# A Lumped-Parameter Model of Multiscale Dynamics in Steam Supply Systems

## TL;DR

This paper develops a simplified lumped-parameter model for multiscale steam supply system dynamics, capturing slow and fast processes, and validates it through theoretical analysis and numerical comparison with detailed simulations.

## Contribution

It introduces a physically-derived lumped-parameter model that preserves multiscale dynamics and provides a theoretical basis for separating short-term and long-term system operations.

## Key findings

- The model accurately captures multiscale dynamics of steam systems.
- Existence of a normally hyperbolic invariant manifold confirms the model's validity.
- Quantitative comparison shows the model's predictions align with detailed simulations.

## Abstract

This paper focuses on multiscale dynamics occurring in steam supply systems. The dynamics of interest are originally described by a distributed-parameter model for fast steam flows over a pipe network coupled with a lumped-parameter model for slow internal dynamics of boilers. We derive a lumped-parameter model for the dynamics through physically-relevant approximations. The derived model is then analyzed theoretically and numerically in terms of existence of normally hyperbolic invariant manifold in the phase space of the model. The existence of the manifold is a dynamical evidence that the derived model preserves the slow-fast dynamics, and suggests a separation principle of short-term and long-term operations of steam supply systems, which is analogue to electric power systems. We also quantitatively verify the correctness of the derived model by comparison with brute-force simulation of the original model.