Energies, Vol. 19, Pages 1262: Conservation-Consistent Modeling of Time-Varying Transfer Delays with Applications in Energy Systems
Energies doi: 10.3390/en19051262
Authors:
Sara Bysko
Krzysztof Ĺakomiec
Krzysztof Fujarewicz
Time delays are intrinsic to energy systems, arising from transport phenomena, communication latency, and control dynamics; however, their accurate modeling remains challenging, particularly under variable operating conditions. The most common delays are constant over time and are easy to model and simulate. However, simulation tools of time-varying delay systems rely on signal-delay representations that fail to enforce conservation laws, leading to unphysical results in applications involving mass or energy transport. This study develops a physically consistent mathematical framework for time-varying transfer delays that explicitly couples kinematic evolution with conservation principles through a dynamic gain term. A systematic classification is introduced, distinguishing between signal delays (information transfer) and transfer delays (physical transport), further categorized by the source of variability in time delay into Types R (variable extraction), W (variable supply), and M (variable medium). The proposed formulation was implemented in Simulink through newly developed functional blocks supporting all delay variants and validated against representative heat transport scenarios. Comparative analysis demonstrates that standard signal-delay models violate energy conservation by generating spurious energy, whereas the proposed transfer-delay formulation preserves physical consistency under variable-flow conditions. The framework provides a rigorous foundation for accurate modeling of district heating networks, renewable energy integration with power-to-gas systems, thermal storage, and smart grid communications, supporting the development of reliable control strategies essential for the ongoing energy transition.