# Optimizing Photovoltaic Power Production in Partial Shading Conditions Using Dandelion Optimizer (DO)-Based MPPT Method

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling of PV Cells and Analysis of Partial Shading Conditions

#### 2.1. Single Diode Model of PV Cell

- ${I}_{pv}$: PV output current, $A$.
- ${I}_{ph}$: photocurrent of PV cell, $A$.
- ${I}_{sat}$: reverse PV cell saturation current, $A$.
- ${V}_{pv}$: PV output voltage, $V$.
- ${N}_{p}$: number of parallel PV cells.
- ${N}_{s}$: number of PV cells in series.
- $e$: electron charge, $1.60217733\times {10}^{-19}\mathrm{C}$.
- $n$: p-n junction diode ideality factor, $1<n<5$.
- ${k}_{B}$: Boltzmann’s constant, $1.380658\times {10}^{-23}\mathrm{J}/\mathrm{K}$.
- ${T}_{o}$: absolute operating temperature, $K$.

- ${I}_{sc}$: short-circuit current at ${\mathrm{V}}_{\mathrm{pv}}=0$.
- ${K}_{i}$: temperature coefficient of short-circuit current, $\mathrm{A}/\mathrm{K}$.
- ${T}_{STC}$: the temperature at standard test conditions, $298.15\mathrm{K}$.
- $G$: PV cell irradiance, $\mathrm{W}/{\mathrm{m}}^{2}$.
- ${G}_{STC}$: standard irradiance for testing purposes, $1000\mathrm{W}/{\mathrm{m}}^{2}$.

- ${I}_{rs}$: reverse saturation current of the diode, $\mathrm{A}$.
- ${E}_{g}$: band-gap energy of the semiconductor material utilized in the PV cell, $\mathrm{J}$.

#### 2.2. Partial Shading Phenomenon

^{2}. Conversely, Figure 5b represents the scenario of partial shading (PS), where the P-V and I-V curves demonstrate a single GMPP and multiple LMPPs due to varying irradiance values of 1000 W/m

^{2}, 700 W/m

^{2}, 600 W/m

^{2}, and 400 W/m

^{2}across the solar panels. In instances of partial shade, the P-V curve comprises numerous LMPPs and just one GMPP. To harvest the maximum amount of solar energy, the PV system must operate at the GMMP. Therefore, a sophisticated MPPT control is necessary to ensure optimal power output despite changes in weather conditions and nonuniform irradiance levels.

## 3. Dandelion Optimizer-Based MPPT Technique

#### 3.1. Dandelion Optimization (DO) Algorithm

#### 3.1.1. Rising Stage

- ${D}_{t}$: position of a dandelion seed in the t
^{th}iteration. - ${D}_{t+1}$: position of a dandelion seed in the (t+1)
^{th}iteration. - $\alpha $: step size parameter.
- ${u}_{x}$: lift coefficient in the horizontal direction.
- ${u}_{y}$: lift coefficient in the vertical direction.
- $\mathrm{ln}Y$: lognormal distribution.
- ${D}_{s}$: random starting position of the dandelion seed.

#### 3.1.2. Declining Stage

- ${\beta}_{t}$: Brownian motion derived from the normal distribution.
- ${D}_{mean\_t}$: average position of the seeds during the t
^{th}iteration. - ${D}_{mean\_t}$ is computed using Equation (15).

#### 3.1.3. Land Stage

- ${D}_{elite}$: optimal position of the dandelion seed in the t
^{th}iteration. - $\delta :$ linearly increasing function that ranges from 0 to 2.
- $levy\left(\lambda \right)$: Levy flight function.
- $\delta $ is calculated using Equation (17).

#### 3.2. Execution of DO Algorithm for MPPT

- Duty Ratio Initialization and Restrictions: The duty ratios in the DO algorithm represent the control signals transmitted to the converter, akin to dandelion seeds in the natural analogy. To begin the optimization process, the duty ratios must be initialized within a certain search space, which is limited by the maximum value $\left({D}_{max}=0.9\right)$ and the minimum value $\left({D}_{\mathrm{min}}=0.1\right)$. The reason for these restrictions is to confine the optimization to a safe and feasible range of duty ratios that do not cause instability or exceed the operational limits of the converter. This ensures that the algorithm starts with reasonable values for power conversion, avoiding any unsafe or impractical configurations.
- Iterative Optimization Process: The DO algorithm proceeds with an iterative optimization process, consisting of three stages: rising, descending, and landing. During the rising stage, the duty ratios undergo random trajectories, allowing for a broad exploration of the search space to identify potential optimal points. In the descending stage, the Brownian motion trajectory is employed to refine the optimization process, focusing on promising regions in the search space. Finally, the landing stage utilizes a linear increasing function with Levy flight to fine-tune the duty ratios, aiming to converge towards the GMPP.
- Obtaining the Optimum Duty Ratio: Through the iterative process, the DO algorithm continuously updates the positions of the duty ratios until it reaches a point of convergence, where the optimum duty ratio representing the GMPP is identified. This duty ratio is then sent to the converter, adjusting the power conversion to operate at the optimal power output of the PV system.

## 4. Simulation Results and Analysis

^{®}Core™ i5-10210U CPU running at 1.60 GHz and 8 GB of RAM. The values of the components used in the simulation are shown in Table 2 and Table 3, displaying the tuned parameters of PSO, CS, and DO for MPPT analysis. Finally, the standard conditions for the simulation are established with a rated solar irradiation of 1000 W/m

^{2}and a temperature of 25 °C. Under these conditions, the PV array produces an output power of ${P}_{pv}$ = 21.837 W, DC link voltage of ${V}_{pv}$ = 4.35 V, and PV system output current of ${I}_{pv}$ = 5.03 A. These case studies give evidence to support the simulation outcomes, proving that the suggested technique outperforms other MPPT strategies.

