Uncertainty Modeling and Price-Based Demand Response Scheme Design in Smart Grid

Transforming conventional passive customers into active participants who interact with the utility in real time is the key idea of demand response (DR) in smart grid. However, an effective and efficient DR scheme relies on precise prediction and modeling of the uncertainties, i.e., renewable generations and load demands. In this paper, we first present a series of linear prediction models for the load prediction purpose, such as standard autoregressive (AR) process and time-varying AR (TVAR) process, according to different assumptions on the stationarity of customer load profile: piecewise stationarity, local stationarity, and cyclostationarity. Two important issues in AR/TVAR models are addressed: determining the order of AR/TVAR models and calculating the AR/TVAR coefficients. The partial autocorrelation function is analyzed to determine the model order, and the minimum mean squared error estimator is adopted to derive the AR/TVAR coefficients, which leads to the Yule-Walker type of equations. With the load prediction problem addressed, we further design a DR scheduling scheme based on utility cost minimization with different customer clustering sizes. The optimal DR load profiles are given in forms of both 1-D and 2-D water-filling solutions. A tradeoff strategy, which attempts to balance the competing objectives (centralized and distributed), is also provided based on the price-of-anarchy analysis. Simulation results of both the load prediction models and the DR schemes are presented and analyzed.

I. Introduction

IN a conventional electrical power market, power generation is usually required to match to power demand. Improved resource efficiency of electricity production is achieved by closer alignment of electricity pricing information with energy consumption behaviors. This is because the distributed nature of power demands, as well as different energy consumption behaviors of customers in the power network, makes power demand fluctuating over time and difficult to be controlled precisely [1], [2]. This behavior is expected to become more significant as high penetration of renewable generations and plug-in hybrid electric vehicles appear in generation side and consumption side, respectively. As a result of the highly time-varying generation and consumption profiles, the utility needs to provide enough electrical power to meet peak demand rather than the average to prevent potential blackout events. However, this static and centralized generation pattern is apparently inefficient and thus costly. For example, the U.S. national load factor is about 55%, and 10% of generation and 25% of distribution facilities are used less than 400 h/year, i.e., 5% of the time [3]. Finding possible approaches to improve this inefficient performance is one of the strong incentives to consider a smart grid [4]– [6]. In smart grid infrastructure, the key feature of matching demand to supply by transforming currently static consumers into active participants is the central idea of demand response (DR) [7], which can greatly improve power system efficiency and thus yield huge savings. There is a growing consensus that DR can play an important role in market design [8], [9]. In [7], for example, DR is defined as “ Changes in electric usage by end-use customers from their normal consumption patterns in response to changes in the price of electricity over time, or to incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized.”