Investigation of Partial Shading Scenarios on a Photovoltaic Array’s Characteristics

The purpose of this study is to investigate the impact of different partial shading scenarios on a PV array’s characteristics in order to develop a simple and easy-to-implement GMPP controller that tracks the PV array’s global maximum power point (GMPP). The P-V characteristic of the PV array becomes more complicated under partial shading, owing to the presence of many power peaks, as opposed to uniform irradiance conditions, when there is only one peak called the maximum power point. In fact, and according to an experiment conducted in this study, when a PV array is partially shaded, the P-V characteristic mostly presents two peaks, given the existence of only two levels of irradiance, one of which is called the global peak (i.e., the GMPP). Furthermore, the first peak is located at Vmpp1 (the PV array’s voltage corresponds to this peak), whereas the second is at Vmpp2. The proposed approach works by estimating the values of Vmpp1 and Vmpp2 using two equations in order to control the DC/DC converter of the PV system. The first equation is used when the GMPP is at the first peak, while the other is used when the GMPP is at the second peak. Several scenarios are simulated and presented in this paper to verify the accuracy of these equations. In addition, some conclusions are drawn to suggest a simple method for tracking the GMPP.


Introduction
Solar PV energy has piqued the curiosity of researchers all around the world in recent years [1,2]. Many researchers are working on the P-V and I-V characteristics of PV panels to extract energy with high reliability and improve their efficiency [3]. Solar irradiation, which is either uniform or non-uniform over a PV panel, has a significant impact on the characteristics of a PV array [4]. Under uniform solar irradiation conditions (i.e., when all PV panels receive the same insolation), the PV array's P-V characteristic has one peak called the maximum power point (MPP). This MPP can be tracked using conventional maximum power point tracking (MPPT) approaches to extract the maximum power from the panels [5][6][7][8].
In the case of non-uniform solar irradiation or partial shading conditions (PSC) (i.e., when the insolation received by some PV panels (shaded panels) is less than that received by the other PV panels), the shaded PV panels act as a load instead of a power generator. This leads to the HOT-SPOT problem, which can damage the shaded panels [9][10][11]. This is why bypass diodes are used and connected in parallel with the panels to force the current from the unshaded PV panels to pass through the bypass diodes of the shaded PV panels to protect them from the HOT-SPOT problem. It should be mentioned that in the case of PSC, the energy production of the PV system could be decreased by 10-70% [12][13][14]. Furthermore, under PSC, the P-V characteristic of the PV array presents many peaks, one of which is the global peak, which reflects the PV array's global maximum power point (GMPP), while the others are the local peaks. Conventional MPPT approaches such as perturb and observe (P&O) and incremental conductance, on the other hand, are unable to discover the GMPP under PSC because they converge to the MPP that comes into contact first and fails to differentiate between a GMPP and a local MPP. To address this issue, a variety of GMPPT strategies have been proposed in the literature, including particle swarm optimization (PSO), artificial bee colony (ABC), artificial neural network (ANN), fuzzy logic control (FLC), and gray wolf optimization (GOW), which can track the true GMPP under PSC [15][16][17][18][19][20][21][22]. However, these techniques are complicated in terms of their real implementation [20]. The high complexity of these techniques requires finding a simple and easy method to track the GMPP of the PV array under PSC. Aside from that, several researchers have investigated the PV array's P-V characteristic under PSC to provide a simple method to track the GMPP. In [23][24][25][26], the authors provide a good explanation of the effect and assessment of PSC on the P-V characteristic. Often, the P-V characteristic of a PV array mostly presents two peaks located in two areas. The GMPP is the high peak between the two peaks, and it is sometimes located in area 1 and other times in area 2. As a result, studying the P-V characteristic curve with various numbers of shaded modules is critical for determining the GMPP's location. In this context, some previously published articles aimed to identify the critical point that separated these two areas [27,28]. Simulations have been performed in these studies with the irradiance value of the shaded panels set to 0, 100, 200, 300, 400, 500, 600, 700, 800, and 900 W/m 2 , whereas in this work, and based on an experimental test, it is found that the irradiance value in the shaded panel area is generally constant around a unique value (in our case 100 W/m 2 ). Subsequently, we assumed that the value of the irradiance of the shaded panels was 100 W/m 2 , a value that would be applied in all test simulations of the different PSC scenarios.
The main goal of this work is to study different partial shading scenarios on PV array characteristics in order to provide a simple and easily applicable method for GMPP tracking. The objective is to estimate the voltage values of the two MPP peaks presented in the P-V curve. To this end, two equations are proposed: Equation (1) for estimating the voltage at the first peak and Equation (2) for estimating the voltage at the second peak. The idea behind this is to propose a simple technique to control the DC/DC converter, using Equation (1) when the GMPP is located at the first peak (area 1) and Equation (2) when the GMPP is located at the second peak (area 2).
The remainder of this paper is organized as follows. Section 2 introduces the PV characteristics under uniform irradiance conditions. In Section 3, the impact of partial shading on the PV array characteristics is investigated. Section 4 presents the findings and discussion. Finally, Section 5 concludes the work and gives some suggestions for future research.

