https://doi.org/10.6113/JPE.2018.18.3.841
ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718
Dual-Algorithm Maximum Power Point Tracking Control Method for Photovoltaic Systems based on Grey Wolf Optimization and Golden-Section Optimization
Ji-Ying Shi*, Deng-Yu Zhang*, Le-Tao Ling**, Fei Xue†, Ya-Jing Li*, Zi-Jian Qin***, and Ting Yang*
*Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, China
**Shenzhen Power Supply Bureau, China Southern Power Grid, Shenzhen, China
†Electric Power Research Institute, State Grid Ningxia Electric Power Company, Yinchuan, China
***Laiwu Power Supply Bureau, State Grid Shandong Electric Company, Laiwu, China
Abstract
This paper presents a dual-algorithm search method (GWO-GSO) combining grey wolf optimization (GWO) and golden-section optimization (GSO) to realize maximum power point tracking (MPPT) for photovoltaic (PV) systems. First, a modified grey wolf optimization (MGWO) is activated for the global search. In conventional GWO, wolf leaders possess the same impact on decision-making. In this paper, the decision weights of wolf leaders are automatically adjusted with hunting progression, which is conducive to accelerating hunting. At the later stage, the algorithm is switched to GSO for the local search, which play a critical role in avoiding unnecessary search and reducing the tracking time. Additionally, a novel restart judgment based on the quasi-slope of the power-voltage curve is introduced to enhance the reliability of MPPT systems. Simulation and experiment results demonstrate that the proposed algorithm can track the global maximum power point (MPP) swiftly and reliably with higher accuracy under various conditions.
Key words: Golden-section optimization, Maximum power point tracking, Modified grey wolf optimization, Partial shading conditions, Photovoltaic systems
Manuscript received Sep. 28, 2017; accepted Jan. 16, 2018
Recommended for publication by Associate Editor Jonghoon Kim.
†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
**Shenzhen Power Supply Bureau, China Southern Power Grid, China
***Laiwu Power Supply Bureau, State Grid Shandong Electric Co., China
Ⅰ. INTRODUCTION
To mitigate the international energy crisis and reduce environmental pollution, the exploitation of renewable energy is experiencing rapid growth around the world. Among various kinds of renewable energy, solar energy is considered to be an important energy source due to it being abundant, inexhaustible and environment-friendly. PV power generation has become an indispensable method for the utilization of solar energy. To harvest PV energy more efficiently, maximum power point tracking (MPPT) techniques are being developed. However, it is essential to tackle two major challenges in the application of a MPPT technique. On the one hand, the power-voltage characteristic curve of a PV array is nonlinear, which depends on solar irradiance and temperature [1]. On the other hand, under partial shading conditions (PSCs) due to clouds, buildings, trees, and so on, local maximum power points (MPP) can appear on the power-voltage curve because it is necessary to make the bypass diode in parallel with PV modules to avoid the hot spot effect [2].
On the whole, MPPT techniques consist of conventional and intelligent MPPT methods [3]. Conventional MPPT methods (including perturb and observe (P&O) [4], incremental conductance (INC) [5], GSO [6], beta method [7], etc.) have simple structures and low equipment requirement. However, these conventional methods can be immersed in local MPPs under PSCs, which decreases the efficiency of a PV system. To improve conventional methods ability to track the actual global MPP under PSCs, several attempts have been suggested in the literature. For example, the authors of [8] reported a MPPT controller that uses a field programmable gate array (FPGA)-based real time INC. This method is capable of having excellent timing performance since one of the most important features of FPGA is the implementing of circuits by hardware description, which gives FPGA the highest timing performance when compared with DSPs, microcontrollers and even analogue circuits. The authors of [9] proposed a modified β-parameter-based method with an optimized scaling factor. However, due to the use of a PV emulator in its experiment, the sampling time for the MPPT controller is long since the PV emulator has dynamic constraints and a slower response speed than a practical crystalline PV.
Intelligent methods include PSO [10], [11], firefly algorithm (FA) [12], [13], cuckoo search (CS) [14], [15] and grey wolf optimization (GWO) [16]. These methods are capable of tracking the global MPP. However, intelligent methods are generally more complex and slower than conventional methods. Recently, a lot work has been done to optimize these algorithms [17]. The authors of [18] proposed a modified FA algorithm that uses the average position of all of the brighter fireflies as the representative point. As a result, the fireflies move toward this point without wandering toward all of the brighter flies. Furthermore, a boost converter with an interleaved topology is used as the dc–dc converter in this method to reduce ripple currents, improve reliability and increase efficiency. The authors of [19] described an optimal control scheme for the single-phase grid-connected PV systems under different fast variation shading patterns. The scheme combines the extended memory searching capabilities and adaptive inertia weight of the modified PSO. In this method, a PWM with permutations of the DC converter switching is applied to balance the switch utilization.
