  In recent years, electricity generation has been responsible for more than a
quarter of the greenhouse gas emissions in the US. Integrating a significant
amount of renewables into a power grid is probably the most accessible way to
reduce carbon emissions from power grids and slow down climate change.
Unfortunately, the most accessible renewable power sources, such as wind and
solar, are highly fluctuating and thus bring a lot of uncertainty to power grid
operations and challenge existing optimization and control policies. The
chance-constrained alternating current (AC) optimal power flow (OPF) framework
finds the minimum cost generation dispatch maintaining the power grid
operations within security limits with a prescribed probability. Unfortunately,
the AC-OPF problem's chance-constrained extension is non-convex,
computationally challenging, and requires knowledge of system parameters and
additional assumptions on the behavior of renewable distribution. Known linear
and convex approximations to the above problems, though tractable, are too
conservative for operational practice and do not consider uncertainty in system
parameters. This paper presents an alternative data-driven approach based on
Gaussian process (GP) regression to close this gap. The GP approach learns a
simple yet non-convex data-driven approximation to the AC power flow equations
that can incorporate uncertainty inputs. The latter is then used to determine
the solution of CC-OPF efficiently, by accounting for both input and parameter
uncertainty. The practical efficiency of the proposed approach using different
approximations for GP-uncertainty propagation is illustrated over numerous IEEE
test cases.
