring the indoor light, which includes the indoor

lighting (coming from electrical lamps) and from daylight. This causes a feedback, and the sensor is

always adjusting the electrical lamps, as the daylight isn’t constant along the day. In an open loop

system, the sensor uses a reference system like time of the day or the schedule of the room, and the

value is transmitted to the controller, adjusting the electrical lamps, in order to provide indoor lighting [2].

(a) Open Loop

(b) Closed Loop

Figure 2.3: Schematic of open and closed loop systems [2].

Table 2.3 shows how different settings can influence the performance of different control systems,

where X means the factor influence those systems. These different systems account for different energy

savings, and its usefulness can change from space to space: for daylight controls systems, savings

can go from 9% to 30%, while with occupancy-based controls savings can range from 3% to 38% [2].

The variation on the results obtained is due to the fact there are different settings, such as daylight

availability, control approach, occupancy patterns, etc. From these results, it becomes apparent that it

is possible to achieve relevant energy savings with automatic control systems. It is however important

that the systems are well adjusted. Due to its robustness, daylight-based controls have been used more

frequently.

A study was conducted in order to discover and determine daylight throughout the day (through

equations that relate indoor and outdoor illuminance), and from that data to regulate the use of indoor

lighting [4]. The data was collected during a period of five months, and the blind had an angle to cover its

complete range of operation (from 0o to 180o). The blind tilt angle, incidence angle and sky conditions

were used to determine the transmittance equation for the studied window. The sky conditions were

16

Affecting factors’ category Affecting factors Timers Occupancy-based Daylight-based

Typology Control strategy X X XOccupancy pattern X X -Sensor’s location - X X

Lighting system’scharacteristics

System efficacy X X X

Relationship between sensor signaland related light output

- - X

Indoor daylightavailability

Outdoor daulight availability - - X

External obstructions - - XGlazing and shading typology - - X

Table 2.3: Effects of different settings (adapted from [15]).

taken as clear sky and overcast sky. The transmittance was determined as the result of dividing the

illuminance measured with the indoor sensors by the illuminance measured in the outside. It was shown,

for overcast days, that the blind’s angle has a strong effect in the measured transmittance. This can be

explained by the fact that for these types of days, most of radiation is diffuse (direct sunlight is blocked

by the clouds in the sky), so the most important parameter in this case is the blind, as it can control how

much radiation can enter the space and as such influence the indoor lighting, and due to this type of

radiation, the incidence angle doesn’t have as much important weight as has the blind.

For the type of windows used and the location this study took place, the maximum transmittance

value was measured for a blind tilt angle of 60o, which corresponds to a transmittance measured of

38.2%. For clear days, as most of radiation that hits the window will be direct, both the incidence angle

and the blind tilt angle will play a strong effect in controlling how much sunlight will enter the room. As

the incidence angle rises, the transmittance of the window will be lower; however, with the blind’s tilt

angle, the transmittance will increase until a certain point, and after that will start to decrease. The blind

also plays an important role in controlling the glare that can affect users. In fact, adjusting the tilt angle

allows to completely avoid glare, as the sunlight that enters the room will enter through reflections the

light suffers from the blind. The maximum transmittance in this conditions was measured as 55%, with

an incidence angle of 15o and a blind tilt angle of 78o.

Besides controlling the blinds and computing the transmittance, it was also controlled the dimming of

the light, to assure that the illuminance on the work plane reached a predetermined set-point (500 lx).

The dimming was calculated for all working hours of the day, both for clear and overcast days. In overcast

days, the dimming greatly improves the illuminance of the space, as it gives a better distribution of light

and ensures the illuminance reaches the set-point. For clear days, when there isn’t enough light, the

lights activate and adjust to reach the set-point. When compared with an office space without dimming

and on/off switch (meaning the lights are always on), the energy savings can be as high as 76% for

overcast days and 92% for clear days. This shows how important using daylight can be to achieve

energy savings.

Another study also measured the electrical lighting in office spaces and how to optimize its usage

17

taking into account the users’ interaction [16]. In the first phase, it was monitored the lighting system,

which users would control manually. This was done so to determine and evaluate the electric consump-

tion related to the lighting systems. The user’s behavior and their response was recorded in order to

analyze the lighting conditions in the offices due to the use of electric lighting. After this, the next phase

took place and was considerably longer than the first one, as it consisted in installing and calibrating

a new automatic lighting system, using the user’s requirements. In this second monitoring, the lighting

control system was operated using automatic and manual control, and it’s objective was to check if the

lighting control system was working as intended and to see it’s efficiency in providing energy savings

and sufficient lighting conditions.

The data was recorded over a year, which included the horizontal illuminance of a desk, the illumi-

nance estimated by the sensor, the percentage of dimming for each luminaire, and the electric energy

consumption. The illuminance measured on the work planes was compared with target values which

were defined before: when the lighting system was controlled manually, the target value was defined

as 500 lx, while when the system was controlled automatically, the target value was defined for each

of the offices, taking into account the requirements of the occupants. It is important to note that the

values were measured in different time periods, and as such, comparisons and conclusions must take

into account the different type of weather and external conditions.

From Fig. 2.4, it is possible to see that using manual control, it was verified the illuminance measured

in a desk (750 lx) was often and substantially higher than the recommended value (500 lx). This can

be explained as it is impossible to control the lighting system as a function of daylight; either it is on

or off, and the system is controlled by the users. However, using automatic control which could be

overruled with manual control – automatic with manual control –, the illuminance measured drastically

decreased (to about 400 lx) and became much closer to recommended value, as the lamps could be

dimmed automatically.

The frequency distribution of illuminance, which is in Fig. 2.5, also sustains this claim, as with manual

control the lighting on the surface of the work plane was as high as almost 70% of times above the

recommended value, but with automatic control, these values decreased to below 50%. These results,

however, could be a consequence of the period of the year in which took place the data acquisition.

