Static Voltage Stability Region In Injection Power Space Of Power Systems

Security and stability are critical issues in power system research. Increasing extra-high voltage, long-distance transmission, and wide-area interconnection of networks drive modern power systems to operate in complex conditions, especially when consideration of environment and economy is gradually enhanced. As the system stability is challenged, studies on more effective approaches for stability assessment become one of the focuses of current research. "Region-wise" methodology is a promising framework which has received increasing concern recently. In this thesis, it is applied to study static voltage stability. The boundary of static voltage stability region (SVSR), which is also the power flow solution boundary is approximated by nonlinear analytical forms in power injection space. Firstly, an analytical expression of SVSR boundary is derived in power injection space for a single-load-single-generator system, and for general power systems a quadratic approximation of SVSR boundary is proposed through Taylor Series Expansion. Then a fitting method and a direct method are respectively presented to obtain the approximate quadratic expression of SVSR boundary. In the fitting method, a reduced quadratic form is proposed based on the analysis of fitting results. To apply the method to practical bulk power systems, modal analysis is also employed to reduce the dimension of injection space by selecting critical nodes in system networks. Simulation conditions are given in detail to search for critical operating points, and by fitting them the coefficients of the approximate quadratic expression can be calculated. Examples show that the reduced quadratic expression in the dimension-reduced injection space can approximate the SVSR boundary with acceptable accuracy over a wide range. In the direct method, first-order and second-order eigenvalue sensitivities and first-order eigenvector sensitivities are calculated for the Jacobian matrix of power flow equations, based on which the coefficients of the quadratic Taylor Series Expansion of SVSR boundary are derived and also the effect of the initial point on the approximation accuracy is studied. Thus the approximate quadratic expression of SVSR boundary can be obtained by the calculation on a given operating point close to the boundary. Besides, the SVSR boundary linearization method is simplified. Finally, a complete framework is presented for the software package of SVSR analysis system. Research on SVSR in power injection space can provide operators with direct information of system stability and guidance for decision making. It lays a basis for the visualization and on-line control of power systems.