Global Maximum Power Point Tracking of Photovoltaic Module Arrays Based on Improved Artificial Bee Colony Algorithm

Abstract

In this paper, an improved artificial bee colony (I-ABC) algorithm for the maximum power point tracking (MPPT) of a photovoltaic module array (PVMA) is presented. Even though the P-V output characteristic curve with multi-peak was generated due to any damages or shading discovered on the PVMA, the I-ABC algorithm could get rid of stuck on tracking the local maximum power point (LMPP), but quickly and stably track the global maximum power point (GMPP), thereby improving the power generation efficiency. This proposed I-ABC algorithm could search for the higher power point of a PVMA by a small bee colony, determine the next tracking direction through the perturb and observe (P&O) method, and keep tracking until the GMPP is obtained. This method could prevent tracking the GMPP for too long due to applying a small bee colony. First, in this study, the photovoltaic modules produced by Sunworld Co., Ltd. were used and were configured as a PVMA with four series and three parallel connections under different numbers of shaded modules and different shading ratios, so that corresponding P-V output characteristic curves with multi-peak values were generated. Then, the GMPP was tracked by the proposed MPPT method. The simulation and experimental results showed that the proposed method performed better both in dynamic response and steady-state performance than the traditional artificial bee colony (ABC) algorithm. According to the experimental results, it showed that the tracking accuracy for the GMPP based on the proposed MPPT with 100 iterations under 5 different shading ratios was about 100%; on the other hand, that of the traditional ABC algorithm was 70%, and that of the P&O method was lower at about 30%.

1. Introduction

When the photovoltaic module array is shaded or failed, multi-peak values will be observed in the P-V output characteristic curve with different conditions. In order to maximize the output power of the photovoltaic module array, it shall be controlled by the maximum power point tracker of the power conditioner [1]. Due to the consideration of development costs, most current commercial power conditioners use traditional methods for MPPT, such as incremental conductance (INC) [2], perturb and observe (P&O) [3], power feedback, and the constant voltage method, etc. However, as the P-V output characteristic curve with multi-peak values is generated due to any shading or failures discovered on the module array, those above-mentioned traditional methods for MPPT will fail to track the GMPP, thereby reducing the output power.

In recent years, many scholars have focused on those methods for the MPPT in response to such a P-V output characteristic curve with multi-peak values, caused by some modules shaded in the photovoltaic module array. To solve the problem of being stuck on the local maximum power point tracking (LMPPT) based on traditional algorithms for MPPT, these studies mainly apply algorithms for artificial MPPT. Most popular algorithms for artificial MPPT are ant colony optimization (ACO) [4], differential evolution (DE) [5], artificial bee colony (ABC) [6], and particle swarm optimization (PSO) [7], etc. The ACO algorithm is a probabilistic algorithm for optimizing routes, and its update formula is exponential as stated in reference [8], thereby making its path length and pheromone concentration as random values. Such random path length and pheromone concentration might get rid of stuck on tracking the LMPP, but it would make the tracking time too long. In addition, the differential evolution is similar to the genetic algorithm (GA), which applies real number coding for specific races and accomplishes searching for the global best value through differencing variance and one-to-one competitive survival strategy. However, it makes tracking time increased due to the multiple formulas that are required for operating while individuals carry out mutation. On the other hand, the ABC algorithm optimizes the group foraging process by sending employed bees to find food sources, wherein those employed bees will transfer information about the location and direction of the food sources to other bees by dancing. However, those employed bees search for food sources randomly, so as to make their search abilities less stable; moreover, the number of employed bees dispatched is proportional to the searching time during the food source search, so it takes much longer if more employed bees are dispatched for searching [8]. In addition, the PSO algorithm, proposed in 1995 by two scholars, Kennedy and Eberhart, who were inspired by the predation behavior of birds, is an artificial algorithm [9]. This algorithm has the advantages of fewer parameters and a simple iterative formula, but if the particle moving is too large, it may not be capable of tracking the GMPP but rather oscillate back and forth in its vicinity; on the contrary, if the particle moving is too small, it is easily stuck on tracking the LMPP, resulting in the tracking speed being slow.

