Thermal Sub-models Research Articles

Virtual Plug-In Hybrid Concept Development and Optimization under Real-World Boundary Conditions

The automotive industry faces development challenges due to emerging technologies, regulatory demands, societal trends, and evolving customer mobility needs. These factors contribute to a wide range of vehicle variants and increasingly complex powertrains. The layout of a vehicle is usually based on standardized driving cycles such as WLTC, gradeability, acceleration test cases, and many more. In real-world driving cycles, however, this can lead to limitations under certain boundary conditions. To ensure that all customer requirements are met, vehicle testing is conducted under extreme environmental conditions, e.g., in Sweden or Spain. One way to reduce the development time while ensuring high product quality and cost-effectiveness is to use model-based methods for the comprehensive design of powertrains. This study presents a layout methodology using a top-down approach. Initially, powertrain-relevant requirements for an exemplary target customer are translated into a specification sheet with specific test cases. An overall vehicle model with detailed thermal sub-models is developed to evaluate the different requirements. A baseline design for a C-segment plug-in hybrid vehicle was developed as part of the FVV research project HyFlex-ICE using standardized test cases, highlighting the influence of customer profiles on the design outcome through varying weighting factors. The target customer’s design is analyzed in four real driving scenarios, considering variations in parameters such as the ambient temperature, traffic, driver type, trailer pulling, and battery state-of-charge, to assess their influence on the target variables. In the next step, the potential of hardware technologies and predictive driving functions is examined in selected driving scenarios based on the identified constraints of the baseline design. As a result, four application-specific technology packages (Cost neutral, Cold country, Hot country, and Premium) for different customer requirements and sales markets are defined, which, finally, demonstrates the applicability of the holistic methodology.

Co-estimation of state-of-charge and state-of-temperature for large-format lithium-ion batteries based on a novel electrothermal model

The safe and efficient operation of the electric vehicle significantly depends on the accurate state-of-charge (SOC) and state-of-temperature (SOT) of Lithium-ion (Li-ion) batteries. Given the influence of cross-interference between the two states indicated above, this study establishs a co-estimation framework of battery SOC and SOT. This framwork is based on an innovative electrothermal model and adaptive estimation algorithms. The first-order RC electric model and an innovative thermal model are components of the electrothermal model. Specifically, the thermal model includes two lumped-mass thermal submodels for two tabs and a two-dimensional (2-D) thermal resistance network (TRN) submodel for the main battery body, capable of capturing the detailed thermodynamics of large-format Li-ion batteries. Moreover, the proposed thermal model strikes an acceptable compromise between the estimation fidelity and computational complexity by representing the heat transfer processes by the thermal resistances. Besides, the adaptive estimation algorithms are composed of an adaptive unscented Kalman filter (AUKF) and an adaptive Kalman filter (AKF), which adaptively update the state and noise covariances. Regarding the estimation results, the mean absolute errors (MAEs) of SOC and SOT estimation are controlled within 1% and 0.4 ​°C at two temperatures, indicating that the co-estimation method yields superior prediction performance in a wide temperature range of 5–35 ​°C.

A Comprehensive Energy Model for an Optimal Design of a Hybrid Refrigerated Van

The path towards decarbonization requires a progressive adaptation of all refrigeration systems, but only stationary ones have been intensely studied to improve their environmental performance. However, refrigerated transport is vital in the cold chain and must be considered in the green transition. In this paper, we propose a model for a hybrid refrigerated van that includes photovoltaic panels and electric batteries to decrease total greenhouse gas emissions from the engine. Thermal, electrical, and battery sub-models are considered and integrated into the comprehensive hybrid solar-powered refrigerated van model. Different technologies are compared, including lithium and lead-acid batteries and three different types of photovoltaic panels. The model was validated regarding van fuel consumption, showing a 4% deviation. Single and multiple delivery scenarios are considered to assess the energy, economic, and environmental benefits. Monthly CO2,e emissions could be reduced by 20% compared to a standard refrigerated van. Despite the environmental benefits provided by this sustainable solution, the payback period is still too long (above 20 years) because of the necessary investment to adapt the vehicle and considering fuel and electricity prices currently.

