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MPPT for PV systems based on a dormant PSO algorithm
Electric Power Systems Research 123 (2015) 100–107
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MPPT for PV systems based on a dormant PSO algorithm Jiying Shi, Wen Zhang ∗ , Yongge Zhang, Fei Xue, Ting Yang School of Electrical Engineering and Automation, Tianjin University, Tianjin, China
a r t i c l e
i n f o
Article history: Received 30 September 2014 Received in revised form 28 January 2015 Accepted 3 February 2015 Keywords: Dormant particle swarm optimization (DPSO) Maximum power point tracking (MPPT) Partially shaded conditions Search sequence of particles Voltage spike
a b s t r a c t Since the power–voltage characteristic curve of photovoltaic (PV) arrays has multiple peaks under partially shaded conditions, the conventional maximum power point tracking (MPPT) control methods will fail to work. However, the particle swarm optimization (PSO) algorithm is very suitable to solve the multi-extreme optimization problem. Then this paper proposes a dual-algorithm search method: first, a dormant particle swarm optimization (DPSO) algorithm is activated to search the area of global peak, and then the algorithm will be switched to conventional incremental conductance (INC) algorithm to track the maximum output power of photovoltaic arrays. During the iteration process of DPSO, if particles happen to search repeatedly or sway in a small region, they will be turned into dormant state so as to reduce convergence time and improve efficiency. Due to the elimination of searching repeatedly, the number of particles can be large to strengthen optimization capability. In addition, the optimal number of particles for DPSO is found by analysis and simulation. Furthermore, the searching sequence of particles is optimized to effectively reduce fluctuation of voltage and suppress output voltage spike. Finally, the excellent performance of the proposed model is verified by simulations and experiments. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Solar energy is a very popular source of renewable energy due to several advantages. Photovoltaic (PV) power systems have been widely used in many countries. However, there are many urgent issues to tackle in the application of PV power systems. One of the central problems is how to improve efficiency [1–3]. Since the PV arrays exhibit a nonlinear power–voltage (P–V) characteristic curve which varies with insolation and temperature, how to achieve maximum power point tracking (MPPT) is a very important technology [4,5]. To date, various conventional MPPT schemes have been proposed including hill-climbing (HC) [6–8], perturb and observe (P&O) [9–12], and incremental conductance (INC) [13–16], etc. These methods have simple structures and low equipment requirement, but they cannot handle the partially shaded conditions (PSC) because P–V curve displays multiple peaks with several local peaks and a global peak (GP), which cannot be differentiated by conventional algorithms. However, PSC occur quite commonly due to sun position, clouds, buildings, trees, and so on, so it is necessary to improve these algorithms to track the actual GP. Then several attempts have been suggested by researchers in Ref. [17–20].
∗ Tel.: +86 15122160704. E-mail address: [email protected] (W. Zhang). http://dx.doi.org/10.1016/j.epsr.2015.02.001 0378-7796/© 2015 Elsevier B.V. All rights reserved.
Authors in Ref. [17] have reported an MPPT scheme that uses Fibonacci sequence to track the GP under PSC. However, the method does not guarantee GP tracking under all conditions. Authors in Ref. [18] proposed a two-stage method to track the GP. In the first stage, the region of the GP is detected using the load line, and in the second stage, the operating point converges to the GP. But, this method may fail to track the GP if the GP lies on the left side of the load line. In another work [19], authors proposed a two-stage approach. Despite its effectiveness, the method needs to scan almost 80% of the I–V curve to find the GP, which will lead slow response. In Ref. [20], authors proposed a dividing rectangle (DIRECT) search method, which is based on a Lipschitz condition to find the GP. However, the algorithm is very complex, which will increase the burden of system significantly. The essential issue of MPPT control is an optimization problem which can be achieved by using evolutionary algorithm. PSO algorithm owns the characteristics of parallel processing, good robustness, and high probability of finding global optimal solution. Because of its good performance in multiple-peak function optimization, PSO is very suited for MPPT control of PV system under PSC [21–27]. However, in all of these PSO methods, the searching paths of particles will overlap. Because some particles will go through the path which have been searched by others lying on the same side of GP. This phenomenon of searching repeatedly is very common in above PSO methods, which results in slow convergence speed. Additional, due to the initial positions of particles
J. Shi et al. / Electric Power Systems Research 123 (2015) 100–107
and distribution of local peaks and global peak, some particles will sway or cannot get to the GP under certain conditions. This paper proposes a new dormant particle swarm optimization (DPSO) algorithm, in which the particles searching repeatedly or swaying in a small region will be turned into dormant state. Thus, the speed and efficiency of MPPT will be greatly improved. The DPSO algorithm, together with INC algorithm which aims at tracking the maximum power point precisely, constitutes the dual-algorithm model, which is simple to implement and can achieve MPPT rapidly and accurately under PSC. The remainder of the paper is organized as follows. Section II briefly introduces the conventional PSO (CPSO); Section III describes the proposed DPSO, the optimal number of particles and reasonable searching sequence; While in Section IV and V, the performance of DPSO to track GP is simulated and experimented, respectively; the main conclusions are made in Section VI. 2. Overview of CPSO PSO, as a new swarm intelligence optimization algorithm, firstly proposed by Kennedy and Eberhart in 1995 [28], has been developing rapidly in recent 20 years. It is modeled according to the behavior of bird flocks. Its advantages are simple realization and fast convergence, and it is well applied to find the global optimal solution in a nonlinear, discontinuous, nondifferentiable curve [29]. In this algorithm, several cooperative particles are used in an ndimensional space. Each particle owns its position pi (distributed randomly) and velocity vi (vi = 0 in initiation). The position of a particle is influenced by its best position so far, Pbesti , and the best position of all particles so far, Gbest . Velocity and position of particles are calculated by
vk+1 = ωvki + c1 r1 (Pbesti − pki ) + c2 r2 (Gbest − pki ) i
(1)
pk+1 = pki + vk+1 i i
(2)
where i = 1,2,. . ., Np , Np is the number of particles, ω is the inertia weight, c1 and c2 are the acceleration coefficients, r1 , r2 are random variables uniformly distributed within [0,1], k is iteration number. This paper has analyzed and improved the structure and parameters of CPSO to make it more practical and effective. Random numbers in equation (1) mainly help to ensure the capacity to search any potential local peaks; however, they are not necessary in MPPT control based on simple P–V curve. Moreover, two potential problems can be observed when simulating [30]. First, if the random number is small with the present information of control variable (duty cycle is adopted in this paper), only a small change in the velocity term of the PSO equation is obtained, which will result in more iterations needed by CPSO. Second, if the random number is close to 1 when the power values of local peaks and GP are similar, CPSO may escape from the GP. To handle these drawbacks, the random numbers are removed and velocity factor is limited to a certain value Vmax , which is set according to the distance between two peaks. Therefore, the iteration formulas of CPSO can be rewritten as
vk+1 = ωvki + c1 (Pbesti − pki ) + c2 (Gbest − pki ) i
(3)
pk+1 i
(4)
=
pki
+ vk+1 i
where vk+1 ≤ Vmax . i
3. Application of DPSO 3.1. DPSO Initially the particles of CPSO are settled randomly, which may lead to over-concentration distribution. As a result, particles have
101
Fig. 1. Distribution, trend, and neighborhoods of particles.