Therefore, in this paper, an I-ABC algorithm for the MPPT of a photovoltaic module array with some modules shaded or failed is developed. It is characterized by less employed bees and a shorter searching time because it can combine with the P&O method to determine the moving direction of the bee colony according to the amount of food source; therefore, it can reduce the number of employed bees and shorten the search time. Compared with the traditional ABC algorithm, this method can quickly find the best food source through less employed bees. Therefore, it could get rid of stuck on tracking the LMPP, and address such time-consuming issues found in traditional artificial algorithms for the global maximum power point tracking (GMPPT), thereby improving the output power of a photovoltaic module array.

2. Traditional Artificial Bee Colony Algorithm

The traditional ABC algorithm is a swarm artificial algorithm, proposed by Karaboga in 2005 [10,11], based on the artificial foraging behavior of bee colonies. In order to find the best nectar during foraging, the bees are divided into employed bees, onlookers, and scouts, wherein the employed bees are responsible for collecting nectar and transferring information, the scouts are responsible for finding food sources, and the onlookers are responsible for optimizing the best flight routes. A scout will search for food sources either based on previous experience or just randomly and become an employed bee to collect nectar and memorize certain information about the food sources found. Later, when it brings the nectar back to the hive, it will pass that information about the food source to the onlooker. As such information has been passed, this employed bee may go back to the mentioned food source to continue nectar collection or return to be a scout to continue a new food source search again based on previous experience or randomly. On the other hand, the onlooker will determine the best route for nectar collection based on the information about food sources taken early or abandon those food sources with less nectar stock. Figure 1 is a schematic diagram of collecting the nectar of a bee colony. According to reference [12], in the traditional ABC algorithm, the tracking speed and steady-state performance will be affected by the number of scouts and there may be some errors of information about food sources memorized by the employed bees; therefore, there may be some errors of the best routes optimized by onlookers if the wrong information is received, which will slow down the tracking speed in the later stage. Therefore, it really needs to introduce other algorithms for improving the tracking speed.

Please refer to the steps of the traditional ABC algorithm as follows:

Step 1. Set initial parameters, including the maximum number of iterations (ME), the number of employed bees (SN), the initial number of food sources searched by each employed bee $x_i^0$, and the initial number of the best and worst food sources searched by all employed bees $v_{best}^0$ and $v_{worst}^0$, and the initial number of iterations j = 0.

Step 2. Substitute the food sources $x_i^j$ randomly searched after the j-th iteration by each employed bee into the random search Equation (1) for searching new food sources.

$$x_i^{j+1}=x_i^j+rand[0,1](v_{best}^j-v_{worst}^j)i=1,2,\dots ,SN;j=0,1,\dots ,ME$$

(1)

wherein, $x_i^{j+1}$ is the value of the (j+1)-th iteration obtained by the i-th employed bee; $x_i^j$ is the value of the j-th iteration obtained by the i-th employed bee; $v_{best}^j$ is the best value of j-th iteration obtained by the SN employed bees; $v_{worst}^j$ is the worst value of the j-th iteration obtained by SN employed bees; and rand [0, 1] is a random number between 0 and 1.

Step 3. Each employed bee moves according to Equation (2) to search for new food sources.

$$v_i^{j+1}=x_i^{j+1}+rand[-1,1](x_i^{j+1}-x_k^{j+1})i=1,2,\dots ,SN;j=0,1,\dots ,ME$$

(2)

wherein, $v_i^{j+1}$ is the new food sources searched after the (j+1)-th iteration by the movement of the i-th employed bee; $x_i^{j+1}$ is the value of the iteration of Equation (1); and $x_k^{j+1}$ is the value of the (j+1)-th iteration obtained by employed bee k which is rounded to closest to $x_i^{j+1}$; and rand[−1, 1] is a random number between −1 and 1. Figure 2 is a schematic diagram of the movement of employed bees at two iterations of Equations (1) and (2).

