# Hybrid Fuzzy-DDPG Approach for Efficient MPPT in Partially Shaded Photovoltaic Panels
## 2 Materials and Methods
### Reinforcement Learning Fuzzy-DDPG
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Maximum Power** & **Fuzzy–DDPG** & **Perturbation** & **Conductance** \\ \hline Case 1 & 670.7761 & 653.2196 & 653.1650 & 653.3130 \\ Case 2 & 367.3563 & 357.5469 & 343.6681 & 343.0770 \\ Case 3 & 155.2448 & 154.7223 & 142.9854 & 142.9300 \\ Case 4 & 293.6100 & 289.5000 & 284.1000 & 283.5800 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Power extracted by each MPPT method (W). which provides a direct measure of how closely each method approximates the global maximum. A lower error percentage indicates a more accurate and robust tracking performance. The summary statistics of these errors are presented in Table 7, which shows the relative error to the maximum theoretical power for all MPPT methods. The Fuzzy-DDPG method exhibits the lowest error across all cases, demonstrating its effectiveness in tracking the global maximum. In contrast, the Perturbation and Conductance methods show significantly higher errors, particularly in cases with partial shading and dynamic irradiance variations. The results confirm that Fuzzy-DDPG maintains a small error margin under all conditions, with a maximum deviation of 2.67%. The Perturbation and Conductance methods perform reasonably well under uniform irradiance (Case 1) but exhibit errors as high as 7.93% under partial shading (Case 3), highlighting their limitation in avoiding local maxima. These findings reinforce the robustness of Fuzzy-DDPG in achieving optimal energy extraction in photovoltaic systems. Additionally, the statistical analysis demonstrates that the Fuzzy-DDPG method achieves higher mean power with lower standard deviation, further validating its superior adaptability to changing environmental conditions. ## 6 Comparison Between Fuzzy-DDPG and Standard DDPG

The proposed Fuzzy-DDPG algorithm exhibits significant advantages over the standard Deep Deterministic Policy Gradient (DDPG) in the context of Maximum Power Point Tracking (MPPT) under partial shading conditions. The main benefits are detailed as follows:

* Accelerated Convergence: Fuzzy-DDPG achieves faster convergence than standard DDPG due to its ability to structure the state space using fuzzy partitioning. This approach provides a more efficient exploration strategy, reducing the number of required training episodes. The function approximation through fuzzy basis functions enhances the agent's learning process by reducing the complexity of the policy search, thus improving sample efficiency. * Enhanced Generalization Capability: By incorporating fuzzy logic into the policy representation, Fuzzy-DDPG generalizes more effectively across varying environmental conditions, such as irradiance and temperature fluctuations. Unlike standard DDPG, which requires extensive retraining to adapt to new conditions, Fuzzy-DDPG demonstrates superior adaptability, achieving optimal performance with fewer modifications to the learned policy. * Improved Tracking Accuracy: Fuzzy-DDPG closely follows the global maximum power point (GMPP) with higher accuracy compared to standard DDPG. The fuzzy partitioning mitigates the risk of premature convergence to local optima, a limitation frequently observed in conventional reinforcement learning methods. Empirical results indicate that Fuzzy-DDPG maintains a lower tracking error, ensuring greater energy efficiency in photovoltaic systems. * Reduced Control Oscillations: Standard DDPG often exhibits fluctuations in the duty cycle before reaching a stable policy, leading to undesirable power oscillations. In \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Fuzzy–DDPG Error (\%)** & **Perturbation Error (\%)** & **Conductance Error (\%)** \\ \hline Case 1 & 2.62 & 2.63 & 2.60 \\ Case 2 & 2.67 & 6.45 & 6.61 \\ Case 3 & 0.34 & 7.90 & 7.93 \\ Case 4 & 1.40 & 3.24 & 3.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Error relative to maximum power for each MPPT method.