#### 4.1. Simulation Study under Partial Shading Conditions

- (1)
- Pattern 1: In the first pattern, the simulation represents a scenario without any shading. In this configuration, all PV panels (G
_{1}, G_{2}, G_{3}, G_{4}) receive an equal irradiation level of 1000 W/m^{2}, resulting in the generation of equal currents. As a result, the P-V curve displays a single peak with the maximum power, referred to as GMPP, as shown in Figure 8a. - (2)
- Pattern 2: In this pattern, the simulation represents a light shade condition. In this configuration, modules G
_{1}, G_{2}, and G_{3}receive an irradiance of 1000 W/m^{2}, while module G_{4}receives only 500 W/m^{2}due to partial shading. Consequently, the current caused by the PV string and the shaded module are equal. However, the maximum current due to the unshaded PV panels can be bypassed through the bypass diodes across each panel. This disparity in currents results in the generation of two distinct peaks in the P-V curves, as illustrated in Figure 8b. - (3)
- Pattern 3: In this pattern, the simulation depicts a scenario where modules G
_{1}and G_{2}obtain an irradiance of 1000 W/m^{2}, while modules G_{3}and G_{4}receive 700 W/m^{2}and 400 W/m^{2}, respectively, due to partial shading. Consequently, the current produced by the PV string aligns with that of the shaded modules (G_{3}and G_{4}). This results in the generation of three distinct peaks in the P-V curves, owing to the variation in currents, as illustrated in Figure 8c. - (4)
- Pattern 4: This pattern represents a strong shade condition, where PV modules G
_{1}, G_{2}, G_{3}, and G_{4}obtain irradiance levels of 1000 W/m^{2}, 750 W/m^{2}, 500 W/m^{2}, and 400 W/m^{2}, respectively. Each module experiences a different degree of shading, leading to the development of distinct currents. Consequently, the P-V curves exhibit multiple peaks, as depicted in Figure 8d. Among these peaks, only one corresponds to the GMPP, while the others are identified as LMPPs.

#### 4.1.1. Shading Condition 1

^{2}. Results show that DO exhibits significantly lower convergence time and negligible size fluctuations compared to PSO and CS. Furthermore, as shown in Figure 9a, DO effectively tracks the MPP of 87.26 W, with a current of 2.94 A at MPP and voltage of 29.59 V at MPP, achieving a tracking efficiency of 99.90% with a measured convergence time of 0.25 s. On the other hand (Figure 10a), CS can track the MPP effectively and has a settling time of only 1.17 s, while DO displays a considerably faster settling time. It settles at a lower value of 86.96 W, with a current of 2.95 A at MPP and voltage of 29.52 V, achieving an efficiency of 99.56% (Figure 11a). PSO successfully tracks the MPP of 86.47 W, with a current of 2.94 A at MPP and voltage of 29.41 V, owing to its exploration and exploitation capabilities. However, it takes longer to settle than DO and CS, at 1.48 s. Despite settling at the MPP, the elevated steady-state oscillations in PSO lead to power losses, reducing its efficiency to 99.00%. In comparison to CS and PSO, DO shows a 492.00% and 368.00% improvement in settling time, respectively. It is worth noting that DO outperforms under full insolation conditions, but metaheuristic algorithms should also be suitable for partial shading scenarios.

#### 4.1.2. Shading Condition 2

^{2}, respectively. As seen in Figure 9b, DO effectively tracks the MPP of 61.71 W with a current of 2.48 A at MPP and voltage of 24.84 V at MPP in a settling time of 0.25 s, achieving an efficiency of almost 99.66% under the PS scenario. As seen in Figure 10b, CS achieves a slightly lesser tracking time of 0.34 s, settling at a lower MPP value of 60.34 W with a current of 2.45 A at MPP and voltage of 24.56 V at MPP and a lower efficiency of 97.44%. from Figure 11b PSO, on the other hand, tracks the MPP of 59.71 W with a current of 2.44 A at MPP and voltage of 24.44 V at MPP and an efficiency of 96.43%, which is lower than both DTBO and CS. Additionally, the settling time of PSO is longer at 1.38 s. When compared to CS and PSO, DO display significant improvement in settling time, with 36.00% and 452% advancement, respectively. These results suggest that DO has many advantages over competing algorithms specifically greater efficiency and shows a significant improvement in convergence rate.

#### 4.1.3. Shading Condition 3

^{2}, and the remaining two panels receive 700 and 400 W/m

^{2}, respectively (Figure 9c). DO achieves the MPP of (Figure 10c), CS takes longer to track the MPP, with a tracking time of 1.17 s, and settles at a lower value of 46.22 W with a current of 2.14 A at MPP and voltage of 21.49 V at MPP, resulting in an efficiency of 96.01%. As seen in Figure 11c, PSO also successfully tracks the MPP at 46.02 W with a current of 2.12 A at MPP and voltage of 21.23 V at MPP, but with a lower efficiency of 95.59% compared to DO. In this case, both CS and PSO exhibit lower efficiencies than DO. Moreover, the tracking time of PSO is longer than both DO and CS at 1.32 s. However, DO experiences fewer fluctuations during the search for the MPP than CS and PSO, leading to a significant reduction in power losses. DO also demonstrates a substantial improvement in settling time compared to CS and PSO, with percentages of 368% and 428%, respectively. These findings suggest that DO is more effective than competing algorithms and shows a significant improvement in convergence speed.

