Coupling Coefficient and Load Estimation for Wireless Power Transfer Systems with Transmitter Side Input Current

This paper presents an online and accurate method for estimating the coupling coefficient in wireless power transfer (WPT) systems with voltage loads using zero-phase angle (ZPA) frequencies. While the characteristics of ZPA-controlled WPT systems have been extensively studied, their applicability has largely been limited to resistive loads. This study investigates the ZPA frequencies of WPT systems with voltage loads, demonstrating that these frequencies depend solely on the coupling coefficient and are largely independent of output voltage in pronounced bifurcation modes. Leveraging this unique characteristic, a rapid and accurate coupling coefficient estimation method is proposed, utilizing self-oscillation to automatically locate ZPA frequencies. The proposed method does not generally affect system design or normal operation, completing the coupling estimation in just 1.5ms. It requires no wireless communication, additional hardware, or complex calculations across the entire coupling range. The effectiveness of the method is validated through simulation and experimental results.

Compared with the traditional plug-in charging system, wireless power transfer (WPT) system has the characteristics of electrical and mechanical isolation. A wireless system is proposed suitable for battery charging under misalignment or range variation, and the constant current (CC) and constant voltage (CV) charging are realized by the estimation of coupling coefficient. Firstly, two different operating frequencies based on SS basic compensation structure are designed to realize CC output and CV output respectively. After circuit analysis, CC and CV output cannot be achieved when the position of the secondary coil changes. To solve this issue, when the coil is under misalignment or range variations, the required system parameters are measured, and the coupling coefficient in the charging process is estimated by using the transconductance amplitude equation. Then the corresponding input voltage or working frequency is calculated and fine-tuned. Therefore, the CC and CV charge of the battery can be realized under misalignment or range variation. Finally, experimental results are presented to verify the feasibility and correctness of this method.

The coupling coefficient determines the transfer efficiency of the wireless power transfer (WPT) system. The magnetic leakage can be reduced, and the coupling coefficient of the coil can be enhanced by adding a magnetic shield. Thus, the transfer efficiency of the WPT system can be improved. However, when the receiving coil is added with magnetic shield and occurs horizontally misaligned, the coupling coefficients between the coils with the magnetic shield can only be calculated by finite element simulation, and there is no calculation method for the coupling coefficient of two circular coils with bilateral finite magnetic shield at horizontal misalignment. Therefore, based on Maxwell's equations and Bessel's function, the formula of the coupling coefficient between circular coils at coaxial is derived by the subdomain hierarchical analysis (SHA) method. On this basis, the coupling coefficient calculation formula between circular coils at horizontal misalignment is further derived by using the boundary vector equivalence (BVE) method. The results show that the maximum experimental error is not more than 5.58%, and the longest average time of the algorithm is not more than 1.282 s, which verifies the effectiveness and rapidity of the proposed method.

A wireless power transfer (WPT) system via magnetic resonance coupling method is attracting attention to high convenience. A WPT system has problems such as power transmitting loss and output voltage fluctuation due to the change in the coupling coefficient and the load state. In previous method, sliding mode control system as a tracking controller considering nonlinearity and uncertainty has been proposed, but the output of this control system had bias and chattering. This paper proposes operator-based nonlinear sliding mode control system to reduce chattering and bias simultaneously for a WPT system using buck converter. First, the model of the WPT system using rectifier and buck converter is explained and dynamics formulas are derived. Next, the proposed operator-based nonlinear sliding mode control system design for the WPT system is described and tracking performance is confirmed. Finally, the result of simulation of constant voltage control and comparison with the previous method is shown.

Transfer efficiency (TE) is an important research topic in the practical application of a wireless power transfer (WPT) system. WPT system is a loosely coupled system; the coupling coefficient changes drastically due to the relative movement of the transmitting and receiving sides. It is difficult to achieve maximum efficiency tracking (MET) only from the research of frequency tracking, impedance matching, and system parameters under a fixed coupling coefficient. This article proposes a novel MET control method of the WPT system with optimized T-type impedance matching network under the real-time identification of a coupling coefficient to realize the MET control. This method synthetically analyzes the nonlinearity of the rectifier circuit, the identification of coupling coefficient, the variation of load resistor, and the controllability of the output voltage, involving the main factors of the MET control. The simulation and experimental results show that the WPT system has a good performance on MET and constant output voltage control; the validity and accuracy of the proposed MET control method are consistently verified.

