Linear Sensitivity Modelling Useful for Voltage Control Analysis Using Power Injections from DER

Abstract

The injection of apparent power to self-consumption buses generates voltage variations during network operation, which, when properly monitored, could support voltage regulation and control. In this paper, we propose a linear sensitivity modelling, quite useful for studies of voltage regulation with distributed energy resources (DER). This modelling consists of two analytical improvement steps: first, a full formulation for the voltage deviations, and second, the influence of line capacitance as Q-injections at the points of common couplings (PCCs). Our proposal is based on the linear topological sensitivity of an existing network (as a function of the line parameters X, R, and Bc), branch power flow (active–reactive power (P-Q)), and power injections at the PCCs. Here, the linear sensitivity algorithm is applied to a modified IEEE 33-bus distribution system to demonstrate its extended effectiveness to voltage monitoring and control scenarios. Its application estimates and compensates in a better way the voltage deviations with regard to the operating desired voltage (|V|op) constraints, using distributed power injections at the PCCs. Numerical results always showed a curtailment of the relative error against common simplifications of the electrical modelling in steady-state, thus simulating two critical scenarios of operation production–consumption for the existing system response. The proposed algorithm was validated considering as reference the voltage profile outputs of the load flow analysis, using the Newton–Raphson method via DIgSILENT, in terms of its accuracy, silhouette shape along the feeder and with regard to the application of reactive compensation as an analytical case study for voltage improvement in active distribution networks.