Quantifying demand response under uncertainty in power systems

Abstract

The new perspective of looking at power system operation is to utilize the flexibility from electricity consumers and distributed energy resources. Demand response, by promoting the interaction and responsiveness of the consumers, offers a broad range of potential benefits on system operation and expansion and on market efficiency. It is therefore crucial to accurately estimate the effect of certain demand response signals, especially given that consumers' behavior is uncertain and noisy. Depending on how the system operator curates consumer data, we develop different ways to estimate this effect using either offline or online data. We first consider that demand response signals are binary and model the consumption behavior by a linear model. We compare several different linear estimators of demand response effect and propose an optimal demand response signal assignment strategy that improves the performance of the linear estimator in terms of optimal reduction in estimation variance. In a more realistic setting where demand response signals from the operator are continuous, i.e., price signals, we assume that the operator does not know the cost function of consumers and cannot have multiple rounds of information exchange with consumers. We formulate an optimization problem for the operator to minimize its operational cost considering time-varying demand response targets and responses of consumers. We develop a joint online learning and pricing algorithm and show that our online algorithm achieves logarithmic regret with respect to the operating horizon. Besides, as a future of urban power system development, the generation of electricity from renewables constitutes a large portion of the total generation in the power grid. The inherent uncertainty of renewables and their wide distribution in the network bring new challenges in planning and operation. We design a decentralized market to engage the participation of small scaled distributed renewable energy resources. It is known that most deterministic capacity games tend to result in very inefficient equilibria, even when there are a large number of similar players. In contrast, we show that due to the inherent uncertainty of renewable resources, the equilibria in our capacity game becomes efficient as the number of players grows and coincides with the centralized decision from the social planner's problem. In addition, we use reactive power compensation as demand response to alleviate the problem of fluctuated voltage resulted from introduction of renewables. We adopt a chance constrained approach that accounts for arbitrary correlations between renewable resources at each of the buses in the system. We show that the problem can be solved efficiently using historical samples via our proposed descent algorithm. We also show that this optimization problem is convex for a wide variety of probabilistic distributions. We use both synthetic generated and real-world energy data to validate the claims and the proposed algorithms.