Thermal Equivalent Circuit Model Research Articles

Temperature Field Calculation and Thermal Circuit Equivalent Analysis of 110 kV Core Cable Joint

In order to indirectly calculate the core temperature of a cable joint, an equivalent transient thermal circuit model of single-core cable joint by considering axial heat dissipation is proposed. Firstly, the temperature field of the middle joint of a 110 kV single-core cable is calculated by finite element method. Based on the heat dissipation path of the core, an improved equivalent thermal circuit model is proposed. The axial heat dissipation of the cable joint core is simplified to a thermal resistance and the temperature rise of the cable body core, the temperature calculation of the cable joint transient process is realized. Compared with the results of finite element simulation, the steady-state temperature errors of the thermal circuit model are within 1 °C, while the maximum temperature errors of the transient process shall not exceed 3 °C, which proves the validity of the model. This method can provide reference for temperature inversion and the dynamic current-carrying capacity prediction of cable joints.

Real-Time Temperature Prediction of Power Devices Using an Improved Thermal Equivalent Circuit Model and Application in Power Electronics.

As a core component of photovoltaic power generation systems, insulated gate bipolar transistor (IGBT) modules continually suffer from severe temperature swings due to complex operation conditions and various environmental conditions, resulting in fatigue failure. The junction temperature prediction guarantees that the IGBT module operates within the safety threshold. The thermal equivalent circuit model is a common approach to predicting junction temperature. However, the model parameters are easily affected by the solder aging. An accurate temperature prediction by the model is impossible during service. This paper proposes an improved thermal equivalent circuit model that can remove the effect of solder aging. Firstly, the solder aging process is monitored in real-time based on the case temperatures. Secondly, the model parameters are corrected by the thermal impedance from chip to baseplate based on the linear thermal characteristic. The simulation and experimental results show that the proposed model can reduce the temperature prediction error by more than 90% under the same aging condition. The proposed method only depends on the case temperatures to correct the model parameters, which is more economical. In addition, the experimental and simulation analysis in this work can help students of power electronics courses have an in-depth knowledge of power devices' mechanical structure, heat dissipation principles, temperature distribution, junction temperature monitoring, and so on.

Electromagnetic-thermal co-optimization to minimize case-to-winding temperature rise in permanent magnet machines

Electrification of aerospace platforms requires efficient heat dissipation from electric machines to meet their temperature requirements while minimizing the weight and size of the onboard thermal management system. It is critical to couple available electromagnetic design optimization approaches with complementary thermal models, so that these thermal management system objectives can be considered, namely to reduce the temperature rise between the sources of heat generation and coolant. In this work, a thermal equivalent circuit model for the stator of a permanent magnet synchronous machine is developed and validated. The thermal network includes a discretization of individual conductors and considers their placement within a slot, compared to previous approaches that assumed a lumped/homogenized representation that is not versatile for robust optimization. The temperature predictions reveal that the choice of conductor sizing and packing within the stator slot significantly affects their peak temperatures. After validation, the thermal model is coupled to an electromagnetic model to perform multi-physics multi-objective design that minimizes machine mass and the temperature rise between the conductors and coolant. This approach contrasts a traditional electromagnetic design trade off between loss and mass. Design studies were performed to generate Pareto-optimal designs for comparison between these objectives. By using the co-optimization design framework with an integrated thermal objective function, the machine operating temperature can be significantly reduced while delivering the same power density at the cost of machine efficiency. The detailed machine designs are analyzed to explain the thermal advantages of the co-optimization design.

Study on temperature rise characteristics of DC charging cable for electric vehicles

In order to accurately calculate the relationship between the loading current and temperature rise of DC charging cable of electric vehicles, this article establishes the equivalent thermal circuit model of DC charging cable of electric vehicle based on the thermal circuit model analysis method, and refers to the principle of adaptive filtering, proposes a method to derive the thermal circuit model parameters of DC charging cable of electric vehicle from the actual temperature rise data, and designs a comparison experiments to verify the accuracy of the thermal circuit model of DC charging cable obtained by this method. The experimental results show that the calculation temperature rise and actual temperature rise error of the EV charging cable thermal circuit model obtained by deriving from the actual temperature rise data in this article is small, which verifies that the EV DC charging cable thermal circuit model obtained by this method has a certain accuracy in analyzing the temperature rise of this type of cable.