#### 4.1.4. Shading Condition 4

^{2}. In this setting (Figure 9d), the DO algorithm performs exceptionally well by accurately tracking the maximum power point (MPP) within just 0.10 s, achieving an impressive efficiency of nearly 97.25%. The DO algorithm also achieves an MPP of 36.85 W with a current of 1.91 A at MPP and a voltage of 19.20 V at MPP. On the other hand (Figure 10d), the CS algorithm exhibits a significantly slower tracking time of 0.48 s and settles at a lower value of 35.68 W with a current of 1.88 A at MPP and voltage of 18.91 V at MPP, resulting in an efficiency of 94.16%. Similarly, (Figure 11d), the PSO algorithm also tracks the MPP, but takes slightly longer than CS with a settling time of 0.54 s, achieving an efficiency of 93.92% and obtaining the MPP of 35.59 W with a current of 1.88 A at MPP and voltage of 18.93 V at MPP. The settling time of the DO algorithm improves by 380% and 440% compared to CS and PSO, respectively. Furthermore, both CS and PSO algorithms exhibit poor performance, as their convergence to the MPP occurs at a significantly slower rate, resulting in higher overall power losses. In conclusion, the DO algorithm outperforms the CS and PSO algorithms in terms of settling time and efficiency in a strong PS situation.

_{mp}), voltage at maximum power (V

_{mp}), maximum power (P

_{mp}), rated power, efficiency, and settling time.

#### 4.2. Simulation Study under Varying Irradiation

^{2}, 1000 W/m

^{2}, 1000 W/m

^{2}, and 500 W/m

^{2}, respectively, in the four PV panels. During the second condition, which is a light shading scenario, the DO tracks the MPP at 61.71 W with an output current and voltage of 2.48 A and 24.84 V, respectively. The DO achieves an efficiency of 99.66% under this condition and settles at the same time as in the previous condition, i.e., 0.25 s. After 1 s, the irradiances on the four PV panels are changed to 1000 W/m

^{2}, 1000 W/m

^{2}, 700 W/m

^{2}, and 400 W/m

^{2}, respectively, in the third condition, which is a partial shading scenario. The DO tracks the MPP at 47.68 W with an output current and voltage of 2.18 A and 21.84 V, respectively. The DO achieves an efficiency of 99.04% under this condition and settles in 0.25 s. Finally, after 1.5 s, the irradiances on the four PV panels are changed to 1000 W/m

^{2}, 750 W/m

^{2}, 500 W/m

^{2}, and 400 W/m

^{2}, respectively, in the fourth condition, which is a strong and complex partial shading scenario. The DO tracks the MPP at 36.85 W with an output current and voltage of 1.91 A and 19.20 V, respectively. The DO achieves an efficiency of 97.25% under this condition, and its settling time is less than the previous conditions at 0.1 s. Furthermore, when solar irradiation suddenly changes, the DO algorithm produces output power, voltage, and current that do not exhibit any oscillations. This indicates that the DO-based MPPT controller has an inherent ability to adapt to different weather conditions and significantly improve the probability of obtaining a high-quality optimum power point through global and local exploration.

## 5. Hardware-in-the-Loop (HIL) Implementation

#### 5.1. Static Shading Conditions

- (1)
- In scenario 1, there is no shading, and all photovoltaic (PV) panels—G
_{1}, G_{2}, G_{3}, and G_{4}—receive an equal irradiation level of 1000 W/m^{2}. This uniform irradiation leads to the generation of equal currents. The corresponding P-V curve demonstrates a solitary peak, referred to as the GMPP, as shown in Figure 15a. - (2)
- In scenario 2, a light shading condition is present, where only the G
_{4}module receives an irradiance of 600 W/m^{2}, while the remaining modules—G_{1}, G_{2}, and G_{3}—receive an irradiance of 1000 W/m^{2}. The presence of bypass diodes enables the bypassing of the maximum current generated by the unshaded PV panels. As a result, the P-V curves have two separate peaks. This behavior is depicted in Figure 15b. - (3)
- In the third scenario, the PV modules experience different levels of irradiance: G
_{1}and G_{2}receive 1000 W/m^{2}, G_{3}receives 700 W/m^{2}, and G_{4}receives 500 W/m^{2}. Consequently, the shaded modules G_{3}and G_{4}generate lower currents than the unshaded modules. This difference in currents, assisted by the bypass diode, causes the P-V curves to exhibit three separate peaks. Figure 15c visually represents these peaks. - (4)
- Scenario 4 is characterized by a significant shading effect, where each PV panel experiences a different level of shading. This circumstance causes several peaks to appear on the P-V curves. Specifically, the G
_{1}, G_{2}, G_{3}, and G_{4}modules receive irradiance levels of 1000 W/m^{2}, 700 W/m^{2}, 600 W/m^{2}, and 400 W/m^{2}, respectively. In this scenario, only one peak corresponds to the GMPP, while the other peaks are regarded as LMPPs. The behavior of the P-V curve under this scenario is illustrated in Figure 15d.

#### 5.1.1. Shading Condition 1

^{2}in terms of tracking time and efficiency. The shading condition, the method used, and important parameters such as I

_{mp}(current at MPP), V

_{mp}(voltage at MPP), P

_{mp}(power at MPP), rated power, efficiency, and tracking time were also taken into account. DO effectively tracks the MPP of 87.08 W, with a current of 2.91 A at MPP and voltage of 29.91 V at MPP, whereas PSO tracks the MPP of 85.33 W, with a current of 2.87 A at MPP and voltage of 29.73 V at MPP, and CS tracks the MPP of 86.96 W, with a current of 2.91 A at MPP and voltage of 29.88 V at MPP, In terms of tracking time, the PSO algorithm has the longest time of 6.8 s, followed by the DO algorithm with a time of 0.8 s, while the CS algorithm has the shortest time of 1.6 s. Regarding efficiency, the DO algorithm has the highest efficiency of 99.02%, followed by the CS algorithm with an efficiency of 98.88%, and the PSO algorithm with the lowest efficiency of 97.03%. In comparison to CS and PSO, DO shows a 100.00% and 750.00% improvement in settling time, respectively. Overall, the DO algorithm seems to be the most efficient of the three algorithms, despite having a longer tracking time than the CS algorithm. Meanwhile, the PSO algorithm has the lowest efficiency and longest tracking time, indicating that it may not be the best choice for this particular scenario.

