Nodal Flexibility Requirements for Tackling Renewable Power Fluctuations

The volatility of renewable energy causes mismatch between real-time generation and demand, calling for sufficient backup to compensate such discrepancy. This paper studies the uncertainty mitigation problem at a given operating point, which entails correctively dispatching obligate generators to maintain power balancing and network power flow constraints. The redispatch problem is modeled via a convex quadratic program parameterized in the real-time renewable output, aiming at minimizing the weighted sum of square of generator incremental output. Such an objective leads to a proper allocation of unbalanced power among generators and ensures a unique optimal solution, therefore circumvents model degeneracy. Based on the first-order optimality condition, the analytical expression of the optimal redispatch policy is proven to be piecewise affine: the renewable output set is partitioned into polyhedral regions; in each region, the optimal redispatch policy of generator is an affine function in the incremental output of renewable plants. Provided with the optimal redispatch policy in the analytical form, the nodal-wise flexibility requirements on obligate generators, including the spinning reserve capacity and the ramping capability, can be easily assessed, which is useful in generation scheduling. Case studies on the PJM 5-bus system and the modified IEEE 118-bus system demonstrate the outcome and validate the effectiveness of the proposed method.