A Particle Swarm Optimization-Based Maximum Power Point Tracking Algorithm PV Operating Under Partially Shaded Conditions

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 4, DECEMBER 2012

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A Particle Swarm Optimization-Based Maximum Power Point Tracking Algorithm for PV Systems Operating Under Partially Shaded Conditions Yi-Hwa Liu, Member, IEEE, Shyh-Ching Huang, Jia-Wei Huang, and Wen-Cheng Liang

Abstract—A photovoltaic (PV) generation system (PGS) is becoming increasingly important as renewable energy sources due to its advantages such as absence of fuel cost, low maintenance requirement, and environmental friendliness. For large PGS, the probability for partially shaded condition (PSC) to occur is also high. Under PSC, the P–V curve of PGS exhibits multiple peaks, which reduces the effectiveness of conventional maximum power point tracking (MPPT) methods. In this paper, a particle swarm optimization (PSO)-based MPPT algorithm for PGS operating under PSC is proposed. The standard version of PSO is modified to meet the practical consideration of PGS operating under PSC. The problem formulation, design procedure, and parameter setting method which takes the hardware limitation into account are described and explained in detail. The proposed method boasts the advantages such as easy to implement, system-independent, and high tracking efficiency. To validate the correctness of the proposed method, simulation, and experimental results of a 500-W PGS will also be provided to demonstrate the effectiveness of the proposed technique. Index Terms—Maximum power point tracking (MPPT), partially shaded condition (PSC), particle swarm optimization (PSO), photovoltaic (PV) generation system (PGS).

I. INTRODUCTION HE ever-increasing world energy demand and growing concern about environmental issues have generated enormous interest in the utilization of renewable energy sources. Among them, the photovoltaic (PV) generation system (PGS) is an established technology and has rapid growth in recent years. The advantages of PGS include absence of fuel cost, low maintenance requirement, and environmental friendliness. However, due to the high investment cost on the PGS, it is vital to make the most of the available solar energy [1]–[5]. A major challenge in using a PGS is to tackle its nonlinear current–voltage (I–V) characteristics, which result in a unique maximum power point (MPP) on its power–voltage (P–V) curve. Since the power

T

Manuscript received May 3, 2012; revised August 10, 2012; accepted September 5, 2012. Date of publication September 29, 2012; date of current version November 16, 2012. This work was supported by the National Science Council of Taiwan and Taiwan Power Company under contract NSC 100-3113-p-110-004. Paper no. TEC-00185-2012 The authors are with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan (e-mail: [email protected]; [email protected]; d9707203@mail. ntust.edu.tw; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEC.2012.2219533

generated from a given PV module mainly depends on solar insolation and panel temperature. As these quantities vary with time, it is essential to develop a maximum power point tracking (MPPT) algorithm to extract maximum power from the PV module at real time. Over the past decades, many MPPT algorithms have been proposed. These methods include perturb and observe (P&O), incremental conductance, short-circuit current, open-circuit voltage, fuzzy logic control, and ripple correlation approaches. Some modified techniques which aim to minimize the hardware requirement or to improve the performance have also been proposed. These methods mentioned earlier are effective and time tested under uniform solar insolation [6]–[8]. In the PGS, multiple PV modules are generally interconnected in series and/or parallel to create a system with the desired voltage and loading current capacity. Therefore, partially shaded condition (PSC) is sometimes inevitable because some parts of the module or the PGS may receive less intensity of sunlight due to clouds or shadows of trees, buildings, and other neighboring objects. PSC can have a significant impact on the power output of PGS, depending on the system configuration, shading pattern, and the bypass diodes incorporated in the PV modules. The effect of PSC on PGS has been analyzed in several publications. Under PSC, PV modules belonging to the same string experience different insolation. The resulting P–V characteristic curve becomes more complex and exhibits multiple peaks [9]–[11]. The presence of multiple peaks reduces the effectiveness of the conventional MPPT algorithms, which assumes a single MPP on the P–V curve. The reason is that these methods are based on the “hill-climbing” principle of moving the next operating point (OP) in the direction in which power increases. If the P–V curve is not unimodal, these methods may only reach a local MPP. Since the occurrence of PSC being quite common, there is a need to develop a suitable MPPT algorithm that can track the global maximum power point (GMPP) under these conditions. Some researchers have worked on GMPP tracking schemes for PGS operating under PSC [12]–[26]. In [12], a new MPPT technique which is able to operate under PSC is presented. To find the GMPP, the voltage factors of all the MPPs have to be previously assessed once. Therefore, the proposed method is system dependent. Kobayashi et al. [13] and Ji et al. [14] propose a two-stage method to track the GMPP. In the first stage, the OP of the PGS is moved to the vicinity of the GMPP using the load line, and in the second stage, it converges to the GMPP. However, these methods cannot obtain the GMPP if the GMPP lies on the left side of the load line. Line search algorithms are utilized in [15] and [16] to find the

