  In this paper, a mathematical formulation of the probabilistic available
transfer capability (PATC) problem is proposed to incorporate uncertainties
from the large-scale renewable energy generation (e.g., wind farms and solar PV
power plants). Moreover, a novel non-intrusive low-rank approximation (LRA) is
developed to assess PATC, which can accurately and efficiently estimate the
probabilistic characteristics (e.g., mean, variance, probability density
function (PDF)) of the PATC. Numerical studies on the IEEE 24-bus reliability
test system (RTS) and IEEE 118-bus system show that the proposed method can
achieve accurate estimations for the probabilistic characteristics of the PATC
with much less computational effort compared to the Latin hypercube sampling
(LHS)-based Monte Carlo simulations (MCS). The proposed LRA-PATC method offers
an efficient and effective way to determine the available transfer capability
so as to fully utilize the transmission assets while maintaining the security
of the grid.
