A Novel Ten Check Maximum Power Point Tracking Algorithm for a Standalone Solar Photovoltaic System

Optimal energy extraction under partial shading conditions from a photovoltaic (PV) array is particularly challenging. Conventional techniques fail to achieve the global maximum power point (GMPP) under such conditions, while soft computing techniques have provided better results. The main contribution of this paper is to devise an algorithm to track the GMPP accurately and efficiently. For this purpose, a ten check (TC) algorithm was proposed. The effectiveness of this algorithm was tested with different shading patterns. Results were compared with the top conventional algorithm perturb and observe (P&O) and the best soft computing technique flower pollination algorithm (FPA). It was found that the proposed algorithm outperformed them. Analysis demonstrated that the devised algorithm achieved the GMPP efficiently and accurately as compared to the P&O and the FPA algorithms. Simulations were performed in MATLAB/Simulink.


Introduction
The depletion of fossil fuels, continuously growing energy demands, greenhouse gas (GHG) emissions, and swelling prices of fossil fuels have turned the world's attention towards renewable and sustainable energy resources, such as solar photovoltaics (SPV) [1,2].
Transforming solar irradiance into electrical energy is the job of SPV [3]. Due to nonlinear electrical characteristics and dependence on weather conditions, the photovoltaic (PV) array cannot operate at its maximum power point (MPP). To do so, electronic trackers termed as maximum power point trackers (MPPTs) are used [4]. MPPTs are governed by different algorithms/techniques. As PV depends on weather conditions, tracking becomes difficult with changing weather conditions, especially in partial shading conditions (PSCs).
In uniform weather conditions (UWCs), all the cells of a PV array receive the same illumination, and there is only one peak in the power-voltage (P-V) curve of a PV array. Partial shading occurs when part of the PV array is shaded. This shaded part acts as a load to the unshaded part of the PV array and creates hotspots. To secure the PV array from hotspots, parallel diodes are connected across PV modules of the PV array called bypass diodes. When a PV module is shaded, it is automatically bypassed by the bypass diodes. This reduces the effect of shading at the PV array output power and prevents PV module hotspots. However, in partial shading, multiple power peaks are created in the P-V curve of the PV array due to bypass diodes. These multiple peaks are known as the local maximum power points (LMPP), except for the one with the highest power, which is called the global maximum power point (GMPP). It is very difficult to find the GMPP out of multiple LMPPs.
Conventional and soft computing (SC) MPP tracking techniques are the existing solutions for extracting maximum power from a PV array. Conventional MPPT algorithms include perturb and In case-1 of Figure 1, there was a condition of zero shading [29]. In case-2, 50% of the PV array was shaded. Two out of four PV modules (half of the PV array) experienced the shading effect of same level (300 W/m 2 ). This created two MPPs in the P-V curve of the PV array, one due to the top two unshaded panels and one due to the two equally shaded panels. In case-3, 75% of the PV array was shaded. Three of the four PV modules received different illuminations (1000, 600, and 300 W/m 2 ), which created three MPPs in the P-V curve of the PV array and formed a more complex situation of GMPP tracking. Bypass diodes were used to avoid "hotspots" [30], and blocking diodes were used to stop the "reverse flow of current" [17]. One single peak was generated in the P-V curve in a uniform illumination condition and multiple peaks were generated in the P-V curve due to the number of peaks depending upon the strength of shading. In case-1 of Figure 1, there was a condition of zero shading [29]. In case-2, 50% of the PV array was shaded. Two out of four PV modules (half of the PV array) experienced the shading effect of same level (300 W/m 2 ). This created two MPPs in the P-V curve of the PV array, one due to the top two unshaded panels and one due to the two equally shaded panels. In case-3, 75% of the PV array was shaded. Three of the four PV modules received different illuminations (1000, 600, and 300 W/m 2 ), which created three MPPs in the P-V curve of the PV array and formed a more complex situation of GMPP tracking. Bypass diodes were used to avoid "hotspots" [30], and blocking diodes were used to stop the "reverse flow of current" [17]. One single peak was generated in the P-V curve in a uniform illumination condition and multiple peaks were generated in the P-V curve due to the number of peaks depending upon the strength of shading.

Problem Formulation
Due to the existence of multiple power peaks in the P-V curve of the PV array, an appropriate algorithm which can accurately and efficiently access the GMPP is desired. The effectiveness of the applied algorithm will affect the overall efficiency of the PV system. Bearing in mind all the above facts, the novel TC algorithm was proposed for tacking the GMPP under all weather conditions.