the probability of converging to a local peak instead of GP. Therefore, in the initial particles are settled evenly at some fixed values. Regardless of environment varying, all particles should be able to gather at GP for the most types of P–V curves. During search process, the region which has been searched by a particle is defined as its neighborhood. Let us assume that three particles (P1, P2, and P3) are used when PV arrays are under PSC. The distribution, trend, and neighborhoods of these particles are shown in Fig. 1. In the process of iteration, three cases that particles search their neighborhoods repeatedly or sway in a small region may occur, leading to long search time and low efficiency. However, in DPSO they will be turned into dormant state and not participate in the next iteration. (1) P1 is already close to the neighborhood of P2 and will enter into it in next iteration. According to principle of CPSO, P1 will repeatedly search the neighborhood of P2; however, in DPSO, P1 will be turned into dormant state and not participate in the later iterations. Moreover, P2 will possess the neighborhood of P1 and update Pbesti and Gbest in its new neighborhood. It is the most common case which is named case 1. (2) Because of the far distance of Pbesti (point LP3) and Gbest (point LP2) of P3 and parameters setting in equation (3), P3 will keep swaying between LP2 and LP3. This case is named case 2. (3) The initial position of P2 is close to GP (point LP2), so P2 can find GP at the beginning. In the later iterations, P2 will sway around GP continuously due to parameter ω, circuit characteristic and accuracy of sensors. This case is common, too, and named case 3. So particles in DPSO have two states: dormant state and active state. And particles dormancy is just as same as volcano dormancy. The dormant volcano is divided into live and dead volcano, as well as dormant particles. Case 1 shown in Fig. 1 is called as dead dormancy, i.e., the particles will not be activated to participate in later iterations forever. Meanwhile, both case 2 and 3 are called as live dormancy, i.e., the dormant particles are possible to be activated to participate in later iterations. Certainly, the reactivated particles may be turned into dormant state again in later iterations. In essence, the reason of turning the particles which happen to case 2 or 3 into dormant state is that they do not update their Pbesti or Gbest in several iterations. Therefore, the judgment of live dormant particles reactivation is whether the Pbesti or Gbest is updated to new values. The initial position of reactivated particles is located at the point of its neighborhood boundary toward the location of new Gbest in order to reduce the iteration number k. To make clear the tracking of maximum power point, an example is given to explain how DPSO works and how particles be turned
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Fig. 2. Operation process of DPSO.
into dormant state during iterations. The coefficients in equations (3) and (4) are w = 0.4, c1 = 0.8, c2 = 1, Vmax = 0.02. Fig. 2a–e show the corresponding iteration process. In the process, Nap is the number of the active particles, and k is the iteration number. Suddenly, a great change in environmental condition occurs; the P–V curve shown in Fig. 2a exhibits multiple peaks. DPSO is activated and initiated to start up the optimization process [22]. The number of particles is assumed as 6 (P1–P6). Those particles start to iterate according to equation (3) and (4), as shown in Fig. 2a. P3 is the current Gbest that represents the global optimal position and its velocity is calculated by ωv3 , so v3 gets smaller and smaller before other particles update new Gbest . In the third iteration, P3 is turned into dormant state as it happens to case 3. Thus, there are 4 active particles left in the fourth and fifth iterations, as shown in Fig. 2b. In the fifth iteration, both P4 and P6 are turned into dormant state due to entering into the neighborhoods of P3 and P5 (case 1), respectively. Furthermore, P5 owns the neighborhood of P6 and update its Pbesti in new neighborhood. The number of active particles Nap turns to 3. They are P1, P2, and P5 shown in Fig. 2c. In the seventh iteration, P1 is turned into dormant state due to case 1. Meanwhile, because of the distance between Gbest and its new Pbesti , P5 happens to case 2 and is turned into dormant state. In the eighth iteration, there is only one active particle (P2) left shown in Fig. 2d. In all of the dormant particles, P3 and P5 are live dormant particles, and the others are dead dormant particles. In this iteration, P2 happens to case 1 and P3 owns the new neighborhood. What is different is that P2 finds new global optimal position and updates Gbest . The change of Gbest satisfies the judgment of reactivation, so P3 and P5 are reactivated, as shown in Fig. 2e. The number of active particles Nap turns to 2. Afterwards, both P3 and P5 are turned into dormant state again in tenth iteration. Then there is no active particle and the GP region is found. 3.2. Number of particles The number of particles Np is an important parameter in CPSO. A large of particles can improve the optimization capability to find GP, but it will spend more time to converge all of particles, moreover, it
will make the situation of searching repeatedly more serious. In the application of CPSO, most studies choose to reduce convergencetime by using a minimum number of particles, regardless of the unstable optimization capability of CPSO during complex shaded conditions [31]. Considering about the potential local peaks in P–V curve under complex conditions, the search area decided by initial positions of all particles is fixed. In theory, the convergence time in DPSO is approximately equivalent value. So DPSO could use a large number of particles to improve the optimization capability. However, if the particles are obviously too many, the dormant judgment may waste time and power. The formula for power loss is written as
Ploss = P tpg − Paop t cg
(5)
where tcg is convergence time, Paop is the average output power of systems in convergence, Ptpg is theoretical power generation. As sample time is 0.02 s, convergence time and power loss of several simulations with different number of particles are shown in Table 1. These simulations are implemented in MATALB when the PV arrays are under standard test conditions (STC, the insolation is 1000 W/m2 , and the temperature is 25 ◦ C). In these simulations, the PV arrays consist of three PV modules connected in series and the MPPT circuit is the standard Boost DC/DC converter, as shown in Fig. 5. Also, the P–V curve of this PV arrays under STC is shown in Fig. 6 (curve 1). The data in Table 1 is obtained by simulating the Table 1 Performance of two PSO with different number of particles (sample time = 0.02 s). NP
3 4 5 6 8 10 12 14
CPSO
DPSO
tcg (s)
Ploss (W s)
tcg (s)
Ploss (W s)
0.789 0.805 1.005 1.320 1.675 2.125 2.670 3.125
56.43 65.52 80.20 85.82 123.25 140.78 155.62 168.73
0.795 0.760 0.735 0.780 0.805 0.830 0.845 0.905
55.43 52.84 51.72 54.95 57.68 62.70 63.56 72.63
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Fig. 3. Voltage waveforms with different searching sequences.
