Equivalent Circuit Network Model Research Articles

Internal temperature estimation for lithium-ion batteries through distributed equivalent circuit network model

Lithium-ion cells experience significant internal thermal gradients during operation, with a direct impact on their safety, performance, cost and lifetime. The estimation of the internal temperature of cells is therefore particularly important. In this work, a 3D distributed electro-thermal model for internal temperature estimation is developed for a cylindrical cell (LG M50T, NMC811). The model is parameterized and comprehensively validated against experimental data for 21700 cells, including direct core temperature measurements. Multiple types of electrical load are considered, including constant current discharge, pulse discharge, drive cycle and instant discharge/charge switching. The developed model is used to estimate core temperature based on surface temperature measurement. The predictions are shown to have good accuracy at relatively low computational cost. We show that the widely adopted two-node lumped thermal estimation model is increasingly inaccurate for more aggressive discharges, when thermal gradients become higher. Compared to the standard two-node model, the distributed equivalent circuit network model predicts the effects of detailed internal cell structure (electrode, current collector, metal can and tab) and distributed internal heat generation. The results are of immediate interest to cell manufacturers and battery pack designers, while the modelling and parameterization framework is a useful tool for energy storage systems design.

Equivalent network modeling of eddy-current transfer functions

The use of eddy-current techniques as a measurement method for material characterization instead of simple fault detection requires transformation of the electrical response signals to quantifiable physical parameters that correlate with material properties. Apart from calibration-curve methods, exact approaches that correctly represent all interactions between excitation field and response field are computationally intensive and not well suited to real-time application. In this work, an equivalent circuit network model is constructed and its analytical equation for the voltage transfer function is derived. This model is then implemented in a soft sensor system. Finally, measurement results from various materials with different electromagnetic properties are presented.

Non-uniform current distribution in parallel-wound no-insulation high-temperature superconductor coil during ramping and fast discharging operations

A parallel-wound no-insulation (PWNI) high-temperature superconductor (HTS) coil is a kind of pancake-shaped no-insulation (NI) coil wound with parallel-stacked HTS tapes, which combines the characteristics of a NI coil and non-twisted stacked-tape cable. It shows a significant advantage in accelerating the ramping response compared with traditional NI HTS coils wound by a single tape, and is a promising alternative for large-scale high-field magnets. The stacked cable approach can lead to current redistribution between parallel tapes during ramping operations. It couples with the turn-to-turn current redistribution and leads to a much more complicated current redistribution inside the PWNI coil, the mechanism of which remains unclear so far. The aim of this work is to investigate electromagnetic behavior of a PWNI HTS coil in ramping and fast discharging process. A simulation model was developed by integrating an equivalent circuit network model and an improved T–A model. A three-tape PWNI coil and its insulated counterpart were wound and tested, and this model was validated by charging and discharging tests. Results show that there is a significant non-uniform current distribution on parallel tapes in the same turn during ramping operations and the maximum azimuthal current (transport current) can be 2.26 times the minimum one in the three-tape PWNI coil in this study. Meanwhile, the radial current shows a considerable accumulation in the tape near turn-to-turn contacts and the radial current through the turn-to-turn contacts can be 4.16 times of that the flow through tape-to-tape contacts (parallel tapes) in the same turn. During the fast discharging process, a significant coupling current is generated in the PWNI coil, leading to a large opposite transport current in local areas; the amplitude of variation of this can be 4.66 times the initial operating current. The radial current shows a similar distribution but opposite direction to that during ramping, and its amplitude is two orders of magnitude higher. These results provide practical guidelines for the design of large-scale high-field HTS magnets.

