Thermal-electrical Model Research Articles

On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model

On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model

Tunable parity-time symmetry vortex laser from a phase change material-based microcavity

Traditional light sources cannot emit an electromagnetic (EM) field with an orbital angular momentum (OAM), limiting their applications in modern optics. The recent development of the OAM laser, mainly based on micro- and nanostructures, can satisfy the increasing requirements for on-chip photonics and information capacities. Nevertheless, the photonic structures have fixed parameters that prevent these OAM lasers from being dynamically tuned. Here, we propose tunable vortex lasing from a microring cavity integrated by a phase change material, Ge2Sb2Te5 (GST225). By modulating the complex refractive index to create an exceptional point (EP) to break the degeneracy of whispering gallery modes with opposite orientations, the microlaser working at the EP can impart an artificial angular momentum, thus emitting vortex beams with well-defined OAM. The grating scatter on the edge of the microring can provide efficient vertical radiation. The vortex laser wavelength from the GST225/InGaAsP dual-layered microring cavity can be dynamically tuned by switching the state of GST225 between amorphous and crystalline without changing the microring geometry. We construct an electric-thermal model to show the tuning range of operating wavelengths (EPs) from 1544.5 to 1565.9 nm in ~25 ns. Our study on high-speed tunable PT-symmetry vortex lasers facilitates the next generation of integrated optoelectronic devices for optical computing and communications in both classical and quantum regions.

Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity

Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity

The Polarization and Heat Generation Characteristics of Lithium-Ion Battery with Electric–Thermal Coupled Modeling

This paper investigates the polarization and heat generation characteristics of batteries under different ambient temperatures and discharge rates by means of using a coupled electric–thermal model. This study found that the largest percentage of polarization is ohmic polarization, followed by concentration polarization and electrochemical polarization. The values of the three types of polarization are generally small and stable under normal-temperature environments and low discharge rates. However, they increase significantly in low-temperature environments and at high discharge rates and continue to rise during the discharge process. Additionally, ohmic heat generation and polarization generation also increase significantly under these conditions. Reversible entropy heat is less sensitive to ambient temperature but increases significantly with the increase in the discharge rate. Ohmic heat generation and polarization heat generation contribute to the total heat generation of the battery at any ambient temperature, while reversible entropy heat only contributes to the total heat generation of the battery at the end of discharge.

Parametric sensitivity analysis of a one-dimensional thermal-electrical model of a photovoltaic solar module

The efficiency of a photovoltaic module decreases with the increase in the temperature of the photovoltaic cell, which makes the determination of this temperature one of the determining factors in the modeling of a photovoltaic module. The objective of this work is to make a detailed study about the input parameters of a developed thermal-electrical model of a photovoltaic module, based on a sensitivity analysis. The model includes a thermal part, in which the temperature varies along the five layers of the module, and an electrical part, which is based on a single diode five parameters model. The coupling of these models into a thermal-electrical model is described. Through differential sensitivity analysis, the parameters that have a significant impact on estimating the photovoltaic cell temperature were determined. The variations of the sensitivity coefficients throughout a simulated day are presented. Parameters with the highest absolute sensitivity coefficients, such as the transmittance-absorptance product and open circuit voltage, are crucial for accurate temperature estimation and were further researched and determined with greater precision, in order to improve the model reliability. Conversely, parameters with lower absolute sensitivity coefficients, such as albedo and parallel resistance, were considered less important and could be simplified to enhance computational efficiency.

