Mutual Inductance Values Research Articles

A Decoupled Modulation Strategy for Constant Voltage/Current Wireless Charging System Under High Coils Misalignment

ABSTRACTOutput fluctuation and lower transmission efficiency under load and mutual inductance variation are hot concerned in the wireless charging system for power batteries. In this paper, a decoupled tracking strategy is proposed to realize constant voltage (CV) or current (CC) output and high transmission efficiency. The circuit model of series–series compensation network is built, and corresponding transmission characteristics can be derived. First, the load and mutual inductance value can be estimated by measuring the primary electrical information, including the inverter output voltage, current, and the phase error between them. Then load‐independent voltage or current output characteristics under coils misalignment can be maintained by tracking the optimal switching frequency of inverter part. In addition, the value of output voltage or current can be adjusted flexibly for different operation occasions by the employment of pulse‐width modulation. As a result, the load‐independent output characteristics realization and output adjustment can be decoupled. Based on only the primary measuring information, the CV/CC output can be maintained via the proposed hybrid control strategy when the coils misalignment and load variation happen, increasing the robustness of whole wireless power transfer (WPT) system. Furthermore, the soft switching of all power switches in the inverter part can be realized to reduce the switching loss. Compared with previous research, the proposed wireless charging system has a higher power density and a simplified control strategy. Finally, an experimental platform with 60‐V charging voltage and 3.6‐A charging current is built to verify the feasibility of the proposed sys‐tem and control method.

Optimal efficiency point membership incorporating fuzzy logic and automatic control of various charging stages for electric vehicles

Introduction: The rapid development of electric vehicle technology in the field of renewable energy has brought significant challenges to wireless charging systems. The efficiency of these systems is crucial for improving availability and sustainability. The main focus of the research is to develop an intelligent charging strategy that utilizes fuzzy logic to optimize the efficiency of wireless charging systems for electric vehicles.Method: Introduce a model that combines fuzzy logic algorithm with automatic control system to improve the wireless charging process of electric vehicles. The model adopts dynamic tracking and adaptive control methods by analyzing the characteristics of static wireless charging systems. Utilizing primary phase shift control and secondary controllable rectifier regulation, combined with optimized fuzzy control algorithm.Result and discussion: The experimental results show that when the secondary coil is stable, the model maintains a stable duty cycle of about 75.6% and a stable current of 5A. It was observed that when the mutual inductance values were set to 10, 15, and 20 uH, the efficiency of the primary coil before applying control decreased with increasing resistance.Conclusion: The proposed system has shown great potential for application in real-world electric vehicle charging systems, demonstrating good applicability and feasibility in controlling the charging process and tracking the optimal efficiency point. The integration of fuzzy logic enhances the system’s ability to adapt to different operating conditions, which may lead to wider implementation and improved operational efficiency.

Optimal design of an LCC-S WPT3 Z1 SAE J2954 compliant system, using NSGA-II with nested genetic algorithms for simultaneous local optimization

Wireless Power Transfer (WPT) for electric vehicles is one of the most promising methods that, given its advantages, will drive the deployment of electric vehicles. This paper presents a mathematical optimization method applied to the complete design of an LCC-S WPT3 Z1 11 kW system that complies with the SAE J2954 standard (Wireless Power Transfer for Light-Duty Plug-in/Electric Vehicles and Alignment Methodology, 2020). A design method based on three phases is proposed, allowing the complete inductor system, including ferrites shielding and compensation circuit components, to function in any relative primary and secondary position. In Phase 1, a multi-objective NSGA-II algorithm is designed, utilizing three nested genetic algorithms. The goal is simultaneously searching for the local optimum between the primary and secondary systems in three positions. This is achieved by modeling the circuit’s electrical and electromagnetic parameters with equations, enabling an iterative process with reduced computational time. The NSGA-II algorithm yields three scenarios: primary copper volume minimization, secondary copper volume minimization, and a compromise solution that optimizes the total volume. The result is then modeled in Phase 2 using a 3D finite element program that includes ferrite and optimal shielding, obtaining the values of inductances and mutual inductance in the three positions, as well as design data for manufacturing. This result is introduced in Phase 3 to optimize compensation circuit components using a second NSGA-II algorithm with three nested genetic algorithms. Again, three scenarios are obtained based on the desired system behavior and the optimal cost of the components. The result is validated through simulation with Matlab-Simulink and experimentally using a prototype constructed for this purpose.

