Thermal-electrical Analogy Research Articles

Thermal-electrical analogy for simulations of superconducting power cables

Due the integration of superconducting technologies into electrical networks around the world, its precise simulations in power grids are increasingly becoming a desirable outcome. Over the years, sophisticated methods have been used to model superconducting power cables and, in this way, predict its behavior under different conditions. Most of the available models, however, are not advisable to be used and embedded in power system simulators. In this manuscript, we focus on the development of a method specifically for modeling superconducting cables in traditional power grid simulators. We start developing the model through a case example, within the basic concepts are introduced and later expanded to general cases. The model also incorporates the transient behavior of the cooling media, which is mandatory for such cables. It has been observed that the proposed model requires less computational effort and is able to deliver accurate results when compared to more advanced methods.

Estimating the Impact of a Recuperative Approach on the Efficiency of Thermoelectric Cooling

Thermoelectric cooling is a prospective technology that has a lot of advantages; however, its main drawback is its low efficiency compared to other technologies. A lot of scientific research is aimed at the improvement of the efficiency of thermoelectric cooling, including the development of new thermoelectric materials, innovative structures, and better power management strategies. The present work further explores a self-developed recuperative power management approach, which takes advantage of the thermoelectric element’s ability to work as an electrical generator. This study relied on the thermal–electrical analogy method to develop a model that is capable of describing the impact of recuperation on the cooling performance while preserving the simplest configuration possible. The influence of different variables was estimated by three suggested quantities for evaluating the gains, losses, and rationality of the recuperative approach. A recovery of up to 10% of the electrical energy supplied to the thermoelectric element was observed experimentally. The ratio between the recovered energy and induced heat losses did not exceed a factor of 0.9. It is concluded that the recuperation process is reasonable only in the case of unavoidable interruption of the cooling process when average-performance thermoelectric elements are used.

Fast thermodynamic simulation of electrical control cabinets via thermal resistor networks

A fine-grid Computational Fluid Dynamics (CFD) simulation without thermo-electric coupling provides an accurate prediction of temperatures inside low-voltage control cabinets. But due to its high computational demand and complexity, the approach is not eligible for a widespread use in pre-production design. This study presents a lightweight and robust model based on the thermal-electrical analogy and Kirchhoff’s current law. The thermal resistor network is created for each control cabinet individually. An isothermal coarse-grid CFD simulation is used to approximate flow resistances. Convective resistances are calculated with Nusselt number correlations. The approach was tested on 120 randomly generated 2D control cabinet configurations. Component temperature errors were evaluated based on a normal distribution approximation. For moderate temperature rises up to 20 K the model had a mean error of 0.38 K and a standard error of 1.51 K compared to the reference fine-grid CFD model and was up to 12.8 times faster.

Cryogenic thermal conductivity of carbon fiber reinforced polymer composite laminates

Carbon fiber reinforced polymer (CFRP) composites with excellent mechanical properties and low thermal conductivity are promising materials for cryogenic facility support structures. However, the temperature dependence and stacking sequence dependence of the laminates’ thermal conductivities challenge their thermo-mechanical design. Previous work dealing with the cryogenic thermal conductivity of laminates was relatively inadequate, and the effect of stacking sequence has not been sufficiently clarified. Herein, the cryogenic thermal conductivity of CFRP composite was investigated, and a theoretical model for the out-of-plane thermal conductivity of laminate was developed. To this end, the thermal conductivities of epoxy resin and laminates were measured at temperatures from 20 K to 293 K. The cryogenic thermal conductivity of carbon fiber was then extrapolated. Subsequently, a theoretical model was developed based on the thermal-electrical analogy method to evaluate the effect of stacking sequence. The obtained model was then validated by numerical analysis and experimental work. Lastly, the effects of lay-up angles and component properties on out-of-plane conductivity were examined. The test results suggested longitudinal thermal conductivity of composites exhibiting significant temperature dependence, with a decreasing trend recorded from 6.317 Wm−1K−1 to 0.355 Wm−1K−1 and transverse thermal conductivity decline from 0.626 Wm−1K−1 to 0.156 Wm−1K−1. The theoretical analysis indicated that the stacking sequence could reduce the out-of-face thermal conductivity by up to approximately 6.5 %, while the lay-up angle did not show any influence. In sum, novel insights into the cryogenic thermal conductivity of CFRP composites were provided, with guidance for the design and analysis of CFRP composites in cryogenic applications.