A Three-Heat-Source Electro-Thermal Coupled Model for Fast Estimation of the Temperature Distribution of a Lithium-Ion Battery Cell

Temperature inconsistency is inevitable during the battery operation, which has a significant impact on its performance. To quickly predict the temperature distribution in a battery cell, a three-heat-source electro-thermal coupled model is proposed in this article. The temperature of four feature regions in a battery cell can be determined in short time, which is potential to be implemented online. In addition, the distributed equivalent circuit model is proposed to calculate the heat generated by different heat sources. To identify the parameters of the electrical and thermal submodels, the experimental test bench is established, and the parameterizations under different conditions are carried out. In addition, the transient parameters, including the internal resistance and entropy coefficient, are adjusted with different state of charges (SOCs) and temperature. Finally, the validity and robustness of the proposed model are demonstrated through various tests of different operating conditions. The results illustrate that the uneven surface temperature distribution of the battery cell can be estimated fast, in less than 1 s. The error deviation of the proposed model is less than 1.4 °C under different conditions.

Advanced Monitoring and Prediction of the Thermal State of Intelligent Battery Cells in Electric Vehicles by Physics-Based and Data-Driven Modeling

Novel intelligent battery systems are gaining importance with functional hardware on the cell level. Cell-level hardware allows for advanced battery state monitoring and thermal management, but also leads to additional thermal interactions. In this work, an electro-thermal framework for the modeling of these novel intelligent battery cells is provided. Thereby, a lumped thermal model, as well as a novel neural network, are implemented in the framework as thermal submodels. For the first time, a direct comparison of a physics-based and a data-driven thermal battery model is performed in the same framework. The models are compared in terms of temperature estimation with regard to accuracy. Both models are very well suited to represent the thermal behavior in novel intelligent battery cells. In terms of accuracy and computation time, however, the data-driven neural network approach with a Nonlinear AutoregRessive network with eXogeneous input (NARX) shows slight advantages. Finally, novel applications of temperature prediction in battery electric vehicles are presented and the applicability of the models is illustrated. Thereby, the conventional prediction of the state of power is extended by simultaneous temperature prediction. Additionally, temperature forecasting is used for pre-conditioning by advanced cooling system regulation to enable energy efficiency and fast charging.

A Novel Method for Thermal Modelling of Photovoltaic Modules/Cells under Varying Environmental Conditions

Temperature has a significant effect on the photovoltaic module output power and mechanical properties. Measuring the temperature for such a stacked layers structure is impractical to be carried out, especially when we talk about a high number of modules in power plants. This paper introduces a novel thermal model to estimate the temperature of the embedded electronic junction in modules/cells as well as their front and back surface temperatures. The novelty of this paper can be realized through different aspects. First, the model includes a novel coefficient, which we define as the forced convection adjustment coefficient to imitate the module tilt angle effect on the forced convection heat transfer mechanism. Second, the new combination of effective sub-models found in literature producing a unique and reliable method for estimating the temperature of the PV modules/cells by incorporating the new coefficient. In addition, the paper presents a comprehensive review of the existing PV thermal sub-models and the determination expressions of the related parameters, which all have been tested to find the best combination. The heat balance equation has been employed to construct the thermal model. The validation phase shows that the estimation of the module temperature has significantly improved by introducing the novel forced convection adjustment coefficient. Measurements of polycrystalline and amorphous modules have been used to verify the proposed model. Multiple error indication parameters have been used to validate the model and verify it by comparing the obtained results to those reported in recent and most accurate literature.