Motor Current Model for Detecting Localized Defects in Planet Rolling Bearings

A motor current model for the diagnosis of localized defects in planet rolling bearings (PRBs) is proposed in this study. A dynamic analysis of the motor-driven planetary gearbox system is conducted, and a translational-torsional vibration model of the system is developed. Both the additional time-varying impact caused by localized defects and the influence of the Hertzian contact and radial clearance on the translational support forces of PRBs are considered in the model. Based on the magnetic equivalent circuit network model, vibrational-electromagnetic coupling analysis is performed with the aid of the air-gap permeance and electromagnetic torque. By iteratively solving the nonlinear algebraic differential equations describing the dynamic characteristics of the coupling system, the motor current variation curve with localized defects in the PRB is obtained. Taking a typical motor-driven planetary gearbox system as the object, electromagnetic finite element calculations and dynamic response tests are performed to verify the proposed motor current model. The results show that the characteristic motor current frequencies are a combination of the fault passing frequency and power supply frequency when the inner race of the PRB has a localized spall fault. When the outer race (or roller) has a localized spall fault, the combination of current characteristic frequencies, which generally consists of the fault passing frequency, power supply frequency, and PRB outer-race rotational frequency (outer-race spall) or cage revolution frequency (roller spall), become complex. By discussing the effect of the spall width on the motor current spectra in detail, the characteristic frequencies sensitive to defects are extracted, providing a theoretical basis for the quantitative diagnosis of PRB-localized defects.

Prediction of Electrical Conductivity of Porous Composites Using a Simplified Monte Carlo 3D Equivalent Electronic Circuit Network Model: LSM-YSZ Case Study

Multiphase electric charge conductors composed of materials with various properties are widely utilized in both research and industrial applications. The composite materials include porous electrodes and other components mainly applied in fuel cell and battery technologies. In this study, a simplified Monte Carlo equivalent electronic circuit (EEC) network model is presented. In comparison to similar models, the present EEC network model allows an accurate prediction of the electrical properties of such materials, thus saving time-consuming experimental determination. The distinct feature of this EEC network model is that it requires only experimentally easily obtainable data as the input parameters: phase composition, porosity and bulk electrical conductivity of the individual constituents. During its run, the model generates a large number of artificial cubically shaped specimens based on random distribution of individual phases according to the input composition. Each of the specimens generated was modelled by a corresponding EEC network. The EEC networks were solved using Kirchhoff's laws, resulting in impedance response simulation for the prediction of composite conductivity values. The EEC network model was validated using lanthanum strontium manganite mixed with yttria-stabilized zirconia. Excellent agreement was obtained between the experimentally determined and the calculated electrical conductivity for sample porosities of 0 to 60 %. Due to its variability, the EEC network model can be suitable for a wide range of practical applications. The presented approach has high potential to save an enormous amount of experimental effort, while maintaining sufficient accuracy, when designing corresponding multiphase electrode structures.

A Parameterized Linear 3D Magnetic Equivalent Circuit for Analysis and Design of Radial Flux Magnetic Gears–Part I: Implementation

Magnetic gears can perform the same function as mechanical gears with the added benefits inherent to contactless power transfer. However, quick and accurate analysis tools are required for magnetic gears to reach their full potential. As end effects can significantly impact the slip torque of a magnetic gear, 2D models often overestimate the slip torques, so 3D models are frequently required. Therefore, this paper proposes a 3D linear Magnetic Equivalent Circuit (MEC) or reluctance network model of radial flux magnetic gears with surface mounted magnets. This is an extension of a previously developed 2D MEC model, and, like the previous 2D model, it is thoroughly parametrized so that it can be directly applied to a wide range of parametric cases. This is Part I of a two-part paper and focuses on the implementation of the 3D MEC model. Part II compares the 3D MEC model against nonlinear finite element analysis (FEA) models to validate the MEC model's accuracy and to develop guidelines for discretizing the geometry.

