developpement et impementation d'un algorithme de ...

EFEEA’10 International Symposium on Environment Friendly Energies in Electrical Applications

2-4 November 2010, Ghardaïa, Algeria

Development of an Algorithm of Maximum Power point tracking for photovoltaic systems using Genetic Algorithms Slimane Hadji*, Krim Fateh Laboratoire d’Electronique de Puissance et Commande Industrielle (LEPCI) – Setif University *

Bejaia University, [email protected]

Abstract— In this article we used Genetic Algorithms (GAs) to track le Maximum Power point (MPP) of photovoltaic cells (PVC) so we can enjoy the maximum of solar energy and tracking quickly this point. The program, based on Gas, maximise a fitness function extracted from the PVC model. Two fitness functions are exposed to prove the utility of this method, one based on the maximum power given by the PVC and the other represents the derivative of P-I curve. In the end, tests and results are presented to prove the method utility.

II.

No-linearity of current-voltage is well known [1,2]. Using the equivalent circuit in fig.1, V-I characteristic of M parallel strings with N series cells per string can be written [3]: * + ( ) (3) Where: Ipv : Photovoltaic Current. Vpv : Photovoltaic Voltage. Isc : Cell short circuit current. I0 : Reserve saturation current. Rs : Series cell resistance. λ : Coefficient depends upon the cell material and temperature.

Index Terms - Photovoltaic cells, Genetic Algorithms, P PV panel, MPPT, Matlab.

I.

THE MODEL :

INTRODUCTION :

Humans are always searching for a novel energy sources with the best ratio price-quality-length of life, and preserving the environment, so using the solar energy. The power of PV cells is very depending with insolation and temperature so the most of researches are turned to track to maximum power point. Genetic Algorithms proved high performances in several areas with its remarkable performances like solving no-linear equations.

RS Vpv

Iph

Id Ipv Fig.1 : Equivalent circuit of PV cell

For a Silicon cell with: M =1, N = 36 and T=25°, using table.1 (manufactured by Iranian Optical Fiber Fabrication Co, OFFC [2]) (3) becomes: * + (4)

Various methods of MPPT are developed [3-6], we can find: - Extreme searching: Analytic search of the optimum: dP/dV < 0 decrease V dP/dV > 0 increase V dP/dV = 0 MPP. This method is the most used but the calculation time depends on initial conditions.

Reverse saturation current Short circuit current Serial resistance Material coefficient

I0 = 0.5 10 – 4 Isc = 2.926 Rs = 0.0277 λ = 0.049

[A] [A] [Ω] [1/V]

Table.1: Specification of Silicon solar panels (manufactured by OFFC)[2]

- Searching with pilot cell: We use a PV cell and measure the short circuit current (Isc) and open circuit voltage (Voc). This method supposes a leaner relation[7] between Voc and the voltage of maximum power (Vmp): Vmp = Mv Voc (1) Mv : Constant called voltage factor.

The fig.2 and fig.3 represent, respectively, the evolution of V-I and P-I characteristics, for constant temperature T = 25°C and different insolation levels: Isc = 1.5 A , Isc = 2A , Isc = 3 A. We can easily see the dependence of panel power with insolation levels. The MPP takes different positions for different levels of insolation.

And between Isc and the current of maximum power (Imp): Imp = Mc Isc (2) Mc: Facteur de Courant. It is a very simple method but in reality the value of Mc or Mv is not constant because of the no-linearity of PV model.

The curves of fig.4 and fig.5 show, respectively, the evolution of V-I and P-I characteristics, for constant insolation level Isc = 2.926 A and different temperatures: T= 70°C, T= 25°C, et T= -20°C In fig.5 we can see that, for different temperatures, the current corresponding for maximum power is approximately constant.

1


III.

Isc=1.5A Isc=2A


PRESENTATION OF THE METHOD :

GAs are an optimisation stochastic algorithms based on natural genetic selection, its principal advantages: 1. In GAs we use in place of parameters its codes. 2. We don’t work with a point but with a population of points. 3. We just need function values and we have not to calculate any other value (exp: differential).

