Formulations and Valid Inequalities for Optimal Black Start Allocation in Power Systems
- Univ. of California, Berkeley, CA (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
The restoration of a power system after a blackout starts around units with enhanced technical capabilities, referred to as black start units (BSUs). We examine the planning problem of optimally allocating these units on the grid subject to a budget constraint. We present a mixed integer programming model based on current literature in power systems. Binary variables are associated with the allocation of BSUs and with the energization state of buses, branches, and generators of the power system over a time horizon. We extract a substructure of the feasible region which imposes the requirement that each island that appears during the restoration process must have at least one operational generator. We discuss three equivalent reformulations for this requirement. We introduce a family of exponentially many, polynomially separable, valid inequalities to strengthen the formulation. Under simplifying assumptions, we show that the convex hull of the feasible region is a full-dimensional polyhedron, and prove that some of the constraints we introduced are facet-defining. We perform experiments to examine the difference in strength between the formulations as well as the computational times to solve the problem to near optimality for synthetic instances of the IEEE-39, IEEE-118, Illinois-200, WECC-225, IEEE-300, South Carolina-500, and Texas-2000 power systems. We illustrate a use case of the model. We conclude by suggesting extensions of the current work for future research.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1798439
- Report Number(s):
- LLNL-JRNL-812285; 1019411
- Journal Information:
- Operations Research, Journal Name: Operations Research; ISSN 0030-364X
- Publisher:
- INFORMS
- Country of Publication:
- United States
- Language:
- English
Similar Records
Stochastic Optimization for Grid Resilience. FY18 Final Technical Report
A Model Predictive Control Based Generator Start-Up Optimization Strategy for Restoration With Microgrids as Black-Start Resources