Chance constrained load frequency control of power systems with wind resources

We propose a semidefinite programming (SDP) framework for load frequency control (LFC) of a power system with significant wind power generation. The presence of stochastic wind and load disturbances causes frequency deviations which may lead to power grid instability, it is reasonable to formulate a stochastic model predictive control (SMPC) framework to suppress the load frequency deviation and minimize the mechanical power cost. To reduce the computational burden, we reformulate the quadratic cost function and chance constraints as linear ones with linear matrix inequalities, which yields a tractable SDP framework. The SDP framework is more computationally efficient than the scenario-based MPC, it also guarantees convergence and recursive feasibility which is lacking in scenario-based MPC. The SDP framework with time-varying feedback control gains achieves 95% reduction in frequency deviation, which outperforms the one that uses constant feedback control gains.