Coupling coefficient calculation and optimization of positive rectangular series coils in wireless power transfer systems

To meet the regulations established to limit human exposure to time-varying electromagnetic fields (EMFs) such as the International Committee on Non-Ionizing Radiation Protection (ICNIRP) guidelines, thin metallic sheets are often used to shield magnetic field leakage in high power applications of wireless power transfer (WPT) systems based on magnetic field coupling. However, the metals in the vicinity of the WPT coils cause the decrease of self and mutual inductances and increase of effective series resistance; as such, the electric performance including transmission power and the efficiency of the system is affected. With the research objective of further investigating excellent shielding effectiveness associated with system performance, the utilization of the optimal magnetic field shielding method by metallic sheets in magnetic field coupling WPT is carried out in this paper. The circuit and 3D Finite Element Analysis (FEA) models are combined to predict the magnetic field distribution and electrical performance. Simulation and experiment results show that the method is very effective by obtaining the largest possible coupling coefficient of the WPT coils within the allowable range and then reducing the value nearest to and no smaller than the critical coupling coefficient via geometric unbroken metallic sheets. The optimal magnetic field shielding method which considers the system efficiency, transmission power, transmission distance, and system size is also achieved using the analytic hierarchy process (AHP). The results can benefit WPT by helping to achieve efficient energy transfer and safe use in metal shielded equipment.

We present a procedure for system identification and tuning of a wireless power transfer (WPT) system with four magnetically coupled resonators, where each resonator consists of a coil and a capacitor bank. The system-identification procedure involves three main steps: 1) individual measurement of the capacitor banks in the system; 2) measurement of the frequency-dependent two-port impedance matrix of the magnetically coupled resonators; and 3) determining the inductance of all coils and their corresponding coupling coefficients using a Bayesian approach. The Bayesian approach involves solving an optimization problem where we minimize the mismatch between the measured and simulated impedance matrix together with a penalization term that incorporates information from a direct measurement procedure of the inductances and losses of the coils. This identification procedure yields an accurate system model which we use to tune the four capacitance values to recover high system-performance and account for, e.g., manufacturing tolerances and coil displacement. For a prototype WPT system, we achieve 3.3 kW power transfer with 91% system efficiency over an air-gap distance of approximately 20 cm.

Wireless power transfer (WPT) systems’ efficiency is significantly impacted by non-monotonic variations in the coupling coefficient. For very short distances or strong-coupling cases, the WPT efficiency is minimal at the natural resonant frequency, with two peaks around this frequency, known as the frequency splitting phenomenon. On the other hand, WPT capability decreases for long distances or weak coupling cases. Therefore, adaptive matching is required for WPT systems with varying distances, like wireless charging systems for electric vehicles (EVs). This paper first presents a detailed analysis of the frequency splitting phenomenon by studying the root locations of the WPT system’s transfer function. Then, a real-time fixed-frequency adaptive impedance matching (IM) method is proposed, in which the amplitude and phase of the input impedance is estimated using the average active power, the average reactive power, and the amplitude of input voltage. Unlike traditional search-and-find techniques, the proposed method calculates the optimal IM network parameters only in a single iteration, which improves the convergent speed. A scaled-down 20-Watt prototype controlled by the TMSF2812 is fabricated and used to validate the effectiveness of the proposed method over a wide range of coil-to-coil distances.

Maximum power transfer tracking (MPTT) is meant to track the maximum power point during the system operation of wireless power transfer (WPT) systems. Traditionally, MPTT is achieved by impedance matching at the secondary side when the load resistance is varied. However, due to a loosely coupling characteristic, the variation of coupling coefficient will certainly affect the performance of impedance matching, therefore MPTT will fail accordingly. This paper presents an identification method of coupling coefficient for MPTT in WPT systems. Especially, the two-value issue during the identification is considered. The identification approach is easy to implement because it does not require additional circuit. Furthermore, MPTT is easy to realize because only two easily measured DC parameters are needed. The detailed identification procedure corresponding to the two-value issue and the maximum power transfer tracking process are presented, and both the simulation analysis and experimental results verified the identification method and MPTT.

