  The fast growth of renewable energies increases the power congestion risk. To
address this issue, the French Transmission System Operator (RTE) has developed
closed-loop controllers to handle congestion. RTE wishes to estimate the
probability that the controllers ensure the equipment's safety to guarantee
their proper functioning. The naive approach to estimating this probability
relies on simulating many randomly drawn scenarios and then using all the
outcomes to build a confidence interval around the probability. Although theory
ensures convergence, the computational cost of power system simulations makes
such a process intractable.
  The present paper aims to propose a faster process using
machine-learning-based proxies. The amount of required simulations is
significantly reduced thanks to an accuracy-aware proxy built with Multivariate
Gaussian Processes. However, using a proxy instead of the simulator adds
uncertainty to the outcomes. An adaptation of the Central Limit Theorem is thus
proposed to include the uncertainty of the outcomes predicted with the proxy
into the confidence interval. As a case study, we designed a simple simulator
that was tested on a small network. Results show that the proxy learns to
approximate the simulator's answer accurately, allowing a significant time gain
for the machine-learning-based process.
