1. 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 observe (P&O) [
5], incremental conductance (InC) [
6], fractional short circuit (FSC) [
7], and fractional open circuit (FOC) [
8]. Conventional algorithms perform efficiently in UWCs and track the MPP but with the drawbacks of oscillations of the operating power point (OPP) around the MPP and failure to perform under PSCs by sticking to the nearest LMPP [
9].
Furthermore, multiple improvements have been carried out in conventional MPPT algorithms, such as the two-stage P&O [
10] and direct search MPPT [
11] techniques. In the first stage of the two-stage P&O technique, the optimized zone is detected, and in the second stage, the GMPP is located [
10]. In the direct search MPPT technique [
11], a two-mode operation is conducted. Initially, GMPP tracking mode is activated and afterwards switches to the other mode of the conventional P&O method. Improved conventional techniques are ineffective in PSCs. Overall, all of the conventional and improved conventional techniques fail to track the GMPP in PSCs. To overcome these drawbacks, researchers have considered SC techniques.
In SC techniques, the artificial neural network (ANN) [
12], and fuzzy logic (FL) [
13] have provided good results. However, a separate sensor arrangement is required for ANN, which increases the cost, and the FL technique needs prior system knowledge to track and requires complex fuzzy rules. These failures of ANN and FL have turned the attention of researchers towards nature-based SC techniques, such as the genetic algorithm (GA) [
14], the particle swarm optimization (PSO) algorithm [
15], the differential evolution (DE) algorithm [
16], the random search method (RSM) [
17], and the artificial bee colony (ABC) algorithm [
18]. However, all of the nature-inspired SC techniques mentioned above are complex and have high computation time and low convergence speed. Still, the PSO algorithm has shown valuable improvement in tracking efficiency.
A recently introduced nature-inspired algorithm is the flower pollination algorithm (FPA) [
19]. The FPA beat the most popular PSO and P&O algorithms and proved to be the top-performing technique for tracking GMPP in PSCs in [
19]. The FPA shows improvement in convergence speed and efficiency. The weaknesses of FPA are its: (1) procedural complexity, (2) difficulty in parameter tuning, and (3) high computation time. FPA has fewer parameters such as switching probability and scaling factor. Nevertheless, fine tuning the switching probability is important in balancing global and local searches. Usually, the value of the switching probability has been fixed at 0.8, although this does not ensure the fine balance between the two types of searches. Such a drawback presents difficulty in GMPP tracking [
20].
Research gaps in conventional techniques include: (1) removing the oscillation of the operating power point around the MPP and (2) tracking GMPP in PSCs.
Research gaps in soft computing techniques include: (1) reducing computation time, (2) increasing convergence speed, (3) reducing complexity, (4) increasing efficiency, and (5) increasing accuracy.
After considering these drawbacks, we proposed a novel method called the ten check (TC) for GMPP tracking of a PV system in PSCs. The TC algorithm has numerous notable qualities that any other conventional or soft computing technique does not have, such as: (1) parameter tuning is not required, (2) GMPP tracking is faster than any existing technique, (3) zero oscillations around MPP, and (4) GMPP is accurately and efficiently tracked.
Different patterns covering diverse weather states were tested through simulation. The results of the proposed algorithm were compared with the state-of-the-art P&O and FPA techniques. Comparisons based on tracking speed, efficiency, accuracy, parameter tuning, steady state oscillations around MPP, procedural complexity, computational complexity, and performance under PSC were made between P&O, FPA, and the proposed TC algorithm.
The TC algorithm has numerous notable qualities, which any other conventional or soft computing technique does not have, such as:
- (1)
no parameter tuning is required,
- (2)
track GMPP faster than any existing technique/algorithm,
- (3)
zero oscillations around MPP,
- (4)
track GMPP accurately and efficiently.
The rest of the paper is ordered as follows.
Section 2 explains the partial shading effects and the TC technique,
Section 3 presents the simulation and results,
Section 4 shows the comparison,
Section 5 presents additional configuration tests, and
Section 6 offers the conclusions.
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 characteristic curves of case-(a) are displayed in
Figure 14a, which are 31.55 V, 3.87 A, and 122.1 W, respectively.
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-b displayed in
Figure 14b were 18.71 V, 5.967 A, and 111.6 W, respectively. 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.
5.1. 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 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.
5.2. 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 case-b. 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.
5.3. 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 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.
5.4. 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.