Nonlinear State and Parameter Estimation for Li-ion Batteries with Thermal Coupling

Advanced Lithium-ion battery management systems rely on accurate cell-level state of charge (SOC) and parameter estimation for safe and efficient real-time monitoring. However, the design of combined state and parameter estimators that are provably convergent is notoriously difficult. A robust observer framework based on a coupled equivalent circuit-thermal model for a cylindrical battery is proposed. The coupled model also takes into account SOC and temperature-dependent electrical parameters for higher accuracy. In the literature, the model parameters are often treated as constants to simplify model structure and observer analysis. The problem considered in this work is particularly challenging due to (i) nonlinear two-way coupling between electrical and thermal sub-models, and (ii) nonlinear dependence of model parameters on the system states. A single aggregated observer for both SOC and thermal estimation becomes intractable due to lack of convergence certification caused by complex model coupling. We tackle this problem by proposing a sequential estimation scheme such that every sub-estimator converges separately, which is mathematically verified by Lyapunov stability analysis. Simulation results demonstrate the performance of the proposed state and parameters estimation framework.

An improved resistance-based thermal model for a pouch lithium-ion battery considering heat generation of posts

An improved three-dimensional thermal model for a pouch battery is established, which seamlessly integrates two thermal sub-models of the battery body and the current collecting posts, taking the heat generated in both the battery and the current collecting posts into account. The thermal sub-model of the battery body considers the effects of the state of charge (SOC), battery temperature, and current rate on heat generation. The thermal sub-model of the posts is based on the identified post resistance and the contact resistance, which is employed to calculate the temperature evolution of the posts. Then, the thermal model is applied to predict thermal evolutions of the pouch Li-ion battery at different ambient temperatures and discharge rates. Extensive experiments are conducted to prove that the proposed model can accurately capture thermal behaviour under different conditions, with a maximum average error of 1.23 K. In addition, comparative studies show that this model significantly outperforms an existing typical counterpart, namely a model whose heat generation estimation only depends on the state of charge.

Extensive analysis of photovoltaic battery self-consumption: Evaluation through an innovative district case-study

Energy storage is one of the key elements within the actual stage of the energy transition, as it is probably one of the most important factors to allow high penetration of fluctuating renewable energies, such as wind or solar, in the existing power systems. Intensive research is being conducted to assess the economic aspects and technical performance of renewable energy-based systems supported by batteries by evaluating different services that batteries can provide to the electric grid or to the end-consumers. In Germany, where the majority of the currently installed 43 GW of PV capacity corresponds to small residential, commercial, or industrial facilities, an interesting market for batteries to enhance local self-consumption and autarky is already booming, with more than 80 000 storage system installations in 2017. In this context, this study presents a comprehensive analysis of the photovoltaic battery model by analyzing the technical and economic consequences that variations on the most relevant system parameters induce. The presented results are based on high resolution data obtained from a representative residential district with an autarky of above 95%. The employed battery model is based on the results obtained through an extensive test campaign and includes electrical and thermal sub-models. The analysis predicts that grid parity of residential PV battery systems can be reached in the upcoming years, with especially great potential of the retrofitting market for those PV installations which run out of the feed-in tariff policy.

Integration of Optical and Thermal Models for Organic Light-Emitting Diodes

This paper proposes a three-dimensional model for combinative analysis of the illuminative and thermal properties of organic light-emitting diodes (OLED). By means of the energy conversion ratio and energy conservation theory, two individual optical and thermal sub-models are integrated to form a single model constructed in a multi-physics platform. According to the measured luminous performance and temperature distribution of the fabricated OLED samples, the proposed model demonstrates sufficient accuracy. Moreover, the temperature distribution on the cross-section of the OLED can be derived from the proposed model and used as a valuable reference for manufacturers to select appropriate organic materials.

Modeling of a District Heating System and Optimal Heat-Power Flow

With ever-growing interconnections of various kinds of energy sources, the coupling between a power distribution system (PDS) and a district heating system (DHS) has been progressively intensified. Thus, it is becoming more and more important to take the PDS and the DHS as a whole in energy flow analysis. Given this background, a steady state model of DHS is first presented with hydraulic and thermal sub-models included. Structurally, the presented DHS model is composed of three major parts, i.e., the straight pipe, four kinds of local pipes, and the radiator. The impacts of pipeline parameters and the environment temperature on heat losses and pressure losses are then examined. The term “heat-power flow” is next defined, and the optimal heat-power flow (OHPF) model formulated as a quadratic planning problem, in which the objective is to minimize energy losses, including the heat losses and active power losses, and both the operational constraints of PDS and DHS are respected. The developed OHPF model is solved by the well-established IPOPT (Interior Point OPTimizer) commercial solver, which is based on the YALMIP/MATLAB toolbox. Finally, two sample systems are served for demonstrating the characteristics of the proposed models.

