Price-driven charging of plug-in electric vehicles in the smart grid

As the number of Plug-in Electric Vehicles (PEVs) increases, it is essential to control their charging schedules and spread the PEV load over time to reduce the energy generation and distribution costs due to this additional demand. Furthermore, due to the limited power capacity of the transmission feeders and the sensitivity of the mid-way distribution transformers to excessive load, it is crucial to control the amount of power through each specific feeder in the distribution network to avoid system overloads that may lead to breakdowns. In this thesis we develop, analyze and evaluate price-driven charging algorithms for PEVs in a smart grid environment. The algorithms we propose minimize the cost incurred on the power distribution system (or the supply cost of the electric utility or aggregator) due to the PEV load, and at the same time prevents overloading of the transmission feeders.;We first develop two convex optimization algorithms for PEV charging that minimize the aggregator's convex cost function subject to transmission feeder overload constraints. The two algorithms are amenable to decentralized implementation, in which the PEVs react to the load signals on their supply paths and the distribution grid on the whole (by adjusting their charging schedules).;We next analyze the equilibrium properties of a natural price-driven charging control game in the distribution grid, between the utility (that sets the time-dependent energy usage price) and selfish PEVs (that choose their own charging schedules to minimize individual cost). We demonstrate, through analysis and simulations, that individual best-response strategies converge to socially optimal charging profiles (also equilibrium solutions) under fairly weak assumptions about the (asynchronous) charging profile update processes. We also discuss how the framework can be extended to consider the topology of the distribution tree and associated transmission feeder capacity constraints.;We then consider the day-ahead price-setting question from the perspective of the utility (or aggregator) that is interested in minimizing the average energy supply costs given the uncertainty in the charging preferences of the PEV owners. Modeling the uncertainty in the PEV charging constraints in a Bayesian framework, we propose a day-ahead pricing policy that can minimize the overall energy supply cost in expectation, subject to transmission feeder capacity constraints. The same pricing policy can be extended to maximize economic surplus, computed as the total valuation of the energy provided to all PEVs minus the total energy supply cost. A simple extension of our approach to real-time pricing of PEV demand is also discussed, and evaluated through simulations.