Lumped Parameter Thermal Model Research Articles

A Transient-State Lumped Parameter Thermal Model for Brushless Wound Field Switched Flux Machines

In this paper, the transient-state lumped parameter thermal model (LPTM) of the wound field switched flux (WFSF) machine is characterized for the first time. The modelling methodology for the LPTM is given in details, including the process of determining the parameters of the LPTM, based on which two LPTMs are compared with the experiments, i.e. the LPTM-I and LPTM-II without and with consideration of the practical winding position in the stator slot. It is found that the practical positions of the DC and AC coils in the slots is important to improve the accuracy of the LPTM, due to the existence of slot empty space caused by overlapped DC and AC windings. By considering the practical positions of the DC and AC coils in the slots, the maximum value of the absolute error between the LPTM model predicted temperature and the measured values of the AC winding are 3.4°C, 5.23°C, 3.18°C and 5.22°C under DC test, steady state test, cycling test-I and cycling test-II, respectively, whilst they are 3.95°C, 2.00°C, 2.28°C and 4.89°C for the DC winding temperature error. The average value of the absolute error between the LPTM model predicted temperature and the measured values of the AC winding are 0.88°C, 1.25°C, 0.85°C and 1.87°C under DC test, steady state test, cycling test-I and cycling test-II, respectively, whilst they are 1.08°C, 1.47°C, 1.06°C and 2.73°C for the DC winding temperature. The temperature of the WFSF machine during a 9-hour experiment can be predicted in 27.8s by the LPTM, which has a more than 1100 times faster calculation speed.

Lifetime prediction of lithium-ion capacitors using electro-thermal-aging co-simulation platform

Lithium-ion capacitors (LICs) have attracted more and more attention as energy storage device candidates because of their high energy density, high power density and high security. It is important to predict lifetime for various applications in advance. Further research is needed for searching suitable application scenarios of LICs. In the paper, a simulation platform for predicting the lifetime of LICs is established, combining fractional-order electrical model, lumped parameter thermal model and aging model. The results show that the coupling between the models can effectively reduce the prediction relative error by 4 %. The platform can be used to predict cycling and calendar lifetime of LICs under actual operating conditions, reducing the investment of trial and error in scenario selection.

Numerical modelling of an electric motor cooling jacket

The automotive industry is amid a sweeping change of propulsion technology to meet the increasingly stringent limits on emissions and fuel consumption. Traditional combustion engines are gradually being replaced by electric motors or hybrid power trains. The efficiency and power density levels achievable by electric motors are entirely dependent on the effectiveness of the employed cooling solution. Therefore, extensive analyses are needed to determine and optimise the thermal performance of these systems. In this work a numerical model is developed to determine the friction losses and the heat transfer properties of an electric motor cooling jacket. The cooling channels, which coil along the circumferential direction within the motor casing, are studied by means of CFD analysis of a basic periodic module. Flow and temperature fields are determined by applying a 3D Finite Volume approach. Numerical solutions are obtained by means of a validated conjugate heat transfer solver. Integral flow field results are employed to derive the equivalent Darcy friction factor and side-wall specific Nusselt numbers for several flow regimes. A lumped parameter thermal model, based on the graph theory and aforementioned CFD results is also developed to determine the overall system performance. The equivalent thermal resistances are computed from geometric parameters and CFD results. Finally preliminary numerical results on friction losses and heat transfer are compared with available experimental data.

Expectation-Maximization Algorithm for Identification of Mesh-Based Compartment Thermal Model of Power Modules

Accurate prediction of temperatures in power modules is crucial for proper thermal management. Lumped parameter thermal models are preferred in this application for their low computational cost. The estimation procedure of the parameters of these models requires measurements of temperatures of all active elements. This requirement is relaxed in this contribution. Specifically, the previously used dark gray-box compartment model is replaced by a structured compartment model utilizing a mesh-based discretization of the physical layout of the module. Compartments are categorized into several types with common parameters for each type. The parameters are identified from the data of the measured elements using the Expectation-Maximization algorithm. The algorithm internally predicts the temperatures of the unmeasured elements. The sensitivity of the estimation to regularization of the process covariance matrix is also studied. The implied high-dimensionality of the state-space increases the computational cost of the conventional estimation procedure, therefore, a simplified procedure with a much lower computation cost is proposed. The performance of the proposed approach is tested on simulated data.

