Efficiency-Risk Tradeoffs in Electricity Markets with Dynamic Demand Response

In order to study the impact of dynamic demand response in the future smart grid, we examine in an abstract framework how a tradeoff between efficiency and risk arises under different market architectures. We first examine the system performance under noncooperative and cooperative market architectures. The statistics of the stationary aggregate demand processes show that, although the noncooperative load scheduling scheme leads to an efficiency loss, the stationary distribution of the corresponding aggregate demand process has a smaller tail, resulting in less frequent aggregate demand spikes. Cooperative dynamic demand response, on the other hand, makes the market place more efficient at the cost of increased risk of aggregate demand spikes. The market architecture determines the locus of the system performance with respect to the tradeoff curve. We also investigate how a properly designed real-time electricity pricing mechanism can help the system operator achieve a target tradeoff between efficiency and risk in a noncooperative market. We further provide a convex characterization of the Pareto front of system performance measures, which serves as a benchmark of the tradeoffs for the system operator to evaluate the pricing rules.