# Power System Recovery Coordinated with (Non-)Black-Start Generators

## TL;DR

This paper introduces a MILP-based recovery model for power systems that effectively coordinates black-start and non-black-start generators, optimizing restoration speed and safety after blackouts.

## Contribution

It develops a novel DCOPF model incorporating binary variables for generator energization and transmission line status, improving recovery coordination.

## Key findings

- Optimized recovery of NBS units and transmission lines.
- Validated on test systems including Puerto Rican grid.
- Demonstrated efficiency and coordination in power restoration.

## Abstract

Power restoration is an urgent task after a black-out, and recovery efficiency is critical when quantifying system resilience. Multiple elements should be considered to restore the power system quickly and safely. This paper proposes a recovery model to solve a direct-current optimal power flow (DCOPF) based on mixed-integer linear programming (MILP). Since most of the generators cannot start independently, the interaction between black-start (BS) and non-black-start (NBS) generators must be modeled appropriately. The energization status of the NBS is coordinated with the recovery status of transmission lines, and both of them are modeled as binary variables. Also, only after an NBS unit receives cranking power through connected transmission lines, will it be allowed to participate in the following system dispatch. The amount of cranking power is estimated as a fixed proportion of the maximum generation capacity. The proposed model is validated on several test systems, as well as a 1393-bus representation system of the Puerto Rican electric power grid. Test results demonstrate how the recovery of NBS units and damaged transmission lines can be optimized, resulting in an efficient and well-coordinated recovery procedure.