After the monitoring, questionnaires were distributed in order to evaluate the degree of satisfaction

of the users. In regards to the first phase, the users were satisfied with the lighting conditions and were

not interested in regulating the luminous flux. For the second phase, which used automatic and manual

control, the users reported that for the different seasons, there were not many situations with too much

or too little light in their work plane, they reported that they were indifferent concerning the others users’

interaction with the system, and the main reason to interact with the system was because it did not work

properly [16]. However, for this last point, this can be explained as the automatic systems seem to be

more accepted when exists a manual override and when they are easy to use [2, 16].

Combining shading with automatic control generally gives the highest energy saving results, as it was

studied in [17]. For example, having a system controlling the blinds position coupled with an occupancy-

based detector allows the control of the blinds, opening them when a user isn’t detected in a room, thus

18

Figure 2.4: Illuminance measured with manual and automatic control (adapted from [16]).

Figure 2.5: Illuminance frequency with manual and automatic control (adapted from [16]).

19

heating the room (due to high solar gains) and reducing the load of heating systems. When, on the other

hand, the user is detected, the blinds close, for glare considerations and to cool the room, reducing the

need to use cooling systems. If necessary, it can be used artificial lighting in case there is a risk to cause

glare to the user if the blinds were open.

This system takes as inputs season, direct outside horizontal illuminance, inside and outside tem-

perature, among others, and optimizes the system to compute the most comfortable setting. The opti-

mization is done each night, with the objective to look for the most efficient set of parameters. This is

done using a genetic algorithm, and applying small variations to the parameters used during the day

to the current controller. This setup shows the differences between two automatic controllers, one well-

adjusted to the space able to control the blinds, and a conventional controller (an on/off switch). The

well-adjusted controller managed to control the heating power and the lighting system whether there

was a user using the room or not, and also managed to avoid overheating the room. Using this setup, it

has been possible to achieve 25% energy savings in comparison with the conventional controller. How-

ever, one problem raised by this controller is the fact that it does not take into account the user’s wishes.

For instance, if the user changes the position of the blind, the system holds that position for a time set

period, and then changes back to the optimal one.

It is important, however, to have in consideration the space in which it is intended to optimize lighting.

There are external factors (such as shading and orientation) that can influence indoor lighting, but there

are as well indoor factors, such as the lifetime of lamps. One initial approach, when dimming lamps, is

to consider the variation of intensity as directly proportional to its energy consumption. This, however,

can produce different result if one intends to have a higher precision.

[18] studied the impact for two types of lamps sets (4 x 14 W fluorescent and LED lamps) the relation

between energy consumption and dimming and found it was not linear, but rather a polynomial function.

Comparing both sets, for higher levels of dimming, the power consumption of the fluorescent lamps

(20.6W) will be considerably higher than the LED lamps (2.8W). Comparing the values measured for no

dimming and for a given percentage of dimming, it is seen that LED lamps have higher luminous efficacy

than fluorescent lamps, as with 0% of dimming the former can output 47.6 lm/W, while the latter can only

output 36.3 lm/W, and with 97% dimming it can output 23.6 lm/W and 3.0 lm/W respectively.

2.4 Visual comfort

Several studies have analyzed the effects of excessive or lack of illuminance in working environments.

Having the illuminance values in a defined threshold can guarantee the comfort of the users. However,

having a well defined threshold is a difficult task. For one, it does not take into account the glare,

and secondly, it is a temporary measurement (can be calculated using expression 1.8, meaning it is

necessary to continuously take measurements. Besides this, the comfortable values are relative to

users: some users may prefer better lit environments than ones less lit. As such, it can be defined a

loose threshold, where there is not a set value which can not be crossed, but rather a suggestion of

values to be used.

20

The space in question, the type of work done and where the work is done weights in the values used.

For a typical classroom, the work surface is the most common surface where this value is measured,

and the value 500 lux is the value considered as the reference value. From certification for sustainable

constructions [19], it is recommended to have illuminance values between 300 and 3000 lux.

The values recommended for office spaces are shown in table 2.4, which were adapted from [20]. As

seen, a consensus set range of acceptable values can not be reached, due to the preferences of each

user in the room. Instead, it is preferable to try to set a range of values for the room in question.

Reference Illuminance recommended

Aries (2005)500 lux is desired for the working plane

but 800 lux is preferredU.S. Green Building Council (2013) Illuminance values between 300 and 3000 lux

Newsham (1994)150 and 500 lux in working plane as

reference values for electrical lightingManav (2007) Users prefer 2000 lux instead of 500 lux

Table 2.4: Reference illuminance values for a classroom (adapted from [20]).

21

22

Chapter 3

Methodology

This chapter presents and explain the method used for this work. The model is divided in three parts:

the first one, involves using the Pèrez model, for the computation of solar radiation in a given point; the

second one, is using the transmittance of classroom’s window, calculated using values measured with

two sensors, and with that determine how much solar radiation enters the room; the third one, is using an

algorithm to determine the distribution of illuminance in the room, using a conversion between radiation

and illumination. A representation of the algorithm proposed is shown in Fig. 3.1.

Figure 3.1: Representation of the algorithm proposed.

The room in which will be studied the illuminance is the classroom V1.10, located in Pavilhão de Civil,

in Instituto Superior Técnico. The classroom is located in the first floor, and is turned to East, meaning

23

the peak of illuminance will be measured during the morning, while in the afternoon will be mostly from

diffuse light.

In the next sub-chapters, not only it will be depicted how the calibration of the sensors was made,

but the relation obtained for the values measured in the window and how it relate to the values near the

walls (across the room) as well.

3.1 Sun radiation

3.1.1 Horizontal data

Instituto Superior Técnico has a meteorological station, located at the top of North Tower, which

measures air temperature, humidity, solar radiation, among others, every minute. The solar radiation is

measured in an horizontal plane. The group managing the weather station also provides hourly weather

forecasts, including solar radiation, which can be used for control.

