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ALGORITHM FOR PARTIALLY SHADED SOLAR PHOTOVOLTAIC ARRAY .... introduced by Price et al [16] over other modern heuristics is finding the true ...
Enhanced Maximum Power Point Tracking using Differential Evolution Algorithm for Partially Shaded Solar Photovoltaic...

ENHANCED MAXIMUM POWER POINT TRACKING USING DIFFERENTIAL EVOLUTION ALGORITHM FOR PARTIALLY SHADED SOLAR PHOTOVOLTAIC ARRAY R. RAMAPRABHA* AND BADRILAL MATHUR Corresponding Author*: Department of Electrical and Electronics Engineering, SSN College of Engineering, Rajiv Gandhi Salai, Kalavakkam-603110, Chennai, Tamilnadu, India, E-mail: [email protected] and [email protected].

Abstract: This paper presents the Differential Evolution (DE) based MPPT scheme for a solar photo voltaic array (SPVA) under partial shaded conditions. Partial shaded PV modules produce several local maximum power points, which makes the tracking of the global maximum power a difficult task. Most of conventional tracking methods fail to work properly under these non uniform insolation conditions. Some methods proposed in the literature track the global peak (GP) with some limitations. This paper proposes DE based GP tracking with the objective of maximizing the power. The proposed method is checked for different shading patterns through simulation and verified. The results show the effectiveness and robustness of the proposed optimization approach. Keywords: SPVA, MPPT, Global Peak, Differential Evolution Technique, MATLAB.

NOMENCLATURE IPV Solar module output current. VPV Solar module output voltage. Iph Photo current of the SPV module. Ish Current through the shunt resistance. VD and ID Voltage drop across and current through the diode. D Diode used in equivalent circuit. Db Bypass diode used in equivalent circuit. Rse Series resistance in the equivalent circuit of the module (mΩ). Rsh Parallel resistance in the equivalent circuit of the module (Ω). RL Load resistance used in the equivalent circuit. IPVmax and IPVmin Maximum and minimum solar PV current. G1, G2, G3 Insolation of Panel-1, Panel-2, and Panel-3.

T Temperature. F (X) Objective function. M Number of design variable. NP Population size. F Scaling factor for mutation. Genmax Maximum generations. 1. INTRODUCTION Considering the high initial capital cost of a SPV source and its low energy conversion efficiency, it is essential to operate the SPV source at Maximum Power Point (MPP) so that maximum power can be extracted. In general, SPV source is operated along with a dc-dc power converter, whose duty cycle is changed in order to track the instantaneous MPP of SPV source. Several MPPT schemes have been proposed by different authors [1] – [11]. Among them popular tracking schemes are perturb and observe (P and O) or hill climbing [2], [6], incremental conductance [1], short circuit current [5], open-circuit voltage [7] and ripple correlation methods [11]. Some modified techniques have also been proposed,

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with the idea of reducing the hardware or improving the performance [3], [4], [7], [8], [9]. The tracking schemes mentioned above are effective and time tested under uniform solar insolation, where the V-P curve of SPV module exhibits only one MPP for a given environmental conditions. Under partial shading a deformation occurs in the overall V-P curve. That is V-P curves often exhibit multiple local maxima at different locations, which may also result in quite odd ratios between global MPP voltage and open-circuit voltage [12]. These factors can present a considerable difficulty to the correct operation of a MPPT. The presence of multiple peaks reduces the effectiveness of the existing MPP tracking (MPPT) schemes, which assume a single peak power point on the V-P characteristic. The occurrence of partially shaded conditions being quite common (e.g., due to clouds, trees, etc.), there is a requirement to develop special MPPT schemes that can track the Global Peak (GP) under these conditions. Some researchers [13] – [15] have worked on GP tracking schemes for PV arrays operating under non uniform insolation conditions. Kobayashi et al. [15] have proposed a two-stage method to track the GP. In this method, if the GP lies on the left side of the load line, the operating point is temporarily shifted to 90% of VOC, thereby missing the GP. State space-based approach to search the GP has been proposed by [14]. This method is fast and accurate but is system specific, complex and requires more sensors. MPPT scheme that uses Fibonacci sequence to track the GP under partially shaded conditions by introducing a new function has been proposed by [13]. In most of the cases this method assured for GP tracking. In this paper the different approach for GP tracking using differential evolution (DE) is proposed. The main advantage of DE based optimization algorithm introduced by Price et al [16] over other modern heuristics is finding the true global minimum of a multi modal search space regardless of the initial parameter values, fast convergence, and use of few control parameters. The results obtained with DE algorithm are verified with binary search method. The results illustrate the effectiveness and robustness of the proposed approach. 2. PROBLEM DEFINITION 2. 1 Need for Optimization Algorithm for SPVA Module Under Partial Shaded Condition The standard one diode or 5 parameter model used to represent a SPV module is shown in Fig. 1. The modeling and simulation of SPVA under partial shaded conditions discussed by [17] – [19] is used in this paper. The partial 160

