| Recently,with the increase in DC transmission,the dynamic characteristics of AC/DC systems have changed greatly compared with traditional AC systems.Due to its complex structure and the characteristics of the involved converter,an AC/DC system is obviously a highly nonlinear and complicated system.Moreover,the interactions at the multi-time scale controls of the dynamic elements,and even the grid topology changes with the switching of control also emerge along with it.Therefore,transient stability analysis of post failure AC/DC systems is very complicated and,thus,essential to investigate.It is urgent to analyze the system transient stability more accurately and to provide reliable quantitative information to guide the transient stability control of AC/DC systems.Currently,the study of the transient voltage stability is mainly based on the time-domain method.The method obtains the change curve of variables as the time increases.However,massive computation time will be consumed,and the stability margin cannot be given by this method.Therefore,the estimation of the transient stability domain is very important in power systems.Additionally,more accurate and less conservative stable domain estimation can reduce unnecessary operation interference and be beneficial in controlling system coordination.Based on the more appropriate estimation method of the transient stability domain,the appropriate operation modes can be selected to improve safety and stability.Some methods based on the energy function and the unstable controlling equilibrium point method are only effective for systems represented by simple models.And when the model changes,the calculations need to be rederived.Therefore,another method,the polynomial Lyapunov function method based on Sum-of-Squre programe is studied in this paper.The advantage of this approach is that it is more convenient and efficient than the energy function method for complex systems,showing that the manual calculation process is shortened,and the calculation efficiency is greatly improved.We aim to explore a method for estimating the transient stability domain of the power system accommodating the switching characteristics of the LCC-HVDC converter controls in practice.The power system with LCC-HVDC is modeled as a switched nonlinear system.The dynamic equations representing the transient characteristics of a DC system after fault are reflected in the process of Lyapunov function construction and transient stability domain estimation in this paper.The necessity of retaining the main control loops of DC converters and their switching characteristics is verified for the system-wise stability analysis based on the Lyapunov function method.Based on engineering practice,considering the switching conditions among the control modes of AC/DC systems and the continuity condition of multiple Lyapunov functions,the continuous piecewise Lyapunov functions of AC and DC systems are solved by iterative optimization algorithm and the stability region estimation is obtained.Under the influence of numerical problems that may occur in some toolbox applications,the effects of different SOS approximation methods on the results are shown in this paper.Considering the influence of the uncertainty of DC control parameters,the feasibility of using the polynomial Lyapunov function method with the approximate sum of squares to estimate and analyze the stability region of AC/DC system is explored.Finally,all the examples are programmed in MATLAB,and the simulation platform is used to build a time-domain simulation model for comparative analysis.The research work of this paper is supported by the National Natural Science Foundation of China(51577071),which is entitled "Research on the Transport of Attraction Domain of P-Q Strong Coupling AC-DC Power Grid". |
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