https://doi.org/10.6113/JPE.2019.19.5.1248
ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718
Moth-Flame Optimization-Based Maximum Power Point Tracking for Photovoltaic Systems Under Partial Shading Conditions
Ji-Ying Shi*, Deng-Yu Zhang**, Fei Xue†, Ya-Jing Li***, Wen Qiao*,Wen-Jing Yang*, Yi-Ming Xu*, and Ting Yang*
†Electric Power Research Institute, State Grid Ningxia Electric Power Company, Yinchuan, China
*Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, China
**China Automotive Technology and Research Center Co., Ltd., Tianjin, China
***INSPUR Co. Ltd., Jinan, China
Abstract
This paper presents a moth-flame optimization (MFO)-based maximum power point tracking (MPPT) method for photovoltaic (PV) systems. The MFO algorithm is a new optimization method that exhibits satisfactory performance in terms of exploration, exploitation, local optima avoidance, and convergence. Therefore, the MFO algorithm is quite suitable for solving multiple peaks of PV systems under partial shading conditions (PSCs). The proposed MFO-MPPT is compared with four MPPT algorithms, namely the perturb and observe (P&O)-MPPT, incremental conductance (INC)-MPPT, particle swarm optimization (PSO)- MPPT and whale optimization algorithm (WOA)-MPPT. Simulation and experiment results demonstrate that the proposed algorithm can extract the global maximum power point (MPP) with greater tracking speed and accuracy under various conditions.
Key words: Maximum power point tracking, Moth-flame optimization, Partial shading conditions, Photovoltaic system
Manuscript received Mar. 28, 2018; accepted Aug. 29, 2018
Recommended for publication by Associate Editor Xiaoqiang Guo.
†Corresponding Author: tjuxf1010@126.com Tel: +86-022-2740-6071, State Grid Ningxia Electric Power Company
*Key Lab. of Smart Grid of Ministry of Education, Tianjin Univ., China
**China Automotive Technology and Research Center Co., Ltd, China
***INSPUR Co. Ltd., China
I. INTRODUCTION
At present, the rapid development of renewable energy is gradually alleviating dependence on fossil energy. The European Union, United States and China have proposed plans where renewable energy will account for 100%, 80% and 60%∼ 70% of the total energy supply by 2050, respectively [1]. Among the various kinds of renewable energy, solar energy as an environmental-friendly and abundant energy source has a promising prospect. To ensure high efficiency of photovoltaic (PV) generation, maximum power point tracking (MPPT) techniques are indispensable [2], [3].
On the whole, MPPT techniques consists of conventional and intelligent MPPT methods [4], [5]. Conventional MPPT algorithms (including the perturb and observe (P&O) MPPT [6], [7], incremental conductance (INC) MPPT [8]-[9], etc.) can easily extract the MPP under uniform solar radiation. However, under partial shading conditions (PSCs), a local maximum power point (MPP) can appear on the P–U curve of a PV array. In this scenario, conventional MPPT algorithms can become immersed in a local MPP because they are unable to discriminate between local MPPs and the global MPP, which reduces the tracking efficiency of PV systems.
The focus of MPPT control is tracking the global MPP swiftly and reliably under various conditions. In order to alleviate the above-mentioned problem, intelligent algorithms have been extensively proposed in the literature. Representative algorithms include particle swarm optimization (PSO) [10]- [12], firefly algorithm (FA) [13], [14], cuckoo search (CS) [15], [16], artificial fish algorithm [17], [18], grey wolf optimization (GWO) [19], [20] and whale optimization algorithm (WOA) [21]-[23]. These intelligent algorithms have gained a lot of attention due to their convergence speeds and their ability to handle multi-peaks.