A Generic Approach to Simulating Temperature Distributions within Commercial Lithium-Ion Battery Systems

Determining both the average temperature and the underlying temperature distribution within a battery system is crucial for system design, control, and operation. Therefore, thermal battery system models, which allow for the calculation of these distributions, are required. In this work, a generic thermal equivalent circuit model for commercial battery modules with passive cooling is introduced. The model approach can be easily adopted to varying system designs and sizes and is accompanied by a corresponding low-effort characterization process. The validation of the model was performed on both synthetic and measured load profiles from stationary and marine applications. The results show that the model can represent both the average temperature and the occurring temperature spread (maximum to minimum temperature) with deviations below 1 K. In addition to the introduced full-scale model, further simplifying assumptions were tested in order to reduce the computational effort required by the model. By comparing the resulting simplified models with the original full-scale model, it can be shown that both reducing the number of simulated cells and assuming electrical homogeneity between the cells in the module offer a reduction in the computation time within one order of magnitude while still retaining a high model accuracy.

Optimization of the thermal management system of battery thermal network model based on coupled liquid cooling of phase change materials

Battery optimization models can extend battery life, improve safety, and maximize battery performance. Previous optimization methods focus more on (Computational Fluid Dynamics) CFD and data mining. However, the two optimization methods apply only to specific battery module structures. In addition, previous studies have focused more on improving optimization algorithms to improve performance, but the computational design of large-scale battery thermal management systems still requires large loads. This paper presents a new optimization method based on the thermal equivalent circuit model (TECM) of battery thermal management system (BTMS) for the efficient design of liquid-cold coupled phase change material BTMS (PCM). The method can easily change and optimize the battery module structure according to different application scenarios. Compared with the reference structure, the TECM Parto solution optimized combined with multi-objective particle swarm optimization (MOPSO) saved 39.51 % of the liquid cooling energy consumption, reduced the maximum temperature rise of BTMS by 0.38 °C, and reduced the maximum temperature difference by 19.81 %. The method adopted can improve the efficiency and quality of BTMS design, reduce the cost of trial and error, and speed up the design process.

Modeling and Analysis of Aluminum Cable Joints in Steady State for New Energy Stations

Compared with copper cables, aluminum cables have certain advantages in engineering costs and transportation costs, but have installation difficulties in the application process. However, limited by the manufacturing process, installation technology, and operating conditions, the intermediate joint of the aluminum cable is prone to failures such as insulation deterioration caused by abnormal temperature. The temperature of the core of the conductor in a steady state in the cable joint is the most direct and effective physical quantity, which can reflect the operating state. So modeling and analysis of the aluminum cable joint, as well as the study of its internal temperature change mechanism and influencing factors, are to improve the process and installation level of the aluminum cable joint and to develop the basis of the corresponding temperature monitoring system. In this paper, the thermal conduction mechanism of aluminum cable joints in a steady state is analyzed by using the thermal circuit theory. Then, the thermal circuit model of aluminum cable joints in a steady state based on the equivalent thermal circuit model and its parameter calculation method are proposed. By building an experimental platform, the validation experiment finally proved the accuracy of the method proposed in this paper.

Thermal Equivalent Circuit Model and Parameter Estimation for High-Capacity Li-Ion Cell

The equivalent circuit model (ECM) has gained popularity as a simplified and computationally efficient battery model. However, an appropriate model is required to accurately calculate terminal voltage, state of charge (SOC), and temperature for high-capacity Li-ion batteries used in hybrid electric and electric vehicles. In this study, we integrate the ECM with an energy balance model to calculate the cell temperature. Furthermore, we propose improved model structures and parameter estimation strategies to effectively characterize high-capacity batteries. First, the actual SOC is calculated considering the actual discharge capacity. Second, as the current increases, the overcalculated resistance is corrected. Finally, ECM parameters are estimated using experimental data and the genetic algorithm (GA). To facilitate the parameter-search process for GA, we employ the dimensionless scale-up method and the Pareto optimal concept. The thermal ECM is validated using experimental data from 57.6 Ah batteries, demonstrating voltage and temperature calculation errors of less than 1.71% and 3.51%, respectively.