Isc=3A

Generate initial population la

Fig.2: Evolution of V-I characteristics for different insolation levels

Start

Evaluation

Get termination condition Yes

The best individuals

No Generate a new population

Selection Crossover Mutation

End

Fig.6: Steps of a simple GA

Steps of a simple GA [8] fig.6:

Isc=1.5A Isc=2A

- Initialization: We should create a random population with N binary individuals, with a choice of the length (bits number S, precision). A population is a binary matrix where the number of lines represents the number of individuals and column number represents the length of individuals. - Evaluation: The individuals must be evaluated by the value of its fitness function (positive function), it is a very important step because it gives the chance of an individual to be selected (The individual is optimum for maximum value of its fitness function). The MPP is located by an objective function which can be optimum for maximum, minimum, or zero value. This means that, sometimes, we must get a relation to pass from fitness function to objective function. Two objective functions are used: 1st function: Power differential: dP/dI. From the relation: P = I V, we can write: (5) x: decoded individual.

Isc=3A

Fig.3: Evolution of P-I characteristics for different insolation levels

T=70°C T=25°C

T=-20°C

Fig.4 : Evolution of V-I characteristics for different temperatures

We get maximum power for f(x)=0. To pass to fitness function a transformation is necessary, we used: (6) 2nd function: The power of PV panel, using the PV model given by (4) [3]. To increase the algorithm speed we can take: (7)

T=70°C T=25°C

T=-20°C

- Genetic operations: They are the base of GA, they don’t exclude probability theories but they give very interesting results, these operations are: 1. Selection: To select, with a rate Tsel, a part of population corresponding to the optimum fitness function.

Fig.5 : Evolution of V-I characteristics for different temperatures

2


2.

3.

4.


Crossover: Cross pairs of individuals, with Trcm probability, to get the novel individuals. Mutation: After crossover, we apply a mutation, with Pm probability, to the new population. Integration: The new population will be integrated to the old population to replace individuals with minimum fitness function.

- Program termination: Executing program creates new best individuals, the program terminates according to these conditions: 1st condition: Set the iterations number, we obtain a constant executing time. 2nd condition: we can terminate the program by testing fitness function value. This means set the precision but it can take a long execution time. In this paper, the program will terminate with one of these conditions. IV.

Fig.08: Evolution of dP/dI with iterations number ( Isc = 0.5 A)

For Isc=3A: 2.5779 A,

13.3975 V , 34.5379 W

We can see, in both high and low insolation level, a quickly convergence with a good precision. 2. Changing bits number: The number of bits S represents the individuals length, it means the individuals precision. A high S value gives more precision but this increases executing. Bellow, simulation results for S = (5, 20) which gives respectively precision: prec = (1, 6). Nind=30, Tsel= 0.8, Trcm = 0.8, Pm = 0.01, Isc = 2 A

TESTS ET RESULTATS :

The algorithm is tested using the two objectives functions, for different insolation levels (short circuit current Isc) and changing GA parameters. We give a comparison with pilot cell method. Curves are presented with current and voltage optimums (corresponding to the maximum power. 1. Changing insolation level: Changing insolation level don’t chance only power but also the precision (numeral number after point: prec) [9]. Where, S: bits number. The figures below show the results which can be obtained with: Isc=0,5A and Isc= 3A. Where: S=16 bits, N= 30 individuals, Tsel = 0.8, Trcm = 0.8, Pm = 0.01

Fig.9: Evolution of maximum fitness function value with iterations number (for S = 5)

Fig.07: Evolution of dP/dI with iterations number ( Isc = 0.5 A)

The MPP, when Isc=0.5A, is given by :

Fig.10: Evolution of maximum fitness function value with iterations number ( for S = 20)

Imp= 0.43508A , Vmp=12,23369V , Pmax=5.32264 W

This gives : S=5 bits S=5 bits

3

1.7 A 13.3 V 23.27 W 1.737630A, 13.397919V, 23.2806346 W



3. Influence of population dimension: The individuals number (population dimension) is very important, a high number of individuals gives a quickly convergence but requires a high time execution. We give an example for: N=10 and N =50. Tsel = 0.8, Trcm = 0.8 Pm = 0.01, Isc = 2 A , S = 16

Fig.13: Evolution of maximum fitness function value with iterations number ( for Tsel = 0.9)

Fig.11: Evolution of maximum fitness function value with iterations number ( for N = 10)

Fig.14: Evolution of maximum fitness function value with iterations number ( for Tsel = 0.1)

Crossover rate Trcm : We can see more changes in population with high value of Trcm, so the chance to get quickly the optimum (or local maximum!). Bellow example for: Trcm=0.9 and Trcm=0.1 N = 20 , Preci = 16 , Tsel = 0.8 , Pm = 0.005 Fig.12: Evolution of maximum fitness function value with iterations number ( for N = 50)

N=10 N=50

1.734370A, 13.422992V, 23.280448W 1.736324 A, 13.408001 V, 23.280635 W

4. Influence of GA parameters: The genetic parameters (selection rate Tsel, crossover rate Trcm, and mutation probability Pm) define the program progress. We can improve the algorithm with a good choice of these parameters. Fig.15: Evolution of maximum fitness function value with iterations number ( for Trcm = 0.9)

- Selection rate Tsel: It gives the number of individuals to be selected, its value change with the problem to solve. The figures bellow show results for: Tsel=0.9 et Tsel = 0.1, using 2nd objective function. With : N=20, Preci= 16, Trcm = 0.8, Pm =0.005

4


Fig.16: Evolution of maximum fitness function value with iterations number ( for Trcm = 0.1)

5.

