The coordination of power system and power electronics-enabled devices can cost-effectively enhance the system transient performance. This paper proposes an advanced nonlinear control method for the coordination of power systems with capacitive-coupled static synchronous compensator (STATCOM). In this method, multiple error surfaces of the time-domain system are constructed based on low-pass filter to avoid the inherent differential explosion of backstepping design. Such dynamic surface control is further combined with fixed-time/preassigned-time control to ensure the expected transient response. Lyapunov function is designed to resolve the closed-loop dynamics of power systems with capacitive-coupled STATCOM. It is proved that the proposed advanced nonlinear control method can ensure the semi-globally fixed-timely uniformly ultimately bounded (SFUUB) within estimable settling time. Case studies on a classical power system are implemented to show its effective and superior transient performances.