Public charging of electric vehicles (EVs) adds a large synchronized load to distribution feeders. In most networks, feeder overloads occur extremely rarely, but when they do they stress transformers and can trigger cascading city‑wide outages. Planners therefore need to estimate very small outage probabilities to ensure high reliability. Plain Monte Carlo (MC) estimation with an expensive grid simulator requires a prohibitive number of runs.
To reduce the simulation budget we propose a control variate (CV) built from a learned outage classifier trained on cheap observable features such as temperature and load forecasts. For any binary learner the variance reduction can be expressed explicitly in terms of its recall $r$ and false‑positive rate $f$: $$\text{Var}_{\text{CV}} = (1 - 2r(1-f))\,\text{Var}_{\text{MC}}.$$
Further analysis shows that a Gaussian proxy of the load loses its effect as outages become rarer, whereas a learner with non‑vanishing precision continues to remove a fixed fraction of the variance even in the extreme rare‑event regime. Numerical experiments with a feeder‑overload simulator span three orders of magnitude of outage probability. A weak learner using a single feature removes about 25% of the variance, while a boosted‑tree learner removes roughly 60%.
We then apply the estimator to the feeder network of Surabaya, Indonesia. Under the same simulation budget the Gaussian load model makes every feeder three to seven times worse than the “one‑day‑in‑ten‑years” blackout target. Planning reserves with the learned CV and a 95% confidence limit reduces city‑wide blackout days by about one third compared with plain Monte Carlo.
These findings demonstrate that learned control variates can help planners design distribution grids that remain reliable against rare outages.
Review