  We consider the problem of determining an optimal strategy for electricity
injection that faces an uncertain power demand stream. This demand stream is
modeled via an Ornstein-Uhlenbeck process with an additional jump component,
whereas the power flow is represented by the linear transport equation. We
analytically determine the optimal amount of power supply for different levels
of available information and compare the results to each other. For numerical
purposes, we reformulate the original problem in terms of the cost function
such that classical optimization solvers can be directly applied. The
computational results are illustrated for different scenarios.
