Generalized Analytical Estimation of Sensitivity Matrices in Unbalanced Distribution Networks

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 unbalanced 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-$\phi$, 2-$\phi$, and 3-$\phi$ 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 and EPRI networks show the accuracy and wide scope of the proposed algorithm compared to the existing benchmark method.