This allows to have experimental data of solar radiation over the course of a given day, which could

be useful for the analysis of the illuminance in the room.

3.1.2 Pèrez Model

The Pèrez model, as described in the previous chapter, is a model that allows to determine the

radiation which hits a certain surface, given its location, orientation, and inclination. The radiation was

computed for an horizontal surface, with the same geographical coordinates and at a given height which

was equal to the IST’s meteorological station, and then both were compared. This was done so to see

if the values predicted by the model were consistent with the values measured.

The values used for the different parameters of Pèrez’s model were adjusted taking into account

the local climate, using the parameters determined in Italy [14], specifically Arcavacata di Rende. It is

located at a latitude extremely close to the latitude of the room in question, as the room has a latitude of

38.736 , where Arcavacata di Rende is at 39.35 , with similar types of climate.

3.2 Windows transmittance

As it was seen in chapter 1, the angle of incidence of a light beam influences the resulting transmitted

light beam. Using Fresnel equation, it is possible to have for an S and P-wave (these types of waves

represent the waves’ polarization) the following reflectance, assuming it is for non-magnetic media

Rs =

n1 cos(θi)− n2√

1−(

n1

n2sin(θi)

)2n1 cos(θi) + n2

√1−

(n1

n2sin(θi)

)2

2

(3.1a)

24

Rp =

n1√

1−(

n1

n2sin(θi)

)2− n2 cos(θi)

n1

√1−

(n1

n2sin(θi)

)2+ n2 cos(θi)

2

. (3.1b)

For a generic wave, in which it is not known the ratio between S and P-wave, it is assumed that the

wave is unpolarised and as such the reflectance is given by:

RT =1

2(Rs +Rp). (3.2)

It was also seen in equation 1.4 that the incidence angle from the sun varies throughout the day.

Using equation 1.4 in equation 3.2 it is possible to calculate the transmittance taking into account the

position of the sun in the sky and thus the variation of the incidence angle since the sun raises until the

sun sets.

Assuming the window does not absorb part of the radiation, then the only phenomena are reflection

and transmission. Having this in consideration, then the transmittance is given by:

τ = 1−RT . (3.3)

3.3 Calibration of sensors

To measure the illuminance of the room, two sensors from Adafruit R© were used. The two TSL2591

Adafruit R© sensors, which could measure the illuminance instantaneously and could also take measure-

ments within a set period the user could define previously. The sensors had different types of gain, as

well as different times of integration. The gain of the sensors had a range of 1, ideal for situations with

plenty of sunlight, until the maximum of 9,876, which was indicated for situations with extremely low light.

Apart from that, the sensor performed an integration of the values measured, and it ranged from 100 ms,

again for situations with bright light, up until 600 ms, typical for environments with low light, as the higher

the integration time, the more light the sensor is able to integrate, being more sensible to low light [21].

The sensors were used with a gain of 1, as it would be hit by direct sunlight, and any gain would saturate

the sensor, and an integration time of 100 ms, being the lowest, again for the same reason.

The sensors have a resolution of 1 lux, and the maximum value it can read is 88,000 lux, after which

the sensor saturates. The code used for the sensors was the code provided by Adafruit open-source.

The sensors would be connected, each one to a single Arduino, and those would be connected to a

computer, in order to record the data. It was considered that a period of 15 minutes provides enough

information to make the necessary adjustments throughout the day.

For the calibration of the sensors, it was used a light meter ISO-TECH 1332A. The light meter was

placed alongside the Adafruit’s sensors, and the values measured were then compared. The light meter

has a resolution of 0.1 lux, and has an accuracy of ±3% for values measured below 10,000 lux. The

light meter was calibrated to a standard incandescent lamp at color temperature of 2,856 K. The spectral

sensitivity characteristic is very close to the C.I.E. (International Commission of Illumination) photopic

25

curve, which is displayed in Fig. 3.2.

Figure 3.2: Characteristic of light meter ISO-TECH 1332A.

Using the values from both types of sensors (Adafruit’s and the light meter) measured near the

window, it is possible to determine a relation. As such, the result obtained between the two is in Fig. 3.3,

using a linear function. The resulting fit allows a conversion from a measurement using an Adafruit

sensor to illuminance in the region. It is important to note the slight dip near the region of 2,000 lux

measured by the light meter. This is due to the working range of the light meter, as one of its range is

2,000. When one switches to another working range (the next one being 20,000 lux), the values near

2,000 are measured lower than with the previous range.

Figure 3.3: Relation between sensors and light meter.

26

The values obtain for a linear function used to fit the data is in table 3.1.

a b χ2red R2

2.510 ± 0.001 1.017 ± 7.145 9.356 × 102 0.997

Table 3.1: Parameters obtained for the fit between sensors and light meter.

3.4 Daylight control

To control the amount of sunlight (and thus illuminance) that enters the room, it is necessary to have

blinds and/or electrical lighting. Having blinds allows to control the amount of direct sunlight, and prevent

glare that users may experience. However, if the illuminance measured in the space is not sufficient to

ensure work in comfortable conditions, then electrical lighting might be needed to raise the lighting

conditions. Both can be used (for example, where the sunlight is too strong but isn’t high enough when

the blinds are open) to ensure the most comfortable conditions to the users. However, it is important to

note that this solution increases the electrical consumption of the building.

The blinds can be controlled using a manual switch located near the window, which anyone can use,

to adjust to the preferred light level. The blinds, when closing, close from the top and descend to the

base of the window. When totally closed, and if one wishes to open them, the top third of the blinds

rotate, being horizontal, and then the rest of the blinds follow, being completely horizontal. After this,

they begin to rise, until the top.

