Lumped Parameter Thermal Network Research Articles

Synergizing Transfer Learning and Multi-Agent Systems for Thermal Parametrization in Induction Traction Motors

Maintaining optimal temperatures in the critical parts of an induction traction motor is crucial for railway propulsion systems. A reduced-order lumped-parameter thermal network (LPTN) model enables computably inexpensive, accurate temperature estimation; however, it requires empirically based parameter estimation exercises. The calibration process is typically performed in labs in a controlled experimental setting, which is associated with a lot of supervised human efforts. However, the exploration of machine learning (ML) techniques in varied domains has enabled the model parameterization in the drive system outside the laboratory settings. This paper presents an innovative use of a multi-agent reinforcement learning (MARL) approach for the parametrization of an LPTN model. First, a set of reinforcement learning agents are trained to estimate the optimized thermal parameters using the simulated data in several driving cycles (DCs). The selection of a reinforcement learning agent and the level of neurons in the RL model is made based on variability of the driving cycle data. Furthermore, transfer learning is performed on a new driving cycle data collected on the measurement setup. Statistical analysis and clustering techniques are proposed for the selection of an RL agent that has been pre-trained on the historical data. It is established that by synergizing within reinforcement learning techniques, it is possible to refine and adjust the RL learning models to effectively capture the complexities of thermal dynamics. The proposed MARL framework shows its capability to accurately reflect the motor’s thermal behavior under various driving conditions. The transfer learning usage in the proposed approach could yield significant improvement in the accuracy of temperature prediction in the new driving cycles data. This approach is proposed with the aim of developing more adaptive and efficient thermal management strategies for railway propulsion systems.

End-to-End Differentiable Physics Temperature Estimation for Permanent Magnet Synchronous Motor

Differentiable physics is an approach that effectively combines physical models with deep learning, providing valuable information about physical systems during the training process of neural networks. This integration enhances the generalization ability and ensures better consistency with physical principles. In this work, we propose a framework for estimating the temperature of a permanent magnet synchronous motor by combining neural networks with the differentiable physical thermal model, as well as utilizing the simulation results. In detail, we first implement a differentiable thermal model based on a lumped parameter thermal network within an automatic differentiation framework. Subsequently, we add a neural network to predict thermal resistances, capacitances, and losses in real time and utilize the thermal parameters’ optimized empirical values as the initial output values of the network to improve the accuracy and robustness of the final temperature estimation. We validate the conceivable advantages of the proposed method through extensive experiments based on both synthetic data and real-world data and then provide some further potential applications.

Thermal analysis of 4-phase 8/6 SRM for EV application

This article provides a comprehensive analysis of the thermal characteristics of a 4-phase 8/6 switching reluctance motor (SRM) designed for use in an e-rickshaw (3-wheeler) application. The determination of core and copper losses is achieved through electromagnetic analysis using Finite Element Analysis (FEA). The analysis is conducted via MOTORCAD, a multiphysics design software. This work includes the examination of both static and transient temperature conditions. Static analysis entails the estimation of losses by taking into account the motor's maximum current and operating the motor under steady-state conditions. Transient analysis involves the examination of two separate scenarios. One possesses a simple transient characteristic, while the other possesses a distinct duty cycle. The losses obtained from the electromagnetic analysis are used as the input for the simple transient thermal analysis. During transient analysis involving the duty cycle, losses are assigned to certain operating conditions, such as changes in the operating speed of the motor. This study employs the Lumped Parameter Thermal Network (LPTN), as well as 3D and 2D FEA techniques to conduct thermal analysis. The findings were compared and subsequently given in the article. The findings produced from the LPTN and 3D FEA approaches demonstrate a strong correlation. The motor's maximum temperature is limited to 180 °C. The findings indicate that the highest temperature, both under static and transient conditions, is below the maximum attainable value.

Accurate Time-Efficient Thermal Modeling and Discretization Methodology Applied to Electric Machines

The increasing power density of electric machines for electric vehicles necessitates accurate thermal analysis in design and real-time condition monitoring through simulations with computation times not exceeding one minute. Existing thermal models are either accurate and complex while requiring large computation times or they are fast but lack accuracy. To address these challenges, a novel hybrid modeling methodology is proposed, combining 3D lumped parameter thermal networks with thermal resistances extracted from 2D finite element models (FEM) to reduce computation demands while preserving accuracy. Further, a methodology is introduced to define the thermal network discretization for a desired threshold accuracy while minimizing computation time. Analysis of this discretization methodology demonstrates that the desired accuracy can be reliably achieved with limited computational effort. Verification of the modeling methodology against 3D FEM in OpenFOAM shows key component temperature deviations of less than 0.67 °C in steady-state simulations and 0.75 °C in transient simulations, comparable to the 3D FEM uncertainty of 0.39 °C. The computation times for steady-state and transient simulations are 18.3 s and 43.5 s respectively compared to 44 h and 175 h for 3D FEM. This highlights the time efficiency of the proposed methodology while maintaining accuracy for key component temperatures.

