Probabilistic Load Forecasting of distribution power systems based on empirical copulas

Accurate and reliable electricity load forecasts are becoming increasingly important as the share of intermittent resources in the system increases. Distribution System Operators (DSOs) are called to accurately forecast their production and consumption to place optimal bids in the day-ahead market. Violations of their dispatch-plan requires activation of reserve-power which has a direct cost for the DSO, and also necessitates available reserve-capacity. Forecasts must account for the volatility of weather-parameters that impacts both the production and consumption of electricity. If DSO-loads are small or lower-granularity forecasts are needed, parametric statistical methods may fail to provide reliable performance since they rely on a priori statistical distributions of the variables to forecast. In this paper, we introduce a Probabilistic Load Forecast (PLF) method based on Empirical Copulas (ECs). The model is data-driven, does not need a priori assumption on parametric distribution for variables, nor the dependence structure (copula). It employs a kernel density estimate of the underlying distribution using beta kernels that have bounded support on the unit hypercube. The method naturally supports variables with widely different distributions, such as weather data (including forecasted ones) and historic electricity consumption, and produces a conditional probability distribution for every time step in the forecast, which allows inferring the quantiles of interest. The proposed non-parametric approach differs significantly from previous forecasting methods based on copulas, which typically uses copulas to model hierarchical dependence. Our approach is highly flexible and can produce meaningful forecasts even at very low aggregated levels (e.g. neighborhoods). The bandwidth of the beta kernel density estimators is optimized using Integrated Square Error (ISE) and such optimization can be performed online (i.e. without knowing the realization). We also investigate rule-of-thumb and Quantile Loss (QL) as objectives for the bandwidth-optimization. We present results from an open dataset and showcase the strength of the model with respect to Quantile Regression (QR) using standard probabilistic evaluation metrics.