关键词: 输电网络, 连锁故障, 连通可靠性, 贝叶斯重要度, 关键线路

Abstract: Large blackouts are typically caused by line cascading failures in a power transmission network. For some key institutions in a city, such as hospitals and command centers for disaster mitigation, there is an essential need for ensuring the connectivity of power lifelines between a power plant and a high-voltage substation in a specific area when the line cascading failures occur. Oriented to this need, there is a vital and challenging problem of determining some critical lines for maintaining the connectivity.
Once these critical lines are determined, on the one hand, efforts can be focused on protecting these critical lines before the blackout occurs, in order to prevent the paralysis of the power transmission network; on the other hand, after the blackout occurs, limited resources can be focused on prioritizing the maintenance of these lines in order to restore the connectivity of the power lifeline as soon as possible.
The current methods to identify critical lines have focused on the vulnerability of the line itself and its role in failure propagation or the serious consequences of the line failure, such as the magnitude of the load loss and the size of the blackout.
However, the current methods fail to identify critical line to maintain the connectivity of power lifelines in the context of line cascading failures, so that they cannot be used to scientifically guide the maintenance and optimization of power transmission networks. To this end, this paper proposes a scientific method to identify critical lines by combining the connectivity and development mechanism of line cascade failures in a power transmission network.
First, to characterize the cascading failure process of lines, a cascading model is developed in which the blackout size is measured by the number of failed lines. The blackout size is a random variable related to the initial disturbance, load threshold, and transfer load. To develop the probability distribution of the blackout size, we summarize a normalized cascading failure model in which the initial load for each link is a uniformly random variable distributed in the interval [0,1]. According to the normalized cascading failure model, we derive the probability distribution of the blackout size, which is a saturating quasibinomial distribution with parameters such as the initial disturbance, load threshold, and transfer load.
Applying the saturating quasibinomial distribution, we develop a formula to calculate the reliability of the power transmission network, where the reliability is the probability that a power plan and a high-voltage substation can be connected by some operational lines. According to the network reliability, a Bayesian importance measure is proposed to quantify the importance of lines for maintaining connectivity. The Bayesian importance measure depends on the distribution of the blackout size and the structure of the power transmission network, where the structure is quantified by the concept of the structural spectrum.
Exactly calculating the structural spectrum is an NP-hard problem; thus, exactly calculating the Bayesian importance measure is difficult. Therefore, a numerical algorithm is constructed to approximately evaluate the Bayesian importance measure, so as to identify the critical lines. The greater the importance of the link is, the more critical the link is, and vice versa.
Finally, a case study on the Taiwan power transmission network is presented to illustrate how the Bayesian importance measure can effectively assist in obtaining the criticality of lines regarding the reliability of the power transmission network in the context of line cascading failures. A sensitivity analysis is discussed for determining the impact of changing parameter in the saturating quasibinomial distribution on the Bayesian importance measure. The experimental results reveal that given a fixed initial disturbance, when the load threshold is larger and the transfer load is smaller, the difference in the criticality degree of the lines becomes more significant. These numerical results show that the proposed method to identify critical lines can aid in decision-making when performing emergency maintenance of a power transmission network and ensuring the connectivity of power lifelines.
In the context of cascading line failures, this paper proposes a method for identifying critical lines, which quantifies the effects of individual links on maintaining the connectivity of the power transmission network. However, this method fails to consider the joint effects of two links on network connectivity. Therefore, for future studies, we will concentrate on the interaction effects of two links on the connectivity of the power transmission network, so as to comprehensively identify critical lines based on these interaction effects.

Key words: power transmission network, cascading failure, connectivity reliability, Bayesian importance measure, critical line