## 5 Discussion  
To further validate the feasibility and effectiveness of the proposed control strategy across different application scenarios, an eleven-level medium-voltage transmission system model was built in PSCAD/EMTDC using the efficient simulation method [42]. The system parameters are provided in Table 4.  
The SOC of all ESMs was initialized between 30% and 40%. The supercapacitor energy storage system operated at a constant charging power of 5 MW, with SOC balancing control activation at t = 2 s. Figures 13 and 14 present the SOC balancing performance and circulating current characteristics comparing both constant and adaptive proportional coefficients in the enhanced balancing strategy. The results demonstrate that ESM balancing occurred independently of startup time. The implementation of adaptive proportional coefficients reduced the balancing time of phases by 1.24 s compared to constant proportional coefficients, while the balancing time of arms decreased by 3.57 s. Furthermore, the adaptive proportional coefficient strategy achieved 8% reduction in the circulating current during initial balancing compared to constant coefficient methods. This occurred because nearest-level modulation (NLM) introduced greater voltage errors in systems with fewer ESMs. The resulting error increased circulating currents, thereby diminishing current suppression effectiveness.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Rated capacity/MVA & 20 & DC voltage/kV & 20 \\ AC voltage/kV & 10 & ESM capacitance/mF & 6.7 \\ Arm inductance/mH & 3.8 & Supercapacitance/F & 8 \\ Number of ESMs & 10 & Energy storage & 10 \\ per arm & & inductance/mH & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Simulation parameters.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Enhanced Balancing** & **Traditional Balancing Strategy** \\ \hline Number of energy storage controllers & 6 & 6 \(N\) \\ Balancing speed & 85\% & 100\% \\ Initial circulating current & 75\% & 100\% \\ Adaptive proportional coefficients? & Yes & No \\ Independent of startup time? & Yes & No \\ Suitable for different capacitance? & Yes & No \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of control architectures between the proposed enhanced SOC balancing strategy and the traditional SOC balancing control strategy.  
Considering a scenario with varying supercapacitor capacitance in phase B, Figure 15 compares the SOC balancing performance between fixed power allocation and capacity-based allocation strategies. The results demonstrated the efficacy of the capacity-based power allocation in achieving SOC balancing with varying capacitance. Significantly, the enhanced balancing strategy maintained its effectiveness in low-level medium-voltage operating conditions, confirming its robust applicability across different voltage regimes.  
Figure 14: Circulating current of the enhanced balancing strategy. (**a**) Circulating current with adaptive proportional coefficients. (**b**) Circulating current with constant proportional coefficients.  
Figure 15: SOC with different capacitance. (**a**) Capacity-based power allocation. (**b**) Fixed power allocation.  
Figure 13: SOC of the enhanced balancing strategy. (**a**) SOC with adaptive proportional coefficients. (**b**) SOC with constant proportional coefficients.