Grey-box modelling and identification of the industrial oven of a shrink tunnel

This paper presents a lumped-parameter grey-box sampled-data state-space model for the industrial oven of a shrink tunnel. The model is derived following the thermal-electrical analogy. A novel discretization strategy is developed to take into account that the sampling time of the system is equal to the lowest period of the pulse-width-modulated voltage signals which drive the heat resistors of the industrial oven. The model parameters are estimated by means of an extensive experimental campaign. Experimental results show that the derived model outperforms state-of-the-art transfer-function models while depending on fewer parameters.

THERMAL CONDUCTIVITY OF UNSATURATED FIBROUS MEDIA BY FRACTAL-MONTE CARLO SIMULATIONS

The effective thermal conductivity of unsaturated fibrous media is simulated by Fractal-Monte Carlo simulations in this work. Based on the probability model and thermal-electrical analogy method, the proposed model of the effective thermal conductivity can be expressed as an explicit function of fractal dimensions, [Formula: see text], [Formula: see text], intrinsic thermal conductivities, [Formula: see text], [Formula: see text], [Formula: see text], the straight capillary length of a unit cell [Formula: see text], liquid saturation [Formula: see text], pore size [Formula: see text] as well as porosity [Formula: see text]. Each parameter of the proposed model has physical meaning and the function has no empirical constant. The results calculated by Fractal-Monte Carlo simulations have been compared with the experimental data available, and an excellent agreement has been shown for an appropriate range of porosity except for the condition at a lower liquid saturation. It is found that, when [Formula: see text] and [Formula: see text], the dimensionless effective thermal conductivity of unsaturated fibrous media decreases with increment in fractal tortuosity dimension and porosity and decrement in liquid saturation. On the other hand, when [Formula: see text] and [Formula: see text], the correlations are opposite. The present Fractal-Monte Carlo technique may have its own advantages in predicting other transports in unsaturated fibrous media.

Size effect on thermal transport performance of inserted Cu/Cu3Sn bilayer

Cu-Sn bonding is widely used in integrated circuits packaging due to the excellent stability and electrical performance, whose thermal transport mechanism is essential to be understood. Here, the size effect on thermal transport performance of Cu/Cu3Sn bilayer inserted between the diamond/carbon nanotube interface was comprehensively investigated. The thermal conductivities of phonon component and electron component were studied by non-equilibrium molecular dynamics simulation and thermal-electrical analogy, respectively. The thermal-electrical analogy was verified to be a promising way to predict the size effect of electron thermal conductivity. In view of interfacial thermal resistance (RK) is determined by phonon-phonon resistance, electron-phonon resistance, and electron-interface resistance, these three components were researched separately. At atomic level, the phenomenon of cross-layer effect and structural disorder were elaborated to reveal the mechanism of phonon heat transfer. The electron effects on RK were also well incorporated, to make our prediction approaching to real-world metal-dielectric interfacial heat transfer. Based on the above results, the total thermal resistance of the inserted Cu/Cu3Sn bilayer was calculated in the last section, revealing the dominant role of RK in micro/nano scale bonding. This work provides a comprehensive understanding of the thermal transport performance of multilayer metal bonding.

Design and optimization of thermoelectric generators for harnessing geothermal anomalies: A computational model and validation with experimental field results

Thermoelectric generators have been recently proved to be a feasible alternative to harness hot dry rock fields with very promising results transforming the geothermal heat into electricity. This research deepens in the study of these generators, developing a versatile computational model that serves as a tool to design and optimize this type of thermoelectric generators. This tool is important to develop this thermoelectric technology on a large scale, to produce clean and renewable electrical energy especially in the Timanfaya National Park, in Lanzarote (Spain), where some of the most important shallow geothermal anomalies in the world are located, in order to promote self-consumption in this zone. However, it could be employed in other areas with different boundary conditions. The model, based in the finite difference method applied to the thermal-electrical analogy of a geothermal thermoelectric generator, has been validated with the experimental field results of two thermoelectric generators installed in two different zones of geothermal anomalies. It has achieved a relative error of less than 10% when predicting the power and between 0.5–1.6% in the annual energy generation, what makes it a very reliable and useful computational tool. The developed model has been employed for the first time to estimate the electrical energy that could be generated if harnessing the characterized area of anomalies in Lanzarote. Here, given the continuity of geothermal energy, 7.24 GWh per year could be generated, which means annually 1.03 MWh/m2.

