A Convex Optimization Model for Bidirectional Vehicle-To-Grid Operation

Global warming is one of the environmental reasons for the adoption of the electric vehicle (VE). This technology is very welcome by society but carries great challenges to electricity distribution networks. VEs will need to be recharged and extra amount power demand could lead to occurrence of several operational problems in the distribution system. An optimization model is required in a concept called vehicle-to-grid or V2G. The main issue of this optimization model lies in the power flow equation which are non-linear and non-convex making the problem hard to be solved for large scale integration of VEs. Therefore, we use a semidefinite approximation of the power flow and evaluate the model in different scenarios. Electric vehicles are coordinated by aggragators that are spatially distributed along a primary feeder. Each aggregator collects a group of EVs of different rate of charger. The objective function is to minimize power loss and maximize state-of-charge (SOC) or owner satisfaction. Several scenarios were taken into account: first, a base case where we compare the proposed model with others models propose in the literature, next we analyze the integration of EVs for 25%, 50%,75% and 100% of the total power demand of the system, with of aim of evaluating the control variables and load loadability on the IEEE 37 nodes and IEEE 29 nodes test feeders.