| In recent years,Chinese power industry has developed rapidly,and its power consumption has continued to grow rapidly.Chinese power grid has shown a new form of large-capacity DC transmission of large-scale wind and photovoltaic power grids.The shape of the structure will last about 5-10 years,and the emergence of this complex structure has brought severe challenges to the stability of the power system.There are many researches on large-perturbation stability analysis methods,and they can be roughly divided into three categories.The first is algorithms based on numerical simulation,the second is algorithms based on Lyapunov's direct method,the third is based on mathematics analytical method of approximation.The simulation method is currently widely used in the problem of large electromechanical transient disturbance stability in engineering,but this method has a low degree of analysis.The direct method has a simple form and fast calculation speed,but the effect is not optimistic for large-scale complex power grids.The analytical solution can focus on the relationship between the stability margin index and the parameters,but the intrusive analytical solution cannot use commercial software,and the non-intrusive analytical solution is difficult to carry out stable analysis with the structural characteristics of the power grid.The ideal large-scale disturbance stability analysis technology of the hybrid power grid is still under development.Power system large disturbance stability includes large disturbance power angle stability and large disturbance voltage stability.Large disturbance power angle stability includes transient stability and large disturbance dynamic stability.The large disturbance stability discussed in this paper is mainly aimed at power system transient stability,and its mathematical model is A set of differential-algebraic equations.In the current mathematical methods,the analysis method of differential-algebraic equations is far less mature than the analysis method of simple differential equations.Based on the above background,this paper proposes a method to deal with the network voltage for AC grid.The main research contents and results of this article are as follows:1.Most of the transient stability analysis methods in engineering use Dommel-Sato iteration.According to its iteration format,this paper points out the key mathematical index of this iteration convergence--spectral radius,and uses spectral radius to explain the effect of failure type on the iteration convergence rate.At the same time,when the Dommel-Sato iteration satisfies the convergence condition,the closed form of the solution is derived.2.According to the closed form of Dommel-Sato iteration,two iteration methods are proposed for the network equation of the AC power grid—the unified iteration method and the alternating iteration method.The unified iteration method can obtain the closed solution of the network voltage when the load adopts the constant impedance model or the constant current model;the alternating iteration method can be used to get the analytical expression of the network voltage amplitude when the AC grid has only a single constant power load or there are multiple constant power loads far apart from each other.Using the closed solution of network voltage,the mathematical model of transient stability analysis can be transformed from differential-algebraic equations to total differential equations,avoiding the alternate iteration between differential equations and algebraic equations in the process.3.According to the closed solution of the network voltage,combining with the short-term grid characteristics after the fault,a discrete linear system for quickly calculating the short-term voltage after the system fault is proposed.The advantage of this discrete linear system is that it does not need to consider the alternate solution process of differential equations and algebraic equations,which improves the calculation speed of state quantities and has certain physical significance. |
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