Step 4. Calculate the fitness P_i of food sources searched after the (j + 1)-th iteration by the SN employed bees through the Equation (3) with the roulette wheel method. Wherein, the maximum fitness P_i of the food source is expressed as $v_{best}^{j+1}$, and the minimum one is expressed as $v_{worst}^{j+1}$.

$$P_i=\frac{v_i^{j+1}}{{\displaystyle {\sum }_{i=1}^{SN}{v}_i^{j+1}}},i=1,2,\dots ,SN$$

(3)

Step 5. Stop to generate iterations until the maximum number of iterations (i.e., j = ME) is reached. Otherwise, set the maximum fitness P_i of food sources $v_{best}^j=v_{best}^{j+1}$, the minimum one $v_{worst}^j=v_{worst}^{j+1}$, and $x_i^j=x_i^{j+1}$, and let $j=j+1$, then skip to step 2 for the next iteration.

Figure 3 is the flowchart of the traditional ABC algorithm. If there are more bees, tracking accuracy will be higher accordingly. However, the searching time is proportional to the number of bees during the algorithm implemented with a microcontroller, i.e., the operation time is longer for a larger population; on the contrary, the operation time of the algorithm can be reduced if the number of bees is reduced, but it will be more difficult to obtain the optimal solution. Therefore, in order to address the issue that the optimal solution cannot be obtained within a limited number of iterations due to the reduction of the number of bees, an I-ABC algorithm with fewer bees combined with the P&O method is presented and applied for the MPPT of photovoltaic module array to fast track the GMPP.

3. Proposed Maximum Power Point Tracker for Photovoltaic Module Array

Figure 4 is the architecture of the maximum power point tracker for photovoltaic module array based on the I-ABC algorithm proposed in this paper, which includes the photovoltaic module arrays, the DC/DC boost converter [13], and the digital signal processor (DSP) [14] for implementing the I-ABC algorithm.

3.1. Composition of Photovoltaic Module Array

In this paper, the SWM-20W modules produced by Sunworld [15] were used to be configured as an array with four series and three parallel connections, and some of those modules were set with different shading ratios and failures. Later, the EKO MP-170 I-V tracker [16] was used to measure output, which was input into the Matlab software to simulate corresponding P-V output characteristic curves. The simulation results of MPPT could be comparable with the test results of the actual photovoltaic module array later. For specifications of electrical parameters of photovoltaic modules SWM-20W under standard test conditions (STC) (i.e., air mass (AM) as 1.5, the intensity of insolation as 1000 W/m², and temperature of the photovoltaic module as 25°C), refer to

Table 1. Specifications of electrical parameters of photovoltaic modules SWM-20W produced by Sunworld [15].

Parameters	Value
Rated maximum output power (Pmp)	20 W
Current of maximum power point (Imp)	1.10 A
Voltage of maximum power point (Vmp)	18.18 V
Short circuit current (Isc)	1.15 A
Open circuit voltage (Voc)	22.32 V
Length and width of module	395 mm × 345 mm

.

3.2. DC/DC Boost Converter

The designed parameter settings of components of the DC/DC boost converter used in this paper are listed in

Table 2. Parameter settings of components of the DC/DC boost converter [17].

Component Name	Models and Specifications
Inductor (Lm)	1.152 mH
Input capacitor (Cin)	390 μF/450 V
Output capacitor (Cout)	390 μF/450 V
Switching frequency (fs)	25 kHz
Power switching transistor (S)	MOSFET IRF460 (500 V/20 A)
Diode (D)	IQBD60E60A1 (600 V/60 A)

[17].

3.3. Improved Artificial Bee Colony Algorithm

In this paper, the digital signal processor TMS320F2809 produced by Texas Instruments was used to implement the I-ABC algorithm with the boost converter for the GMPPT of a photovoltaic module array while the photovoltaic module shaded or failed partially. The I-ABC algorithm used was obtained from improving the traditional ABC algorithm described in step 4, Section 2, and applied for the MPPT of a photovoltaic module array, wherein $v_{best}^{j+1}$ was the duty cycle of the boost converter at the optimal output power of the photovoltaic module array. The specific practice was as follows:

The practice substituted the optimal solution $v_{best}^{j+1}$ (which was obtained in step 4, Section 2 about the traditional ABC algorithm) into the P&O method [3] to increase or decrease the terminal voltage of the photovoltaic module array with a fixed disturbance, and to determine the direction where the output power increased, thereby keeping perturbing in this direction for the optimal solution $v_{best}^{j+1}$ of the next iteration. This method addressed such time-consuming issues of searching the local maximum values found in the traditional ABC algorithm, which only searched values randomly in the vicinity, so the I-ABC algorithm could determine the correct searching direction only through the P&O to quickly get rid of stuck on tracking the LMPP, thereby quickly tracking to the GMPP.

