S U B M I T T E D B Y

C . S . S U P R I Y A

M . S I D D A R T H A N

I V Y E A R E E E

G U I D E D B Y

D R . M . V A R A D A R A J A N

S A R A N A T H A N C O L L E G E O F E N G I N E E R I N G

Optimization of a Grid connected Hybrid PV-Wind

System

Objective of the Project

To design an optimum PV-wind hybrid energy system, interconnected to the grid (especially for remote areas) so as to:

o minimize the electricity production cost ($/KWh)

o ensure that the load is served reliably

o minimize the power purchased from the grid

Scope of the Project

The assumptions made for this formulation are:

o the converter which converts the dc power from the PV panels and wind turbines is assumed to be ideal

o the system is always connected to the grid; isolated PV panels and/or wind turbines are not taken into account; no battery is considered

o operation of wind and PV generators at their maximum power operating points is ensured through Peak Power Trackers

Overall Scheme

Mathematical Model of PV Modules- Power Output

Power output of a PV panel is given as:

where,

η is the conversion efficiency of PV panel

I is the irradiance (kW/m2)

nηISPs

Mathematical Model of PV Modules- Cost function

Initial and maintenance costs are given as:

where,

Sc is the cost per 1 m2 of PV panel

λs is reliability coefficient of PV panels

Sy is lifetime of PV panels

Sn is number of PV panels to be determined

y

ncic

S

SSS

y

nsicmc

S

S)λ-(1SS

Graphical Representation of Power Output of Wind Generators

Mathematical Model of Wind Generators- Power Output

The power output can be mathematically written as follows:

Pw=0 (Wout<WS<Win)

(Win<WS<Wrs)

Pw=WrpWn (Wrs<WS<Wout)

where,

Win is the cut-in speed (m/s)

Wout is the cut-out speed (m/s)

WS is the wind speed (m/s)

Wrp is the rated power (W)

ξ is the slope between Win and Wrs (W/m/s)

-3nin 10 x W)Wξ(WS-Pw

Mathematical Model of Wind Generators- Cost function

Initial and maintenance costs are given as:

where,

Wc is the cost per one generator of wind turbines

λw is reliability coefficient of wind turbines

Wy is lifetime of wind turbines

Wn is number of wind turbines to be determined

y

ncic

W

WWW

y

nwicmc

W

W)λ-(1WW

Objective Function

The objective function is to minimize the total cost of a grid connected hybrid PV and wind system:

Min (Tc) = Min (Sic+Smc+Wic+Wmc+CpUp)

where,

Sic, Smc are initial and maintenance costs of PV panels used ($)

Wic, Wmc are initial and maintenance costs of wind turbines used ($)

Cp is the cost/kWh of power drawn from utility ($)

Up is the number of units of electric power to be drawn from the grid (kWh)

Objective Function (cont.)

Thus the objective function can be written as:

pp

y

nwc

y

nc

y

nsc

y

ncUC

W

W)λ(1W

W

WW

S

S)λ(1S

S

SSmin

2

2

2

2

Constraints

The constraints are set so as to minimize magnitude of the difference between generated power (Pgen) and the power demand (Pdem)

where, Pgen = Ps+ Pw+ Up

Ps, Pw, Up are the power outputs of solar panels, wind turbines and the power taken from the grid respectively.

demgen PPΔP

Constraints (cont.)

The total generated and demanded energy (Egen, Edem) over a year:

For generation and load to balance over a given period of time, the curve of ∆P versus time must have an average of zero over the same time period (in this case, over a year)

8760

1n

pwsgen T))((UT))((PT))((PE

8760

1n

demdem T))((PE

demgen EEΔPdtΔE

Constraints (cont.)

