Optimal allocation of wind capacity considering the impact of generation uncertainty based on zonotope limited security regions

The increasing wind capacity integration brings new challenges to power system planning and operation, due to the intermittency and uncertainty of its power generations. This paper determines the optimal allocation of wind capacity with considerations of the impact of uncertainty in wind generation using the zonotope-based method, for the sack of reducing the possible violations of operation limits caused by wind power fluctuations. The uncertain variations of wind power are bounded by a zonotope and then propagated through a linearised power flow to get another zonotope, which captures all possible values of the system state variables. The state-bounding zonotope is then added to the optimal model to quantify and assess the impact of generation uncertainty on system static performance. The proposed method is applied to IEEE 33-bus system, the results prove the validity of the method and show that the zonotope based set-theoretic method is more efficient than probabilistic methods when focusing on the operation limits with considerations of the uncertainty of multiple renewable energy sources.