Voltage Stability Study Based On Local Bifurcation Theory

Power system stability boundary is constrained by three kinds of local bifurcations: Saddle-Node bifurcation,Hopf bifurcation and Singularity-Induced bifurcation.The determination of local bifurcation points and the trajectories of corresponding control parameters are very important for the power system stability evaluation,safe and economic operation as well as reliable generation scheduling.This thesis focuses on the local bifurcation occurance phenomenon,based on bifurcation theory of nonlinear dynamic system, with the dynamic characteristics of generators and excitation systems consideration.More explicitly speaking,this thesis mainly studied the reason which causes The work and attribute of the thesis is shown below:1) Dynamic voltage stability is deeply studied based on the local bifurcation theory with load increase pattern consideration.Load increase pattern is regarded as control parameters which lead the dynamic system to the stability boundary.Saddle-node bifurcation points are found with a given load increase pattern and the closest Saddle-node bifurcation point is found through the proposed iterative method,followed with the most dangerous load increase pattern obtained.2) There are two types of voltage instabilities:monotonic voltage instability and oscillatory one.The oscillatory voltage instability corresponds to the Hopf bifurcation.In this thesis,the voltage stability boundary is the combined boundary which correspond to Saddle-node bifurcations and Hopf bifurcations.The closest Hopf bifurcation point is found through the proposed iterative method under the assumption that the Hopf hypersurface is continuous and convex.The most dangerous load increase pattern is alos obtained.3) Voltage stability margin(VSM) is the smallest geographic distance of the current load level to the load level where bifurcation occurs.Nonlinear planning optimization algorithm is adopted in this thesis to reschedule the active power output of generators and shed load to satisfy the VSM requirement of power system operations.4) Eigenvalue calculation is the most important part in local bifurcation studies.To solve the difficulties in large scale power system eigenvalue calculation and obstacles eigenvalue analysis in large scale state matrix,modified implicit restared Arnoldi method is adopted with the sparse matrix technology usage.Math library IMSL and the open sourse math library Arpack are combined in this thesis to realized the above mentioned technologies.The most sensitive eigenvalue to the control parameters is selected by employing SPA method and the critical eigenvalue is determined based on the calculated eigenvalue.