Changes in Cascading Failure Risk with Generator Dispatch Method and System Load Level

Industry reliability rules increasingly require utilities to study and mitigate cascading failure risk in their system. Motivated by this, this paper describes how cascading failure risk, in terms of expected blackout size, varies with power system load level and pre-contingency dispatch. We used Monte Carlo sampling of random branch outages to generate contingencies, and a model of cascading failure to estimate blackout sizes. The risk associated with different blackout sizes was separately estimated in order to separate small, medium, and large blackout risk. Results from $N-1$ secure models of the IEEE RTS case and a 2383 bus case indicate that blackout risk does not always increase with load level monotonically, particularly for large blackout risk. The results also show that risk is highly dependent on the method used for generator dispatch. Minimum cost methods of dispatch can result in larger long distance power transfers, which can increase cascading failure risk.Comment: Submitted to Transmission and Distribution Conference and Exposition (T&D), 2014 IEEE PE

Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology

In a cascading power transmission outage, component outages propagate non-locally, after one component outages, the next failure may be very distant, both topologically and geographically. As a result, simple models of topological contagion do not accurately represent the propagation of cascades in power systems. However, cascading power outages do follow patterns, some of which are useful in understanding and reducing blackout risk. This paper describes a method by which the data from many cascading failure simulations can be transformed into a graph-based model of influences that provides actionable information about the many ways that cascades propagate in a particular system. The resulting "influence graph" model is Markovian, in that component outage probabilities depend only on the outages that occurred in the prior generation. To validate the model we compare the distribution of cascade sizes resulting from $n-2$ contingencies in a $2896$ branch test case to cascade sizes in the influence graph. The two distributions are remarkably similar. In addition, we derive an equation with which one can quickly identify modifications to the proposed system that will substantially reduce cascade propagation. With this equation one can quickly identify critical components that can be improved to substantially reduce the risk of large cascading blackouts.Comment: Accepted for publication at the IEEE Transactions on Power System

Calculation of the Autocorrelation Function of the Stochastic Single Machine Infinite Bus System

Critical slowing down (CSD) is the phenomenon in which a system recovers more slowly from small perturbations. CSD, as evidenced by increasing signal variance and autocorrelation, has been observed in many dynamical systems approaching a critical transition, and thus can be a useful signal of proximity to transition. In this paper, we derive autocorrelation functions for the state variables of a stochastic single machine infinite bus system (SMIB). The results show that both autocorrelation and variance increase as this system approaches a saddle-node bifurcation. The autocorrelation functions help to explain why CSD can be used as an indicator of proximity to criticality in power systems revealing, for example, how nonlinearity in the SMIB system causes these signs to appear.Comment: Accepted for publication/presentation in Proc. North American Power Symposium, 201