Probabilistic Load Forecasting for the City of Milan based on Subseasonal Predictions

Summer heatwaves are a major concern for electricity distribution companies due to the high electrical loads they can place on urban distribution networks. These load peaks, driven by increased cooling demand, pose a serious threat to network infrastructure by accelerating the deterioration of underground components. During the summer, these components are prone to failure, resulting in cascading blackouts across multiple urban areas. In addition to meteorological forecasting of heat waves, it is therefore crucial to accurately estimate the probability that the electrical load in urban areas will exceed pre-defined thresholds.

In this study, temperature outputs from sub-seasonal forecasts are used to derive probabilistic forecasts of the expected electrical load. A machine learning approach is used, focusing on a single grid point representing the urban area of Milan. The chosen algorithm is Random Forest, where the target variable is the daily electrical load in Milan. The period used to train and validate the algorithm ranges from 2013 to 2023, and the predictors include the Degree Days (DD) and the "week of the year", since the electrical load shows strong seasonal variations.

The time series of the daily load in Milan, used to train the model, shows a significant shift from 2020 onwards due to the pandemic and the associated lockdowns, resulting in lower load values on average with respect to the 2013-2019 period. To ensure comparability between the pre-pandemic and the post-pandemic period (2021-2023), the historical series were detrended using a seasonal trend decomposition (STL) based on LOESS (Locally Estimated Scatterplot Smoothing), making the series almost stationary over the period analysed.

With the detrended electricity load time series, two forecasting models, both based on Random Forest, were implemented and tested. The first, called the Ensemble Model, trains the Random Forest with the Degree Days (DD) derived from ERA5 temperatures for 2013-2019 and applies the learned relationship to each of the bias-corrected seasonal S2S ensemble members for 2021-2023 to predict the electric load in the test period. The final load prediction in this case is the ensemble mean load.

The second approach, called the Quantile-Based model, uses the quantiles of the DD distribution derived from the bias-corrected S2S temperatures as predictors, providing greater flexibility for different ensemble configurations (e.g. 50 or 100 members). It is also tailored to specific forecast lead times and includes a simplified version based on the DD median.

The models have been evaluated using both deterministic and probabilistic metrics. The results indicate that while both models provide more reliable load forecasts than climatology, the Quantile-Based model outperforms the Ensemble Model beyond the third forecast week. It provides probability distributions that are more centred on the observed load, thereby improving forecast reliability.

These forecasting methods can help distribution system operators to address critical peak demand issues with preventive or more timely interventions.