CPSO and DPSO with different number of particles. The data here confirms the previous analysis. When the number is increasing, the tcg and Ploss of CPSO are increasing quickly; however, the data of DPSO is relatively stable. Then, five particles are chosen as the optimal selection for DPSO. 3.3. Searching sequence The parameters Pbesti , Gbest , pi , and vi in equations (3) and (4) are not affected by different searching sequences of particles because they are updated at the end of each iteration, and so are the iteration number and convergence time. Nevertheless, the searching sequence determines, at one level, the quality of output voltage waveform, and also affects power loss of systems in a degree. Three typical searching sequences and the corresponding output voltage waveforms in four iterations tested under STC are shown in Fig. 3. The sampling period of DPSO (TDPSO ) is 0.02 s and the particle number is five, then iteration time is 0.1 s. As shown in Fig. 3, for three searching sequences, the output voltage waveforms have many points in common, and the convergence time is same, moreover, the power losses which should be same in theory are 46.44, 44.73, and 44.67 W s, respectively. Among these sequences, sequence 1 is the most common used but its effect is the worst. In terms of fluctuation of waveform, the voltage of sequence 1 shocks most quickly with one peak and one trough in each iteration under STC. In contrast, the voltage fluctuation is obviously slight in sequence 2, and especially gentle in sequence 3 with one peak and one trough in every two iterations. As for voltage spike, the reason of its generation is that there is at least one local peak between two continuous particles. i.e., the more times two continuous particles leap over local peaks, the more voltage spikes generate. Sequence 1 will leap over each local peak one time in each iteration, and leap over all local peaks between two continuous iterations where sequences 2 and 3 generate less voltage spikes. However, what is different is sequence 3 has more voltage spikes than sequence 2 due to leaping over local peaks frequently. After considering comprehensively, sequence 2 is regarded as the optimal selection and adopted in the DPSO proposed in this paper. The reason is that searching in sequence 2, both the fluctuation of output voltage waveform and the voltage spike can be ensured in the acceptable range, which is helpful to maintain stability of DC-bus voltage in PV power system. 3.4. Dual-algorithm model A dual-algorithm model is proposed in this paper consisting of DPSO algorithm and INC algorithm. If the inequality in equation (6) is fulfilled during the period of INC algorithm maintaining system
Fig. 4. Flowchart for the dual-algorithm model.
work, the occurrence of PSC is confirmed and DPSO is activated immediately. DPSO is applied to find the area of GP rapidly with local peaks interfering. During iteration, the particles are turned into dormant state one after one until there is no activate particle (i.e., Nap = 0), and at this moment the area of GP is located. Then, it will be replaced by INC algorithm which has stable performance in single peak curve [32]. The flowchart of this dual-algorithm model is shown in Fig. 4. To deal with the condition of a local peak changing into a new GP with shading varying slowly [33], the delay time to restart automatically is set as 2 min [34].
Pnew − Pold P ≥ P
(6)
old
where Pnew (equals as IPV VPV ) and Pold are power values of PV arrays in two successive sample periods during INC algorithm working. P is a limited parameter analyzed in Ref. [31]. 4. Simulation 4.1. Simulation environment Standard boost converter is utilized to implement MPPT control in this paper, as shown in Fig. 5. In the mode, the PV arrays consist of three commercial PV modules MSX-60 connected in series. Table 2 provides the key parameters of the module including sampling time of two algorithms TDPSO and TINC , number of particles Np , and initial positions of these particles pi . The other parameters are analyzed in Refs. [30,31].
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MPPT CONTROL Fig. 5. Simulation model of PV system. Table 2 Basic parameters.
Fig. 6. Varied P–V curves used in the simulation.
NP
5
ω
0.4
Vmax
0.02
n P pi
1 0.15 0.3,0.45,0.6,0.75,0.9
c1 c2
0.8 1.0
TDPSO (s) TINC (s)
0.020 0.001
Fig. 6 shows the simulation P–V curves of the PV arrays under three different complex environments. Initially, the PV arrays are under STC (curve 1). At t = 1 s, the insolation suddenly changes to 240, 400, and 800 W/m2 , and temperature changes to 10 ◦ C
(curve 2). Then at t = 2 s, the insolation changes to 400, 900, and 1200 W/m2 , and temperature changes to 40 ◦ C (curve 3). And the optimal operating points for every P–V curve are labeled as points GP1, GP2, and GP3. 4.2. Simulation results and analysis Fig. 7 shows the simulation results for the output power, duty cycle, and number of activated particles, respectively. At the
Fig. 7. Simulation curves of DPSO and INC.
Fig. 8. Simulation curves of CPSO and INC.
J. Shi et al. / Electric Power Systems Research 123 (2015) 100–107
105
Fig. 9. Simulation curves of conventional INC.
beginning, the PV arrays are under STC. The current P–V curve labeled as curve 1 is shown in Fig. 6. The DPSO algorithm is activated immediately to start to search the area of GP by five particles P1–P5 whose initial positions are fixed. Then, the five particles start to iterate according to sequence 2. Until the sixth iteration, P3 is turned into dormant state due to entering into neighborhood of P2. In the later iteration, P2 happened to case 3 and is turned into dormant state. At present, there are only three active particles left. They are turned into dormant state owing to entering to the neighborhoods of P2, P3, and P4, respectively, in ninth iteration. At t = 0.8 s, the number of activated particles turns to zero, which confirms that the area of GP1 is successfully located by DPSO. Then, DPSO is replaced by INC algorithm to maintain operating point at GP1. Due to the short sample time and small fixed step of INC algorithm, the corresponding wave fluctuation is very stable. At t = 1 s, P–V curve is replaced by curve 2 with multiple local peaks. There are two characteristics in curve 2. First, CPSO may fail to track GP2 with interference of other local peaks because their values are quite close. Second, it is easy that particles happen to sway because of the far distance between GP2 and local peak. At this point, inequality in equation (6) is fulfilled. As before, DPSO is activated to start the tracking process. After six iterations, P3 is turned into dormant state due to case 3, and then, the other particles converge with it until they are turned into dormant state in eighth and ninth iterations. So far, DPSO is replaced by INC algorithm without any activated particles, Nap = 0. When a sudden change of insolation and temperature occurs at t = 2 s, P–V curve changes to curve 3. In forth iteration, P2 is turned into dormant state due to case 3. And after several iterations other particles are turned into dormant state, too. Then the algorithm is switched to INC algorithm to maintain operating point at GP3. As we can see in Fig. 8, with the same sampling time, the dualalgorithm model with CPSO and INC algorithm need take longer time than DPSO to converge all particles under STC. Under some special conditions, not all particles will converge to GP, and some of them may sway between Gbest and its Pbesti (i.e., case 2). Then, in brief, CPSO is low efficient because particles search repeatedly or sway. In addition, Fig. 9 can be obtained by adopting the conventional INC algorithm to track the maximum power point when PV arrays are under partially shaded condition (i.e., insolation is 400, 900, and 1200 W/m2 in turn, and temperature is 40 ◦ C, so the P–V curve of PV arrays is curve 3. Obviously, the conventional INC algorithm tracks a local peak instead of the GP. So the conventional INC algorithm is not suitable to handle partially shaded conditions. Simulation results show that the dual-algorithm model consisting of DPSO algorithm and INC algorithm could find GP quickly and successfully and maintain the operating point at GP no matter how
Fig. 10. Experiment devices.
complex the P–V curves are. Meanwhile, under three shaded conditions, the convergence times are almost the same and obviously shorter than CPSO.
