Scenario based stochastic programming for aggregate electricity demand scheduling using Moroccan smart meter data

Abstract

Electricity retailers and load aggregators must schedule energy before actual demand is known. This study develops a data-to-decision framework for an experimental aggregate demand portfolio constructed from high-resolution smart-meter measurements for Laayoune, Boujdour, Foum El Oued, and Marrakech, Morocco. Seventeen city-zone series are converted to a common unit, aggregated into four city-level series, and aligned on common 30-minute timestamps. Persistence, seasonal-naive, and Random Forest forecasts are compared using chronological training and validation periods, with a held-out test period reserved for final evaluation. The validation-selected Random Forest produces recursive 96-period forecasts, and its validation-calibration residuals are sampled in contiguous blocks to generate 10,000 demand scenarios. The point forecast supports deterministic scheduling, while \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K=100$$\end{document} representative scenarios support risk-neutral two-stage stochastic programming (SP), Conditional Value-at-Risk (CVaR), and periodwise maximum absolute cost-deviation stochastic programming (PMAD-SP). On a separately generated common 10,000-scenario evaluation set, SP reduced expected normalised cost by 12.72% relative to the deterministic policy. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.95$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda =0.5$$\end{document}, CVaR reduced empirical CVaR95 by 0.54% relative to SP. PMAD-SP kept expected cost nearly unchanged while reducing scenario-total cost standard deviation by 39.86%. Seven consecutive non-overlapping 48-hour historical windows also gave lower realised cost for SP, but this evidence is descriptive because the windows share estimation and calibration inputs. The findings show how forecast uncertainty can affect scheduling decisions, subject to a single-node experimental portfolio, normalised costs, and simplified operational limits.