Fig18: Changing of (Vmp) with (Voc)

We can see that the relations (1) and (2) are not really linear but the approximation is acceptable. GAs can be used the determinate the current and voltage factors.

Comparison with pilot cell method :

- Relation between short circuit current (Isc) and optimal current (Imp): With GAs, for differents Isc values we note optimal currents Imp values, we get the table.02. Isc (A)

0. 5

1

1. 5

2

2. 5

3

3. 5

4

Imp (A)

0.433

0.875

1.312

1.735

Imp/Isc

0. 8 6

0. 8 7

0. 8 7

0. 8 6

2.187

2.578

2.952

3.390

0. 8 7

0. 85

0. 8 4

0. 8 4

V.

Using Mc = 0.86 given by OFFC [3] and the relation (4) [7], the figure bellow shows changing of maximum power current Imp with short circuit current Isc with the two methods (results with GAs presented by stars).

VI. [1]

- Relation between optimal (Vmp) voltage and open ciruit voltage (Voc) : The table.03 gives some open circuit voltage (Voc) values and correspondents voltage of maximum power (Vmp) values. The results shown on fig.18. 17.5

18.21

18.72

19.11

19.44

19.71

Vmp (V)

12.57

13.67

14.30

14.77

15.12

15.42

15.66

Vmp/Voc

0.77

0.78

0.78

0.78

0.79

0.79

0.79

REFERENCES:

H. S. Rauschenbach, Solar Cell Array Design Handbook; The principles and technology of Photovoltaic Energy conversion, New York: Van Nostrand, 1980. [2] Z. M. Salameh, B. S. Borowy, and A. R. A. Amin, "Photovoltaic module-site matching based on the capacity factors", IEEE Trans. Energy Conversion, vol. 10, pp. 226332, June 1995. [3] M. A. S. Masoum, H. Dehbonei, and Ewald F.Fuchs, "Theoretical and experimental analysis of photovoltaic systems with voltage, and Current, based maximum power point tracking", IEEE Trans. Energy Conversion, vol. 17, N°4, Dec. 2002, pp. 514-522. [4] C. Boisvineau, M. Nougared and J. Perard, "Optimisation du fonctionnement d’un générateur photovoltaïque : Asservissement extrémale de la puissance", Revue Physique Appliquée, N° 17, pp 329-336, mai 1992. [5] M. Drif, Contribution au développement d’un dispositif de régulation et de contrôle à base de MC pour systèmes photovoltaïques autonomes, mémoire de magister, Université de Sétif, mars 1999. [6] Y. Chau Kuo. T. Juu Liang, and J. Fuh Chen.Novel, "Maximum power point tracking controller for photovoltaic", Energy Conversion, IEEE Trans on Industrial Electronics, vol. 48, n° 3, June 2001. [7] M. A. S. Masoum and H. Dehbonei, "Optimal power point tracking of photovoltaic System under Operating Conditions". 17th Congress of the World Energy Council, Houston, TX, Sept 12-18, 1998. [8] D. Goldberg, Genetic algorithm in Search, optimization and machine learning, Addison-Wesley, 1992 [9] Zbigniew Michalewicz, "Genetic Algorithms + Data Structures = Evolution Programs", Springer edition, 1996.

Fig.17: Changing of Imp with Isc

16.27

CONCLUSION:

This article prove that Genetics Algorithms give an interesting results, the problems of initial conditions and divergence are not exposed, it gives very interesting results with acceptable time executing. GAs parameters should be chosen in adaptation with the problem and the results wanted (rapidity, precision, executing time, …). In order to get better results, we chose two objective functions, we also put both two terminate conditions. A disadvantage of GAs is in using probability relations so the result is unpredictable and we can’t control it.

Table.02: Imp values for different Isc values given by GAs

Voc (V)


Tableau.03: Vmp values for different Voc values given by GAs

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