Voltage Behaviour in Radial Distribution Systems under the Uncertainties of Photovoltaic Systems and Electric Vehicle Charging Loads

Abstract

This paper presents a probabilistic method that accurately verifies the fulfilment of voltage constraints in radial distribution systems (RDSs) with photovoltaic (PV) systems and electric vehicle (EV) charging loads. This problem has not been comprehensively discussed. The proposed probabilistic method (PPM) involves the calculation of input variable cumulants, the linearization of load-flow equations, and the application of the cumulant method and the Cornish-Fisher expansion. Obviously, it is first necessary to model the PV systems and EV charging loads as random variables. In addition, the correlation of the input variables is suitably handled. As part of this research, a Monte Carlo simulation (MCS) was performed, which confirmed the accuracy of the results obtained with the PPM. As an added value, when compared to the MCS, there was a significant reduction in computational cost. The results obtained by the PPM demonstrate that the connection of PV systems in the IEEE 33-node RDS with EVs clearly contributes to keeping voltages within regulatory limits, once the distributions of the RDS output variables are inspected. Nonetheless, the greater dispersion in the distributions in combined PV and EV scenarios means that voltage constraint fulfilment cannot be absolutely guaranteed. This probabilistic approach provides a more accurate assessment than one based on a simple deterministic vision. Thus, the PPM is extremely useful because it provides a better understanding of the combined technical impact under different correlated and uncorrelated scenarios.