Nonlinear optimal control for the VSC-HVDC transmission system

A nonlinear H-infinity (optimal) control method is proposed for the problem of control of the VSC-HVDC transmission system (Voltage Source Converter - High Voltage DC transmission system). Approximate linearization, round a local operating point, is performed for the dynamic model of the VSC-HVDC transmission system. This local equilibrium consists of the present value of the state vector of the VSC-HVDC model and of the last value of the control input that was exerted on it, and is re-calculated at each time instant. To accomplish this linearization, Taylor series expansion and the computation of the associated Jacobian matrices are performed. The robustness of the control scheme allows to compensate for the modelling error which is due to truncation of higher order terms from the Taylor expansion. Next, an H-infinity feedback controller is designed. After solving an algebraic Riccati equation at each iteration of the control algorithm, the feedback gain is computed. Lyapunov stability analysis is used to prove that the control loop satisfies an H-infinity tracking performance criterion. This also indicates elevated robustness to model uncertainty and external perturbations. Moreover, under moderate conditions it is proven that the control loop is globally asymptotically stable.