Therefore, in this paper, an algorithm that could quickly track the GMPP was proposed by combining with the P&O method and the ABC algorithm. First, the GMPP was tracked by the ABC algorithm. Then, the global peak value was tracked quickly by the P&O method. This method could address the time-consuming issue of searching the global maximum values when there is a small bee colony, and the failure to track the GMPP issue due to multi-peak values presented by the P&O method. For its detailed flowchart, refer to Figure 5.

In order to shorten the operation time of the I-ABC algorithm, small bee colonies were applied in this paper. For its parameter settings, refer to

Table 3. Parameter settings of the I-ABC algorithm.

Parameter Name	Settings
Number of bees (SN)	8
Number of iterations (ME)	50
Disturbance (∆d)	0.5% (duty cycle)

. In addition, in order to confirm its tracking performance, tests of the MPPT were performed on the photovoltaic module array with four series and three parallel connections under five different working conditions, as shown in

Table 4. Five different shading and failure conditions selected for testing.

Case	Parallel Series Configuration and Shading Ratio	The Number of Peaks in the P-V Curve
1	4 series and 3 parallel (shaded 0%)	Single-peak
2	4 series and 3 parallel (one module with shaded 30%)	Double-peak
3	4 series and 3 parallel (two modules with shaded 30% and 50%, respectively)	Triple-peak
4	4 series and 3 parallel (three modules with shaded 30%, 50%, and 70%, respectively)	Quadruple-peak
5	4 series and 3 parallel (one module with snail trails)	Double-peak

.

4. Simulation Results

In this paper, Matlab software was used to read the data measured by the MP-170 I-V checker under five different test conditions (as shown in Table 4), and to simulate MPPT based on the I-ABC algorithm, traditional ABC algorithm, and the P&O method, respectively, as well as to compare the tracking performance among different methods.

The initial voltage of the MPPT during simulation in this paper was set to 0.8 times of the voltage (about 58.176 V) of the maximum output power point (V_mp) of modules with four series connections under the standard test condition (STC), because according to reference [18], the voltage of the maximum power point of a photovoltaic module array under any conditions was about 0.8~1.1 times of V_mp under STC. Figure 6 shows the P-V characteristic curve of the photovoltaic module array under normal operating conditions and the intensity of insolation as 742 W/m² in Case 1, wherein the single-peak value was presented (P_mp = 183.29 W). According to the simulation results of the three tracking methods shown in Figure 7, it was observed that as the single-peak value presented, the GMPP could be tracked quickly either based on the I-ABC algorithm or the P&O method, but it could be tracked slowly based on the traditional ABC algorithm. In order to be fair in the tracking performance, the number of bees was set as eight both in the traditional ABC algorithm and the I-ABC algorithm; however, the required time for tracking the GMPP was longer based on the former algorithm due to the smaller bee colony.

Figure 8 shows the P-V characteristic curve of the photovoltaic module array under the intensity of insolation as 712 W/m² and one module shaded 30% in Case 2, wherein double-peak values were presented and the real MPP P_mp was 147.28 W. If the shading position of modules changed, only the double-peak values of the P-V characteristic curve would be changed accordingly. In order to speed up the tracking speed, the initial tracking voltage in this case was still set as 0.8 times of the voltage V_mp of the maximum output power point of the module array under the STC condition, i.e., 58.176 V. According to the simulation results of the three tracking methods shown in Figure 9, it was observed that the P&O method failed to track the GMPP (P_mp = 147.2 W) due to being stuck on the LMPP (P_pv = 135 W), and that the traditional ABC algorithm could track the GMPP, but its tracking speed was slower than that of the I-ABC.

