Simplified Physics-based Model Research Articles

A novel physics-based computational framework to model spacecraft solar array power under degradation: application to European Space Agency (ESA) Cluster mission

Accurate modeling and simulation (M&S) of spacecraft solar array power under degradation is essential for mission planning, remaining useful life assessment, and lifetime extension. A relevant example is ESA’s Cluster spacecraft fleet, launched in 2000 and operated at the European Space Operation Centre (ESOC), whose solar arrays have suffered severe degradation due to space radiation that has caused challenges to routine operations and mission planning. However, currently available physics-based and machine learning models have been proven ineffective in modeling the drastic reduction in power generation over the long operational life of the spacecraft.In response to these limitations, this work introduces a framework to model solar array degradation and predict power generation. It embeds a novel simplified physics-based model and a meta-heuristic optimization algorithm which exploits domain-specific knowledge and monitoring data for robust model parameter calibration and accurate power generation predictions. The results show the effectiveness of the proposed approach in avoiding overfitting and providing an accurate estimate of Cluster solar array power evolution.

Physics-guided federated learning as an enabler for digital twins

Digital twins bring the potential to increase the efficiency of assets, systems, and processes by building virtual replicas through real-time data and modeling. However, data are often confidential and distributed, high-fidelity models based on physical principles tend to be slow and require detailed knowledge about the asset design that may not be available, simplified models lack accuracy, and data-driven models are not interpretable and limited to their training space. We demonstrate the interplay of two enabling technologies, namely federated learning and hybrid analysis and modeling, to combine the strengths of physics-based and data-driven models on distributed data sets that are kept confidential by different stakeholders. Throughout the work, an ensemble of physics-guided neural networks is designed, optimized, and validated to infer the parameters of digital twin components. The physics-guided neural network is injected with output from a simplified physics-based model in intermediate layers for increased performance, and the injection layer is optimized through weight regularization. The model is then integrated into a simulation of the digital twin asset and validated there. It is shown that the model outperforms the simplified physics-based and the data-driven models both on component and on asset level. In the final step, the physics-guided neural network is trained using federated methods, which allows training on confidential data owned by different stakeholders without requiring the stakeholders to share their data. We show that federated hybrid models can – with the right training strategy – by design achieve results that are always identical and potentially superior to models trained on a central data set. The problem chosen for this demonstration is the prediction of airfoil lift and drag coefficients based on the airfoil shape and the angle of attack, which is a task crucial for simulating wind turbines. Using the physics-guided neural network, the estimation of the airfoil coefficients experiences a speedup of several orders of magnitude compared to the high-fidelity simulation, and integration into blade element momentum theory shows that the turbine thrust, torque, and mechanical power can be accurately calculated. The federated approach makes it possible to extend the training of the model to any number of distributed confidential data sets from both simulations and experiments to further increase the model’s accuracy.

An Analytical Model for Predicting the Rate Performance of Battery Cells Under Mixed Kinetic Control

The prediction of battery performance conventionally relies on resource-intensive numerical simulations based on the porous electrode theory. For computational speedup, simplified physics-based models have proven attractive as they still capture the underlying reaction mechanisms to a certain degree. In this class of models, physical complexity is usually reduced by assuming a single rate-limiting reaction. For example, the single particle model describes battery cells limited only by the solid diffusion pathway [1]. On the flipside, our previous analytical model exploited inefficiency of electrolyte transport, particularly in thick electrodes [2]. With advancement in both electrode and electrolyte technologies, however, it becomes challenging for these models to handle more realistic batteries.In this work, we propose an improved physics-based analytical model that enables mixed control of both kinetic processes, reflecting both salt depletion and particle size effect. An extension to our uniform reaction (UR) model, the new model uses salt distribution in electrolyte to probe the accessible lithium in the electrode level. The added solid diffusion module calculates the equilibrium potential at particle surface, lithium concentration at particle surface (Cs), and in turn the particle-level depth of discharge. We refer to the model as the URCs model, recognizing its two components. The model features higher tunability as it now accepts function-valued electrode and electrolyte properties. It also allows for prediction of discharge voltage curves and energy output of the cell.The model is compared with numerical simulation over a wide range of cell parameters. It shows good agreement with simulated results in rate performance test, specific energy output test, and discharge voltage curves. Better alignment is observed for the NMC/Li half cell than the NMC/Gr full cell, likely due to mixed reaction type in the graphite anode. Figure 1 shows the comparison of voltage curves across various C rates for a half cell with 70um NMC electrode and particles of 4um radius. Additionally, the cells are optimized for their specific capacity against electrode thickness and porosity. The optimal parameters predicted by the model lie closely to the global optimum from numerical simulation. Figure 2 shows the optimization results for a full cell with particles of 4um radius, overlaid on contour lines generated from the URCs model.The model offers a speed up of over 500 times compared with state-of-art P2D solvers [3]. Furthermore, its compatibility with gradient-based optimization algorithms opens possibilities for more efficient global optimization schemes, in which the number of function calls can be reduced. The high efficiency and the analytical nature of the URCs model render it a powerful tool for both on-board applications and battery cell design.[1] Doyle, M. and Newman, J., 1997. Analysis of capacity–rate data for lithium batteries using simplified models of the discharge process. Journal of Applied Electrochemistry, 27, pp.846-856.[2] Wang, F. and Tang, M., 2020. A quantitative analytical model for predicting and optimizing the rate performance of battery cells. Cell Reports Physical Science, 1(9).[3] Sulzer, V., Marquis, S.G., Timms, R., Robinson, M. and Chapman, S.J., 2021. Python battery mathematical modelling (PyBaMM). Journal of Open Research Software, 9(1). Figure 1