3.4.1 Blinds

In order to understand the distribution of illuminance from sunlight through the room, a set of points

were picked and made measurements in those points. The measurements were made for different

stages of blinds: from completely open to completely closed. There is another stage of the blinds, which

is when the top third is open (parallel to ground) and the bottom two thirds is closed (named special). The

time of measurement was in the early morning, in order to have the room hit entirely by direct sunlight.

The points chosen were at the top of the tables, the same as working plane, and went from the window

to the wall, being P1 the point closest to the window, and P5 the point closest to the wall. The points of

interest are represented in Fig. 3.4.

The measurements are represented in Fig. 3.5 and in Fig. 3.6. From it it can be seen the impact

the blinds have for the illuminance. When totally open, the illuminance measured is extremely high,

throughout the room. As the blinds begin to close, it can be seen that the values measure stay below

10,000 lux, a drastic decrease when compared with blinds totally open. Although it is higher value than

recommended, it is no longer uncomfortable to work in the environment. As the blinds continue to close,

the illuminance continues to decrease, as there is less direct sunlight hitting the room, until it is totally

closed, at which point the illuminance measured will be the lowest for all points. It is important to note

that when the blinds are in position special, the points P3 to P5 have higher illuminance than points P1

27

Figure 3.4: Representation of interest points.

and P2, as the sun hits that zone of the room (due to the top part of the blinds being open) but not the

zone near the window.

Figure 3.5: Illuminance measurements throughout the room.

3.4.2 Electrical lighting

Electrical lighting is another strategy used to allow the illuminance to stay at comfortable values, only

in this case it is used to lift the illuminance measured. A method which can be used to compute the

distribution of the provided light is considering the lamps as a single point and an uniform distribution,

and using inverse square law [10], which is described by the following formula

28

Figure 3.6: Illuminance measurements throughout the room with log scale.

I = E · d2, (3.4)

where

I - luminous intensity;

E - illuminance;

d - distance between the light source and the point of interest.

Switching d for its relation with the height of the lamps and its angle to the point of interest, the

expression can be written as

I =E · h2

cos2 θ. (3.5)

An algorithm is portrayed in Fig. 3.7. First, it checks if it is necessary to use electrical lighting. If it is

not needed, then the lamps are turned/remain off; if it is needed, taking into account the position of the

lamps, its power and the position of points of interest, it computes the artificial lighting provided and sets

the configuration of the lamps.

The position of the lamps is in Fig. 3.8. In the figure all lamps are turned on (displayed with the color

yellow), and it was chosen this column as it is the same column as the points of interest.

29

Figure 3.7: Representation of the algorithm for electrical lighting.

Figure 3.8: Representation of the position of the lamps.

30

Chapter 4

Results

In this chapter the results obtained will be presented. Firstly will be presented the results for the

prediction of the lighting in the room using a ratio between radiation and illuminance, the transmittance

determined for the window in the room using the sensors, and the distribution of illuminance in the room.

A threshold was defined for comfortable levels of illuminance to the users, and depending of the value

predicted, a control method is applied to bring the illuminance to that range.

4.1 Radiation to lux conversion

With the values from Pèrez’s model and the values measured from IST’s meteorological station, it is

possible to estimate the radiation that hits a horizontal plane. Likewise, with the values measured from

Arduino R©’s sensors, it is possible to know the illuminance in two points in the room. From this, it can be

done a simple relation between incident radiation and illuminance outside the room. This allows to give

an estimate and it is not necessary to permanently use a sensor to measure the illuminance.

This conversion is made over the values measured experimentally. As such, the results obtained

could only be used for this location, as for different locations (different latitude and longitude), the radia-

tion that hits produces different values of illuminance, as the angle of incidence of the sun is different.

Using the values measured from the meteorological station located in Instituto Superior Técnico, and

the values measured from the Adafruit’s sensors, for the same time, it was then compared, as it can be

seen from table 4.1. From those values, a relation from radiation and luxs was then determined, using

different approaches.

Firstly, it was attempted an average between all the values, from morning until early afternoon (de-

fined as all day). However, the difference between calculated values and experimental data was high.

Afterwords, the data was split into two categories: the first one, included all the values measured during

the morning, which was when sunlight was hitting the sensors directly; the second one, included the

values which was measured with diffuse light (called split average in table 4.2). The point in which the

division was made is after 12h17m28s, local time. It was also used values determined in Italy for the

brightness coefficient for Pèrez anisotropic sky, represented in table 2.1, to see if it could predict the

31

Local time Adafruit sensors [lx] MeteoIST[W ·m−2

]Ratio

[W ·m−2 · lx−1

]09:37:59 21,398.415 766 0.035809:47:29 20,601.830 789 0.038309:57:29 34,672.614 796 0.023010:07:29 23,781.726 831 0.034910:17:29 32,419.631 849 0.026210:27:29 52,377.068 861 0.016410:37:29 59,279.954 914 0.015410:47:29 62,453.492 929 0.014910:57:29 63,095.573 757 0.012011:07:29 58,450.552 1,058 0.018111:17:29 57,308.533 1,033 0.018011:27:29 54,016.046 992 0.018411:37:29 49,954.701 1,082 0.021711:47:29 42,948.936 1,034 0.024111:57:29 37,055.649 1,017 0.027412:07:29 16,925.888 993 0.058712:17:28 5,558.041 991 0.178312:27:28 6,413.490 1,001 0.156112:37:29 5,345.791 1,029 0.192512:47:30 4,776.763 995 0.208312:57:30 3,794.610 996 0.262513:02:45 3,262.040 995 0.3050

Table 4.1: Relation between radiation and illuminance for day

illuminance in the room without a high error [14].

After calculating the ratios, it was then computed the prediction of illuminance in the room. For this

computation, it was used the radiation measured from meteoIST, and divided by the ratio previously

calculated. This value, defined as lux prediction in table 4.2, was then compared to the value measured

with the sensors, to see the difference between the two. This would give an indication if the value was

close to the value perceived in the room or not.