Mathematical Model of a Nonlinear Power Transformer for Needs of Relay Protection

In this work, a mathematical model of a three-phase nonlinear transformer is suggested. The model enables simulating the transformer operation with allowance for its nonlinearity and covers needs of the relay protection. Our model has been developed on the basis of a mathematical model with phase coordinates, where differential equations are composed by the Kirchhoff’s phase-voltage law. Based on this model, we first compose a mathematical model for simulating steady-state operation modes of a transformer, taking into account the asymmetry and nonlinearity of its ferromagnetic core. In this model, the initial values of inductances and mutual inductances of loops are determined from the main phase inductance calculated by the experimentally found no-load current, and their current values are determined from the currents in windings and the magnetic fluxes in legs of the transformer core. The magnetic fluxes are calculated by the nodal-pair method. This improved mathematical model is verified through a comparison between the calculated harmonic components of the phase currents and the experimental results. The harmonic components are calculated with the use of Fourier expansion of the calculated phase currents. Their experimental values are determined with a spectrum analyzer. The calculated and experimental harmonic components of the currents of phase A during no-load and rated-load operation of the transformer are tabulated. The comparison of these results shows that the mathematical model of a three-phase transformer we suggest makes it possible to simulate currents in transformer windings under steady-state operation modes with accuracy acceptable for relay protection.

Calculation of mutual inductance between arbitrarily positioned planar spiral coils for wireless power applications

Mutual inductance is one of the main parameters required to determine the power link’s performance (output voltage, efficiency) in wireless power transfer. The coils are often misaligned angularly in these applications, which affects the mutual inductance and thus the performance. Hence, an accurate calculation of mutual inductance is necessary to decide the working region of the coil. This paper presents an analytical calculation of mutual inductance between two planar spiral coils under angular misalignment conditions. By solving the Neumann integral formula, mutual inductance is derived for constant current-carrying coils, and the final mutual inductance value is calculated numerically. The influence of angular misalignment of the coil, which can be due to nutation and spin angles, on mutual inductance is studied in detail. The mutual inductance of the spiral coil is calculated for different misalignment cases. The accuracy of the calculation results is verified by comparing it with conventional formulas (mainly the Liu, the Babic formula, and the Poletkin formula) and by simulation using the finite element method. The proposed method is a more generalized and simpler one that can be used to calculate the mutual inductance of any size of coils, either spiral or circular, with any lateral and angular misalignments. Finally, a couple of spiral coils are fabricated to validate it experimentally. The comparison of the simulation and experiment results with the calculation result shows its accuracy. Thus, the proposed method can be applied to compute mutual inductance in any angularly misaligned coupling coils for the optimization of the wireless power transfer and their design.

Calculation and regulation of mutual inductance of wireless charging coils with metal shielding materials based on multiple intelligent optimization algorithms

SummaryIn wireless charging systems for electric vehicles, fluctuations in coil mutual inductance can affect both system output power and efficiency. This paper introduces a coil mutual inductance model that accounts for metal shielding material. The formula for coil mutual inductance is derived using Maxwell's equations and boundary conditions. Additionally, the paper presents a tactic for adapting the mutual inductance with the aid of an intelligent optimization algorithm, which is utilized for steadying the mutual inductance of the transmission coil. Lastly, a model of the transmission coil is developed to authenticate the practicality of the mutual inductance equation and the adaptation scheme. Measurement and calculation results indicate that the difference between the calculated value of the mutual inductance formula and the actual mutual inductance value of the coil, following deflection and offset, is below 5%. Moreover, the algorithm, along with the employed adaptation strategy, consistently demonstrates effectiveness in maintaining the mutual inductance value within a predefined range. The temporal efficiency of the algorithm, as measured by the time taken to determine this coordinate position, is consistently under 1 s. This ensures that the algorithm exhibits a rapid response time, a crucial attribute in ensuring its practical utility.

Parameter Optimization of Wireless Power Transfer Based on Machine Learning

Wireless power transfer (WPT) has become a crucial feature in numerous electronic devices, electric appliances, and electric vehicles. However, traditional design methods for WPT suffer from numerous drawbacks, such as time-consuming computations and high error counts due to inaccurate model parameters. As artificial intelligence (AI) continues to gain traction across industries, its ability to provide quick decisions and solutions makes it highly attractive for system optimizations. In this paper, a method for optimizing WPT parameters based on machine learning is proposed. The convolutional neural network is adapted for training and predicting the performance of a pair of coupled coils under a set of input parameters. The performance parameters include the spatial magnetic field distribution map, quality factor, inductance value, and mutual inductance value, which are critical in determining the efficiency and selecting optimal coil parameters such as the number of turns and wire diameter. Moreover, the spatial magnetic field distribution map is also helpful for identifying design compliance with the electromagnetic field safety standards. The training results reveal that the proposed method takes an average of 3.2 ms with a normalized image prediction error of 0.0034 to calculate the results to calculate one set of parameters, compared to an average of 23.74 s via COMSOL. This represents significant computational time savings while still maintaining acceptable computational accuracy.

Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis

This paper employed an electrical circuit simulator to investigate an electrodynamic suspension system (EDS) for passenger rail transport applications. Focusing on a null-flux suspension system utilizing figure-eight-shaped coils (8-shaped coils), the aim was to characterize the three primary electromagnetic forces generated in an EDS and to compare the findings with existing literatures. The dynamic circuit theory (DCT) approach was utilized to model the system as an electrical circuit with lumped parameters, and mutual inductance values between the superconducting (SC) coil and the upper and lower loops of the 8-shaped coil were calculated and inputted into the simulator. The results were compared with experimental data obtained from the Yamanashi test track. The comparison demonstrated close alignment between the theoretical expectations and the obtained experimental curves, validating the accuracy of the proposed model. The study highlights the advantages of this new approach, including faster computation times and efficient implementation of modifications. Overall, this work contributes to the ongoing development and optimization of null-flux suspension Maglev systems.

Analysis of the behavior of asynchronous electric drive with a closed scalar control system when changing the inductance of the magnetizing circuit

The article was devoted to the study of an automated electric drive with a scalar closed-loop speed control system. Severe duty and operating modes of electric drive determine the actual service life. Wear of the induction motor, as a key link of the electric drive, was associated with deviation from nominal parameters. The deviation of parameters of the induction motor equivalent circuit determined the resultant change of characteristics. The parameters of the equivalent circuit determined the accuracy of the adjustment of regulators and optimal algorithms in the control system of the electric drive. In continuous operation modes the possibility of auto-tuning regulators, which requires stopping or no-load mode, was excluded. The paper considered the influence of the magnetization circuit mutual inductance value of the induction motor on the behavior of the electric drive control system. Evaluation of the behavior of the scalar closed-loop speed control system was performed on the basic energy (power factor, efficiency factor) and mechanical (speed, electromagnetic torque) characteristics of the electric drive.

Artificial Neural Network-Based Parameter Identification Method for Wireless Power Transfer Systems

In this paper, a Wireless Power Transfer (WPT) system parameter identification method that combines an artificial neural network and system modeling is presented. During wireless charging, there are two critical parameters; specifically, mutual inductance and load resistance, which change due to the movement of the transmitter/receiver and battery conditions. The identification of these two uncertain parameters is an essential prerequisite for the implementation of feedback control. The proposed method utilizes an Artificial Neural Network (ANN) to acquire a mutual inductance value. A succinct system model is formulated to calculate the load resistance of the remote receiver. The maximum error of the mutual inductance estimation is 2.93%, and the maximum error of the load resistance estimation is 7.4%. Compared to traditional methods, the proposed method provides an alternative way to obtain mutual inductance and load resistance using only primary-side information. Experimental results were provided to validate the effectiveness of the proposed method.

On-Line Foreign Object Detection Using Double DD Coils in an Inductive Wireless Power Transfer System.

This paper proposes an on-line method for foreign object detection in a double DD coil system. The foreign object is detected by real-time measurement of the mutual inductance between the transfer pads. Measurement of the mutual inductance between coils can be performed at the start, during initialisation, or during the wireless power transfer. The coils in the double DD coil structure can be used separately; one coil can be used for power transfer and the other can be used for the mutual inductance measurement. The mutual inductance measurement is based on the voltage measurement across the open circuit receiver coil. The measured value of mutual inductance between the transmitter and the receiver pad can be used in a control algorithm and in a foreign object detection algorithm. Additionally, a 2DDq coil structure can be used as a replacement for the double DD coil structure, which increases the power transfer density. The DD coils in the double DD coil structure can also be driven using two phase-shifted voltages, which enables better location and detection of foreign objects. The method also helps to differentiate the mutual inductance change due to the distance change from the mutual inductance change due to the presence of a foreign object.

Simplified Mutual Inductance Calculation of Planar Spiral Coil for Wireless Power Applications.

