Switched Moving Boundary Modeling of Phase Change Thermal Energy Storage Systems

TL;DR

This work tackles the challenge of obtaining control-friendly models for phase change thermal energy storage by contrasting traditional fixed-grid (FG) representations with a switched moving boundary (MB) framework. The MB method employs a graph-based structure to model heat flows and a finite state machine to switch among four modes that capture freezing, melting, and fully solid/liquid states, using only six states and three PCM enthalpy variables plus SOC. Numerical results show the MB approach can reproduce FG behavior for complete freezing/melting cycles with SOC errors below about 0.05 and about five times faster run times; however, accuracy deteriorates in partial-freezing scenarios due to unmodeled geometrical complexity. The proposed method enables real-time, predictive control (e.g., MPC) of TES systems, and future work will validate experimentally, incorporate natural convection effects, and extend to three-dimensional geometries.

Abstract

Thermal Energy Storage (TES) devices, which leverage the constant-temperature thermal capacity of the latent heat of a Phase Change Material (PCM), provide benefits to a variety of thermal management systems by decoupling the absorption and rejection of thermal energy. While performing a role similar to a battery in an electrical system, it is critical to know when to charge (freeze) and discharge (melt) the TES to maximize the capabilities and efficiency of the overall system. Therefore, control-oriented models of TES are needed to predict the behavior of the TES and make informed control decisions. While existing modeling approaches divide the TES in to multiple sections using a Fixed Grid (FG) approach, this paper proposes a switched Moving Boundary (MB) model that captures the key dynamics of the TES with significantly fewer dynamic states. Specifically, a graph-based modeling approach is used to model the heat flow through the TES and a MB approach is used to model the time-varying liquid and solid regions of the TES. Additionally, a Finite State Machine (FSM) is used to switch between four different modes of operation based on the State-of-Charge (SOC) of the TES. Numerical simulations comparing the proposed approach with a more traditional FG approach show that the MB model is capable of accurately modeling the behavior of the FG model while using far fewer states, leading to five times faster simulations.

Figures (6)

• Figure 1: Fixed Grid modeling framework. LEFT: Cylindrical TES with inner and outer walls and the PCM divided into $n$ grid sections. TOP RIGHT: Identification of key radii used to model the 1-dimensional radial heat transfer. BOTTOM RIGHT: Graph-based FG model with $n$ PCM vertices.
• Figure 2: Computational comparisons of the FG and MB approaches. TOP: Time the model estimates for the PCM to completely freeze, $t_{freeze}$. MIDDLE: Computational time, $t_{comp}$. BOTTOM: Number of time steps taken with the ode23tb variable step solver, $n_{steps}$. All results are taken as an average over 50 simulations.
• Figure 3: Proposed MB modeling framework. LEFT: Cylindrical TES with inner and outer walls and the PCM divided into solid and liquid regions, with states $h_S$ and $h_L$, respectively. TOP RIGHT: Identification of key radii used to model the 1-dimensional radial heat transfer. BOTTOM RIGHT: Graph-based MB model with three vertices for the PCM.
• Figure 4: FSM with switching criteria for the four modes of the MB model.
• Figure 5: Differences between FG (with $n = 35$) and MB models for two complete freezing and melting cycles.