Hence the constraints can be written as follows:

Since ∆T=1 hour in this case, the constraints can be further modified as:

Therefore, by substituting the various terms for Ps, Pw, the constraints can be written as:

8760

1n

8760

1n

T)(Pdem)(T)(Up)(T)(Pw)(T)(Ps)(

8760

1n

dem

8760

1n

p

8760

1n

w

8760

1n

s PUPP

8760

1n

dem

8760

1n

8760

1n

p3

nin

8760

1n

n PU10W)Wξ(WSηIS

Procedure to balance the demand and generation

After obtaining the results yearly optimization,

for every hour, Sn and Wn are fixed as obtained above and Up is varied to meet the demand

if Ps+Pw<Pdem, Up=Pdem-Ps-Pw

if Ps+Pw>Pdem, Up=0; the excess power is dumped into controlled resistors

Implementation of Quadratic Programming

p

n

n

p

y

c

y

c

p

n

n

y

wc

y

sc

pnn

U

W

S

CW

W

S

S

U

W

S

000

0W

)λ(1W0

00S

)λ(1S

UWSmin2

2

The objective function and constraint obtained can be written in matrix form as follows:

subject to:

dem

p

n

n

3in P

U

W

S

1)10)W(WSξ()ηI(

Implementation of Quadratic Programming (cont.)

The above formulation is of the form: min (0.5 XT H X +fT X)

sub to: Aeq X = beq

where,

000

0W

)λ(1W0

00S

)λ(1S

H2

2

y

wc

y

sc

p

n

n

U

W

S

X

1)10)Wξ(WS()ηI( 3ineqA demeq Pb

p

y

c

y

c

CW

WS

S

f

Carbon Emission

Apart from cost, our objective is also to reduce the amount of CO2 emitted from the system

Carbon emission is reduced by increasing the use of renewable sources and thereby, reducing the power consumption from grid

Amount of CO2 emitted from grid 0.98 kg/kWh

Case Study I

Hourly average data for load demand, insolation and wind speed of a day are taken and the same is projected for a year

Using quadratic programming, yearly optimization is run by fixing maximum number of panels and turbines arbitrarily based on minimum and maximum demands; graphs are obtained

Maximum number of panels and turbines are fixed on the basis of ∆P curve against number of modules

Optimization is run again, similar graphs are obtained and results are tabulated

Region of optimal operation is obtained based on the cost versus carbon emission curves for increasing number of each module

Conventional Grid System

Grid Connected PV System – Using 32 Panels

Grid Connected Wind System – Using 4 Turbines

Grid Connected Hybrid System – Using 8 Panels and 4 Turbines

Fixing Maximum Number of Modules

Maximum Panels: 74 Maximum Turbines: 8

Grid Connected PV System – 74 Panels

Grid Connected Wind System – 8 Turbines

Grid Connected Hybrid System – 5 Panels and 8 Turbines

Comparison of Results – Case Study I

Configuration / Type of

analysis

Grid connected

hybrid system

Grid connected

wind system

Grid connected PV system

Grid system (Convention

al)

Cost per year ($)

1044.6 607.578 2331.5 5716.3

Power drawn from grid

(kWh)2954.7 6455.2 9197.8 17,013

Per yearemission of

CO2 (kg)2895.9 6326.1 9013.8 16,672

Optimal Region of Operation

Case Study II

Hourly average data for load demand, insolation and wind speed of a year are taken

Using quadratic programming, yearly optimization is run by fixing maximum number of panels and turbines arbitrarily based on minimum and maximum demands; graphs are obtained

Maximum number of panels and turbines are fixed on the basis of ∆P curve against number of modules

Optimization is run again, similar graphs are obtained and results are tabulated

Region of optimal operation is obtained based on the cost versus carbon emission curves for increasing number of each module

Conventional Grid System

Grid Connected PV System (Power Demand and Generation) – Using 75 Panels

Grid Connected PV System (Power Demand and Split-up of Generation) – Using 75 Panels

Grid Connected Wind System (Power Demand and Generation) – Using 10 Turbines

Grid Connected Wind System (Power Demand and Split-up of Generation) – Using 10 Turbines

Grid Connected Hybrid System (Power Demand and Generation) – Using 100 Panels and 10 Turbines

Grid Connected Hybrid System (Power Demand and Split-up of Generation) – Using 100 Panels and 10 Turbines