5. Experimental results Solar panel TOP90(12)1210 × 560 is used in experiment with following specifications: the maximum power of solar panel (under STC) PMPP = 90 W, voltage at maximum power point (MPP) VMPP = 17.5 V, current at MPP IMPP = 5.4 A, open circuit voltage VOC = 22 V, short circuit current ISC = 6.02 A. The switching frequency of boost converter is 50 kHz. The main experiment devices are shown in Fig. 10. The sun is shining brightly at noon during experiments. As DC/DC converter is connected with purely resistive load, we acquire the voltage waveform (similar to power waveform) of load. First, the output voltage waveform of the PV arrays under partially shaded condition shown in Fig. 11a is obtained by utilizing global scanning method. According to it, we know that the output of the PV arrays under this partially shaded condition contains a global peak point and two local peak points. Then the dualalgorithm model with DPSO and INC, dual-algorithm model with CPSO and INC and conventional INC algorithm are respectively used to track the maximum power point when the PV arrays are under this partially shaded condition. The experiment results shown in Fig. 11b–d prove that both of DPSO and CPSO algorithm can find the GP successfully, but conventional INC algorithm falls into a local peak point. However, obviously, convergence time of DPSO is quit shorter than CPSO, and voltage waveform of DPSO is gentler, too.
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Fig. 11. Experimental waveforms. a. Output voltage waveform of the PV arrays under partially shaded condition. b. Dual-algorithm model with DPSO and INC. c. Dualalgorithm model with CPSO and INC. d. Conventional INC algorithm.
6. Conclusion In this paper, a dual-algorithm MPPT control model based on DPSO and INC is proposed. The results of simulation and experiment show that, compared with CPSO and conventional INC, the DPSO greatly shortens the searching time, reduces the fluctuation of output waveform and improves the efficiency through particles dormancy and activation control, optimal number of particles algorithm and search sequence selection. Meanwhile, the INC guarantees that the GP can be tracked precisely. This dual-algorithm model has good performance no matter how complex shaded conditions the PV arrays are under. Acknowledgements This work was sponsored by the National Program of International S&T Cooperation (2013DFA11040), the National Natural Science Foundation of China (61172014), and the Natural Science Foundation of Tianjin (12JCZDJC21300) References [1] Z. Li, S. Kai, X. Yan, et al., A modular grid-connected photovoltaic generation system based on DC bus, J. IEEE Trans. Power Electron. 26 (2011) 523–531. [2] Y. Bo, L. Wuhua, Z. Yi, H. Xiangning, Design and analysis of a gridconnected photovoltaic power system, J. IEEE Trans. Power Electron. 25 (2010) 992–1000. [3] N.A. Rahim, K. Chaniago, J. Selvaraj, Single-phase seven-level grid-connected inverter for photovoltaic system, J. IEEE Trans. Ind. Electron. 58 (2011) 2435–2443. [4] J. Doo-Yong, J. Young-Hyok, P. Sang-Hoon, et al., Interleaved soft-switching boost converter for photovoltaic power-generation system, J. IEEE Trans. Power Electron. 26 (2011) 1137–1145. [5] T. Esram, P.L. Chapman, Comparison of photovoltaic array maximum power point tracking techniques, J. IEEE Trans. Energy Convers. 22 (2007) 439–449. [6] B.N. Alajmi, K.H. Ahmed, S.J. Finney, et al., Fuzzy-logic-control approach of a modified hill-climbing method for maximum power point in microgrid
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J. Shi et al. / Electric Power Systems Research 123 (2015) 100–107 [20] N. Tat, L. Luat, L. Kay-Soon, A global maximum power point tracking scheme employing DIRECT search algorithm for photovoltaic systems, J. IEEE Trans. Ind. Electron. 57 (2010) 3456–3467. [21] V. Phimmasone, T. Endo, Y. Kondo, et al., Improvement of the maximum power point tracker for photovoltaic generators with particle swarm optimization technique by adding repulsive force among agents, in: Electrical Machines and Systems (ICEMS), 2009, pp. 1–6. [22] K. Ishaque, Z. Salam, M. Amjad, S. Mekhilef, An improved particle swarm optimization (PSO)-based MPPT for PV with reduced steady-state oscillation, J. IEEE Trans. Power Electron. 27 (2012) 3627–3638. [23] L. Yi-Hwa, H. Shyh-Ching, H. Jia-Wei, et al., A particle swarm optimizationbased maximum power point tracking algorithm for PV systems operating under partially shaded conditions, J. IEEE Trans. Energy Convers. 27 (2012) 1027–1035. [24] H. Jing, W. Si-jie, X. Wei, et al., Application of PV-MPPT control based on particle swarm optimization, J. Power Electron. 46 (2012) 31–33. [25] L.L. Jiang, D.L. Maskell, J.C. Patra, A novel ant colony opti’mization-based maximum power point tracking for photovoltaic systems under partially shaded conditions, J. Energy Build. 58 (2013) 227–236. [26] K. Sundareswaran, S. Peddapati, S. Palani, MPPT of PV systems under partial shaded conditions through a colony of flashing fireflies, J. IEEE Trans. Energy Convers. 29 (2014) 463–472. [27] K.L. Lian, J.H. Jhang, I.S. Tian, A maximum power point tracking method based on perturb-and-observe combined with particle swarm optimization, J. IEEE J. Photovolt. 4 (2014) 626–633. [28] R. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in: Proceedings of 6th International Symposium on MHS, 1995, pp. 39–43. [29] C. Ze, Z. Hang, Y. Hongzhi, Research on MPPT control of PV system based on PSO algorithm, in: 2010 Chinese Control and Decision Conference (CCDC), 2010, pp. 887–892. [30] K. Ishaque, Z. Salam, A deterministic particle swarm optimization maximum power point tracker for photovoltaic system under partial shading condition, J. IEEE Trans. Ind. Electron. 60 (2013) 3195–3206. [31] M. Miyatake, M. veerachary, F. Toriumi, et al., Maximum power point tracking of multiple photovoltaic arrays: a PSO approach, J. IEEE Trans. Aerosp. Electron. Syst. 47 (2011) 367–380. [32] D. Sera, L. Mathe, T. Kerekes, et al., On the perturb-and-observe and incremental conductance MPPT methods for PV systems, J. IEEE J. Photovolt. 3 (2013) 1070–1078. [33] R. Bruendlinger, B. Bletterie, M. Milde, et al., Maximum power point tracking performance under partially shaded PV array conditions, C, in: Proceedings of 21st EUPVSEC, Dresden, Germany, 2006, pp. 2157–2160. [34] Z. Yanwei, S. Xinchun, D. Yangqing, et al., Application of PSO algorithm in global MPPT for PV array, J. Proc. CSEE 32 (2012) 42–48. Jiying Shi was born in Tianjin City, China, in 1959. He received M.E. and Ph.D. degrees from Tianjin University, Tianjin, China in 1993 and 1996, respectively. He was a visiting scholar and also a post-doctor with The Hong Kong University of Science and Technology in Hong Kong from July 1996 to November 1999. He is currently an Associate Professor at Electrical Engineering and Automation, Tianjin University, China. His research interests include power electronic techniques, renewable energy, and soft switching techniques.