The values are displayed in table 4.2. As it is possible to see from the table, making an average taking

into account all the values recorded during a day will have the values with the highest difference between

values predicted and values measured. This can be easily explained as the type of radiation that hits the

sensors is different, that is, in the morning the prevailing type of radiation is direct (in this specific case),

while in the afternoon there will only be diffuse radiation. As such, the value obtained when the average

is being made includes both types, thus having higher difference; the error determined to this ratio can

be as high as 550%. Using the value obtained for a location in Italy, it can be seen that the absolute

values predicted are higher, even higher than the values recorded, meaning it over-estimates the values

measured. The errors measured for this ratio do not fluctuate much; even though they are high, they

range from 30% to about 85% for direct sunlight, and are at around 95% for diffuse sunlight. Finally, for

the split average, there is a single point which has a high difference (the point at 10h57m29s) but overall

it predicts the illuminance with an error lower than 40%. This ratio is the ration which could potentially

have the best results, as the ratio would depend whether direct sunlight hit the room or not. As such,

of the three methods, it is the one which has the lowest errors for the direct sunlight. For the diffuse

32

Ratio average Lux prediction [lx] Difference (%)

Local time All day Italy Split All day Italy Split All day Italy Split

09:37:59 9,878.554 89,277.389 30,392.994 116.61 76.03 29.5909:47:29 10,175.169 91,958.042 31,305.577 102.47 77.60 34.1909:57:29 10,265.443 92,773.893 31,583.320 237.76 62.63 9.7810:07:29 10,716.813 96,853.147 32,972.034 121.91 75.45 27.8710:17:29 10,948.946 98,951.049 33,686.230 196.10 67.24 3.7610:27:29 11,103.701 100,349.650 34,162.360 371.71 47.81 53.3210:37:29 11,787.204 106,526.807 36,265.270 402.92 44.35 63.4610:47:29 0.0252 11,980.649 108,275.058 36,860.433 421.29 42.32 69.4310:57:29 9,762.488 88,228.438 30,035.896 546.31 28.49 110.0711:07:29 13,644.269 123,310.023 41,978.835 328.39 52.60 39.2411:17:29 0.0775 0.0086 13,321.862 120,396.270 40,986.897 330.18 52.40 39.8211:27:29 12,793.115 115,617.716 39,360.118 322.23 53.28 37.2411:37:29 13,953.780 126,107.226 42,931.096 258.00 60.39 16.3611:47:29 13,334.758 120,512.821 41,026.574 222.08 64.36 4.6911:57:29 13,115.522 118,531.469 40,352.056 182.53 68.74 8.1712:07:29 12,806.011 115,734.266 39,399.795 32.17 85.38 57.0412:17:28 ——– 12,780.218 115,501.166 4,564.483 56.51 95.19 21.7712:27:28 12,909.181 116,666.667 4,610.542 50.32 94.50 39.1012:37:29 0.2171 13,270.277 119,930.070 4,739.508 59.72 95.54 12.7912:47:30 12,831.803 115,967.366 4,582.906 62.77 95.88 4.2312:57:30 12,844.700 116,083.916 4,587.512 70.46 96.73 17.2813:02:45 12,831.803 115,967.366 4,582.906 74.58 97.19 28.82

Table 4.2: Prediction using different ratios.

component, it behaves in the same manner. A visualization of the values obtained using different ratios

is represented in Fig. 4.1. The values predicted at 10h57m29s do not follow the pattern for the values

predicted before and afterwords. This is because at the time of the measurement a cloud crossed the

sky and influenced the measurement of the meteorological station, resulting in a lower than expected

measured radiation (as it can be seen in table 4.1. As such, it is recommended that this point is not

considered, as the conditions of measurement are different than the other values.

However, this raises an important dilemma. It isn’t relevant to have high accuracy at high levels of

illuminance because at that point the users will be uncomfortable due to glare and direct sunlight. As

such, having a high accuracy for lower values of illuminance (values that are lower than the illuminance

set-point defined for the space in question, after-which the users become troubled with the sunlight) is

more valuable than a model that has average accuracy for the range of illuminance the sensor has.

Overall, using a ratio does not provide great results. For one, the radiation measured is on an

horizontal plane, while the radiation that enters the room is through a window, which is on a vertical

plane. This means that once the sun passes the vertical plane of the window, the radiation that enters

the room is diffuse, which in turn decreases the illuminance measured, while on the horizontal plane

there will not be a significant change in radiation measured. As such, using a ratio with the horizontal

measurements will only result in an estimate of the illuminance measured, with considerable errors, and

in order to obtain good results it is recommended to use a split value for direct and diffuse radiation

to convert it to illuminance, in order to have the same behavior, otherwise, there will be an over or

under-estimate of values measured.

33

Figure 4.1: Comparison of the results obtained using different ratios.

4.2 Window’s transmittance

Initially it was planned to use the formulas shown in the previous chapter (equations 3.1a and 3.1b)

to determine the transmittance of the window and use those values in the program. However, this raised

a couple of questions: in order to correctly predict the illuminance, the user had to input always the date

and time to have a transmittance value, and the transmittance has values extremely low as the sun tends

to it’s higher point.

Figure 4.2: Window’s transmittance expected in the classroom.

The results can be seen in Fig. 4.2. At a first glance, it seems to indicate that for higher angles of

incidence, the transmittance tens to be zero. However, that is not entirely true: the transmittance for

direct sunlight tends to zero, as expected, but the room continues to receive sunlight. The sunlight it re-

34

ceives is from diffuse sunlight, which has not a defined angle of incidence, and thus is not affected by the

expressions 3.1a and 3.1b. As such, the transmittance value used was one determined experimentally.

