Control of the Power Flows of a Stochastic Power System

Abstract: How to determine the vector of power supplies of a stochastic power system for the next short horizon, such that the probability is less than a prespecified value that any phase-angle difference of a power line of the power network exits from a safe set? The power system is modelled such that the differential equation of each frequency is affected by a Brownian motion process. A safe set can be selected to be any subset of the interval $(-\pi/2, ~ +\pi/2)$, which is a sufficient condition for not losing synchronization. That the controlled system has an improved performance is shown by numerical results of three academic examples including a particular eight-node academic network, a twelve-node ring network, and a Manhattan-grid network.