Simplified Physics-Based Battery Model for Stationary Energy-Storage Applications

To perform safe battery operation and avoid unnecessary degradation, battery models are needed. How complex, or close to reality the model should be, depends on the purpose of the model and the computational power available. The possibility for accurate parameterization before model implementation is another crucial aspect for the validity. Physics-based models have the advantage to solve for internal battery states, which includes important information to avoid accelerated degradation and to evaluate state of health. But the parameterization effort can be extensive and the computational cost too high to solve for in real time. Identifying the most essential processes and if possible, simplify the model is therefore motivated.Parameter sensitivity is a powerful tool to investigate how much certain parameters and the related processes effect the output signal, i.e. battery voltage. Under normal operating conditions the cells are rarely completely discharged, and as a result the diffusion processes show low sensitivity during operation [1]. In this work we therefore explore the utilization of a physics-based model solving for the electrolyte dynamics, rather than the solid phase diffusion commonly applied in the so-called single particle model. By neglecting the diffusion processes, the second dimension in the pseudo-two-dimensional (P2D) model can be ignored and the computational complexity simplified. The parameterization strategy and validation of the model is further discussed.We evaluate our model by comparing simulations with experimental data from batteries subjected to stationary energy storage applications. The cells are commercial 18650-type NMC/Graphite cells with 2.6 Ah capacity. Different service cycles have different needs in terms of current and voltage, see examples in Figure 1. Capturing these behaviours with a physics-based model might pose different challenges and will further affect the degradation of the cells [2]. A wide range of models exist in literature to capture degradation mechanisms during battery operation [3]. To keep the computational and parameterization effort as low as possible, our methodology is not to include more physics, but instead update the parameters to the processes already included in the model [4]. We explore this strategy comparing the behaviour from different types of services, as well as batteries where the application changes, to see the model response and analyse the battery state of health, see Figure 2. Electrochemical techniques such as differential voltage analysis and electrochemical impedance spectroscopy is included to support our conclusions.Our results highlight the value of application considerations when designing battery models, rather than only focusing on physical extreme points. We present an alternative physics-based model with the ability to capture crucial degradation phenomena and validate it against operational data. We believe our findings can be of value for smarter battery operating strategies and a greater understanding of application dependant lithium-ion battery degradation.Figure 1. Some of the application duty cycles part of the experimental study. a) Current profile peak shaving b) Current profile frequency regulation c) Voltage response peak shaving d) Voltage response frequency regulation.Figure 2. Degradation trends from the experimental study. Purple cell initially performing PS following application change to FR_high cycling a) Capacity evolution of the cycled cells b) tortuosity parameter evolution obtained from model parameter fitting c) Measured impedance response during cell reference performance tests d) Calculated charge transfer resistance from measured impedance data.