Ten Check Algorithm
The proposed TC algorithm smartly tackles the tracking process in 10 simple steps. Initially, 10 random samples (duty cycles) are generated in the given range of variables "A and B" (0-0.1) in the first iteration using MATLAB command rand (1,1). (This generates uniformly distributed pseudorandom numbers drawn from the standard uniform distribution on the open interval (0, 1)). Power against each sample is calculated. The sample with highest power is saved as the "1st best" solution. In the second iteration, variables "A and B" are incremented to (0.1-0.2). The same process is repeated for the new range of variables "A and B" to get the "2nd best". This process repeats until the number of sets reach their defined threshold value of "TEN" with variables "A and B" at "0.9-1.0", respectively, and an array of the top 10 solutions (one solution at the end of each iteration) is obtained. The proposed TC algorithm picks the best solution from the solution array. The TC algorithm then stays with the best achieved solution and starts checking for changing weather conditions using Equations (1) and (2) [26,30]. The reinitialization of tracking process depends on the detection of changing weather. When a change is sensed, the parameters will reset automatically, and the tracking process will start again. This simple technique is equally effective in UWCs and PSCs. The TC technique is more accurate, efficient, and effective than any other existing MPPT technique. A flowchart of the TC algorithm is displayed in Figure 2.
Avoiding complex procedures of generating random numbers and time-wasting comparisons at each step, the TC algorithm enhances GMPP tracking speed and accuracy.
The characteristics of the PV array directly depend on weather conditions. The GMPP changes with the change in illumination and temperature; therefore, the detection of weather changes is obligatory. This change can be detected by the amount of change in voltage or current. The threshold values for the change in voltage (dV) and change in current (dI) set by the experimental trials performed in [26][27][28][29][30] are "0.2-V and 0.1 A", respectively. These conditions are sensitive for the change of 50 W/m 2 . The present operating values of voltage and current are compared with their values obtained at the end of tracking process.
Vpv(t) is the voltage of a PV array at the t-th iteration and Vpv(t − 1) is the voltage of array at the preceding iteration. Ipv(t) is the current of a PV array at the t-th iteration and Ipv(t − 1) is the current of a PV array at the preceding iteration.

Simulation and Results
The performance evaluation and comparison of the TC algorithm with the P&O and FPA algorithms was performed in MATLAB/Simulink. The three different shading patterns discussed in Figure 1 were used for the evaluation. The system's configuration at which the algorithms were tested was 64-bit Operating System, intel i3 Processor, and 4.00 GB RAM. The structure of the PV system with the MPPT controller is displayed in Figure 3. The TC algorithm was coded in the MATLAB/Simulink's function block, displayed in light blue color of Figure 3. The algorithm generated a number in the range 0-1, which was injected as a duty cycle input to the DC-DC converter to change the DC voltage level. The sample time among inputs (duty cycles) was set as 0.03 s for the FPA algorithm, as mentioned in [29]. The parameter values for the P&O, FPA, and TC algorithms are presented in Table 1.

Simulation and Results
The performance evaluation and comparison of the TC algorithm with the P&O and FPA algorithms was performed in MATLAB/Simulink. The three different shading patterns discussed in Figure 1 were used for the evaluation. The system's configuration at which the algorithms were tested was 64-bit Operating System, intel i3 Processor, and 4.00 GB RAM. The structure of the PV system with the MPPT controller is displayed in Figure 3. The TC algorithm was coded in the MATLAB/Simulink's function block, displayed in light blue color of Figure 3. The algorithm generated a number in the range 0-1, which was injected as a duty cycle input to the DC-DC converter to change the DC voltage level. The sample time among inputs (duty cycles) was set as 0.03 s for the FPA algorithm, as mentioned in [29]. The parameter values for the P&O, FPA, and TC algorithms are presented in Table 1.

