Generalized Analytical Estimation of Sensitivity Matrices in Unbalanced Distribution Networks

Abstract: Fast and accurate estimation of sensitivity matrices is significant for the enhancement of distribution system modeling and automation. Analytical estimations have mainly focused on voltage magnitude sensitivity to active/reactive power injections for unbalance networks with Wye-connected loads and neglecting DERs' smart inverter functionality. Hence, this paper enhances the scope of analytical estimation of sensitivity matrices for unbalanced networks with 1-phase, 2-phase, and 3-phase Delta/Wye-connected loads, DERs with smart inverter functionality, and substation/line step-voltage regulators (SVR). A composite bus model comprising of DER, Delta- and Wye-connected load is proposed to represent a generic distribution bus, which can be simplified to load, PV, or voltage-controlled bus as required. The proposed matrix-based analytical method consolidates voltage magnitude and angle sensitivity to active/reactive power injection and tap-position of all SVRs into a single algorithm. Extensive case studies on IEEE networks show the accuracy and wide scope of the proposed algorithm compared to the existing benchmark method.