Chao Zhai

Chao Zhai, Hehong Zhang, Gaoxi Xiao et al.

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.

Chao Zhai, Gaoxi Xiao, Hehong Zhang et al.

This paper aims to investigate the risk identification problem of power transmission system that is integrated with renewable energy sources. In practice, the fluctuation of power generation from renewable energy sources can lead to severe consequences to power transmission network. By treating the fluctuation of power generation as the control input, the risk identification problem is formulated with the aid of optimal control theory. Thus, a control approach is developed to identify the fluctuation of power generation that results in the worst-case cascading failures of power systems. Theoretical analysis is also conducted to obtain the necessary condition for the worst fluctuations of power generation. Finally, numerical simulations are implemented on IEEE 9 Bus System to demonstrate the effectiveness of the proposed approach.

Chao Zhai, Gaoxi Xiao, Hehong Zhang et al.

This paper addresses the cooperative control problem of Thyristor-Controlled Series Compensation (TCSC) to eliminate the stress of cyber-physical power system. The cyber-physical power system is composed of power network, protection and control center and communication network. A cooperative control algorithm of TCSC is developed to adjust the branch impedance and regulate the power flow. To reduce computation burdens, an approximate method is adopted to estimate the Jacobian matrix for the generation of control signals. In addition, a performance index is introduced to quantify the stress level of power system. Theoretical analysis is conducted to guarantee the convergence of performance index when the proposed cooperative control algorithm is implemented. Finally, numerical simulations are carried out to validate the cooperative control approach on IEEE 24 Bus Systems in uncertain environments.

Junhao Ren, Kai Zhao, Guangxiao Zhang et al.

Parallel cyber-physical attacks (PCPA) simultaneously damage physical transmission lines and block measurement data transmission in power grids, impairing or delaying system protection and recovery. This paper investigates the fault diagnosis problem for a linearized (DC) power flow model under PCPA. The physical attack mechanism includes not only line disconnection but also admittance modification, for example via compromised distributed flexible AC transmission system (D-FACTS) devices. To address this problem, we propose a fault diagnosis framework based on meta-mixed-integer programming (MMIP), integrating graph attention network-based fault localization (GAT-FL). First, we derive measurement reconstruction conditions that allow reconstructing unknown measurements in attacked areas from available measurements and the system topology. Based on these conditions, we formulate the diagnosis task as an MMIP model. The GAT-FL predicts a probability distribution over potential physical attacks, which is then incorporated as objective coefficients in the MMIP. Solving the MMIP yields optimal attack location and magnitude estimates, from which the system states are also reconstructed. Experimental simulations are conducted on IEEE 30/118 bus standard test cases to demonstrate the effectiveness of the proposed fault diagnosis algorithms.

Chao Zhai, Hung D. Nguyen

This paper introduces a novel framework to construct the region of attraction (ROA) of a power system centered around a stable equilibrium by using stable state trajectories of system dynamics. Most existing works on estimating ROA rely on analytical Lyapunov functions, which are subject to two limitations: the analytic Lyapunov functions may not be always readily available, and the resulting ROA may be overly conservative. This work overcomes these two limitations by leveraging the converse Lyapunov theorem in control theory to eliminate the need of an analytic Lyapunov function and learning the unknown Lyapunov function with the Gaussian Process (GP) approach. In addition, a Gaussian Process Upper Confidence Bound (GP-UCB) based sampling algorithm is designed to reconcile the trade-off between the exploitation for enlarging the ROA and the exploration for reducing the uncertainty of sampling region. Within the constructed ROA, it is guaranteed in probability that the system state will converge to the stable equilibrium with a confidence level. Numerical simulations are also conducted to validate the assessment approach for the ROA of the single machine infinite bus system and the New England $39$-bus system. Numerical results demonstrate that our approach can significantly enlarge the estimated ROA compared to that of the analytic Lyapunov counterpart.

Chao Zhai, Gaoxi Xiao, Hehong Zhang et al.

Due to the evolving nature of power systems and the complicated coupling relationship of power devices, it has been a great challenge to identify the contingencies that could trigger cascading blackouts of power systems. This paper aims to develop a universal approach for identifying the initial disruptive contingencies that can result in the worst-case cascading failures of power grids. The problem of contingency identification is formulated in a unified mathematical framework, and it can be solved by the Jacobian-Free Newton-Krylov (JFNK) method in order to circumvent the Jacobian matrix and relieve the computational burden. Finally, numerical simulations are carried out to validate the proposed identification approach on the IEEE $118$ Bus System.

Chao Zhai, Gaoxi Xiao, Hehong Zhang

This paper aims to identify and analyze the initial contingencies or disturbances that could lead to the worst-case cascading failures of power grids. An optimal control approach is proposed to determine the most disruptive disturbances on the branch of power transmission system by regarding the disturbances as the control inputs. Moreover, protective actions such as load shedding and generation dispatch are taken into account in a convex optimization framework to prevent the cascading outages of power grids. In theory, the necessary conditions for identifying the most disruptive disturbances are obtained by solving an integrated system of algebraic equations. Finally, numerical simulations are carried out to validate the proposed approach on the IEEE RTS 24 Bus System.

Hehong Zhang, Chao Zhai, Gaoxi Xiao et al.

Potential critical risks of cascading failures in power systems can be identified by exposing those critical electrical elements on which certain initial disturbances may cause maximum disruption to power transmission networks. In this work, we investigate cascading failures in power systems described by the direct current (DC) power flow equations, while initial disturbances take the form of altering admittance of elements. The disruption is quantified with the remaining transmission power at the end of cascading process. In particular, identifying the critical elements and the corresponding initial disturbances causing the worst-case cascading blackout is formulated as a dynamic optimization problem (DOP) in the framework of optimal control theory, where the entire propagation process of cascading failures is put under consideration. An Identifying Critical Risk Algorithm (ICRA) based on the maximum principle is proposed to solve the DOP. Simulation results on the IEEE 9-Bus and the IEEE 14-Bus test systems are presented to demonstrate the effectiveness of the algorithm.