Case-1: Zero Shading
In this case, where all the modules in the PV array received the same illumination and temperature, there was only one peak power point in the P-V curve. Achieving MPP here was an easy task for the P&O, FPA, and TC algorithms. The P-V and current-voltage (I-V) characteristic curves of the PV array for the zero shading condition are displayed in Figure 4. The values of the three variables-voltage (V), current (I), and power (P)-at MPP in P-V and I-V characteristic curves displayed in Figure 4 were 40 V, 3 A, and 120 W, respectively. It can be seen

Case-1: Zero Shading
In this case, where all the modules in the PV array received the same illumination and temperature, there was only one peak power point in the P-V curve. Achieving MPP here was an easy task for the P&O, FPA, and TC algorithms. The P-V and current-voltage (I-V) characteristic curves of the PV array for the zero shading condition are displayed in Figure 4. The values of the three variables-voltage (V), current (I), and power (P)-at MPP in P-V and I-V characteristic curves displayed in Figure 4 were 40 V, 3 A, and 120 W, respectively. It can be seen

Case-1: Zero Shading
In this case, where all the modules in the PV array received the same illumination and temperature, there was only one peak power point in the P-V curve. Achieving MPP here was an easy task for the P&O, FPA, and TC algorithms. The P-V and current-voltage (I-V) characteristic curves of the PV array for the zero shading condition are displayed in Figure 4.

Case-1: Zero Shading
In this case, where all the modules in the PV array received the same illumination and temperature, there was only one peak power point in the P-V curve. Achieving MPP here was an easy task for the P&O, FPA, and TC algorithms. The P-V and current-voltage (I-V) characteristic curves of the PV array for the zero shading condition are displayed in Figure 4.  The values of the three variables-voltage (V), current (I), and power (P)-at MPP in P-V and I-V characteristic curves displayed in Figure 4 were 40 V, 3 A, and 120 W, respectively. It can be seen in Figure 5 that the TC algorithm achieved the target of 119.7 W with 99.75% efficiency and zero oscillations, P&O extracted the full power of 120 W with 100% efficiency but with oscillations around the MPP, and FPA was successful in extracting 119.2 W with the efficiency of 99.33% and without oscillations. in Figure 5 that the TC algorithm achieved the target of 119.7 W with 99.75% efficiency and zero oscillations, P&O extracted the full power of 120 W with 100% efficiency but with oscillations around the MPP, and FPA was successful in extracting 119.2 W with the efficiency of 99.33% and without oscillations. Discussion of Figure 5 The extracted power and MPP tracking time of the FPA, P&O, and TC algorithms were 119.2 W in 0.75 s with an efficiency of 99.33%, 120 W in 0.09 s with an efficiency of 100%, and 119.7 W in 0.4972 s with an efficiency of 99.75%, respectively, in a uniform or zero shading condition, as displayed in Figure 5a-c. The P&O algorithm performed better but with a drawback of oscillation around MPP. The TC algorithm outperformed the FPA algorithm in all aspects and beat the P&O algorithm with zero oscillations. So, the proposed TC algorithm was the best choice, with a 99.75% efficiency and zero oscillations.

Case-2: Weak Partial Shading
In case-2 of Figure 1, weak partial shading was introduced. This created two power peaks in the P-V curve of the PV array. The P-V and I-V characteristic curves of PV array for this case are displayed in Figure 6. Discussion of Figure 5 The extracted power and MPP tracking time of the FPA, P&O, and TC algorithms were 119.2 W in 0.75 s with an efficiency of 99.33%, 120 W in 0.09 s with an efficiency of 100%, and 119.7 W in 0.4972 s with an efficiency of 99.75%, respectively, in a uniform or zero shading condition, as displayed in Figure 5a-c. The P&O algorithm performed better but with a drawback of oscillation around MPP. The TC algorithm outperformed the FPA algorithm in all aspects and beat the P&O algorithm with zero oscillations. So, the proposed TC algorithm was the best choice, with a 99.75% efficiency and zero oscillations.

Case-2: Weak Partial Shading
In case-2 of Figure 1, weak partial shading was introduced. This created two power peaks in the P-V curve of the PV array. The P-V and I-V characteristic curves of PV array for this case are displayed in Figure 6.

Case-3: Strong Shading
In case-3, strong partial shading was applied at the PV array. This created three power peaks in the P-V curve. The P-V and I-V characteristic curves of a PV array under this strong PSC are displayed in Figure 8. It is very difficult to track the GMPP in this condition.

