Markov Chain Sampling of Hidden Relay States for Economic Dispatch with Cascading Failures

Independent system operators (ISO) of electric power networks aim to dispatch electricity economically while maintaining system reliability. NERC (North America Electric Reliability Council) requires the transmission network to be (N-1)-secure, i.e., to have sufficient supply to satisfy demand in the event of the failure of any single resource in the network. Such a policy is … Read more

Epi-convergence of Sample Averages of a Random Lower Semi-continuous Functional Generated by a Markov Chain and Application to Stochastic Optimization

The purpose of this article is to establish epigraphical convergence of the sample averages of a random lower semi-continuous functional associated with a Harris recurrent Markov chain with stationary distribution $\pi$. Sample averages associated with an ergodic Markov chain with stationary probability distribution will epigraphically converge from $\pi$-almost all starting points. The property of Harris … Read more

A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversi cation. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation … Read more