Thermal-electrical Model Research Articles

Analysis of the Effect of Thermal Runaway Initiation Conditions on the Severity of Thermal Runaway—Numerical Simulation and Machine Learning Study

The main goal of this work is to understand the effect of thermal runaway initiation conditions on the severity of thermal runaway (TR) of Graphite—NMC (111) cells. A coupled electrical-thermal model is developed, which includes the initial energy input, the chemical decomposition processes of the anode, cathode and the electrical energy released by an internal short circuit. 780 different thermal runaway events are simulated and the output is analysed by machine learning techniques such as principal component analysis and clustering. It was found that TR events form 5 clusters between no thermal runaway and severe thermal runaway. Sensitivity analysis is applied on the 39 input invariants and the triggering energy input, resistance ratio, the heat convection coefficient, the ratio of activation energy of oxygen liberation and electrolyte evaporation are found to be the most important parameters. The later one determines the amount of electrolyte combustion. The probability of thermal runaway is calculated taking into account the most important parameters and their interactions. Finally, a combination of initiation parameters is suggested, which most likely results in a repeatable and reproducible outcome.

Dynamic piezo-thermoelectric generator for simultaneously harvesting mechanical and thermal energies

In recent decades, the development of eco-friendly technology has attracted tremendous attention due to the energy crises and environmental issues in modern society, especially for the enhancement of energy efficiencies and the energy harvesting of secondary or waste energies. Conventional approaches in the energy recovery of industrial waste heat mainly focus on heat scavenging, whereas the kinetic energy is neglected. Nonetheless, mechanical/kinetic energy harvesting of the heating fluid has a critical effect on the power density improvement of waste energy utilization. Herein, a dynamic piezo-thermoelectric generator (dPTEG) prototype is designed and fabricated based upon the Brayton cycle system and demonstrated for the simultaneous harvesting of low-grade mechanical and thermal energies. In this dPTEG, radial PVDF-based piezoelectric generators (PEG) and annular Bi2Te3-based flexible thermoelectric generators (TEG) are used to simultaneously utilize the mechanical and thermal energies of working fluids. PEG and TEG energy converters are optimized from energy flow and thermal-electrical equivalent circuit model perspectives to illustrate the mechanical-thermal-electrical coupling of piezo-thermoelectric energy recovery. The length-specific power of the dPTEG with series and parallel connections of 55 μW/cm and 19 μW/cm, respectively, are achieved under steady-state flow (473 cm3/s and 4 K temperature difference). Moreover, the series and parallel electrical outputs are improved by 35% and 158%, respectively, compared with traditional single TEG energy conversion under similar working conditions. These results indicate that the dPTEG presented here offers a feasible solution to utilize the low-grade mechanical/thermal energy and industrial waste heat of heating fluids. Additionally, the long-time stability and reliability evaluation of the dPTEG further verifies the potential application of this system in day/night environments with multi-range temperatures and flow rates.

Management of the Output Electrical Power in Thermoelectric Generators

Thermoelectric Generators (TEGs) are devices for direct conversion of heat into electrical power and bear a great potential for applications in energy scavenging and green energy harvesting. Given a heat source, the conversion efficiency depends on the available temperature difference, and must be maximized for optimal operation of the TEG. In this frame, the choice of materials with high thermoelectric properties should be accompanied by the identification of criteria for an optimal exploitation of the electrical power output. In this work, we briefly review the main properties of TEGs, focusing on the electrical power output and the thermal-to-electrical conversion efficiency. Besides, we discuss principles of operation of TEGs enabling the optimization of the electrical power output, based on the suitable choice of the electrical load. In particular, we comparatively present and discuss the conditions for matching the electrical load—yielding to maximum power transfer—and those for maximizing the conversion efficiency. We compare the two conditions applying them to the exploitation of a heat reservoir for energy storage and to the recovery of heat from a heat exchanger. We conclude that the difference between the two conditions is not significant enough to justify the complexity required by the implementation of the maximum efficiency. In addition, we consider the effect of the thermal contact resistance on the electrical power output. Using a simple thermal-electrical model, we demonstrate that the equivalent electrical resistance measured between the terminals of the TEG depends on the thermal exchange. Hence, for maximum power transfer, the electrical load of the TEG should not match its parasitic resistance, but the equivalent electrical resistance in each specific operating conditions, which determine the thermal fluxes. The model can be applied for the development of efficient alternative algorithms for maximum power point tracking.

