Fast solution of load shedding problems via a sequence of linear programs

Given a power network consisting of nodes (generators/loads) and edges (lines), there exist a set of constraints that must be satisfied in order for the system to be operational. When one or more power lines are cut, the bus phases and load/generator power values may need to be altered in order to restore the system to operation. The load shedding problem is to find the smallest adjustment to the loads that achieves this restoration. In this work, we show how to solve this nonlinear optimization problem by solving a sequence of linear programs. On random graphs with 1500 edges, we find that our method is at least 40 times faster than competing nonlinear optimization methods. We show that our method is capable of solving load shedding problems for a real graph with 19840 edges, and that the method scales with an O(n²) running time where n is the number of edges. For real subgraphs with hundreds of edges, we are able to rapidly solve all possible load shedding problems in which at most two lines are deleted. This work takes a first step towards a scalable load shedding algorithm capable of handling large networks that will arise in the future.