## 4 Case and Discussion  
### Case Condition  
To analyze and validate the SSO methodology, this paper has carried out the analysis based on the DES in the IEEE 33 distribution network as shown in Figure 1. And the lithium-ion battery energy storage system has been adopted as the BESS in this paper. Table 2 has represented the case parameters and condition of the power grid, DG, photovoltaic power station, wind power station and BESS. The computational environment of this example is Matlab 2020a under Win10 system, the computer memory is 32 G, the CPU is Intel Core i7, the main frequency is 2.3 GHz and the number of cores is 16. Figure 4 shows the power curves of the power load and photovoltaic and wind power stations in a typical day system. The time interval \(\Delta t=1\) h, and the typical day \(T=24\) h.  
In Table 2 and Figure 4, it can be seen that the apparent power of the load is less than 10 MVA, and the total rated power of new energy stations is greater than 10 MVA. Additionally, the apparent power of the load is much greater than the actual maximum output power of the new energy stations at 5-11 h and 16-24 h, respectively. It means that there is an imbalance between power supply and consumption in the distribution network system and a reasonable control of BESS and DG is necessary.  
Meanwhile, this paper compares the SSO method with other common multi-objective optimization methods. Method 1 is an equal-weight summation method, method 2 is a Euclidean distance minimization method, and the optimization objective functions are shown in Expressions (17) and (18), respectively. In addition, the constraint conditions for method 1 are shown in Expression (15), and the constraint conditions for method 2 are shown in Expression (16). Further, as the method 3, the traditional NSGA method combined with TOPSIS [9] has been used for a comparison of the proposed  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case Parameter** & **Numerical Value** & **Case Parameter** & **Numerical Value** \\ \hline Capacity of power grid & 10 MVA & Rated power of DG & 10 MVA \\ Nominal voltage & 12.66 kV & Cost coefficient \(k_{1}\) of DG & 40,000 V/kWh\({}^{2}\) \\ The voltage range & \(\pm 10\%\) & Cost coefficient \(k_{2}\) of DG & 650 V/kWh \\ The maximum branch current & 456 A & Cost coefficient \(k_{3}\) of DG & 8 V \\ Charge/discharge efficiency of BESS & 95\%, 92\% & Rated power of photovoltaic at \#6 node & 4 MW \\ SOE range of BESS & 90\%, 10\% & Rated power of photovoltaic at \#13 node & 2 MW \\ Initial SOE of BESS & 50\% & Levelized cost of photovoltaic & 0.293 V/kWh \\ Rated power of BESS & 3.3 MW & Rated power of wind farm at \#22 node & 3 MW \\ Rated capacity of BESS & 13.2 MWh & Rated power of wind farm at \#22 node & 2 MW \\ Levelized cost of BESS & 0.574 V/kWh & Levelized cost of wind farm & 0.3 V/kWh \\ Initial stepper parameter \(\Delta c\) & 0.1 & The stop threshold \(\lambda\) & \(1\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters and conditions.  
Figure 4: Electricity generation and consumption curve from new energy stations and load under typical day.  
methods. The maximum iterative number is 30, and the number of individuals is 20 in the population.  
\[\text{minimize}\quad J(\mathbf{X})=\frac{J_{1}(\mathbf{X})}{|\min(J_{1}(\mathbf{X}))|}+\frac{ J_{2}(\mathbf{X})}{|\min(J_{2}(\mathbf{X}))|} \tag{17}\]  
\[\text{minimize}\quad J(\mathbf{X})=r_{1}^{2}+r_{2}^{2} \tag{18}\]