## 2 Grid-Connected PV Generation System
### Failure Analysis of GMPPT under PSC  
The PV array model proposed in this paper, based on (2) and (3), is shown in Figure 2c, where \(G_{ij}\) (\(i\) = 1-3; \(j\) = 1-12) is region A, and the other region is region B. \(N_{s}\) = 6, \(N_{p}\) = 12, and \(N_{s1}\) = 3. The parameters of a single solar panel are shown in Table 1. For regions A and B with different lighting conditions, the PV output characteristic curve can be measured as shown in Figure 3.  
It can be observed from Figure 3 that the MPP of the entire PV array is changed if the irradiance of the area A is 200 W/m\({}^{2}\) and the illumination condition of area B is changed. Considering the possibilities of dynamic irradiance changes, we make the following assumptions, to make the simulation conditions as specific as possible:  
1. Assuming that the illumination characteristic of the PV array at the moment \(t\) is given by the L3-R3 curve, and that the lighting condition changes at moment \(t+1\), the output characteristic curve of the PV array becomes L1-R1, and the actual PV output becomes S1. As the PV curve exhibits a multi-peak shape, the traditional MPP R1 cannot be obtained by searching the LMPP L1 using the gradient information as in the P & O and INC methods. Some experts found that the overall output power of the PV array changed greatly in this process. Global search algorithms such as the particle swarm optimization (PSO) algorithm or the artificial bee colony (ABC)  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline \(V_{\alpha c}\) (open-circuit voltage) & 65.2 V \\ \(I_{\infty}\) (short-circuit current) & 5.96 A \\ \(V_{m}\) (MPP (maximum power point) voltage) & 54.7 V \\ \(I_{m}\) (MPP current) & 5.58 A \\ \(P_{m}\) (MPP power) & 305.2 W \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the solar cell.  
Figure 3: \(V\)–\(P\) characteristics of PV array under PSC (maximum power point).  
algorithm can be used for global optimization, by using the amplitudes of the output power variations and the \(t+1\) global optimal solution R1 to solve the local shadow problems of the PV output characteristics with multiple peaks.
2. The light characteristic curve of the PV array is assumed to be the L1-R1 curve at moment \(t\), and the curve of the PV characteristic becomes L3-R3 at moment \(t+1\), which indicates that the MPP of the PV system should change from R1 to L3.  
In this process, as the suboptimal solution R3 of the L3-R3 curve is near R1, the power change is not very large. Therefore, the global search algorithm can be started, which results in the failure of the MPPT algorithm. As can be seen in Figure 4, in this failure case, the power loss ratio is approximately three.  
The threshold of the algorithm is inversely proportional to the starting frequency. However, the global optimization search algorithm usually needs a long time to search in an iterative manner, and it is difficult to perform the maximum power search in time when the irradiance changes frequently or continuously.  
Therefore, it is difficult to solve the multi-peak problem of local shadowing using the traditional method. The global search algorithm has the problem of slow convergence, and it is difficult to start the global optimization search algorithm using only the current and voltage definitions.  
Therefore, it is necessary to use the environment information to make the search judgments, and to utilize fast and efficient tracking algorithms to solve the multi-peak problem of GMPPT under dynamic local shadow conditions.