Emergency voltage control based on MPC, Radau collocation and moving finite elements technique

The nonlinear model predictive control method is applied to design emergency voltage controller. Based on quasi-steady-state approximation, the receding dynamic optimization model is established which subjected to differential-algebraic equations with continuous-discrete time variables. To enhance computational efficiency and control precision of solving this dynamic optimization model, direct dynamic optimization approach combined with moving finite elements are proposed to solve the problem of dynamic optimization. Firstly, the research interval is divided into finite elements. Radau collocation method is used to convert the optimization model into a nonlinear programming by approximating state variable, algebraic variable and control variable profiles by a family of polynomials on each element. Then moving finite elements is introduced to adjust the length of each interval dynamically, achieve the precise positioning of control variable and improve the accuracy of the algorithm. The interior-point algorithm given by AMPL as a mathematical optimization solver is used to solve the problem. Simulation results on New England 10-machine 39-bus system verify effectiveness of the proposed method.