Dynamic Heat Dissipation Model of Distributed Parameters for Oil-Directed and Air-Forced Traction Transformers and Its Experimental Validation

A traction transformer with narrow oil channels is usually cooled with the ODAF or "Oil Directed Air Forced" method, where its temperature greatly depends on the Joule heat of windings, the conjugate heat transfer in the transformer, and the secondary heat release via oil cooler, together with the oil flowrate generated by oil pump. Neither the thermal-electric analogy nor the CFD simulation approach is qualified to predict the temporal and spatial temperature variations in this type of transformer. In the current work, the distributed parameter models are built for traction transformers and oil coolers with the assumption of a one-dimensional temperature field in the oil flow direction, respectively. Then, the two models are combined with the lumped parameter ones of oil pumps and pipes via the flow rate, temperature and pressure continuities at their interfaces, resulting in the derivation of the dynamic heat dissipation model of oil-directed and air-forced traction transformers. Additionally, an efficient algorithm is proposed for its numerical solution, and the temperature rise experiment is performed for model validation. Finally, the fundamental of dynamic heat dissipation in traction transformers is investigated with the current numerical model and the effects of ambient temperature are studied.

Experimental investigation, CFD and theoretical modeling of two-phase heat transfer in a three-leg multi-channel heat pipe

Muti-channel flat heat pipe is an innovative technology recently used at the rear of photovoltaic cells to absorb and reuse the wasted heat. To better understand the fundamentals of two-phase heat transfer (boiling and condensation) taking place inside multi-channel heat pipes, a unique three-leg heat pipe has been built. This one-of-a-kind heat pipe was used to develop both computational fluid dynamic (CFD) and theoretical models of a multi-channel heat pipe. To simulate the heat pipe operation with ANSYS Fluent, the Volume of Fluid (VOF) approach and Lee model were investigated. Different types of Lee models using user defined function (UDF) were compared and the influence of the condenser's boundary condition, saturation temperature, and mass transfer coefficient on the simulations was studied. For the first time, major limits of the Lee model for the simulation of heat pipes are identified. It is concluded that the available Lee model cannot predict the heat pipe temperature as it shows low physical meaning and can easily be manipulated to adjust the simulation's results. Based on the three-leg heat pipe experimental data, a new multi-channel theoretical model was developed that uses the thermal-electrical resistance analogy to predict the three-leg heat pipe thermal resistance. By selecting the optimum correlations for pool boiling and filmwise condensation, the developed iterative theoretical model was able to predict the three-leg heat pipe thermal resistance with an error of 8.2%.

Finite-time parameter estimation for an online monitoring of transformer: A system identification perspective

The effective online monitoring of thermal performance is the principal criterion that determines the Loss-of-Life (LoL), ageing rate, and loading capability of the transformer. To assess transformer thermal performance and life expectancy, Top-oil Temperature (TOT) and Hot spot Temperature (HST) should be accurately estimated. In general, the first-principle approach with a thermal-electrical analogy is used for the first-order dynamical model based on the Resistance-Capacitance (RC) circuit structure to approximate the evolution of thermal performance. Traditionally, the TOT model parameters are identified by looking for the input-output data that minimize the error between estimated and actual values. The Gradient Estimator (GE) based on the least-square minimization principle ensures the parameter convergence to their actual value and the parametric estimation error to zero only when the regressor (information vector) signals fulfill the stringent Persistence of Excitation (PE) condition. As the choice of input-output data plays crucial role in parameter estimation, the Design of Experiment (DoE) is generally conducted in the laboratory to satisfy the PE condition. Therefore, the TOT model parameter estimation problem is reformulated from a system identification perspective by exploring the finite-time estimators (FTEs) that accurately identify and estimate the TOT model parameters for the streaming data from real-time working transformers without any laboratory experiments and DoE. The experimental analysis on the sufficiency of data for parameter convergence is carried out on MATLAB to demonstrate the identified PE problem, the effect of DoE, and the performance of finite time estimators for real-time scenario based non-PE data in thermal modeling of the transformer.