Predicting real-time roadway pluvial flood risk: A hybrid machine learning approach coupling a graph-based flood spreading model, historical vulnerabilities, and Waze data

Urban pluvial flash flooding (PFF), driven by extreme weather and urban expansion, introduces complex challenges that arise from the dynamic interaction of rainfall hazard, road vulnerability, and traffic exposure. These three critical components must be interconnected to provide a comprehensive prediction of roadway PFF risk. Our integrated approach combines historical data and real-time Waze flood alerts using a simplified physics-based PFF model and hybrid machine learning methods to predict flash flooding risk at the road segment scale. In a Dallas case study with four intersections, we trained multiple models with data from 15 storms and tested on 5 storms. The XGBoost method excels in test precision, while a Random Forest model offers better recall, and both methods outperform Support Vector Machines (SVM). The choice between models depends on factors such as negative class (prediction of unflooded areas) uncertainty and false positive cost (i.e., predicting no flooding incorrectly). For the case study, our approach could boost flood awareness, enhance safety, and improve urban flood management by correctly predicting 73% of risk observations during the test storm events.

A Hybrid Control-Oriented PEMFC Model Based on Echo State Networks and Gaussian Radial Basis Functions

The goal of increasing efficiency and durability of fuel cells can be achieved through optimal control of their operating conditions. In order to implement such controllers, accurate and computationally efficient fuel cell models must be developed. This work presents a hybrid (physics-based and data-driven), control-oriented model for approximating the output voltage of proton exchange membrane fuel cells (PEMFCs) while operating under dynamical conditions. First, a physics-based model, built from simplified electrochemical, membrane dynamics and mass conservation equations, is developed and validated through experimental data. Second, a data-driven, neural network (echo state network) is trained, fitted and tested with the same dataset. Then, the hybrid model is formed as a parallel structure, where the simplified physics-based model and the trained data-driven model are merged through an algorithm based on Gaussian radial basis functions. The merging algorithm compares the output of both single models and assigns weights for computing the prediction of the hybrid result. The proposed hybrid model structure is successfully trained, validated and tested with an experimental dataset originating from fuel cells within an automotive PEMFC stack. The hybrid model is assessed through the mean square error index, with the result of a low tracking error.

Detection and analysis of inner potential dynamics in vanadium redox flow batteries

The interconnectedness of the inner potential dynamics during the charge–discharge operation of a vanadium redox flow battery is studied by in-situ measurements of the through-plane potential distribution of the battery cell and the states of charge of the electrolytes. For a quantitative investigation, experimentally probed information is integrated and analyzed using simplified physics-based theoretical models, which collectively enable accurate detection and interpretatation of the inner potential dynamics from the individual components to the single-cell battery level. It has been demonstrated that this collective analysis makes quantifying the ohmic-kinetic and mass transport resistances of the electrodes possible. In particular, the sluggish transport of vanadium ions near the membrane interface of both electrodes leads to additional diffusion overpotential at the beginning of charging and discharging in the electrode. The membrane potentials, which can be detected experimentally, reflect highly coupled conditions of the electrolytes on both sides that affect the voltage of each electrode and the state of charges of the battery. This work demonstrates that unveiling the internal dynamics within a cell leads to an in-depth understanding of the charge–discharge behavior of vanadium redox flow batteries.

Neural Network Control of Green Energy Vehicles with Blended Braking Systems

A neural network-based control system is offered, which ensures high quality blended braking of the green energy vehicles in both the intensive and the gradual deceleration scenarios, with energy recovery at the changing road pavement. In this study, a neural network controller provides the torque gradient control without a tire model resulting in returning maximal energy to the hybrid energy source during the braking process. To meet the conflicting requirements of different braking modes and road surfaces, an allocation algorithm determines how to distribute the driver’s torque request between the friction and electrical brakes. Simulation demonstrates effectiveness of the proposed braking system. Model states and inputs are used as a guidance to learn a coupled two-layer neural network capable to capture various dynamic behaviours that could not be included in the simplified physics-based model. An experimental part of the research proves the model and simulation validity.

Optimal sensor placement for bridge structural health monitoring: Integration of physics-based models with data-driven approaches

Optimization of sensor configurations for cost-efficient structural health monitoring (SHM) plays a pivotal role in ensuring the safety and longevity of critical infrastructures such as bridges while minimizing maintenance expenses. Infrastructure systems may evolve over time, and their monitoring needs may change. Hence, the best sensor configuration must be designed to be scalable and adaptable to future requirements without major overhauls.The present work explores this optimization problem as an essential step of the development and implementation of a robust digital twinning strategy, by combining the strengths of physics-based models with data-driven insights. Conventional methods for sensor placement typically rely on expert knowledge, oftentimes resulting in suboptimal configurations and excessive installation costs. Conversely, physics-based models provide a rigorous comprehension of the structural behavior and can inform sensor placement procedures by assessing the impact of sensor locations on the monitoring accuracy. However, these models have limitations, such as simplifying assumptions, uncertainties, and computational complexities. To overcome these issues and upgrade the sensor placement process, data-driven approaches can be integrated to extract patterns, correlations, and unforeseen anomalies.To demonstrate the effectiveness and benefits of this hybrid framework, a case study of an existing bridge instrumented with sensors is presented. First, a simplified physics-based model is developed and calibrated through real-world data obtained from an extensive dynamic identification campaign comprising 108 instrumented degrees of freedom. Then, a reduced number of sensors are selected through a data-driven optimization strategy as best candidates for the deployment of a long-term monitoring system. Finally, the virtual model is employed to simulate varying damage scenarios and validate whether the sensor location experimentally identified as optimal would remain the best even when structural conditions change. The ultimate goal is to foster proactive maintenance strategies by striking a balance between data quality, sensor coverage, and SHM cost.