Coupled Thermal-Mechanical Progressive Damage Model with Strain and Heating Rate Effects for Lightning Strike Damage Assessment

This paper proposes a progressive damage model incorporating strain and heating rate effects for the prediction of composite specimen damage resulting from simulated lightning strike test conditions. A mature and robust customised failure model has been developed. The method used a scaling factor approach and non-linear degradation models from published works to modify the material moduli, strength and stiffness properties to reflect the effects of combined strain and thermal loading. Hashin/Puck failure criteria was used prior to progressive damage modelling of the material. Each component of the method was benchmarked against appropriate literature. A three stage modelling framework was demonstrated where an initial plasma model predicts specimen surface loads (electrical, thermal, pressure); a coupled thermal-electric model predicts specimen temperature resulting from the electrical load; and a third, dynamic, coupled temperature-displacement, explicit model predicts the material state due to the thermal load, the resulting thermal-expansion and the lightning plasma applied pressure loading. Unprotected specimen damage results were presented for two SAE lightning test Waveforms (B & A); with the results illustrating how thermal and mechanical damage behaviour varied with waveform duration and peak current.

Coupled electrical-thermal modelling of photovoltaic modules under dynamic conditions

This paper presents a coupled electrical-thermal model for solar photovoltaic (PV) modules, under an unsteady state and various conditions, including ambient temperature, solar radiation and wind velocity. Validation shows that the electrical and thermal models present high agreement with the experimental data. The developed model after validation is then applied to investigate the distribution of thermal resistance, the influence of environmental conditions and cooling methods. Results show that the radiative and convective thermal resistances play a significant role in PV electrical-thermal performance, while conductive thermal resistance can be neglected for simplification in some cases. The results also demonstrate the effects of weather conditions including solar radiation, ambient temperature and wind velocity on PV performance vary and they need to be selected carefully during parameters design. Moreover, a dynamic estimation of different seasons and a long-term evaluation of an entire year for a specific PV array have been done to assess the performance of the coupled model. The simulated results are in good agreement with the experimental data in spite of the weather conditions, in which the relative errors of daily energy in four different seasons are just 1.06%–6.17%, while the average monthly energy based on the proposed model (1185.4 kWh) only deviates 4.66% from that extracted by PVsyst software (1132.6 kWh), which both verify the accuracy of the proposed model again.

Thermal damage analysis of aircraft composite laminate suffered from lightning swept stroke and arc propagation

Lightning strike is a complicated process involving multi-field coupling. In order to investigate the thermal damage mechanism of carbon fiber reinforced composites subject to lightning swept stroke, a complete numerical method is presented. Numerical model of lightning discharge is established based on Magneto Hydro Dynamics (MHD) and calculated by FLUENT secondary development technology. Considering aerodynamic flow effect, channel formation and evolution process during lightning discharge is analyzed for lightning current waveform A. Thermal-electric Coupling model is presented according to Radial Basis Function (RBF) interpolation theory, which is implemented by compiling program to make lightning current and heat energy inject into composite laminate. Consequently, damage mechanism of composite laminate under lightning swept stroke is studied based on the coupled numerical model and element deletion method. Ablation damage morphology of composite laminate is analyzed to understand plasma expansion and reattachment in arc root. The results show that aerodynamic flow makes the lightning channel move fast and composite laminate is deteriorated due to thermal damage.