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GMPP. These methods compare the values of measured power at two OPs and then determine the OP movement. These techniques are similar to the P&O method with variable step size; the only difference here is that the step size is determined by the Fibonacci sequence in [15], and by the dividing rectangles (DIRECT) in [16]. These approaches too cannot guarantee to find the GMPP under all conditions. Patel and Agarwal [17] and Renaudineau et al. [18] also propose two-stage methods to track the GMPP. In [17], a global stage is used to find the regions of local MPPs, while the local stage employs P&O to locate the GMPP. In [18], a “scanning process” is first utilized to detect the regions which contain the GMPP. After the scanning process, a P&O algorithm with variable step is used to find the GMPP. The tracking speeds of these methods are limited because almost all local MPPs should be found and compared to obtain the GMPP. Lei et al. [19] propose a sequential extremum seeking control (ESC)-based MPPT algorithm which is based on approximate modeling and analysis for the characteristics of PV modules under variable PSCs. The proposed MPPT algorithm is based on segmental search with consistent definition of searching range, which can achieve better computational efficiency than sweeping search. However, this method possesses steady-state errors and is system dependent. In [20], a novel MPPT algorithm is proposed using artificial neural network (ANN) and fuzzy logic with polar information controller. The ANN with three layer feed-forward is trained once for several PSCs to determine the GMPP voltage; therefore, it is system dependent. Moreover, this method uses insolation and temperature as inputs to obtain GMPP, while these information are often not available in PGS. Another option to deal with PSC is to use intelligent PV modules or alternating current modules [21]–[23]. In [21], a distributed MPPT for PGS is proposed and analyzed. A switching converter dedicated to each module and performing the MPPT is used. In [22], several PV modules with each coupled to its own dc–dc boost converter are cascaded on the same dc bus and interfaced to the grid by means of a dc–ac inverter. Each PV generator is equipped with a second control law aiming at limiting the converter’s output voltage. In these configurations, each PV module is treated as one unit that tracks its own MPP; therefore, the PGS can always track the GMPP. However, these methods incur extra hardware and cost. Moreover, a good MPPT algorithm should also be implemented in each unit to track the MPP when a module is shaded. Gao et al. [23] propose a PV system which adopts the parallel configuration at the individual cell level so that every cell in the PV module can achieve its MPP under PSC. Since the input voltage of this configuration is very low, this may increase the difficulty of designing an appropriate power converter. Moreover, the proposed configuration is only suitable for low power applications. Chen et al. [24] present a novel MPPT method based on biological swarm chasing behavior to increase the MPPT performance. This method is only applicable when the entire module is under uniform insolation conditions, hence PSC is not considered. In [25], an adaptive perceptive particle swarm optimization (APPSO)-based MPPT algorithm is presented. Also, Miyatake et al. [26] attempted to approach the GMPP using the particle swarm optimization (PSO) algorithm. In these investigations, the authors try to re-

Fig. 1.

