An advanced LMI-based-LQR design for voltage control of grid-connected wind farm

This paper presents an innovative voltage control scheme for a grid-connected wind farm. In wind power generation systems, operating conditions are changing continually by wind speed fluctuations and load changes. Therefore, a robust control mechanism is necessary. To enable a linear and robust control framework, the overall system is represented by a set of reduced-order linear systems that cover an operating range of interest determined by variations of the load. A control-design technique known as the linear quadratic regulator (LQR) can be conveniently utilized for multi-input multi-output systems. However, to make this approach applicable simultaneously to several linear systems, the LQR problem needs to be reformulated for finding a common Lyapunov function for the set of considered linear systems. This is accomplished by representing the underlying control optimization problem in terms of a system of linear-matrix-inequality (LMI) constraints and matrix equations that are simultaneously solved. The solution of LMI equations involves a form of quadratic Lyapunov function that not only gives the stability property of the controlled system but can also be used for achieving certain performance specifications. In addition, to make the control design applicable to realistic systems, with noise and disturbances in the measured signals, we consider a state observer. A candidate wind farm site on Vancouver Island, Canada, is conducted for simulation study. The proposed methodology is also flexible and readily applicable to larger wind farms of different configurations. (C) 2007 Elsevier B.V. All rights reserved.