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Wen Zhang was born in Zhangjiakou City, China, in 1990. He received B.E. degree in electrical engineering and automation from Hebei University of Technology, Tianjin, China, in 2013. He is currently working toward the M.E. degree in Tianjin University, Tianjin, China. His research interest includes maximum power point tracking technology and power electronic techniques.
Yongge Zhang was born in Shijiazhuang City, China, in 1988. He received B.E. degree in electrical engineering and automation from Hebei University of Technology, Tianjin, China, in 2012. He is currently working toward the M.E. degree in Tianjin University, Tianjin, China. His research interest includes maximum power point tracking technology and power electronic techniques.
Fei Xue was born in Guyuan City, China, in 1994. He received B.E degree in electrical engineering and automation from Tianjin University, China, in 2014. He currently is working toward the M.E degree in Tianjin University, Tianjin, China. His research interest includes maximum power point tracking technology and power electronic techniques.
Ting Yang is a Professor of Electrical Engineering at Tianjin University, China. He is the winner of Education Ministry’s New Century Excellent Talents Supporting Plan. Professor Yang is the author/co-author of four books, more than 60 publications in technical journals and conferences, and the chairman of two workshops of IEEE International Conference. He is a member of International Society for Industry and Applied Mathematics (SIAM), and a senior member of the Chinese Institute of Electronic, the committee member of electronic circuit and system. Professor Yang’s research effort is focused on power electronic techniques and renewable energy.
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
MPPT for PV systems based on a dormant PSO algorithm Jiying Shi, Wen Zhang ∗ , Yongge Zhang, Fei Xue, Ting Yang School of Electrical Engineering and Automation, Tianjin University, Tianjin, China
a r t i c l e
i n f o
Article history: Received 30 September 2014 Received in revised form 28 January 2015 Accepted 3 February 2015 Keywords: Dormant particle swarm optimization (DPSO) Maximum power point tracking (MPPT) Partially shaded conditions Search sequence of particles Voltage spike
a b s t r a c t Since the power–voltage characteristic curve of photovoltaic (PV) arrays has multiple peaks under partially shaded conditions, the conventional maximum power point tracking (MPPT) control methods will fail to work. However, the particle swarm optimization (PSO) algorithm is very suitable to solve the multi-extreme optimization problem. Then this paper proposes a dual-algorithm search method: first, a dormant particle swarm optimization (DPSO) algorithm is activated to search the area of global peak, and then the algorithm will be switched to conventional incremental conductance (INC) algorithm to track the maximum output power of photovoltaic arrays. During the iteration process of DPSO, if particles happen to search repeatedly or sway in a small region, they will be turned into dormant state so as to reduce convergence time and improve efficiency. Due to the elimination of searching repeatedly, the number of particles can be large to strengthen optimization capability. In addition, the optimal number of particles for DPSO is found by analysis and simulation. Furthermore, the searching sequence of particles is optimized to effectively reduce fluctuation of voltage and suppress output voltage spike. Finally, the excellent performance of the proposed model is verified by simulations and experiments. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Solar energy is a very popular source of renewable energy due to several advantages. Photovoltaic (PV) power systems have been widely used in many countries. However, there are many urgent issues to tackle in the application of PV power systems. One of the central problems is how to improve efficiency [1–3]. Since the PV arrays exhibit a nonlinear power–voltage (P–V) characteristic curve which varies with insolation and temperature, how to achieve maximum power point tracking (MPPT) is a very important technology [4,5]. To date, various conventional MPPT schemes have been proposed including hill-climbing (HC) [6–8], perturb and observe (P&O) [9–12], and incremental conductance (INC) [13–16], etc. These methods have simple structures and low equipment requirement, but they cannot handle the partially shaded conditions (PSC) because P–V curve displays multiple peaks with several local peaks and a global peak (GP), which cannot be differentiated by conventional algorithms. However, PSC occur quite commonly due to sun position, clouds, buildings, trees, and so on, so it is necessary to improve these algorithms to track the actual GP. Then several attempts have been suggested by researchers in Ref. [17–20].
∗ Tel.: +86 15122160704. E-mail address: [email protected] (W. Zhang). http://dx.doi.org/10.1016/j.epsr.2015.02.001 0378-7796/© 2015 Elsevier B.V. All rights reserved.
Authors in Ref. [17] have reported an MPPT scheme that uses Fibonacci sequence to track the GP under PSC. However, the method does not guarantee GP tracking under all conditions. Authors in Ref. [18] proposed a two-stage method to track the GP. In the first stage, the region of the GP is detected using the load line, and in the second stage, the operating point converges to the GP. But, this method may fail to track the GP if the GP lies on the left side of the load line. In another work [19], authors proposed a two-stage approach. Despite its effectiveness, the method needs to scan almost 80% of the I–V curve to find the GP, which will lead slow response. In Ref. [20], authors proposed a dividing rectangle (DIRECT) search method, which is based on a Lipschitz condition to find the GP. However, the algorithm is very complex, which will increase the burden of system significantly. The essential issue of MPPT control is an optimization problem which can be achieved by using evolutionary algorithm. PSO algorithm owns the characteristics of parallel processing, good robustness, and high probability of finding global optimal solution. Because of its good performance in multiple-peak function optimization, PSO is very suited for MPPT control of PV system under PSC [21–27]. However, in all of these PSO methods, the searching paths of particles will overlap. Because some particles will go through the path which have been searched by others lying on the same side of GP. This phenomenon of searching repeatedly is very common in above PSO methods, which results in slow convergence speed. Additional, due to the initial positions of particles
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and distribution of local peaks and global peak, some particles will sway or cannot get to the GP under certain conditions. This paper proposes a new dormant particle swarm optimization (DPSO) algorithm, in which the particles searching repeatedly or swaying in a small region will be turned into dormant state. Thus, the speed and efficiency of MPPT will be greatly improved. The DPSO algorithm, together with INC algorithm which aims at tracking the maximum power point precisely, constitutes the dual-algorithm model, which is simple to implement and can achieve MPPT rapidly and accurately under PSC. The remainder of the paper is organized as follows. Section II briefly introduces the conventional PSO (CPSO); Section III describes the proposed DPSO, the optimal number of particles and reasonable searching sequence; While in Section IV and V, the performance of DPSO to track GP is simulated and experimented, respectively; the main conclusions are made in Section VI. 2. Overview of CPSO PSO, as a new swarm intelligence optimization algorithm, firstly proposed by Kennedy and Eberhart in 1995 [28], has been developing rapidly in recent 20 years. It is modeled according to the behavior of bird flocks. Its advantages are simple realization and fast convergence, and it is well applied to find the global optimal solution in a nonlinear, discontinuous, nondifferentiable curve [29]. In this algorithm, several cooperative particles are used in an ndimensional space. Each particle owns its position pi (distributed randomly) and velocity vi (vi = 0 in initiation). The position of a particle is influenced by its best position so far, Pbesti , and the best position of all particles so far, Gbest . Velocity and position of particles are calculated by
vk+1 = ωvki + c1 r1 (Pbesti − pki ) + c2 r2 (Gbest − pki ) i
(1)
pk+1 = pki + vk+1 i i
(2)
