Uncertainty modeling and prediction for customer load demand in smart grid

Abstract

In this study, we propose two types of approaches to model the uncertainty in customer load demand. The first approach is based on a first order non-stationary Markov chain. A maximum likelihood estimator (MLE) is derived to estimate the time variant transition matrix of the Markov chain. The second approach is based on time series analysis techniques. We present linear prediction models such as standard autoregressive (AR) process and time varying autoregressive (TVAR) process, according to different assumptions on the stationarity of customer load profile: piecewise stationarity, local stationarity and cyclo-stationarity. 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 (PACF) is analyzed to determine the model order and the minimum mean squared error (MMSE) estimator is adopted to derive the AR/TVAR coefficients, which leads to the Yule-Walker type of equations. For the AR model, the customer load profile is divided into small segments which can be considered to be stationary. For the TVAR model, by doing basis function expansion based coefficient parametrization, we replace the scalar process with a vector one and turn the original non-stationary problem into a time-invariant problem. All the proposed models are tested against the same set of real measured customer load demand data. Prediction performances of different models are analyzed and compared, advantages and disadvantages are discussed.