Bifurcation Analysis Of Steady-State Voltage Stability And Research On Full Derivative Method

Since the 1960s,with the rapid increase of electric power demand,large-scale blackouts have occurred all over the world due to voltage collapse.This triggered an upsurge on the study of the hidden voltage stability problem.Nowadays,voltage stability analysis,different from the power angle stability,has become an important branch of power system security and stability analysis.The mechanism of voltage stability can be well explained by bifurcation theory.Saddle Node Bifurcation Point(SNBP)and Limit Induced Bifurcation Point(LIBP)are exemplified as the important causes of the voltage collapse.Main methods for calculation of bifurcations based on mathematical model can be classified as indirect and direct method.The two types of methods have issues on convergence/accuracy and calculation speed respectively,which is hard to meet the requirements of voltage security and stability analysis in modern power system.Therefore,this dissertation takes the analysis and calculation of steady-state voltage stability bifurcation as the main research object,and puts forward new theory and technologies in the field,so as to realize accurate,stable and fast analysis and calculation of SNBP and LIBP.The creative achievements and significance of the dissertation are as follows:(1)In order to solve the problem that Continuation Power Flow(CPF)needs multiple power flow calculations to locate SNBP,the total derivative equation is derived.Based on the equation,the concept of P’Q bus is introduced.The P’Q bus is the bus that full derivative of its active power with respect to its voltage magnitude and its reactive power are known;based on the fact that the proposed full derivative is zero at SNBP,the problem of the calculation of SNBP is transformed into a primary power flow calculation problem by bus converting method.In order to simplify programming,the method of supplementing bus is proposed.Futhermore,the case of multi load growth and multi generator regulation is considered.The convergence of the proposed power flow method is much less affected by the initial value than that of the Point of Collapse(POC)method,and the computational efficiency is much higher than that of CPF.The simulations in several standard systems proves the correctness of the above conclusions.(2)Based on the concept of P’Q bus,the full derivative extended calculation system is constructed.The method of solving the system by Newton method is denoted as Boundary Derivative Direct Method(BDDM).In order to explain the convergence of BDDM over POC,a two-scale convergence analysis method is proposed by analogy with the multi-time scale analysis method in power system.Specifically,the convergence process is divided into two convergence scales:the convergence of the extended equation and the system equilibrium equation.It is considered that the system equilibrium equation converges fast.Thus,the influence of the convergence of the equilibrium equation can be ignored when analyzing the convergence trajectory of the extended equation.The two-scale convergence analysis method simplifies the convergence analysis of Newton method in hyperspace to that in a visual space,greatly reducing the difficulty of convergence analysis.The divergence cases of BDDM are explained by means of the proposed two-scale convergence analysis method.Based on the hypothesis of the two-scale convergence analysis method,an improved POC algorithm is proposed,significantly ameliorating its convergence.The divergence issue of BDDM is solved by introducing Tangent Vector Index(TVI)to identify the voltage weak bus in the system.Futher,the proposed algorithm can identify the transition of weak buses during the iteration.(3)In order to solve the problem that the total derivative algorithm can not calculate LIBP,a hybrid direct method is proposed.The basic idea of the hybrid direct method is as follows:firstly,based on the two-scale convergence analysis method,the assumption that the intermediate solution of each iteration in BDDM is approximated as the equilibrium point is proposed;Secondly,the inequality constraint equations of the system are linearized in the iteration period so that the parameter that preferentially reaches the limit can be easily detected;Finally,the LIBP generated by the overshot parameter is located directly by a specific extended equation.Through one main iteration of BDDM and several built-in iterations,the whole computing system can track the LIBP and SNBP that may occur in the rising process of uncontrollable parameter.What is more,the complementary constraint of reactive power of generator is introduced.The complementary constraint may result in a special situation that some parameters that have reached the limit are released in the process of uncontrollable parameter change.This will lead to a limit induced dynamic bifurcation.Taking the result of the standard CPF as a reference,numerical examples show that the proposed method has better accuracy and the computing efficiency is less affected by the size of the system compared with the interior point method.(5)Due to the fluctuation of new energy output,the power parameter in the system model may not be a fixed value,but a probability density function or interval.Therefore,the calculated bifurcation points would also produce fluctuations correspondingly.The optimal Affine Arithmetic(AA)interval algorithm combined with BDDM is proposed to calculate the fluctuation interval of steady-state voltage stability bifurcation point.Compared with the combination of the interval algorithm and CPF,the proposed method is more efficient and accurate.Another solution of steady-state voltage stability analysis with consideration of power fluctuation is the construction of the steady-state voltage stability region.A fast high-order piecewise fitting method for steady-state voltage stability region boundary is presented by combining the asymptotic numerical method with the extended equation of POC.Compared with the point-by-point method,the calculation efficiency of the proposed method is improved;compared with the first-order or second-order Taylor expansion method,the fitting range and accuracy are greatly improved.