REAL-TIME PRICING IN SMART GRID: IMPACTS OF DATA, INTERACTIONS AND LEARNING

Abstract

In modern deregulated electricitymarket, price is playing a key role in signaling the economic benefits to all participants. In particular, real-time price dynamically reflects the actual marginal cost of generating electricity and directly associates with market settlement. Methods of quantifying the effect of real-time pricing and optimal pricing policy design are needed to ensure reliable system operation and improve economic efficiency. In this thesis, three problems associated with real-time pricing in smart grid are studied. First, the impacts of data quality on real-time locational marginal price (LMP) is characterized. Because the real-time LMP is computed from the estimated network topology and system state, bad data that cause errors in topology processing and state estimation affect real-time LMP. It is shown that the power system state space is partitioned into price regions of convex polytopes. Under different bad data models, the worst case impacts of bad data on realtime LMP are analyzed. Numerical simulations are used to illustrate worst case performance for IEEE-14 and IEEE-118 networks. Second, the problemof designing dynamic price of electricity in retailmarket is considered. For the day-ahead hourly pricing (DAHP) scheme, a Stackelberg game model is formulated with the retailer as a leader and its customers as followers. By solving a real-time load control problem, an affine structure between the optimal demand response and day-ahead retail price is established and the trade-off curve between consumer surplus (CS) and retail profit (RP) is characterized as a concave Pareto front, on which each point is an equilibrium of the Stackelberg game with a particular retailer’s payoff function. Effects of renewable energy and storage are also analyzed under the same Stackelberg game model. It is shown that the tradeoff curves with renewable energy or storage on the retailer side have significantly different characteristics from those ones on the consumer side. Simulations based on actual weather and price data are used to verify our statements. Finally, the problem of optimal dynamic pricing for retail electricity with an unknown demand model is considered. Without knowledge on the aggregated demand function of its customers, a retailer aims to maximize its retail surplus by sequentially adjusting its price based on the behavior of its customers in the past. An online learning algorithm, referred to as piecewise linear stochastic approximation (PWLSA), is proposed. It is shown that PWLSA achieves the optimal rate of learning defined by the growth rate of cumulative regret. In particular, the regret of PWLSA is shown to grow logarithmically with respect to the learning horizon, and no other on-line learning algorithm can have the growth rate slower than that of PWLSA. Simulation studies are presented using traces of actual day-ahead prices, and PWLSA compares favorably under both static and dynamically changing parameters.