PV Characteristics under Uniform Irradiance Conditions
The one-diode model of the PV cell, as shown in Figure 1, is used to characterize the PV array in this work [29]. Multiple PV panels (or modules) are connected in series, parallel, or series-parallel to form a PV array. A PV panel, on the other hand, is a collection of cells connected in series or parallel. The characteristics of the PV panel used are shown in Table 1 [30]. Figure 2 shows the configuration of the PV array under consideration, which was composed of six PV panels connected in series and having the same characteristics. Figure 3 depicts the P-V curves of the PV array obtained for different levels of uniform irradiation (all PV panels received the same insolation) from 100 to 1000 W/m 2 . As seen in this figure, each P-V curve had just one peak point, known as the MPP.

PV Characteristics under Non-Uniform Irradiance Conditions
When one or more of the PV panels are shaded, as can be seen in Figure 4, they ac as loads instead of an energy source. Therefore, the shaded PV panels will be damage under long-term working conditions (the HOT-SPOT phenomena). As a solution, each PV panel is connected in parallel with bypass diodes to force the current from the unshade PV panels to pass through the bypass diodes of the shaded PV panels to prevent th shaded panels from self-heating [31]. In addition, under the non-uniform irradiation con ditions (partial shading), the PV array's P-V characteristic exhibits numerous peaks, ow ing to the presence of different levels of irradiation; one of them is the global peak, whic reflects the PV array's MPP (GMPP), while the others are the local peaks. . PV array with three PV panels exposed to shade. Figure 5 shows a simulation result of the PV array's P-V characteristic for three di ferent tests, including the uniform and non-uniform irradiance conditions for STC (all PV panels received the same solar irradiation of 1000 W/m²) and for two shading scenario The first test of the shading scenarios was performed with an irradiance value of 100 W/m for five shaded PV panels and 300 W/m 2 for the remaining unshaded PV panel, while th 2 Figure 3. The PV array's P-V curves at various irradiation levels.

PV Characteristics under Non-Uniform Irradiance Conditions
When one or more of the PV panels are shaded, as can be seen in Figure 4, they act as loads instead of an energy source. Therefore, the shaded PV panels will be damaged under long-term working conditions (the HOT-SPOT phenomena). As a solution, each PV panel is connected in parallel with bypass diodes to force the current from the unshaded PV panels to pass through the bypass diodes of the shaded PV panels to prevent the shaded panels from self-heating [31]. In addition, under the non-uniform irradiation conditions (partial shading), the PV array's P-V characteristic exhibits numerous peaks, owing to the presence of different levels of irradiation; one of them is the global peak, which reflects the PV array's MPP (GMPP), while the others are the local peaks.

