## 4 Proposed MCSO
### MCSO with Fixed Initial Tracking Voltage Combined with Tracking Pace Adjusted by Inertia Weight  
In CSO, inertia weight is an important parameter. Since the selection and adjustment of inertia weight could have a significant effect on the tracking performance of the algorithm, minor adjustments to this parameter could affect the balance of the optimization process and lead to better tracking results. Therefore, the parameter of inertia weight was added to Equation (1) to update the CSO speed in this paper. In addition to fixing the initial tracking voltage at 0.8 \(V_{\text{mp}}\), the learning rate was combined to adjust the tracking pace. The equation for updating the MCSO speed can be expressed as Equation (5):  
\[v_{i}(t+1)=w^{*}v_{i}(t)+r^{*}c^{*}[x_{best}(t)-x_{i}(t)] \tag{5}\]  
The values in Equation (5) can be used to adjust the inertia weight (\(w\)). The distance represents the difference between the optimal location found so far and the present location of each cat in CSO. Table 3 lists the adjustment relations between distance change \(|\,x_{best}(t)-x_{i}(t)\,|\) and parameter \(w\). When the distance is smaller, it indicates that the cat is already close to the MPP. For more accurate convergence at such a point and to reduce the oscillation amplitude of tracking back and forth, a smaller inertia weight (\(w\)) will be used. Conversely, if the distance is greater, it indicates that the cat is farther away from the GMP. A greater inertia weight (\(w\)) will then be used to enhance the tracking speed. Therefore, in addition to increasing the tracking speed, it was possible to accurately work near the MPP to reduce power loss during the tracking process.  
Figure 4: Interval division relations for parameters automatically adjusted according to slope of P-V characteristic curve under MCSO.  
\begin{table}
\begin{tabular}{c c} \hline \hline \(a\)=\(|\,x_{best}(t)-x_{i}(t)\,|\) & **The Inertia Weight (\(w\)) in Equation (5)** \\ \hline \(1\geq a\geq 0.6\) & \(w=0.4\) \\ \(0.6>a\geq 0.5\) & \(w=0.35\) \\ \(0.5>a\geq 0.4\) & \(w=0.3\) \\ \(0.4>a\geq 0.3\) & \(w=0.25\) \\ \(0.3>a\geq 0.2\) & \(w=0.2\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Adjustment relations between distance change \(|\,x_{best}(t)-x_{i}(t)\,|\) and inertia weight, \(w\).  
MCSO with Fixed Initial Tracking Voltage Combined with Tracking Pace Adjusted by the Slope of P-V Curve and Inertia Weight  
The use of distance \(\mid x_{best}(t)-x_{i}(t)\mid\) to determine the achievement of GMPP tracking was not sufficient because it was possible that the location with the current optimal fitness was the LMPP instead of the GMPP. Therefore, to increase the tracking speed and determine whether the GMPP instead of the LMPP was tracked more accurately, MCSO is proposed in this paper. In addition to fixing the initial tracking voltage at 0.8 \(V_{\text{mp}}\), it is combined with the slope of the P-V curve and the inertia weight at the same time to adjust the tracking pace. This tracking method can help to determine the status of the current work point more precisely; at the same time, the tracking pace can be increased by combining multiple parameters, which reduces the oscillation amplitude and enhances the tracking efficiency.