Analytical Computation of Power Grids’ Sensitivity Coefficients with Voltage-Dependent Injections

With the increasing need of real-time regulation in power systems, grid-aware-control-frameworks are relying more often on sensitivity coefficients (SCs) to formulate and efficiently solve optimal control problems. As known, SCs are the derivatives of controlled quantities (e.g. nodal voltages at PQ nodes and branch currents) with respect to control variables i.e. nodal active and reactive power injections at PQ nodes, nodal voltage magnitudes and nodal active power injections at PV nodes and nodal voltage magnitudes and phase-angles at slack nodes. In a real control application, the knowledge of the system state, coming from a state-estimation process, allows for the direct computation of SCs without the need of a load-flow. Algorithms for this computation have been already proposed in the literature for PQ nodes’ nodal voltage SCs under the assumption of constant nodal power injections. The aim of this paper is to propose an analytical derivation of all node types (i.e. PQ, PV and slack) nodal voltage SCs for power grids with generic topologies, number of phases and voltage-dependent nodal power injection models. The paper also includes an exhaustive list of all other SCs that can be directly computed using nodal voltage SCs, a computational complexity analysis of the proposed method and a numerical benchmarking.