Research on Improved Fault Current Analysis Method for Flexible Direct Current Power Grid Considering Alternating Current Feed

Flexible direct current (DC) grid can realize large-scale renewable energy, wide-area coordinated complementation, and reliable power transmission. It is an important development that can be used to support high-voltage and large-capacity flexible DC transmission in the future. The short-circuit current of the DC line is one of the important bases for the selection of key main equipment parameters such as converter valves, DC circuit breakers, and reactors in the flexible DC grid. In this paper, a flexible DC grid equivalent circuit network model with alternating current (AC) feed-in is established. Aiming at the monopolar ground fault of the flexible DC grid grounded through the metal loop, an optimized traditional matrix calculation method is proposed to obtain the accurate line fault current value. On this basis, with an actual engineering background, the equivalent circuit model of the four-terminal bipolar flexible DC power grid is established, and the influence of grounding position, grounding parameters, and current-limiting reactor on the fault current of the DC line is analyzed. Finally, simulation using the PSCAD software verifies the effectiveness and accuracy of the proposed method. The method proposed in this paper can provide the necessary bases and references for the selection of flexible DC grid equipment.

No-Insulation High-Temperature Superconductor Winding Technique for Electrical Aircraft Propulsion

High-temperature superconductor (HTS) machine is a promising candidate for the electrical aircraft propulsion due to its great advantage in high power density. However, the HTS machine always suffers the problem of low thermal stability during quench. In this article, we apply a no-insulation (NI) coil technique on the rotor windings of HTS machines to enhance the stability and safety of the electrical aircraft. The NI HTS rotor windings experience ripple magnetic fields, which leads to induced eddy currents through turn-to-turn contacts. This induced current and accompanying losses will considerably affect the practicality of this technique. To study this issue, an equivalent circuit network model is developed, and it is validated by experiments. Then, analysis using this model shows that most of induced current flows in the outermost turns of the NI HTS coil because of skin effect, and lower turn-to-turn resistivity leads to higher transport current induced and more significant accumulation of turn-to-turn loss. A grading turn-to-turn resistivity is proposed to reduce the transport current induced and ac loss accumulation and meanwhile keep the high thermal stability of the NI HTS coil. Optimization of turn-to-turn resistivity is required when the NI HTS coil is applied in the machines' environments.

Using Lumped Element Equivalent Network Model to Derive Analytical Equations for Interpretation of Transformer Frequency Responses

Frequency Response Analysis (FRA) is regarded as the most effective technique for detecting mechanical faults in transformer windings. However, the main challenge in applying the FRA technique lies in the correct interpretation of the differences between the diagnosis and the reference frequency spectra. A transformer can be modeled as an equivalent circuit network comprising inductances (L) and capacitances (C), where L and C are electrical parameters dependent on the winding geometry; a relationship exists between the winding geometry, the electrical components of the equivalent circuit network and the measured FRA spectra. Through electromagnetic circuit analysis, this paper provides a theoretical basis to develop a fundamental understanding of FRA spectra and their resulting interpretation. The FRA spectra are first explained for a single air core winding with uniform structure, and then the complexity is gradually increased by taking into consideration the iron core, the mutual inductive coupling between parts of the same winding and then between the separate windings of the transformer. Mathematical expressions are developed to represent the relationship between the FRA characteristics and the corresponding electrical components of the equivalent circuit network model.

Modelling and experimental research on the equivalent magnetic circuit network of hybrid magnetic couplers considering the magnetic leakage effect

In this work, the massive modelling and computation costs required by the calculation of the magnetic leakage coefficient were avoided by using the three-dimensional finite element method (3D-FEM) in the initial design and optimisation of hybrid magnetic couplers (HMCs). The equivalent magnetic circuit network model of HMCs was established, and the equivalent reluctance of the model was calculated to obtain the analytic expression of the magnetic leakage coefficient of HMCs. A set of 1:2 prototypes was designed and manufactured. Simulation analysis and experimental tests were conducted to verify the correctness of the calculation of magnetic leakage. The calculated and experimental values of the magnetic leakage coefficient and the 3D-FEM were in good agreement. The output torque value of the HMC was analysed and calculated by considering that the air-gap leakage was closer to the test value and was more accurate than the value calculated without considering the air-gap leakage effect. This study provided a theoretical reference for the design and investigation of HMCs.