Recently, Mirjalili et al. developed a new metaheuristic algorithm known as moth-flame optimization (MFO) [24], which was inspired by the navigation method of moths in nature called transverse orientation. MFO, like the WOA, is a non-linear optimization method based on spiral trajectories. The authors of Refs. [21]-[23] demonstrated that the WOA, through app lying spiral optimization, is effective in tracking the global MPP of PV arrays under PSCs. Additionally, the MFO algorithm has shown satisfactory performance in many fields such as the modeling of the multi-crystalline solar cells [25], training multi-layer perceptrons [26], and optimal power flow calculations [27]. The MFO algorithm requires fewer parameters for adjustment and less operators when compared to other evolutionary approaches, which is an advantage when a rapid design process is considered. After a thorough literature search, it was observed that MFO has not been exploited for the design of an MPPT control scheme. Hence, this work attempts to exploit MFO algorithm for designing an MPPT method to obtain efficient tracking performance under PSCs.
Conventional MPPT control schemes usually consist of control loops and proportional integral (PI) controllers. However, such control schemes have a number of defects [28]. They have a complex structure, are time-consuming; and require PI gain tuning [29]. Furthermore, due to the nonlinear characteristics of PV systems and unpredictable environmental conditions, PI controllers are not appropriate for standalone PV systems [30]. In addition, MPPT controllers can be operated in the absence of control loops, which is known as direct MPPT control. The PI control loops are eliminated and the duty cycle is computed directly with algorithms. In this study, a direct MPPT control scheme based on the power–duty curve is adopted.
The rest of this paper is organized as follows. Section II introduces the MFO algorithm and its application in MPPT. Sections III and IV present simulation and experiment results. Finally, some conclusions are made in Section V.
II. MFO AND ITS APPLICATION IN MPPT
A. MFO Algorithm
Moths have a special navigation method at night which is called transverse orientation. In this mechanism, they fly by maintaining a fixed angle with respect to the moon, which is very helpful for traveling long distances in a straight line. When a light source is close, moths fly spirally around it and finally converge toward it after a few corrections. Based on the flight characteristics of moths, Mirjalili proposed a new optimization algorithm, MFO algorithm.
In the MFO algorithm, every moth is required to move around a unique corresponding flame, which results in a better exploration of a search space and a lower probability of local optima stagnation. Therefore, a set of flame locations can be represented in a matrix with the same dimensions as moth positions. Furthermore, it is noted that both the moths and the flames are solutions. The difference between them is the way they are treated and updated in each iteration. The moths are actual search agents that move around the search space. Meanwhile, flames are the best solutions obtained by moths so far. In other words, flames can be considered as flags or pins that are dropped by moths when exploring a search space. Each moth searches around a flame and updates it in case of finding a better solution. With this mechanism, a moth never loses its best solution.
In order to mathematically model this behavior, each moth position is updated with respect to a flame using the following equation:
(1)where Mi indicates the i-th moth, Fj indicates the j-th flame, and S is the spiral function.
The utilized spiral function should subject to the following conditions.
a) The moth position is the initial point of a spiral.
b) The flame location is the final point of a spiral.
c) The fluctuation range of the spiral should not exceed the search space.
After considering these requirements, the spiral function can be represented as follows:
(2)
(3)where Di indicates the distance between the i-th moth and the j-th flame, b is a constant for defining the spiral shape, and t is a random number in [r,1]. The adaptive convergence constant r linearly decreases from -1 to -2 to accelerate the convergence around a flame over the course of iterations. The lower the value of t, the closer the distance between the i-th moth and the j-th flame. Fig. 1 depicts the spiral flight of a moth around its corresponding flame.
Fig. 1. Spiral flight of a moth around its corresponding flame.
If moths were required to move around N different flames all the time, this would deteriorate the exploitation of the best solution. To resolve this concern, the number of flames is adaptively decreased over the iterations as Eq. (4). After the reduction in the number of flames in each generation, the corresponding moth updates its position according to the worst flame position.
(4)where l is the current iteration, N is the maximum number of flames, and T indicates the maximum number of iterations. The adaptive mechanism for the flame number provides an efficient balance between the exploration and exploitation in a solution space.
B. Application of MFO for MPPT
Considering the superior ability of the MFO algorithm in terms of local optima avoidance and convergence, this paper adopts it to solve multiple peaks and to track the global MPP of a PV system under PSCs. Simultaneously, a direct MPPT control scheme based on a power–duty curve is adopted in this paper. To implement the MFO-based MPPT, every duty is defined as a moth and each moth’s best position is considered as a flame.