A thermo-elasto-hydrodynamic model for air foil thrust bearings including self-induced convective cooling of the rotor disk and thermal runaway

A 3D thermo-elasto-hydrodynamic model for air foil thrust bearings (AFTBs) is presented. A detailed shell model is applied for the foils. The deformation of the rotor disk is modeled by axisymmetric Navier-Lamé equations taking into account thermal expansion effects. The pressure in the lubricating gap of the AFTB is calculated by the Reynolds equation and the temperature by a 3D energy equation. Particular emphasis is put on detailed thermal submodels for the bearing parts. An analytic formula is presented for the effective thermal resistance of the bump foil incorporating thermal contact resistances between the bump foil and the top foil as well as between the bump foil and the base plate. The self-induced cooling flow at the backside of the rotor disk is modeled by appropriate boundary layer equations including an eddy viscosity turbulence model. The heat flux through the tight gap between the outer part of the disk and the housing is accounted for as well. The presented model is used to reveal thermal features of AFTBs. The main finding is that load capacity increases with rotor speed only up to a critical value, above which load capacity is even found to decrease with increasing speed. This thermal runaway is proved to originate from a thermally induced bending of the disk that leads to an unfavorable gap function. Furthermore, experimentally observed beneficial effects on unit load capacity of AFTBs - as for example a forced cooling flow and a reduced number of pads - are successfully reproduced by the presented model. Finally, the relative magnitude of the different heat fluxes occurring in AFTBs is analyzed in detail.

A modified approach for numerical simulation of capillary tube-suction line heat exchangers

This paper presents a modified approach for numerical simulations of capillary tube-suction line heat exchangers (CTSLHE). This approach is based on an approximate solution methodology previously presented. This methodology models the expansion process separately from the heat transfer process, giving rise to two sub-models, namely hydrodynamic and thermal sub-models. In the present paper, a two-step predictor–corrector model is proposed, one for the refrigerant mass flux and another for the refrigerant enthalpy path. Simulation results of mass flow rate and suction line outlet temperature were compared with experimental data, empirical correlations and well ranked distributed models. The simulation results showed good agreement with experimental data, with almost all mass flow rate results were within ±20% error bands and most suction line outlet temperature results within ±5°C. Reasonable agreement was observed when the predicted results of mass flow rate, critical pressure and suction line outlet temperature were compared against the results from well ranked literature numerical models. Both, the influence of the capillary tube inner diameter and the suction line inner diameter over performance parameters were also investigated. No convergence problems were observed during the simulations.

Development of Software for the Simulation of Rolling Steel Under the Coexistence of Liquid and Solid State / Rozwój Oprogramowania Do Symulacji Walcowania Stali W Warunkach Współistnienia Fazy Ciekłej I Stałej

The paper presents the results of the application simulating the rolling process of steel in terms of coexistence of liquid and solid phases. The created mathematical models can be the basis for creation of systems that simulate the final phase of the continuous casting process relying on using a roller burnishing machine for continuous casting of steel. For a complete description of the performance of the material during deformation in these conditions, the constructed mathematical model is a fully three-dimensional model and consists of three parts: thermal, mechanical, and density variation submodels. The thermal model allows the prediction of temperature changes during plastic deformation of solidifying material. The mechanical model determines the kinetics of plastic continuum flow in the solid and semi-solid states, and the resulting deformation field. The temperature of the process forces supplementing the description of the performance of the material with a density variation model that allows the prediction of changes in the density of the material during the final phase of solidification with simultaneous plastic deformation. For the purpose built model, experimental studies were performed using a physical simulator Gleeble 3800®. They allowed the determination of the necessary physical properties of the metal within the temperature of change state. In addition to presenting the developed models the work also includes the description of the author’s application that uses the above mathematical models. The application was written in the fully object-oriented language C++ and is based on the finite element method. The developed application beside the module data input, also consist of a module of three-dimensional visualization of the calculations results. Thanks to it, the analysis of the distribution of the particular rolling parameters in any cross-section of the rolled strip will be possible. The paper presents the results of the authors’ research in the area of the advanced computer simulation.

