  Electricity production currently generates approximately 25% of greenhouse
gas emissions in the USA. Thus, increasing the amount of renewable energy is a
key step to carbon neutrality. However, integrating a large amount of
fluctuating renewable generation is a significant challenge for power grid
operating and planning. Grid reliability, i.e., an ability to meet operational
constraints under power fluctuations, is probably the most important of them.
In this paper, we propose computationally efficient and accurate methods to
estimate the probability of failure, i.e. reliability constraints violation,
under a known distribution of renewable energy generation. To this end, we
investigate an importance sampling approach, a flexible extension of
Monte-Carlo methods, which adaptively changes the sampling distribution to
generate more samples near the reliability boundary. The approach allows to
estimate failure probability in real-time based only on a few dozens of random
samples, compared to thousands required by the plain Monte-Carlo. Our study
focuses on high voltage direct current power transmission grids with linear
reliability constraints on power injections and line currents. We propose a
novel theoretically justified physics-informed adaptive importance sampling
algorithm and compare its performance to state-of-the-art methods on multiple
IEEE power grid test cases.