Thermal and electrical performance analysis of monofacial double-glass photovoltaic module with radiative cooling coating on the rear surface

The monofacial double-glass photovoltaic modules are still seriously affected by the temperature effect. The coatings with spectral regulation characteristics are expected to reduce the impact from the temperature effect. A coupled thermal-electrical model was established to evaluate the thermal and electrical performance of the monofacial double-glass modules applied with different spectral regulation coatings, including sub-bandgap reflection coating, mid-infrared emission coating and a combination of the two coatings. The cooling effect and output power gain of these coatings on the front and rear surface of the modules were compared comprehensively. The results show that the most suitable cooling coating for the module is the mid-infrared emission coating (i.e. radiative coating) on the rear surface when absorption loss of solar cell caused by spectral regulation coating was considered. Thus, we prepared the radiative coatings of TPX/SiO2 by doping SiO2 particles into the TPX polymer matrix. The thermal and electrical performances of the modules applied with different coatings on the rear surfaces of PV modules were calculated to optimize the coating parameters, such as thickness, size and volume fractions of SiO2 particles. The results reveal that the module applied with the TPX/SiO2 coating (size: 50 nm, volume fraction: 5 vol%, thickness: 60 μm) on the rear surface exhibited the lowest temperature and the highest output power. In the outdoor experiments, the radiative coating realized the cooling effect of ∼1 °C, and the efficiency improvement of 0.21 %. This work demonstrates that radiative cooling coating on the rear surface can bring PV module heat dissipation. Further research and development of radiative coatings would improve the cooling and electrical performances of PV module.

Numerical and experimental study of a novel vacuum Photovoltaic/thermal (PV/T) collector for efficient solar energy harvesting

Photovoltaic/thermal (PV/T) technology can generate electricity and heat simultaneously and improve solar energy harvesting efficiency. However, flat-plate PV/T collectors have strong heat loss in cold conditions and the collected heat is low-grade thermal energy, which limits the practical application of the PV/T collectors on a large scale. Herein, the vacuum environment is introduced to the flat-plate PV/T collector, conductive and convective heat loss are blocked, improving the efficiency and operating temperature of the PV/T collector. In this paper, a novel design of the vacuum PV/T collector has been proposed and fabricated, which maintains both the upper and lower space of the absorber in a vacuum state without additional glass cover causing energy loss. Performance comparison between the vacuum PV/T collector and the air–gap PV/T collector has been conducted, demonstrating that the vacuum condition can decrease the heat loss coefficient by 16.08%. In addition, a combined thermal-electrical mathematical model is constructed and validated. The predicted results reveal that the annual thermal energy outputs of the vacuum PV/T collectors without and with ideal low emissivity coating are 124.88% and 346.58% higher than that of the air–gap PV/T collector when the operating temperature is 50 °C. In summary, the vacuum PV/T collector exhibits great potential in improving thermal performance while slightly reducing the output of electrical energy. This work contributes to extending the working time of the PV/T collector and guides the design of the new generation of highly efficient PV/T collectors.

Investigation on the temperature control performance and optimization strategy of a battery thermal management system combining phase change and liquid cooling

For ensuring the safety of lithium-ion batteries in application, keeping the temperature of the battery pack in the desired range is crucial under different operating condition. This paper incorporates experiments and the numerical model to design a novel thermal management system with the combination of the phase change material and liquid cooling for twelve cylindrical lithium-ion batteries. The experimental results reveal that at the ambient temperature of 35 °C, the maximum temperature and temperature difference of the blank control system during 1 C charge and 2 C discharge are 57.6 °C and 4.1 °C, while the maximum temperature difference is 3.6 °C with single liquid cooling. Compared with them, the maximum temperature of the coupled system is only 44.8 °C and the maximum temperature difference is less than 2 °C with superior cycling performance. Moreover, an electric-thermal model is proposed to study the cooling effect of coolant, from which controlling the coolant flow within 250 mL/min is the best choice. Based on these results, an optimization strategy of hierarchical management is proposed for the coolant flow and inlet temperature by monitoring the maximum temperature of the battery pack and ambient temperature. This strategy not only controls the temperature of the system in desired range under different ambient temperatures, but also reduces the unnecessary energy consumption of liquid cooling. The proposed system is scalable to be applied to the other types of batteries for thermal management.