A multi-fidelity approach for reliability-based risk assessment of single-vehicle crashes

Road vehicles are highly susceptible to single-vehicle crashes (SVCs) under complex road geometry and inclement weather, which can significantly threaten traffic safety and mobility of the whole traffic system. Most existing studies involve various simplifications and approximations to assess the associated SVC risks promptly, and therefore the assessment accuracy is often compromised. A novel multi-fidelity approach is developed for the reliability-based risk assessment of SVCs to balance the simulation accuracy and efficiency. Specifically, a high-fidelity transient dynamic vehicle model is introduced for a robust estimation of the vehicle dynamics under various driving environments, assisted by a low-fidelity simplified physics-based vehicle model to improve the computational efficiency. Based on the simulations of the two models, a new multi-fidelity improved cross entropy-based importance sampling (MFICE) algorithm is proposed for integrating multi-fidelity information and facilitating accurate and efficient reliability analysis. Five demonstrative cases are studied to evaluate the performance of the proposed approach, including the comparison with existing representative approaches. The results show that the proposed innovative multi-fidelity approach can provide a reliability evaluation of SVCs both accurately and efficiently, with obviously superior performance over typical state-of-the-art counterparts. Therefore, the proposed approach bears great potential on developing proactive and near real-time intelligent traffic operation and management strategies against SVCs in both normal and hazardous conditions.

A simplified modelling approach for predicting shrinkage and sensitive material properties during low temperature air drying of porous food materials

Many food materials are dried to enhance shelf-life. Drying is an energy-intensive process, and accurate drying models could be used in real time process control of drying equipment to drive cost optimizations. However, most physics-based models suffer from two shortcomings: they require thermo-physical properties of the food materials to be known a priori, and they usually neglect material shrinkage due to moisture loss. In this work, we first develop a simplified physics-based transport model to predict temperatures and moisture content and corresponding spatial and temporal shrinkage during low temperature air drying process, where volumetric shrinkage is dominated by moisture loss. This model agrees well with experiments conducted by us (reported in this paper) as well as with those conducted by others (taken from the literature) on food samples. Further, using the validated modelling framework, we have developed an experimentally validated deep learning-based artificial neural network (ANN) model for properties' estimation. This ANN model is designed to estimate solid density, initial porosity, and initial water saturation of a given food material, using temperature and moisture data from a set of simple experiments with error less than 1%. Using these predicted parameters as input, the physics-based model can predict temperature and moisture for real-time drying to within 5% accuracy. The method proposed in this work could play an important role in industrial drying process optimisation and will find wide applications in the food processing industry. • A physics-based shrinkage model for low-temperature drying is developed. • A novel indirect method for property estimation is proposed. • Properties are estimated using a trained artificial neural network and simple experiments. • Modelling results are in excellent agreement with experiments.

SmartScan: An intelligent scanning approach for uniform thermal distribution, reduced residual stresses and deformations in PBF additive manufacturing

Parts produced by laser or electron-beam powder bed fusion (PBF) additive manufacturing are prone to residual stresses, deformations, and other defects linked to non-uniform temperature distribution during the manufacturing process. Several researchers have highlighted the important role scan sequence plays in achieving uniform temperature distribution in PBF. However, scan sequence continues to be determined offline based on trial-and-error or heuristics, which are neither optimal nor generalizable. To address these weaknesses, we have articulated a vision for an intelligent scan sequence optimization approach to achieve uniform temperature distribution, hence reduced residual stresses and deformations, in PBF using physics-based and data-driven thermal models. This paper proposes SmartScan, our first attempt towards achieving our vision using a simplified physics-based thermal model. The conduction and convection dynamics of a single layer of the PBF process are modeled using the finite difference method and radial basis functions. Using the model, the next best feature (e.g., stripe or island) that minimizes a thermal uniformity metric is found using control theory. Simulations and experiments involving laser marking of a stainless steel plate are used to demonstrate the effectiveness of SmartScan in comparison to existing heuristic scan sequences for stripe and island scan patterns. In experiments, SmartScan yields up to 41% improvement in average thermal uniformity and 47% reduction in deformations (i.e., warpage) compared to existing heuristic approaches. It is also shown to be robust, and computationally efficient enough for online implementation in the future.