#### 5.1.2. Shading Condition 2

^{2}, respectively, on the four modules of the PV array. DO effectively tracks the MPP of 62.84 W, with a current of 2.51 A at MPP and voltage of 25.07 V at MPP, whereas PSO tracks the MPP of 58.91 W, with a current of 2.41 A at MPP and voltage of 24.08 V at MPP, and CS tracks the MPP of 59.60 W, with a current of 2.42 A at MPP and voltage of 24.21 V at MPP. Under these conditions, DO achieves the highest efficiency of 99.54%, with a tracking time of 0.8 s and a duty ratio of 0.51. CS achieves an efficiency of 94.40% with a tracking time of 2.4 s and the same duty ratio as DO. PSO has the lowest efficiency of the three, at 93.31%, with a tracking time of 5 s and the same duty ratio as the other two algorithms. In comparison to CS and PSO, DO shows a 200.00% and 525.00% improvement in settling time, respectively. Overall, DO appears to be the most efficient and fastest algorithm under these shading conditions, followed by CS and then PSO. Nevertheless, it should be acknowledged that the effectiveness of each algorithm may differ based on the specific shading conditions and other contextual factors within a particular application.

#### 5.1.3. Shading Condition 3

^{2}. Figure 16c, Figure 17c and Figure 18c illustrate these comparisons. The DO achieved I

_{mp}at 2.22 A, with V

_{mp}at 22.16 V, and P

_{mp}at 49.79 W. Its overall efficiency is calculated to be 99.89% with a tracking time of 1.0 s. CS resulted in slightly lower values, with I

_{mp}at 2.02 A, V

_{mp}at 20.20 V, and P

_{mp}at 49.12 W. The efficiency of CS is found to be 98.55% with a tracking time of 2.0 s. PSO has similar I

_{mp}values of 2.02 A, V

_{mp}at 20.19 V, and P

_{mp}at 49.11 W. Its efficiency is slightly lower than CS at 98.53%, and the tracking time is the longest at 4.8 s. In comparison to CS and PSO, DO demonstrated a 100.00% and 380.00% improvement in settling time, respectively. Overall, DO exhibited the best efficiency and tracking time, followed by PSO and CS.

#### 5.1.4. Shading Condition 4

^{2}. DO achieved an I

_{mp}value of 2.05 A, with V

_{mp}at 20.47 V, and P

_{mp}at 41.92 W. Its overall efficiency is found to be 99.28%, with a tracking time of 1.0 s. CS has a slightly lower I

_{mp}value of 1.99 A, with V

_{mp}at 19.85 V, and P

_{mp}at 39.42 W. The overall efficiency of CS is significantly lower than DO at 93.36%, and it requires a longer tracking time of 2.6 s. PSO obtained the lowest I

_{mp}value of 1.94 A, with V

_{mp}at 19.43 V, and P

_{mp}at 37.76 W. Its efficiency is the lowest among the three algorithms for this condition at 89.43%, and it has the longest tracking time of 4.0 s. Comparing the results, the DO outperformed both CS and PSO with a settling time improvement of 160.00% and 300.00%, respectively. In terms of efficiency and tracking time, the DO algorithm demonstrated the highest effectiveness, followed by CS and PSO algorithms.

_{mp}, V

_{mp}, P

_{mp}, rated power, efficiency, and settling time for the different irradiance conditions.

#### 5.2. Dynamic Changes in Shading Pattern

_{mp}of 2.40 A and V

_{mp}of 23.99 V, with a P

_{mp}of 57.57 W and an efficiency of 98.22%, with a tracking time of 1.0 s. In condition 2, the DO algorithm attains a maximum efficiency of 98.84%, tracking the P

_{mp}with a tracking time of 1.6 s at 68.35 W, and an I

_{mp}value of 2.59 A. Lastly, under condition 3, the DO algorithm achieves a maximum efficiency of 99.89%, with an I

_{mp}value of 2.22 A and a V

_{mp}of 22.42 V, with a tracking time of 1.6 s. In addition, the DO algorithm is observed to produce stable output power, voltage, and current when the solar irradiation suddenly changes. This suggests that the DO-based MPPT controller can effectively adapt to varying weather conditions and increase the likelihood of achieving an optimal power point through both global and local exploration.

## 6. Discussion

- Three-Stage Process: DO models the dandelion seed flight dynamics as a three-stage process: rise, descent, and landing. Each stage is designed to serve a specific purpose in the optimization process, making the algorithm more effective in capturing the GMPP.
- Incorporation of Random Trajectories: In the rising stage, DO incorporates random trajectories. By doing so, the algorithm can easily adjust to different weather conditions, which is particularly beneficial in real-world PV systems that experience varying environmental factors. This adaptability allows DO to efficiently explore the search space and avoid becoming trapped in local optima.
- Utilization of Brownian Motion and Levy Flight: In the descending stage, DO employs Brownian motion trajectory, which adds a level of randomness to the movement, helping to further explore the search space. Additionally, in the landing stage, DO uses a linear increasing function with Levy flight. Levy flight is known for its ability to perform long-range jumps, facilitating a more thorough exploration of the search space.
- Harmonious Exploration and Exploitation: The trajectory patterns exhibited by DO, combining random trajectories, Brownian motion, and Levy flight, enable the algorithm to achieve a harmonious balance between exploration (discovering new areas in the search space) and exploitation (focusing on promising regions). This balance is essential in effectively locating the GMPP, as it prevents premature convergence and ensures that the algorithm explores potential optimal solutions.
- Precision in GMPP Localization: By incorporating these trajectory patterns and balancing exploration and exploitation, DO enhances the precision in locating the GMPP. The algorithm can quickly and accurately track the optimal power output, leading to improved MPPT performance and higher energy harvesting efficiency in PV systems.