Heat generation and transfer simulation of a high temperature heat pipe under induction heating based on a coupled model

High temperature heat pipes are highly efficient heat transfer devices, and induction heating is often utilized in their performance tests. However, issues exist in evaluating the equivalence between induction heating and surface heating encountered in typical application scenarios, and in quantifying the accurate input heat flux of induction heating. In order to identify the key influencing factors and investigate their effects on heat generation and transfer within high temperature heat pipes under induction heating, a finite element thermal-electrical coupled model is developed based on the pseudo wick thermal conductivity model and electromagnetic theory. The effects of frequency (10 kHz, 100 kHz, 300 kHz), loaded current (10 ∼ 890A), cooling coefficient (10 ∼ 250Wm-2K−1) and temperature (300 ∼ 1000 K) are investigated. Over 98% of the induction heat is found to be generated in the evaporator section, with a considerable proportion generated in the annular channel (38 ∼ 52%) and the capillary wick (23 ∼ 26%) at low frequency (10 kHz). The wall temperature of the evaporator section is slightly lower than the temperature of the annular flow channel or even the capillary wick at weak cooling boundary conditions (<130Wm-2K−1@10 kHz, <50Wm-2K−1@100 kHz, <30Wm-2K−1@300 kHz). Quantitative calibration formulas of induction heat are established in relation to frequency, current, and temperature via two sets of quadratic polynomial fitting. The results can be used as reference for design and evaluation of transient and steady-state tests of heat pipes under induction heating.

Thermal-Electric Modeling: A New Approach for Evaluating the Impact of Conservation Voltage Reduction on Cooling Equipment

It has been suggested in the literature that by reducing the incoming voltage at a distribution feeder head or at the supply side of buildings, significant electricity savings can be achieved. This technique is called Conservation Voltage Reduction (CVR). Data-based analysis with and without CVR is primarily used to support such assertions, which does not explain the physics behind reduction in energy consumption with CVR. This paper presents a new approach for evaluating the impact of CVR on cooling equipment. In this approach, a thermal-electric model of the cooling process is developed in MATLAB’s SIMSCAPE toolbox that can be used to explain the physics behind energy reduction with CVR. This model includes an accurate model of a compressor coupled to an induction motor whose supply voltage can be varied to simulate CVR. Simulations performed using this model show that the Coefficient of Performance (COP) of cooling equipment improves with a reduction in supply voltage. However, the energy lost in the motor windings may nullify the impact of the improvement in the COP and render the CVR programs ineffective if the range of speed change is small over the allowable voltage change. The simulation results show an increase in energy consumption of 4% at 90% rated voltage compared to the energy consumed at the rated voltage. However, if variable frequency drives-based cooling equipment is appropriately controlled, it is possible to reduce their net energy consumption using CVR. Simulations performed keeping the ratio of the supply voltage and the frequency constant showed a reduction in energy consumption of 2.5% at 90% rated voltage compared to the energy consumed at the rated voltage. Thermal-electric modeling of building cooling equipment is, therefore, vital to accurately evaluating the benefits of CVR as smart, power electronics-based end-use equipment is globally adopted.

Simulation and experimental study on the energy performance of a pre-fabricated photovoltaic pavement