shade has more impact on series connected modules. The multiple peaks are mainly introduced by series connection in any configuration. The simulation of series connected SPVA array characteristics under partial shaded condition with bypass diode is shown in Fig. 2. The model is developed using MATLAB M-file. For understanding the characteristics of SPVA under partial shaded conditions with bypass diode, initially, three modules connected in series have been taken. The detailed explanation of the effect of bypass diodes in the characteristics has been discussed by [20]-[21]. Figure 2 shows the electrical characteristics of SPVA with bypass diodes under uniform insolation and partial shaded conditions. Number of peaks in the V-P characteristics is less than or equal to the number of zones receiving different insolation.

Fig. 1: Five Parameter Model of SPV Cell with Bypass Diode

From Fig. 2, it is observed that the V-I characteristic has multiple steps and V-P characteristic has multiple peaks due to partial shading [18]-[19]. Among the multiple peaks one is global peak (GP) and others are local peak power points. In this situation the conventional MPPT algorithm could fail to determine the actual GP or even traps into one of the local peaks. Therefore, considerable amount of possible SPV power is not utilized. Hence the power should be optimized to harvest the maximum power produced by SPVA. 2.2 Objective Function A Nonlinear optimization problem can be stated in mathematical terms as follows: Find X = ( x1 , x 2 , ..... x n ) such that F (X) is minimum or maximum ... (1) Subject to gj (X) ≥ 0, j = 1, 2… m and xjL ≤ xi ≤ xjU, j = 1, 2... n, ... (2)

International Journal of Electrical Engineering and Embedded Systems, 2 (2) July-December 2010

Enhanced Maximum Power Point Tracking using Differential Evolution Algorithm for Partially Shaded Solar Photovoltaic...

Where F is the objective function to be minimized or maximized, xj’s are variables, gj is constraint function, xjL and xUj are the lower and upper bounds on the variables. In this work the objective function considered is F (X) = Maximization of SPVA power, PPV. The variable xi = SPVA current, IPV. The constraint is IPVmax ≥ IPV ≥ IPVmin. Here, xjU = IPVmax = Isc, short circuit current of SPVA and xjL = IPVmin = 0. 3. OVERVIEW OF DIFFERENTIAL EVOLUTION ALGORITHM DE algorithm is a population based algorithm like genetic algorithms using crossover, mutation and selection operators. DE uses the differences of randomly sampled pairs of object vectors to guide the mutation operation instead of using the probability distribution function as other evolutionary algorithms. DE based optimization process is described below [21]: 3.1 Initialization DE starts with a population of NP M-dimensional search variable vectors. The i th vector of the population at the current generation is given by  X i (t ) =  xi , 1 (t ), xi , 2 (t ), xi , 3 (t ) .......... xi , M (t ) 

... (3) There is a feasible numerical range for each searchvariable, within which value of the parameter should lie for better search results. Initially the problem parameters or independent variables are initialized in their feasible numerical range. If the j th parameter of the given problem has its lower and upper bound as xLj and xUj respectively, then the j th component of the i th population members is initialized as xi , j (0) = x Lj + rand (0, 1) ⋅ ( xUj − x Lj )