where i = 1,2,. . ., Np , Np is the number of particles, ω is the inertia weight, c1 and c2 are the acceleration coefficients, r1 , r2 are random variables uniformly distributed within [0,1], k is iteration number. This paper has analyzed and improved the structure and parameters of CPSO to make it more practical and effective. Random numbers in equation (1) mainly help to ensure the capacity to search any potential local peaks; however, they are not necessary in MPPT control based on simple P–V curve. Moreover, two potential problems can be observed when simulating [30]. First, if the random number is small with the present information of control variable (duty cycle is adopted in this paper), only a small change in the velocity term of the PSO equation is obtained, which will result in more iterations needed by CPSO. Second, if the random number is close to 1 when the power values of local peaks and GP are similar, CPSO may escape from the GP. To handle these drawbacks, the random numbers are removed and velocity factor is limited to a certain value Vmax , which is set according to the distance between two peaks. Therefore, the iteration formulas of CPSO can be rewritten as
vk+1 = ωvki + c1 (Pbesti − pki ) + c2 (Gbest − pki ) i
(3)
pk+1 i
(4)
=
pki
+ vk+1 i
where vk+1 ≤ Vmax . i
3. Application of DPSO 3.1. DPSO Initially the particles of CPSO are settled randomly, which may lead to over-concentration distribution. As a result, particles have
101
Fig. 1. Distribution, trend, and neighborhoods of particles.
the probability of converging to a local peak instead of GP. Therefore, in the initial particles are settled evenly at some fixed values. Regardless of environment varying, all particles should be able to gather at GP for the most types of P–V curves. During search process, the region which has been searched by a particle is defined as its neighborhood. Let us assume that three particles (P1, P2, and P3) are used when PV arrays are under PSC. The distribution, trend, and neighborhoods of these particles are shown in Fig. 1. In the process of iteration, three cases that particles search their neighborhoods repeatedly or sway in a small region may occur, leading to long search time and low efficiency. However, in DPSO they will be turned into dormant state and not participate in the next iteration. (1) P1 is already close to the neighborhood of P2 and will enter into it in next iteration. According to principle of CPSO, P1 will repeatedly search the neighborhood of P2; however, in DPSO, P1 will be turned into dormant state and not participate in the later iterations. Moreover, P2 will possess the neighborhood of P1 and update Pbesti and Gbest in its new neighborhood. It is the most common case which is named case 1. (2) Because of the far distance of Pbesti (point LP3) and Gbest (point LP2) of P3 and parameters setting in equation (3), P3 will keep swaying between LP2 and LP3. This case is named case 2. (3) The initial position of P2 is close to GP (point LP2), so P2 can find GP at the beginning. In the later iterations, P2 will sway around GP continuously due to parameter ω, circuit characteristic and accuracy of sensors. This case is common, too, and named case 3. So particles in DPSO have two states: dormant state and active state. And particles dormancy is just as same as volcano dormancy. The dormant volcano is divided into live and dead volcano, as well as dormant particles. Case 1 shown in Fig. 1 is called as dead dormancy, i.e., the particles will not be activated to participate in later iterations forever. Meanwhile, both case 2 and 3 are called as live dormancy, i.e., the dormant particles are possible to be activated to participate in later iterations. Certainly, the reactivated particles may be turned into dormant state again in later iterations. In essence, the reason of turning the particles which happen to case 2 or 3 into dormant state is that they do not update their Pbesti or Gbest in several iterations. Therefore, the judgment of live dormant particles reactivation is whether the Pbesti or Gbest is updated to new values. The initial position of reactivated particles is located at the point of its neighborhood boundary toward the location of new Gbest in order to reduce the iteration number k. To make clear the tracking of maximum power point, an example is given to explain how DPSO works and how particles be turned
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Fig. 2. Operation process of DPSO.
into dormant state during iterations. The coefficients in equations (3) and (4) are w = 0.4, c1 = 0.8, c2 = 1, Vmax = 0.02. Fig. 2a–e show the corresponding iteration process. In the process, Nap is the number of the active particles, and k is the iteration number. Suddenly, a great change in environmental condition occurs; the P–V curve shown in Fig. 2a exhibits multiple peaks. DPSO is activated and initiated to start up the optimization process [22]. The number of particles is assumed as 6 (P1–P6). Those particles start to iterate according to equation (3) and (4), as shown in Fig. 2a. P3 is the current Gbest that represents the global optimal position and its velocity is calculated by ωv3 , so v3 gets smaller and smaller before other particles update new Gbest . In the third iteration, P3 is turned into dormant state as it happens to case 3. Thus, there are 4 active particles left in the fourth and fifth iterations, as shown in Fig. 2b. In the fifth iteration, both P4 and P6 are turned into dormant state due to entering into the neighborhoods of P3 and P5 (case 1), respectively. Furthermore, P5 owns the neighborhood of P6 and update its Pbesti in new neighborhood. The number of active particles Nap turns to 3. They are P1, P2, and P5 shown in Fig. 2c. In the seventh iteration, P1 is turned into dormant state due to case 1. Meanwhile, because of the distance between Gbest and its new Pbesti , P5 happens to case 2 and is turned into dormant state. In the eighth iteration, there is only one active particle (P2) left shown in Fig. 2d. In all of the dormant particles, P3 and P5 are live dormant particles, and the others are dead dormant particles. In this iteration, P2 happens to case 1 and P3 owns the new neighborhood. What is different is that P2 finds new global optimal position and updates Gbest . The change of Gbest satisfies the judgment of reactivation, so P3 and P5 are reactivated, as shown in Fig. 2e. The number of active particles Nap turns to 2. Afterwards, both P3 and P5 are turned into dormant state again in tenth iteration. Then there is no active particle and the GP region is found. 3.2. Number of particles The number of particles Np is an important parameter in CPSO. A large of particles can improve the optimization capability to find GP, but it will spend more time to converge all of particles, moreover, it
will make the situation of searching repeatedly more serious. In the application of CPSO, most studies choose to reduce convergencetime by using a minimum number of particles, regardless of the unstable optimization capability of CPSO during complex shaded conditions [31]. Considering about the potential local peaks in P–V curve under complex conditions, the search area decided by initial positions of all particles is fixed. In theory, the convergence time in DPSO is approximately equivalent value. So DPSO could use a large number of particles to improve the optimization capability. However, if the particles are obviously too many, the dormant judgment may waste time and power. The formula for power loss is written as
Ploss = P tpg − Paop t cg
(5)
where tcg is convergence time, Paop is the average output power of systems in convergence, Ptpg is theoretical power generation. As sample time is 0.02 s, convergence time and power loss of several simulations with different number of particles are shown in Table 1. These simulations are implemented in MATALB when the PV arrays are under standard test conditions (STC, the insolation is 1000 W/m2 , and the temperature is 25 ◦ C). In these simulations, the PV arrays consist of three PV modules connected in series and the MPPT circuit is the standard Boost DC/DC converter, as shown in Fig. 5. Also, the P–V curve of this PV arrays under STC is shown in Fig. 6 (curve 1). The data in Table 1 is obtained by simulating the Table 1 Performance of two PSO with different number of particles (sample time = 0.02 s). NP
3 4 5 6 8 10 12 14
CPSO
DPSO
tcg (s)
Ploss (W s)
tcg (s)
Ploss (W s)
0.789 0.805 1.005 1.320 1.675 2.125 2.670 3.125
56.43 65.52 80.20 85.82 123.25 140.78 155.62 168.73
0.795 0.760 0.735 0.780 0.805 0.830 0.845 0.905
55.43 52.84 51.72 54.95 57.68 62.70 63.56 72.63
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Fig. 3. Voltage waveforms with different searching sequences.
