*4.5. Statistics of Results and Analysis*

To provide a clearer insight into the performance indicators of each algorithm, statistical tables are created summarizing the results obtained using the above-mentioned three algorithms. The performance of each algorithm is assessed originating from various evaluation metrics, including convergence time, optimization value, projected annual loss cost, and tracking efficiency, as shown in Table 4.


**Table 4.** Performance comparison of algorithms.

As illustrated in Table 4, the PSO-BOA algorithm outperforms both the BOA and PSO in all four simulations, achieving faster and smoother convergence to GMPP. It is worth noting that the PSO-BOA algorithm shows a faster convergence speed. The convergence time of PSO-BOA is 54.43% relative to PSO and 57.33% relative to the BOA under uniform irradiance, and is reduced to 37.5% relative to PSO and 51.22% relative to the BOA under local shading conditions. Based on the local electricity prices and assuming an average daily sunlight duration of 12 h, this study calculates the annual cost of losses. In scenarios with abrupt lighting condition changes, the PSO algorithm results in the highest annual loss cost, whereas the PSO-BOA algorithm proves effective in mitigating these losses and reducing costs. Meanwhile, the PSO algorithm achieves faster convergence in cases of sudden changes in irradiance and temperature, but is more prone to falling into local optima, resulting in the worst convergence accuracy. The convergence rate of the BOA is sluggish, with many oscillations occurring over the course of convergence. In contrast, the PSO-BOA algorithm is able to maintain stable and higher optimization accuracy than both the BOA and PSO across all four simulations. These results suggest that the PSO-BOA algorithm effectively addresses the issues of large search oscillation in the BOA and low optimization accuracy in PSO while also improving convergence speed.
