Yang Yang, Motter Adilson E
Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA.
Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev Lett. 2017 Dec 15;119(24):248302. doi: 10.1103/PhysRevLett.119.248302. Epub 2017 Dec 14.
In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in a closed form using a global Hamiltonian-like function. From this function, we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that, in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.
在网络系统中，局部扰动在传播过程中可能会放大，从而有可能导致大规模的级联故障。在此，我们推导了一个连续模型，以增进我们对电网网络中级联故障的理解。该模型既考虑了输电线路的故障，也考虑了发电机的失步，并纳入了级联连续步骤之间的瞬态动力学。在此框架下，我们表明级联事件是从高能平衡态到低能平衡态的相空间转变，这可以用一个类似全局哈密顿函数的封闭形式适当地描述。从这个函数中，我们表明受扰系统并不总是能达到准稳态级联模型所预测的平衡态，该平衡态对应的故障数量会减少，反而可能会经历更大规模的级联。我们还表明，在存在两个或更多扰动的情况下，结果强烈依赖于各个扰动的顺序和时机。这些结果为当前对级联动力学的理解提供了新的见解，对控制干预具有潜在影响。