A two-dimensional semi-analytic thermal model for global temperature distribution predicting and hot spot monitoring in interior permanent magnet synchronous motor

A two-dimensional semi-analytical thermal model (SATM) is presented, aiming to quickly and accurately achieve global temperature distribution predicting and hot spot monitoring for interior permanent magnet synchronous motor (IPMSM). Thereby, it provides a reliable analysis tool for thermal behavior evaluation and prevents undesired consequences induced by excessive temperature rise, which is of great worth and significance in promoting the flourishing of IPMSM. SATM combines the analytical method, lumped parameter thermal network, and finite element analysis to obtain an analytical solution for thermal behavior through mathematical derivation by considering the complicated configuration, heat source distribution, heat dissipation condition, and material thermal dependence. Through SATM, it is possible to observe the global temperature distribution as well as the location and size of hot spots in each element. The temperature distribution gradient on the static is more pronounced than that on the dynamic; secondly, the area with the most severe heating is mainly found on the winding; furthermore, the hot spot on the winding is mainly located a little bit inside the center. Moreover, the thermal behavior of IPMSM at rated load is investigated by numerical analysis and experiments. A comprehensive comparison with SATM is done. The computational deviations between SATM and numerical analysis regarding the hot spot, minimum, and average temperatures on each element are all within 4.06%. However, SATM consumes only 20.92% of the time and 68.29% of the storage of the numerical analysis. The measured data also fully prove the reliability and validity of the comparison. It is certain that SATM can well break through the limitation of the existing non-numerical technique to quickly and accurately achieve global temperature distribution predicting and hot spot monitoring of IPMSM. It provides researchers and engineers engaged in thermal behavior evaluation with good analysis means, design guidance, and optimization direction.

Transient Thermal Exchange Analysis of an External Rotor Hub Motor for Electrified Defense Vehicles Applications Based on FVM and TNM

This paper investigates the transient temperature distribution law of a 75kW external rotor hub motor for electrified defense vehicles (EDV) using the finite volume method (FVM) and the thermal network method (TNM). Based on thermal exchange and fluid flow theories, both a transient fluid-solid coupled thermal exchange model and a lumped parameter thermal network model (LPTNM) with transient thermal capacity parameters are established. An iterative algorithm for the heat transfer coefficient is proposed to improve the accuracy of LPTNM. Compared with existing methods, this algorithm exhibits higher accuracy and stronger practicality. In addition, an experimental platform of the hub motor temperature rise is built for measuring the end winding temperature. The calculated results are in good agreement with the experimental results, verifying the rationality of the 3D transient fluid-solid coupled thermal exchange model and the LPTNM. The axial parallel water channel structure was adopted to improve the cooling performance of the end winding, taking into account the structural characteristics and assembly mode of the hub motor. This paper provides theoretical references for the transient thermal analysis and cooling structure design of the EDV hub motor.

Innovative Refrigeration Technology for Machine Tools with Sustainable Refrigerants and Digital Twins

This article investigates the trend of assessing energy efficiency, sustainability and greenhouse gas emissions in the operation of 5- axis milling machine tools. This research aims to predict the cooling load by thermal models control within the main spindle system to ensure that cooling devices are dimensioned adequately and to keep it running under optimal conditions leading to improve the overall efficiency. In order to achieve this goal, a digital twin approach is currently being developed utilizing commercial software which consists of four primary models. A simulation model for material removal is used to predict the mechanical load required for the milling process to finish the CAD model. The second model is the spindle control model to determine the electric currents needed to operate the induction motor at the specified mechanical power. This model provides the electric current data to the lumped-parameter thermal networks (LPTN) model, which is proposed to accurately represent the heat dissipation from the motor and spindle systems towards the cooling channel in the main spindle system. Subsequently, the task at hand involves making an estimate of the necessary outlet temperature derived from the refrigeration unit model, which is essential for effectively covering the thermal energy produced by the spindle system.

