Linear Method for Radial Distribution Systems including Voltage Control Devices

Linear methods for steady-state analysis of distribution systems are receiving more attention due to the wide spreading of distributed energy resources (DERs). A new constrained Jacobian-based method has recently been presented. It provides the sensitivity matrices that linearly relate the variations of the electrical variables characterizing the supplying substation and each branch of the network to the variations of the powers injected by DERs. In this paper this method is extended to account for the presence of voltage control devices (VCDs). A new model of the supplying substation is proposed to account for changes on the operating conditions of the higher voltage network as well as to include the presence of HV/MV transformer with on-load tap-changer (OLTC). Furthermore, step-voltage regulators (SVRs) and magtech voltage boosters (MVBs) are modeled to take into account the presence of VRDs along the feeders. Numerical results are presented to give evidence of the effectiveness of the proposed approach.