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Belhachat, F.; Larbes, C. Comprehensive review on global maximum power point tracking techniques for PV systems subjected to partial shading conditions. Sol. Energy
**2019**, 183, 476–500. [Google Scholar] [CrossRef] - Yang, B.; Zhu, T.; Wang, J.; Shu, H.; Yu, T.; Zhang, X.; Yao, W.; Sun, L. Comprehensive overview of maximum power point tracking algorithms of PV systems under partial shading condition. J. Clean. Prod.
**2020**, 268, 121983. [Google Scholar] [CrossRef] - Yang, B.; Zhong, L.; Zhang, X.; Shu, H.; Yu, T.; Li, H.; Jiang, L.; Sun, L. Novel bio-inspired memetic salp swarm algorithm and application to MPPT for PV systems considering partial shading condition. J. Clean. Prod.
**2019**, 215, 1203–1222. [Google Scholar] [CrossRef] - Rehman, H.; Sajid, I.; Sarwar, A.; Tariq, M.; Bakhsh, F.I.; Ahmad, S.; Mahmoud, H.A.; Aziz, A. Driving training-based optimization (DTBO) for global maximum power point tracking for a photovoltaic system under partial shading condition. IET Renew. Power Gener.
**2023**, 17, 2542–2562. [Google Scholar] [CrossRef] - Zafar, M.H.; Khan, N.M.; Mirza, A.F.; Mansoor, M. Bio-inspired optimization algorithms based maximum power point tracking technique for photovoltaic systems under partial shading and complex partial shading conditions. J. Clean. Prod.
**2021**, 309, 127279. [Google Scholar] [CrossRef] - Sajid, I.; Sarwar, A.; Tariq, M.; Bakhsh, F.I.; Hussan, R.; Ahmad, S.; Mohamed, A.S.N.; Ahmad, A. Runge Kutta optimization-based selective harmonic elimination in an H-bridge multilevel inverter. IET Power Electron.
**2023**. [Google Scholar] [CrossRef] - Sajid, I.; Iqbal, D.; Alam, M.S.; Rafat, Y.; Al Ammar, E.; Alrajhi, H. Feasibility Analysis of Open Vehicle Grid Integration Platform (OVGIP) for Indian Scenario. In Proceedings of the 2022 2nd International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies, ICAECT, Bhilai, India, 21–22 April 2022. [Google Scholar] [CrossRef]
- Seyedmahmoudian, M.; Soon, T.K.; Horan, B.; Ghandhari, A.; Mekhilef, S.; Stojcevski, A. New ARMO-based MPPT Technique to Minimize Tracking Time and Fluctuation at Output of PV Systems under Rapidly Changing Shading Conditions. IEEE Trans. Ind. Inform.
**2019**. [Google Scholar] [CrossRef] - Awan, M.M.A.; Asghar, A.B.; Javed, M.Y.; Conka, Z. Ordering Technique for the Maximum Power Point Tracking of an Islanded Solar Photovoltaic System. Sustainability
**2023**, 15, 3332. [Google Scholar] [CrossRef] - Yousri, D.; Babu, T.S.; Allam, D.; Ramachandaramurthy, V.K.; Etiba, M.B. A Novel Chaotic Flower Pollination Algorithm for Global Maximum Power Point Tracking for Photovoltaic System Under Partial Shading Conditions. IEEE Access
**2019**, 7, 121432–121445. [Google Scholar] [CrossRef] - Pervez, I.; Pervez, A.; Tariq, M.; Sarwar, A.; Chakrabortty, R.K.; Ryan, M.J. Rapid and Robust Adaptive Jaya (Ajaya) Based Maximum Power Point Tracking of a PV-Based Generation System. IEEE Access
**2021**, 9, 48679–48703. [Google Scholar] [CrossRef] - Abdel-Salam, M.; El-Mohandes, M.-T.; Goda, M. An improved perturb-and-observe based MPPT method for PV systems under varying irradiation levels. Sol. Energy
**2018**, 171, 547–561. [Google Scholar] [CrossRef] - Fatemi, S.M.; Shadlu, M.S.; Talebkhah, A. Comparison of Three-Point P&O and Hill Climbing Methods for Maximum Power Point Tracking in PV Systems. In Proceedings of the 2019 10th International Power Electronics, Drive Systems and Technologies Conference (PEDSTC), Shiraz, Iran, 12–14 February 2019; pp. 764–768. [Google Scholar] [CrossRef]
- Safari, A.; Mekhilef, S. Simulation and Hardware Implementation of Incremental Conductance MPPT With Direct Control Method Using Cuk Converter. IEEE Trans. Ind. Electron.