Motor cooling method using flow boiling of two-phase refrigerant and its analysis with lumped parameter thermal model

To improve the stability and efficiency of electric motors, an advanced cooling method that can replace the existing water-cooling method is required. Even though various studies utilized a liquid refrigerant in the cooling system, none of studies explicitly presented the cooling performance enhancement of motor by the superior heat transfer of flow boiling. In this study, a flow boiling cooling method using R134a is applied with a conventional water-cooled motor design, and its cooling performance is compared to that of a water-cooled motor. A transient three-dimensional lumped parameter thermal model based on cylindrical coordinates is developed. This model can calculate the heat loss of an electric motor, and determine the heat transfer and temperature change inside a motor under a given driving condition. The results indicate that the flow boiling cooling method maintains the winding at a temperature lower than the conventional water-cooling method. The power consumption of the pump required for motor cooling is reduced reliably by applying flow boiling cooling. However, it is necessary to use the appropriate refrigerant flow rate by considering the heat lost from the motor. If not, the two-phase heat transfer stops owing to complete vaporization of the refrigerant inside the motor. To realize efficient flow boiling cooling, the minimum required volume flow rate of R134a considering the motor driving condition is suggested in this study.

Performance evaluation of lithium battery pack based on MATLAB simulation with lumped parameter thermal model

AbstractThe capacity of lithium batteries varies under different temperature conditions. However, many studies still neglect the influence of temperature on battery capacity. Besides, some studies only considered the combination of the heat and electricity of the battery monomer and failed to study the performance of the battery pack in groups. This paper investigates a new method for dynamic situations that takes the influence of temperature on battery capacity into consideration. After acquiring the parameter through experiment, we can substitute the performance parameters into the thermoelectric coupling model and use MATLAB to realize the iterative calculation of thermoelectric coupling. By combining the grouping mode with the model, we can simulate the thermodynamic and electrical properties of the battery cell in the pack. The novelty is evident because the paper focused on the battery pack instead of a single cell and the lumped parameter thermal model is adopted. Besides, the method proposed in this paper considered the influence of temperature on battery capacity. The program of calculation process can be solidified on the vehicle system. After the simulation, we can get the available capacity of the battery pack at different initial temperatures, with different grouping modes and different inconsistency of parameters. The results predicted by MATLAB model are compared with the results of MATLAB‐FLUENT thermoelectric coupling simulation. The result reflects that the prediction by the MATLAB model about the available capacity, temperature, and residual electricity is of good precision.

Experimental validation of computationally efficient lumped parameter thermal model developed for hybrid excited linear flux switching machine

Regarding thermal analysis of electrical machines, Lumped Parameter Thermal Model (LPTM) is preferred over Thermal Finite Element Analysis (TFEA) due to computational efficiency and ease of model formation. In this paper, thermal performance of the proposed Hybrid Excited Linear Flux Switching Machine (HELFSM) is analysed by proposing computationally efficient LPTM based on differential equations. LPTM is established for worst case scenario i.e., locked-primary and MATLAB software is utilized to solve temperature rise equations. Firstly, to define hot spots of proposed machine, thermal analysis results up to steady state maximum temperature under 100 % duty cycle are investigated. All three heat flow mechanisms i.e. conduction, convection, and radiation are accounted. Secondly, 75 % and 50 % duty cycles solutions for the hottest parts of proposed machine are investigated by LPTM. Finally, 3-D Thermal FEA (3DTFEA) is developed to validate results of proposed LPTM, followed by experimental validations utilizing thermographic analysis.