Case-3: Strong Shading
In case-3, strong partial shading was applied at the PV array. This created three power peaks in the P-V curve. The P-V and I-V characteristic curves of a PV array under this strong PSC are displayed in Figure 8. It is very difficult to track the GMPP in this condition. Electronics 2018, 7, x FOR PEER REVIEW 12 of 29

Comparison
The results of the P&O, FPA, and TC algorithms for zero, partial weak, and partial strong shadings are summarized in Table 2, and the performance assessment of the TC algorithm with all the well-known algorithms published in the reputable journals is presented in Table 3.
From the summary presented in Table 2, it can be concluded that the P&O algorithm was the best choice for tracking MPP in zero shading but could not be adopted due to its failure in weak and strong partial shading conditions.
The TC algorithm beat the FPA algorithm in efficiency and tracking speed for MPP and GMPP tracking in zero, weak, and strong PSCs. Based on the performances of the TC, P&O, and FPA algorithms shown in Table 2, the TC algorithm seems to be the best choice to track MPP and GMPP in all weather conditions.

Comparison
The results of the P&O, FPA, and TC algorithms for zero, partial weak, and partial strong shadings are summarized in Table 2, and the performance assessment of the TC algorithm with all the well-known algorithms published in the reputable journals is presented in Table 3.
From the summary presented in Table 2, it can be concluded that the P&O algorithm was the best choice for tracking MPP in zero shading but could not be adopted due to its failure in weak and strong partial shading conditions.
The TC algorithm beat the FPA algorithm in efficiency and tracking speed for MPP and GMPP tracking in zero, weak, and strong PSCs. Based on the performances of the TC, P&O, and FPA algorithms shown in Table 2, the TC algorithm seems to be the best choice to track MPP and GMPP in all weather conditions.

Analysis of TC for Partial Shading
The performance of the TC algorithm was checked for zero, weak, and strong PSCs, separately. Figure 10 shows the performance assessment of the TC algorithm undergoing case-1 to case-2 and then case-3 together. The rise and fall in illumination due to different actions, such as clouds, birds, falling leaves, etc., was considered and simulated, and the results are presented in Figure 10.

Analysis of TC for Partial Shading
The performance of the TC algorithm was checked for zero, weak, and strong PSCs, separately. Figure 10 shows the performance assessment of the TC algorithm undergoing case-1 to case-2 and then case-3 together. The rise and fall in illumination due to different actions, such as clouds, birds, falling leaves, etc., was considered and simulated, and the results are presented in Figure 10.  Discussion of Figure 10 The success of TC can be clearly seen in Figure 10. It started with zero partial shading (case-1); after 1 s, the PV array underwent weak partial shading (case-2), and after 2 s, the PV array experienced strong partial shading (case-3). In all the three cases, the TC algorithm retained its performance in terms of tracking time, tracking accuracy, and stability (zero oscillations). The performance analysis of the TC algorithm undergoing these three cases is summarized in Table 4.  Figure 11 shows the performance assessment of the TC algorithm in UWCs. The rise and fall in illumination due to different actions, such as clouds, birds, falling leaves, etc., was considered and simulated, and the results are presented in Figure 11.  The success of TC can be clearly seen in Figure 10. It started with zero partial shading (case-1); after 1 s, the PV array underwent weak partial shading (case-2), and after 2 s, the PV array experienced strong partial shading (case-3). In all the three cases, the TC algorithm retained its performance in terms of tracking time, tracking accuracy, and stability (zero oscillations). The performance analysis of the TC algorithm undergoing these three cases is summarized in Table 4. Table 4. Performance analysis of the TC algorithm undergoing three cases.  Figure 11 shows the performance assessment of the TC algorithm in UWCs. The rise and fall in illumination due to different actions, such as clouds, birds, falling leaves, etc., was considered and simulated, and the results are presented in Figure 11.     Figure 12 shows that the MPPs of the PV array at 250 and 750 W/m 2 were at 32 and 92.47 W, respectively, as displayed in Figure 12a,b. Also, it is clearly displayed in Figure 4 that the MPP was at 120 W for zero shading.

Uniform Shading Test
The TC algorithm has achieved a power of 119.7 W in 1000 W/m 2 with 99.75% efficiency, 31.61 W in 250 W/m 2 with 99.78% efficiency, and 92.47 W in 750 W/m 2 with 99.98% efficiency. The detailed performance analysis of the TC algorithm for uniform shading is summarized in Table 5.

More Configurations Test
Two PV arrays in parallel with each array having four PV modules in series (4S2P) is the configuration presented in cases "a" and "b" of Figure 13 for two different shading conditions. The PV arrays with six modules in series (6S) is the configuration presented in cases "c" and "d" of Figure  13 for two different shading conditions. These weather conditions were adopted from [19].  Figure 12 shows that the MPPs of the PV array at 250 and 750 W/m 2 were at 32 and 92.47 W, respectively, as displayed in Figure 12a,b. Also, it is clearly displayed in Figure 4 that the MPP was at 120 W for zero shading.
The TC algorithm has achieved a power of 119.7 W in 1000 W/m 2 with 99.75% efficiency, 31.61 W in 250 W/m 2 with 99.78% efficiency, and 92.47 W in 750 W/m 2 with 99.98% efficiency. The detailed performance analysis of the TC algorithm for uniform shading is summarized in Table 5.