**2010**, 58, 1154–1161. [Google Scholar] [CrossRef] - Sher, H.A.; Murtaza, A.F.; Noman, A.; Addoweesh, K.E.; Al-Haddad, K.; Chiaberge, M. A New Sensorless Hybrid MPPT Algorithm Based on Fractional Short-Circuit Current Measurement and P&O MPPT. IEEE Trans. Sustain. Energy
**2015**, 6, 1426–1434. [Google Scholar] [CrossRef] - Baimel, D.; Tapuchi, S.; Levron, Y.; Belikov, J. Improved Fractional Open Circuit Voltage MPPT Methods for PV Systems. Electronics
**2019**, 8, 321. [Google Scholar] [CrossRef] - Debnath, A.; Olowu, T.O.; Parvez, I.; Dastgir, M.G.; Sarwat, A. A Novel Module Independent Straight Line-Based Fast Maximum Power Point Tracking Algorithm for Photovoltaic Systems. Energies
**2020**, 13, 3233. [Google Scholar] [CrossRef] - Algarín, C.R.; Giraldo, J.T.; Álvarez, O.R. Fuzzy Logic Based MPPT Controller for a PV System. Energies
**2017**, 10, 2036. [Google Scholar] [CrossRef] - Jyothy, L.P.; Sindhu, M.R. An Artificial Neural Network based MPPT Algorithm for Solar PV System. In Proceedings of the 2018 4th International Conference on Electrical Energy Systems (ICEES), Chennai, India, 7–9 February 2018; pp. 375–380. [Google Scholar] [CrossRef]
- Li, X.; Wen, H.; Hu, Y.; Jiang, L. A novel beta parameter based fuzzy-logic controller for photovoltaic MPPT application. Renew. Energy
**2019**, 130, 416–427. [Google Scholar] [CrossRef] - Hai, T.; Zhou, J.; Muranaka, K. An efficient fuzzy-logic based MPPT controller for grid-connected PV systems by farmland fertility optimization algorithm. Optik
**2022**, 267, 169636. [Google Scholar] [CrossRef] - Hayder, W.; Ogliari, E.; Dolara, A.; Abid, A.; Ben Hamed, M.; Sbita, L. Improved PSO: A Comparative Study in MPPT Algorithm for PV System Control under Partial Shading Conditions. Energies
**2020**, 13, 2035. [Google Scholar] [CrossRef] - Alshareef, M.; Lin, Z.; Ma, M.; Cao, W. Accelerated Particle Swarm Optimization for Photovoltaic Maximum Power Point Tracking under Partial Shading Conditions. Energies
**2019**, 12, 623. [Google Scholar] [CrossRef] - Mosaad, M.I.; El-Raouf, M.O.A.; Al-Ahmar, M.A.; Banakher, F.A. Maximum Power Point Tracking of PV system Based Cuckoo Search Algorithm; review and comparison. Energy Procedia
**2019**, 162, 117–126. [Google Scholar] [CrossRef] - Cuong-Le, T.; Minh, H.-L.; Khatir, S.; Wahab, M.A.; Tran, M.T.; Mirjalili, S. A novel version of Cuckoo search algorithm for solving optimization problems. Expert Syst. Appl.
**2021**, 186, 115669. [Google Scholar] [CrossRef] - Gonzalez-Castano, C.; Restrepo, C.; Kouro, S.; Rodriguez, J. MPPT Algorithm Based on Artificial Bee Colony for PV System. IEEE Access
**2021**, 9, 43121–43133. [Google Scholar] [CrossRef] - Boutasseta, N.; Bouakkaz, M.S.; Fergani, N.; Attoui, I.; Bouraiou, A.; Neçaibia, A. Experimental Evaluation of Moth-Flame Optimization Based GMPPT Algorithm for Photovoltaic Systems Subject to Various Operating Conditions. Appl. Sol. Energy
**2022**, 58, 1–14. [Google Scholar] [CrossRef] - Guo, K.; Cui, L.; Mao, M.; Zhou, L.; Zhang, Q. An Improved Gray Wolf Optimizer MPPT Algorithm for PV System with BFBIC Converter Under Partial Shading. IEEE Access
**2020**, 8, 103476–103490. [Google Scholar] [CrossRef] - Mansoor, M.; Mirza, A.F.; Ling, Q.; Javed, M.Y. Novel Grass Hopper optimization based MPPT of PV systems for complex partial shading conditions. Sol. Energy
**2020**, 198, 499–518. [Google Scholar] [CrossRef] - Kaya, C.B.; Kaya, E.; Gökkuş, G. Training Neuro-Fuzzy by Using Meta-Heuristic Algorithms for MPPT. Comput. Syst. Sci. Eng.
**2022**, 45, 69–84. [Google Scholar] [CrossRef] - Zhao, S.; Zhang, T.; Ma, S.; Chen, M. Dandelion Optimizer: A nature-inspired metaheuristic algorithm for engineering applications. Eng. Appl. Artif. Intell.
**2022**, 114, 105075. [Google Scholar] [CrossRef] - Oliva, D.; Cuevas, E.; Pajares, G. Parameter identification of solar cells using artificial bee colony optimization. Energy
**2014**, 72, 93–102. [Google Scholar] [CrossRef] - Ghani, F.; Rosengarten, G.; Duke, M.; Carson, J. The numerical calculation of single-diode solar-cell modelling parameters. Renew. Energy
**2014**, 72, 105–112. [Google Scholar] [CrossRef] - Bastidas-Rodriguez, J.; Petrone, G.; Ramos-Paja, C.; Spagnuolo, G. A genetic algorithm for identifying the single diode model parameters of a photovoltaic panel. Math. Comput. Simul.
**2017**, 131, 38–54. [Google Scholar] [CrossRef]

