Dispatchability Maximization for Co-Optimized Energy and Reserve Dispatch With Explicit Reliability Guarantee

In this paper, we consider dispatchability as the set of all admissible nodal wind power injections that will not cause infeasibility in real-time dispatch (RTD). Our work reveals that the dispatchability of the affine policy based RTD (AF-RTD) is a polytope whose coefficients are linear functions of the generation schedule and the gain matrix of affine policy. Two mathematical formulations of the dispatchability maximized energy and reserve dispatch (DM-ERD) are proposed. The first one maximizes the distance from the forecast to the boundaries of the dispatchability polytope subject to the available production cost or reserve cost. Provided the forecast value and variance of wind power, the generalized Gauss inequality (GGI) is adopted to evaluate the probability of infeasible RTD without the exact probability distribution of wind power. Combining the first formulation and the GGI approach, the second one minimizes the total cost subject to a desired reliability level through dispatchability maximization. Efficient convex optimization based algorithms are developed to solve these two models. Different from the conventional robust optimization method, our model does not rely on the specific uncertainty set of wind generation and directly optimizes the uncertainty accommodation capability of the power system. The proposed method is also compared with the affine policy based robust energy and reserve dispatch (AR-ERD). Case studies on the PJM 5-bus system illustrate the proposed concept and method. Experiments on the IEEE 118-bus system demonstrate the applicability of our method on moderate sized systems and its scalability to large dimensional uncertainty.