Photovoltaic pavement (PVP) is an emerging technology to harvest solar energy from roads, which could use the limited urban area renewable energy production, especially under the carbon neutrality targets. This study proposes a thermal-electrical mathematical model for a PVP system based on the Finite Difference method on heat nodes and a 5-parameter PV generation model. An outdoor test is conducted for model validation, showing 1.68% and 3.60% mean absolute percentage errors for PV cell temperature and output. Lab tests and road anti-skid property tests are also conducted. The experiment results show that the module PV output on a sunny day could reach 0.68 kWh/m2, with electrical efficiency of 14.71%. Based on the proposed model, two cases, in Hong Kong and Shanghai, are analyzed for an entire year. The parametric analyses recommend epoxy resin filling instead of air filling, with the annual maximum PVP module surface temperature reduction at 8.6% (Shanghai) and 8.4% (Hong Kong). The influence of road surface materials and asphalt concrete depth variation are also discussed. Besides the obvious heat island effect alleviation in Summer found from the surface temperature decrease, the snow melting potential in Winter could also be found with the increase of minimum surface temperature by 1.02 °C (Shanghai). Moreover, the potential of PVP application is also analyzed for more than 200 Chinese cities, demonstrating the heat and electrical performances with seasonal average results, with maximum seaonsal average road surface temperature reduction at −4.18 °C in summer and maximum increase, e.g., for Beijing up to 3.36 °C in Winter. The cities in the west and northeast China are shown with higher PVP generation potential.

Feedback-based fault-tolerant and health-adaptive optimal charging of batteries

The key technology barriers that hinder the growth of Electric Vehicles (EVs) are long charging time, the shorter life-time of EV batteries, and battery safety. Specifically, EV charging protocols have significant effects on battery lifetime and safety. If not charged properly, the battery could end up with shorter life, and more importantly, improper charging can cause battery faults leading to catastrophic failures. To overcome these barriers, we propose a closed-loop feedback based approach, that enables real-time optimal fast charging protocol adaptation to battery health and possess active diagnostic capabilities in the sense that, during charging, it detects real-time faults and takes corrective action to mitigate such fault effects. We utilize battery electrical–thermal model, explicit battery capacity and power fade aging models, and thermal fault model to capture battery behavior. In conjunction with the models, we adopt linear quadratic optimal control techniques to realize the feedback-based control algorithm. Simulation studies are presented to illustrate the effectiveness of the proposed scheme.

Performance Analysis of Spectrum-Dependent Integrated Thermal–Electrical Model of a PV Module

The diurnal and seasonal changes in the solar spectrum affect the photovoltaic (PV) module performance. In this article, the transient solar spectrum was integrated with the thermal–electrical model of the PV module for precise estimation of diurnal and seasonal PV performance. The transient meteorological parameters were considered for determining the dynamic power output of the PV. The SMARTSv2.9.5, COMSOL Multiphysics, and MATLAB were used for modeling different sections and integrated throughout. The cell temperature and power output were obtained and experimentally validated for various seasons. The statistical errors, such as mean absolute error (MAE), mean relative error, and root-mean-square error (RMSE) values, and the coefficient of determination ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) value were calculated for the developed model during various seasons. The RMSE of back surface temperature and power output from monocrystalline ranges from 1.67 to 2.59 °C and 1.83 to 2.92 W, respectively, and the same for polycrystalline PV module ranges from 1.93 to 2.29 °C and 1.70 to 3.63 W, respectively. The MAE of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">oc</sub> ranges between 0.10 and 0.29 A and 0.41 and 0.58 V, respectively, for monocrystalline, 0.13–0.43 A and 0.39–0.52 V, respectively, for polycrystalline PV modules. The present model is a simple integration and uses basic mathematical equations and parameters to predict the PV outputs.

Performance analysis of a novel PV/T hybrid system based on spectral beam splitting

Photovoltaic/thermal (PV/T) hybrid utilization is a promising method for efficient solar energy harvesting. However, a low operating temperature is required for photovoltaic (PV) conversion to make PV efficiency at a high level, while a relatively high operating temperature is preferred for photothermal (PT) conversion to improve the quality of collected heat, which causes a temperature conflict and induces certain limitations on the efficiency and scale promotion of PV/T. Herein, a novel PV/T system is proposed based on the spectral beam splitting and serial thermal circuit to decouple the power generation and heat collection, which aims to reduce the intrinsic temperature conflict and improve efficiency. A combined thermal-electrical model of the PV/T system is developed and parametric analysis is performed. Predicted results show that the temperature of the solar cells is 7.7 °C lower than the outlet water temperature in the novel PV/T system, demonstrating the temperature-decouple effect. Compared with the traditional PV/T system, the outlet water temperature is 3.9 °C higher and the solar cell temperature is 9.4 °C lower in the proposed system, showing a comprehensive efficiency improvement of 17.9%. In summary, this work provides an alternative way for efficient PV/T utilization by decoupling the operating temperature of PV and PT processes.