Figure 10 shows the P-V characteristic curve of the photovoltaic module array under insolation intensity as 525 W/m² and two modules shaded 30% and 50%, respectively, in Case 3, wherein triple-peak values were presented and the real MPP P_mp was 102.18 W. According to the tracking simulation results of the three tracking methods shown in Figure 11, it was observed that both the I-ABC algorithm and the traditional ABC algorithm could track the GMPP (P_mp = 102.1 W). Still, the later algorithm was easier to stop near the GMPP. The reason was that if a smaller bee colony was applied in the traditional ABC algorithm, it would slow down the speed of finding the nectar sources significantly, thereby causing difficulty for the bee colony to quickly track the GMPP. On the other hand, the I-ABC algorithm proposed in this paper could quickly track the GMPP (P_mp = 102.1 W) by combining it with the P&O method. However, if only the traditional P&O method was adopted, it would only track the LMPP (P_pv = 75 W).

Figure 12 shows the P-V characteristic curve of the photovoltaic module array under insolation intensity as 534 W/m² and three modules shaded 30%, 50%, and 70%, respectively, in Case 4, wherein quadruple-peak values were presented and the real MPP P_mp was 83.84 W. According to the simulation results of the three tracking methods shown in Figure 13, it was observed that the I-ABC algorithm could track the GMPP (P_mp = 83.8 W) with only 5 iterations, but 25 for the traditional ABC algorithm. As per the P&O method, the initial tracking voltage was near the point at the valley area where the GMPP was located, so the GMPP could be tracked smoothly but more iterations are needed.

Figure 14 shows the P-V characteristic curve of the photovoltaic module array under the intensity of insolation as 639 W/m², wherein double-peak values were presented while one module with snail trails [19,20] and the real MPP P_mp was 133.59 W. From the simulation results of the three tracking methods in Figure 15, it was observed that both the improved and traditional ABC algorithms could track the GMPP (P_mp = 133.5 W), as could the P&O method with the initial tracking voltage as 58.176 V. However, the I-ABC algorithm still performed best in the tracking response among the three methods.

In this paper, the traditional ABC and the I-ABC were applied to perform 50 MPPT tests for the selected five cases, respectively. The numbers of iterations required for each GMPPT were summed up and averaged. For those results, refer to

Table 5. Comparison of the average number of iterations of the GMPPT based on two algorithms in 5 cases.

Case	Number of Peaks in the P-V Characteristic Curves	Average Number of Iterations
		Traditional ABC Algorithm	I-ABC Algorithm
1	Single-peak	10.64	4.56
2	Double-peak	15.23	6.45
3	Triple-peak	34.42	7.39
4	Quadruple-peak	38.86	10.18
5	Double-peak	27.13	10.57

. Although both algorithms could track the GMPP, it was observed that the average number of iterations required by the I-ABC in the five cases was less than the one by the traditional ABC in Table 5. This showed a better tracking performance in the proposed I-ABC for the MPPT, especially because the greater the number of peaks in the P-V characteristic curves, the greater difference in tracking performance.

In order to reduce the calculation time of the traditional ABC algorithms for speeding up the tracking response, this can only be achieved by means of the reduction of the number of bees, resulting in getting lost for GMPP and increasing the difficulty of finding the GMPP in traditional ABC algorithms. So, in this paper, we introduced the method of identifying and tracking moving directions by combining with the P&O method, and made those straying bees find their correct tracking direction after the reduction of the number of bees. By combining these two algorithms, not only could the calculation time be reduced, but also the correct tracking direction could be found during the tracking process. According to the simulation results, the proposed MPPT method of the I-ABC algorithm performed much better in tracking than the traditional ABC algorithms under the same number of bees.