Multiobjective Optimization of a Traction Motor in Driving Cycles Using a Coupled Electromagnetic–Thermal 1D Simulation

This paper proposes an electric propulsion system model for computationally efficient multiobjective optimization considering overall driving cycles using coupled electromagnetic–thermal 1D simulation. The proposed system model uses equivalent circuit networks rather than finite element method to obtain high computational efficiency because considering both driving cycles and motor temperature change during optimization requires considerable computational cost. The magnetic saturation effect and temperature change of traction motor during operation are examined by constructing look-up tables. This study first integrated the lumped parameter thermal network into the system model to consider the motor temperature change without any iterative process. The 1D simulation results over urban and highway driving cycles indicate that the changes in the induced current, efficiency, and motor temperature could be predicted while driving. The Pareto optimal solution of traction motor cross-sectional geometry including reduction ratio is successfully obtained by multiobjective optimization with the maximum output torque constraint. Constructing the proposed system model once, optimal design for multiple target driving cycles can be obtained without any driving cycle analysis. In addition, high computational efficiency indicates that the proposed system model is practical in the early design stage of various electric propulsions.

Electro-Mechanical Characteristics of Dual-Winding Motor According to Winding Arrangement for Brake Systems in Highly Automated Driving Vehicles

Manufactures of automotive parts are struggling to secure redundancy in various ways. An alternative is to configure the system via a dual-winding motor and two electronic control units (ECUs). The dual-winding motor contains different winding arrangements according to poles/slots, and when only one of the two circuits is used owing to a failure, the electrical and mechanical characteristics differ depending on the winding arrangement. In this study, the electrical and mechanical characteristics were analyzed and compared according to the winding arrangement when the failure occurs. In particular, the winding arrangement of the motor is divided into line symmetry, point symmetry, and alternating symmetry. For each winding arrangement, the back-electromotive force, torque, and torque ripple were compared and analyzed through simulation and test. Also, vibration caused by electromagnetic force was analyzed. Here, to consider the tooth modulation effect, concentrated force was investigated and tangential force as well as radial force were considered. Additionally, the thermal characteristics were analyzed during fault operation using a lumped parameter thermal network with piecewise stator-housing modules. Lastly, the mechanical design characteristics of the motor hardware size that need to be changed according to the winding arrangement of the brake motor are explained. This study provides guidelines for the winding arrangement selection of a dual-winding motor with a similar magnetic field distribution suitable for the design purpose, by analyzing the electromechanical characteristics and size according to the winding arrangement during fault operation. The characteristics of other motor types or pole and slot number combinations can also be inferred from the results of this study, since the magnetic flux density distribution will be determined with line, point and alternating symmetry.

Analytical temperature estimation process of the air supply system of the proton exchange membrane fuel cell stack in fuel cell electric vehicles

The air supply system of the proton exchange membrane fuel cell stack in fuel cell electric vehicles should be included as one of the components of the balance of plant. However, the air supply system consists of a centrifugal air compressor, driven by an ultra-high-speed motor. Therefore, there occurs a large amount of thermal energy from losses and the temperature of the air supply system should be considered. Accordingly, this study suggests the temperature estimation process for an air supply system based on a lumped parameter thermal network (LPTN). First, performance modeling is introduced using not only the empirical approach but also electromagnetic finite element analysis (FEA). Subsequently, thermal modeling based on the LPTN is presented. For this procedure, optimization techniques, screening, and surrogate model-based optimization are used. Finally, the results of LPTN construction are investigated. Furthermore, an additional experiment is conducted, and the result of this study is verified.

Improved LPTN-Based Online Temperature Prediction of Permanent Magnet Machines by Global Parameter Identification

This paper presents an improved lumped parameter thermal network (LPTN) based online temperature prediction method of permanent magnet (PM) machines by global parameter identification. The proposed global parameter identification incorporates not only the loss but also the magnetic information into a fifth-order LPTN and identifies the multi-physical magneto-thermal parameters as a whole. In the identification process, the nonlinear characteristics, including the magnetic saturation, the cross-saturation, the strand skin effect, and the speed-dependent convective heat transfer, are all considered. It can eliminate the cumbersome magnetic and loss measurement efforts and improve the overall identification accuracy compared to the traditional step by step identification method. Based on the identified multi-physical magneto-thermal model, the critical temperatures of the PM machines, together with the online losses and torque, can then be predicted in real time. The experimental results show that the proposed online temperature prediction method can track the real temperature variation with errors within 5°C.