3-D Thermal-Electric Finite Element Model of a Nb3Sn Coil During a Quench

High field superconducting magnets for particle accelerators often exhibit premature quenches. Once a normal zone is generated within the conductor, the quench may propagate causing temperature and resistive voltage rise along the coil. The resulting thermal gradients can potentially cause new peak stresses that might exceed the tolerable limits, degrading the conductor. The computation of the strain state in the coils during quench then becomes of paramount importance for magnet design, and requires a complete three-dimensional (3-D) analysis of quench phenomena. The objective of this paper is to present the first multiphysics modeling activities towards a new full 3-D methodology for the analysis of magnet mechanics during quench. As a first step, a 3-D thermal-electric finite element model of a Nb 3 Sn superconducting coil is developed and explained here. The model uses direct coupled-field elements to solve the system of thermal and electrical equations. A solving algorithm has also been implemented in order to investigate the physics behind quench transients. The output from this model, built in ANSYS APDL, can be easily coupled in a later stage to a mechanical model in order to estimate the strain state in the coil windings. A very good agreement has been observed between the numerical results and experimental tests performed in individual superconducting cables and real superconducting magnets.

Sequential finite element modelling of lightning arc plasma and composite specimen thermal-electric damage

Highly complex phenomena such as lightning strikes require simulation methods capable of capturing many different physics. However, completing this in one simulation is not always desired or possible. In such instances there can be a need for a methodology to transfer loading boundary conditions from one simulation to the next while accounting for the characteristic form of the loading and the dissimilar domain and mesh geometries. Herein, the objective is to combine two models to enable the automatic sequential simulation of a lightning arc and a composite test specimen. The approach is developed using Finite Element models, with a Magnetohydrodynamics model representing the lightning plasma and a thermal-electric model representing the specimen. The specimen mesh and loading boundary conditions are automatically generated based on the predicted output of the preceding plasma model. The precision, run-time and flexibility of the proposed approach is demonstrated, with thermal damage predictions generated in approximately 33 h. Resulting from the integrated modelling capability is the first time prediction of damage representing the test electric boundary conditions rather than assumed specimen boundary conditions (herein using test ‘Waveform B’).

Investigation into effects of non-uniform irradiance and photovoltaic temperature on performances of photovoltaic/thermal systems coupled with truncated compound parabolic concentrators

This work concerns a type of efficient and promising solar energy utilization systems namely concentrating photovoltaic/thermal (CPV/T) systems. In CPV/T systems, uneven irradiance and PV temperature introduced by concentrators cause a rise in ohmic loss, decrease in PV fill factor and electrical efficiency, and local hot spot. Thus, the objective of this work is to develop a two-dimensional optical-thermal-electrical coupled model to predict PV temperature distribution and investigate effects of non-uniform irradiance and temperature on performance of linear concentrating CPV/T systems. Firstly, rays tracing of two kinds of truncated compound parabolic concentrators (CPCs) with different concentration ratios was simulated by TracePro to obtain their irradiance profiles. These two kinds of CPCs were designed and defined as HEMR and LEMR respectively in our previous work. Then, rays tracing results namely non-uniform irradiance distributions functioned as the inputs of a two-dimensional electrical-thermal coupled model developed by FORTRAN to obtain temperature distribution of PV array and performances of CPV/T systems. Meanwhile, a CPV/T prototype was set up to validate the theoretical results. The degrees of illumination and PV temperature non-uniformity were weighed based on the concept of standard deviation. Ultimately, the effects of non-uniform irradiance and temperature on performances of the CPV/T system were investigated with different concentration ratios. Results revealed that with a rise in concentration ratio, irradiance and PV temperature non-uniformity in the case of LEMR concentration experience a rapider increase than those in the case of HEMR concentration. Correspondingly, with increasing concentration ratios, both the fill factor and the electrical efficiency in the case of LEMR concentration experience a rapider decrease than those in the case of HEMR concentration. When the concentration ratio was 8, compared to HEMR concentration case, non-uniformity of irradiance and PV temperature in the case of LEMR concentration is increased by 63.1% and 65.7% respectively; the fill factor and the electrical efficiency in the case of LEMR concentration are decreased by 2.6% and 2.1% respectively.

