Optimal probabilistic framework for grid cost operation considering voltage probability constraints and high penetration of EVs, wind and PV generation

The increasing integration of renewable generation and electrified transport, driven by global policies aiming at zero-carbon emissions, introduces significant challenges to the operation of the electricity distribution system (EDS). These networks were not designed to accommodate the variability and uncertainty associated with the high penetration of photovoltaic (PV) and wind (WT) generation, as well as the electric vehicle (EV) demand, which increases the risk of overvoltage, overload, and reverse power flows. Addressing these challenges requires probabilistic tools capable of modeling and optimizing the system under uncertain conditions. Thus, this paper proposes an optimal probabilistic framework to minimize grid operational costs and carbon emissions while mitigating overvoltage risks. Different from previous proposals, this work analyzes and compares different probabilistic optimal power flow methods, evaluating their efficiency and accuracy, while addressing uncertainties in PV and WT generation and EV demand, along with environmental considerations. The novelty of this work lies in the combination of four aspects not jointly addressed in previous studies: (i) uncertainty in renewable generation and EV demand, (ii) comparison of different probabilistic optimal power flow methods, (iii) integration of environmental aspects, and (iv) implementation of probabilistic voltage constraints based on confidence intervals. The approach is validated using the IEEE 33-bus distribution system adapted with the presence of PV/WT units and EV charging stations. Finally, the results show that the Edgeworth-extended cumulant method achieves high accuracy, with relative errors for power, voltage, and cost operation below 1%, and computational efficiency 217 times faster than Monte Carlo simulation for probabilistic power flow analysis.