Investigation of winding cooling enhancement and thermal modelling of large‐power high‐torque‐density direct‐drive PMSM

AbstractLarge‐power high‐torque‐density direct‐drive permanent magnet synchronous motors (LHDPMSM) are more and more frequently used to drive ball mills, belt conveyors, scraper conveyors, etc. Aiming at the characteristics of large copper loss and high winding temperature rise of the LHDPMSM, an effective winding cooling enhancement technology based on winding overall potting (WOP) is presented. The manufacturing process and cooling principle of WOP is described in detail and compared with the traditional vacuum pressure impregnation (VPI). In order to solve the problem of complex modelling process and long calculation time of LHDPMSM thermal field caused by large volume and asymmetric fluid cooling structure, the lumped parameter thermal network (LPTN) considering both fluid cooling and winding potting is proposed. Then, the cooling capacity of WOP and VPI are compared by LPTN, and the influence of some major cooling system parameters on LHDPMSM temperature rise are also researched. Finally, in order to verify the correctness of the theoretical calculation results, two 450 kW LHDPMSM prototypes adopt WOP and VPI are manufactured, tested and compared. The theoretical and experimental results are highly consistent, which proves the effectiveness of WOP in winding cooling enhancement of LHDPMSM.

Robust Rotor Temperature Estimation of Permanent Magnet Motors for Electric Vehicles

As the mainstream powertrain of electric vehicles, permanent magnet motors are facing the challenge of durability and thermal failure. Therefore, the real-time rotor temperature monitoring plays a critical role, however, it is hard to online measure with sensors. To this end, a rotor temperature estimation method based on the lumped-parameter thermal networks and dual H infinity filters is proposed. Firstly, the lumped-parameter thermal network of three nodes, such as the stator, rotor and bearing, is numerically formulated to determine the power loss. Accordingly, the discretized state-space expressions are specified for the time-step iterative solution. Then, to address the uncertainty of model parameters, the dual H infinity filters are used in the rotor temperature estimation process. Finally, the simulation and experimental tests are performed to validate the effectiveness and the real-time executability of the proposed method. The test results show that the proposed method can well track the actual temperature tendency with estimation errors of less than 7.5 °C. Compared with the existing methods, the worst-case estimation accuracy has been improved by at least 25 %; besides, the proposed method presents good robustness against the parameter uncertainty; meanwhile, the higher estimation convergence is made in the face of huge model deviations.

Transient thermal models of induction machines under Inter‐turn short‐circuit fault conditions

AbstractInduction machines are the working horses in a lot of industries. Inter‐turn short‐circuit (ITSC) fault is one of the most common failure modes taking place in them. It can generate large fault currents that lead to a local temperature rise in the faulty stator slot, which deteriorates the working performance of the machine or even cascades to a complete machine breakdown. This article focuses on developing transient thermal models for an induction machine under ITSC faults. The aim of these thermal models is to understand the thermal behaviour of the induction machine at different ITSC fault propagation stages. The first thermal model is based on finite element method (FEM) simulation that includes a physics‐based model for the thermal contact resistance. The second thermal model is a lumped parameter thermal network that models the stator as inter‐connected slot‐number parts. They are both capable of modelling the characteristic of non‐uniform temperature along the circumferential direction for the induction machine operating under ITSC fault conditions. After area‐weighted averaging the results of the FEM simulation, it is found they are quantitatively consistent, with an average relative error magnitude of 5%, as well.

End‐winding wire‐insulation heat conduction model for precise thermal predictions of permanent magnet synchronous machines

AbstractAccurate thermal calculations of end‐winding temperature rises are the key issue in designing and developing cooling systems of permanent magnet synchronous machines (PMSMs). Due to the complex connections of the end‐windings, it is challenging to precisely predict the heat dissipation capacities through a traditional wire‐insulation equivalent model. Numerical simulations and lumped parameter thermal networks (LPTN) are used by the authors to develop thermal models that illustrate the end‐winding properties of a 2.1‐kW PMSM. As multi‐strand end wires are bent and bound together by ribbons, they have thermal interrelations which can hardly be considered in LPTN models. An equivalent coefficient enhancing the axial heat conduction capacities of end‐windings is proposed for LPTN calculations to model the aforementioned thermal interrelations with circumferential symmetric structures. To correctly model the mutual thermal coupling between various strands of end‐windings, the thermal conductivity of the equivalent insulation sheets between the multi‐strand end‐windings is determined for exact numerical calculations. The external insulation sheet thickness is calculated based on the equivalent thermal conductivity. After developing heat conduction models for LPTN and numerical simulations, LPTN and FEA are used to determine the PMSM's temperature rise characteristics. To verify the approaches, the computation findings are contrasted with experimental ones.

