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.

中文翻译：

---

在需求不确定的情况下对电力输入进行最佳控制

我们考虑确定面对不确定电力需求流的最佳电注入策略的问题。该需求流通过Ornstein–Uhlenbeck过程进行建模，并带有一个附加的跳跃分量，而功率流由线性传输方程表示。我们通过分析确定适用于不同级别的可用信息的最佳电源量，并将结果相互比较。出于数值目的，我们根据成本函数重新构造了原始问题，以便可以直接应用经典的优化求解器。说明了不同情况下的计算结果。