**Figure 1.**Structure of standard PV cell with DC-DC boost converter and MPPT control. (G: irradiance (W/m

^{2}), I

_{pv}: PV current (A), V

_{pv}: PV Voltage (V), C

_{in}: input-side capacitance (μF), L: inducatance (mH), D: diode, M: MOSFET, C

_{out}: output-side capacitance (μF), R

_{L}: resistive load (Ω)).

**Figure 4.**P-V and I-V characteristics at an ambient temperature of 25 °C under varying solar irradiance.

**Figure 5.**P-V and I-V curves of series-connected PV modules under (

**a**) nonuniform irradiance; (

**b**) uniform irradiance.

**Figure 6.**Trajectories of dandelion seeds during the three stages of DO implementation: (

**a**) rising stage; (

**b**) descending stage; and (

**c**) landing stage.

**Figure 8.**P-V and I-V plots were obtained for (

**a**) condition 1, (

**b**) condition 2, (

**c**) condition 3, and (

**d**) condition 4.

**Figure 9.**Plots of PV output power, current, voltage, and duty ratio produced for DO in (

**a**) condition 1, (

**b**) condition 2, (

**c**) condition 3, and (

**d**) condition 4.

**Figure 10.**Plots of PV output power, current, voltage, and duty ratio produced for CS in (

**a**) condition 1, (

**b**) condition 2, (

**c**) condition 3, and (

**d**) condition 4.

**Figure 11.**Plots of PV output power, current, voltage, and duty ratio produced for PSO in (

**a**) condition 1, (

**b**) condition 2, (

**c**) condition 3, and (

**d**) condition 4.

**Figure 12.**Step changes in solar irradiation of the four PV modules under different partial shading conditions.

**Figure 13.**The PV output power, current, voltage, and duty ratio plots obtained for DO as the irradiance pattern on the four PV panels is changed from condition 1 to condition 2, then to condition 3, and finally to condition 4 at intervals of 0.5 s.

**Figure 15.**P-V and I-V plots obtained for (

**a**) condition 1, (

**b**) condition 2, (

**c**) condition 3, and (

**d**) condition 4.

**Figure 16.**PV output power, current, voltage, and duty ratio plots obtained for DO in (

**a**) condition 1, (

**b**) condition 2, (

**c**) condition 3, and (

**d**) condition 4.

**Figure 17.**PV output power, current, voltage, and duty ratio plots obtained for CS in (

**a**) condition 1, (

**b**) condition 2, (

**c**) condition 3, and (

**d**) condition 4.

**Figure 18.**PV output power, current, voltage, and duty ratio plots obtained for PSO in (

**a**) condition 1, (

**b**) condition 2, (

**c**) condition 3, and (

**d**) condition 4.

**Figure 19.**The PV array output power, current, voltage, and duty ratio plots obtained for DO as the irradiance pattern on the four PV panels is changed from irradiance condition 1 to condition 2, then to condition 3.

Parameters | Values |
---|---|

Number of PV modules in series | 4 |

$\mathrm{Number}\mathrm{of}\mathrm{series}\mathrm{connected}\mathrm{cells}\mathrm{per}\mathrm{module}({N}_{s})$ | 72 |

$\mathrm{Maximum}\mathrm{operating}\mathrm{power}({P}_{mp})$ | 87.348 W |

$\mathrm{Maximum}\mathrm{operating}\mathrm{current}({I}_{mp})$ | 5.02 A |

$\mathrm{Maximum}\mathrm{operating}\mathrm{voltage}({V}_{mp})$ | 17.4 V |

Short-circuit current $({I}_{sc})$ | 5.34 A |

Open-circuit voltage $({V}_{oc})$ | 21.7 V |

$\mathrm{Temperature}\mathrm{coefficient}\mathrm{of}{I}_{sc}({K}_{i})$ | 0.075%/°C |

$\mathrm{Temperature}\mathrm{coefficient}\mathrm{of}{V}_{oc}({K}_{v})$ | −0.37501%/°C |

$\mathrm{Photogenerated}\mathrm{current}({I}_{ph})$ | 5.3624 A |

$\mathrm{Diode}\mathrm{saturation}\mathrm{current}({I}_{sat})$ | 3.052 × 10^{−10} A |

$\mathrm{Diode}\mathrm{ideality}\mathrm{factor}\left(n\right)$ | 0.12439 |

$\mathrm{Series}\mathrm{resistance}({R}_{s})$ | 79.3172 Ω |

$\mathrm{Shunt}\mathrm{resistance}({R}_{sh})$ | 0.081018 Ω |

Components | Values |
---|---|

$\mathrm{Power}\mathrm{rating}\mathrm{of}\mathrm{the}\mathrm{PV}\mathrm{module}\left({P}_{pv}\right)$ | 21.837 W |

$\mathrm{Input}\mathrm{capacitance}\left({C}_{in}\right)$ | $47\mathsf{\mu}\mathrm{F}$ |

$\mathrm{Output}\mathrm{capacitance}\left({C}_{out}\right)$ | $470\mathsf{\mu}\mathrm{F}$ |

$\mathrm{Inductor}\left(L\right)$ | $1.478\mathrm{mH}$ |

$\mathrm{Switching}\mathrm{frequency}\left(f\right)$ | $20\mathrm{kHz}$ |

$\mathrm{Load}\left({R}_{L}\right)$ | 10 Ω |

Parameters | PSO | CS | DO |
---|---|---|---|

$\mathrm{Number}\mathrm{of}\mathrm{particles}\left(pop\right)$ | 4 | 4 | 4 |

$\mathrm{Maximum}\mathrm{number}\mathrm{of}\mathrm{iterations}\left({t}_{max}\right)$ | 10 | 10 | 10 |