Material Flow Based Power Demand Modeling of an Oil Refinery Process for Optimal Energy Management

Oil refining is an energy-intensive industry, that is often equipped with different types of distributed generation (DG) resources. Optimal energy management of the refinery's load and its DG resources, under dynamic electricity pricing, improves electricity consumption behavior of the facility and hence reduces its energy costs. An energy management system (EMS) model is proposed in this paper for minimizing electricity consumption costs of an oil refinery facility considering on-site cogeneration capability. The energy management is based on power demand modeling of the oil refinery process. A joint electrical–thermal model is used for the cogeneration units to account for the electricity and steam production. The developed EMS model is also used as part of a demand response strategy to illustrate the impact of EMS decisions on distribution system operations.

Computational modelling approach for the optimisation of a pulsed electric field system for liquid foods

The microbial inactivation and specific energy of a pulsed electric field treatment system are dependent on the electric field distribution and treatment time since they have opposite behaviour in relation to these parameters, featuring a problem of multi-objective optimisation. This study proposes a computational methodology capable of providing Pareto optimal solutions for these two objectives, using a coupled electrical-thermal model, solved by COMSOL, which has been integrated to a multi-objective algorithm NSGA-II implemented in MatLab. The simulations were run for a computational design of experiment with the following variables: applied voltage, treatment time and the internal electrode radius (three levels for each one). In the post-processing analysis, the Pareto curves were plotted for two typical microorganisms of grape juice: E. coli and S. aureus, providing a set of solutions in terms of the log of the survival rate versus the specific energy. The methodology enables the decision maker to select the best solution from the Pareto curves as a function of a required microbial inactivation and energy features.

Non-isothermal Ragone plots of Li-ion cells from datasheet and galvanostatic discharge tests

Ragone plot is a conventional tool to compare different energy storage systems in terms of energy and power densities. The selection of the most suitable Li-ion technology for a given application is usually based on the specific energy and power extracted from datasheets at ambient temperatures (25 °C). However, these values are highly temperature-dependent. This study investigates experimentally and via numerical simulations a quantification of the energy and power densities for two different Li-ion chemistry cells in a wide operating temperature range. The experimental results reveal that these values determined from constant current discharge are approximately 15% higher than those determined for a constant power discharge. Therefore, a simple and efficient coupled electrical–thermal model based on an equivalent circuit model (ECM) is proposed, which is able to estimate the voltage, temperature, and available discharged energy of 18,650 Li-ion cells with a good accuracy. Moreover, all parameters in the model can be directly identified with manufacturer’s datasheets at 25 °C. Then, the proposed Ragone plot model can be extended to wider temperature and power ranges. The relative error of the simulated energy density is below 2% for both technologies for all operating conditions from – 20 °C to 55 °C. Thus, a non-isothermal Ragone plot is established by considering the thermal effect for the first time. The proposed method could be employed as a conception aid tool for the selection of Li-ion cells in a system design process.

Stability modeling of the LHC Nb-Ti Rutherford cables subjected to beam losses

The Large Hadron Collider (LHC) at CERN is being prepared for its full energy exploitation during run III, i.e., an increase of the beam energy beyond the present 6.5 TeV, targeting the maximum discovery potential attainable. This requires an increase of the operating field of the superconducting dipole and quadrupole magnets, which in turn will result in more demanding working conditions due to a reduction of the operating margin while the energy deposited by particle loss will increase. Beam-induced magnet quenches, i.e., the transition to normal conducting state, will become an increasing concern, because they could affect the availability of the LHC. It is hence very important to understand and be able to predict the quench levels of the main LHC magnets for the required values of current and generated magnetic fields. This information will be used to set accurate operating limits of beam loss, with sufficient but not excessive margin, so to achieve maximal beam delivery to the experiments. In this study we used a one-dimensional, multistrand thermal-electric model to analyze the maximum beam losses that can be sustained by the LHC magnets, still remaining superconducting. The heat deposition distribution due to the beam losses is given as an input for the stability analysis. Critical elements of the model are the ability to capture heat and current distribution among strands, and heat transfer to the superfluid helium bath. The computational model has been benchmarked against energy densities reconstructed from beam-induced main dipole quenches during LHC operation at 6.5 TeV. The model was then used to evaluate the stability margin of both main dipole and main quadrupole magnets at different beam energies, up to the expected ultimate operating energy of the LHC, 7.5 TeV. The comparison between the quench levels underlines how the increase of beam energy implies a substantial reduction of magnets stability and will require much stricter setting on the allowable beam losses to avoid resistive transitions during operation.

