# Hybrid Fuzzy-DDPG Approach for Efficient MPPT in Partially Shaded Photovoltaic Panels
## 2 Materials and Methods
### Reinforcement Learning Fuzzy-DDPG
### Case 4: Dynamic Environmental Changes

The fourth scenario simulates dynamic environmental conditions, where the irradiance values change linearly with time. Specifically, \(G_{1}\) decreases from 1000 W/m\({}^{2}\) to 600 W/m\({}^{2}\), and \(G_{2}\) decreases from 800 W/m\({}^{2}\) to 400 W/m\({}^{2}\) over a period of 20 s, while both panels are maintained at \(T_{1}=T_{2}=30\,^{\circ}\)C. As observed in Figure 10, the open-loop power curve displays multiple local maxima along with one global maximum. Figure 11 further reveals that, under these transient conditions, the Fuzzy-DDPG algorithm exhibits a high degree of adaptability, enabling it to closely follow the global maximum power point with minimal deviation, even under dynamically changing conditions, whereas the P&O and IC methods are prone to settling at one of the local peaks. \[\overline{x}_{m}=\frac{1}{n}\sum_{k=1}^{n}x_{m,k}\]2 Comparison of MPPT methods for Case 4: Fuzzy–DDPG, Perturb and Observe, and Incremental Conductance under dynamic environmental changes. \[\overline{x}_{m}=\frac{1}{n}\sum_{k=1}^{n}x_{m,k}\]3 Open-loop power curve under dynamic environmental conditions, showing multiple local maxima and one global maximum. ### Overall Analysis

An integrated analysis of Figures 4-11 confirms that the Fuzzy-DDPG method consistently tracks the global maximum power point (GMPP) across a wide range of environmental conditions. In contrast, conventional methods such as Perturb and Observe and Incremental Conductance frequently converge to local maxima, particularly under partial shading and dynamic irradiance scenarios. The enhanced performance of Fuzzy-DDPG is attributed to its ability to structure the state space using fuzzy partitioning, thereby facilitating a more robust and adaptive search for the GMPP. In summary, the Fuzzy-DDPG approach demonstrates the following:

* Superior tracking accuracy with minimal oscillatory behavior. * Faster convergence towards the global maximum power point. * Robust adaptability under both static and dynamically changing conditions. These results substantiate the effectiveness of the proposed method in enhancing the energy extraction efficiency of photovoltaic systems under complex operating conditions. ## 5 Performance Analysis of MPPT Methods

Table 5 presents the power extracted by each MPPT method across four test cases. The theoretical maximum power is shown for reference, representing the highest achievable value under ideal conditions. The Fuzzy-DDPG method consistently tracks the global maximum more accurately than the Perturbation and Conductance methods, which tend to converge to local maxima, especially under partial shading and dynamically varying conditions. ### Summary Statistics

The statistical summary in Table 6 highlights the mean power, standard deviation, and range for each MPPT method. The Fuzzy-DDPG method demonstrates the highest mean power extraction with the lowest deviation, reinforcing its reliability. The Perturbation and Conductance methods show slightly lower means and higher deviations, indicating susceptibility to local maxima. ### Error Analysis for All MPPT Methods

In order to rigorously assess the tracking accuracy of each MPPT method, we quantify the deviation of the extracted power from the theoretical maximum power (\(P_{\text{max}}\)) obtained under ideal (open-loop) conditions. For each experimental trial, the relative error is computed as

\[\overline{x}_{m}=\frac{1}{n}\sum_{k=1}^{n}x_{m,k}\]4 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Mean Power (W)** & **Std Dev (W)** & **Min Power (W)** & **Max Power (W)** \\ \hline Fuzzy-DDPG & 363.25 & 174.86 & 154.72 & 653.22 \\ Perturbation & 356.98 & 174.41 & 142.99 & 653.17 \\ Conductance & 355.50 & 174.61 & 142.93 & 653.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary statistics of MPPT performance.