Equivalent circuit of the PV cell.

alize centralized MPPT control of the modular (multimodule) PGS. These MPPT algorithms have good performance under various PSC; however, these methods are only suitable for systems that consist of multiple converters. However, for PGS, the use of one central high-power single-stage electronic converter is very common for economical reasons and the relative simplicity of the overall system. Ishaque et al. [27] present an improved PSO-based MPPT algorithms for PGS, the advantages of using PSO in conjunction with the direct duty cycle control are discussed in detail. However, no system design guidelines and practical design considerations are provided in these papers. This paper aims to develop an accurate and systemindependent MPPT algorithm for centralized-type PGS operating under PSC. The PSO method has been successfully employed to solve different engineering optimization problems [28]–[33]. According to these investigations, the PSO method is a simple and effective metaheuristic approach that can be applied to optimization problems having many local optimal points. Consequently, it will be adopted in this paper to realize the MPPT algorithm which is suitable for centralized PGS under PSC. In this paper, the standard version of PSO will be modified to meet the practical consideration of PGS under PSC. Detailed design procedures which take the hardware limitation into account will be presented first, and a 500-W prototype will be implemented to demonstrate the validity of the proposed MPPT algorithm. Experimental results show that the proposed MPPT technique can obtain the GMPP in all the test cases no matter where the GMPP locates. The tracking efficiencies in all test cases are higher than 99.5%. The proposed MPPT algorithm is simple, accurate and system independent, and can be realized using a low cost digital signal controller (DSC). II. CHARACTERISTICS OF THE PGS UNDER PSC A. Basic Characteristics of a PV Cell A PV cell can be represented by an electrical equivalent onediode model as shown in Fig. 1. This model contains a current source Ig , a diode D, and a series resistance RS , which represents the resistance inside each cell and in the connection between the cells. The net current IPV is the difference between the photocurrent Ig and the diode current ID : q(Vpv + Ipv · RS ) Ipv = Ig − IS exp −1 (1) nkT where n is the diode ideality factor, k is Boltzmann’s constant, q is the electron charge, T is the temperature in Kelvin, RS is

LIU et al.: PARTICLE SWARM OPTIMIZATION-BASED MAXIMUM POWER POINT TRACKING ALGORITHM

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III. OVERVIEW OF THE PSO ALGORITHM PSO is a swarm intelligence optimization algorithm developed by Eberhart and Kennedy in 1995, which is inspired by the social behavior of bird flocking and fish schooling. PSO is a global optimization algorithm for dealing with problems on which a point or surface in an n-dimensional space represents a best solution. In this algorithm, several cooperative agents are used, and each agent exchanges information obtained in its respective search process. Each agent, referred to as a particle, follows two very simple rules, i.e., to follow the best performing particle, and to move toward the best conditions found by the particle itself. By this way, each particle ultimately evolves to an optimal or close to optimal solution. The standard PSO method can be defined using the following equations [34]: Fig. 2. curve.

“3s2p” system under three different PSCs. (a) I–V curve. (b) P–V

vi (k + 1) = wvi (k) + c1 r1 · (pb est,i − xi (k)) + c2 r2 · (gb est − xi (k)) xi (k + 1) = xi (k) + vi (k + 1)

(2) (3)

i = 1, 2, . . . , N

Fig. 3. I–V and P–V curves of the “3s2p” system shown in Fig. 2. (a) I–V curve. (b) P–V curve.

the equivalent series resistance, and Is is the saturation current, respectively. B. Effect of PSC on PGS A PV module consists of several PV cells connected in parallel to increase current and in series to produce a higher voltage. Several PV modules are then connected in series/parallel to form a PGS. Under PSC, the P–V curve of PV module will display multiple MPPs because of the bypass diodes. The characteristics of a PV module under PSC with bypass diodes connected at module terminal can be explained as follows. Under PSC, the shaded cells behave as a load instead of a generator and create the hot spot. Therefore, bypass diodes of these shaded cells will conduct to avoid this problem. Since the shaded cells are bypassed, multiple peaks in the P–V curve will be presented. As an example, a simple PV module with six cells organized in three serial groups of two parallel cells as shown in Fig. 2 is considered. This configuration is named “3s2p” connection. When this system is under different shading patterns as shown in Fig. 2, the resulting I–V curves are shown in Fig. 3(a). These characteristic curves can then be utilized to obtain the P–V characteristic curves as shown in Fig. 3(b). From Fig. 3, it can be observed that the GMPP can occur in either the lower or higher voltage range, depending on the type of shading pattern. This phenomenon makes it difficult to directly apply the conventional MPPT algorithms.