Moths are required to update their positions with respect to their corresponding flames during optimization, and the sequence of the flames is dynamically adjusted based on updated best fitness values in each iteration. If the updated fitness value of a moth position is superior to its corresponding flame, its updated location is selected as the flame location in the next iteration.
The adaptive mechanism for the flame number provides an efficient solution to the coordination problem between global and local searching during MPPT. In other word, the MFO algorithm is able to swiftly and accurately track the global MPP.
If s PV system is severely affected by extrinsic factors, the MFO algorithm would be executed again to track a new global MPP. The restart condition can be described as a scenario in which:
(5)where P0 is the power in the steady state, P1 is the power in the next sampling period, and 
is the restart tolerance. A flow chart of the MFO algorithm is presented in Fig. 2.
Fig. 2. Flowchart of the MFO algorithm.
III. SIMULATION RESULTS AND ANALYSIS
MATLAB/Simulink software is used to implement a number of simulations. The simulation model of a PV MPPT system consists of five parts, including a PV array (5×1), a boost convertor, a MPPT control module, and a linear resistive load as shown in Fig. 3. The components for the designed MPPT system are chosen as MOSFET Frequency f = 50 kHz, C1 = 100 
, L = 0.5 mH, C2 = 100 
and Rload = 40 
. An equivalent model [31] replaces the PV module to carry out the simulation. The principal simulation parameters of the model under STC are Pmax = 100 W, Vmp =18.48 V, Imp = 5.41 A, Uoc = 22.92 V and Isc = 5.7 A.
Fig. 3. Simulation model of a PV MPPT system.
In order to validate the performance of the proposed algorithm, tracking performances of the MFO are compared with those from P&O, INC, PSO and WOA in three scenarios. To ensure a fair comparison among these algorithms, the number of particles in PSO, the number of whales in WOA and the number of moths in MFO are set to be identical. Furthermore, PSO, WOA and MFO continue to operate until reaching the same maximum iteration. The principal parameters of the five algorithms and the initial positions are summarized in Table I. In this table, Np, Nw, Nm and tmax represent the numbers of particles, the number of whales, the numbers of moths and the maximum iteration, respectively.
| Algorithms |
Parameters |
Initial positions |
| P&O |
∆D = 0.02 |
1.0 |
| INC |
∆D = 0.02 |
1.0 |
| PSO |
|
0.1,0.3,0.5,0.7,0.9 |
| WOA |
|
0.1,0.3,0.5,0.7,0.9 |
| MFO |
|
0.1,0.3,0.5,0.7,0.9 |
, 
A. Uniform Illumination Condition
In this condition, the irradiance of each module is 1000 W/m2 and the temperature is 25℃. A single MPP exists in the corresponding P-U curve as shown in Fig. 4(a), whose value is about 502.30 W. Tracking traces for five algorithms are shown in Fig. 4(b)-(f).
|
(a) |
|
(b) |
|
(c) |
|
(d) |
|
(e) |
|
(f) |
The performances of five algorithms are shown in Fig. 5. Under uniform illumination condition, all five algorithms can track the MPP. P&O and INC take about the same time to reach the MPP due to an identical step size ∆D. Although adopting a small step, they fluctuate around the MPP as shown in Fig. 4(b) and (c), which wastes some of the available energy. PSO does not have special operators to coordinate global and local searching. Thus, it spends more time tracking the MPP than the WOA and MFO. When compared to PSO and WOA, the tracking time of MFO is shortened by 11.76% and 4.26% due to the adaptive mechanism for the number of flames.
Fig. 5. Performances of five algorithms under the uniform illumination condition.
As shown in Fig. 4(f), the position of the global MPP was found in the sixth iteration. However, the sequence of the flames changes very little during this period, which causes the moth locations to rarely move. After the flames number is reduced from three to two in the next iteration, the MFO algorithm quickly converges to the global MPP.
