A Markovian Influence Graph Formed From Utility Line Outage Data to Mitigate Large Cascades

Abstract

We use observed transmission line outage data to make a Markovian influence graph that describes the probabilities of transitions between generations of cascading line outages. Each generation of a cascade consists of a single line outage or multiple line outages. The new influence graph defines a Markov chain and generalizes previous influence graphs by including multiple line outages as Markov chain states. The generalized influence graph can reproduce the distribution of cascade size in the utility data. In particular, it can estimate the probabilities of small, medium and large cascades. The influence graph has the key advantage of allowing the effect of mitigations to be analyzed and readily tested, which is not available from the observed data. We exploit the asymptotic properties of the Markov chain to find the lines most involved in large cascades and show how upgrades to these critical lines can reduce the probability of large cascades.

Interaction Graphs for Cascading Failure Analysis in Power Grids: A Survey

“…Further, three categories are defined for data-driven interaction graphs based on the method used for analyzing the data.These include: (1) methods based on outage sequence analysis , (2) risk-graph methods [38][39][40][41], and (3) correlation-based methods [29,30,42,79]. The category of outage sequence analysis is further divided into four sub-categories including (i) consecutive failure-based methods [13][14][15][16][17][18][19][20], (ii) generation-based methods [21][22][23][24][25][26], (iii) influence-based methods [27][28][29][30], and (iv) multiple and simultaneous failure-based methods [31][32][33][34][35][36][37]. This novel taxonomy is used to classify thirty detailed research studies, including conference and journal publications, in the data-driven category into various subcategories.…”

“…In addition to the review of various methods for constructing interaction graphs, various reliability analysis and studies performed using these graphs are also briefly reviewed. Some studies of interaction graphs are focused on identifying critical components in the cascade process of power grids [14][15][16][17][18][19][20][21][22][23][24][27][28][29][30][31][38][39][40]48,[56][57][58][59]. These studies can have different purposes such as (1) identifying the vulnerable or most influential components of the system in the cascade process by utilizing standard centrality metrics [14][15][16][17][18][19][20]50,54] or defining new centrality metrics [21][22][23][24] and (2) identifying the set of components whose upgrade (for instance, by increasing the power flow capacity of transmission lines) or protection can help in mitigating the risk of cascading failures and large blackouts [27,28,31,58] or quantifying the performance of the grids after addition of new transmission lines [58,…”

“…Moreover, the work in [44] uses interaction graphs to identify transmission lines that when switched off create partitions that limit the propagation of failures in the power grid. Some studies [31,42] also use the structures and patterns in interaction graphs to characterize and predict the distribution of cascade sizes. Similarly, structures in interaction graphs have been used for reliability analysis of zonal patterns [51] and partitioning into voltage control regions [78].…”

A Probabilistic Cascading Failure Model for Dynamic Operating Conditions

“…In this study, we consider transmission lines and transformers among power system components, while the methodology can be extended to other components. The initiating event (i.e., generation 1) of each case in the cascade data is the failure of one or several system components, followed by subsequent failures (generations) until no more failures take place, or the system becomes unstable [26]. An example of the cascade data is shown in Fig.…”

“…While these models reveal the cascade size, the contribution of each component to a cascading failure, a necessary information for online operations, e.g., generation ramping, cannot be derived. To address the drawbacks of the statistical models, data-driven statistical models such as the influence graph model [25], [26] and the interaction model [27]- [29] are developed to simulate cascading failures using the interactions among system components. An interaction is defined as the probability of one component's failure, given the failure of other components.…”