3.2 Mutation

... (4)

 In each iteration, to change the population member X i (t ),   a Donor vector Vi (t ) is created. To Vi (t ) create for each i th member, three other parameter vectors (r1, r2, r3 vectors) are selected in random fashion from the current population. A scalar number F scales the difference of any two of the three vectors and the scaled difference is

 added to the third one to obtain the donor vector Vi (t ) . The mutation process for j th component of each vector is expressed by equation.

vi , j (t + 1) = xr1, j (t ) + F ⋅ ( xr 2, j (t ) − xr 3, j (t )) ... (5)

The method of creating donor vector demarcates between various DE schemes. Price and storn have suggested ten different mutation strategies. The above mutation strategy is referred as DE/rand/1. This scheme  uses a randomly selected vector X r1 and only one   weighted difference vector F ⋅ ( X r 2 − X r 3 ) is used to perturb it. In this work mutation strategy DE/best/1 is used. In this scheme the vector to be perturbed is the best vector of the current population and the perturbation is caused by single difference vector. vi , j (t + 1) = xbest (t ) + F ⋅ ( xr1, j (t ) − xr 2, j (t )) ... (6)

3.3 Crossover To increase the potential diversity of the population a crossover operator is used. DE uses two kinds of cross over schemes namely “Exponential” and “Binomial”. In this work binomial crossover is used. In this crossover scheme, the crossover is performed on each of the D variables whenever a randomly picked number between 0 and 1 is within the crossover (CR) value. The scheme may be outlined as ui , j (t ) = vi , j (t )

if (rand (0, 1))  CR

... (7)

xi , j (t ) else

 In this way for each trial vector X i (t ) an offspring  vector U i (t ) is created. 3.4 Selection Selection operator is used to determine which one of the target vector and the trial vector will survive in the next generation. DE involves the Darwinian principle of “Survival of the fittest” in its selection process. The selection process may be outlined as     X i (t + 1) = U i (t ) if f (U i (t )) ≤ f ( X i (t )) ... (8)    = X i (t ) if f ( X i (t )  f (U i (t ))

Where f is the function to be minimized. If the new trial vector yields a better value of the fitness function, it

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replaces its target in the next generation; otherwise the target vector is retained in the population. 4. APPLICATION OF DIFFERENTIAL EVOLUTION TO OPTIMIZE POWER FOR SPVA UNDER PARTIAL SHADED CONDITION In this work, the DE is used to find SPVA current which ensure that the function F (X) has a maximum value (Eq. (1)). The procedure to get the optimum power of SPVA under partial shaded condition is given below. The algorithm for design optimization process is given below: Step 1: Initialize DE parameters like M, CR, NP, F and Genmax.

color) with that of the binary search method (marked in red color). In all the cases, DE gives the optimum power (global peak) which is matched with the result of binary search. The comparison between DE and binary search for different shading scenarios are tabulated in Table 2. It is observed that the error did not exceed 2%. Table 1 Differential Evolution Parameters Number of Design Variables M

1

Population Size NP

20

Crossover constant, CR

0.7

Scaling Factor for Mutation F

0.8

Maximum Generations Genmax

20

Step 2: Randomly generate initial population. Step 3: Evaluate the population by objective function (1) and determine best fit vector. Step 4: For every vector in the population find the vector difference of two randomly selected vectors and mutate with the best vector of the current population to obtain donor vector using Eq. (6). Step 5: Obtain the trial vector based on preset crossover constant using (7). Step 6: For the entire population, evaluate the objective function value of trial vector and create a new population by selecting the target or trial vector based on the value of objective function. Step 7: Test convergence. If satisfied then stop else go to Step 3. The DE parameters used in this work are given in Table 1. The DE code has been written in M-file. Figure 3 plots the convergence of total power computed by DE over the number of iterations for different shading patterns. Initial population is randomly initialized. Therefore, the initial power is always high. This initial power corresponds to the 0 th iteration. As the algorithm progresses, the convergence is drastic and it finds a global maxima very quickly. The number of iterations needed for the convergence is seen to be 5 – 10, for this application environment. Figure 4 presents the simulation results of SPVA consists of three modules in series for four set of different shading patterns. The performance of the DE is validated graphically by comparing its output (marked in green 162

Fig. 3: The Trend of Convergence of DE with the Number of Iterations for Different Shading Patterns Table 2 Comparison between DE and Binary Search Method Insolation (W/m2) Methods for finding Global Peak G1 G2 G3 Parameters Binary search DE method

1000 1000 1000

Pm Im Vm

111.3 2.26 49.23

111.8 2.26 49.47

1000 1000 800

Pm Im Vm

97.54 1.91 51.07

97.83 1.9 51.49

1000 800

800

Pm Im Vm

92.78 1.85 50.15

93.43 1.85 50.50

1000 1000 200

Pm Im Vm

74.17 2.26 32.82

74.5 2.26 32.96

International Journal of Electrical Engineering and Embedded Systems, 2 (2) July-December 2010

Enhanced Maximum Power Point Tracking using Differential Evolution Algorithm for Partially Shaded Solar Photovoltaic...

Fig. 4: Validation of DE for GP Tracking of Partial Shaded SPVA

5. CONCLUSION Since the efficiency of the solar panel is only 13%, it is necessary to operate it at its maximum power point. If the solar panel operates at a point other than the point where it delivers maximum power, the power loss can be as high as about 70%. Hence it is necessary to the track the GP under partial shaded conditions. In this paper, the differential evolution technique is used to track the GP under partial shaded conditions. Characteristics of the SPV have been presented for developing the accurate model of SPV. It is proved that the DE tracks the GP when multiple peaks exist in the V-P characteristics using MATLAB software. The tracking implemented here is purely electrical tracking. The SPV module may be fully utilized throughout the day by implementing both electrical and mechanical tracking but mechanical tracking is more complicated, not cost effective and requires maintenance which will overcome the advantage of using SPV system. Even by proper selection of array configuration maximum power can be tracked from the array. The tracking time can be minimized by using intelligent controllers and FPGA processors.

ACKNOWLEDGEMENT The authors wish to thank the management of SSN College of Engineering, Chennai for providing all the experimental and computational facilities to carry out this work. REFERENCES [1] K.H. Hussein and I. Muta, “Maximum Photovoltaic Power Tracking: An Algorithm for Rapidly Changing Atmospheric Conditions”, Proc. Inst. Electr.Eng.-Generation, Transmission Distribution, 142 (1), pp. 59 – 64. [2] C. Hua, J. Lin, and C. Chen, “Implementation of a DSPcontrolled Photovoltaic System with Peak Power Tracking”, IEEE Trans. Ind. Electron., 45 (1), pp. 99 – 107, Feb. 1998. [3] N. Kasa, T. Iida, and H. Iwamoto, “Maximum Power Point Tracking with Capacitor Identifier for Photovoltaic Power System”, Proc. Inst. Electr. Eng.-Electr. Power Appl., 147 (6), pp. 497 – 502, Nov. 2000. [4] M. Veerachary, T. Senjyu, and K. Uezato, “Maximum Power Point Tracking Control of IDB Converter Supplied PV System”, Proc. Inst.Electr. Eng.-Electr. Power Appl., 148 (6), pp. 494 – 502, Nov. 2001.

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R. Ramaprabha and Badrilal Mathur [5] T. Noguchi, S. Togashi, and R. Nakamoto, “Short-current Pulse-based Maximum-power-point Tracking Method for Multiple Photovoltaic and Converter Module System”, IEEE Trans. Ind. Electron., 49 (1), pp. 217 – 223, Feb. 2002.

[14] E.V. Solodovnik, S. Liu, and R.A. Dougal, “Power Controller Design for Maximum Power Tracking in Solar Installations”, IEEE Trans. Power Electron., 19 (5), pp. 1295 – 1304, Sep. 2004.