Model correction and updating of a stochastic degradation model for failure prognostics of miter gates

Understanding the degradation of the quoin block is vital for failure prognostics in miter gates. Due to the complicated degradation mechanism, degradation models based on simplifications and assumptions cannot accurately describe the damage evolution. It is observed that small errors in a simplified degradation model can lead to a large discrepancy in the remaining useful life estimation attributed to error accumulation over time. Aiming to address this issue in failure prognostics, this paper presents a dynamic model correction framework for a simplified degradation model using strain measurements. In the proposed framework, a polynomial chaos expansion (PCE) model is employed to compensate the missing physics in a simplified stochastic degradation model. A maximum likelihood estimation method is developed to estimate the uncertain parameters of the simplified physics-based degradation model along with the unknown PCE model parameters using strain measurements as the observables. The updated damage degradation model is then applied to failure prognostics of a miter gate. Results of a case study show that the proposed approach can effectively improve the accuracy of failure prognostics in miter gates.

Quantifying the Tradeoff Between Energy Consumption and the Risk of Airborne Disease Transmission for Building HVAC Systems

It has been established that combinations of increased ventilation, improved filtration, and other HVAC techniques can reduce the likelihood of airborne disease transmission in buildings. However, with only qualitative guidance, it is difficult for building managers to make informed decisions. Furthermore, the possible actions almost always require additional energy consumption, which is generally not well characterized. To address this knowledge gap, we propose simplified physics-based models that can be used to quantify both the expected transmission rate and the associated energy consumption that result from HVAC system operation. By formulating all disinfection mechanisms in terms of “equivalent outdoor air”, a common basis is established for comparing and combining different strategies. The transmission rate can thus be modeled by considering the airborne concentration of infectious particles that would result from an infector in the space. Energy consumption is then estimated by considering the change in HVAC variables and applying standard analysis. To illustrate the insights provided by these models, we present examples of how the proposed analysis can be applied to specific spaces, highlighting the fact that underlying transmission risk and energy-optimal disinfection strategies can vary significantly based on space characteristics.

Neural Network-Based Model Reference Control of Braking Electric Vehicles

The problem of energy recovery in braking of an electric vehicle is solved here, which ensures high quality blended deceleration using electrical and friction brakes. A model reference controller is offered, capable to meet the conflicting requirements of intensive and gradual braking scenarios at changing road surfaces. In this study, the neural network controller provides torque gradient control without a tire model, resulting in the return of maximal energy to the hybrid energy storage during braking. The torque allocation algorithm determines how to share the driver’s request between the friction and electrical brakes in such a way as to enable regeneration for all braking modes, except when the battery state of charge and voltage levels are saturated, and a solo friction brake has to be used. The simulation demonstrates the effectiveness of the proposed coupled two-layer neural network capable of capturing various dynamic behaviors that could not be included in the simplified physics-based model. A comparison of the simulation and experimental results demonstrates that the velocity, slip, and torque responses confirm the proper car performance, while the system successfully copes with the strong nonlinearity and instability of the vehicle dynamics.

Using a CFD analysis of the flow capacity in a twin-entry turbine to develop a simplified physics-based model

The current paper presents a flow behaviour analysis of twin-entry radial turbines by means of experimental measurements and computational fluid dynamics (CFD) simulations. The experimental data were measured at partial, unequal and full admission conditions, and was used to globally validate CFD simulations. The experimental results hinted towards considering twin-entry turbines as two separated single-entry turbines working in parallel when used in simplified physics-based models such as in one-dimensional simulations. After analysing the CFD results, a simple flow capacity model was developed, exploiting some of the observed characteristic phenomena to reduce the number of fitting parameters to their minimum while keeping its accuracy and extrapolation capabilities.

