Statistical modelling of load profiles incorporating correlations using Copula

The growth in stochastic local renewable generation and the increase in new high peak power loads such as electric vehicles and heat pumps warrants the use of more detailed load models to properly assess grid adequacy. In this paper a method is proposed to develop load and generation models based on statistical analyses of measurement data using Gaussian Mixture Models and Copula functions. The two stage approach enables separate modelling of the marginal distributions and correlation structures and is shown to be able to provide a good representation of the statistical behaviour of measured electric household load. The fitted models are then used to stochastically generate load profiles and assess the peak shaving potential and required size of an energy storage unit. Taking into account the correlations is shown to be important for a proper representation of the profiles and may have a substantial effect on the results of the analysis.