A Thick Cu Layer Buried in Si Interposer Backside for Global Power Routing

A layer of thick Cu metal is buried in the backside of a Si interposer and provides low resistivity and high capacitance for high-performance on-die power delivery networks (PDNs). The backside buried metal (BBM) layer can be as thick as $10 ~\mu \text{m}$ or even larger, and the stripes formed on the layer for interleaving power supply ( $V_{\mathrm {DD}}$ ) and ground ( $V_{\mathrm {SS}}$ ) wirings have large cross-sectional areas. The process flow developed for BBM is fully compatible with via-last type through-silicon via manufacturing. The Si interposer with BBM is stacked over an integrated circuit (IC) chip for improving PDN performance and suppressing power supply noise, as an over-the-top Si interposer (OVTT-SiIP). A test device of 65-nm CMOS digital IC chip and OVTT-SiIP was manufactured. The noise suppression ratio of 59.6% by the OVTT-SiIP technology is demonstrated by simulation with a full-chip PDN equivalent circuit network model and consistent with 49.7% by measurements on the test device with on-chip power noise monitoring function.

State of Charge Estimation for Lithium-Bismuth Liquid Metal Batteries

Lithium-bismuth liquid metal batteries have much potential for stationary energy storage applications, with characteristics such as a large capacity, high energy density, low cost, long life-span and an ability for high current charge and discharge. However, there are no publications on battery management systems or state-of-charge (SoC) estimation methods, designed specifically for these devices. In this paper, we introduce the properties of lithium-bismuth liquid metal batteries. In analyzing the difficulties of traditional SoC estimation techniques for these devices, we establish an equivalent circuit network model of a battery and evaluate three SoC estimation algorithms (the extended Kalman filter, the unscented Kalman filter and the particle filter), using constant current discharge, pulse discharge and hybrid pulse (containing charging and discharging processes) profiles. The results of experiments performed using the equivalent circuit battery model show that the unscented Kalman filter gives the most robust and accurate performance, with the least convergence time and an acceptable computation time, especially in hybrid pulse current tests. The time spent on one estimation with the three algorithms are 0.26 ms, 0.5 ms and 1.5 ms.

Lithium–Sulfur Battery State-of-Charge Observability Analysis and Estimation

Lithium–Sulfur (Li–S) battery technology is considered for an application in an electric-vehicle energy storage system in this study. A new type of Li-S cell is tested by applying load current and measuring cell's terminal voltage in order to parameterize an equivalent circuit network model. Having the cell's model, the possibility of state-of-charge (SOC) estimation is assessed by performing an observability analysis. The results demonstrate that the Li–S cell model is not fully observable because of the particular shape of cell's open-circuit voltage curve. This feature distinguishes Li-S batteries from many other types of battery, e.g., Li-ion and NiMH. As a consequence, a Li-S cell's SOC cannot be estimated using existing methods in the literature and special considerations are needed. To solve this problem, a new framework is proposed consisting of online battery parameter identification in conjunction with an estimator that is trained to use the identified parameters to predict SOC. The identification part is based on the well-known prediction-error minimization algorithm; and the SOC estimator part is an adaptive neuro-fuzzy inference system in combination with coulomb counting. Using the proposed method, a Li-S cell's SOC is estimated with a mean error of 4% and maximum error of 7% in a realistic driving scenario.

Numerical simulation and circuit network modelling of flow distributions in 2-D array configurations

Packing configuration is widely used in chemical industries such as chemical re-action and chromatograph where the flow distribution has a significant effect on the performance of heat and mass transfer. In the present paper, numerical simulation is carried out to investigate the fluid-flow in three 2-D array configurations including in-line array, staggered array and hexagonal array. Meanwhile, a simplified equivalent circuit network model based on the Voronoi tessellation is proposed to simulate the flow models. It is found that firstly, the local Reynolds number could be used as a criterion to determine the flow regime. Flow with maximum local Reynolds number less than 40 could be regarded as Darcy flow. Secondly, the flow pattern can be well represented by the network model in the range of Darcy flow with the determination method of hydraulic resistance pro-posed in the present paper.