5. Experimental Results

In order to verify the correctness of the simulation results in the previous section, in this paper, the 62050H-600S programmable DC power supply produced by Chroma Co., Ltd. (Taipei, Taiwan) [21] was applied to simulate the actual output P-V characteristic curves of the photovoltaic module array under STC in five cases. The MPP was tracked based on the improved and traditional ABC algorithms, respectively. The test curve was presented by the output voltage V_PV and current I_PV of the photovoltaic module array, and the tracked power P_PV was obtained by multiplying the mentioned V_PV by I_PV with the internal operation function of the oscilloscope. The initial voltage of the MPPT was still set to 0.8 times (about 58.176 V) of the voltage of the maximum output power point V_mp under the STC, and the pros and cons of the response speed of the MPPT based on the traditional ABC and the I-ABC were observed, respectively.

5.1. Case 1 (0% Shaded)

Figure 16a shows the P-V characteristic curve of the photovoltaic module array with four series and three parallel connections under STC in Case 1, which was simulated by the 62050H-600S programmable DC power supply produced by Chroma CO., Ltd., and the single-peak value (P_mp = 247.5 W) was presented. The simulated photovoltaic module arrays were tracked based on the traditional ABC and the I-ABC, respectively. From the test results shown in Figure 16b,c, it was observed that the traditional and improved ABC algorithms both could track the MPP. Still, the response speed of the MPPT based on the I-ABC algorithm was about 0.16 s faster than that of the traditional ABC.

5.2. Case 2 (One Module with 30% Shaded)

Figure 17a shows the P-V characteristic curve of the photovoltaic module array with four series and three parallel connections under STC in Case 2, and double-peak values were presented due to one module shaded and its GMPP P_mp was 200.3 W. From the test results shown in Figure 17b,c, it was observed that the response speed of the MPPT based on the I-ABC algorithm was about 0.84 s faster than that of the traditional ABC.

5.3. Case 3 (Two Modules with 30% and 50% Shaded, Respectively)

Figure 18a shows the P-V characteristic curve under STC in Case 3, and triple-peak values were presented due to two modules shaded with different ratios and its GMPP P_mp was 148.9 W. From the test results of the MPPT based on two algorithms shown in Figure 18b,c, it was observed that the response speed of the MPPT based on the I-ABC algorithm was about 0.26 s faster than that of the traditional ABC.

5.4. Case 4 (Three Modules with 30%, 50%, and 70% Shaded, Respectively)

Figure 19a shows the P-V characteristic curve of the photovoltaic module array with four series and three parallel connections under STC in Case 4, and quadruple-peak values were presented due to three modules shaded with different ratios and its GMPP P_mp was 107.7 W. From the test results of the MPPT based on two algorithms shown in Figure 19b,c, it was observed that the response speed of the MPPT based on the I-ABC algorithm was about 0.33 s faster than that of the traditional ABC.

5.5. Case 5 (Three Modules with 30%, 50%, and 70% Shaded, Respectively, in Each Series)

Figure 20a shows the P-V characteristic curve of the photovoltaic module array with four series and three parallel connections under STC. Multiple-peak values were presented due to three modules shaded with different ratios in each series and its GMPP P_mp was 77.27 W. From the test results of the MPPT based on two algorithms shown in Figure 20b,c, it was observed that the two algorithms both could track the MPP. Still, the response speed of the MPPT based on the I-ABC algorithm was about 0.96 s faster than that of the traditional ABC.

By combining with the traditional P&O, the I-ABC algorithm can increase its accuracy when determining the direction of the MPPT. In addition, comparing with traditional ABC algorithms, it can reduce the possibility of losing direction and increase the tracking speed. Although the traditional P&O has a simple structure and fast-tracking response for normal operated PVMAs, it will only track the LMPP when some modules are shaded or failed. On the other hand, the I-ABC algorithm can get rid of stuck on tracking LMPP, so that the PVMAs will operate at the GMPP accordingly. The particle swarm optimization (PSO) proposed in [7] is an intelligent algorithm, commonly used in recent years. To improve the tracking accuracy, it needs to use a large number of particle swarms, thereby making a longer time for the global tracking; on the other hand, it may get lost during the global tracking based on the reduced number of particle swarms, which makes it difficult to track the GMPP eventually. For the I-ABC algorithm, it can confirm the tracking directions with the characteristics provided by the P&O method, which is not lost even with the reduction of the number of bees. Photovoltaic module arrays with four series and three parallels under five different shading ratios as shown in Table 4 were used to perform 100 times of the tracking based on different MPPT methods, respectively, and the average values of the two performance indicators, response time and the tracked GMPP are listed in

Table 6. Comparison of experimental results for the five selected cases.

