Model-free wide-area monitoring of power grids via cutset voltages

The so-called cutset voltage has previously been proposed as a model-based circuit reduction technique, and as a method to calculate an aggregate measure of grid stress from wide-area synchrophasor measurements. Here we contribute to the theory of the cutset voltage by showing that it can be written as the difference between the mean voltage levels on either side of the chosen cut, plus an accompanying error term. We then show that this error vanishes under a simple graph-theoretic condition on the weighted degrees of nodes adjacent to the cutset. In this case, the model-based cutset voltage can be computed in a model-free manner by taking wide-area voltage measurements and averaging. We extend our results to the case of a voltage defined across an entire area of the network.