B. Partial Shading Condition
Under this condition, the temperature of five modules is 25℃ and the irradiance values of five PV modules are set to 400, 800, 800, 1000 and 1000 W/m2. A corresponding P-U curve under the PSC is shown in Fig. 6(a). Three peaks exist in the curve, and the second peak is the global MPP whose value is about 100.73 W. MPPT traces for five algorithms are shown in Fig. 6(b)-(f).
|
(a) |
|
(b) |
|
(c) |
|
(d) |
|
(e) |
|
(f) |
The performances of five algorithms are shown in Fig. 7. The P&O and INC converge to a local MPP because they are unable to discriminate between local MPPs and the global MPP. The PSO, WOA and MFO achieve the goals of reaching the global MPP. When compared to PSO and WOA, the tracking time of MFO is reduced by 17.65% and 10.64% in this scenario.
Fig. 7. Comprehensive performances of five algorithms under the PSC.
Although WOA and MFO can provide efficient solutions to the coordination problem between global and local searching during MPPT, they are different in terms of how they are realized. WOA depends on two main internal parameters (A and C), while MFO relies on a dynamically updated flame sequence and an adaptive number of flames. Remarkably, unlike A which is decreased linearly over the course of iterations, C provides random values throughout optimization. The vector C is very helpful for the avoidance of local optima, especially at later stages. Nevertheless, there is no such thing as a free lunch. In final iterations, some of the whales still attempt to search for better prey, which is unnecessary and wastes a massive amount of tracking time. This is why the convergence time of MFO is faster than that of WOA.
In the MFO algorithm, moths are required to update their positions with respect to their corresponding flames, which advances high diversification and guarantees the avoidance of local MPPs. Simultaneously, the adaptive mechanism for the number of flames provides an efficient solution to the coordination problem between global and local searching during MPPT. Therefore, the MFO algorithm can exhibit better performance than P&O, INC, PSO and WOA in terms of tracking time and tracking efficiency.
C. Rapidly Changing Irradiation Condition
In order to investigate and verify the performance of the proposed algorithm under sudden changes in the condition of the environment, a step change is set from the uniform irradiation condition to the PSC. Initially, the PV array is under the uniform irradiation condition and the irradiance values of five PV modules are set as 1000 W/m2. At t = 2 s, the illumination condition suddenly changes to the PSC. The irradiances of each module under the PSC are 400, 800, 800, 1000 and 1000 W/m2. The corresponding P-U curve is shown in Fig. 8(a). The trails for the P&O, INC, PSO, WOA and MFO algorithms are plotted in Fig. 8(b)-(f).
|
(a) |
|
(b) |
|
(c) |
|
(d) |
|
(e) |
|
(f) |
The comprehensive performances of the five algorithms are summarized in Fig. 9. As shown in Fig. 8(b) and (c), the tracking trajectories of the P&O and INC algorithms still have steady-state oscillations. However, they can immediately track a new global MPP when the environment suddenly changes. PSO and WOA reach the global MPP again. However, they consume more time than MFO.
Fig. 9. Comprehensive performances of five algorithms under the rapidly changing condition.
IV. EXPERIMENTAL RESULTS
To verify the effectiveness of the proposed algorithm, two experimental scenarios are designed: the uniform illumination condition and the partial shading condition. The PV array is composed of five PV panels configuration in series. The solar panels used in the experiment have the following specifications: maximum power of a solar panel (under STC) PMPP = 100 W, voltage at MPP VMPP = 18.48 V, current at MPP IMPP = 5.41 A, open circuit voltage VOC = 22.92 V and short circuit current ISC = 5.70 A. The specifications of the experimental system are the same as those in the simulation. In order to create the PSC, one PV module is shaded with semi-transplant film (12mm). In this experiment, a DSP (Digital Signal Processor) (TI TMS320F28335) is used to execute MPPT algorithms and to control the DC/DC boost converter. The switching frequency of the boost converter is 50 kHz. A photograph of the experimental devices is shown in Fig. 10.
Fig. 10. Photograph of experimental devices.
