Probabilistic Available Transfer Capacity Evaluation of Power Systems Using Polynomial Chaos Expansion

The growing uncertainty level caused by the increasing penetration of wind power generation poses a formidable challenge in the available transfer capability (ATC) evaluation of bulk power systems. The existing probabilistic ATC(PATC) calculation methods can solve the ATC of power system with the increasing uncertain wind power, but they may fail in the computational accuracy or efficiency. To handle this challenge, a Polynomial Chaos Expansion(PCE) based chance-constrained PATC calculation method is developed in this paper. The chance-constrained PATC model is formulated, and the polynomial basis is determined according to the probabilistic distributions of wind power forecasting error. Using the determined polynomial basis, the wind power forecasting error and its dependent network variables are represented by the PCE, and the formulated chance-constrained PATC model can be further reformulated as a one-shot deterministic ATC model by using the PCE with the Galerkin projection and moment-based chance constraint representation. Hence, the reformulated ATC model casts the chance-constrained PATC model as a finite dimensional nonlinear program(NLP) with the PCE coefficients as decision variables, and the optimal PCE coefficients can be achieved by solving the reformulated ATC model via the existing optimization solver. Using the solved optimal PCE coefficients and determined polynomial basis, the probabilistic characteristics (e.g., mean, variance, probability distribution) of PATC can be obtained. Numerical studies on the modified PJM 5-bus test system, modified IEEE 118-bus test system and western Jilin power grid validate the proposed PCE-based PATC method, achieving accurate estimation for the probabilistic characteristics of PATC with a high efficiency. ©2024 Chin.Soc.for Elec.Eng.