Comparing power flow models in tree networks with stochastic load demands

The process of charging electric vehicles (EVs) within an electricity network is a complex stochastic process. Various factors contribute to this complexity, including the stochastic arrivals and demands of users at charging stations, the nonlinear nature of power flow in the network, and the need to uphold reliability constraints for the network's proper functioning. While nonlinear power flow equations can be approximated by computationally simpler linear equations, the consequences of linearizing the physics in such a complex stochastic process require careful examination. In this study, we apply a blend of analytical and simulation techniques to compare the performance of the nonlinear Distflow model with the linear Linearized Distflow model in the context of EV charging. The results demonstrate that across various parameter settings, the network's performance is comparable when using either of the power flow models. Specifically, in terms of the mean number of EVs and mean charging time, there is a relative difference of less than 5% between the two models. These findings suggest that the Linearized Distflow model can be effectively employed as a simplified approximation for the Distflow model, providing a faster yet efficient analysis of network performance.