Fig. 11(a) and Fig. 12(a) provide experimental power–duty curves under the uniform illumination condition and the PSC, respectively. The power–duty curves are obtained by utilizing global scanning and the scan step size is chosen as 0.01. In P&O, 
=0.02; in INC, 
=0.02; in PSO, the number of particles is Np =5, ω=0.2, c1 =0.3, c2 =0.5 and tmax=10; in WOA, the number of whales is Nw =5, tmax=10; in MFO, the number of moths is Nm =5, tmax=10.
|
(a) |
|
(b) |
|
(c) |
|
(d) |
|
(e) |
|
(f) |
|
(a) |
|
(b) |
|
(c) |
|
(d) |
|
(e) |
|
(f) |
Under the uniform illumination condition, all five algorithms are able to successfully track the MPP whose value is about 400.22 W, as shown in Fig. 11(b)-(f). The simulation and experimental performances of the five MPPT algorithms are summarized in Table II. As can be seen in Table II, the MFO algorithm converges quickly to the MPP and sharply shortens the tracking time when compared with the other four algorithms.
| Scenario |
Global MPP (W) |
Algorithms |
Tracking time (s) |
Tracking power (W) |
Tracking efficient |
| Uniform illumination condition |
502.30 |
P&O |
0.66 |
497.33-502.02 |
99.01%-99.94% |
| INC |
0.66 |
497.32-502.03 |
99.01%-99.95% |
||
| PSO |
1.02 |
502.19 |
99.98% |
||
| WOA |
0.94 |
502.26 |
99.99% |
||
| MFO |
0.90 |
502.29 |
99.99% |
||
| PSC |
330.75 |
P&O |
0.40 |
183.70-187.87 |
55.54%-56.80% |
| INC |
0.40 |
183.69-187.87 |
55.54%-56.80% |
||
| PSO |
1.02 |
330.73 |
99.99% |
||
| WOA |
0.94 |
330.27 |
99.85% |
||
| MFO |
0.84 |
330.73 |
99.99% |
||
| Rapidly changing condition |
330.75 |
P&O |
0.04 |
326.32-330.73 |
98.66%-99.99% |
| INC |
0.04 |
326.44-330.72 |
98.70%-99.99% |
||
| PSO |
1.04 |
330.70 |
99.98% |
||
| WOA |
1.00 |
330.61 |
99.96% |
||
| MFO |
0.80 |
330.73 |
99.99% |
||
| Uniform illumination condition (experimental) |
400.22 W |
P&O |
1.52 |
398.46 |
99.56% |
| INC |
1.52 |
398.52 |
99.58% |
||
| PSO |
1.02 |
399.96 |
99.94% |
||
| WOA |
1.02 |
399.98 |
99.94% |
||
| MFO |
0.26 |
400.06 |
99.96% |
||
| PSC (experimental) |
292.64W |
P&O |
0.98 |
231.58 |
79.13% |
| INC |
0.98 |
232.14 |
79.33% |
||
| PSO |
1.02 |
292.15 |
99.83% |
||
| WOA |
1.02 |
292.23 |
99.86% |
||
| MFO |
0.24 |
292.28 |
99.88% |
In Fig. 12 (a), it is easy to see that there are two peaks in the power–duty curve and that the global maximum power is about 292.64W. Fig. 12 (b) and (c) show the tracking trajectories of the P&O and INC. It is easy to confirm that they get trapped in local MPPs whose values are about 231.58 W. However, PSO, WOA and MFO successfully track the global MPP as shown in Fig. 12 (d)-(f). Tracking takes about 1.02 s, 1.02s and 0.24 s by using PSO, WOA and MFO, respectively. When compared to PSO and WOA, the MFO algorithm reduces the tracking time by 76.47% because the adaptive mechanism for the flame number provides an efficient solution to the coordination problem between global and local searching. Therefore, the obtained experimental results verify that the proposed algorithm has a higher tracking accuracy and tracking speed in comparison with P&O, INC, PSO and WOA.
