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.