  In an effort to reduce power system-caused wildfires, utilities carry out
public safety power shutoffs (PSPS) in which portions of the grid are
de-energized to mitigate the risk of ignition. The decision to call a PSPS must
balance reducing ignition risks and the negative impact of service
interruptions. In this work, we consider three PSPS scheduling scenarios, which
we model as dynamic programs. In the first two scenarios, we assume that N
PSPSs are budgeted as part of the investment strategy. In the first scenario, a
penalty is incurred for each PSPS declared past the Nth event. In the second,
we assume that some costs can be recovered if the number of PSPSs is below $N$
while still being subject to a penalty if above N. In the third, the system
operator wants to minimize the number of PSPS such that the total expected cost
is below a threshold. We provide optimal or asymptotically optimal policies for
each case, the first two of which have closed-form expressions. Lastly, we
establish the applicability of the first PSPS model's policy to critical-peak
pricing, and obtain an optimal scheduling policy to reduce the peak demand
based on weather observations.