PV Characteristics under Non-Uniform Irradiance Conditions
When one or more of the PV panels are shaded, as can be seen in Figure 4, they act as loads instead of an energy source. Therefore, the shaded PV panels will be damaged under long-term working conditions (the HOT-SPOT phenomena). As a solution, each PV panel is connected in parallel with bypass diodes to force the current from the unshaded PV panels to pass through the bypass diodes of the shaded PV panels to prevent the shaded panels from self-heating [31]. In addition, under the non-uniform irradiation conditions (partial shading), the PV array's P-V characteristic exhibits numerous peaks, owing to the presence of different levels of irradiation; one of them is the global peak, which reflects the PV array's MPP (GMPP), while the others are the local peaks. . PV array with three PV panels exposed to shade. Figure 5 shows a simulation result of the PV array's P-V characteristic for three different tests, including the uniform and non-uniform irradiance conditions for STC (all PV panels received the same solar irradiation of 1000 W/m²) and for two shading scenarios. The first test of the shading scenarios was performed with an irradiance value of 100 W/m 2 for five shaded PV panels and 300 W/m 2 for the remaining unshaded PV panel, while the second test was performed with an irradiance value of 100 W/m 2 for three shaded PV panels and 700 W/m 2 for the other unshaded PV panels. From this figure, the P-V curve . PV array with three PV panels exposed to shade. Figure 5 shows a simulation result of the PV array's P-V characteristic for three different tests, including the uniform and non-uniform irradiance conditions for STC (all PV panels received the same solar irradiation of 1000 W/m 2 ) and for two shading scenarios. The first test of the shading scenarios was performed with an irradiance value of 100 W/m 2 for five shaded PV panels and 300 W/m 2 for the remaining unshaded PV panel, while the second test was performed with an irradiance value of 100 W/m 2 for three shaded PV panels and 700 W/m 2 for the other unshaded PV panels. From this figure, the P-V curve showed only one peak point under STC, while it showed two peaks for both shading scenarios. Each of these peaks was characterized by its own voltage and power: Vmpp1 and Pmpp1 for the first peak and Vmpp2 and Pmpp2 for the second one. While the largest value between Pmpp1 and Pmpp2 represents the GMPP, which sometimes existed in area 1 and other times in area 2.
Electronics 2022, 11, x FOR PEER REVIEW 5 of 13 showed only one peak point under STC, while it showed two peaks for both shading scenarios. Each of these peaks was characterized by its own voltage and power: Vmpp1 and Pmpp1 for the first peak and Vmpp2 and Pmpp2 for the second one. While the largest value between Pmpp1 and Pmpp2 represents the GMPP, which sometimes existed in area 1 and other times in area 2. To apprehend the current flow direction of the PV array under PSC, consider the PV array shown in Figure 6 consisting of six PV panels, three of which were unshaded, while the others were shaded. In addition, as shown in Figure 5, the P-V curve of the PV array under PSC could be divided into two areas. In area 1, the bypass diode of each shaded PV panel conducted as a short circuit. Figure 6a depicts the equivalence diagram of the current flow direction of the PV array when the load demanded more than the current value of the shaded PV panels. Therefore, the equation of Vmpp1 can be expressed mathematically as follows: where Vmpp1 is the voltage at the first peak, Ns is the number of PV panels, Nsh is the number of shaded panels, and Vmpp,STC is the voltage at the MPP of the PV array under STC. By contrast, in area 2, the bypass diodes of all PV panels were not conducting. Figure  6b depicts the equivalence diagram of the current flow direction of the PV array when the load demanded less than the current value of the shaded PV panels. Therefore, the equation of Vmpp2 can be expressed mathematically as follows: where Vmpp2 is the voltage at the second peak. Ns is the number of PV panels, and Vmpp,STC is the voltage at the MPP of the PV array under STC. To apprehend the current flow direction of the PV array under PSC, consider the PV array shown in Figure 6 consisting of six PV panels, three of which were unshaded, while the others were shaded. In addition, as shown in Figure 5, the P-V curve of the PV array under PSC could be divided into two areas. In area 1, the bypass diode of each shaded PV panel conducted as a short circuit. Figure 6a depicts the equivalence diagram of the current flow direction of the PV array when the load demanded more than the current value of the shaded PV panels. Therefore, the equation of Vmpp1 can be expressed mathematically as follows: where V mpp1 is the voltage at the first peak, N s is the number of PV panels, N sh is the number of shaded panels, and V mpp,STC is the voltage at the MPP of the PV array under STC. To