Passive control design for multi-terminal VSC-HVDC systems via energy shaping

This paper investigates a passive control (PC) scheme for multi-terminal voltage source converter (VSC) based high voltage direct current (VSC-HVDC) systems, which can provide a reliable and effective integration of electrical power from renewable energy. A storage function is constructed for each terminal and reshaped into a desired output strictly passive form via feedback passivation with an extra system damping. The beneficial nonlinearities are retained which results in a better transient dynamics of the active power, reactive power, and direct current cable voltage. Then the retained internal dynamics related to the direct current (DC) cable current and common DC voltage is proved to be asymptotically stable by zero-dynamics technique of output dynamics, thus the closed-loop system can be asymptotically stabilized. Case studies are carried out on a four-terminal VSC-HVDC system, under six conditions, e.g., active power and reactive power regulation with parameter uncertainties, faults at alternating current (AC) bus and DC cable, offshore wind farm connection, weak AC grid connection, and robustness of DC cable resistance uncertainties. Simulation results verify the effectiveness of PC against that of linear proportional-integral (PI) control and nonlinear feedback linearization control (FLC) under various operation conditions.