Digital twin of an apparatus for combined thermoelectric measurements

A high thermoelectric (TE) figure of merit zT of materials enables a high energy conversion efficiency. The quantity zT is defined by the Seebeck coefficient (S), the electric (σ) and thermal (κ) conductivity, and the absolute temperature (T). In this paper, we report on a computational model of the Combined ThermoElectric Measurement (CTEM) apparatus, which is a simultaneous characterization method capable of measuring the full set of above-mentioned thermoelectric transport properties between −190 and 600 °C. Currently, the measurement results show deviations due to unidentified error sources. As a solution approach of identifying possible error sources, a digital twin of the CTEM was developed. The computational thermal-electrical circuit model mainly consists of thermal sieving chains representing the relevant sample holder components, in particular two metallic blocks and a TE sample. For a computational consistency check of the measuring principles, ideal conditions are assumed, while no potential error sources are implemented, yet. Here, we present the measurement principles and procedures of creating the computational model of the CTEM. After studies on local discretization, the computational model undergoes a consistency check for model validation. The deviations between input parameters and simulated results of the three mentioned thermoelectric properties have been found negligibly small (≪1%) for ideal measurement conditions. This agreement certifies a realistic representation of the behavior of the sample holder by the digital twin with a satisfying reproduction of ideal measurement conditions by simplifying assumptions and the applicability of underlying measurement principles and evaluation protocols.

A coupled thermal-electrical-structural model for balloon-based thermoplasty treatment of atherosclerosis

Objectives The outcome of balloon-based atherosclerosis thermoplasty is closely related to the temperature/stress distribution during the treatment. For precise prediction of a required thermal lesion in the heterogeneous and thin atherosclerotic vessel, a numerical model incorporating heat-induced tissue expansion or shrinkage and the strain caused by balloon dilation is necessary. Methods A fully coupled thermal-electrical-structural new model was established. The model features a heterogeneous structure including eccentric plaque, healthy artery and surrounding tissue. Tissue expansion/shrinkage and hyperelasticity material model were taken into consideration. Different heating strategies and plaque mechanical properties were investigated. The temperature distribution was compared with the traditional thermal-electrical coupled model. The possibility of thermoplasty treatment using balloons with different sizes was also explored. Results The temperature, the electrical intensity and the stress during the thermoplasty were obtained. Lower stress was found in the heating region where tissue shrinkage occurred. The ablation depth was predicted to be ∼0.42 mm larger without coupling the biomechanical influence. The mechanical properties and input condition significantly affect the temperature and stress distribution considering the small dimensions of the tissue. Besides, with a 12.5% reduction of balloon diameter, the largest Von Mises stress decreases by 25.4%. Conclusions It is confirmed that a coupled thermal-electrical-structural model is needed for precise temperature prediction in the balloon-based thermoplasty of the heterogeneous and thin tissue. The model presented may help with future development of optimized treatment planning considering both ablation depth and minimum stress.

On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model

В данной работе мы предложили систему нелинейных уравнений относительно потенциала электрического поля и температуры, описывающую процесс нагрева полупроводниковых элементов электрической платы с последующим тепловым "пробоем". Для данной системы уравнений мы доказали существование непродолжаемого во времени классического решения, а также получили достаточные условия разрушения решения за конечное время. Библиография: 20 названий.