A hardware-in-the-loop test rig for development of electric vehicle battery identification and state estimation algorithms

This paper describes a hardware-in-the-loop (HIL) test rig for the test and development of electric vehicle battery parameterisation and state-estimation algorithms in the presence of realistic real-world duty cycles. The rig includes two electric machines, a battery pack, a real-time simulator, a thermal chamber and a PC for human-machine interface. Other parts of a vehicle powertrain system are modelled and used in the real-time simulator. A generic framework has been developed for real-time battery measurement, model identification and state estimation. Measurements are used to extract parameters of an equivalent circuit network model. Outputs of the identification unit are then used by an estimation unit trained to find the relationship between the battery parameters and state-of-charge. The results demonstrate that even with a high noise level in measured data, the proposed identification and estimation algorithms are able to work well in real-time.

Lithium–Sulfur Cell Equivalent Circuit Network Model Parameterization and Sensitivity Analysis

Compared to lithium-ion batteries, lithium–sulfur (Li-S) batteries potentially offer greater specific energy density, a wider temperature range of operation, and safety benefits, making them a promising technology for energy storage systems especially in automotive and aerospace applications. Unlike lithium-ion batteries, there is not a mature discipline of equivalent circuit network (ECN) modelling for Li-S. In this study, ECN modelling is addressed using formal ‘system identification’ techniques. A Li-S cell's performance is studied in the presence of different charge/discharge rates and temperature levels using precise experimental test equipment. Various ECN model structures are explored, considering the tradeoffs between accuracy and speed. It was concluded that a ‘2RC’ model is generally a good compromise, giving good accuracy and speed. Model parameterization is repeated at various state-of-charge (SOC) and temperature levels, and the effects of these variables on Li-S cell's ohmic resistance and total capacity are demonstrated. The results demonstrate that Li-S cell's ohmic resistance has a highly nonlinear relationship with SOC with a break-point around 75% SOC that distinguishes it from other types of battery. Finally, an ECN model is proposed which uses SOC and temperature as inputs. A sensitivity analysis is performed to investigate the effect of SOC estimation error on the model's accuracy. In this analysis, the battery model's accuracy is evaluated at various SOC and temperature levels. The results demonstrate that the Li-S cell model has the most sensitivity to SOC estimation error around the break-point (around 75% SOC) whereas in the middle SOC range, from 20% to 70%, it has the least sensitivity.

Ramping turn-to-turn loss and magnetization loss of a No-Insulation (RE)Ba2Cu3Ox high temperature superconductor pancake coil

This paper is to study ramping turn-to-turn loss and magnetization loss of a no-insulation (NI) high temperature superconductor (HTS) pancake coil wound with (RE)Ba2Cu3Ox (REBCO) conductors. For insulated (INS) HTS coils, a magnetization loss occurs on superconducting layers during a ramping operation. For the NI HTS coil, additional loss is generated by the “bypassing” current on the turn-to-turn metallic contacts, which is called “turn-to-turn loss” in this study. Therefore, the NI coil's ramping loss is much different from that of the INS coil, but few studies have been reported on this aspect. To analyze the ramping losses of NI coils, a numerical method is developed by coupling an equivalent circuit network model and a H-formulation finite element method model. The former model is to calculate NI coil's current distribution and turn-to-turn loss, and the latter model is to calculate the magnetization loss. A test NI pancake coil is wound with REBCO tapes and the reliability of this model is validated by experiments. Then the characteristics of the NI coil's ramping losses are studied using this coupling model. Results show that the turn-to-turn loss is much higher than the magnetization loss. The NI coil's total ramping loss is much higher than that of its insulated counterpart, which has to be considered carefully in the design and operation of NI applications. This paper also discusses the possibility to reduce NI coil's ramping loss by decreasing the ramping rate of power supply or increasing the coil's turn-to-turn resistivity.

