一种求解电力系统稳定边界上不稳定平衡点的方法

提出一种基于伴随系统和变号系统的求解电力系统经典模型稳定边界上不稳定平衡点的方法。对于一个非线性自治动力系统，存在一个伴随系统，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，并且每一平衡点存在解析形式的Lyapunov函数。变号系统能将电力系统经典模型降维系统的稳定平衡点变为I型不稳定平衡点，利用该平衡点的1维不稳定流形，生成一族轨迹，沿轨迹寻找伴随系统Lyapunov函数达到极小值的点，这些点一般位于某平衡点伴随系统的稳定域内。以该点为初值对伴随系统进行积分即可收敛到该平衡点。该方法能快速有效的寻找到稳定边界上的不稳定平衡点。在IEEE-10机39节点系统和IEEE-17机162节点系统上仿真，验证了该方法的有效性。

A New Method to Compute Unstable Equilibrium Points on the Stability Boundary of Power System

A new method based on adjoint system and minus system to compute unstable equilibrium points on the stability boundary of power system classical model is proposed. For a nonlinear autonomous dynamic system,there exists an adjoint system,which is a gradient system. All equilibrium points of the original system are stable equilibrium points in the adjoint system. And each has an analytical Lyapunov function. The stable equilibrium point of power system classical model dimension-reduction system is type-I unstable equilibrium point in the minus system. Search along the unstable manifolds to find the minimum points of Lyapunov function. The trajectories of adjoint system from these minimum points generally converge to equilibrium points. The method can find the equilibrium point on the stability boundary fast and efficiently,which is verified on IEEE 39-bus system and IEEE 162-bus system.