Simple thermal-electrical model of photovoltaic panels with cooler-integrated sun tracker

This paper presents a simple thermal-electrical model of a photovoltaic panel with a cooler-integrated sun tracker. Based on the model and obtained weather data, we analyzed the improved overall efficiency in a year as well as the performance in each typical weather case for photovoltaic panels with fixed-tilt systems with a tilt angle equal to latitude, fixed-tilt systems with cooler, a single-axis sun tracker, and a cooler-integrated single-axis sun tracker. The results show that on a sunny summer day with few clouds, the performance of the photovoltaic panels with the proposed system improved and reached 32.76% compared with the fixed-tilt systems. On a sunny day with clouds in the wet, rainy season, because of the low air temperature and the high wind speed, the photovoltaic panel temperature was lower than the cooler’s initial set temperature; the performance of the photovoltaic panel with the proposed system improved by 12.55% compared with the fixed-tilt system. Simulation results show that, over one year, the overall efficiency of the proposed system markedly improved by 16.35, 13.03, and 3.68% compared with the photovoltaic panel with the fixed-tilt system, the cooler, and the single-axis sun tracker, respectively. The simulation results can serve as a premise for future experimental models.

Fully–coupled thermal–electric modeling of thermoelectric generators

Numerical models of thermoelectric generators require quantification of discretization uncertainty, the scrutinization of thermoelectric phenomena on model energy imbalances and simultaneous thermal–electric predictions, and the rectification of disagreement with analytic models when considering temperature-dependent material properties. Within this methods paper, two fully coupled, thermal–electric unicouple-level models are developed and evaluated over various thermal and electrical conditions to address the aforementioned issues—a numeric model in ANSYS CFX and an iterative analytic model. Model results were compared to ANSYS Thermal–Electric (TE) and ANSYS Fluent. Agreement between all models’ electrical and thermal predictions was achieved, albeit ANSYS Fluent’s thermal predictions exhibited high percent differences (7–8%) and had global energy imbalances on the order of 15% due to incongruent thermal–electrical power output predictions. ANSYS TE congruently predicts power output when considering the device’s thermal behavior and electrical performance separately, with disagreement on the order of a percent. Through incorporating all thermoelectric phenomena, ANSYS CFX’s global energy imbalances were hundredths to thousandths of a percent; exclusion of pertinent thermoelectric phenomena such as Thomson and Bridgman heating caused imbalances of tens of percent. The inclusion of Thomson heat is imperative when modeling thermoelectric devices. The analytic model’s thermal and electrical performance predictions are within ANSYS CFX’s uncertainty (2–5%), and these predictions yielded percent difference of less than 1% in comparison to ANSYS CFX when the unicouple produces ±50% maximum power. By using temperature-integrated averages of material properties, analytic modeling is sufficient for the thermal–electric characterization of unicouples with interconnectors operating under Dirichlet thermal boundary conditions.

A lumped electro-thermal model for a battery module with a novel hybrid cooling system

An accurate thermal model is one of the keys to a thermal management system. However modeling of these battery modules based on lumped thermal model is challenging. The extension of the single battery model to a multi-battery model requires not only the connection between the electrical models of the multiple batteries, but also the consideration of the heat transfer between the batteries and the BTMS. In this paper, a lumped electrical-thermal model is proposed for the investigation of a complex hybrid cooling systems. The proposed model enables the cell to cell temperature variations analysis with the hybrid cooling thermal management system under the 1D level, which has considerable time savings compared to running a 3D numerical model simulation. A good agreement between experimental and simulation results is observed. The maximum error for the voltage calculation is 1.64%. The maximum differences between the modelled and experimental results for battery module temperatures are 4.5% and 1.7%, corresponding to the battery in the middle and at the ends of the module, respectively. To compare with the 3D numerical model, similar CFD simulations have been performed. Although this model has an approximate accuracy loss of around 1%, the model only requires 3.9% of the time required by the CFD model. The proposed model is computationally efficient and can be easily used to optimise algorithms to optimise temperature control during battery module operation.