# Hybrid Fuzzy-DDPG Approach for Efficient MPPT in Partially Shaded Photovoltaic Panels
## 2 Materials and Methods
### Reinforcement Learning Fuzzy-DDPG
G1 = G2 = 1000 W/m\({}^{2}\), T1 = 25 \({}^{\circ}\)C, T2 = 45 \({}^{\circ}\)C. This scenario highlights the impact of temperature variation on tracking efficiency. * Case 2: Partial Shading with Moderate Temperature. G1 = 1000 W/m\({}^{2}\), G2 = 500 W/m\({}^{2}\), T1 = T2 = 35 \({}^{\circ}\)C. This case replicates conditions where one panel is partially shaded by clouds or objects. * Case 3: Severe Partial Shading with Low Temperature. G1 = 400 W/m\({}^{2}\), G2 = 200 W/m\({}^{2}\), T1 = T2 = 15 \({}^{\circ}\)C. This scenario reflects early morning or cold climate conditions with extreme shading. * Case 4: Dynamic Environmental Changes. G1 and G2 vary linearly from 1000 W/m\({}^{2}\) to 600 W/m\({}^{2}\) and from 800 W/m\({}^{2}\) to 400 W/m\({}^{2}\) over 20 s, respectively, with T1 = T2 = 30 \({}^{\circ}\)C. This models transient conditions such as moving clouds to test adaptability. ## 4 Discussion of Simulation Results

The simulation results presented in this study provide a comprehensive evaluation of the Maximum Power Point Tracking (MPPT) methods under a variety of environmental conditions. In particular, four distinct cases were examined to assess the performance of the proposed Fuzzy-DDPG algorithm in comparison with conventional Perturb and Observe (P&O) and Incremental Conductance (IC) techniques. ### Case 1: Uniform Irradiance with Different Temperatures

Under uniform irradiance conditions (\(G_{1}=G_{2}=1000\) W/m\({}^{2}\)) with differing temperatures (\(T_{1}=25\,^{\circ}\)C and \(T_{2}=45\,^{\circ}\)C), the open-loop power curve, as depicted in Figure 4,

Figure 3: Boxplot comparison. exhibits a single global maximum. Figure 5 compares the performance of Fuzzy-DDPG, P&O, and IC methods. While all three approaches approximate the theoretical maximum power (as verified in the open-loop test), both P&O and IC display pronounced oscillations around the operating point. In contrast, the Fuzzy-DDPG method converges smoothly to the global maximum, underscoring its robustness even in the presence of temperature gradients. Figure 4: Open-loop power curve where the input voltage is varied under uniform irradiance (\(G_{1}=G_{2}=1000\) W/m\({}^{2}\)) and differing temperatures (\(T_{1}=25\,^{\circ}\)C, \(T_{2}=45\,^{\circ}\)C). Figure 5: Comparison of MPPT methods: Fuzzy–DDPG, Perturb and Observe, and Incremental Conductance for Case 1. ### Case 2: Partial Shading with Moderate Temperature

In the second scenario, partial shading is simulated by setting \(G_{1}=1000\) W/m\({}^{2}\), \(G_{2}=500\) W/m\({}^{2}\), with both panels maintained at \(T_{1}=T_{2}=35\,^{\circ}\)C. The open-loop power curve in Figure 6 clearly indicates the presence of both local and global maximum power points. As illustrated in Figure 7, conventional methods (P&O and IC) tend to converge towards the local maximum, thereby missing the true global optimum. Conversely, the Fuzzy-DDPG algorithm successfully identifies and tracks the global maximum, demonstrating its enhanced capability under partial shading conditions. Figure 6: Open-loop power curve under partial shading conditions, highlighting both local and global MPPT. Figure 7: Comparison of MPPT methods for Case 2: Fuzzy–DDPG, Perturb and Observe, and Incremental Conductance. ### Case 3: Severe Partial Shading with Low Temperature

Case 3 is characterized by severe partial shading and lower temperatures (\(G_{1}=400\) W/m\({}^{2}\), \(G_{2}=200\) W/m\({}^{2}\), \(T_{1}=T_{2}=15\,^{\circ}\)C). Figure 8 shows an open-loop power curve with a distinct local minimum at approximately 143.11 W and a global maximum near 155.24 W. As depicted in Figure 9, the Fuzzy-DDPG method effectively tracks the global maximum, whereas both the P&O and IC methods converge only to the suboptimal local maximum. \[\overline{x}_{m}=\frac{1}{n}\sum_{k=1}^{n}x_{m,k}\]0 Open-loop power curve for Case 3 under severe partial shading and low temperature conditions. \[\overline{x}_{m}=\frac{1}{n}\sum_{k=1}^{n}x_{m,k}\]1 MPPT method comparison for Case 3: Fuzzy–DDPG, Perturb and Observe, and Incremental Conductance.