V. CONCLUSIONS
This paper introduces a new optimization algorithm called the MFO algorithm to extract the maximum power for PV systems, and its performance is compared with P&O, INC, PSO and WOA. Table II presents a performance comparison of the P&O, INC, PSO, WOA and MFO algorithms in terms of tracking speed and tracking efficiency under all of the simulation and experimental conditions. From Table II, it is observed that the proposed MPPT algorithm exhibits superior performance when compared to the other four MPPTs under various conditions including the PSC. However, the proposed algorithm has a longer response time in comparison with other algorithms. This is a disadvantage of the MFO algorithm that will be the subject of future studies.
ACKNOWLEDGMENT
This paper was supported by the National Key Research and Development Program of China (2017YFE0132100); National Natural Science Foundation of China (61571324); Headquarters Research Projects of State Grid Corporation of China (5700-201946239A-0-0-00).
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Ji-Ying Shi was born in Tianjin, China, in 1959. He received his M.S. and Ph.D. degrees from Tianjin University, Tianjin, China, in 1993 and 1996, respectively. He was a Visiting Scholar and a Postdoctoral Researcher at the Hong Kong University of Science and Technology, Hong Kong, China, from July 1996 to November 1999. He is presently working as an Associate Professor of Electrical Engineering and Automation at Tianjin University. His current research interests include power electronic techniques, renewable energy and soft switching techniques.
Deng-Yu Zhang was born in Hengshui, China, in 1993. He received his B.S. degree in Aeronautical Automation from the Civil Aviation University of China, Tianjin, China, in 2016; and his M.S. degree in Electrical Engineering from Tianjin University, Tianjin, China, in 2019. He is presently working as an Engineer in the China Automotive Technology and Research Center Co., Ltd., Tianjin, China. His current research interests include maximum power point tracking technology, renewable energy, power electronic techniques and electromagnetic compatibility (EMC).
Fei Xue was born in Guyuan, China, in 1994. He received his B.S. and M.S. degrees in Electrical Engineering from Tianjin University, Tianjin, China, in 2014 and 2017, respectively. He is presently working as an Engineer in the Electric Power Research Institute, State Grid Ningxia Electric Power Company (NEPC), Ningxia, China. His current research interests include maximum power point tracking technology, renewable energy, and the modeling and planning of distribution networks.
Ya-Jing Li was born in Handan, China, in 1995. She received her B.S. degree in Electrical Engineering and Automation from Yanshan University, Qinhuangdao, China, in 2016; and her M.S. degree in Electrical Engineering from Tianjin University, Tianjin, China, in 2019. She is presently working as a Hardware Engineer in INSPUR Co., Ltd., Jinan, China. Her current research interests include power electronic techniques, renewable energy and active distribution network planning.
Wen Qiao received her B.S. degree from the Taiyuan University of Technology, Taiyuan, China. She is presently working towards her M.S. degree at Tianjin University, Tianjin, China. Her current research interests include the modeling and planning of active distribution networks, renewable energy and solid-state transformers.
Wen-Jing Yang is presently working towards her M.S. degree at Tianjin University, Tianjin, China. Her current research interests include the reactive power optimization technology of distribution networks, renewable energy and power electronic techniques.
Yi-Ming Xu was born in Tangshan, China, in 1994. He received his B.S. degree from the Hebei University of Science and Technology, Shijiazhuang, China, in 2017. He is presently working toward his M.S. degree at Tianjin University, Tianjin, China. His current research interests include the analysis and design of permanent magnet synchronous motors and renewable energy harvesting.
Ting Yang is a Professor of Electrical Engineering at Tianjin University, Tianjin, China. He was a winner of the Education Ministry's New Century Excellent Talents Supporting Plan. Professor Yang is the author or co-author of four books, and more than 60 publications in technical journals and conference proceedings. He served as the chairman of two IEEE international conference workshops. He is a Member of International Society for Industry and Applied Mathematics (SIAM), a Senior Member of the Chinese Institute of Electronic, and a Committee Member of Electronic Circuit and Systems. His current research interests include power electronic techniques and renewable energy.