GWO is an intelligent algorithm proposed in 2014 by Mirjalili [20]. A large body of research has demonstrated that GWO shows satisfactory performance in various fields such as wind turbines [21], solar thermal power systems [22], large scale power systems [23] and smart grids [24]. Four merits of GWO can be summarized as: simplicity, flexibility, efficient exploitation and exploration [20]. This paper presents a dual-algorithm search method combining GWO and GSO to track the global MPP under various conditions. In the original GWO [16], wolf leaders possess the same impact on decision-making. In the proposed algorithm, the decision weights of the wolf leaders are automatically adjusted with hunting progression, which is helpful for hunting prey rapidly and efficiently. The concept of search density is also introduced as reference for deciding the maximum iteration and number of wolves. At the later stage, the algorithm is switched to the local search implemented by GSO, which is advantageous for avoiding unnecessary search and reducing the tracking time. In addition, conventional restart judgment based on the power change ratio can be invalid in the case of particular rapid changes in irradiation conditions. Therefore, a novel restart judgment based on the quasi-slope of power-voltage curve is introduced to enhance the reliability of MPPT systems.
Conventional MPPT control schemes usually consist of control loops and proportional integral (PI) controllers. However, such control schemes have the following defects [25]: complex structure; (2) time-consuming; and (3) the need to tune the PI gain. Furthermore, due to the nonlinear characteristics of PV systems and unpredictable environmental conditions, PI controllers are not appropriate for standalone PV systems [26]. In addition, MPPT controllers can be operated in the absence of control loops, which is known as the direct MPPT control scheme. The PI control loops are eliminated and the duty cycle is computed directly with algorithms. In this study, the direct MPPT control scheme based on the power–duty curve is adopted.
The rest of this paper is organized as follows. Section II briefly introduces the basics of GWO and GSO. Section III describes the proposed algorithm. Section IV and V present simulation and experiment results. Some conclusions are made in Section VI.
Ⅱ. BASIC OF GWO AND GSO
A. GWO
GWO originates from the social hierarchy and hunting mechanism of grey wolves in nature. Grey wolves are inclined to live in a pack and the size of the pack is usually between 5 and 12. The size of the wolf pack in this paper is six. They have a rather strict social dominant hierarchy. Four types of grey wolves, alpha (α), beta (β), delta (δ), and omega (ω), are used to simulate the social hierarchy of a grey wolf whose dominance decreases from front to rear. Four main steps are implemented for realizing optimization in GWO, which are chasing, approaching, encircling and attacking. Encircling behavior can be modeled by the following equations:
where t is the current iteration, 
is the position vector of the prey, and 
is the position vector of the grey wolf. 
and 
are the only intermediate coefficient vectors, which are obtained by:
Because 
is decreased linearly from 2 to 0, the iteration can be used as the intermediate variable. Consequently, 
is described as:
decreases linearly from 2 to 0 during the course of optimization, and r1 and r2 are random vectors in [0, 1]. Consequently, 
and lie inside the interval of 
and [0, 2], respectively. Wolves attack towards prey when 
. When the values of 
and 
are bigger than 1, GWO shows random behavior to avoid being trapped in local optima. Grey wolves diverge from prey in hopes of finding better prey when 
.
The hunting mechanism in GWO is dominated by the social hierarchy in a wolf pack. Specifically speaking, the three best wolves lead the wolf pack to hunt prey. In other words, the three best wolves are the leaders of the pack. In the next hunting, the positions of the wolf leaders are saved and the other wolves have to update their positions according to the positions of the wolf leaders. The positions of common wolves in the next iteration are proposed as follows:
In this paper, search density is first introduced as reference for deciding the maximum iteration and number of wolves. The search density is defined as:
where 
is the search density, Nw and tmax represent the number of wolves and the maximum number of iterations, respectively. A larger search density increases tracking efficiency but reduces the tracking speed. On the other hand, a small search density reduces the tracking time, but degrades search accuracy. A reasonable search density gives an optimal tradeoff between tracking time and tracking accuracy. After repeated simulations, the search density threshold is identified to be 0.03. In other words, the search density ρ must satisfy equation (14). In this paper, Nw is set to be six and tmax is set as 7. Therefore, the value of 
is 0.0238.
where ρ is the search density threshold.