where xi is the position of particle i; vi is the velocity of particle i; k denotes the iteration number; w is the inertia weight; r1 and r2 are random variables uniformly distributed within [0,1]; and c1 , c2 are the cognitive and social coefficient, respectively. The variable pb est,i is used to store the best position that the ith particle has found so far, and gb est is used to store the best position of all the particles. The flowchart of a basic PSO algorithm is illustrated in Fig. 4. From Fig. 4, the operating principles of a basic PSO method can be described as follows: Step 1 (PSO Initialization): Particles are usually initialized randomly following a uniform distribution over the search space, or are initialized on grid nodes that cover the search space with equidistant points. Initial velocities are taken randomly. Step 2 (Fitness Evaluation):Evaluate the fitness value of each particle. Fitness evaluation is conducted by supplying the candidate solution to the objective function. Step 3 (Update Individual and Global Best Data): Individual and global best fitness values (pb est,i and gb est ) and positions are updated by comparing the newly calculated fitness values against the previous ones, and replacing the pb est,i and gb est as well as their corresponding positions as necessary. Step 4 (Update Velocity and Position of Each Particl)e: The velocity and position of each particle in the swarm are updated using (1) and (2). Step 5 (Convergence Determination): Check the convergence criterion. If the convergence criterion is met, the process can be terminated; otherwise, the iteration number will increase by 1 and goto step 2.

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Fig. 5.

Fig. 4.

Flowchart of a standard PSO [34].

IV. APPLICATION OF PSO TO MPPT The PSO method described in Section III is now applied to realize the MPPT algorithm for PGS operating under PSC, wherein the P–V curve exhibits multiple local MPPs. Due to the uniqueness of this problem, the standard version of PSO will be modified to meet the practical consideration of PGS under PSC. Detailed design procedures which take the hardware limitation into account will be presented in the following. Fig. 5 depicts the block diagram of the proposed system. From Fig. 5, the presented system consists of a series-connected PV module, a dc–dc converter and a digital controller in which the proposed MPPT algorithm is implemented. In this paper, a simple boost converter is used to interface the voltage from the PV mod-

Block diagram of the proposed system.

ule to the load. The implementation of this part of circuit is conventional, therefore, will not be discussed further here. Fig. 6 shows the flowchart of the proposed PSO-based MPPT technique. In Fig. 6, the steps which are different from the standard PSO will be marked in different colors. From Fig. 6, the main blocks are described in detail in the following: Step 1 (Parameter Selection): In the proposed system, the particle position is defined as the duty cycle value d of the dc–dc converter, and the fitness value evaluation function is chosen as the generated power PPV of the whole PGS. From the algorithm point of view, a larger number of particles result in more accurate MPP tracking even under complicated shading patterns. However, a larger number of particles also lead to longer computation time. Therefore, a tradeoff should be made to ensure good tracking speed and accuracy. According to the literature, there exist at most m MPPs in the P–V curve for PV modules consist m series connected PV cells [9]. Consequently, the particle number N is chosen as the number of the series connected cells in the PGS. Step 2 (PSO Initialization): In PSO initialization phase, particles can be placed on fixed position or be placed in the space randomly. Basically, if there is information available regarding the location of the GMPP in the search space, it makes more sense to initialize the particles around it. According to [17], the peaks on the P–V curve occur nearly at multiples of 80% of the module open voltage VOC m o dule , and the minimum displacement between successive peaks is also nearly 80% of VOC m o dule . Therefore, the particles are initialized on fixed positions which cover the search space [Dm in , Dm ax ] with equal distances in this paper. Dm ax and Dm in are the maximum and minimum duty cycle of the utilized dc-dc converter, respectively. Step 3 (Fitness Evaluation): The goal of the proposed MPPT algorithm is to maximize the generated power PPV . After the digital controller output, the PWM command according to the position of particle i (which represents the duty cycle command), the PV voltage