investigate the effects of partial shading on the PV array characteristics, multiple partial shading scenarios had to be simulated by changing the number of shaded panels and the incident irradiance value on the PV panels. An experimental test was conducted for this purpose in order to identify the irradiance value of the shaded panels that would be employed in all shading scenario simulations. Figure 7 presents the experimental setup for this test, which included a PV panel and two pyranometers: one for measuring irradiance levels in an unshaded place and the other for measurements in a shaded place. By contrast, in area 2, the bypass diodes of all PV panels were not conducting. Figure 6b depicts the equivalence diagram of the current flow direction of the PV array when the load demanded less than the current value of the shaded PV panels. Therefore, the equation of V mpp2 can be expressed mathematically as follows: where V mpp2 is the voltage at the second peak. N s is the number of PV panels, and V mpp,STC is the voltage at the MPP of the PV array under STC.
To investigate the effects of partial shading on the PV array characteristics, multiple partial shading scenarios had to be simulated by changing the number of shaded panels and the incident irradiance value on the PV panels. An experimental test was conducted for this purpose in order to identify the irradiance value of the shaded panels that would be employed in all shading scenario simulations. Figure 7 presents the experimental set-up for this test, which included a PV panel and two pyranometers: one for measuring irradiance levels in an unshaded place and the other for measurements in a shaded place. To investigate the effects of partial shading on the PV array characteristics, multiple partial shading scenarios had to be simulated by changing the number of shaded panels and the incident irradiance value on the PV panels. An experimental test was conducted for this purpose in order to identify the irradiance value of the shaded panels that would be employed in all shading scenario simulations. Figure 7 presents the experimental setup for this test, which included a PV panel and two pyranometers: one for measuring irradiance levels in an unshaded place and the other for measurements in a shaded place.      Table 2 lists all the tests applied to the simulation of the PV array in the Matlab Simulink environment, and Figure 9 presents the P-V characteristic obtained in each test. As can be seen in this figure, the GMPP was sometimes located at Vmpp1 and other times at Vmpp2, according to the number of shaded panels and the irradiance value of the unshaded panel. In the case of tests 1 and 2, the GMPP appeared at Vmpp1 when the irradiance value varied between 200 and 1000 W/m 2 while it appeared at Vmpp2 when the irradiance value varied between 0 and 200 W/m 2 . In the case of test 3, the GMPP appeared at Vmpp2 when the irradiance value of the unshaded panels was between 0 and 200 W/m 2 2 Figure 8. The variation in irradiance levels during a day in shaded and unshaded places. Table 2 lists all the tests applied to the simulation of the PV array in the Matlab Simulink environment, and Figure 9 presents the P-V characteristic obtained in each test. As can be seen in this figure, the GMPP was sometimes located at Vmpp1 and other times at Vmpp2, according to the number of shaded panels and the irradiance value of the unshaded panel. In the case of tests 1 and 2, the GMPP appeared at Vmpp1 when the irradiance value varied between 200 and 1000 W/m 2 while it appeared at Vmpp2 when the irradiance value varied between 0 and 200 W/m 2 . In the case of test 3, the GMPP appeared at Vmpp2 when the irradiance value of the unshaded panels was between 0 and 200 W/m 2 and appeared at Vmpp2 when this value was between 200 and 1000 W/m 2 . As for tests 4 and 5, analogous scenarios could be noted where the GMPP was located at Vmpp1 when the irradiance value of the unshaded panels was above a certain threshold, and it was located at Vmpp2 when the irradiance value was below a certain threshold.   Tables 3-7 present the simulation data of the P-V characteristic for the five shading scenarios, including the values of Vmpp1 and Vmpp2, and their corresponding estimated values. The estimated value of Vmpp1 by Equation (1) was almost equal to the corresponding simulated value, with a maximum error of about 0.63% in test 1, 0.65% in test 2, 0.62% in test 3, 0.81% in test 4, and 0.64% in test 5. On the other hand, the estimated value of Vmpp2 by Equation (2) and the corresponding simulated value were different, with a maximum error of up to 16% in test 1, 10% in test 2, 6% in test 3, 4% in test 4, and 2% in test 5. However, when the GMPP was located at the second peak, the maximum error of the estimated value of Vmpp2 could reach 3.8%. Therefore, we could consider Equation (2) to estimate the value of Vmpp2. From these results, many critical observations can be extracted, such as the following:

