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 at best an ad hoc rule that may be both overly conservative in considering all potential single-resource failures and excessively optimistic in inherently underestimating the economic consequences of correlated and cascading failures. More conservative approaches consider all possible combinations of N-k resources for k > 1 but including such combinations significantly increases the number of contingency scenarios even for low values of k and ignores the actual likelihood of these events. A significant challenge in determining event likelihoods is that the failure states of network elements are highly correlated through their interactions and common exposures, making direct determination of their joint distribution intractable. To address this issue, we develop a computational methodology to generate samples from the distribution of potential failure scenarios including correlated and cascading events using a Markov chain Monte Carlo (MCMC) algorithm. We demonstrate the method using the well-known IEEE 118-bus system and highlight the significant differences between the expected costs of dispatch using the MCMC model to generate failures and the costs that results from assuming only single unit failures and of assuming that failures are independent instead of being drawn from the correlated joint distribution.


University of Chicago, November/2020



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