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.