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VPV and current IPV can be measured and filtered using digital finite impulse response filters. These values can then be utilized to calculate the fitness value PPV of particle i. It should be noted that in order to acquire correct samples, the time interval between successive particle evaluations has to be greater than the power converter’s settling time. Step 4 (Update Individual and Global Best Data): If the fitness value of particle i is better than the best fitness value in history pb est,i , set current value as the new pb est,i . Then, choose the particle with the best fitness value of all the particles as the gb est . This step is similar to step 3 of the standard PSO method. Step 5 (Update Velocity and Position of Each Particle): After all the particles are evaluated, the velocity and position of each particle in the swarm should be updated. In conventional PSO method, the update is performed using (1) and (2), in which the parameters w, c1 , and c2 are constants. In this paper, the parameters w, c1 , and c2 are set as variables to speed up the convergence. Therefore, (1) can be rewritten as vi (k + 1) = w(k)vi (k) + c1 (k)r1 (pb est,i − xi (k)) + c2 (k)r2 (gb est − xi (k)).

(4)

In (3), the first term w(k)vi (k) is utilized to keep the particle moving in the same direction it was originally heading; therefore, it controls the convergence behavior of PSO. To accelerate convergence, the inertia weight shall be selected such that the effect of vi (k) fades during the execution of the algorithm. Thus, a decreasing value of w with time is preferable. A very common choice is to initially set the inertia weight to a larger value for better exploration and gradually reduce it to get refined solutions. In this paper, a linearly decreasing scheme for w is used, as shown in (4) [35] w(k) = wm ax −

k (wm ax − wm in ) kM AX

(5)

In (4), wm in and wm ax are the lower and upper bounds of w, and kM AX is the maximum allowed number of iterations. Similarly, the cognitive and social parameters can be modified. In (3), the values of c1 and c2 can affect the search ability of PSO by biasing the direction of a particle. Choosing c1 > c2 would bias sampling toward the direction of pb est , i, while in the opposite case, c1 < c2 , sampling toward the direction of gb est would be favored. In this paper, these two parameters are defined as linearly decreasing and linearly increasing functions, respectively. c1 (k) = c1,m ax − Fig. 6.

Flowchart of the proposed algorithm.

c2 (k) = c2,m in +

k (c1,m ax − c1,m in ) (6) kM AX k kM AX

(c2,m ax − c2,m in ). (7)

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TABLE I PARAMETERS OF THE UTILIZED PV MODULE

TABLE II SPECIFICATIONS OF THE IMPLEMENTED BOOST CONVERTER

TABLE III PARAMETER SETTINGS OF THE IMPLEMENTED ALGORITHM

In (5) and (6), c1,m in , c1,m ax and c2 ,m in , c2,m ax are the lower and upper bounds of c1 and c2 , respectively. It should be noted that due to the stochastic nature of PSO, the calculated new position x1 (k + 1) may become very far away from the previously outputted position xN (k). Since x(k) represents the duty cycle command of the utilized dc–dc converter, this sudden duty cycle change will result in very large voltage stress on the power switch. One method to deal with this condition is to sort the obtained particle positions according to the last outputted duty cycle command in advance, and output the nearest particle first. This will reduce the voltage stress significantly. Step 6 (Convergence Determination): Two convergence criteria are utilized in this paper. If the velocities of all particles become smaller than a threshold, or if the maximum number of iterations is reached, the proposed MPPT algorithm will stop and output the obtained gb est solution. Step 7 (Reinitialization): Typically PSO method is used to solve problems that the optimal solution is time invariant. However, in this application, the fitness value (global maximum available power) often changes with environments as well as loading conditions. In such cases, the particles must be reinitialized to search for the new GMPP again. In this paper, the following constraint is utilized to detect the insolation change and shading pattern changes. The proposed PSO algorithm will reinitialize the particles whenever the following condition as shown in (7) is satisfied: |PPV ,new − PPV ,last | ≥ ΔP (%). PPV ,last