Impact of superconducting fault current limiters on Delayed Current Zeros in industrial power systems

Electric power systems may exhibit fault currents with high asymmetry when generators are close to large motors and loads. In this condition and depending on the fault inception instants, the fault current waveforms may present Delayed Current Zeros (DCZ). During transient studies, in some cases, breakers do not see the current zero-crossing for several cycles. Indeed, if the breaker opens just after a transient when the current has not reached steady-state and may be offset by a slow exponentially decaying DC component, then, the breaker will fail to open as the current will not cross zero within the interruption time. Here, the main concern associated with DCZ is however related to the interruption of the circuit breakers on a current wave crossing zero. At this moment, the interruption is accompanied of an electrical arc having the potential to damage equipment. Resistive superconducting fault current limiters (r-SFCL) are a known solution to reduce the magnitude of short-circuit current in electrical systems. It is a versatile technology that can tackle both fault and stability issues in aging and modern power grids alike. As a side benefit, it may also address the DCZ problem. The present work aims at investigating the impact that an r-SFCL may have on DCZ and, in particular, its ability to eliminate this issue altogether. To that end, a r-SFCL based on an existing design was modeled using the consolidated thermal–electrical analogy. This approach has proven to be fairly accurate to model the transient behavior of the superconducting device. Here, the case study simulates a solid short-circuit at the terminal of a generator in a specific bus, simulating an industrial power system, that includes a circuit breaker, a motor load, and a r-SFCL. The electromagnetic transient computations were carried out considering load and no-load conditions with and without the r-SFCL. Eight scenarios were considered, showing that r-SFCLs can actually address DCZ in addition to limit the fault level.

A Top-Oil Thermal Model for Power Transformers That Considers Weather Factors

The aim of this work is to develop a top-oil thermal model based on the thermal-electrical analogy and heat transfer principles that captures the thermal influence of prevailing winds and solar radiation which can be generally applied to large power transformers. The key improvements of the proposed thermal model are calculating the heat transfer coefficient of the radiator on the air side using the Nusselt number of combined forced and natural convection, and including the solar radiation as an addition heat source. The proposed model is validated with the operational measurements of 3 transformers that are comprised of a 120/240-MVA unit and two 90/180-MVA units. The results are also compared with the predictions based on the IEEE-Annex G model. The proposed model is more accurate over windy and summer periods as expected.

A Fractal Model for Effective Thermal Conductivity in Complex Geothermal Media

Thermal conductivity is an important macroscopic thermo-physical parameter due to its significant effects on the temperature field distribution and heat flow magnitude in the material at heat conduction equilibrium. However, because of the extremely complex pore structure and disordered pore distribution, a well-accepted relationship between effective thermal conductivity (ETC) and geometric structural parameters is still lack. In this study, a novel fractal model with variation pore diameter is established systematically based on the assumption that the rough elements of wall surface, pore size distribution and capillary tortuosity follow the fractal scaling law. Thermal-electrical analogy is introduced to predict the ETC of unsaturated geothermal media. The proposed model explicitly relates the ETC to the microstructural parameters (relative roughness, porosity, fractal dimensions and radius fluctuation amplitude) and fluid properties. The proposed model is validated by comparing with existing experimental data. A parametric analysis is performed for presenting the effects of the structural parameters and fluid properties on the ETC. The results show that pore structure has significant effect on ETC of unsaturated porous media. ETC gradually decreases with the increment of porosity, relative roughness, and fractal dimensions. The present study improves the accuracy in predicting ETC and sheds light on the heat transfer mechanisms of geothermal media.

Heat Transfer Model of Composite Multi-Layer Structure Based on the Thermal-Electrical Analogy Method

Heat Transfer Model of Composite Multi-Layer Structure Based on the Thermal-Electrical Analogy Method

An electro-thermal model and its electrical parameters estimation procedure in a lithium-ion battery cell

In this work, an electro-thermal model of a single lithium-ion battery cell has been developed in Simulink-Simscape environment. The model is divided in two interacting parts: the electrical and the thermal one. The electrical model consists of one Resistor-Capacitor branch circuit that is coupled to a thermal model consisting of a discretized volume, representing the battery cell, built on the basis of the thermal-electrical analogy. The heat generated by the cell is estimated using a lumped heat source approach. One of the novel aspects of the work is the definition and detailed description of an automatic procedure to extract the parameters of the RC circuit from pulse discharge tests, based on a Multi-Linear Regression Model approach. The electrical and thermal performance of the model was validated with dynamic and static measured data: the mean square error of the voltage prediction in dynamic conditions is 0.00027 V2. In static conditions, the mean square error of the voltage and temperature predictions are 0.014 V2 and 2.28 °C2, respectively. This model, due to its ease of application, can be used as a tool to define new modules architecture, as well as to support the design of the battery cooling system.

