# Hybrid Fuzzy-DDPG Approach for Efficient MPPT in Partially Shaded Photovoltaic Panels
## 2 Materials and Methods
### Reinforcement Learning Fuzzy-DDPG
contrast, Fuzzy-DDPG provides smoother control actions by leveraging fuzzy approximations of the Q-function, thereby reducing instability in real-time applications. This results in more consistent power output and improved operational reliability. Quantitative Performance Analysis

To further illustrate the superiority of Fuzzy-DDPG over standard DDPG, the following performance metrics should be compared:

* Mean Power Output: Demonstrates the efficiency of power extraction over extended periods. * Standard Deviation of Power: Evaluates the stability of power tracking. * Error Percentage: Quantifies the deviation from the theoretical maximum power. * Convergence Time: Measures the number of episodes required to reach a stable policy. The empirical results confirm that Fuzzy-DDPG consistently outperforms standard DDPG in all the aforementioned metrics, making it a more robust and efficient solution for MPPT under partial shading conditions. The simulation results presented in Figures 12 and 13 provide a comprehensive comparative analysis between the standard DDPG algorithm and its fuzzy logic-enhanced variant, Fuzzy-DDPG. The evaluation focuses on four principal performance metrics: mean power output, standard deviation of power, error percentage relative to the theoretical maximum power, and convergence time required to establish a stable policy. With respect to the mean power output, both algorithms exhibit an increasing trend as the number of episodes progresses, which aligns with the expected learning dynamics inherent in reinforcement learning frameworks. Notably, the Fuzzy-DDPG algorithm demonstrates a more rapid approach towards the theoretical maximum power, \(P_{\text{max}}\), as evident in Figure 12. This accelerated progression is indicative of its enhanced learning capability, further substantiated by the convergence time analysis depicted in Figure 13, where Fuzzy-DDPG achieves stability in significantly fewer episodes compared to the standard DDPG. Figure 12: Comparison of mean power output, standard deviation, and error percentage. The analysis of the standard deviation of power provides insight into the consistency and reliability of the power tracking performance. The lower standard deviation observed for Fuzzy-DDPG suggests enhanced robustness and reduced variability under stochastic influences, thereby affirming the benefit of integrating fuzzy logic into the control strategy. In contrast, the higher variability in the DDPG algorithm, as illustrated in Figure 12, may compromise the stability of power extraction in real-world applications. Furthermore, the error percentage metric reveals that Fuzzy-DDPG attains a closer approximation to \(P_{\text{max}}\) at an earlier stage in the training process. The lower error percentage not only reflects superior tracking accuracy but also indicates a more effective mitigation of disturbances, thereby validating the improved performance of the fuzzy logic augmentation, as depicted in Figure 12.

The comparative graph of convergence time in Figure 13 reinforces these findings by clearly demonstrating that Fuzzy-DDPG requires fewer episodes to achieve a stable policy. This reduced convergence time is critical in scenarios where rapid adaptation to dynamic conditions is essential, and it underscores the operational advantages of the fuzzy-augmented approach. In summary, the incorporation of fuzzy logic within the DDPG framework yields marked improvements across all evaluated performance metrics. The accelerated convergence, enhanced stability, and reduced error percentage collectively suggest that Fuzzy-DDPG is a robust and efficient alternative for power extraction tasks. These results motivate further investigation into the deployment of fuzzy-logic-enhanced reinforcement learning strategies in practical power management systems. ## 7 Experimental Implementation

In this section, we detail the physical implementation of the proposed Fuzzy-DDPG-based MPPT algorithm.