Green Design Studio: A modular-based approach for high-performance building design

A modular-based Green Design Studio (GDS) platform has been developed in this study for fast and accurate performance analysis for early stage green building design. The GDS platform aims to simplify the design and analysis process by embedding performance parameters into design elements in modules and employing near-real-time model for whole building performance simulation as well as by providing an easy-to-use and intuitive user interface to assist users without extensive knowledge on building physics. The platform consists of building modules as fundamental building blocks, performance predicting models, and a user interface for visualization and interactive design. In the platform, a whole building is composed of modules organized in a hierarchical structure, including spaces, enclosures, service systems, sustainable resource systems and sites. Both physics-based and data-driven models can be used to simulate the building performance and optimize building systems. A simplified physics-based model, the Resistance–Capacitance (RC) model, has been proposed as a generic simulation model for the flows of heat, air, moisture and pollutants, which is significantly faster than conventional simulation tools such as EnergyPlus, and hence more practical for use in real-time design interaction and optimization. A pilot case study is conducted to illustrate the modular-based design approach using a section of an office building. Compared to conventional building performance analysis tools, the GDS platform can provide fast and reliable feedback on performance prediction for early design. The modular approach makes it easier to modify the building design and evaluate the potentials and contributions of various green design features and technologies.

Application of a physics-based lumped parameter model to evaluate reservoir parameters during CO2 storage

Evaluating reservoir performance could be challenging, especially when available data are only limited to pressures and rates from oil field production and/or injection wells. Numerical simulation is a typical approach to estimate reservoir properties using the history match process by reconciling field observations and model predictions. Performing numerical simulations can be computationally expensive by considering a large number of grids required to capture the spatial variation in geological properties, detailed structural complexity of the reservoir, and numerical time steps to cover different periods of oil recovery. In this work, a simplified physics-based model is used to estimate specific reservoir parameters during CO2 storage into a depleted oil reservoir. The governing equation is based on the integrated capacitance resistance model algorithm. A multivariate linear regression method is used for estimating reservoir parameters (injectivity index and compressibility). Synthetic scenarios were generated using a multiphase flow numerical simulator. Then, the results of the simplified physics-based model in terms of the estimated fluid compressibility were compared against the simulation results. CO2 injection data including bottom hole pressure and injection rate were also gathered from a depleted oil reef in Michigan Basin. A field application of the simplified physics-based model was presented to estimate above-mentioned parameters for the case of CO2 storage in a depleted oil reservoir in Michigan Basin. The results of this work show that this simple lumped parameter model can be used for a quick estimation of the specific reservoir parameters and its changes over the CO2 injection period.

On the Round-Trip Efficiency of an HVAC-Based Virtual Battery

Flexible loads, especially heating, ventilation, and air-conditioning (HVAC) systems can be used to provide a battery-like service to the power grid by varying their demand up and down over a baseline. Recent work has reported that providing virtual energy storage with HVAC systems leads to a net loss of energy, akin to a low round-trip efficiency (RTE) of a battery. In this paper, we rigorously analyze the RTE of a virtual battery through a simplified physics-based model. We show that the low RTEs reported in recent experimental and simulation work are an artifact of the experimental/simulation setup. When the HVAC system is repeatedly used as a virtual battery, the asymptotic RTE is 1. Robustness of the result to assumptions made in the analysis is illustrated through a simulation case study.

A novel approach for modelling thermal energy storage with phase change materials and immersed coil heat exchangers

A novel modelling approach is presented for a thermal energy storage system with immersed coil heat exchangers. The energy store consists of a water tank in which rectangular phase change material (PCM) modules are submerged. The immersed coil heat exchangers are placed at the bottom and top sections of the tank for charging and discharging, respectively. This design promotes thermal mixing inside the tank when charged from the bottom coil and discharged from the top coil. In addition, the location of the coil heat exchangers favorably limits the heat transfer when charged through the top coil or discharged through the bottom coil giving rise to the thermal diode effect. PCMs can offer large storage capacity since they store large amounts of thermal energy in the form of latent heat of phase change (solid-liquid). This paper proposes a simplified physics-based numerical model of the heat transfer and phase change in the thermal storage tank. The model discretizes the storage tank one-dimensionally into three fully-mixed control volumes; two control volumes surrounding the immersed coil heat exchangers and one control volume in the middle of the tank including the PCM modules. All the heat transfer dynamics between the control volumes, the heat exchangers and the PCM modules are considered. Experimental validations, using a full-scale test facility, are carried out for systems with and without PCMs under various operation scenarios and the results are found to agree well within the experimental uncertainties. Such model potentially provides high computational efficiency that is desirable in simulating the performance of storage systems under long-term operations.