In this paper, a simplified method for the calculation of a mutual inductance of the planar spiral coil, motivated from the Archimedean spiral, is presented. This method is derived by solving Neumann’s integral formula in a cylindrical coordinate system, and a numerical tool is used to determine the value of mutual inductance. This approach can calculate the mutual inductances accurately at various coaxial and non-coaxial distances for different coil geometries. The calculation result is compared with the 3D finite element analyses to verify its accuracy, which shows good consistency. Furthermore, to confirm it experimentally, Litz wire is used to fabricate the sample spiral coils. Finally, the comparison of a simplified method is also studied relative to the coupling coefficient. The accuracy of the calculation results with the simulation and the measurement results makes it a good candidate to apply it in wireless power applications.

Finite element models of dynamic-WPTS: a field-circuit approach

PurposeThe paper aims to propose a a field-circuit method for investigating the magnetic behavior of a wireless power transfer system (WPTS) for the charge of batteries of electric vehicles. In particular, a 3D model for finite element analysis (FEA) for the field simulation of a WPTS is developed. Specifically, the effects of aluminum shield and steel layer, representing the car frame, on the self and mutual inductances are investigated. An equivalent electric circuit is then built, and the relevant lumped parameters are identified by means of the FEAs.Design/methodology/approachThe finite element model is used to evaluate self and mutual inductances in several transmitting-receiving coil configurations and relative positions. In particular, the FEA simulates the aluminum and steel layers as shell elements in a 3D domain. The self and mutual inductance values in the aligned coil case are also used as input parameters in a circuit model to evaluate the onload current.FindingsThe use of shell elements in FEA substantially reduces the number of mesh elements needed to simulate the eddy currents in the steel and aluminum layer, so putting the ground for low-cost field analysis. Moreover, the FEA gives an accurate computation of the self and mutual inductance to be used in a circuit model, which, in turn, provides a fast update of the onload induced current.Originality/valueTo save computational time, the use of 2D shell elements to model thin conductive regions introduces a simplified FEA that could be used in the WPTS simulation. Moreover, the dynamic behavior of WPTS, i.e. the operation when the receiving coil is moving with respect to the transmitting one, is considered. Because of the lumped parameters’ dependence upon the relative positions of the two coils, the proposed method allows identifying the circuit parameters for several configurations so substantially reducing the computational burden.

Self and Mutual Inductance Behavioral Modeling of Square-Shaped IPT Coils With Air Gap and Ferrite Core Plates

The design and optimization of coils for Inductive Power Transfer (IPT) systems is an iterative process conducted in Finite Element (FE) tools that takes a lot of time and computational resources. In order to overcome such limitations in the design process, new empirical equations for the evaluation of the self-inductance and mutual inductance values are proposed in this work. By means of a multi-objective genetic programming algorithm, the self-inductance, the mutual inductance and the coupling factor values obtained from FE simulations of IPT link are accounted by analytical equations, based on the geometric parameters defining the IPT link. The behavioral modeling results are compared with both FE-based and experimental results, showing a good accuracy.

Magnetic Coupling-Based Battery Impedance Measurement Method

The battery impedance is an important indicator of battery health status. In this paper, a magnetic coupling-based impedance measurement method for electrochemical batteries is proposed. Without affecting the energy injection stage, the designed suppression resistance can minimize the influence of the primary circuit response, and the under-damped oscillation waveform containing the battery impedance information can be directly obtained on the primary inductance. The change of the mutual inductance value within a certain range will not affect the measurement results. Therefore, the measurement system has high stability and robustness. By utilizing the discrete Fourier transform (DFT)-based algorithm to calculate the damped oscillation parameters, the battery impedance is accurately derived from the calculated attenuation coefficient and damped oscillation frequency. The accuracy of this method under different coupling parameters is analyzed and verified by simulation and experiment on a Li-ion battery, which could be employed to estimate the state of charge (SOC).

Minimization of Torque Ripple in the Brushless DC Motor Using Constrained Cuckoo Search Algorithm

This paper presents the application of the cuckoo search (CS) algorithm in attempts to the minimization of the commutation torque ripple in the brushless DC motor (BLDC). The optimization algorithm was created based on the cuckoo’s reproductive behavior. The lumped-parameters mathematical model of the BLDC motor was developed. The values of self-inductances, mutual inductances, and back-electromotive force waveforms applied in the mathematical model were calculated by the use of the finite element method. The optimization algorithm was developed in Python 3.8. The CS algorithm was coupled with the static penalty function. During the optimization process, the shape of the voltage supplying the stator windings was determined to minimize the commutation torque ripple. Selected results of computer simulation are presented and discussed.

