Power line control under uncertainty of ambient temperature

This paper discusses a control scheme for maintaining low tripping probability of a transmission system power line under thermal stress. We construct a stochastic differential equation to describe the temperature evolution in a line subject to randomness of the ambient temperature. When the distribution of the ambient temperature changes, so does the dependence of the tripping probability as a function of line current. The theory of extremes of Gaussian random fields is used to guide the size of the underlying frequency inspection so as to insure that current is effective for controlling the risk of overheating. In particular, we show that only when the change of temperature is suitably light-tailed (according to a precise definition discussed in the paper), the current provides a powerful enough mechanism to control tripping probabilities due to overheating. We then provide bounds that can be used to control the tripping probability in our stochastic model.