Probabilistic generation of time-coupled aggregate residential demand patterns

For distribution system studies, a relevant aspect is the characterisation of the aggregate demand in a feeder. The probabilistic model of the aggregate demand is very useful for system operators or aggregators to extract information about the demand side behaviour in the operation of smart grids and microgrids. The time step used to scan the aggregate demand pattern is very important to preserve the information about the consumers´ behaviour and the related uncertainty. The conventional models of aggregate electrical demand consider an average value for a specific time step (e.g. 30 min to 1 h). In this study, a faster time step (1 min) is considered to construct a time-coupled probabilistic model of the aggregate residential demand based on Beta distributions. For a given number of aggregate loads, the parameters of the Beta distributions are found by taking into account the aggregate demand pattern variations at two successive time steps. The probabilistic model is then used to generate a number of aggregate demand scenarios. The effectiveness of the proposed scenario generation method is evaluated by using goodness of fit tests such as the Kolmogorov-Smirnov test and the average mean absolute percentage error.