基于伴随系统理论的电力系统主导不稳定平衡点求解方法

提出了一种基于伴随系统理论的电力系统主导不稳定平衡点的求解方法。对于一大类非线性自治动力系统,可以构造原系统的伴随系统, 该伴随系统是一个梯度系统,原始系统的所有平衡点都是伴随系统的渐近稳定平衡点,并且每一稳定平衡点存在解析形式的 Lyapunov函数。通过研究故障中轨迹在伴随系统中的势能变化, 可求得一个沿故障中轨迹分布的不稳定平衡点的集合, 进而采用切平面筛选法可以快速求解与故障中轨迹相关的主导不稳定平衡点。该方法不仅具有概念清楚、计算步骤简洁等优点, 而且不依赖于系统能量函数的存在性, 因而较以往的方法更具通用性。通过对 IEEE 39 节点电力系统的实际仿真结果表明, 该方法可以快速准确地求解电力系统的主导不稳定平衡点。

Computing the Controlling Unstable Equilibrium Point Based on the Theory of Adjoint Systems

A new method based on the theory of adjoint systems to compute the controlling unstable equilibrium point is presented. For a nonlinear autonomous dynamic system, there exists an adjoint system that is a gradient system. All equilibrium points of the nonlinear autonomous dynamic system are stable equilibrium points in its adjoint system. Studying the potential energy along the fault-on trajectory in the adjoint system, the controlling equilibrium point can be found accurately with this method. Simulation results on the power systems of IEEE-39 nodes prove that the method can find the controlling equilibrium point of power systems quickly.