Application Of Polynomial Approximation To Power System Parametric Stability Problems

Stability is a major problem in power system planning and operation.Nowadays,China is witnessing the structures and operational scenarios of power grids becoming ever more complex and volatile,making power system stability facing challenges.To ensure the se-curity in operation,power system stability under various operational conditions should be analyzed and evaluated.However,due to the nonlinearity nature,it is difficult to find the an-alytical expressions of stability related states and indices under the scenarios with extensive uncertainty and wide-range variation of the parameters,and however,the existing approxi-mation based approaches are not yet perfect and need improvement.For this purpose,based on the idea of Galerkin method,this thesis develops polynomial approximation approaches for several typical power system stability problems characterized by different types of mathe-matical models.The proposed methods explicitly depict the quantitative relationship between the parameters and the states,indices,and stability limits,which improve the ability of power system stability analysis under complex,volatile and uncertain operational conditions,and provide references to the theory and methodology for other parametric problems in power system analysis.Main work of this thesis includes:(1)Formulating the criteria equations of static voltage stability region boundaries(SVSRB)as nonlinear parametric algebraic equations based on saddle node bifurcation conditions.Then,based on the idea of Galerkin method,formulating polynomial basis functions and pro-jection equations in the inner product space of functions to compute the polynomial approxi-mation expressions of the SVSRB,the corresponding states and eigenvector with global and controllable precision on the parameter domain.The proposed method overcomes the defects of traditional voltage stability margin evaluation based on fixed parameter increase patterns,and shows largely enhanced precision compared to the existing security region boundary approximation methods.(2)Characterizing the SVSRB considering generator reactive power limits by parameter-izing a nonlinear optimization model,and transforming it into parametric algebraic equations using parametric KKT conditions.Then,based on Galerkin method and classical primal-dual interior point method,the corresponding global polynomial approximation approach for the SVSRB considering generator reactive power limits is proposed,which overcomes the diffi-culty that the combination of active constraints may change when the parameter varies.(3)Based on the local bifurcation theory of power system differential-algebraic equation(DAE)model,characterizing the small-signal stability region boundary(SSSRB)as para-metric nonliterary algebraic equations using Hopf bifurcation,saddle node bifurcation and singularity induced bifurcation conditions.Then,applying the Galerkin method on the non-linear parametric algebraic equations to calculate the global polynomial approximations of the SSSRB and the corresponding eigenvector,which provide valuable information for small-signal stability evaluation and control.(4)Extending a generalized Galerkin designed for parametric algebraic equations to au-tonomous DAE models to compute the high-order trajectory sensitivities of power systems over continuous dynamics;modeling the discrete-time switching events as parametric alge-braic equations and using the generalized Galerkin to compute the jumping of the high-order trajectory sensitivities at the switching events.The above constitute the methodology of high-order trajectory sensitivity analysis for power system piecewise autonomous DAE models,which overcomes the defects of traditional linear trajectory sensitivity analysis losing accu-racy under the conditions of strong nonlinearity and wide-range variation of the parameters,thus enhancing the adaptability and precision of power system dynamic evaluation.