A Stochastic Program for Black Start Allocation

Abstract

The fast and secure restoration of the power system after an extended blackout highly depends on the location of Black Start (BS) resources. In contrast to most generators, BS units have the ability to start without being connected to an already energized power grid. Selecting a unit to provide BS services is associated with costly technical upgrades, continuous testing, and compensation for the services, and once a unit is selected as BS it is expected to provide that service for several years. For these reasons, the selection process to allocate new BS units is very important and currently handled by experts in the field. Building on the existing literature for power system restoration and black start allocation, we formulate an optimization problem aimed at allocating BS units optimally in the power grid. While restoration plans are usually examined under the assumption of a total blackout, in reality most blackouts are partial, leaving parts of the grid energized and certain elements damaged. In order to account for these cases during the selection process, we formulate a two-stage stochastic program that optimizes the allocation of BS resources over a number of outage scenarios. We use a scenario decomposition algorithm to solve the resulting optimization problem to near-optimality in a high performance computing environment. We conduct numerical experiments using the proposed model and decomposition method on the IEEE-39.