Session: 02-01 Intelligent Modeling and Predictive Analytics for Energy Systems

Paper Number: 174266

174266 - Data-Driven State of Charge Estimation for Thermal Energy Storage Using Hysteresis Modeling Enhanced Koopman State Observer 

Latent-heat thermal energy storage (LHTES) based on phase change materials (PCMs) has great potential for reducing energy cost for various applications in building, transportation and industrial sectors. For optimal system operation of PCM-LHTES based systems, estimation of the State of Charge (SoC) is critical. For PCM based LHTES, the SoC is defined as the portion of usable enthalpy in terms of the total enthalpy change throughout the phase-transition process. SoC is a convenient single-index variable that can ease the energy management for system operation. However, many types of high-capacity PCM bear strong nonlinearities and especially hysteresis, which implies intrinsic complexity for control and estimation. At the device level, PCM-based LHTES challenges SoC estimation with its nonlinear, distributed and time-varying characteristics. Sensor intensive solutions to SoC estimation would further make it cost prohibitive. Data-driven modeling approaches are an appealing pathway to meet such challenges.

In this work, a sensor-frugal data-driven SoC estimation approach is proposed for a one-dimensional PCM-LHTES device, which requires the information of only three measurements at the heat transfer fluid (HTF) side: flow rate, inlet temperature and outlet temperature. The approach is a two-step procedure. The first step is a Koopman-operator model based state observer for PCM temperature estimation, and the second step is a learning-based Preisach differential model for the hysteretic temperature-enthalpy mapping for PCM. The Koopman-operator model is a kernel based lifting framework for approximating nonlinear dynamic system to linear system of higher dimension state space. Koopman subspace model allows a global linearization for nonlinear dynamics, which allows the use of design and analysis tools for linear systems, thus enabling computationally efficient optimization, controls and estimation. Via model identification algorithms such as Extended Dynamic Mode Decomposition (EDMD), Koopman modeling paradigm can be easily coined into a data-driven nonlinear dynamic modeling framework. In this study, a Koopman-model based state observer is designed to estimate the PCM temperatures for discretized PCM volumes using a small set of measurements as indicated above.

Regarding the hysteretic temperature-enthalpy relation for PCM, the well-received Preisach model is considered with the machine learning perspective, for which the key respect is on the estimation of hysteron density function. While the quality of estimation with parametric Preisach modeling can be affected by the actual characteristics, non-parametric Preisach modeling offers more flexibility while it may suffer from the intrinsic discontinuity. Therefore, a differentiable non-parametric Preisach modeling method is adopted in this study, with which better computational efficiency can be obtained compared to other machine learning methods for hysteresis modeling.

To evaluate the proposed approach, simulation based study is conducted for a conceptual one-dimensional LHTES device recently developed by Lawrence Berkeley National Lab for the application of heat pump water heater based space heating. A Modelica based dynamic simulation model is develop with Dymola and the slPCMLib library. Simulation results show that the proposed method can achieve good SoC estimation. In particular, as for the data-driven hysteresis modeling for the PCM temperature-enthalpy relation, the proposed method demonstrates remarkable capability of generalization: with limited number of charging-discharging cycle for training, good validation results are obtained for charging-discharging cycles not encountered in the training process. Besides the computational advantages demonstrated in the state-observer design and learning for challenging nonlinear dynamics, the proposed method promises the possible avoidance for using temperature sensor array within the distributed PCM for SoC estimation, which is advantageous for cost-effective deployment.

Presenting Author: Yaoyu Li University of Texas At Dallas

Presenting Author Biography: Dr. Yaoyu Li is a Professor in the Department of Mechanical Engineering at University of Texas at Dallas. His research interests are controls, modeling and simulation for energy systems, including building HVAC and renewable energy, and energy storage. Dr. Li received his Ph.D. degree in mechanical engineering from Purdue University in 2004.