Improving a model of the induction traction motor operation involving non-symmetric stator windings

The analysis of operating conditions of induction traction motors as part of traction electric drives of electric locomotives reported here has revealed that they are powered by autonomous voltage inverters with asymmetric non-sinusoidal voltage. It was established that the induction motor operation may be accompanied by defects caused by the asymmetrical modes of the motor stator. A model of the induction motor has been proposed that takes into consideration changes in the values of mutual inductance of phases and complete inductance of the magnetization circuit due to changes in the geometric dimensions of the winding caused by a certain defect. An algorithm that considers the saturation of the magnetic circuit of the electric motor has been proposed. This approach to modeling an induction motor is important because if one of the stator's windings is damaged, its geometry changes. This leads to a change in the mutual inductance of phases and the complete inductance of the magnetization circuit. Existing approaches to modeling an induction motor do not make it possible to fully take into consideration these changes. The result of modeling is the determined starting characteristics for an intact and damaged engine. The comparison of modeling results for an intact engine with specifications has shown that the error in determining the controlled parameters did not exceed 5 %. The modeling results for the damaged engine demonstrated that the nature of change in the controlled parameters did not contradict the results reported by other authors. The discrepancy in determining the degree of change in the controlled parameters did not exceed 10 %. That indicates a high reliability of the modeling results. The proposed model of an induction electric motor could be used to investigate electromagnetic processes occurring in an electric motor during its operation as part of the traction drive of electric locomotives

Estimation of Critical Current of HTS RF-SQUID

The operation of the RF SQUID is restricted by the condition that the inductance parameter β L must be in the range of 1−3. However, since both ends of the Josephson junction (JJ) of RF-SQUID are shorted, it is difficult to non-destructively estimate the critical current (IC ). Thus, we proposed a technique for the non-destructive measurement of the IC of a high-temperature superconducting (HTS) RF-SQUID ring by evaluating the behaviour of the flux in superconducting thin films using a SQUID magnetometer. A superconducting ring sample with JJ was placed below the HTS SQUID magnetometer and cooled down to 77 K. The change in the SQUID output was monitored on application of the magnetic field. When increasing the field, the waveforms indicated that the screening current of the ring sample exceeded the I C of the JJ, and the JJ became a normal-conducting state. As a result, we estimated the IC of the JJ of this sample as 134 μA using the values of mutual inductance and the coupling coefficient α between the coil and the sample.

Modeling and statistical analysis of distribution parameters of random cable bundles based on image recognition technology

In this paper, a modeling method of actual bending random bundled wire harness is proposed. Firstly, based on image recognition technology, the three-dimensional coordinates of bending wire harness axis are reconstructed by using two photos of actual wire harness in side view and top view; then the random bundled wire harness is realized based on random transfer path method. Based on this modeling method, this paper analyzes the statistical characteristics of distribution parameters of bending random wire harness by Monte Carlo simulation, and finds that the variation trend of self inductance, mutual inductance and mutual capacitance along the line is consistent with the variation trend of wire harness height, while the trend of self capacitance is opposite; the coefficient of variation of self capacitance, self inductance and mutual inductance has negative correlation with wire harness height; the bundling randomness is not obvious It will change the mean value of self inductance and self capacitance, but reduce the mean value of mutual capacitance and mutual inductance.

Design of a Rectangular Pickup Coil Fabricated on a PCB Using WBG Power Semiconductor in Discrete Package

Power semiconductors based on wide bandgap (WBG) devices are capable of fast switching and have low on-resistance. Accordingly, a fast sensor with a higher bandwidth is required for circuit inspection based on switch current measurements. Thus, it is necessary to have a current sensor in the printed circuit board (PCB) circuit for diagnosis and protection of the surface mount device (SMD) type circuit system. Accordingly, a pickup coil with the advantages of a high degree of sensor configuration freedom, wide bandwidth, and low cost can be a good alternative. This study analyzes the influence of coil shape and parameters on sensor design as a guideline for embedding a pickup coil in an SMD-type PCB circuit of a WBG power semiconductor-based, half-bridge structure. The mutual inductance and self-inductance values of the coil are considered large variables in the design of a sensor coil for simultaneously maintaining high bandwidth and sensor sensitivity. Therefore, magnetic and frequency response analyses were conducted to verify the correlation with inductance, the influence of coupling capacitance, and the influence of the magnetic field formation via the current flowing through the external trace inside the PCB. The coil model is verified and discussed through simulation and double pulse tests.