Polynomial Approximation Method For Parametric Problems Of Power Systems And Its Applications To The Analyses Of AC/DC Receiving-end System

The energy resources are scattered widely across our country,but the distribution is uneven.Thus,to develop the preferred future energy system,the long-distance bulk power transmission is desired,which can be supported by the emerging high voltage direct current(HVDC)technology.With the development of ultra-high voltage AC/DC hybrid system,the research area of the safety and stability has drawn much attention,where the commutation failure in receiving-end system threats the safety of power system.In this thesis,the theory of polynomial approximation and its applications to the analyses of AC/DC receiving-end system are studied and discussed in-depth.As for the theoretical research,the polynomial approximation method and its fast solution approach is studied.In the application of polynomial approximation,we focus on the commutation failure preventive and defence ability in the AC/DC receiving-end systems.In the analyses of power systems,one category focuses on the influences of parameters(or inputs)on system states(or outputs),which is uniformly called parametric problems.Based on Galerkin method,the polynomial approximation method for parametric problems in power sys-tems is proposed in this thesis.Here,the unknown coefficients are determined by solving Galerkin equation formed by projection in the form of integration,instead of according to the local in-formation of some specific sampled points.Thus,the approximation is global rather than local.Moreover,the proposed method enjoys excellent error convergence property,and gains optimal approximation results with the specific polynomial order if the orthogonal basis are chosen.Case studies are used to show the basic properties and the application potentials to practical problems.High dimensionality and massive amounts of parameters are the basic characteristics of power systems,and the application of polynomial approximation to power system analyses may engage in the "curse of dimensionality" problem.So,it is very important to find fast and efficient solution methods for the application of polynomial approximation.Aiming at this issue,a fast solution approach based on generalized Galerkin method is proposed,where special trial and test basis are selected to form decoupled-solvable Galerkin equations.The coefficients are determined succes-sively in an iterative approach,rather than by solving a group of high-dimensional equations at one go.Case studies show that the proposed method can gain high computational efficiency.Based on the research work of theoretical aspects,the application to parametric problems of AC/DC receiving-end systems is analysed in-depth.To be specific,for the commutation failure problem in AC/DC receiving-end systems,we study the preventive of commutation failures and the defence of continuous commutation failures respectively.Most of the current research concerning with commutation failures treats the AC network as Thevenin-equivalent,so the influence of fault position difference cannot be considered.In this thesis,the fault position is treated as parameter,thus the analyses of influence can be regarded to be parametric problem.By using polynomial approximation,a fast and accurate method is proposed to determine the critical fault positions which can just right trigger the commutation failures,so that the area of vulnerability to commutation failures can be obtained.Based on the derived area,a quantitative evaluation index for the influence of installing additional synchronous compensators is proposed,based on which the optimal installation allocation strategy is further established.The effectiveness of polynomial approximation for solving area of vulnerability is verified by case studies,and the influence of installing synchronous compensator on the preventive of commutation failures is analysed.Once the commutation failure happens,the recovery of commutating voltage is very impor-tant for the defence of continuous commutation failures,which may lead to the block of converter.The dynamic characteristics of synchronous compensator and shunt capacitor are different,so the static var output allocation will influence the transient voltage response.Both time and the static var allocation are regarded as parameters,so the parametric problem can be resolved by polynomial approximation method,which is extended to the time-domain analyses.Different from the tradi-tional sampling method and numerical integration method,Galerkin method is applied to find the analytical expression of commutating voltage time-domain response,which can both accelerate the computation process and facilitate the analyses of transient process.Based on the polynomial ap-proximation,the influence of static var allocation on the defence ability of continuous commutation failures is studied.