The transmissivity of the window depends on the materials that constitutes it. To determine exper-

imentally the transmittance of the window, two Adafruit sensors TSL2591 were used coupled with two

micro-controllers Arduino R©. One sensor was placed outside the window, and the other sensor was

placed at the same point in the window, but inside the room. By making the ratio between the value that

was measured inside over the value measured outside, is possible to have an estimate of the transmit-

tance of the window. In other words,

τ =Illuminance measured inside

Illuminance measured outside× 100 (%) (4.1)

A representation of the apparatus is depicted in Fig. 4.3.

Figure 4.3: Representation of the setup used to measure window’s transmittance.

Mounting a setup as displayed in Fig. 4.3 allowed to measure the transmittance of the window. The

measurement took place in the morning and early afternoon. The values obtained can be visualized in

Fig. 4.4. It can be seen that the average value for the window’s transmittance for the morning is between

70% to 80%, raising steadily until 90%, and then dips. This sudden decrease in transmittance can be

explained as as the sun rises in the sky until noon, the angle of incidence rises as well, up until the

point where one sensor is hit by direct sunlight, but the other is not, resulting in the valley observed

in the figure. After that point where the room is not lit by direct sunlight, but by diffuse sunlight, the

transmittance stabilizes in around 60%.

4.3 Natural lighting

The validation of the natural lighting consists in using the program to predict, at a certain measured

illuminance, the distribution of natural illuminance in the room and then measure using the light meter to

compare the results obtained.

It is important to note that due to the location and orientation of the room, the peak of illuminance

will be measured during the morning, and after noon, it will be mostly diffuse radiation that will light the

35

Figure 4.4: Transmittance of the window measured in the classroom.

room. Also, due to the position of the room, the nearby trees will influence the recorded illuminance,

as it will not be possible to have the sun light all the room„ that is, it is not possible for the room to be

completely illuminated from direct sunlight.

The distribution of the illuminance inside the room is represented in Fig. 4.5, and the data was

measured in the 5th of April. In the figure it is represented the illuminance measured for P1 (near the

window) and P5 (near the wall). It can be seen that for the early morning the value measured near the

wall is higher than the value measured near the window. This can be explained as the vegetation near

the room (tall trees) can influence how the direct sunlight hits the room, that is, due to the fact that the

trees are about the same height as the window of the room, the tree itself blocks the sunlight near the

window, but not towards the wall, giving the value near the wall higher. As the sun continues to rise, the

impact of the vegetation is decreasing continuously, until the point it no longer influences the distribution

of illuminance. After that point, the illuminance measured near the window is higher, and continues to

rise, up until around noon, which is the point the sun hits the window with an angle of near 90 . On

the opposite side, the value near the wall is lower, and starts to decrease, as it no longer is hit by direct

sunlight, and because the angle of incidence starts to be more and more perpendicular, the amount of

direct sunlight that enters the room is lower. After noon, all the light that enters the room is diffuse light

– after which point it is possible to see a sharp decrease in the illuminance measured near the window

–, and as such the illuminance measured is decreasing slowly. The scale of the illuminance measured

is in logarithmic scale, as with this scale is possible to have both data measured in the same graph and

see it’s evolution throughout the day.

36

Figure 4.5: Distribution of illuminance inside the room provided by natural lighting.

4.4 Artificial lighting

To measure the impact the artificial lighting has in the illuminance distribution, it was measured in

the five points of interest how the lights being turned on or off influence the measurement. To do so, the

blinds were closed totally, and then it was measured the illuminance in the five points. As there are 4

rows of 4 lamps each, it will be named L1 to L4 the lamps in the same row the points of interest, being

lamp L1 the lamp near the window, and lamp L4 the lamp near the wall.

The values measured are represented in Fig. 4.6. From the figure, it can be seen that turning L4

on, the values near points P5 and P4 are higher than the rest. Turning L2 on raises the value of point of

interest P3, as the lamp is located exactly on top of the point. The lamp also affects the other points of

interest, as the values measured are higher than the values measured with only L4 on. Turning L3 on

in conjunction with the L4 and L3 on rises considerably the values measured in P4 and P5, while rising

slightly the illuminance measured in points P3, P2 and P1. Finally, having all lamps turned on, it can be

seen that the value for the points of interest P4, P3, P2 and P1 are approximately constant and equal,

while the value measured for point P5 is lower. This can be explained as the point P5 does not have a

lamp exactly on top of it, and the lamp has an object in the way to block direct lighting to the point of

interest, resulting in a lower than expected measurement.

Due to the orientation of the room, the values measured near the wall will always be lower than the

values measured near the window provided there is not an obstacle to impact the illuminance. Due to

this fact, it makes sense to turn on lamp L4 first rather than for example lamp L1, as the illuminance

measured in the wall is lower. As such, a simplification can be made: if turning the lamp farthest away

from the window does not provided satisfactory illuminance to the entire room, then it is required to turn

the second farthest away lamp, and so forth. Doing so allows for a faster and smarter optimization as

well as using only the necessary lamps to ensure comfortable working environment. Following this sim-

37

Figure 4.6: Distribution of illuminance provided by lamps.

plification, then several setups of lamps turned on and off can be rejected, and only a few configurations

are useful to be used, which are the ones displayed in Fig. 4.6.

It is however important to note that the partial switching of the lamps are not linear. That is, con-

sidering a switch for that controls lamp L4, when turned on, it will turn on two lamps of the same row,

and two other lamps of the row L3, as an alternated lighting switch, represented in Fig. 4.7. This is

valid for all four lamps, meaning each lamp on the room (there are four) turns on 25% of lamps in the

room. As such, having the switch that controls L4 and L2 turned on has half the lamps in the room

turned on, alternated, as represented in Fig. 4.7. Likewise, having L4 and L3 turned on has also half

the lamps turned on, but only the lamps near the wall, which is displayed in Fig. 4.8. It is considered for

the purposes of lighting turning on the lamps directly above the points of interest, and not the alternating

lamps. Fig. 4.6 presents the used configurations, where configuration “L4” represents having half of the

lamps from row L4 and the alternated half of L3 turned on; configuration “L4 + L2” represents half of the

lights in the room turned on; “L4t + L2 + L3t” represents all the lamps from row L4 and L3 turned on and

half of L2 and L1 turned on; and finally, the final configuration represents all the lights turned on.

