## 4 Proposed MCSO
### MCSO with Fixed Initial Tracking Voltage  
Although the P-V characteristic curve of the PVMA will change under different solar irradiance levels or the partial shading of modules, it can be observed from Figure 3 that upon a sudden change in solar irradiance (from 1000 to 500 W/m\({}^{2}\)), there was no extensive difference in MPP voltage. To improve the tracking speed of the conventional CSO, the initial tracking voltage \(V_{\text{begin}}\) was first fixed at 0.8 times the MPP voltage \(V_{\text{mp}}\) (i.e., \(V_{\text{begin}}=0.8~{}V_{\text{mp}}\)). Therefore, each tracking would commence from \(V_{\text{begin}}\). Despite the change in solar irradiance, the initial tracking voltage was approximately around the GMPP; therefore, this method can swiftly and steadily track the GMPP. Figure 3: P-V characteristic curve upon sudden change in solar irradiance with partial module shading. MCSO with Fixed Initial Tracking Voltage Combined with Tracking Pace Adjusted with Slope of P-V Curve  
Although the MCSO with a fixed initial tracking voltage provided better tracking speed, it still used the same fixed tracking pace as the conventional CSO. Therefore, if the tracking pace is set to be excessively small, the tracking speed of the system will be affected. Conversely, if the tracking pace is set to be excessively large, although the tracking speed could increase, there will be a greater amplitude of oscillation when tracking in the vicinity of the MPP, where the tracking efficiency will be reduced. To solve this problem and not affect the tracking speed at the same time, MCSO with a fixed initial tracking voltage was adopted in this study. In addition, the change intervals of the slope for the P-V characteristic curve in Table 2 were utilized to automatically adjust the speed coefficient (_c_) the MSCO in Equation (1). Therefore, the tracking pace could be adjusted to be smaller when the work point was close to the GMPP, which prevented excessive tracking oscillation and a loss of output power. Similarly, when the work voltage point was far away from the GMPP, the tracking pace could be increased to accelerate the tracking speed. This method of control could increase the tracking speed and reduce the oscillation amplitude near the MPP at the same time. Moreover, upon sudden changes in solar irradiance, the system could adjust the tracking pace instantly to realize fast and accurate MPPT. Figure 4 displays the adjustment relations between the slope of the P-V characteristic curve and speed coefficient (_c_) in Table 2 for the proposed MCSO, where \(m\) is the slope of the P-V characteristic curve. From Figure 4, the following can be observed:  
1. When slope \(m\) is less than zero, it indicates that the system has tracked to the right side of the MPP, and the tracking direction is heading toward the MPP at the left. 2. When slope \(m\) is greater than zero, it indicates that the system has tracked to the left side of the MPP, and the tracking direction is heading toward the MPP at the right. 3. When slope \(m\) is zero, it indicates that the system has tracked the MPP. The slope (_m_) and power variation (d_P_) are defined by Equations (3) and (4), respectively: \[m=\frac{\mathrm{d}P}{\mathrm{d}V}=\frac{P_{k}-P_{k-1}}{V_{k}-V_{k-1}}\] (3) \[\mathrm{d}P=P_{k}-P_{k-1}\] (4)  
where \(P_{k}\) and \(V_{k}\) are the power and voltage values of the current operating point, respectively, and \(P_{k-1}\) and \(V_{k-1}\) are the power and voltage values of the previous operating point. \begin{table}
\begin{tabular}{c c} \hline
**Slope Interval of P-V Characteristic Curve** & **Speed Coefficient (_c_) in Equation (1)** \\ \hline Interval \(m_{1}\): \(m>2\) & \(c\) = 1.4 \\ Interval \(m_{2}\): \(2>m\geq 1.3\) & \(c\) = 1.3 \\ Interval \(m_{3}\): \(1.3>m\geq 0.8\) & \(c\) = 1.2 \\ Interval \(m_{4}\): \(0.8>m\geq 0\) & \(c\) = 1.1 \\ Interval \(m_{5}\): \(0>m\geq-1\) & \(c\) = 1.0 \\ Interval \(m_{6}\): \(m\leq-1\) & \(c\) = 1.2 \\ \hline \end{tabular}
\end{table}