## Materials and Methods
### Three-Point Fuzzy MPPT Algorithm of Variable Step Size  
Presently, the commonly used MPPT control algorithms include the fixed voltage method, perturbation and observation method, and incremental conductance method. Table 1 presents a comparison of the three commonly used MPPT tracking control methods. The following can be deduced from the table:  
1. The fixed voltage method needs fewer detection parameters and less hardware, but yields a poor control performance, thus, it is usually used in low power cases;
2. The disturbance observation method is simple to implement and yields a very good control performance. The disadvantage is that it easily produces oscillation near the maximum power point, and may lose its tracking ability when the light intensity changes abruptly. 3. The incremental conductance method yields the best control performance, but the hardware requirement of a photovoltaic power generation system is also higher, which increases the cost of the equipment. In this study, the perturbation observation method, one of the three traditional tracking algorithms, was improved, and we proposed a new perturbation observation method with the following characteristics. The main approach is to include the constant voltage method to accelerate the tracking speed of the low power section at the initial stage of tracking, and use the three-point method combined with a variable step size disturbance to judge the near maximum power point so as to improve the tracking accuracy and final steady state. 1. The constant pressure method was used in the start-up phase of the disturbance observation method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Fixed Voltage Method** & \
\begin{tabular}{c} **Perturbation and** \\ **Observation Method** \\ \end{tabular} &
\begin{tabular}{c} **Incremental** \\ **Conductance Method** \\ \end{tabular} \\ \hline
92.8\% & 97.1\% & 98.4\% & \\
88.2\% & 96.6\% & 98.3\% & \\ Advantages & \
\begin{tabular}{c} Less parameters \\ Simple realization \\ \end{tabular} & Better control & Better control \\ Disadvantages & Poor control & Power oscillation exists &
\begin{tabular}{c} Accuracy of sampling is high and \\ amount of computation is large \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Advantages and disadvantages of three maximum power point tracking (MPPT) methods. Figure 5: PI-based closed-loop charging control algorithm. Three-point method of perturbation and observation method control. The principle of the three-point control is as follows: A, B, and C are selected from left to right near the vertex of the PV characteristic curve of the solar cells, and Flag_3 is set as the change mark. Among them, V\({}_{A}\), I\({}_{A}\), V\({}_{B}\), I\({}_{B}\), V\({}_{C}\), and \(I_{C}\) represent the voltage and current of A, B, and C, respectively, and \(P_{A}\), \(P_{B}\), and \(P_{C}\) represent the corresponding power of A, B, and C, respectively. Setting the voltage corresponding to the maximum power point of A, B, and C as \(V_{max}\), the three-point method judges the working point mode mainly as shown in Figure 6, that is, \(V_{max}=V_{C}\), \(V_{max}=V_{B}\), or \(V_{max}=V_{A}\). When \(P_{B}\leq P_{C}\), Flag_3P = 1, and when \(P_{B}>P_{C}\), set Flag_3P = \(-1\);  
When \(P_{A}<P_{B}\), Flag_3P = 1, and when \(P_{A}\geq P_{B}\), set Flag_3P = \(-1\). By judging the Flag_3P value twice, we can make a judgment of the direction of the disturbance. If Flag_3P = 2, \(P_{A}<P_{B}\) & \(P_{B}\leq P_{C}\), increase the disturbance quantity;  
If Flag_3P = 0, \(P_{A}<P_{B}\) & \(P_{B}>P_{C}\), the maximum point is fine-tuned. If Flag_3P = \(-2\), \(P_{A}\geq P_{B}\) & \(P_{B}>P_{C}\), the disturbance will be reduced. At a rapidly changing sunlight intensity, \(P_{A}\geq P_{B}\) and \(P_{B}\leq P_{C}\) will also occur. Because Flag_3P = 0 at this time, it can be classified as the situation of reaching the maximum power point, that is, the working point does not change, thus avoiding any misjudgment caused by a rapid change in sunlight intensity.