(8)

V. SIMULATION AND EXPERIMENTAL RESULTS To verify the correctness of the proposed MPPT method, a 500-W prototyping circuit is implemented from which simulations and experiments are carried out accordingly. The parameters of the utilized PV module are listed in Table I. The specifications of the implemented boost converter are listed in Table II. In this paper, the simulations are made using MATLAB. According to the design guideline illustrated in Section IV, the parameter settings of the implemented PSO-based MPPT algorithm are listed in Table III. The effect of PSC on PV module characteristic curves is simulated by arbitrary set the insolation of the series connected PV cells. In our simulation, cell temperature is assumed to be constant at 25 ◦ C. Unshaded cells are con-

TABLE IV SIMULATION RESULTS OF THE TWO PSO-BASED MPPT ALGORITHM

sidered fully illuminated at 1000 W/m2 . Insolation on shaded cells is considered uniform and varies from 0 to 1000 W/m2 with a step of 100 W/m2 . In order to verify the effectiveness of the proposed algorithm, the Monte Carlo method is adopted in this paper [36]. Two PSO-based MPPT algorithms are tested for 1000 different shading patterns and the simulation results are presented in Table IV. In Table IV, the method denoted as variable-PSO represents the proposed method, and the method named constant-PSO utilizes the following parameter: w = 1.0, c1 = 2, and c2 = 2, which remains constant in the whole MPPT process. In Table IV, the tracking efficiency η is defined as η=

PO × 100% PM AX

(9)

where PO is the averaged output power obtained under steady state and PM AX is the maximum available power of the PV module under certain shading pattern. From Table IV, the proposed method requires lesser iteration to converge, and the averaged tracking efficiency is higher. A prototyping circuit using the parameters shown in Tables I and II is also constructed. In the prototyping system, the PSO-based MPPT algorithm is realized using the low-cost DSC dsPIC33FJ16GS502 from Microchip Corporation. The execution time of the whole procedure is less than 80 μs when the CPU speed is set as 40 MIPS. The implemented algorithm allocates 5.632 kB (35%) of program memory. The proposed algorithm is validated using the Chroma 62150 H-600 S Solar Array Simulator in SAS mode [37]. Using the “SHADOW I-V CURVE SIMULATION” function, the user is able to program various I–V curves which can be used to verify the MPPT capability of the proposed algorithm. Three different patterns are used to test the correctness of the proposed method; experimental results of these shading patterns are shown in Fig. 7 through Fig. 13. Fig. 7 shows the I–V and P–V curves of the shading pattern 1. In Fig. 7, the measured MPPT tracking efficiency is 99.6%. Fig. 8 shows


Fig. 7.

Fig. 8.

Fig. 9.

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I–V and P–V curves of shading pattern 1 (GMPP at right). Fig. 10.

I–V and P–V curves of shading pattern 2 (GMPP at middle).

Fig. 11.

Measured waveforms of shading pattern 2.

Fig. 12.

I–V and P–V curves of shading pattern 3 (GMPP at left).


Zoomed version of Fig. 8.

the measured waveforms of the shading pattern 1. From Fig. 8, the proposed MPPT algorithm converges after eight iterations. Fig. 9 shows the zoomed version of the first six iterations of Fig. 8. From Fig. 9, the standard deviation of the found solution decreases steadily; therefore, the proposed algorithm can obtain a converged solution. Fig. 9 also shows that after the sorting process, the first particle V1 of the nth iteration is always closet to the last particle V5 of the (n − 1)th iteration. Similarly, Figs. 10 and 12 show the characteristic curves of shading pattern 2 and 3, and Figs. 11 and 13 show the measured waveforms of shading pattern 2 and 3, respectively. From these experimental results, the proposed method can successfully deal with PSCs no matter where the GMPP locates. Figs. 14 and 15 show the dynamic tracking capability of the proposed algorithm. Fig. 14 shows the changing sequence of the test shading patterns. In Fig. 14, the utilized three shading patterns are the same as those in Figs. 7, 10 and 12. In Fig. 14, each shading pattern lasts 25 s. Fig. 15 shows the measured waveforms for the dynamic tracking test. From Fig. 15, the proposed algorithm can successfully detect the

