Adaptive Residual Modeling for Scenario Learning in Probabilistic Load Forecasting

Abstract

Uncertainties in weather, user behavior, and distributed energy production introduce significant variability into feeder power. Effective power system operations require both multi-horizon load forecasts and well-calibrated extreme quantiles for the forecast. Nevertheless, standard objectives that fit the full forecast distribution often underemphasize rare observations and extremes. Conversely, applying heavy tail-weighting in the distribution to capture these extremes can distort the underlying probability distribution. To address this issue, this paper proposes adaptive residual modeling for scenario learning (ARMSL), a two-stage framework. Particularly, Stage I in our framework sequentially models environmental response, history-dependent load patterns, persistent residual deviations, and the remaining innovations. Upon the modeling, we then generate joint active- and reactive-power scenarios with state-dependent dispersion. Stage II keeps the scenario model fixed and calibrates extreme marginal quantiles using a simple, channel-specific reference forecast (an anchor). Only outward deviations from this anchor are admitted, with their contribution determined by local calibration history and the current operating state. From our numerical simulations on FeederBW dataset, Stage I outperforms diffusion baselines in energy and variogram scores. Our complete framework achieves an active-power 0.99-quantile pinball loss of 0.1932 (a 30.08% to 85.33% reduction relative to three baselines) with 1.054% exceedance rate against a nominal 1%. From simulations on the Rolle dataset, we observe decreased losses by 5.39%--14.40% compared to the active-power-only anchor. Furthermore, the unchanged Stage I scenarios in the simulation yield a correlation of 0.953 between predicted and observed feeder event rates, with 90.0% of feeder errors falling within two percentage points.