  The increasing penetration of renewable energy along with the variations of
the loads bring large uncertainties in the power system states that are
threatening the security of power system planning and operation. Facing these
challenges, this paper proposes a cost-effective, nonparametric method to
quantify the impact of uncertain power injections on the load margins. First,
we propose to generate system uncertain inputs via a novel vine copula due to
its capability in simulating complex multivariate highly dependent model
inputs. Furthermore, to reduce the prohibitive computational time required in
the traditional Monte-Carlo method, we propose to use a nonparametric,
Gaussian-process-emulator-based reduced-order model to replace the original
complicated continuation power-flow model. This emulator allows us to execute
the time-consuming continuation power-flow solver at the sampled values with a
negligible computational cost. The simulations conducted on the IEEE 57-bus
system, to which correlated renewable generation are attached, reveal the
excellent performance of the proposed method.
