# Hybrid Fuzzy-DDPG Approach for Efficient MPPT in Partially Shaded Photovoltaic Panels
## 2 Materials and Methods
### Reinforcement Learning Fuzzy-DDPG
* Statistical Analysis: Confidence intervals and hypothesis testing are employed to ensure statistical robustness in the comparisons, demonstrating the reliability and superiority of the proposed approach. * Dynamic and Steady-State Behaviors: The dynamic tracking response and steady-state oscillations of each method are critically evaluated. Specific emphasis is placed on the proposed method's ability to avoid local maxima and achieve stable operation without oscillations. * Environmental Sensitivity: The methods are tested across various irradiance and temperature scenarios to assess robustness against environmental fluctuations. \begin{table}
\begin{tabular}{c l} \hline \hline
**Component** & **Description** \\ \hline \(r_{\text{mpp}}\) & Penalizes deviation from the maximum observed power \(P_{\text{MPP},\text{max}}\) \\ \(r_{1}\) & Proportional reward based on the extracted power \\ \(r_{2}\) & Encourages power increase based on \(\Delta P\) \\ \(r_{3}\) & Penalizes voltages beyond the open-circuit voltage limit \\ \(r_{4}\) & Penalizes sudden voltage variations (\(dV\)) \\ \(r_{5}\) & Additional penalty for large voltage changes \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Definition of the reward function components. Through the following subsections, the data are presented via boxplots, performance curves, and statistical summaries to ensure comprehensive and precise insights. Experimental conclusions are drawn to validate the effectiveness of the proposed hybrid MPPT algorithm. ### Experimental Design

Factors, Levels, and Response Variables

Two main factors dictate the operational state of PV modules:

* Irradiance \(G\): \(\{800,600,400\}\) W/m\({}^{2}\). * Temperature \(T\): \(\{25\,^{\circ}\text{C},35\,^{\circ}\text{C},45\,^{\circ}\text{C}\}\). By combining these three irradiance levels with three temperature settings, we obtain nine distinct environmental configurations. For each MPPT method, we execute 30 independent runs in each configuration, yielding \(9\times 30=270\) data points per method. The chosen performance metrics are the following:

1. Efficiency \(\eta\in[0,1]\), measuring how close the controller maintains the operating point to the true maximum power. 2. Oscillations \(\sigma\in\mathbb{R}_{\geq 0}\), capturing the amplitude of power fluctuations at or near the steady state. In more formal terms,

\[\eta=\frac{P_{\text{extracted}}}{P_{\text{max}}},\quad\sigma=\max_{t\in T}\left| P(t)-\overline{P}\right|,\]

where \(P_{\text{max}}\) is the theoretical maximum power under the current \(G\) and \(T\), \(P(t)\) is the instantaneous power output, and \(\overline{P}\) is the mean steady-state power. ### Data Generation and Implementation

1. Algorithmic Loop: For each of the three methods, Fuzzy-DDPG, P&O, and IC, we invoke a simulation procedure that produces \(\eta\) and \(\sigma\) values for each run. 2. Environmental Loop: For each irradiance level \(G\in\{800,600,400\}\) and temperature \(T\in\{25\,^{\circ}\text{C},35\,^{\circ}\text{C},45\,^{\circ}\text{C}\}\), simulation data were generated to reflect realistic operational noise and parameter uncertainties typical of real-world PV modules. 3. Replicas: For each \((G,T)\) pair, 30 runs are executed, ensuring a broad sampling of random variations. The implementation is conducted in Matlab/Simulink, integrating the PV panel models, MPPT algorithms, and statistical analysis tools. As shown in Table 4, the proposed Fuzzy-DDPG method demonstrates superior efficiency and minimal oscillations compared to the traditional methods. ### Statistical Analysis

Descriptive Statistics and Confidence Intervals

Let \(\{x_{m,1},x_{m,2},\ldots,x_{m,n}\}\) denote the sample of either efficiencies or oscillations for method \(m\). We define the following: