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In this paper, a mathematical formulation of the probabilistic availabletransfer capability (PATC) problem is proposed to incorporate uncertaintiesfrom the large-scale renewable energy generation (e.g., wind farms and solar PVpower plants). Moreover, a novel non-intrusive low-rank approximation (LRA) isdeveloped to assess PATC, which can accurately and efficiently estimate theprobabilistic characteristics (e.g., mean, variance, probability densityfunction (PDF)) of the PATC. Numerical studies on the IEEE 24-bus reliabilitytest system (RTS) and IEEE 118-bus system show that the proposed method canachieve accurate estimations for the probabilistic characteristics of the PATCwith much less computational effort compared to the Latin hypercube sampling(LHS)-based Monte Carlo simulations (MCS). The proposed LRA-PATC method offersan efficient and effective way to determine the available transfer capabilityso as to fully utilize the transmission assets while maintaining the securityof the grid.

A Non-Intrusive Low-Rank Approximation Method for Assessing the Probabilistic Available Transfer Capability