The study of the behavior of smart distribution systems under increasingly dynamic operating conditions requires realistic and time-varying load profiles to run comprehensive and accurate simulations of power flow analysis, system state estimation and optimal control strategies. However, due to the limited availability of experimental data, synthetic load profiles with flexible duration and time resolution are often needed to this purpose. In this paper, a top-down stochastic model is proposed to generate an arbitrary amount of synthetic load profiles associated with different kinds of users exhibiting a common average daily pattern. The groups of users are identified through a preliminary Ward’s hierarchical clustering. For each cluster and each season of the year, a time-inhomogeneous Markov chain is built, and its parameters are estimated by using the available data. The states of the chain correspond to equiprobable intervals, which are then mapped to a time-varying power consumption range, depending on the statistical distribution of the load profiles at different times of the day. Such distributions are regarded as Gaussian Mixture Models (GMM). Compared with other top-down approaches reported in the scientific literature, the joint use of GMM models and time-inhomogeneous Markov chains is rather novel. Furthermore, it is flexible enough to be used in different contexts and with different temporal resolution, while keeping the number of states and the computational burden reasonable. The good agreement between synthetic and original load profiles in terms of both time series similarity and consistency of the respective probability density functions was validated by using three different data sets with different characteristics. In most cases, the median values of synthetic profiles’ mean and standard deviation differ from those of the original reference distributions by no more than ±10% both within a typical day of each season and within the population of a given cluster, although with some significant outliers.
Mobile Emergency Generator Planning in Resilient Distribution Systems: A Three-Stage Stochastic Model With Nonanticipativity Constraints