(a) Configuration L4 (b) Configuration L4+L2

Figure 4.7: Representation of the lamps turned on using configurations “L4” and “L4+L2”.

38

(a) Configuration L4t+L3t (b) Configuration L4t+L2+L3t

Figure 4.8: Representation of the lamps turned on using configurations “L4t+L3t” and “L4t+L2+L3t”.

The impact of each configuration and each lamp turned on can be seen in Fig. 4.9. Again, the

configuration “L4”, “L3”, “L2” and “L1” represents having half of the row’s lamps turned on, and the

corresponding lamp above the point of interest turned on as well.

Figure 4.9: Impact of each lamps and configuration.

Using configuration “L4” impacts the most points of interest P5 and P4 while configuration “L2” and

“L1” impacts P1 and P2 while having neglectable effect on point of interest P5.

4.5 Prediction of the illuminance

For the prediction of illuminance, the program designed will ask for the illuminance measured from

the Adafruit sensors or use the radiation from the weather station, though for the latter it may have high

errors. It is important to note that for the first step, it converts the illuminance measured from the sensors

to the values it would be measured from the light meter, and the values are more precise for lower end

39

of the values read. This is relevant as for very high values the precision does not matter much, because

the users will be uncomfortable the same; but for lower values (values below 1,500 lux, for example),

the precision is important because it will be the difference if the blinds stay open and disturb the users

due to direct sunlight, or if the blinds close and the users remain in a comfortable range of illuminance

values. A schematic of the final algorithm used is in Fig. 4.10, which will be explained.

Figure 4.10: Representation of the algorithm used.

The illuminance prediction takes into account the distance between interest points. As such, if one

wishes to compute different interest points, it has to be changed in the program. The prediction uses

40

a ratio between interest points, and takes into consideration the position of the blinds. If the blinds are

open, it is considered only the distance between them; if the blinds are closed, it considered the distance

between them multiplied by a value related to the position of the blinds, which represents the attenuation

it suffers. If the illuminance throughout the classroom is within acceptable values for the blinds position

it was used as input, then the program just computes the distribution.

Some results are displayed in Fig. 4.11 and in table 4.3. The blinds are completely open, and it can

be seen that for the values at P1, the value measured 82,400 lx, while the value predicted 71,452 lx. As it

was said before, this error in precision does not matter much as the users will be uncomfortable; however,

for the remaining points of interest, the values are not well predicted. This is because the program

assumes that farthest points of interest are hit by the sunlight, when in fact they are not, due to the fact

of high angle of incidence. As such, it is expected that for the blinds open and with direct sunlight, the

values predicted for the farthest will have a high error, specially point of interest P5. Nevertheless, when

the sensor is not hit by direct sunlight but by diffuse sunlight, then it is expected the values predicted to

be in the same range of values as the ones measured.

Figure 4.11: Prediction of illuminance for blinds completely open during morning.

Measured value [lx] Predicted value [lx] Error (%)

P1 82,400 71,452 13.29P2 83,000 46,765 43.66P3 6,740 30,608 354.12P4 3,970 20,033 404.61P5 1,170 13,111 1,020.60

Table 4.3: Prediction of illuminance for blinds completely open during morning.

After the measurement of the sensor’s value, the program predicts the illuminance in the room. If

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there are points of interest that are above a certain threshold (values too high), which can be defined

previously, then the program computes the different setups the blinds can have (from being completely

open to completely closed) to determine at which percentage the blinds must be closed to ensure com-

fortable environment. From that percentage, the program then recalculates the illuminance in every point

of interest. However, if the value measured is below a second threshold (values too low), then the pro-

gram computes the distribution of illuminance the electrical lighting provides, and turns one on, to check

if the illuminance is within acceptable values. If it is not, then turns another one on, and checks again.

After the illuminance throughout the room is within acceptable values, then the program computes the

electrical consumption. The range of values considered for the room is between 150 lux (lower thresh-

old) and 1,500 lux (higher threshold), which were considered suitable to the room. Although 150 lux

seems low, it still guarantees the visual comfort of the users, and having 1,500 lux as the upper bound

allows the users to have plenty of illuminance to work.

In Fig. 4.12 is displayed a first measurement and it’s prediction. As it can be seen, the value mea-

sured and predicted for point of interest P1 is very high (higher than the threshold defined as 1,500 lux).

As such, it is necessary to use the blinds to reduce the illuminance. The program predicted that using

blinds at 82% would guarantee that the illuminance measured would be lower than the threshold, and it

is possible to see that the value is indeed below. The prediction and measurement are close in value

(the error is slightly more than 26%), measured for the point of interest P3.

Figure 4.12: Prediction of illuminance and it’s correction using blinds at 82%.

On the other hand, when the value does not reach a certain threshold which was previously defined

(when the point of interest P5 does not reach 150 lux), then the electrical lighting turns on in order to

raise the values. The prediction and correction using the electrical lighting is shown in Fig. 4.13. Initially,

the values recorded near the wall are lower than recommended: P3, P4 and P5 are below than 150

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lux. This type of conditions is uncomfortable for users because the it is too dark and as such, electrical

lighting is required. Using only lamp L4 guarantees that the values are above the threshold. From the

figure it can be seen that all points were raised, and in particular both predicted and measured values

for P1, P2 and P3 are extremely closed, showing the good prediction of the program. For points P4 and

P5 the values are overestimated, but well above the threshold defined.

