Learned Control Variates for Rare Grid-Outage Estimation at Electric Vehicle Charging Stations

Sulyman Iyanda; Mansur Arief

cs.AIOct 19, 2026

Learned Control Variates for Rare Grid-Outage Estimation at Electric Vehicle Charging Stations

Authors: Sulyman Iyanda, Mansur Arief

Organizations: Industrial and Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

Abstract

Public charging of electric vehicles (EVs) adds a large and synchronized load to the distribution feeders. In most networks, it is rare to overload a feeder at the same time. When it does happen, the consequences can be severe: an overloaded feeder stresses its transformers and can trigger cascading outages across a city. Planners who design for high reliability therefore need to estimate very small outage probabilities. To that end, plain Monte Carlo estimation with an expensive grid simulator can require a prohibitively large number of runs for this task. To reduce the number of runs, we propose a control variate (CV) built from a learned classifier of the outage, trained on cheap observable features such as temperature and load forecasts. We show that for any binary learner, the variance reduction is an explicit function of its recall and false-positive rate. Furthermore, we show that control variate based on a Gaussian proxy of the load loses its effect as outages become rarer, while a learner with non-vanishing precision keeps removing a fixed fraction of the variance even in the extreme rare-event regime. We verify these results in numerical experiments using a feeder-overload simulator across three orders of magnitude of outage probability and obtain that even weak learner with a single feature can remove a quarter of the variance, while a boosted-tree learner is able to remove about 60%. We then apply the estimator to the feeder network of Surabaya, Indonesia, in which the Gaussian load model leaves every feeder three to seven times the one-day-in-ten-years blackout target. At the same simulation budget, planning the reserve with the learned CV and a 95% confidence limit reduces the city-wide blackout days by a third compared with Monte Carlo. These results show that learned control variates can help planners design distribution grids that stay reliable against rare outages.

Figures & tables

Fig. 1: (a) Variance reduction

\rho^{2}

of each control as the outage becomes rarer. (b) Running estimate at

\theta=10^{-4}

as the sample grows: median (line) and 95% range (shaded) over 400 samples, for Monte Carlo (black, dashed) and the boosted-tree control on the same days (solid); The true value is shown as the dotted line. (c) Simulator runs needed to achieve a 10% relative error.

$\theta$	Estimator	$\rho^{2}$	$\frac{1}{1-\rho^{2}}$	RMSE	theory	bias	cov.
$10^{-3}$	MC	0.000	1.00	0.233	0.223	+0.015	0.94
	GP	0.001	1.00	0.233	0.223	+0.015	0.94
	ST (weak)	0.274	1.38	0.191	0.190	+0.008	0.95
	LL (weak)	0.396	1.66	0.175	0.174	+0.005	0.94
	BT	0.638	2.76	0.135	0.135	+0.008	0.95
	BP	0.652	2.87	0.134	0.132	+0.010	0.95

TABLE I: Replication study at about 20 outages per replication

Fig. 2: Expected blackout days per year after a charging station is added and the reserve is sized for one day in ten years by (a) the Gaussian load model of the earlier work, (b) Monte Carlo with $10^{4}$ days and the point estimate, and (c) the learned control variate on the same days with a 95% upper limit.

Procedure	city days/yr	$>$ target	$>2\times$	90th pct.	pop.
Gaussian model	5.73	1.00	1.00	0.521	1.00
MC, point est.	1.17	0.46	0.08	0.192	0.46
CV, point est.	1.16	0.49	0.02	0.162	0.49
MC, 95% limit	0.78	0.24	0.02	0.139	0.23
CV, 95% limit	0.77	0.15	0.00	0.110	0.15

TABLE II: City-wide outcome over 200 replications of

10{,}000

days

Rare-Event Estimation

Rare-event estimation measures probabilities of failures, extremes, or transitions that ordinary sampling may miss.

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Abstract

Rare-Event Estimation

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