Optimal Software Patching Plan for PMUs

Phasor measurement units (PMUs) deployed to monitor the state of an electrical grid need to be patched from time to time to prevent attacks that exploit vulnerabilities in the software. Applying some of these patches requires a PMU reboot, which takes the PMU offline for some time. If the PMU placement provides enough redundancy, it is possible to patch a set of PMUs at a time while maintaining full system observability. The challenge is then to find a patching plan that guarantees that the patch is rolled out to all PMUs in the smallest number of rounds possible while full system observability is maintained at all times. We show that this problem can be formulated as a sensor patching problem, which we demonstrate to be NP-complete. However, if the grid forms a tree, we show that the minimum number of rounds is two and we provide a polynomial-time algorithm that finds an optimal patching plan. For the non-tree case, we formulate the problem as a binary integer linear programming problem and solve it using an integer linear programming (ILP)-solver. We also propose a heuristic algorithm to find an approximate solution to the patching problem for grids that are too large to be solved by an ILP-solver. Through simulation, we compare the performance of the ILP-solver and the heuristic algorithm over different bus systems.