Design and development of a multi-winding high-frequency magnetic link for grid integration of residential renewable energy systems

Recent advances in magnetic material characteristics and solid-state semiconductors have provided the feasibility of replacing the electrical buses with the high-frequency multi-winding magnetic links in small-scale renewable energy systems. This effectively reduces the number of conversion stages and improves the system’s efficiency, cost, and size. Other advantages are galvanic isolation between the ports, bidirectional power flow capability and flexibility in energy management and control. Despite the advantages, design and development of the multi-winding magnetic links is relatively complex and based on computationally expensive numerical methods. Furthermore, the non-sinusoidal nature of voltage and currents, high-frequency parasitic effects and nonlinearity of magnetic material characteristics increase the design complexity. In this paper, the reluctance network modeling as a fast analytical method is used to design a three winding magnetic link. The core and copper losses of the designed component are evaluated taking into account duty ratio, amplitude and phase shift of the non-sinusoidal excitation voltage and currents. The thermal analysis is carried out using an accurate thermal-electric model. A prototype of the magnetic link was developed for application in a residential renewable energy system using amorphous magnetic materials. A set of experimental tests are conducted to measure the electrical parameters, magnetic characteristics, core loss, copper loss and temperature rise of the designed component and the results are compared to the specifications to validate the design procedure.

A Modeling Approach for Time-Dependent Geometry Applied to Transient Heat Transfer of Aluminum Electrolysis Cells

The thermal balance of aluminum electrolysis cells (AEC) have to be rigorously controlled in order to improve the efficiency and sustainability of this industrial process. A new modeling strategy is developed to consider the displacements of solid bodies and moving boundaries in finite element models. The transient thermal-electric modeling of the AEC demonstrates the effect of an increase in operating voltage on both the anode cover and the side ledge. With higher heat generation, the anode cover deteriorates and the side ledge thickness decreases. Since the anode cover is characterized by irreversible transformations, the top heat dissipation remains higher even when the operating voltage comes back to its typical value. For the first time, the transient temperature and electric fields throughout the anode life are simulated and validated by industrial measurements. The modeling predictions have been validated from instrumented anodes and manual measurements, all performed on operating AEC.

Condition Monitoring of IGBT Modules Based on Changes of Thermal Characteristics

Condition monitoring (CM) of insulated-gate bipolar transistor (IGBT) modules is significant for improving power converter reliability and reducing the loss caused by IGBT failure. In this paper, we present an advanced method to evaluate the aging condition of an IGBT based on the changes of thermal characteristics in the module, which can be described by the junction and case temperatures. The variation of the case temperature distribution is used to monitor the solder fatigue. The estimated level of solder fatigue is used to update the parameters in the electrical-thermal model. Then, the junction temperature can be accurately estimated by the updated electrical-thermal model. The difference between junction temperatures estimated from the updated model and temperature-sensitive electrical parameter (TSEP) is utilized to monitor the aging of bond wires. The proposed CM method permits both of health level evaluation and accurate junction temperature estimation of IGBT in real time to prevent catastrophic failure caused by defective modules. The experimental results on a commercialized IGBT product have validated the feasibility of the proposed method.