Multi-temperature state-dependent equivalent circuit discharge model for lithium-sulfur batteries

Abstract Lithium-sulfur (Li-S) batteries are described extensively in the literature, but existing computational models aimed at scientific understanding are too complex for use in applications such as battery management. Computationally simple models are vital for exploitation. This paper proposes a non-linear state-of-charge dependent Li-S equivalent circuit network (ECN) model for a Li-S cell under discharge. Li-S batteries are fundamentally different to Li-ion batteries, and require chemistry-specific models. A new Li-S model is obtained using a ‘behavioural’ interpretation of the ECN model; as Li-S exhibits a ‘steep’ open-circuit voltage (OCV) profile at high states-of-charge, identification methods are designed to take into account OCV changes during current pulses. The prediction-error minimization technique is used. The model is parameterized from laboratory experiments using a mixed-size current pulse profile at four temperatures from 10 °C to 50 °C, giving linearized ECN parameters for a range of states-of-charge, currents and temperatures. These are used to create a nonlinear polynomial-based battery model suitable for use in a battery management system. When the model is used to predict the behaviour of a validation data set representing an automotive NEDC driving cycle, the terminal voltage predictions are judged accurate with a root mean square error of 32 mV.

A physically meaningful equivalent circuit network model of a lithium-ion battery accounting for local electrochemical and thermal behaviour, variable double layer capacitance and degradation

A novel electrical circuit analogy is proposed modelling electrochemical systems under realistic automotive operation conditions. The model is developed for a lithium ion battery and is based on a pseudo 2D electrochemical model. Although cast in the framework familiar to application engineers, the model is essentially an electrochemical battery model: all variables have a direct physical interpretation and there is direct access to all states of the cell via the model variables (concentrations, potentials) for monitoring and control systems design. This is the first Equivalent Circuit Network -type model that tracks directly the evolution of species inside the cell. It accounts for complex electrochemical phenomena that are usually omitted in online battery performance predictors such as variable double layer capacitance, the full current-overpotential relation and overpotentials due to mass transport limitations. The coupled electrochemical and thermal model accounts for capacity fade via a loss in active species and for power fade via an increase in resistive solid electrolyte passivation layers at both electrodes. The model’s capability to simulate cell behaviour under dynamic events is validated against test procedures, such as standard battery testing load cycles for current rates up to 20 C, as well as realistic automotive drive cycle loads.

Influence of turn-to-turn resistivity and coil geometrical size on charging characteristics of no-electrical-insulation REBCO pancake coils

High temperature superconductor (HTS) no-electrical-insulation (NEI) coils demonstrate great advantages in thermal stability and self-protection features. However, an intrinsic delay is observed in the charging process and as a result there maybe a possible settle-out problem. It becomes more critical for large HTS coils with more turns, such as the magnets for the accelerator system and DC induction heater applications. This paper presents detailed studies on the charging characteristics of NEI coils. Firstly, two different no-electrical-insulation coils are wound: the first is directly wound using only REBCO tapes with brass lamination, which is called a no-insulation (NI) coil. The other one is co-wound with stainless steel (SS) strips and REBCO tapes whose copper stabilizer is electroplated, which is called a metallic insulation (MI) coil. Fast discharging tests are performed on the two coils and their equivalent turn-to-turn resistivity is calculated. A similar discharging delay is observed on both coils, but the turn-to-turn resistivity of the SS co-wound coil is much higher than that of the first coil. Then the resistivity data is directly applied to an equivalent circuit network model which is developed to predict the charging behaviours. The model calculates coil voltage, currents along the azimuthal and radial directions, as well as the induced magnetic field. A practical charging time is defined to characterize the field ramping process considering the charging delay between field ramping and current charging. The charging behaviours are extensively analyzed and compared in terms of three primary factors: equivalent turn-to-turn resistivity, coil size and ramping rate. The results show that the charging time increases dramatically with the coil size and may be too long to be practical for large-scale applications using HTS coils with low turn-to-turn resistivity. Increasing the turn-to-turn resistivity enables one to accelerate the charging process effectively. Therefore, the SS co-wound coil with higher turn-to-turn resistivity shows a much shorter charging time, which indicates that it may be more suitable for large-scale HTS magnets.