B. GSO
GSO is a classical solution to the single peak optimizing problem. A search interval [a, b] of length L is divided by two points X1 and X2, which must satisfy equation (15).
where the value of λ is equal to 0.618. After comparing the corresponding function values f(X1) and f(X2), GSO selects the next search space according to the following rules. If f(X1) < f(X2), the maximum must lie in the range of [X1, b], which is taken as a new interval for the next iteration. On the other hand, if f(X1) > f(X2), [a, X2] is taken in the next iteration. The new interval is always 0.618 times the original interval. The process is repeated continuously until the distance between X1 and X2 is less than a certain chosen precision.
Ⅲ. PRINCIPLE OF PROPOSED ALGORITHM
The authors of [16] reported a MPPT scheme that uses GWO to track the global MPP. However, the method requires numerous iterations resulting in substantial power losses. Compared with the original GWO, three promising features of the proposed algorithm can be summarized as follows.
A. Automatically Adjusting the Decision Weights
In this paper, the size of the wolf pack is six and the best two wolves are selected to be the leaders of the pack. The two leaders of the pack are represented by α and β, which are considered to have better knowledge concerning the potential location of prey. In this paper, the global MPP is regarded as prey. In the beginning of the search, α and β possess the same influence in terms of leading the wolf pack. As the search advances, the decision weights of α and β are adjusted automatically to accelerate the tracking speed. Specifically, the decision weight of α becomes increasingly heavy and the decision weight of β becomes increasingly light as given by equations (19) and (20). This is helpful for speeding up the tracking. On the one hand, if the leaders possess the same decision weights all the time, there may be a delay in decision-making. On the other hand, after the decision weights are dynamically adjusted, the wolf pack possesses a more specific tracking target. In every iteration, the positions of α and β are saved and the rest of wolves are obliged to move their positions as follows:
In the search process, wolves jump to the place where prey is likely to exist. All of the wolves track the prey based on the encircling behavior of GWO. With the tracking advancing, the size of the encirclement comprising of the wolf pack shrinks by degrees. The size of the encirclement is indicated by the distance between the two farthest wolves in the exploitation, which narrows by degrees as depicted in Fig. 1.
Fig. 1. Distance between the two farthest wolves as the exploitation narrows by degrees.
B. Local Search Stage
The algorithm is transformed from the global search to the local search when either of two conditions is achieved: the first one is reaching the maximum iteration; the second one is satisfying the judgment of successful hunting. The judgment of successful hunting is expressed by equation (22).
where d1-2 is the distance between α and β, and N is the number of PV modules in a series. It is considered that the desired prey is found when both α and β acquire the approximate position of the global MPP. Then tracking is switched to the local search. Otherwise, at the later stage, some of the wolves still attempt to explore for better prey, which is unnecessary and wastes a massive amount of tracking time. The local search is implemented by GSO. Before the algorithm enters GSO, the positions of two wolf leaders are selected to serve as initial search interval endpoints. However, it is possible that the global MPP does not lie within the initial search interval. Therefore, the initial search interval is expanded by desi as shown in Fig. 2. The formula for desi is written as:
desi is large enough to ensure that the global MPP is covered in the initial search interval.
Fig. 2. Expanding the initial search interval of GSO.
Due to the characteristic of GSO, the tracking time is shortened a lot and oscillation hardly exists in the steady state.
C. Modified Restart Judgment
If a PV system is severely affected by extrinsic factors, it is necessary to execute the procedure again to track a new global MPP. Detecting the power change ratio is one of the conventional restart judgments. It can be described as the scenario in which:
where P0 is the power in the steady state, P1 is the power in the next sampling period, and 
is the restart tolerance.
However, it is possible for this restart judgment to be invalid when a tiny variation cannot be detected as given by:
where τ is the power change ratio. Power-duty curve under a particular rapidly changing irradiation condition is depicted in Fig. 3. The value of τ is 0.001 in the case of Fig. 3, which is difficult to detect. Considering that the slope of the power-voltage curve can serve as a reference for restarting the algorithm, the quasi-slope of the power-voltage curve is introduced to enhance the reliability of the restart judgment, which is inspired by the INC. The quasi-slope can be described as:
Fig. 3. Power-duty curve under a particular rapidly changing irradiation condition.
where the value of μ is set to be 0.001 to prevent a zero- denominator. The quasi-slope is 6.02 under the circumstance of Fig. 3, which is big enough to detect and restart. This allows the PV system to reliably detect variations in the irradiation condition and reduce power loss. The above-proposed improvement is summarized in the flowchart shown in Fig. 4.
Fig. 4. Flowchart for the GWO-GSO algorithm.