Effect of core losses on thermal analysis of 3ɸ- Squirrel Cage Induction Motor using lumped parameter thermal model

The proposed Lumped Parameter Thermal Model (LPTM) is complex enough to predict temperatures in most parts of the 3ɸ- Squirrel Cage Induction Motor (3ɸ-SCIM), including the end winding and rotor surface temperatures. It is easily adaptable to a variety of frame sizes because it is formulated using dimensional information and constant thermal coefficients. The solution of linear differential equations adequately describes the thermal behavior of the 3ɸ-SCIM. The application of the thermal model on 15 kW 3ɸ-SCIM is discussed. The rise in temperature at different parts of motor is estimated considering copper loss, constant and variable core loss. The maximum flux density derived from Finite Element Method (FEM) analysis, used to calculate core loss at various loads of a 3ɸ-SCIM. Variable core loss causes deviation in temperature rise, from the results, it is observed that, the relative percentage error considering variable core loss to constant core loss is about 19 %.

A Novel Experimental Testing Setup and Calibration Procedures for Cylindrical Cell Thermal Models

Temperature is known to have a significant impact on the performance and ageing of Li-ion batteries. Because of it, their temperature is monitored and controlled implementing a Battery Thermal Management System (BTMS) in which lumped-parameter thermal models are commonly used to estimate the cells’ thermal behavior, due to their low computation effort. In this regard, it is important to plan a proper calibration procedure able to accurately assess the cell’s thermal properties. While literature presents several methodologies with different levels of accuracy and complexity, there is a lack of a systematic approach. Furthermore, only a few works take into account the heat lost through the cell holder by conduction. In this work, a re-designed cell holder is introduced to minimize its thermal interaction with the cell during testing, then it provides a better understanding of thermal models calibration by comparing two simple, but effective, testing procedures. The specific heat capacity of a cylindrical cell is evaluated by carrying out two testing procedures in which heat flow direction is inverted. In the first procedure, heat is actively generated from the cell, while in the second procedure it is externally provided using a flexible polyimide heater. This has led to two different formulations of the energy balance equation that differ from the internal thermal dissipation modeling. At the end, a validation has been carried out implementing a current profile generated from the UDDS drive cycle. Both formulations have shown to have the similar temperature prediction with a RMSE of 0.484 °C.

Lumped Parameter Thermal Model of Heat-Generating General Geometry in Cylindrical Coordinate System

Lumped Parameter Thermal Model of Heat-Generating General Geometry in Cylindrical Coordinate System

Perspective of Thermal Analysis and Management for Permanent Magnet Machines, with Particular Reference to Hotspot Temperatures

Permanent magnet (PM) machines have been extensively used for various applications. Nevertheless, thermal effect, particularly hotspot temperature, not only severely restricts power/torque density but also leads to deteriorations in electromagnetic performance, service life, and reliability. Starting with foundations of PM machines and heat transfer mechanisms, this paper reviews the development of thermal analysis methods over the last thirty years and the state-of-the-art research achievements, and the hotspot temperatures of winding and PM are particularly evaluated. In the overview, various machine losses and cooling techniques are first introduced, which are the essential reasons for temperature rise and the most straightforward way to remove the generated heat. Afterwards, the mainstream thermal analysis techniques, i.e., numerical techniques, lumped-parameter thermal model, and hybrid thermal models, as well as the online electrical parameter-based and thermal model-based temperature monitoring techniques, are reviewed and assessed in depth. In addition, this paper also reviews the analytical thermal modelling methods for winding and PM. Finally, future research trends are highlighted.

Fast self-heating battery with anti-aging awareness for freezing climates application

Lithium-ion batteries (LIBs) need to be heated before use at low temperatures to avoid poor electric vehicle performance. In this study, a self-heating method for LIBs at low temperatures is proposed, where the influence of various heating parameters on heating performance is explored experimentally. To make the balance between heating speed and capacity degradation while achieving efficient preheating, a lumped parameter thermal model and an empirical capacity fade model are established to determine appropriate duty ratio and external resistance, which can predict the corresponding time required for LIBs to be heated to the target temperature and reveal the capacity loss of LIBs quantitatively after repeated heating. A multi-objective optimization method based on non-dominated sorting genetic algorithm II (NSGA-II) is employed to obtain the Pareto optimal front between heating speed and capacity degradation, which leads to the selection of the optimal electrical parameters with the help of K-means clustering algorithm and three newly defined heating performance indicators. Finally, the duty ratio and external resistance are preferably 80% and 203.98 mΩ through the NSGA-II method, respectively. The experimental results verify the optimal heating strategy which can heat the LIB quickly from – 20.56 °C to 0 °C within 70 s. This optimal heating strategy is applied to heat the LIB for 200 times, the battery capacity degradation is only about 7.72%.

