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| Research on Minimum Switching Frequency Tracking Control for High-Voltage DC Direct-Connected Energy Storage |
| Lu Wenze1, Ji Ke1, Han Minxiao1, Xiong Lingfei2, Chen Siqi2 |
1. School of Electrical and Electronic Engineering North China Electric Power University Beijing 102206 China;
2. State Grid Economic and Technological Research Institute Co. Ltd Beijing 102209 China |
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Abstract The high-voltage direct current direct-connected energy storage（HVDC-DCES）adopts a modular multilevel series structure. It is arranged between the positive and negative poles of the DC system line. It can support DC voltage and, in cooperation with the flexible DC converter, enable functions such as power smoothing, double-terminal grid forming, and fault ride-through. However, HVDC-DCES faces problems such as a high overall switching frequency and output current ripple. To address these issues, this paper derived a formula for the switching frequency of HVDC-DCES and designed a minimum switching-frequency tracking（MSFT）control strategy that utilizes the functional relationship between the switching frequency and the DC voltage. The HVDC-DCES with MSFT control can track the optimal DC voltage operating point and reduce the switching frequency.
Firstly, the topology and control strategy of HVDC-DCES were briefly introduced. The discrete, stepped-voltage output characteristic of HVDC-DCES results in high-frequency switching actions, and the rounding function in the controller introduces randomness. Subsequently, the rounding function was replaced with a bias-relay function with a hysteresis loop, and the formulas for the output current ripple amplitude and switching frequency of HVDC-DCES were derived. When the switching frequency is lower than the control frequency, the output is a parabolic function of the difference between the DC voltage and the energy-storage stepped voltage. As the difference decreased, the switching frequency reduced. The MSFT control strategy was designed by incorporating a fixed-step gradient-descent algorithm into the original DC voltage control strategy. This strategy searched for the DC operating point and minimized the switching frequency. Meanwhile, to address potential parameter inconsistencies among the sub-modules, an improved valve control strategy was designed. The sub-modules could take turns performing switching tasks, thereby balancing the state of charge（SOC）of the sub-module batteries and eliminating the impact of sub-module placement on the output voltage of HVDC-DCES. Finally, an optimization design method for several main circuit and control parameters of HVDC-DCES was proposed.
Simulation results for the flexible DC transmission system with HVDC-DCES showed that replacing the rounding control with hysteresis control reduced the HVDC-DCES switching frequency from 20 kHz to 12.5 kHz. When the ratio of the hysteresis loop width b to the current loop proportional control coefficient kp is 0.02, the output current ripple amplitude was limited to 0.01 in per unit, which was consistent with the calculation formula. At the same time, as the DC voltage gradually increased, the relationship between the switching frequency and the voltage difference conformed to the derived formula. After adopting MSFT control, the switching frequency was reduced from 12.5 kHz to about 500 Hz, the switching power loss of the IGBT devices was reduced by about 96%, and the DC voltage was reduced by only 0.65%. When a DC power disturbance was applied, or the sub-module battery capacity was reduced, MSFT control could still effectively reduce the switching frequency. Finally, the hardware-in-the-loop（HIL）test results were consistent with the simulation results.
The following conclusions can be drawn.（1）After replacing the rounding control with hysteresis control, the switching frequency of HVDC-DCES is reduced, and the ripple amplitude of the output current and the switching frequency are consistent with the proposed calculation formulas.（2）MSFT control can significantly reduce the switching frequency of the HVDC-DCES by adjusting the DC voltage. It has anti-interference capability that prioritizes maintaining DC voltage stability when disturbances occur in the DC system.（3）When the terminal voltage of the sub-modules of HVDC-DCES changes, MSFT control can quickly track the voltage change and effectively reduce the switching frequency.
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Received: 13 August 2025
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2026, Vol. 41 