A real-time temperature rise prediction method for PM motor varying working conditions based on the reduced thermal model

Real-time and accurate temperature rise calculation can play a preventive role in preventing overheating motor damage. This article proposes a temperature rise calculation method for varying working conditions PM motors based on a reduced order model. The calculation model of this method consists of a thermal conductance matrix and a heat source matrix. The thermal conductance matrix is obtained by reducing the order of the detailed lumped parameter thermal network (DLPTN) conductance matrix, which significantly reduces the model order while retaining computational accuracy. A loss prediction function is introduced in acquiring the heat source matrix, which is constructed based on the relationship between motor loss and speed and power. It can predict the stator iron loss and PM loss with different speeds and powers in real-time, ensuring the accuracy of heat source loading. The experimental results show that this method can predict the temperature rise of critical nodes of the PM motor in real-time under varying working conditions. Its calculation results have high accuracy, providing an effective method for overheating PM motor protection.

Thermal Analysis of a Flux-Switching Permanent Magnet Machine for Hybrid Electric Vehicles

This paper investigates the loss and thermal characteristics of a three-phase 10 kW flux-switching permanent magnet (FSPM) machine, which is used as an integrated starter generator (ISG) for hybrid electric vehicles (HEVs). In this paper, an improved method considering both DC-bias component and minor hysteresis loops in iron flux-density distribution is proposed to calculate core loss more precisely. Then, a lumped parameter thermal network (LPTN) model is constructed to predict transient thermal behavior of the FSPM machine, which takes into consideration various losses as heat sources determined from predictions and experiments. Meanwhile, a simplified one-dimensional (1D) steady heat conduction (1D-SHC) model with two heat sources in cylindrical coordinates is also proposed to predict the thermal behavior. To verify the two methods above, transient and steady thermal analyses of the FSPM machine were performed by computational fluid dynamics (CFD) based on the losses mentioned above. Finally, the predicted results from both LPTN and 1D-SHC were verified by the experiments on a prototyped FSPM machine.

Thermal Analysis for Improving the Design of Radial Flux Permanent Magnet Synchronous Generators

In this paper, the analytical thermal model of a radial flux permanent magnet synchronous generator (RF-PMSG) is developed for applications in variable speed direct-drive low-power wind turbines. The thermal model takes the form of a lumped parameter thermal network to estimate temperatures and heat fluxes for a wide operating range of the RF-PMSG. The proposed thermal model is fully coupled with the electromagnetic solution of a flexible analytical design methodology of RF-PMSGs and its algorithmic solution is coded in Matlab. The thermal analysis is an essential requirement for enhancing the design performance of radial flux permanent magnet synchronous generators. Finally, the performance of a 10 kW RF-PMSG is analyzed using the thermal model, for a wide steady-state operation range.

Thermal Modeling and Analysis of Hybrid-Magnetic-Circuit Variable Flux Memory Machine

Variable flux memory machine (VFMM) can be regarded as a promising candidate for electric vehicles (EVs) owing to its advantages of excellent flux adjustment capability and overall efficiency improvement over an extended operating range. However, the uncertain internal thermal behavior due to magnetization state (MS) change has an immense influence on electromagnetic performance of permanent magnet, which makes the precise MS estimation of low coercive force PM a challenging issue. To explore the benefits of MS manipulation on temperature rise reduction and provide an effective method to accurately evaluate temperature rise in VFMM, a magnetic-thermal coupling model of the newly developed hybrid-magnetic-circuit VFMM accounting for different MSs is established in this article. The lumped parameter thermal network (LPTN) model and computational fluid dynamics based finite-element (FE) method are employed to analyze the temperature characteristics, respectively. First, the losses of the investigated machine are calculated by adopting both the FE method and analytical equations. Afterward, the equivalent thermal resistances and heat transfer coefficients are determined by employing the LPTN model. Meanwhile, FE modeling is employed to analyze the three-dimensional thermal field distribution. Finally, a prototype machine is fabricated and experimentally measured, which can confirm the validity of the theoretical analyses.

Development and validation of lumped parameter thermal network model on rotational oil spray cooled motor for electric vehicles

The rotational oil-spray-cooling method with motor has recently attracted attention because of its compact design and cooling performance. Rotational oil-spray-cooled motors require high computational resources and manufacturing costs; therefore, a precise simulation model is required. In this study, an asymmetric lumped parameter thermal network (LPTN) model of a rotational oil-spray-cooling motor is developed. The heat loss is calculated using correlation equations and electro-magnetic analysis, and the internal temperature distribution of the motor is predicted using conjugate heat transfer and multiphase flow computational fluid dynamics (CFD) analysis. The temperature of the coil inside the motor is measured using experiments. The developed LPTN model determined that the temperature prediction errors of coil parts were 0.15% and 4.42% at the nominal and maximum speeds, respectively.