Accurate Polynomial Approximation of Bifurcation Hypersurfaces in Parameter Space for Small Signal Stability Region Considering Wind Generation

The loss of small signal stability under parameter variation (e.g., fluctuation of loads and wind powers) can be ascribed to local bifurcations, i.e., saddle-node, Hopf, singularity-induced, and limit-induced bifurcations. Classic bifurcation calculation methods like the direct method and continuation method can only provide a single bifurcation point or two-parameter bifurcation curve. Based on Galerkin method and the implicit function theorem, this paper proposes accurate polynomial approximations of bifurcation hypersurfaces in the multi-dimensional parameter space of interest. The proposed method can ensure high accuracy in the whole parameter space of interest, and thus is preferable to the existing Taylor expansion-based local approximation method, given the intrinsic large-variation characteristic of wind powers. The acquired bifurcation hypersurfaces are immediately used to construct the small signal stability region of the continuous system, and then compute the stability margin when the operating point is subjected to uncertainty of wind generation. Besides, the validity scope of the proposed method is analyzed, and the handling of limit-triggered equation switching as well as its computational difficulty is discussed. Computational results on the two-parameter 11-bus two-area and six-parameter IEEE 145-bus test systems validate the high accuracy and effectiveness of the proposed method.