CPSO and DPSO with different number of particles. The data here confirms the previous analysis. When the number is increasing, the tcg and Ploss of CPSO are increasing quickly; however, the data of DPSO is relatively stable. Then, five particles are chosen as the optimal selection for DPSO. 3.3. Searching sequence The parameters Pbesti , Gbest , pi , and vi in equations (3) and (4) are not affected by different searching sequences of particles because they are updated at the end of each iteration, and so are the iteration number and convergence time. Nevertheless, the searching sequence determines, at one level, the quality of output voltage waveform, and also affects power loss of systems in a degree. Three typical searching sequences and the corresponding output voltage waveforms in four iterations tested under STC are shown in Fig. 3. The sampling period of DPSO (TDPSO ) is 0.02 s and the particle number is five, then iteration time is 0.1 s. As shown in Fig. 3, for three searching sequences, the output voltage waveforms have many points in common, and the convergence time is same, moreover, the power losses which should be same in theory are 46.44, 44.73, and 44.67 W s, respectively. Among these sequences, sequence 1 is the most common used but its effect is the worst. In terms of fluctuation of waveform, the voltage of sequence 1 shocks most quickly with one peak and one trough in each iteration under STC. In contrast, the voltage fluctuation is obviously slight in sequence 2, and especially gentle in sequence 3 with one peak and one trough in every two iterations. As for voltage spike, the reason of its generation is that there is at least one local peak between two continuous particles. i.e., the more times two continuous particles leap over local peaks, the more voltage spikes generate. Sequence 1 will leap over each local peak one time in each iteration, and leap over all local peaks between two continuous iterations where sequences 2 and 3 generate less voltage spikes. However, what is different is sequence 3 has more voltage spikes than sequence 2 due to leaping over local peaks frequently. After considering comprehensively, sequence 2 is regarded as the optimal selection and adopted in the DPSO proposed in this paper. The reason is that searching in sequence 2, both the fluctuation of output voltage waveform and the voltage spike can be ensured in the acceptable range, which is helpful to maintain stability of DC-bus voltage in PV power system. 3.4. Dual-algorithm model A dual-algorithm model is proposed in this paper consisting of DPSO algorithm and INC algorithm. If the inequality in equation (6) is fulfilled during the period of INC algorithm maintaining system
Fig. 4. Flowchart for the dual-algorithm model.
work, the occurrence of PSC is confirmed and DPSO is activated immediately. DPSO is applied to find the area of GP rapidly with local peaks interfering. During iteration, the particles are turned into dormant state one after one until there is no activate particle (i.e., Nap = 0), and at this moment the area of GP is located. Then, it will be replaced by INC algorithm which has stable performance in single peak curve [32]. The flowchart of this dual-algorithm model is shown in Fig. 4. To deal with the condition of a local peak changing into a new GP with shading varying slowly [33], the delay time to restart automatically is set as 2 min [34].
Pnew − Pold P ≥ P
(6)
old
where Pnew (equals as IPV VPV ) and Pold are power values of PV arrays in two successive sample periods during INC algorithm working. P is a limited parameter analyzed in Ref. [31]. 4. Simulation 4.1. Simulation environment Standard boost converter is utilized to implement MPPT control in this paper, as shown in Fig. 5. In the mode, the PV arrays consist of three commercial PV modules MSX-60 connected in series. Table 2 provides the key parameters of the module including sampling time of two algorithms TDPSO and TINC , number of particles Np , and initial positions of these particles pi . The other parameters are analyzed in Refs. [30,31].
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MPPT CONTROL Fig. 5. Simulation model of PV system. Table 2 Basic parameters.
Fig. 6. Varied P–V curves used in the simulation.
NP
5
ω
0.4
Vmax
0.02
n P pi
1 0.15 0.3,0.45,0.6,0.75,0.9
c1 c2
0.8 1.0
TDPSO (s) TINC (s)
0.020 0.001
Fig. 6 shows the simulation P–V curves of the PV arrays under three different complex environments. Initially, the PV arrays are under STC (curve 1). At t = 1 s, the insolation suddenly changes to 240, 400, and 800 W/m2 , and temperature changes to 10 ◦ C
(curve 2). Then at t = 2 s, the insolation changes to 400, 900, and 1200 W/m2 , and temperature changes to 40 ◦ C (curve 3). And the optimal operating points for every P–V curve are labeled as points GP1, GP2, and GP3. 4.2. Simulation results and analysis Fig. 7 shows the simulation results for the output power, duty cycle, and number of activated particles, respectively. At the
Fig. 7. Simulation curves of DPSO and INC.
Fig. 8. Simulation curves of CPSO and INC.
