Modeling and Identification of Worst-Case Cascading Failures in Power Systems
For power system operators, this work provides a method to systematically trace sources of cascading failures, but the approach is incremental and limited to DC power flow assumptions.
The paper develops a mathematical model for cascading failures in power systems using DC power flow and optimal control theory, and proposes an iterative search algorithm to identify worst-case initial disturbances. Simulations on IEEE 9 and 14 bus systems validate the approach.
Cascading failures in power systems normally occur as a result of initial disturbance or faults on electrical elements, closely followed by errors of human operators. It remains a great challenge to systematically trace the source of cascading failures in power systems. In this paper, we develop a mathematical model to describe the cascading dynamics of transmission lines in power networks. In particular, the direct current (DC) power flow equation is employed to calculate the transmission power on the branches. By regarding the disturbances on the elements as the control inputs, we formulate the problem of determining the initial disturbances causing the cascading blackout of power grids in the framework of optimal control theory, and the magnitude of disturbances or faults on the selected branch can be obtained by solving the system of algebraic equations. Moreover, an iterative search algorithm is proposed to look for the optimal solution leading to the worst case of cascading failures. Theoretical analysis guarantees the asymptotic convergence of the iterative search algorithm. Finally, numerical simulations are carried out in IEEE 9 Bus System and IEEE 14 Bus System to validate the proposed approach.