Results and Discussion
(i) The first peak was created by the unshaded PV panels; (ii) The second peak was affected by shading on the PV panels; (iii) The localization of the GMPP was influenced by the irradiance value of the unshaded panels and the number of shaded panels.   As the results of all the simulation tests show that the GMPP sometimes existed in area 1 and other times in area 2, it was necessary to determine the area of the GMPP or the critical point to control the DC/DC converter using Equation (1) for area 1 and Equation (2) for area 2 for the purpose of extracting the GMPP from the PV system. Figure 10 presents the variation of Pmpp1 and Pmpp2 according to the irradiance value of the unshaded panel for the five tests. From this figure, the critical point is the intersection of the Pmpp1 and Pmpp2 curves. In addition, it is observed that the critical point was influenced by the irradiance value of the shaded panel and the number of shaded panels. Furthermore, the critical point changed when the number of shaded panels and the irradiance value of the shaded panels changed, as shown in Figure 10. Therefore, the GMPP was Pmpp1 in the case where the irradiance value of the shaded panel was less than or equal to the critical point value, whereas it was Pmpp2 in the case where the irradiance value was greater than or equal to the critical point value.

Conclusions
The goal of this paper is to investigate the impact of different partial shading scenarios on the PV array's characteristics. First, an experimental test was performed to determine the irradiance value of the shaded panels, which was then used in all shading scenario simulations. The test, which was performed on two different days in two different months, showed that the irradiance value in a shaded location remained relatively constant. Then, two equations were given to estimate the voltages corresponding to two peaks presented in the P-V characteristic: Equation (1) for the first peak and Equation (2) for the second one. In addition, to check the accuracy of these proposed equations, simulation tests were performed for different partial shading scenarios. The obtained results showed that the estimated value of the voltage corresponding to the first peak by Equation (1) was almost equal to the simulated value with a maximum error of about 0.81%. Whereas the estimated value of the voltage corresponding to the second peak by Equation (2) and the corresponding simulated value were different, with a maximum error of up to 16% for test 1, 10% for test 2, 6% for test 3, 4% for test 4, and 2% for test 5. Based on the obtained research results, it was observed that the error of the estimate value of the voltage corresponding to the second peak was almost equal to the simulated value, with a difference of 2% when the GMPP was located at the second peak.
The following two aspects will be the focus of future research: (1) Finding the critical point in the form of an equation using a multiple regression algorithm or an artificial intelligence algorithm, which will allow us to know the area of the global peak in order to control the DC/DC converter using the two equations given in this work: Equation (1) when the GMPP is located at the first peak and Equation (2) when the GMPP is located at the second peak; (2) Design a GMPPT controller based on the proposed method and validate its feasibility of implementation in a real PV system.

Conclusions
The goal of this paper is to investigate the impact of different partial shading scenarios on the PV array's characteristics. First, an experimental test was performed to determine the irradiance value of the shaded panels, which was then used in all shading scenario simulations. The test, which was performed on two different days in two different months, showed that the irradiance value in a shaded location remained relatively constant. Then, two equations were given to estimate the voltages corresponding to two peaks presented in the P-V characteristic: Equation (1) for the first peak and Equation (2) for the second one. In addition, to check the accuracy of these proposed equations, simulation tests were performed for different partial shading scenarios. The obtained results showed that the estimated value of the voltage corresponding to the first peak by Equation (1) was almost equal to the simulated value with a maximum error of about 0.81%. Whereas the estimated value of the voltage corresponding to the second peak by Equation (2) and the corresponding simulated value were different, with a maximum error of up to 16% for test 1, 10% for test 2, 6% for test 3, 4% for test 4, and 2% for test 5. Based on the obtained research results, it was observed that the error of the estimate value of the voltage corresponding to the second peak was almost equal to the simulated value, with a difference of 2% when the GMPP was located at the second peak.
The following two aspects will be the focus of future research: (1) Finding the critical point in the form of an equation using a multiple regression algorithm or an artificial intelligence algorithm, which will allow us to know the area of the global peak in order to control the DC/DC converter using the two equations given in this work: Equation (1) when the GMPP is located at the first peak and Equation (2) when the GMPP is located at the second peak; (2) Design a GMPPT controller based on the proposed method and validate its feasibility of implementation in a real PV system.