Dynamic Pricing Problems Arising in the Adoption of Renewable Energy

There are two problems at the interface of electrical power and economics that are examined in this thesis. The first problem addresses the issue of optimally operating electric vehicle (EV) charging stations, where price as well as scheduling of purchasing, storing, and charging play key roles. The second problem addresses the challenge faced by electric power system operators who have to balance power generation and demand at all times, and are faced with the task of maximizing the social welfare of all affected entities comprised of producers, consumers and prosumers (e.g., homes with solar panels who may be producers at some times and consumers at other times). For the first problem, we have developed a layered decomposition approach that permits a holistic solution to solving the scheduling, storage and pricing problems of charging stations. The key idea is to decompose problems by time-scale. For the second problem, we have shown that for the special case of LQG agents, by careful construction of a sequence of layered VCG payments over time, the intertemporal effect of current bids on future payoffs can be decoupled, and truth-telling of dynamic states is guaranteed if system parameters are known and agents are rational. We have also shown that a modification of the VCG payments, called scaled-VCG payments, achieves Budget Balance and Individual Rationality for a range of scaling, under a certain identified Market Power Balance condition