$\mathrm{Social}\mathrm{parameter}\left(c2\right)$ | 1.2 | $-$ | $-$ |

$\mathrm{Cognitive}\mathrm{parameter}\left(c1\right)$ | 1.6 | $-$ | $-$ |

$\mathrm{Inertia}\mathrm{weight}\left(w\right)$ | 0.4 | $-$ | $-$ |

$\mathrm{Step}\mathrm{size}\left(\alpha \right)$ | $-$ | 0.8 | $-$ |

$\mathrm{Variance}\left(\phi \right)$ | $-$ | 1.5 | 1.5 |

$s$ | $-$ | $-$ | 0.01 |

Shading Condition | Insolation (W/m^{2}) | Method | I_{mp}(A) | V_{mp}(V) | P_{mp}(W) | Rated Power (W) | Eff. (%) | Settling Time (s) | |||
---|---|---|---|---|---|---|---|---|---|---|---|

G_{1} | G_{2} | G_{3} | G_{4} | ||||||||

1 | 1000 | 1000 | 1000 | 1000 | DO | 2.94 | 29.59 | 87.26 | 87.34 | 99.90 | 0.25 |

CS | 2.95 | 29.52 | 86.96 | 99.56 | 1.17 | ||||||

PSO | 2.94 | 29.41 | 86.47 | 99.00 | 1.48 | ||||||

2 | 1000 | 1000 | 1000 | 500 | DO | 2.48 | 24.84 | 61.71 | 61.92 | 99.66 | 0.25 |

CS | 2.45 | 24.56 | 60.34 | 97.44 | 0.34 | ||||||

PSO | 2.44 | 24.44 | 59.71 | 96.43 | 1.38 | ||||||

3 | 1000 | 1000 | 700 | 400 | DO | 2.18 | 21.84 | 47.68 | 48.14 | 99.04 | 0.25 |

CS | 2.14 | 21.49 | 46.22 | 96.01 | 1.17 | ||||||

PSO | 2.12 | 21.23 | 46.02 | 95.59 | 1.32 | ||||||

4 | 1000 | 750 | 500 | 400 | DO | 1.91 | 19.20 | 36.85 | 37.89 | 97.25 | 0.10 |

CS | 1.88 | 18.91 | 35.68 | 94.16 | 0.48 | ||||||

PSO | 1.88 | 18.93 | 35.59 | 93.92 | 0.54 |

Shading Condition | Insolation (W/m^{2}) | Method | I_{mp}(A) | V_{mp}(V) | P_{mp}(W) | Rated Power (W) | Eff. (%) | Settling Time (s) | |||
---|---|---|---|---|---|---|---|---|---|---|---|

G_{1} | G_{2} | G_{3} | G_{4} | ||||||||

1 | 1000 | 1000 | 1000 | 1000 | DO | 2.91 | 29.91 | 87.08 | 87.34 | 99.70 | 0.8 |

CS | 2.91 | 29.88 | 86.96 | 99.56 | 1.6 | ||||||

PSO | 2.87 | 29.73 | 85.33 | 97.69 | 6.8 | ||||||

2 | 1000 | 1000 | 1000 | 600 | DO | 2.51 | 25.07 | 62.84 | 63.13 | 99.54 | 0.8 |

CS | 2.42 | 24.21 | 59.60 | 94.40 | 2.4 | ||||||

PSO | 2.41 | 24.08 | 58.91 | 93.31 | 5.0 | ||||||

3 | 1000 | 1000 | 700 | 500 | DO | 2.22 | 22.16 | 49.79 | 49.84 | 99.89 | 1.0 |

CS | 2.02 | 20.20 | 49.12 | 98.55 | 2.0 | ||||||

PSO | 2.02 | 20.19 | 49.11 | 98.53 | 4.8 | ||||||

4 | 1000 | 700 | 600 | 400 | DO | 2.05 | 20.47 | 41.92 | 42.22 | 99.28 | 1.0 |

CS | 1.99 | 19.85 | 39.42 | 93.36 | 2.6 | ||||||

PSO | 1.94 | 19.43 | 37.76 | 89.43 | 4.0 |

Irradiance Condition | Insolation (W/m^{2}) | I_{mp}(A) | V_{mp}(V) | P_{mp}(W) | Rated Power (W) | Eff. (%) | Settling Time (s) | |||
---|---|---|---|---|---|---|---|---|---|---|

G_{1} | G_{2} | G_{3} | G_{4} | |||||||

1 | 1000 | 1000 | 700 | 600 | 2.40 | 23.99 | 57.57 | 87.34 | 98.22 | 1.0 |

2 | 1000 | 1000 | 700 | 1000 | 2.59 | 25.89 | 68.35 | 63.13 | 98.84 | 1.6 |

3 | 1000 | 500 | 700 | 1000 | 2.22 | 22.42 | 49.79 | 49.84 | 99.89 | 1.6 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sajid, I.; Gautam, A.; Sarwar, A.; Tariq, M.; Liu, H.-D.; Ahmad, S.; Lin, C.-H.; Sayed, A.E.
Optimizing Photovoltaic Power Production in Partial Shading Conditions Using Dandelion Optimizer (DO)-Based MPPT Method. *Processes* **2023**, *11*, 2493.
https://doi.org/10.3390/pr11082493

**AMA Style**

Sajid I, Gautam A, Sarwar A, Tariq M, Liu H-D, Ahmad S, Lin C-H, Sayed AE.
Optimizing Photovoltaic Power Production in Partial Shading Conditions Using Dandelion Optimizer (DO)-Based MPPT Method. *Processes*. 2023; 11(8):2493.
https://doi.org/10.3390/pr11082493

**Chicago/Turabian Style**

Sajid, Injila, Ayushi Gautam, Adil Sarwar, Mohd Tariq, Hwa-Dong Liu, Shafiq Ahmad, Chang-Hua Lin, and Abdelaty Edrees Sayed.
2023. "Optimizing Photovoltaic Power Production in Partial Shading Conditions Using Dandelion Optimizer (DO)-Based MPPT Method" *Processes* 11, no. 8: 2493.
https://doi.org/10.3390/pr11082493