J. Shi et al. / Electric Power Systems Research 123 (2015) 100–107
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Fig. 9. Simulation curves of conventional INC.
beginning, the PV arrays are under STC. The current P–V curve labeled as curve 1 is shown in Fig. 6. The DPSO algorithm is activated immediately to start to search the area of GP by five particles P1–P5 whose initial positions are fixed. Then, the five particles start to iterate according to sequence 2. Until the sixth iteration, P3 is turned into dormant state due to entering into neighborhood of P2. In the later iteration, P2 happened to case 3 and is turned into dormant state. At present, there are only three active particles left. They are turned into dormant state owing to entering to the neighborhoods of P2, P3, and P4, respectively, in ninth iteration. At t = 0.8 s, the number of activated particles turns to zero, which confirms that the area of GP1 is successfully located by DPSO. Then, DPSO is replaced by INC algorithm to maintain operating point at GP1. Due to the short sample time and small fixed step of INC algorithm, the corresponding wave fluctuation is very stable. At t = 1 s, P–V curve is replaced by curve 2 with multiple local peaks. There are two characteristics in curve 2. First, CPSO may fail to track GP2 with interference of other local peaks because their values are quite close. Second, it is easy that particles happen to sway because of the far distance between GP2 and local peak. At this point, inequality in equation (6) is fulfilled. As before, DPSO is activated to start the tracking process. After six iterations, P3 is turned into dormant state due to case 3, and then, the other particles converge with it until they are turned into dormant state in eighth and ninth iterations. So far, DPSO is replaced by INC algorithm without any activated particles, Nap = 0. When a sudden change of insolation and temperature occurs at t = 2 s, P–V curve changes to curve 3. In forth iteration, P2 is turned into dormant state due to case 3. And after several iterations other particles are turned into dormant state, too. Then the algorithm is switched to INC algorithm to maintain operating point at GP3. As we can see in Fig. 8, with the same sampling time, the dualalgorithm model with CPSO and INC algorithm need take longer time than DPSO to converge all particles under STC. Under some special conditions, not all particles will converge to GP, and some of them may sway between Gbest and its Pbesti (i.e., case 2). Then, in brief, CPSO is low efficient because particles search repeatedly or sway. In addition, Fig. 9 can be obtained by adopting the conventional INC algorithm to track the maximum power point when PV arrays are under partially shaded condition (i.e., insolation is 400, 900, and 1200 W/m2 in turn, and temperature is 40 ◦ C, so the P–V curve of PV arrays is curve 3. Obviously, the conventional INC algorithm tracks a local peak instead of the GP. So the conventional INC algorithm is not suitable to handle partially shaded conditions. Simulation results show that the dual-algorithm model consisting of DPSO algorithm and INC algorithm could find GP quickly and successfully and maintain the operating point at GP no matter how
Fig. 10. Experiment devices.
complex the P–V curves are. Meanwhile, under three shaded conditions, the convergence times are almost the same and obviously shorter than CPSO.
5. Experimental results Solar panel TOP90(12)1210 × 560 is used in experiment with following specifications: the maximum power of solar panel (under STC) PMPP = 90 W, voltage at maximum power point (MPP) VMPP = 17.5 V, current at MPP IMPP = 5.4 A, open circuit voltage VOC = 22 V, short circuit current ISC = 6.02 A. The switching frequency of boost converter is 50 kHz. The main experiment devices are shown in Fig. 10. The sun is shining brightly at noon during experiments. As DC/DC converter is connected with purely resistive load, we acquire the voltage waveform (similar to power waveform) of load. First, the output voltage waveform of the PV arrays under partially shaded condition shown in Fig. 11a is obtained by utilizing global scanning method. According to it, we know that the output of the PV arrays under this partially shaded condition contains a global peak point and two local peak points. Then the dualalgorithm model with DPSO and INC, dual-algorithm model with CPSO and INC and conventional INC algorithm are respectively used to track the maximum power point when the PV arrays are under this partially shaded condition. The experiment results shown in Fig. 11b–d prove that both of DPSO and CPSO algorithm can find the GP successfully, but conventional INC algorithm falls into a local peak point. However, obviously, convergence time of DPSO is quit shorter than CPSO, and voltage waveform of DPSO is gentler, too.
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Fig. 11. Experimental waveforms. a. Output voltage waveform of the PV arrays under partially shaded condition. b. Dual-algorithm model with DPSO and INC. c. Dualalgorithm model with CPSO and INC. d. Conventional INC algorithm.
6. Conclusion In this paper, a dual-algorithm MPPT control model based on DPSO and INC is proposed. The results of simulation and experiment show that, compared with CPSO and conventional INC, the DPSO greatly shortens the searching time, reduces the fluctuation of output waveform and improves the efficiency through particles dormancy and activation control, optimal number of particles algorithm and search sequence selection. Meanwhile, the INC guarantees that the GP can be tracked precisely. This dual-algorithm model has good performance no matter how complex shaded conditions the PV arrays are under. Acknowledgements This work was sponsored by the National Program of International S&T Cooperation (2013DFA11040), the National Natural Science Foundation of China (61172014), and the Natural Science Foundation of Tianjin (12JCZDJC21300) References [1] Z. Li, S. Kai, X. Yan, et al., A modular grid-connected photovoltaic generation system based on DC bus, J. IEEE Trans. Power Electron. 26 (2011) 523–531. [2] Y. Bo, L. Wuhua, Z. Yi, H. Xiangning, Design and analysis of a gridconnected photovoltaic power system, J. IEEE Trans. Power Electron. 25 (2010) 992–1000. [3] N.A. Rahim, K. Chaniago, J. Selvaraj, Single-phase seven-level grid-connected inverter for photovoltaic system, J. IEEE Trans. Ind. Electron. 58 (2011) 2435–2443. [4] J. Doo-Yong, J. Young-Hyok, P. Sang-Hoon, et al., Interleaved soft-switching boost converter for photovoltaic power-generation system, J. IEEE Trans. Power Electron. 26 (2011) 1137–1145. [5] T. Esram, P.L. Chapman, Comparison of photovoltaic array maximum power point tracking techniques, J. IEEE Trans. Energy Convers. 22 (2007) 439–449. [6] B.N. Alajmi, K.H. Ahmed, S.J. Finney, et al., Fuzzy-logic-control approach of a modified hill-climbing method for maximum power point in microgrid
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Wen Zhang was born in Zhangjiakou City, China, in 1990. He received B.E. degree in electrical engineering and automation from Hebei University of Technology, Tianjin, China, in 2013. He is currently working toward the M.E. degree in Tianjin University, Tianjin, China. His research interest includes maximum power point tracking technology and power electronic techniques.
Yongge Zhang was born in Shijiazhuang City, China, in 1988. He received B.E. degree in electrical engineering and automation from Hebei University of Technology, Tianjin, China, in 2012. He is currently working toward the M.E. degree in Tianjin University, Tianjin, China. His research interest includes maximum power point tracking technology and power electronic techniques.
Fei Xue was born in Guyuan City, China, in 1994. He received B.E degree in electrical engineering and automation from Tianjin University, China, in 2014. He currently is working toward the M.E degree in Tianjin University, Tianjin, China. His research interest includes maximum power point tracking technology and power electronic techniques.
Ting Yang is a Professor of Electrical Engineering at Tianjin University, China. He is the winner of Education Ministry’s New Century Excellent Talents Supporting Plan. Professor Yang is the author/co-author of four books, more than 60 publications in technical journals and conferences, and the chairman of two workshops of IEEE International Conference. He is a member of International Society for Industry and Applied Mathematics (SIAM), and a senior member of the Chinese Institute of Electronic, the committee member of electronic circuit and system. Professor Yang’s research effort is focused on power electronic techniques and renewable energy.