Power System Stability Analysis Based On Region Theory, Bifurcation Analysis And Recursive Projection Method

The vigorous development of power industry has put forward higher demand for power system stability and security analysis. There are increasing needs for exploring more effective computational tools and analytical methods. To maintain power system operational stability and security, a fundamental requirement is to guarantee the existence of an equilibrium point and its small signal stability. It is also the emphasis of this thesis. The major work can be summarized as follows:(1) A dimension reduction method for voltage stability region is proposed through a map from node load space to area total load space. We make thorough discussions with respect to the construction of voltage stability region in area total load space, its local approximation and visualization strategies, boundary topological features, as well as the search for the most sensitive parameter variation direction. On this basis, a voltage security monitoring and control scheme is presented using the voltage stability region in area total load space. The proposed scheme has a lot of merits, such as intuitive expression, simplified description, and easy implementation for online voltage stability assessment and control.(2) For a given operational control parameter, recursive projection method (RPM) is investigated to extract power system steady state and small signal stability information from existing time-domain simulation codes (TDSCs). With RPM, the full state space is decomposed into an unstable/slow invariant subspace and its orthogonal complement subspace. A Newton type of method and the original integration scheme of TDSC are implemented on the two subspaces respectively. As a result, the convergence of original fixed point iteration can be significantly enhanced. In the meanwhile, dominant eigenspectrum of the integration scheme is also obtained as byproduct, from which system small signal stability features can be reconstructed.(3) With the quasi-static parameter variation, the Jacobian matrix of Newton iteration on unstable/slow subspace may become singular at some operating point. RPM iteration is then combined with continuation technique to mitigate singularity problems and enable the equilibrium manifold tracing to go beyond singular points. Along the equilibrium tracing path, saddle node bifurcations and Hopf bifurcations can be detected conveniently via the small signal stability information from the RPM procedure. Thus the proposed method can avoid full state space linearization and large scale eigenspectrum computation in conventional bifurcation approaches. With the (continuation scheme of) recursive projection method, existing TDSCs are enabled to perform user designated tasks, such as equilibrium calculation, equilibrium manifold tracing, small signal stability analysis and bifurcation analysis. Consequently, an effective computational tool is developed for power system equilibrium manifold tracing and bifurcation analysis based on full system dynamic models (DAE models). At the same time, modeling and numerical advantages of original software resources (TDSCs) are preserved and extra programming costs are saved.