Multi-time-scale stability analysis and design conditions of a VSC terminal with DC voltage droop control for HVDC networks

This paper addresses the problem of analyzing the dynamic limitations of a VSC terminal with DC voltage droop control. Thanks to its fast response, DC voltage droop control is usually used to adjust the DC voltage in case of power imbalance. To ensure the stability of the VSC terminal, the dynamics between the dq currents (i_l,dq) and the DC voltage (u_c) must be well distinguished. Therefore, the choice of the droop control gain K_u and the d_q current control gains K_dq is still a challenging problem. First, we assume that there exist K_u and K_dq such that a slow and a fast dynamics can be imposed on u_c and i_l,dq, respectively. Then, we propose a novel methodology based on separation of dynamics to prove the existence of these control gains. Subsequently, a detailed stability analysis is carried out via Lyapunov theory, from which a necessary condition and a sufficient condition are derived for the control gains. To verify this methodology, numerical simulations are carried out in MATLAB/SIMULINK.