Model Predictive Control with Adaptive Building Model for Heating Using the Hybrid Air-Conditioning System in a Railway Station

A model predictive control (MPC) system with an adaptive building model based on thermal-electrical analogy for the hybrid air conditioning system using the radiant floor and all-air system for heating is proposed in this paper to solve the heating supply control difficulties of the railway station on Tibetan Plateau. The MPC controller applies an off-line method of updating the building model to improve the accuracy of predicting indoor conditions. The control performance of the adaptive MPC is compared with the proportional-integral-derivative (PID) control, as well as an MPC without adaptive model through simulation constructed based on a TRNSYS-MATLAB co-simulation testbed. The results show that the implementation of the adaptive MPC can improve indoor thermal comfort and reduce 22.2% energy consumption compared to the PID control. Compared to the MPC without adaptive model, the adaptive MPC achieves fewer violations of constraints and reduces energy consumption by 11.5% through periodic model updating. This study focuses on the design of a control system to maintain indoor thermal comfort and improve system efficiency. The proposed method could also be applied in other public buildings.

Tests and recovery under load simulations of a novel bifilar resistive SFCL having undulated shape configuration

Power systems are becoming more interconnected and complex. The distributed generation expands and spreads across the grids, reducing the distance between the load and the generation. In addition, several substations are aging after decades of operation and their equipment struggle to sustain the ever increasing fault levels. In this context, the fault current limiter (FCL) arrived as a solution to mitigate this problem. Considering the FCL devices, the resistive superconducting FCL (R-SFCL) is the most mature technology with potential to be produced in mass scale, due to its ability to quickly change its impedance during a fault current and its high current density capacity. In this paper, a novel R-SFCL topology is presented, which has an unique design that allows a compact size and the possibility of modulated assembly. These characteristics enable setups for various voltage and current levels. One advantage of this topology is the compromise between volume and high heat exchange that can reduce the recovery time under load. One bench prototype was modeled using the thermal–electrical analogy implemented in ATPDraw, tested in two different labs. Tests were performed at faults levels of 12 kA, 5 kA and 2.7 kA for 137 V. Measured and simulated results were compared, resulting in a relative error of less than 12%. Two contributions can be highlighted: the new design of the R-SFCL and the inclusion in the convection heat exchange model curves for the heating (during the quench) and cooling (after fault), which allows to predict the recovery under load.

Transformer Bushing Thermal Model for Calculation of Hot-Spot Temperature Considering Oil Flow Dynamics

Thermal stress plays a prominent role in the reliability of bushings and contributes to the reliability of power transformers, especially during overload conditions. Thus, exploring the temperature distribution in the bushings is essential. This paper proposes a new thermal model to estimate the hotspot temperature (HST) of oil-impregnated paper (OIP) bushings, based on a modified thermal-electrical analogy model. The proposed model is developed based on the finite element method (FEM) to accurately model all fluid flow and internal convection as well as the thermal conduction mechanism. To this end, convection thermal resistances are defined, and their nonlinear characteristics are calculated for different overloading conditions. The proposed approach is applied on a 245 kV, 800 A OIP bushing to analyze not only the normal loading condition but also short-term overloading beyond the rated current. In addition, the oil flow condition with different load currents and transformer top oil temperatures (TTOT) are investigated. The results show a consistent temperature rise with the typical test conditions with no identified problematic situation. However, during overloading, the temperature rise exceeds beyond the permissible limits recommended by IEEE C57.19. Hence, the overloading of transformers may deteriorate the bushing insulation and reduce its lifetime.

Computational study of geothermal thermoelectric generators with phase change heat exchangers

The use of thermoelectric generators with phase change heat exchangers has demonstrated to be an interesting and environmentally friendly alternative to enhanced geothermal systems (EGS) in shallow hot dry rock fields (HDR), since rock fracture is avoided. The present paper studies the possibilities of the former proposal in a real location: Timanfaya National Park (Canary Islands, Spain), one of the greatest shallow HDR fields in the world, with 5000 m2 of characterized geothermal anomalies presenting temperatures up to 500 °C at only 2 m deep. For this purpose, a computational model based on the thermal-electrical analogy has been developed and validated thanks to a real prototype, leading to a relative error of less than 8%. Based on this model, two prototypes have been designed and studied for two different areas within the park, varying the size of the heat exchangers and the number of thermoelectric modules installed. As a result, the potential of the solution is demonstrated, leading to an annual electricity generation of 681.53 MWh thanks to the scalability of thermoelectric generators. This generation is obtained without moving parts nor auxiliary consumption, thus increasing the robustness of the device and removing maintenance requirements.