A lumped-parameter electro-thermal model for cylindrical batteries

Combining several existing lumped-parameter models, this paper presents an electro-thermal model for cylindrical batteries. The model consists of two sub-models, an equivalent-circuit electrical model and a two-state thermal model which are coupled through heat generation and temperature dependence of the electrical parameters. The computationally efficient 5-state model captures the state of charge (SOC), terminal voltage, surface temperature and the often neglected core temperature of a battery for wide range of operating conditions. The proposed parameterization scheme allows separate identification of the electric and thermal sub-models, greatly reducing the complexity of the parameterization process. The methodology is applied to a LiFePO4/graphite battery. Comparison with the electrochemical impedance spectroscopy data clarifies the frequency range of the model fidelity. The model is further validated with two drive-cycle tests, covering SOC range 25%–100%, temperature 5 °C–38 °C, and maximum C-rate of 22C.

Mathematical Model of Thermal and Microstructural Evolution during Austempering of Ductile Iron

Austempering of ductile iron is a heat treating process designed to improve the mechanical properties of ductile iron: Increasing its strength and wear resistance while maintaining the tenacity and ductility associated with the untreated condition. This task is achieved by rapidly cooling the part from the austenitizing temperature to the austempering temperature and holding it during a specific time. Austempering promotes the formation of an ausferrite matrix, i.e., a mixture of bainitic ferrite and retained austenite, along with graphite nodules. In order to achieve the required microstructural control, a detailed knowledge of the phase transformation evolution coupled with a heat transfer analysis is required. Thus a thermostructural model has been developed to simulate the phase transformations during austempering of a ductile iron cylindrical probe. The thermal and microstructural submodels were coupled within the Abaqus software. The predictions were validated by austempering ductile iron probes from an austenitizing temperature of 920°C to an austempering temperature of 300°C in a molten salt bath and comparing predictions versus experimental data. It was concluded that the model is suitable to predict the thermal behavior and the final microstructure of the austempered ductile iron.

Hierarchical thermal analysis of large IC modules

This paper presents a new approach to hierarchical thermal modeling using libraries of parametrized sub-models. It is demonstrated how to efficiently create thermal sub-models based on a parametrized model reduction technique. These sub-models are then used for fast simulation of complex parts using a hierarchical modeling building methodology that nests sub-models within sub-models. As an example of such a model parametrized thermal sub-models of a GaAs power cell, an integrated GaAs microwave power amplifier and an InP optical modulator are generated. A complete module is then built by attaching these sub-models to detailed models in a hierarchical manner, creating a thermal model of the entire system. This methodology allows a quick thermal analysis to be performed of very large systems. The thermal sub-models are small in size, boundary condition independent, have very short simulation times, and predict with high accuracy (better then 2% error) all internal temperatures. Finally, the optical modulator model is used as example of the computational efficiency of the methodology. Although an absolute speed-up is difficult to define two cases were provided with gains of around 30 to 40 times calculated. System memory requirements were also reduced by a factor of three.

Pseudo bond graphs of circulating Fluids with application to solar Heating design

Two different bond-graph schemes for the modeling of circulating fluids are discussed and compared. The first uses a heuristic approach wherein the flow path is broken into segments. Each segment has separate hydraulic and thermal submodels which are linked with active bonds. The model is general enough to handle natural convective flows, heat storage, conduction, forced convective heat transfer and heat energy sources. The second method, applicable to pumped flows, uses a modal analysis approach to derive state equations for the modal temperatures, the time varying coefficients of the spatially varying mode shapes in a separation of variables solution for the temperature partial differential equation. Two examples are worked to illustrate the models. Numerical simulation results are presented using the first method and a simple analytic solution given to illustrate the second.