Ⅳ. SIMULATION RESULTS AND ANALYSIS
In order to verify the performance of the proposed algorithm, MATLAB/Simulink software is used to implement simulations. An equivalent model [27] replaces the PV module to carry out the simulation. The principal simulation parameters of the model under STC are Pmax = 60 W, Vmp = 17.1 V, Imp = 3.5 A, Uoc = 21.1 V and Isc = 3.8 A.
The simulation model for a PV MPPT system consists of five parts, including a PV string, boost circuit, MPPT control module, PWM 50kHz module and load as shown in Fig. 5. 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 = 120 
.
Fig. 5. Simulation model for a PV MPPT system.
The results obtained with the GWO-GSO are compared with those from the P&O, PSO, GWO and GWO-P&O under various environmental conditions. It is necessary to ensure a fair comparison among these algorithms. Therefore, the numbers of particles and wolves are set to be identical. The principal parameters of the five algorithms are summarized in Table I. In this table, Np and Nw are the numbers of particles and wolves, respectively. tmax represents the maximum number of iterations.
| Algorithms |
Adjustable parameters |
Initial positions |
| P&O |
ΔD = 0.01 |
1.0 |
| PSO |
|
0.1,0.3,0.4,0.6,0.7,0.9 |
| GWO |
|
0.1,0.3,0.4,0.6,0.7,0.9 |
| GWO-P&O |
|
0.1,0.3,0.4,0.6,0.7,0.9 |
| GWO-GSO |
|
0.1,0.3,0.4,0.6,0.7,0.9 |
,
A. Uniform Illumination Condition
The irradiance of each module is 1000 W/m2, and a single MPP exists in the corresponding power-duty curve as shown in Fig. 6(a), whose value is about 239.40 W. Tracking traces for the five algorithms are also shown in Fig. 6.
|
(a) |
|
(b) |
|
(c) |
|
(d) |
|
(e) |
|
(f) |
The comprehensive performances of the five algorithms are shown in Table II. It can be seen that the five algorithms all can reach the MPP. However, the steady-state efficiency of GWO-P&O is reduced due to the fixed-step size P&O at the later stage as shown in Fig. 6(e). Compared to PSO, GWO and GWO-P&O, the tracking time of the GWO-GSO is shortened by 39.53%, 39.53% and 40.91%, respectively.
B. Partial Shading Condition
The irradiance values of four PV modules are set as 300, 500, 850 and 1000 W/m2, which is the most complicated situation for a 4×1 string. The corresponding power-duty curve under PSC is shown in Fig. 7(a). Four peaks exist in the curve, and the third peak is the global MPP whose value is about 100.73 W. The MPPT traces for the five algorithms are also shown in Fig. 7.
|
(a) |
|
(b) |
|
(c) |
|
(d) |
|
(e) |
|
(f) |
The comprehensive performances of the five algorithms are listed in Table 3. P&O converges to a local MPP because it is unable to discriminate between a local MPP and the global MPP. PSO, GWO, GWO-P&O and GWO-GSO achieve the goals of reaching the global MPP. The steady-state oscillation of GWO-P&O still exists due to the fixed-step size P&O as shown in Fig. 7(e). Compared to PSO, GWO and GWO-P&O, the tracking time of the GWO-GSO is reduced by 25.58%, 25.58% and 27.27% in this scenario.
C. Rapidly Changing Irradiation Conditions
A novel restart judgment is examined and analyzed in this scenario. A step change is set from PSC to uniform irradiation condition. Initially, the PV string is under PSC. The irradiance values of four PV modules under PSC are set as 300, 500, 850 and 1000 W/m2. At t = 1.5 s, the isolation suddenly changes to uniform irradiation condition. The irradiance of each module under uniform irradiation condition is 810 W/m2. The corresponding power-duty curve and the trails for these five algorithms are plotted in Fig. 8.
|
(a) |
|
(b) |
|
(c) |
|
(d) |
|
(e) |
|
(f) |
The comprehensive performances of the five algorithms are summarized in Table 4. In this scenario, P&O gets trapped in local MPP3 before t = 1.5 s. Subsequently, P&O is capable of tracking the global MPP because the irradiation condition is uniform after t = 1.5 s. However, PSO and GWO fail to restart because the conventional restart judgment cannot detect tiny variations in power as depicted in Fig. 8(c) and 8(d). GWO-P&O is capable of restarting and tracking the global MPP with the help of the perturbing in P&O. The proposed algorithm overcomes the drawbacks of the conventional restart judgment and responds accurately under irradiation changes as shown in Fig. 8(f). Furthermore, the GWO-GSO has the fastest tracking speed and the lowest power loss among all of the algorithms. Generally speaking, the GWO-GSO clearly outperforms the other four algorithms in this scenario.