This paper presents a theoretical analysis, an optimal design method, and experimental results for a wireless power transfer (WPT) system with an intermediate coil. The analytical expression of the dc voltage transfer function is presented and discussed. In a two-coil WPT system, which has low coupling coefficient, the intermediate coil boosts the apparent self-inductance and magnetizing inductance of the primary side at around the resonance frequency of the intermediate coil, so that the apparent coupling coefficient is compensated. The coupling coefficient makes the system efficiency increase and induces bifurcation phenomenon. From the analysis, this paper proposes an optimal design method using the second resonance frequency operation with the bifurcation phenomenon and presents design procedure for high efficiency. A prototype of the WPT system with the intermediate coil is implemented and experimented to verify the validity of the analysis and the proposed design method. The prototype operates at 100 kHz switching frequency and has an air gap between primary and secondary side of 200 mm. An overall system efficiency of 95.57% has been achieved at 6.6 kW of output power.

The magnetic fields (MF) generated in close proximity to high power wireless power transfer (WPT) systems generally exceed exposure limits and might also violate basic restrictions (BR). However, there are as yet no available standards describing methods to measure the MF generated by WPT systems. In this study, a new method for demonstration of compliance with the BR in the close proximity to sources at frequencies from 3 kHz to 10 MHz is proposed. This approach mitigates overestimation by incident field assessment in strong field gradients close to WPT systems. The spatial peak MF amplitude and gradient generated by WPT systems are measured with a field gradient probe at the closest location to the source. The induced fields and absorbed power are then calculated on the basis of specific transformation functions for testing of compliance with the BR of all international safety guidelines.

The wireless power transfer (WPT) system based on parity-time (PT) symmetry has the advantages of robustness, stable, and efficient power transmission. However, the region of PT symmetry is limited, which cannot satisfy some practical requirements. Multiple transmitting coils have been shown to improve the misalignment tolerance of WPT systems. Towards this end, a parity-time-symmetric-based WPT (PT-based WPT) system with double-transmitting coil is presented in this article. First, an approximate equivalent circuit model of this PT-based WPT system was developed. Second, compared with the conventional single transmitting coil PT-based WPT system, the proposed system expands the PT symmetry region and provides higher output power and transmission efficiency. Furthermore, the mutual inductance between two transmitting coils can be designed to meet the requirements of different scenarios, which improves the freedom of system design. Finally, a 30 W prototype is designed to evaluate the proposed WPT system. Experimental results show that the critical coupling coefficient is reduced by about 12.5% at <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> = 0.51, which implies a longer transmission distance. Moreover, the maximum output voltage fluctuation in the strongly coupled region is only 3.5%, while the transfer efficiency is approximately constant, which implies stable and efficient power transfer.

In multi‐input and multi‐output (MIMO) wireless power transfer (WPT) systems, the destructive interference between multiple transmitters and receivers brings a serious impact on power transmission efficiency. This paper proposes a voltage control strategy to maximize the transmission efficiency of a MIMO WPT system by controlling the amplitude and phase of the transmitter voltages. However, the complexity of the realistic WPT circuit topology and the uncertainty in the related parameters obstruct the establishment of an accurate closed‐form description of the WPT model to optimize the transmission efficiency of the system. In this paper, a simple multi‐port network model is introduced to simulate a MIMO system to avoid the complex circuit topology and a large number of circuit elements. To determine the parameters of the proposed model, a simple yet efficient methodology, by sequentially changing the excitations of the input ports and sampling the responses at the out ports, is proposed. A voltage control methodology to optimize the transmission efficiency of a MIMO wireless power transfer system is finally developed. To validate the proposed model and voltage control methodology, a three‐input and three‐output WPT prototype is designed and fabricated and used as the experimental platform. The performances of the proposed voltage control methodology are compared to both the experimental ones and those without the proposed voltage control methodology.

In this letter, we compare two operating frequency tuning methods—the zero phase angle (ZPA) and the minimum reflection coefficient magnitude (MRCM) frequency tuning methods—to enhance the power transfer efficiency and output power in the wireless power transfer (WPT) system. For the MRCM frequency tuning method which has been introduced recently, the WPT system can be analyzed by considering the system as a matching network connected to a generator and a load. Through experiments, in the over-coupled region, the MRCM frequency tuning method has higher output power and efficiency than the ZPA frequency tuning method. Above all, the MRCM frequency tuning method does not need the information on the coupling coefficient as well as the primary and secondary resonators.