基于稳定约束的电力系统稳定平衡解模型

Stable equilibrium solution model of power system based on stability constraints

为直接计算电力系统的静态稳定解,提出了基于稳定约束的稳定平衡解模型,并对该模型提出了一种直接求解稳定平衡解的新方法。通过稳定约束与电力系统典型的平衡方程结合,建立了稳定平衡解模型;稳定约束由非线性半光滑代数不等式构成,针对不同稳定类型所对应雅可比矩阵的特性,运用矩阵变换、谱函数性质等数学理论构造了不同的稳定约束表达式。利用牛顿光滑化方法将该模型转换为光滑方程,从而解决了稳定平衡解模型的数值求解问题。稳定平衡解模型将非稳定解排除在可行解之外,使求解过程得到简化,避免了计算稳定极限和求多个平衡解等复杂过程,而且通过参数调整能满足更高的稳定性能要求。通过典型的电力系统的数值计算,验证了所提方法的有效性。

A stable equilibrium solution model based on stability constraints is presented to directly calculate the static stable solutions of power systems. It combines the classical equilibrium equations with the stability constraints,which are nonlinear algebraic inequations constructed, according to the features of Jacobian matrix for different stable types,by applying different mathematic theories, such as matrix transform,spectral function characters and so on. The model is transformed into smooth equations using smoothing Newton- Type method to calculate its numerical solutions. The stable equilibrium solution model excludes the unstable solutions to simplify the computation and avoid the stable boundary determination. Higher stability demand can be satisfied by parameter regulation. The computation of a typical system,as an example,shows the feasibility and validity of proposed model.