Design of a Medium-Voltage High-Power Brushless Doubly Fed Motor With a Low-Voltage Fractional Convertor for the Circulation Pump Adjustable Speed Drive

The brushless doubly fed motor (BDFM) shows great potential for use in large medium-voltage adjustable-speed drive (ASD) systems due to its high reliability and cost benefits of a partially rated low-voltage power electronics converter. However, undesired performance caused by rich useless space-harmonics restricts the application of the BDFM in medium-voltage high-power ASD systems. In this article, a medium-voltage wound rotor BDFM consisting of specially designed stator and rotor windings is developed. First, the wound rotor with unequal turns and unequal pitches is designed and then compared with a nested loop counterpart. In addition, a 10 kV single-layer winding with shifted slot number in the stator is proposed to further reduce the space-harmonics by equivalent pitched effect. The finite element model of the BDFM is established to analyze electromagnetic performance and the influence of magnetic slot wedges. A lumped parameter thermal model is developed to quickly evaluate the average temperature rise of the proposed prototype. Field tests of driving a circulation water pump in a steel rolling mill were conducted to validate the feasibility of the proposed scheme.

Simplified 3-D Hybrid Analytical Modelling of Magnet Temperature Distribution for Surface-mounted PMSM With Segmented Magnets

In this article, a simplified three-dimensional (3-D) hybrid analytical thermal model for surface-mounted permanent magnet (PM) synchronous machines is proposed and applied to investigate the influence of PM segmenting strategies on the spatial PM temperature distributions and hotspots. The developed 3-D hybrid thermal model synergies the lumped-parameter thermal model and analytical method and is able to estimate 3-D spatial temperature distributions and hotspots for both unsegmented and segmented surface-mounted PMs accounting for the uneven PM eddy current loss distributions. Meanwhile, by utilizing the proposed matrix-based post-processing methods, the developed hybrid analytical thermal model has a simple mathematical expression but persists in high estimation accuracy. Finally, the proposed hybrid analytical modelling method is validated by 3-D electromagnetic-thermal coupled FEA and experiments.

Thermal Analysis of Axial-Flux Permanent Magnet Motors for Vehicles Based on Fast Two-Way Magneto-Thermal Coupling

Axial-flux permanent magnet motor (AFPMM) have small size and high power density. It has a good application prospect in the field of new energy vehicle driving. In this paper, based on a 56 kW AFPMM, the magnetic circuit characteristics are calculated by the split loop method, considering the influence of pulse width modulated (PWM) power supply. The loss is taken as the heat source, combined with the motor structure characteristics and cooling conditions, the lumped-parameter thermal network model of the motor is established to solve the steady-state and transient temperature distribution of each structure. By this way, fast and accurate thermal calculation of the motor is realized in design stage. The accuracy of the lumped-parameter thermal network model is verified by experiment. At the same time, the effects of spliting the permanent magnet (PM) into pieces, flow rate of cooling water, and loss distribution on temperature rise are analyzed. This research work provides an effective fast thermal calculation method for AFPMM and provides a reference basis for the design of similar motors. It has important value of theoretical significance and engineering practical.

Real-time identification of PMSM losses through a novel past-time averaging method

The aim of this paper is the identification of unknown losses in a permanent-magnet synchronous motor through the thermal assessment of the motor behavior. These unknown losses can be sometimes hardly determined with analytical calculations. Their influence could be critical to some materials of the electric motor, such as windings and rotor, which are sensitive to hot-spot temperatures. The evaluation of the evolution of these unknown losses during cycles of mission is a crucial step in the motor conception phase. The applied method consists in solving a heat transfer inverse problem in real time. A new approach is used in this study for the regularization of the solution. It is based on a past-time averaging method. The work is numerically carried out based on a lumped-parameter thermal model developed for a high specific-power motor for the propulsion of hybrid aircrafts. Few reachable temperature nodes with known data are considered for the simulation. A dynamical mission profile is studied herein for a flight scenario of a hybrid aircraft, propelled by motors having around 1 MW of power. Three cases are investigated for the losses identification using the inverse technique. A study on the number of past time steps for the regularization of the ill-posed problem is presented. The results show that the thermal heat dissipated due to losses can be accurately estimated with an acceptable average error. The proposed procedure allows real-time determination of losses and monitoring of critical temperatures.