Thermal Modeling and Prediction of The Lithium-ion Battery Based on Driving Behavior

Real-time monitoring of the battery thermal status is important to ensure the effectiveness of battery thermal management system (BTMS), which can effectively avoid thermal runaway. In the study of BTMS, driver behavior is one of the factors affecting the performance of the battery thermal status, and it is often neglected in battery temperature studies. Therefore, it is necessary to predict the dynamic heat generation of the battery in actual driving cycles. In this work, a thermal equivalent circuit model (TECM) and an artificial neural network (ANN) thermal model based on the driving data, which can predict the thermal behavior of the battery in real-world driving cycles, are proposed and established by MATLAB/Simulink tool. Driving behaviors analysis of different drivers are simulated by PI control as input, and battery temperature is used as output response. The results show that aggressive driving behavior leads to an increase in battery temperature of nearly 1.2 K per second, and the average prediction error of TECM model and ANN model is 0.13 K and 0.11 K, respectively. This indicates that both models can accurately estimate the real-time battery temperature. However, the computational speed of the ANN thermal model is only 0.2 s, which is more efficient for battery thermal management.

Performance and experimental investigation for a novel heat storage based thermoelectric harvester for hypersonic vehicles

Health monitoring systems for hypersonic vehicles, based on plenty of sensor nodes, are of great importance to improve safety and reliability, and are limited by power supply because of extra wire mass or cost of batteries changing. Energy harvester is one of the potential solutions. In this study, a novel energy harvesting device including thermoelectric generators, heat storage units, and electrical storage units is proposed. The thermal equivalent circuit model is developed, and the accuracy of that is verified by principle experimental. The effects of device parameters on the performance are investigated and optimized. The supply capacity of the device during actual flight is evaluated. The results show that the electrical storage unit can improve the lifetime by 33% of the device even with a lower output power. Optimal values exist for the volume fraction of PCMs in the HSU which is influenced by the dimension and power consumption. The ideal PCMs are those with low melting point and large latent heat of melting. The optimized device can provide more than 2.5 W of power output repetitively without maintenance, which matches the power level of wireless sensors, and offers a unique powering solution for health monitoring systems.

Variable duty cycle heating strategy based online two-dimensional model for self-heating lithium-ion battery

It is a challenge to online obtain the time-varying temperature distribution of self-heating lithium-ion battery (SHLB), which results in a lack of theoretical basis for heating strategies to optimize heating time and temperature distribution uniformity. To reveal the evolution of temperature distribution and improve the temperature distribution uniformity of SHLB during heating, a variable duty cycle heating strategy with online two-dimensional model is proposed. Distributed thermal equivalent circuit model coupled with electrical model can obtain the two-dimensional temperature distribution of battery in real-time. The results show that the maximum temperature gap between the proposed model and the finite element model (FEM) is only 1.2 °C, while 90 % of the calculation time is saved. The proposed model can calculate the temperature distribution almost as accurately as FEM under different conditions. Based on the proposed model, heating currents of different values and duty cycles are applied to investigate their effects on the temperature distribution evolution of SHLB. Finally, we propose a variable duty cycle heating strategy that can automatically switch the duty cycle of the heating current according to the heating uniformity requirements in order to consider both heating time and the temperature distribution uniformity. The results show that compared with constant duty cycle heating, the variable duty cycle heating strategy can reduce the temperature difference by 35 % and limit the temperature difference to the pre-set boundary. The proposed strategy and method have considerable potential for use as improved temperature uniformity in battery management system.

Analysis and optimization of temperature field of high-speed permanent magnet motor

High-speed permanent magnet motor (HSPMM) has a wide application prospect in machinery, energy, and other industries. The temperature field of HSPMM was analyzed and optimized in order to reduce the operating temperature and improve the service life and efficiency. Two new methods were proposed to reduce the copper loss and iron loss. Response surface method was employed to improve permanent magnet parameters. The response surface results demonstrate that then factor A is 7.7 mm, factor B is 5.0 mm, and factor C is 134.9°, the core loss is minimum with 32.91 W. On the premise of comprehensively considering the thermal convection, conduction, and radiation effects, the equivalent thermal circuit model of HSPMM was creatively established. The theoretical analysis data show that the temperature of each position of the optimized motor is reduced by 8.2°C–10.2°C. In order to verify the correctness of the above theoretical analysis, a temperature measuring experiment was conducted. The temperature error between the measured data and the theoretical calculation data is acceptable, and the average error is only 4.01%. The research methods and conclusions can be widely extended to the temperature field optimization of other permanent magnet motors.