Ⅴ. EXPERIMENTAL RESULTS
The experimental devices consist of a PV string (4×1), a DC-DC boost converter, a purely resistive load, and a DSP (Digital Signal Processor) (TI TMS320F28335), which is used to execute MPPT algorithms. Solar panels are used in the experiment with the following specifications: the 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 main components for the boost converter are the same as those in the simulation. A picture of the experimental setup is shown in Fig. 9.
Fig. 9. Picture of the experimental setup.
A current sensor (CC65) is used to sense the current of the PV string Ipv. The voltage of the PV string Vpv can be acquired directly from the voltage divider circuit of the PV string. The Vpv and Ipv signals are transmitted to the DSP via sensor circuits and A/D converters. Then optimization algorithms are implemented by the DSP, which sends out a PWM signal to the gate driver for controlling the MOSFET switch. The switching frequency of the boost converter is 50 kHz. Therefore, the MPPT sampling period for the experiment is 20 
. The MPPT sampling period is set as an identical value to compare the performances of these algorithms fairly.
To validate the proposed algorithm, a case under PSC is investigated. In order to create PSC, PV modules are shaded with different semi-transplant films (12mm). Fig. 10(a) provides the power-duty curve under PSC, which is obtained by utilizing global scanning, where the scan step size is chosen as 0.01. In P&O, 
=0.01; in PSO, the number of particles is Np =6, ω=0.5, c1 =0.5, c2 =1.0 and tmax=7; in GWO, the number of wolves is Nw =6, tmax=7, 
=0.05; in GWO-P&O, the number of wolves is Nw =6, tmax=7, the step length is 0.0015; in the GWO-GSO, the number of wolves is Nw =6, tmax=7, 
=2. The experimental tracking trajectories of the five algorithms are shown in Fig. 10.
|
(a) |
(b) |
|
(c) |
(d) |
|
(e) |
(f) |
It is easy to confirm that P&O gets trapped in a local MPP as shown in Fig. 10(a). PSO, GWO, GWO-P&O and the GWO-GSO successfully find the global MPP. It takes about 0.86s, 0.86s, 0.88s and 0.54s to track the global MPP by using PSO, GWO, GWO-P&O, and the GWO-GSO, respectively. After satisfying the judgment of successful hunting, the proposed algorithm is switched to the local search and thus saving a lot of tracking time. The judgment of successful hunting can reduce inefficient searching and unnecessary iterations, which shortens the tracking time by 37.21% in this case. Fig. 10 indicates that the tracking time of the GWO-GSO is the shortest among all of the algorithms. Therefore, the experiment results verify that the proposed algorithm has a higher tracking speed and tracking accuracy in comparison with P&O, PSO, GWO and GWO-P&O.
Ⅵ. CONCLUSIONS
This paper introduces a dual-algorithm search method for MPPT and demonstrates its ability to extract the global MPP. Simulation and experiment results show that the tracking time of the proposed algorithm is greatly reduced due to variations in the decision weights and the mechanism of successful hunting. The extracted power also becomes higher due to the local search implemented by GSO at the later stage. In addition, a novel restart judgment based on the quasi-slope of the power-voltage curve enhances the reliability of a MPPT system. In terms of tracking time and output power, the proposed GWO-GSO exhibits better performance than P&O, PSO, GWO and GWO-P&O under various conditions.
ACKNOWLEDGMENT
This paper is supported by the National Key Research and Development Program of China (2017YFB0903000); National Natural Science Foundation of China (61571324); Natural Science Foundation of Tianjin (16JCZDJC30900); and National Program of International S&T Cooperation (2013 DFA11040).
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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. He is presently working toward his M.S. degree at Tianjin University, Tianjin, China. His current research interests include maximum power point tracking technology, renewable energy and power electronic techniques.
Le-Tao Ling received his M.S. degree from Tianjin University, Tianjin, China, in 2018. He is presently working for the Shenzhen Power Supply Bureau, China Southern Power Grid (CSG), Shenzhen, China. His current research interests include the maximum power point tracking of photovoltaic and wind power systems, renewable energy and power electronic techniques.
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 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 received her B.S. degree in Electrical Engineering and Automation from Yanshan University, Qinhuangdao, 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 power electronic techniques.
Zi-Jian Qin was born in Laiwu, China, in 1990. He received his M.S. degree from Tianjin University, Tianjin, China, in 2017. He is presently working for the Laiwu Power Supply Bureau, State Grid Shandong Electric Power Company, Laiwu, China. His current research interests include the modeling and simulation of microgrids and the maximum power point tracking of photovoltaic and wind energy generation systems.
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. Professor Yang's current research interests include power electronic techniques and renewable energy.