Abstract
SummaryIn this article, we address the task of setting up an optimal production plan taking into account an uncertain demand. The energy system is represented by a system of hyperbolic partial differential equations and the uncertain demand stream is captured by an Ornstein‐Uhlenbeck process. We determine the optimal inflow depending on the producer's risk preferences. The resulting output is intended to optimally match the stochastic demand for the given risk criteria. We use uncertainty quantification for an adaptation to different levels of risk aversion. More precisely, we use two types of chance constraints to formulate the requirement of demand satisfaction at a prescribed probability level. In a numerical analysis, we analyze the chance constrained optimization problem for the Telegrapher's equation and a real‐world coupled gas‐to‐power network.
Highlights
INTRODUCTIONSignificant attention has been paid to the energy market. On the one hand, this is due to climate protection policies
In recent years, significant attention has been paid to the energy market
We apply deterministic discrete adjoint calculus to solve the deterministically reformulated stochastic optimal control (SOC) problem (23). This is implemented in ANACONDA, a modularized simulation and optimization environment for hyperbolic balance laws on networks that allows the inclusion of state constraints, which has been developed in Reference 34
Summary
Significant attention has been paid to the energy market. On the one hand, this is due to climate protection policies. The novelty of our chance-constrained stochastic optimal control framework consists in a joint consideration of the very generic choice of hyperbolic balance laws to describe the supply system on the one hand and the exact deterministic reformulation of the SCC and in particular the JCC for the OUP modeling a time-dependent uncertain demand stream on the other hand. This combination of the hyperbolic nature of the time-dependent supply system (no steady-state assumption), and advantageous stochastic process modeling choice for the uncertain demand stream has not been investigated yet to the best of our knowledge
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