  Despite significant economic and ecological effects, a higher level of
renewable energy generation leads to increased uncertainty and variability in
power injections, thus compromising grid reliability. In order to improve power
grid security, we investigate a joint chance-constrained (CC) direct current
(DC) optimal power flow (OPF) problem. The problem aims to find economically
optimal power generation while guaranteeing that all power generation, line
flows, and voltages simultaneously remain within their bounds with a
pre-defined probability. Unfortunately, the problem is computationally
intractable even if the distribution of renewables fluctuations is specified.
Moreover, existing approximate solutions to the joint CC OPF problem are overly
conservative, and therefore have less value for the operational practice. This
paper proposes an importance sampling approach to the CC DC OPF problem, which
yields better complexity and accuracy than current state-of-the-art methods.
The algorithm efficiently reduces the number of scenarios by generating and
using only the most important of them, thus enabling real-time solutions for
test cases with up to several hundred buses.
