Transmission system repair and restoration

This paper studies the use of mathematical programming for the repair and restoration of a transmission system after a significant disruption (e.g., a natural disaster). Such blackouts may last several days and have significant impact on human and economic welfare. The transmission system repair and restoration problem (TSRRP) consists in dispatching crews to repair damaged electrical components in order to minimize the size of the blackout. The TSRRP can be modeled as a large-scale mixed nonlinear, nonconvex program, including both routing components and the nonlinear steady-state power flow equations. To tackle its daunting computational complexity, this paper proposes a 2-stage approach, decoupling the restoration and repair aspects. The first step is a restoration ordering problem, a mixed nonlinear, nonconvex program which is approximated by a mixed integer program. The approximation does not use the traditional DC power flow approximation which is plagued by convergence issues and inoperable dispatches; rather, it uses the recent LPAC approximation that captures reactive power and voltage magnitudes. The second stage is a pickup and repair routing problem which is solved using a constraint-programming model, large neighborhood search, and a randomized adaptive decomposition. Experimental results on benchmarks based on the US electrical infrastructures and state-of-the-art damage scenarios indicate that the 2-stage approach provides significant improvements over the “best practice” in the field.