Sensitivity-Based Discrete Coordinate-Descent for Volt/VAr Control in Distribution Networks

The discrete coordinate-descent algorithm is a practical approach that is currently used in centralized Volt/VAr Control (VVC) implementations, mainly due to its good performance and speed for real-time applications. Its viability is however challenged by the increasing number of distributed generation that contribute to the VVC solution, in addition to the conventional transformer taps and switched capacitors. This paper presents the exact computation of sensitivity factors that speed up the discrete coordinate-descent implementation, by significantly reducing the number of forward/backward substitutions in the current injection power flow method; the speed up is achieved without affecting the control setting quality of the original implementation. The optimality of the discrete coordinate-descent solutions is investigated by computing the gaps relative to mixed-integer linear programming set-points, derived from a polyhedral reformulation of the VVC problem. The sensitivity-based discrete coordinate-descent algorithm is tested starting from two initial points, the default one given by the current control set-points, and a continuous solution obtained from a linear approximation of the VVC problem. Numerical results on networks with up to 3145 nodes show that the sensitivity-based approach significantly improves the runtime of the discrete coordinate-descent algorithm, and that the linear programming initialization leads to VVC solutions with gaps relative to the mixed-integer set-points that are less than 0.5%.