Improved heat transfer modeling of the top of aluminum electrolysis cells

Abstract A thermal-electric model is developed using finite elements and thoroughly validated against thermal measurements performed in industrial aluminum electrolysis cells (AEC). Knowledge about the geometries of anode cover material (ACM) and anode crust is improved by measuring their profiles in industrial cells. Moreover, the shape of the cavity formed by the melting of the anode crust is predicted with the numerical model, using a radiosity module combined to an iterative method. The thermal conductivity and the emissivity of both ACM and anode crust are also evaluated based on experimental measurements. The thermal-electric model accurately predicts the measurements obtained from heat flux sensors and thermocouples installed on industrial anodes. Modeling results show that increasing the ACM thickness reduces the top heat losses and increases the heat dissipation from the side, while the bottom losses remain constant. With thicker top insulation, the side ledge shrinks and the anode crust melts. The impact of a film of sludge under the liquid aluminum is quantified with the model. Accordingly, the sludge increases the cathode voltage drop (CVD), enlarges the cavity, reduces the side ledge thickness and amplifies the side heat dissipation. The thermal-electric modeling provides insights to improve the design and operation of AEC in order to reach higher efficiency.

Investigation on the nonlinear thermal-electrical properties coupling performance of converter transformer

Thermal state and insulation ability of converter transformer are significant to evaluate condition, while the impacts of nonlinear thermal-electric coupling impact are often ignored in the design analysis, and might result in misestimating its actual performance. In this paper, a bilateral thermal-electric coupling method is proposed to investigate the thermal and insulation performance of converter transformer on basis of an actual size. In addition, the influence of non-uniform temperature on the overall winding losses and the nonlinear thermal-electric coupling of insulation system are considered. Firstly, the thermal-electrical parameters coupling characteristics of insulation system in converter transformer are investigated based on the built experimental platform. Results indicate that temperature distribution would change the electrical performance all the time, while electrical-dependent characteristic of oil increases with electric field in U type curve. Then, the impact of non-uniform temperature is discussed based on the built bilateral thermal-electric coupling model, and it is proved that temperature would decrease obviously in considering the losses calculated by bilateral coupling. Finally, the nonlinear thermal-electric coupling performance of converter transformer is studied. It indicates that comprehensive factors of temperature dependence and electric filed dependence have great influences on the insulation properties. Significantly, the electric field of pressboard would decrease by 12.8% under hybrid voltage condition.

Steady state electrical–thermal coupling analysis of TSV* * Project supported by the National Natural Science Foundation of China (Nos. 61574106, 61574104), the National Defense Pre-Research Foundation of China (No. 9140A23060115DZ01062), and the Key Science and Technology Special Project of Shaanxi Province (No. 2015KTCQ01-5).

This paper presents a blended analytical electrical–thermal model for steady state thermal analysis of through-silicon-via (TSV) in three-dimensional (3D) integrated circuits. The proposed analytical model is validated by the commercial FEM tool—COMSOL. The comparison between the results of the proposed analytical formulas and COMSOL shows that the proposed formulas have very high accuracy with a maximum error of 0.1%. Based on the analytical model, the temperature performance of TSV is studied. Design guide lines of TSV are also given as: (1) the radius of the TSV increases, the resistance decreases and the temperature can be increased; (2) the thicker the dielectric layer, the higher the temperature; (3) compared with carbon nanotube, the Cu enlarges the temperature by 34 K, and the W case enlarges the temperature by 41 K.

Integrated Dispatch Model for Combined Heat and Power Plant With Phase-Change Thermal Energy Storage Considering Heat Transfer Process

Combined heat and power (CHP), with its limited flexibility, is one of the leading causes for the curtailment problem of variable renewable energy source (VRES) in Northern China. To increase the flexibility for CHP, thermal energy storage (TES) is considered to be an effective solution, and a phase-change TES demonstration pilot project is now being constructed in Northern China. Almost all the previous studies have modeled the TES device without considering the heat transfer process, which is a main constraint in thermal system analysis. Thus, in this contribution, we consider the heat transfer process for the phase-change TES device installed in a CHP plant based on the steam's three-stage heat transfer model and the entransy dissipation-based thermal resistance theory. An integrated electrical-thermal dispatch model concerning conventional thermal units, VRESs, and CHP units with phase-change TES device is given, and an iteration method for solving this nonlinear programming problem is proposed. Case studies show that it is vital to consider the heat transfer process in the modeling of CHP plant with phase-change TES device, and it has significant influence on the flexibility that the TES device can provide when the working conditions vary.