Estimation of 3-D Magnet Temperature Distribution Based on Lumped-Parameter and Analytical Hybrid Thermal Model for SPMSM

This paper presents a hybrid analytical thermal model by utilizing the synergies of the lumped-parameter thermal model (LPTM) and the analytical thermal model to estimate the 3-dimensional (3-D) permanent magnet (PM) temperature distribution as well as the hotspot for surface-mounted PM synchronous machines (SPMSMs). The hybrid analytical thermal model is firstly developed based on 2-dimensional analytical models in radial-circumferential and radial-axial planes, and then extended to three dimensions, in which the uneven distributions of PM eddy current loss are taken into account. The analytical solutions are obtained by solving the Poisson's equations under the Dirichlet and the convection boundary conditions, which are extracted from the synergized LPTM. The proposed hybrid thermal model is applied to a totally enclosed SPMSM and validated by the 3-D electromagnetic-thermal coupled finite element method and experiments.

Improved Low-Order Thermal Model for Critical Temperature Estimation of PMSM

The low-order lumped parameter thermal models (LPTMs) are one of the most competitive online approaches to estimate the critical temperatures in electrical machines. Firstly, this paper explores the correlation between the conventional high-order and low-order LPTMs and then presents some critical modelling guidelines of low-order LPTM together with an improved four-order LPTM. Secondly, a simple dynamic quasi-linear model (DQM) is proposed to define convection thermal resistances, which can be used in both conventional high-order and low-order LPTMs. The application of DQM can improve the estimation accuracy by indirectly introducing more degrees of freedom, which is especially beneficial for the magnet temperature estimation in the low-order LPTM due to its highly abstract rotor thermal modelling. Finally, a prototype permanent magnet synchronous machine is used for experimental validation under different operation profiles.

Estimation of Two- and Three-dimensional Spatial Magnet Temperature Distributions for Interior PMSMs Based on Hybrid Analytical and Lumped-parameter Thermal Model

A hybrid analytical and lumped-parameter thermal model is proposed in this paper to estimate the transient and steady-state two- and three-dimensional (2/3-D) spatial magnet temperature distributions for an interior permanent magnet synchronous machine (IPMSM). On the basis of a lumped-parameter thermal model (LPTM), the magnet analytical thermal models (ATMs) are synergized to establish the hybrid thermal model. By utilizing the transient or steady-state boundary conditions calculated by the LPTM, the ATMs are obtained by solving the heat conduction equations to estimate the spatial magnet temperature distributions in the 2-D horizontal-vertical and axial-vertical planes, which can also be extended to the 3-D temperature distribution by utilizing the multi-slice method. Meanwhile, the non-uniform magnet eddy current loss is also considered. Finally, both electromagnetic-thermal coupled finite element analysis method and experiments are used for verification based on a totally enclosed IPMSM.

Tracking of Winding and Magnet Hotspots in SPMSMs Based on Synergized Lumped-parameter and Sub-domain Thermal Models

Lumped-parameter thermal models (LPTMs) have been widely used to estimate critical temperatures in permanent magnet synchronous machines (PMSMs). However, in some cases, they may be incapable of predicting the hotspots and even cause temperature misestimation. In this paper, the synergized lumped-parameter and sub-domain thermal models are proposed for surface-mounted PMSMs to track the hotspots in the most vulnerable components, i.e. active/end-windings and rotor magnet. Firstly, the T-type elementary network based LPTM is developed to predict the average temperatures in main components and the boundary conditions. Secondly, the boundary conditions are applied to three sub-domain thermal models for the active/end-windings and the rotor magnet to predict the respective hotspots and to further correct the misestimated average temperatures. Finally, the proposed synergized thermal model is verified by the experiments on a prototype surface-mounted PMSM under various load conditions.