Stochastic Analysis of Cascading-Failure Dynamics in Power Grids

A scalable and analytically tractable probabilistic model for the cascading failure dynamics in power grids is constructed while retaining key physical attributes and operating characteristics of the power grid. The approach is based upon extracting a reduced abstraction of large-scale power grids using a small number of aggregate state variables while modeling the system dynamics using a continuous-time Markov chain. The aggregate state variables represent critical power-grid attributes, which have been shown, from prior simulation-based and historical-data-based analysis, to strongly influence the cascading behavior. The transition rates among states are formulated in terms of certain parameters that capture grid\u27s operating characteristics comprising loading level, error in transmission-capacity estimation, and constraints in performing load shedding. The model allows the prediction of the evolution of blackout probability in time. Moreover, the asymptotic analysis of the blackout probability enables the calculation of the probability mass function of the blackout size. A key benefit of the model is that it enables the characterization of the severity of cascading failures in terms of the operating characteristics of the power grid.

Assessment of grid-friendly collective optimization framework for distributed energy resources

Distributed energy resources have the potential to provide services to facilities and buildings at lower cost and environmental impact in comparison to traditional electric-gridonly services. The reduced cost could result from a combination of higher system efficiency and exploitation of electricity tariff structures. Traditionally, electricity tariffs are designed to encourage the use of ‘off peak’ power and discourage the use of ‘onpeak’ power, although recent developments in renewable energy resources and distributed generation systems (such as their increasing levels of penetration and their increased controllability) are resulting in pressures to adopt tariffs of increasing complexity. Independently of the tariff structure, more or less sophisticated methods exist that allow distributed energy resources to take advantage of such tariffs, ranging from simple pre-planned schedules to Software-as-a-Service schedule optimization tools. However, as the penetration of distributed energy resources increases, there is an increasing chance of a ‘tragedy of the commons’ mechanism taking place, where taking advantage of tariffs for local benefit can ultimately result in degradation of service and higher energy costs for all. In this work, we use a scheduling optimization tool, in combination with a power distribution system simulator, to investigate techniques that could mitigate the deleterious effect of ‘selfish’ optimization, so that the high-penetration use of distributed energy resources to reduce operating costs remains advantageous while the quality of service and overall energy cost to the community is not affected

Optimization of investments to upgrade an island distribution system:

Summary: An electric utility operates the power system on an island, and wishes to implement system upgrades, including the installation of distribution-level solar photovoltaic (PV) arrays and battery energy storage systems (BESS) at various sites around the island. The residential and light commercial loads are dispersed throughout the island, primarily near the coast. Currently five medium-voltage distribution feeders emanate from a single power station, which is located near the coast and accessible from the sea. Two of these feeders are primarily responsible for serving remote customers. Power generation is via four sets of tandem diesel generators. There is no connection to a larger power system from the mainland. Because it is difficult to choose among the many potential upgrade options available, including resource siting and capacity, the DER-CAM+ optimization tool was utilized to provide insight into the characteristics of an optimal solution. The tool is a recent upgrade on DERCAM, itself a product of Lawrence Berkeley National Laboratory's research program. The upgrade includes the ability to model power distribution systems and considers possible investment options, by examining their effect on the cost of energy and on CO2 emissions. In the present study, the addition of PV and BESS at a number of pre-selected sites was considered. The analysis showed that the addition of large PV arrays, with peak power essentially matching the peak load on the system, is economically advantageous. Multiple sites allow larger overall PV deployment than a single site, as a result of distribution system constraints. The analysis also showed that the economics of optimal resource dispatch alone are not sufficient to justify the deployment of battery storage. However, battery storage could be mandatory to satisfy operational needs. Further exploration of the optimization surface revealed that, while not optimal, the cost of operation with battery storage is still lower than for the base case of diesel generation only, and not much different from the optimal case

Impacts of Operators’ Behavior on Reliability of Power Grids During Cascading Failures

Human operators play a key role in the reliable operation of critical infrastructures. However, human operators may take actions that are far from optimum. This can be due to various factors affecting the operators\u27 performance in time-sensitive and critical situations such as reacting to contingencies with significant monetary and social impacts. In this paper, an analytic framework is proposed based on Markov chains for modeling the dynamics of cascading failures in power grids. The model captures the effects of operators\u27 behavior quantified by the probability of human error under various circumstances. In particular, the observations from historical data and information obtained from interviews with power-system operators are utilized to develop the model as well as identify its parameters. In light of the proposed model, the noncritical regions of power-system\u27s operating characteristics with human-factor considerations are characterized under which the probability of large cascading failures is minimized