More Configurations Test
Two PV arrays in parallel with each array having four PV modules in series (4S2P) is the configuration presented in cases "a" and "b" of Figure 13 for two different shading conditions. The PV arrays with six modules in series (6S) is the configuration presented in cases "c" and "d" of Figure 13 for two different shading conditions. These weather conditions were adopted from [19]. Characteristic curves for all the configurations of Figure 13 are presented in Figure 14. The values of the three variables voltage (V), current (I), and power (P) at the GMPP in the P-V and I-V   The values of the three variables voltage (V), current (I), and power (P) at the GMPP in P-V and I-V characteristic curves of case-c displayed in Figure 14c were 42.04 V, 1.58 A, and 66.45 W, respectively. The values of the three variables voltage (V), current (I), and power (P) at the GMPP in the P-V and I-V characteristic curves of case-d displayed in Figure 14d were 41.64 V, 1.671 A, and 69.58 W, respectively.

Case-(a), Shading of 4S2P
The results of the FPA and TC algorithms for case-(a) shading 4S2P are presented in Figure 15.

Case-(a), Shading of 4S2P
The results of the FPA and TC algorithms for case-(a) shading 4S2P are presented in Figure 15. The results proved that the TC algorithm performed far better than the FPA algorithm in casea. The FPA attained 101.9 W in 0.75 s, whereas the TC algorithm extracted 122.1 W in 0.49 s, as displayed in Figure 15a,b. The TC algorithm performed better in terms of time and tracked power.

Case-(b), Shading of 4S2P
The results of the FPA and TC algorithms for case-(b) shading 4S2P are presented in Figure 16. The results proved that the TC algorithm performed far better than the FPA algorithm in case-a. The FPA attained 101.9 W in 0.75 s, whereas the TC algorithm extracted 122.1 W in 0.49 s, as displayed in Figure 15a,b. The TC algorithm performed better in terms of time and tracked power.

Case-(b), Shading of 4S2P
The results of the FPA and TC algorithms for case-(b) shading 4S2P are presented in Figure 16. The results show that the TC algorithm extracted the same power as the FPA algorithm in caseb. Both algorithms were successful in tracking the GMPP. The FPA attained 110.8 W in 0.760 s, whereas the TC algorithm extracted 110.8 W in 0.5016 s, as displayed in Figure 16a,b. The TC algorithm performed better in terms of tracking time.

Case-(c), Shading of 6S
The results of the FPA and TC algorithms for case-(c) shading 6S are presented in Figure 17.

Case-(c), Shading of 6S
The results of the FPA and TC algorithms for case-(c) shading 6S are presented in Figure 17. The results show that the TC algorithm extracted the same power as the FPA algorithm in caseb. Both algorithms were successful in tracking the GMPP. The FPA attained 110.8 W in 0.760 s, whereas the TC algorithm extracted 110.8 W in 0.5016 s, as displayed in Figure 16a,b. The TC algorithm performed better in terms of tracking time.

Case-(c), Shading of 6S
The results of the FPA and TC algorithms for case-(c) shading 6S are presented in Figure 17.

Case-(d), Shading of 6S
The results of the FPA and TC algorithms for case-(d) shading 6S are presented in Figure 18.

Case-(d), Shading of 6S
The results of the FPA and TC algorithms for case-(d) shading 6S are presented in Figure 18. The results show that the TC algorithm outperformed the FPA algorithm in case-c. The FPA attained 66.05 W in 0.75 s, whereas the TC algorithm extracted 66.31 W in 0.4962 s, as displayed in Figure 17a,b. The TC algorithm performed better in terms of extracted power and tracking time.

