MIQP-Based Algorithm for the Global Solution of Economic Dispatch Problems with Valve-Point Effects

Even in a static setting, the economic load dispatch problem (ELDP)-namely the cost-optimal distribution of power among generating units to meet a specific demand subject to system constraints-turns out to be a challenge owing to the consideration of valve-point effects (VPE), which make the cost function nonsmooth and nonconvex. We present a new method, termed Adaptive Piecewise-Quadratic Under-Approximation (APQUA), for the global solution of the ELDP with VPE. Unlike the many existing methods for this problem, APQUA produces at each iteration an upper and a lower bound on the globally optimal cost, and the gap between the two bounds is guaranteed to converge to zero as the iteration number grows. Consequently, APQUA is guaranteed to compute the global optimum of the ELDP within any user-prescribed accuracy. Even though APQUA has to call an MIQP solver on increasingly large surrogate problems in order to achieve this unprecedented optimality guarantee, our experiments indicate that the total computation time remains reasonable even when the prescribed accuracy is very high

Loss reduction in a windfarm participating in primary voltage control using an extension of the Convex DistFlow OPF

One of the largest French onshore wind farms is requested by the transmission system operator (TSO) to participate in primary voltage control. This implies exchanging reactive power with the grid, by using both the wind turbines and static switchable capacitor and inductor banks installed in the windfarm. The reactive power setpoint dispatch between the wind turbines and the static units is currently suboptimal, leading to additional energy losses inside the collector grid of the wind farm. An extension of the Convex DistFlow OPF model accounting for real-network elements is presented in order to perform an optimal reactive dispatch minimizing energy losses on the collector grid. The proposed model is a Mixed-Integer Second Order Cone Program (MISOCP) that is further relaxed with an efficient linear outer approximation of conic constraints to alleviate the computational burden. This approach is then compared to a Matpower-based approach to assess its accuracy and computational efficiency on a wide range of operating conditions. The developed model exhibits a satisfying accuracy and outperforms Matpower on a significant fraction of tested cases