# Hybrid Fuzzy-DDPG Approach for Efficient MPPT in Partially Shaded Photovoltaic Panels
## 2 Materials and Methods
### Reinforcement Learning Fuzzy-DDPG
\begin{table}
\begin{tabular}{l c} \hline
**Parameter** & **Value** \\ \hline \multicolumn{3}{c}{Fuzzy Membership Functions} \\ \hline Number of membership functions per variable & 7 \\ Type of membership functions & Gaussian \\ Number of state variables & 7 \\ State variables & Voltage, Current, Power, G1, G2, \(\Delta P\), \(\Delta V\) \\ \hline \multicolumn{3}{c}{Actor Network Architecture} \\ \hline Input & 7 (States with fuzzy features) \\ Normalization layer & Yes \\ Fuzzy feature layer & Yes \\ Number of hidden layers & 2 \\ Number of neurons per layer & 128 \\ Activation function & ReLU \\ Output layer & 1 neuron (action) with Tanh \\ \hline \multicolumn{3}{c}{Critic Network Architecture} \\ \hline Input & 7 (States) + 1 (Action) \\ Normalization layer & Yes \\ Fuzzy feature layer & Yes \\ Number of hidden layers & 2 \\ Number of neurons per layer & 128 \\ Activation function & ReLU \\ Output layer & 1 neuron (Q-Value) \\ \hline \multicolumn{3}{c}{Training Hyperparameters} \\ \hline Actor learning rate & \(10^{-5}\) \\ Critic learning rate & \(10^{-4}\) \\ Discount factor (\(\gamma\)) & 0.99 \\ Batch size & 256 \\ Target smooth factor (\(\tau\)) & \(10^{-3}\) \\ Experience buffer size & \(10^{6}\) \\ \hline \multicolumn{3}{c}{Training Options} \\ \hline Number of episodes & 100 \\ Maximum steps per episode & 15,000 \\ Score averaging window length & 10 \\ Sampling time interval & 0.06 s \\ \hline \end{tabular}
\end{table} 
Table 2: Specifications of the photovoltaic panel used in simulations. \begin{table}
\begin{tabular}{l c} \hline
**Parameter** & **Value** \\ \hline Number of Parallel Strings & 1 \\ Number of Series-Connected Modules per String & 1 \\ Maximum Power (\(P_{max}\)) [W] & 352.408 \\ Cells per Module (\(N_{cell}\)) & 60 \\ Open-Circuit Voltage (\(V_{cc}\)) [V] & 49.9 \\ Short-Circuit Current (\(I_{sc}\)) [A] & 9.0 \\ Voltage at Maximum Power Point (\(V_{mp}\)) [V] & 40.6 \\ Current at Maximum Power Point (\(I_{mp}\)) [A] & 8.68 \\ Temperature Coefficient of \(V_{oc}\) [\(\%\)/\({}^{\circ}\)C] & \(-0.36099\) \\ Light-Generated Current (\(I_{L}\)) [A] & 9.1365 \\ Diode Saturation Current (\(I_{b}\)) [A] & \(3.3113\times 10^{-10}\) \\ Diode Ideality Factor & 1.3468 \\ Shunt Resistance (\(R_{sl}\)) [\(\Omega\)] & 1063.7078 \\ \hline \end{tabular}
\end{table} 
Table 1: Hyperparameters and configuration of the fuzzy DDPG agent. voltage fluctuations. The total reward \(R\) is defined as the sum of multiple components, each addressing a specific aspect of the MPPT process:

\[R=r_{\text{mpp}}+r_{1}+r_{2}+r_{3}+r_{4}+r_{5} \tag{35}\]

where each term contributes to guiding the agent towards maximizing power extraction while maintaining system stability. Table 3 summarizes the definition of each component. The components of the reward function are computed as follows:

\[r_{\text{mpp}} = \begin{cases}-2\frac{|P-\text{MPP}_{\text{max}}|}{\text{MPP}_{ \text{max}}},&\text{if }P_{\text{MPP},\text{max}}>0\\ 0,&\text{otherwise}\end{cases}  \tag{36}\] \[r_{1} = \begin{cases}0.1\frac{P}{\text{MPP}_{\text{max}}},&\text{if }P_{ \text{MPP},\text{max}}>0\\ 0,&\text{otherwise}\end{cases} \] (37) \[r_{2} =\text{sign}(\Delta P)\] (38) \[r_{3} = \begin{cases}0,&0\leq V_{\text{new}}\leq V_{\text{oc,total}}\\ -2,&\text{otherwise}\end{cases} \] (39) \[r_{4} =-0.1|dV|\] (40) \[r_{5} =-0.5\frac{|dV|}{2} \tag{41}\]

This function encourages the agent to maximize the extracted power while preventing excessive voltage variations that could lead to instability. The inclusion of \(r_{3}\) ensures that the voltage remains within the safe operating range, while \(r_{4}\) and \(r_{5}\) penalize abrupt changes, promoting smooth control actions. The results are structured to illustrate the following:

* Methodological Comparisons: The performance metrics--such as global maximum power point (GMPP) tracking efficiency, stability, and adaptability under partial shading conditions--are systematically analyzed across methods.