shading pattern changes and reinitialize the MPPT process accordingly. Due to limited space, more test results are presented at https://sites.google.com/site/pvtestrecord/pvtest_record, in which the test results are recorded as video files. To compare the performance of the proposed method with other MPPT techniques, the methods proposed in [16] and [17] are also implemented. The convergence criteria (Δdcr in [16] and perturbation step in [17]) for all the three methods are all set as 0.3%. The simulations and experiments are conducted with the same shading patterns as shown in Figs. 7, 10 and 12. Table V summarizes the obtained results. From Table V, all these algorithms can successfully track the GMPP with similar MPPT tracking efficiency. Comparing to the method proposed in [17], the proposed algorithm requires fewer search steps. Although the required iteration number of the proposed method is higher than [16], only the proposed method can successfully obtain the GMPP in all the 1000 simulation cases.

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Fig. 13.



are also utilized to experimentally validate the correctness of the proposed system. According to the experimental results, the proposed method can obtain the GMPP in all the test cases no matter where the GMPP locates. Experimental results also show that the proposed method can successfully detect the shading pattern changes and reinitialize the MPPT process. The tracking efficiencies in five test cases are all higher than 99.5%. The proposed technique boasts the following advantages: 1) Comparing to other GMPP searching methods, the tracking efficiency of the PSO-based MPPT algorithm is very high. 2) PSO-based method is a good candidate for MPPT algorithms, as it is easy to implement and converges to the desired solution in a reasonable time. 3) The proposed method requires knowledge only of the number of the series cells; therefore, it is system independent. It is well known that the choice of PSO parameters may have some impact on optimization performance; this aspect will be investigated in the future work. REFERENCES

Fig. 14.

Shading pattern change sequence.

Fig. 15.

Measured waveforms of dynamic tracking tests. TABLE V PERFORMANCE COMPARISON WITH OTHER MPPT METHODS

VI. CONCLUSION AND DISCUSSION The main purpose of this paper is to develop an accurate and system-independent MPPT algorithm for centralized-type PGS operating under PSC. The standard version of PSO is modified to meet the practical consideration of PGS operating under PSC. The problem formulation, design procedure, and parameter setting method which takes the hardware limitation into account are described and explained in detail. According to the simulation results of 1000 test cases, the proposed method can reach the GMPP in less than 27 iterations, and the averaged tracking efficiency is higher than 99.9%. Four different shading patterns

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Yi-Hwa Liu (M’01) received the Ph.D. degree in electrical engineering from National Taiwan University, Taipei, Taiwan, in 1998. He joined the Department of Electrical Engineering, Chang-Gung University, Taoyuan, Taiwan, in 2003. He is currently with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan. His current research interests include the areas of power electronics and battery management.

Shyh-Ching Huang was born in new Taipei, Taiwan, in 1957. He received the B.S. degree in electronic engineering from Chung Yuan University, Taipei, Taiwan, in 1986, and the M.S. degree in electronic engineering from the National Taiwan University of Science and Technology, Taipei, Taiwan, in 2007, and he is currently working toward the Ph.D. degree in the Department of Electrical Engineering, in the same university, where he focuses on switching power supply field. His research interests include power electronics converter design and renewable energy applications.

Jia-Wei Huang was born in Hsinchu, Taiwan, in 1987. He received the Bachelor’s and Ph.D. degrees both in electrical engineering from the National Taiwan University of Science and Technology, Taipei, Taiwan, in 2008 and 2012, respectively. He is currently with the National Taiwan University of Science and Technology. His research interests include photovoltaic system design and maximum power point tracking technology.

Wen-Cheng Liang received the Bachelor’s and Master’s degrees both from the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, in 2009 and 2012, respectively. He is currently with the National Taiwan University of Science and Technology. His current research interest includes photovoltaic system.

A Particle Swarm Optimization-Based Maximum Power Point Tracking Algorithm PV Operating Under Partially Shaded Conditions

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