The Onset of Congestion in Charging of Electric Vehicles for Proportionally Fair Network Management Protocol

Abstract

With the expected uptake of electric vehicles in the near future, we are likely to observe overloading in the local distribution networks more frequently. Such development suggests that a congestion management protocol will be a crucial component of future technological innovations in low voltage networks. An important property of a suitable network capacity management protocol is to balance network efficiency and fairness requirements. Assuming a stochastic model, we study the proportional fairness (PF) protocol managing the network capacity in charging of electric vehicles. We explore the onset of congestion by analysing the critical arrival rate, i.e. the largest possible vehicle arrival rate that can still be fully satisfied by the network. We compare the proportionally fair management protocol with the max-flow (MF) management protocol. By numerical simulations on realistic networks, we show that proportional fairness leads not only to more equitable distribution of power allocations, but it can also serve slightly larger arrival rate of vehicles. We consider simplified setup, where the power allocations are dependent on the occupation of network nodes, but they are independent of the exact number of vehicles, and to validate numerical results, we analyse the critical arrival rate on a network with two edges, where the optimal power allocations can be calculated analytically.