Consideration of graphene material in PCM with aluminum fin structure for improving the battery cooling performance

Phase change material (PCM) based battery thermal management system (BTMS) provides even heat distribution and lower maximum temperature, but it suffers from low thermal conductivity. In this study, the impact of graphene additive on PCM was analyzed by presenting three experiments with various structures to solve PCM's low thermal conductivity problem. The results demonstrate that there is no positive impact of graphene additive in the first and third structures. The PCM-graphene additive between the second structure's fins significantly improves the battery heat transfer by allowing the battery to cool down 1500 seconds earlier than the graphene-free structure. Moreover, a thermal equivalent circuit model was derived for the second structure because of its enhanced performance. It is shown that the model works accurately and proves its ability to control not only temperature fluctuations but also transient behavior of the battery. This model provides that the battery temperature can be analyzed without experimentation for different charge-discharge scenarios in lithium-ion batteries with a shorter computation time.

Differential heat-flow-type warmth sensor for object material discrimination with reduced sensor output error due to object temperature

This paper presents a differential heat-flow-type warmth sensor for highly accurate material discrimination by robots. In the previous study, we demonstrated a warmth sensor that identifies the material of a contacted object by its heat-flow-peak value. However, the previous heat-flow-type warmth sensor had a sensor output error in which the heat-flow-peak value changed depending on the temperature of the contacted object. In the present effort, to reduce the sensor output error, we propose a differential-type sensor composed of the two warmth sensors, based on the thermal equivalent circuit. First, the transient thermal equivalent circuit model was simulated to confirm the principle that it cancels the sensor output error. Then, a differential heat-flow-type warmth sensor with dimensions of 10.0 × 24.0 × 5.0 mm3 was fabricated by integrating two warmth sensors with thermal insulators. Finally, experimental results successfully demonstrated that the sensor output error can be reduced to − 0.17 mW/°C or less, which is almost 1/16 the error of the previous sensor.

A Thermal Circuit Representing Frequency Dependent Dynamic Heating Between Electron and Lattice in SOI-FinFET

A thermal circuit model that represents dynamic heating between electron and lattice at different frequencies has been demonstrated here. The model is effective for circuit based predictive simulations of the phenomenon as found in scaled metal-oxide-semiconductor field effect transistor (MOSFET), where electron heating substantially impacts its electrical characteristics including hot carrier reliability. High field or frequencies of the input signal as in the case of radio frequency (rf) MOSFET restrict heat transfer from electron to the lattice due to weak energy relaxation via low energy acoustic phonons, as a result soon a thermal non-equilibrium is established whose thermal equivalent circuit representation is not known until now. T-CAD based hydrodynamic-thermodynamic (HD-TD) modeling though can extract electron and lattice temperatures employing their detail energy balance relations, yet its numerical solver is cumbersome. In this context, we found that numerical complexities can be reduced without compromising generality, if heating between electron and lattice would be represented by an equivalent thermal circuit model with physically justified circuit elements, which would be valid over a frequency band of the input signal till the isothermal frequency where self-heating is a concern. In this context, from detail thermodynamic principle we calculated electron thermal capacitance, resistance and thermal inductance those were incorporated to the existing standard thermal circuit model. The new model was furthermore validated employing a calibrated 14 nm SOI-FinFET.

Fast identification method for thermal model parameters of Lithium-ion battery based on discharge temperature rise

An accurate thermal model of lithium-ion battery is extremely important for the safe operation of electric vehicles. The entropy coefficient is a key thermal characteristic of the battery, which is usually measured in advance. However, traditional measurement methods require a long test time or expensive equipment. In this paper, a novel thermal model parameter identification method with fast and continuous entropy coefficient identification is proposed, in which thermal parameters are obtained with lower time and equipment costs. First, a lumped thermal equivalent circuit model is established to describe the dynamic behaviors of battery temperature. Second, the thermal model parameters are identified based on experiments and calculations. The entropy coefficient is calculated based on temperature rise responses with different discharge currents. Finally, the identification results of the entropy coefficient are compared with traditional methods, which are found to be in good agreement. Furthermore, the thermal models are thoroughly verified under both galvanostatic discharge tests and dynamic profiles over the temperature range from 0 °C to 40 °C. Three kinds of thermal models with different entropy coefficient treatments are compared in terms of temperature errors, which indicates the superiority of the model with dynamic entropy coefficient, especially at high temperatures.

