## 4 Case and Discussion
### Result Analysis
In the AB section, as \(J_{1}\) slowly increases, \(J_{2}\) rapidly decreases, which means that by alleviating the requirements for target \(J_{1}\), greater benefits can be obtained on target \(J_{2}\). On the other hand, in the BC section, as \(J_{1}\) increases significantly, \(J_{2}\) slowly decreases, which means that the substantial reduction of the requirements for the target \(J_{1}\) has limited improvement in the direction of the target \(J_{2}\). Therefore, the optimization results of method 1 and 3 are located in the BC section and are far from point B, which is bad for the whole system. Meanwhile, the search results of both method 2 and the SSO method are close to point B, the point of the slope mutation of the pareto front, which means that the results of these two methods are better for the overall system. (3) The search process of the SSO method takes \(\Delta c=0.1\) and \(\Delta c=0.2\). Figure 6: Comparison results of operational performance of different distribution network methods. as the step, and, after updating five times, it gradually decreases for three times, resulting in \(\Delta c=0.0125\), and then \(\text{abs}(J_{1}/\mid\min(J_{1})\mid-J_{2}/\mid\min(J_{2})\mid)<\lambda\) is searched. This implies that the stepper search method proposed in this paper is effective and can search for the recommended solution quickly. From the operating curves of the DG presented in Figure 5(a), the curves of method 2 and the SSO method are basically the same, and the trend of the output power during a typical day is basically consistent with the load power demand, whereas in method 1, in order to significantly reduce power loss (optimization objective \(J_{1}\)), the distributed power supply continuously outputs a large amount of reactive power and reduces the active power output. From the comparison of the operating curves from PV and wind power generation system shown in Figure 5(b), the actual power of wind power generation has been well consumed based on the three scheduling strategies, but there is a phenomenon of photovoltaic power abandonment in the application of method 1, which is concentrated in the peak of PV power generation and the low valley of load power consumption between 12\(\sim\)15 h. Additionally, it can be seen that method 2 and the SSO method are better than method 1. Figure 5(c) shows the output active power curve and energy state of the BESS. Between 0:00 and 6:00, the BESS takes the initiative to charge and dissipate the wind power generation that is larger than the load demand. Between 6:00 and 11:00, the load active power is greater than the maximum output power of the new energy, and the BESS discharges to support the load power demand. Between 11:00 and 16:00, due to more photovoltaic power generation, the new energy generation is greater than the load demand, and the BESS is reasonably charged again, ready to cope with the next decline in photovoltaic power generation caused by the difference between the load power and the new energy power supply. The BESS has solved the power balance problem and ensured the economic operation of the DES. Figure 5(d) shows the voltage curves of each node from the power grid at different times under different optimization methods. It can be seen that compared with method 1, the voltage of each node from the power grid is close to 1.21 (the square of 110% of the reference voltage) in the whole time period under method 2 and the SSO method, thus reducing the line current and power loss.