动态电压稳定模型中二维参数分岔边界的计算

Calculation of 2-Dimensional Parameter Bifurcation Boundary in the Dynamic Voltage Stability Model

基于延拓法的原理,提出应用该方法来直接追踪动态电压稳定微分一代数联立方程中的奇异性、鞍结点和霍普夫等分岔的二维参数边界。为达到此目的,首先应用延拓法来追踪该模型的平衡解曲线(流形),以便间接得到单个参数的局部分岔点;然后,从计算所得的单个参数分岔点出发,继续应用延拓法来求解描述该模型中的局部分岔的代数方程,以便直接追踪二维参数的分岔边界。最后,应用该方法来计算一简单的电压稳定算例,所得结果表明该方法是可行和有效的。

Based on the principle of the continuation method (indirect method), it is proposed that this method be used to directly trace 2-dimensional singularity induced, saddle-node and Hopf bifurcations boundary occurring in the differential-algebraic equations (DAEs) that model power system voltage stability. To this end, the continuation method is first applied in tracing the equilibrium curve (or equilibrium manifold) of voltage stability to calculate one-parameter local bifurcation points. Then by proceeding from the calculated points, the continuation method is again used in solving the algebraic equations that describe the local bifurcations in the DAEs model to directly trace 2-dimensional parameter local bifurcation boundary. Finally, the method is applied in a simple example of power system voltage stability. The results obtained show that it is feasible and effective.