[6] N. Fernia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optimization of Perturb and Observe Maximum Power Point Tracking Method”, IEEE Trans.Power Electron., 20 (4), pp. 963 – 973, Jul. 2005.

[15] K. Kobayashi, I. Takano, and Y. Sawada, “A Study of a two Stage Maximum Power Point Tracking Control of a Photovoltaic System Under Partially Shaded Insolation Conditions”, Sol. Energy Mater. Sol. Cells, 90 (18/19), pp. 2975 – 2988, Nov. 2006.

[7] C. Dorofte, U. Borup, and F. Blaabjerg, “A Combined Twomethod MPPT Control Scheme for Grid-connected Photovoltaic Systems”, in Proc. Eur. Conf. Power Electron. Appl., Sep. 11 – 14, 2005, pp. 1 – 10. [8] N. Kasa, T. Iida, and L. Chen, “Flyback Inverter Controlled by Sensorless Current MPPT for Photovoltaic Power System”, IEEE Trans. Ind. Electron., 52 (4), pp. 1145 – 1152, Aug. 2005. [9] D. Sera, T. Kerekes, R. Teodorescu, and F. Blaabjerg, “Improved MPPT Method for Rapidly Changing Environmental Conditions”, in Proc. IEEE Int. Ind. Electron. Symp., Jul. 2006, 2, pp. 1420 – 1425. [10] V. Salas, E. Olias, A. Barrado, and A. Lazaro, “Review of the Maximum Power Point Tracking Algorithms for Stand-alone Photovoltaic Systems”, Sol. Energy Mater. Sol. Cells, 90 (11), pp. 1555 – 1578, Jul. 2006. [11] T. Esram, J.W. Kimball, P.T. Krein, P.L. Chapman, and P. Midya, “Dynamic Maximum Power Point Tracking of Photovoltaic Arrays using Ripple Correlation Control”, IEEE Trans. Power Electron., 21 (5), pp. 1282 – 1291, Sep. 2006. [12] W. Xiao, N. Ozog, and W.G. Dunford, “Topology Study of Photovoltaic Interface for Maximum Power Point Tracking”, IEEE Trans. Ind. Electron., 54 (3), pp. 1696 – 1704, Jun. 2007. [13] M. Miyatake, T. Inada, I. Hiratsuka, H. Zhao, H. Otsuka, and M. Nakano, “Control Characteristics of a Fibonacci-searchbased Maximum Power Point Tracker when a Photovoltaic Array is Partially Shaded”, in Proc. IEEEIPEMC, 2004, 2, pp. 816 – 821.

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[16] K. Price, R. Storn and J. Lampinen, “Differential Evolution — A Practical Approach to Global Optimization”, Springer, 2005, Berlin Heidelberg New York. [17] R. Ramaprabha and B.L. Mathur, “MATLAB Based Modelling to Study the Influence of Shading on Series Connected SPVA”, Second International Conference on Emerging Trends in Engineering and Technology, ICETET-09 , Dec. 2009, pp. 30 – 34. [18] H. Patel and V. Agarwal, “MATLAB-Based Modeling to Study the Effects of Partial Shading on PV Array”, IEEE Transactions on Energy Conversion, 23 (1), March 2008, pp. 302 – 310. [19] H. Patel and V. Agarwal, “Maximum Power Point Tracking Scheme for PV Systems Operating Under Partially Shaded Conditions”, IEEE Transactions on Industrial Electronics, 55 (4), April 2008 pp. 1689 – 1698. [20] R. Ramaprabha and B.L. Mathur (June 2008). “Modelling and Simulation of Solar PV Array Under Partial Shaded Conditions”. ICSET 2008. 7 – 11. Retrieved on May 6, 2009, from IEEExplore. [21] S. Silvestre, A. Boronat and A. Chouder, “Study of Bypass Diodes Configuration on PV Modules”, Applied Energy, 86, 2009, pp. 1632 – 1640. [22] www.mathworks.com.

International Journal of Electrical Engineering and Embedded Systems, 2 (2) July-December 2010