Injected Current Sensitivity Based Load Flow Algorithm for Multi-Phase Distribution System in the Presence of Distributed Energy Resources

This paper presents an injected current sensitivity (ICS) based multi-phase load flow (LF) methodology with minimal Jacobian computation for the three-phase unbalanced distribution system with multiple Distributed Energy Resources (DERs). In the proposed approach, first, a generalized bus admittance and Jacobian matrix have been formulated that include various distribution system components such as lines, shunt capacitors, voltage control devices such as regulators, different transformer connections, and load models. Second, DERs are modeled as a PV bus and incorporated into the proposed LF algorithm by formulating a reactive power injection-based sensitivity matrix that iteratively computes its net power injections. Unlike the traditional Jacobian matrix-based LF methods where an update of Jacobian (size and element) is required for each PV bus, this method does not require any update, hence, making it faster and more flexible to include a large number of DERs. From the various tests performed on the standard IEEE three-phase distribution network and their derivatives, it has been observed that the proposed approach is accurate, efficient, computationally less complex, and scalable.