Case	Number of Peak(s) of the P-V Curve	PSO Proposed in [7]		Traditional P&O		Traditional ABC		I-ABC Proposed in This Study
		Average Tracking Time	Average Maximum Power	Average Tracking Time	Average Maximum Power	Average Tracking Time	Average Maximum Power	Average Tracking Time	Average Maximum Power
1	1	0.57 s	246.2 W	0.41 s	246.7 W	0.54 s	246.4 W	0.38 s	246.6 W
2	2	1.62 s	194.7 W	0.58 s	197.6 W	1.47 s	196.2 W	0.63 s	198.6 W
3	3	2.50 s	147.8 W	0.72 s	147.5 W	1.15 s	148.1 W	0.89 s	148.8 W
4	4	2.61 s	106.2 W	Trap in LMMP	91.2 W	1.81 s	106.8 W	1.48 s	107.1 W
5	Multiple	3.27 s	76.2 W	Trap in LMMP	46.2 W	2.10 s	76.4 W	1.14 s	77.1 W

for comparison. According to the results of the different shading ratios seen in Table 6, the I-ABC algorithm proposed in this paper performed better in various tracking performances than those similar algorithms.

6. Conclusions

In order to enhance the power generation efficiency of the photovoltaic power generation system, an artificial GMPPT based on an I-ABC algorithm was proposed in this paper. It combined with the P&O method to determine the direction for next tracking, so that it could accurately and quickly track the GMPP. From the multiple simulation results based on the proposed I-ABC in each case, it was observed that the average numbers of iterations of the GMPPT were all less than that of the traditional ABC, especially the worst ones shown in Case 3 (with triple-peak values) and Case 4 (with quadruple-peak values) based on the traditional ABC. For other cases with failures such as snail trails found, the corresponding tracking performance was not satisfied either, due to multiple-peak values and certain similar local solutions presented in the P-V characteristic curves, resulting in the fact that the traditional ABC would be stuck easily on tracking the LMPP and need more iterations for the GMPPT. In addition, from the test results, it was also observed that the tracking response speed would be much faster if the initial voltage of the MPPT was still set to 0.8 times of the voltage of the maximum output power point V_mp under STC, but not zero voltage. Moreover, those tracking speeds based on the I-ABC in different cases were all faster than those of the traditional ABC, because the proposed I-ABC algorithm would combine with the P&O method, which made it not be stuck easily on tracking the LMPP, and the number of iterations reduced significantly. The time required for the GMPPT shortened, thereby dramatically improving the output power of the photovoltaic module array accordingly. It mainly focused on improving the power generation efficiency of PVMAs in this paper. To set PVMAs under the conditions for obtaining the best efficiency, the GMPP was tracked within the shortest time based on the I-ABC algorithm, thereby reducing the power generation lost during the tracking process. In addition, this algorithm was also suitable for the photovoltaic power generation system (PVPGS) connected with the grid. In the PV grid-connected system, the PV inverter generally controls its output voltage and current, which both are sine waves and the same phase, as no abnormal fluctuation is found in the system voltage and its output power factor (PF) is 1.0. Therefore, the PVPGS can output all as active power to the grid-connected system. On the other hand, if the insolation rises or falls sharply, the power of the large PV grid-connected system delivered into the grid system will also rise or drop sharply. If the load end cannot consume or make up for the sudden power rise or drop, the voltage at the grid connection point will also rise or drop sharply, which will cause the load end equipment to be damaged accordingly. To avoid such a situation, it is recommended to adjust the active and reactive power by a smart inverter for stabilizing the voltage at the grid connection point. Therefore, it is recommended to address the problem of unstable voltage of the power supply in the grid system caused by the fluctuation of load power consumption or the fluctuation of electricity supplied by smart inverter for controlling voltage-power or by establishing an energy storage system, which is irrelevant to the MPPT method proposed in this paper. The power-voltage regulation of a smart inverter will be the topic of future research.