Modeling

Abstract

The optimization and control of energy systems represent a strategic challenge of major importance, both from an industrial and a scientific standpoint. With the continuous rise in energy demand, the pressing need for higher efficiency, and the global imperative to minimize environmental impact, it has become essential to develop advanced tools capable of effectively modeling, analyzing, and monitoring such systems. A robust model should not merely reproduce observed behavior; it must also accurately capture the system’s internal structure, thereby providing deep insight into its dynamic properties and internal interactions. Within this framework, structural analysis stands out as a rigorous and autonomous methodology, independent of exact numerical parameters. It enables the study of a system based solely on its topological configuration and interconnections, identifying measurable variables, computable variables, and those that remain inaccessible. This approach is particularly valuable for assessing the controllability and observability potential of a system before performing simulations or experimental tests. The first chapter of this work introduces the classical structural analysis approach. This method relies on a conventional mathematical representation—typically through differential or algebraic equations—that characterizes the system’s dynamic behavior. Although it provides a solid theoretical basis for understanding model logic, it may become less intuitive when applied to complex, multi-energy systems, where different energy domains interact simultaneously. To overcome these limitations, the Bond Graph formalism is introduced in the second chapter. This unified modeling language is founded on the principle of power exchange. Its major strength lies in its ability to describe multi-domain systems—electrical, mechanical, thermal, and hydraulic—within a single coherent framework. By explicitly defining energy flows and interconnection ports, this approach promotes a global and unified understanding of system operation and naturally extends toward structural analysis. The third chapter combines the Bond Graph formalism with structural analysis, forming a key integrative stage that merges the descriptive power of the Bond Graph with the analytical depth of the structural approach. This synergy enables the extraction of the model’s internal structure while preserving a comprehensive 6energetic perspective—an essential aspect for complex energy systems characterized by strong inter-subsystem interactions. Finally, the fourth chapter explores the concept of the degree of observability, a fundamental notion in control and supervision theory. Observability defines the ability to reconstruct a system’s internal state from its measurable outputs. Quantifying this property makes it possible to evaluate sensor performance, detect potential observability gaps, and design more efficient diagnostic and control strategies.