Fixing Maximum Number of Modules

Maximum Panels: 135 Maximum Turbines: 13

Grid Connected PV System (Power Demand and Generation) – 135 Panels

Grid Connected PV System (Power Demand and Split-up of Generation) – 135 Panels

Grid Connected Wind System (Power Demand and of Generation) – 13 Turbines

Grid Connected Wind System (Power Demand and Split-up of Generation) – 13 Turbines

Grid Connected Hybrid System (Power Demand and Generation) – 8 Panels and 13 Turbines

Grid Connected Hybrid System (Power Demand and Split-up of Generation) – 8 Panels and 13 Turbines

Comparison of Results – Case Study II

Configuration / Type of

analysis

Grid connected

hybrid system

Grid connected

wind system

Grid connected PV system

Grid system (Convention

al)

Cost per year ($)

1690 1440.4 4213 13098

Power drawn from grid

(kWh)9922.2 10597 22054 38982

Per yearemission of

CO2 (kg)9723.8 10597 21612 38202

Optimal Region of Operation

Conclusion

On basis of cost, the grid-wind system may seem to be the best

But carbon emission is also a major criterion to be taken into account

Besides, the cost of grid-hybrid system is not too high compared to grid-wind system

Thus grid-hybrid system is concluded to be the best configuration which makes maximum use of renewable sources

Future Scope

If a contract could be signed by incorporating a selling price for the excess power produced, there would be a considerable reduction in the cost

Introduction of more efficient PV panels can further decrease the cost of grid-PV system and particularly that of grid-hybrid system

Thus, the grid-hybrid system would become the best type of configuration in terms of cost as well in near future

References

[1] Ashok, S., “Optimised Model for Community-Based Hybrid Energy System” RENEWABLE

ENERGY, VOL. 32, NO.7, JUNE 2007, PP: 1155–1164.

[2]Bagul, A.D., Salameh, Z.M., Borowy, B., “Sizing of Stand-Alone Hybrid PV/Wind System using a Three-Event Probabilistic Density Approximation.” JOURNAL OF SOLAR ENERGY

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References (cont.)

[7] Kellogg, W.D., Nehrir, M.H., Venkataramanan, G. and Gerez, V., “Optimal Unit Sizing for a Hybrid PV/Wind Generating System.” ELECTRIC POWER SYSTEM RESEARCH, VOL. 39, 1996, PP: 35-38.

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[9] Musgrove, A.R.D., “The Optimization of Hybrid Energy Conversion System using the Dynamic Programming Model – RAPSODY.” INTERNATIONAL JOURNAL ON ENERGY

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[10] Ramakumar, R., Shetty, P.S., and Ashenayi, K., “A Linear Programming Approach to the Design of Integrated Renewable Energy Systems for Developing Counntries” IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. EC-1, NO. 4, DECEMBER 1986, PP: 18-24.

[11] Senjyu, T., Hayashi, D., Urasaki, N., and Funabashi, T., “Optimum Configuration for Renewable Generating Systems in Residence Using Genetic Algorithm” IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006, PP: 459-466.

[12] Wang, C., Nehrir, M.H., “Power Management of a Stand-Alone Wind/Photovoltaic/Fuel Cell Energy System” IEEE TRANSACTIONS ON ENERGY

CONVERSION, VOL. 23, NO. 3, SEPTEMBER 2008, PP: 957-967.

References (cont.)

[13] Yang, H.X., Burnett, J., Lu, L., “Weather Data and Probability Analysis of Hybrid Photovoltaic Wind Power Generation Systems in Hong Kong.” RENEWABLE ENERGY, VOL. 28, 2003, PP: 1813-1824.

[14] Yokoyama, R., Ito, K., Yuasa, Y., “Multi-Objective Optimal Unit Sizing of Hybrid Power Generation Systems Utilizing PV and Wind Energy.” JOURNAL OF SOLAR ENERGY

ENGINEERING, VOL. 116, 1994, PP: 167-173.

[15] Energy Analysis of Power Systems - World Nuclear Association [Online], 2009[Cited July 2009]; Available from: http://www.world-nuclear.org/info/inf11.html

[16] Singiresu. S. Rao, Engineering Optimization- Theory and Practice, 3rd edition, New Age International (P) Ltd.; 1996