Figure 4.13: Prediction of illuminance and it’s correction using lamp L4.

The table 4.4 provides a summary of the values measured throughout the day, and alongside the

control method used to have the illuminance in the previously defined range of acceptable values. The

time of the measurements were made in the local time, in early May, and were made over the points

of interest. The values measured and predicted are side by side, and after applying a control method

(either blinds or electrical lighting), the values are again displayed, now lower/higher depending of the

control method.

For the morning, it is expected that the prevailing control method to be the blinds, as the room

is facing East, and the peak of illuminance is measured in the morning. The electrical lighting will

only be necessary if the sunlight can not provide sufficient illuminance to the users, and if the season

considered is Summer, when the days are longer, then only at late afternoon/night will be necessary

that type of control. As the day progresses, and with diffuse sunlight to light the room, the blinds will

have a considerable weight in reducing the illuminance. Due to the fact that diffuse daylight lights the

room not by direct incidence but through multiple reflections inside the room, changing the position of

the blinds will greatly influence how the reflections occur. As such, the program will predict a higher than

necessary percentage of closed blinds to have the illuminance in the acceptable range, meaning the

illuminance measured will be lower than expected.

From the data provided by the table, it can be concluded that for the morning and for clear skies, it is

necessary to use the blinds to lower the illuminance and bring it to comfortable range, as the high levels

of illuminance can cause glare to the users in the room. It is suggested the use of blinds throughout

43

Illuminance [lx] Illuminance [lx]

Local time Point of interest Measured Predicted Control method Measured Predicted

9h30

P1 84500 81992

Blinds at 83%

1567 1386P2 79300 53664 1088 804P3 10530 35123 693 527P4 3360 22988 445 344P5 1581 15045 191 225

11h00

P1 77300 66627

Blinds at 82%

1673 1392P2 79300 43607 1068 654P3 74100 28541 697 428P4 4350 18680 468 280P5 1664 12226 212 183

13h20

P1 10280 17198

Blinds at 80% with lamp L4 ON

1377 1269P2 5710 11256 545 264P3 2020 7367 429 226P4 790 4821 352 388P5 226 3155 304 314

16h10

P1 4520 3324

Blinds at 78% with lamps L4+L2 ON

1724 1824P2 1910 2176 445 622P3 1220 1424 710 676P4 671 932 580 475P5 152 610 449 415

Table 4.4: Summary table for the values measured.

the morning in order to control the amount of direct sunlight that enters the room and therefore the

illuminance measured. After the moment where direct sunlight does not hit the window, the illuminance

measured decreases and the blinds have an extra weight in the control of the room’s illuminance. That

can be observed for the measurements made after noon, as the suggested position of the blinds bring

the illuminance to extremely low values, which in turn have to be compensated with electrical lighting.

For these cases, the prediction of the position of the blinds does not yield good results; in fact, it would

be recommended not using the blinds or using a lower percentage, in order to increase the overall

illuminance without compromising the values the users desire.

The program designed will have the most impact during the morning as is during this time the room

is light by direct sunlight. The values measured for 1st of June are represented in Fig. 4.14. Using

daylight allows the lighting of the room without artificial lighting, reducing the use of electrical energy. As

such, savings can be achieved. Assuming a reduction of 1 kWh during the morning, for 5 working day of

the week, 28 weeks in which Instituto Superior Técnico has classes, plus the 8 weeks of examinations,

gives a total of 540 hours of morning use, resulting in a saving of 540 kWh electrical consumption.

Assuming a price per kWh of 0.12e, this gives a monetary saving of 64.80e in electrical bills, only from

not using artificial lighting but using daylight in the morning. This saving can be higher if it is taken into

consideration the reduced use of cooling and heating systems.

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Figure 4.14: Electrical consumption in the room.

45

46

Chapter 5

Conclusions

5.1 Achievements

This work proposed to develop an autonomous system capable to measure and determine the illu-

minance in a classroom, and from those values decide if the use of blinds or electrical lighting to ensure

the users worked in a comfortable range of illuminance. To do so several methods to predict illuminance

were studied and analyzed. After this, a method was designed for this classroom. The final model was

tested and validated in a classroom in Instituto Superior Técnico, a classroom which had controllable

blinds and electrical lighting.

It was concluded through measurements that the program could predict the distribution with an ad-

missible error, and it’s suggestions to control the illuminance to the range of values recommended is

successful as well. It was given an emphasis in the conversion to lower values of illuminance as for

high values, it does not matter the precision as it will be uncomfortable for the users. The program was

designed in Python, with which is possible to use in future work to automate the optimization.

This work managed to predict and optimize the distribution of daylight throughout a room and main-

tain a level of illuminance adequate for a good working environment using electrical lighting and blinds.

In the lack of a sensor, this work proposes a simple approach to provide an estimate of illuminance

taking into account the solar radiation measured in the exterior of the room.

5.2 Future work

Despite the prediction and management of the space is acceptable, more improvements can be

made. For one, a more detailed study of the room can be made taking into account the light that can

come in through the window from the corridor. A second improvement one can make is to try to predict

the radiation the room will receive with more precision, avoiding that way the use of a sensor.

An important improvement that can be made is combining the program designed with an Arduino

and a Raspberry Pi. The program was designed to take this into consideration, as with a Raspberry Pi it

can be run in the room hidden from the users and used to determine the distribution. Coupling this with

47

an Arduino allows for the Raspberry Pi to control both the blinds and/or the electrical lighting to ensure

the illuminance stays in the range defined previously and the users are comfortable. The time for the

measurements and the optimization made can be defined on the Raspberry Pi, deciding at which time of

the program runs. It is suggested that running every 15 minutes provides a good estimate of the values

and does not disturb frequently the users in case it is needed to control the blinds and/or the electrical

lighting.

48

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