Temperature Analysis of Switched Reluctance Motor Based on Equivalent Heat Circuit Method

This paper mainly takes a 6/4 switched reluctance motor (SRM) as an example to analyze the temperature of the motor. In order to establish the equivalent thermal circuit model (ETCM) conveniently, the mechanical structure of the motor is simplified to a certain extent, and the characteristic nodes are divided. Then the heat transfer process in the rotor region, the stator region and the whole motor during the operation of the motor is analyzed, and the ETCM of those regions are established respectively. This method of establishing ETCM is also applicable to superconducting motors. Based on the basic principles of heat transfer, the calculation method of thermal resistance in each ETCM is given in this paper. Then, the three-dimensional (3-D) finite element (FE) temperature field model of the motor is built and compared with the ETCM. Finally, the accuracy of the ETCM is verified by experiments.

Rapid thermal response and sensitivity analysis of proton exchange membrane fuel cell stack with ultra-thin vapor chambers

Vapor chamber (VC) embedded in proton exchange membrane fuel cell (PEMFC) stacks is an effective approach for thermal management of PEMFC stacks due to high thermal conductivity and temperature uniformity of VC. To quantitatively analyze the effect of VC on the dynamic thermal response of PEMFC stacks, a thermal equivalent circuit model is developed for PEMFC stacks cooled by VC. Each component in the stacks is regarded as a corresponding thermal resistance in the heat transfer process. The heat capacity of components is also applied on the model to couple the dynamic response. A series of key parameters on the thermal performance of the stacks are analyzed. The analysis result shows that the stacks have the fast temperature rise within 60 s of the start-up phase and VC nicely decrease the thermal response time of stacks. Parameters on temperature sensitivity of the stacks are also discussed. Thermal contact resistance and cooling velocity are significant factors on temperature sensitivity of stacks, but the temperature sensitivity becomes lower and even less than 0.01 with the increase of velocity. These works will help to design and optimize the thermal management system of PEMFC stacks.

A Real-Time Adaptive IGBT Thermal Model Based on an Effective Heat Propagation Path Concept

The information of junction temperature is crucial for the operational management of insulated-gate bipolar transistor (IGBT) modules. In practice, the junction temperature is typically estimated by using an electrothermal model. IGBT modules are subject to various aging processes during operation, some of which, e.g., substrate solder crack, change the thermal impedance of the IGBT module. However, few works in the literature have included the aging effect on the online thermal behavior modeling of IGBT modules. This article proposes an effective heat propagation path (EHPP)-based real-time adaptive thermal model for IGBT modules, where the EHPP is proposed to quantify the impact of substrate solder cracks on the heat propagation inside the IGBT modules. A straightforward relationship between substrate solder crack and the degree of nonuniformity of case temperature distribution is established. This relationship is then used to approximate the EHPP of the IGBT module in different substrate solder health conditions in real time using the measured nonuniformity of case temperature distribution. Based on the change of the EHPP, the parameters of a thermal equivalent circuit (TEC) model, e.g., an improved Cauer-type TEC, are adjusted online and in real time to track the thermal behavior changes of the IGBT modules caused by substrate solder cracks, leading to a real-time substrate-solder-aging-adaptive thermal model. The proposed real-time adaptive thermal model is validated by simulation studies and experimental tests for a commercial IGBT module.

Research on Optimal Control Strategy for Unpowered Downslope of High-Voltage Inspection Robot Based on Motor Temperature Rise in Complexity Microgrid Networks

In order to avoid the motor damage caused by excessive temperature rise of armature winding of the walking motor during braking of high-voltage inspection robot in complexity microgrid networks, an unpowered downhill speed and energy recovery optimization control strategy is proposed based on temperature rise characteristics of the walking motor. Firstly, the thermal equivalent circuit model of the walking motor is established, and the mapping relationship between the armature winding temperature of the walking motor and ambient temperature is solved; secondly, the influence of armature winding temperature on unpowered downhill speed and energy recovery control strategy of robot is analyzed; thirdly, according to the temperature of front and rear wheel walking motors and the temperature difference between them, the optimal control strategy of unpowered downhill speed and energy recovery of robot is put forward; fourthly, by adjusting the duty ratio u of the energy consumption speed control system and the front wheel feedback brake distribution factor λ , the temperature difference between the front and rear wheel walking motors is reduced. Through the experimental analysis on the simulated line, it is verified that the unpowered downhill speed and energy recovery optimization control method based on the temperature rise characteristics of the walking motor can effectively reduce the temperature difference between the front and rear wheels.