Case-(d), Shading of 6S
The results of the FPA and TC algorithms for case-(d) shading 6S are presented in Figure 18.   The results show that the TC algorithm extracted the same power as the FPA algorithm in case-d. Both algorithms were successful in tracking the GMPP. The FPA attained 69.58 W in 0.751 s, whereas the TC algorithm extracted 69.58 W in 0.48 s, as displayed in Figure 18a,b. The TC algorithm performed better in terms of tracking time.
The performance of the FPA and TC algorithms for four new configurations, introduced in Figure 13, is summarized in Table 6. The performance comparison of the FPA and TC algorithms for the four new configurations introduced in Figure 13 is summarized in Table 6. For the case-a "4S2P", the TC algorithm tracked the GMPP with 100% efficiency, while the performance of the FPA algorithm was limited to 83.46%. It could not be wrong to state that the FPA algorithm failed for this condition. In terms of tracking time, the TC algorithm performed 34% faster than the FPA algorithm. For case-b of "4S2P", the TC and FPA algorithms tracked the GMPP with 99.28% efficiency, whereas in terms of tracking time, the TC algorithm performed 34% faster than the FPA algorithm, thus making it most suitable for GMPP tracking in PSCs.
For case-c "6S", the TC algorithm tracked the GMPP with 99.8% efficiency, while the FPA algorithm tracked the GMPP with 99.4% efficiency. The TC algorithm's efficiency was 0.4% improved compared with the FPA algorithm. In terms of tracking time, the TC algorithm performed 34.1% faster than the FPA algorithm. For the case-d of "6S", the TC and FPA algorithms tracked the GMPP with 100% efficiency. In terms of tracking time, the TC algorithm performed 35.7% faster than the FPA algorithm, which makes it the most suitable for GMPP tracking in PSCs.
The threshold values for the change in voltage (dV) and change in current (dI) set by the experimental trials were 0.1 V and 0.1 A and are displayed in Equations (3) and (4), respectively, for the configuration of 4S2P. The values are 0.25 V and 0.1 A and are displayed in Equations (5) and (6), respectively, for the configuration of 6S. These conditions were sensitive for the change of 50 W/m 2 .

Appendix A. Modeling and Characteristics of Photovoltaic Cell
Mainly, two modeling approaches exist: (1) the one/single-diode model [21] and (2) the two/double-diode model [22]. The two-diode model is more accurate, but the one-diode model is mostly used because of its simplicity [23,24]. The one/single-diode model of a PV cell is displayed in Figure A1. After applying kirchhoff's current law, in Figure A1, the current at the output of the PV cell is: (A1) This single-diode model has following five parameters: Ipv, ID, Rs, Rsh, and α, where Ipv = current of the PV cell, ID = diode current, Rs = resistance in series, Rsh = parallel resistance, and α = diode ideality factor VD.
The diode current can be expressed as in Equation (A2): where VD = diode voltage, IO = reverse saturation current, and VT = thermal voltage. After applying kirchhoff's current law, in Figure A1, the current at the output of the PV cell is: This single-diode model has following five parameters: Ipv, I D , Rs, Rsh, and α, where Ipv = current of the PV cell, I D = diode current, Rs = resistance in series, Rsh = parallel resistance, and α = diode ideality factor V D .
The diode current can be expressed as in Equation (A2): where V D = diode voltage, I O = reverse saturation current, and V T = thermal voltage. The thermal voltage formula is expressed in Equation (A3): where k = Boltzmann constant = 1.3805 × 10 −23 , Ns = number of series connected cells, T = temperature at standard test condition (STC), and q = electron charge = 1.9 × 10 −19 • C. The PV array's current can be calculated using Equation (A4): where Npp = number of parallel connected cells, Nss = number of series connected cells, I = array current, and Ipv = array current. The power-voltage (P-V) and current-voltage (I-V) characteristic curve is displayed in Figure A2. It can be clearly seen how the change in voltage affects the power of the PV cell. This voltage level was changed by changing the duty cycle of the DC-DC converter using MPPTs, which were governed by algorithms. where Npp = number of parallel connected cells, Nss = number of series connected cells, I = array current, and Ipv = array current. The power-voltage (P-V) and current-voltage (I-V) characteristic curve is displayed in Figure A2. It can be clearly seen how the change in voltage affects the power of the PV cell. This voltage level was changed by changing the duty cycle of the DC-DC converter using MPPTs, which were governed by algorithms.  Figure A2a shows that the power increases for a positive change in voltage until the MPP is reached; this happens because value of the current remains constant for a changing voltage. This is a  Figure A2a shows that the power increases for a positive change in voltage until the MPP is reached; this happens because value of the current remains constant for a changing voltage. This is a characteristic curve for a uniform illumination condition or zero shading condition. Characteristic curves for changing illumination and temperature are also presented in Figure A2b.