Abstract: Inductively coupled wireless power transfer (S/SP) offers high transmission power and efficiency, making it suitable for wireless charging of electric vehicles. However, it requires precise alignment of the primary and secondary coils of the loosely coupled transformer. Changes in the relative positions of the primary and secondary coils cause variations in mutual inductance and leakage inductance, thus affecting the system's transmission power and efficiency. This paper first analyzes the input and output currents of four basic compensation topologies when the positions of the primary and secondary coils change. Then, it analyzes the impact of changes in leakage inductance on the output power and transmission efficiency of the S/SP compensation topology. Addressing the problems of the four basic compensation topologies when the positions of the primary and secondary coils change, this paper analyzes the S/SP compensation topology. By changing the value of the compensation capacitor on the secondary side of the loosely coupled transformer, and verifying the results through Matlab simulations, the S/SP compensation topology can achieve rated power transmission and maintain constant voltage and current on the secondary compensation capacitor when the horizontal positions of the primary and secondary coils change.
1 Introduction
In recent years, to meet the demands of energy conservation, environmental protection, and a low-carbon economy, the development of electric vehicles (EVs) has become a trend. Wired charging and wireless charging technology (WPT) are the two main methods of charging electric vehicles. As a new type of charging method, wireless charging is more convenient and safer than wired charging, with no risk of sparks or electric shock, and can adapt to harsh environments and weather conditions.
Inductively coupled power transfer (ICPT) offers high power transmission and efficiency, making it well-suited for wireless charging of electric vehicles. However, it requires precise alignment of the primary and secondary coils of the loosely coupled transformer. In actual charging, varying ground cleanliness or parking offset can reduce output power and transmission efficiency, and prolong charging time. Coil misalignment can cause changes in leakage inductance, leading to a loss of full compensation. Numerous studies, both domestic and international, have addressed this issue, including coil optimization and design, matching network design, and compensation topology design. One method, employing unequal primary and secondary coil sizes, ensures minimal change in coupling coefficient when axial or lateral coil misalignment occurs; however, this method is only applicable to circular planar coils. Another method, using two orthogonally placed secondary windings, reduces coupling coefficient changes and improves system transmission efficiency during coil misalignment, but increases the number of windings and complicates the structure. A method for optimizing helical coil design achieves maximum output power and system transmission efficiency during coil misalignment, but this is only applicable to near-field coupling. A SP/S compensation topology is proposed, which enables the coil to transmit rated power even at high offset rates. However, the voltage and current of the compensation capacitors on the primary and secondary sides are not analyzed.
This paper first analyzes the input and output currents of four basic compensation topologies when the primary and secondary coils of a loosely coupled transformer are offset, and then analyzes the impact of changes in leakage inductance of the primary and secondary coils on the output power and transmission efficiency of the S/SP compensation topology. Addressing the problems of the four basic compensation topologies, this paper analyzes the S/SP compensation topology. By changing the value of the secondary compensation capacitor, the paper analyzes the system transmission power and the voltage and current values of the secondary compensation capacitor when the relative horizontal positions of the primary and secondary coils change.
2 coil offset
Most loosely coupled transformers have symmetrical primary and secondary coils with fixed self-inductance. When aligned, they achieve a high coupling coefficient and thus higher power output. However, in actual wireless charging of electric vehicles, coil misalignment frequently occurs, reducing system transmission power and efficiency. The coil offset structure is shown in Figure 1. This paper mainly studies the impact of lateral coil offset (i.e., the relative change in the horizontal position of the primary and secondary coils) on the output characteristics of the S/SP compensation topology. Figure 2 shows the effect of axial and horizontal position changes of the primary and secondary coils of a loosely coupled transformer on the mutual inductance M. Figure 3 shows the effect of lateral offset of the primary and secondary coils of a loosely coupled transformer on the input current i1 and output current i2 of four basic compensation topologies.
Figure 1. Structural diagram of primary and secondary coil offset.
As can be seen from Figure 2, when the coil is deflected, the mutual inductance M decreases rapidly with the increase of the deflection distance, which in turn affects the system's transmission power and transmission efficiency.
Figure 2. Curves showing the variation of mutual inductance M with lateral offset c and axial offset h.
As can be seen from Figure 3, when the primary side uses series compensation, the primary side current increases with the increase of the lateral offset distance, which can easily exceed the power supply capacity; when the primary side uses parallel compensation, the output current i2 decreases rapidly and cannot reach the rated output power.
Figure 3 shows the curves of input current i1 and output current i2 as a function of lateral offset distance c for four basic compensation topologies.
3S/SP Compensation Topology
3.1S/SP Compensation Topology
Figure 4 shows the S/SP compensation topology diagram, and Figure 5 shows the S/SP compensation topology principle diagram.
Figure 4 S/SP compensation topology
Figure 5. Equivalent schematic diagram of S/SP
uAB is the effective value of the output voltage after high-frequency inverter operation using a series compensation topology on the primary side.
The secondary side uses an LC filter circuit. Considering only the fundamental component, the rectifier section and the load RL can be equivalent to Re:
3.2 Effect of changes in primary and secondary side leakage inductance on the output characteristics of S/SP compensation topology
When the relative positions of the primary and secondary coils of a loosely coupled transformer change, the leakage inductances L11 and L12 of the primary and secondary coils also change, resulting in a loss of complete compensation, which in turn affects the transmission power and transmission efficiency. This paper analyzes the impact of changes in the leakage inductance of the primary and secondary coils of an S/SP compensation topology on the output power and transmission efficiency.
As can be seen from Figures 6 and 7, changes in the leakage inductance of the primary and secondary sides have a significant impact on the output power and transmission efficiency. This indicates that changes in the leakage inductance parameters caused by variations in the primary and secondary sides of a loosely coupled transformer can have a substantial impact on the S/SP compensation topology.
3.3 Values of Primary and Secondary Side Compensation Capacitors
To address the issues arising from the offset of the primary and secondary coils in the four basic compensation topologies, an S/SP compensation topology is introduced. By introducing a coefficient KC (where KC≤1), the values of the secondary compensation capacitors C2 and C3 are altered. This allows for the transmission of rated power even when the coil is offset, while also stabilizing the current value of the secondary compensation capacitor C2 and the voltage value of the capacitor C3. This saves costs when selecting compensation capacitors and does not increase the voltage and current stress on the capacitors.
By changing the values of the secondary compensation capacitors of the loosely coupled transformer, the rated output power is ensured to be transmitted when the coil is deflected. The values of the primary and secondary compensation capacitors C1, C2, and C3 are as follows:
Where KC≤1
Where: L1 and L2 are the inductances of the primary and secondary windings, respectively; C1, C2, and C3 are the primary and secondary compensation capacitors, respectively; ω is the resonant frequency; and KC is a coefficient less than or equal to 1. By changing the value of the coefficient KC, the values of the secondary compensation capacitors C2 and C3 are changed.
The equivalent impedance Zr from the secondary side to the primary side of a loosely coupled transformer:
System input impedance Zin:
In order for this compensated topology to operate at the resonant point, the imaginary part of Zin should be zero, therefore:
According to the above formula, the compensation capacitor C3 can be obtained:
in:
3.4 Output Characteristic Analysis
This article analyzes and calculates the transmission power, secondary compensation capacitor voltage, and current values when the primary and secondary windings of an S/SP compensated topology loosely coupled transformer experience a horizontal positional shift.
S/SP compensated topology output power Pout:
Current values of secondary-side compensation capacitor C2 and voltage values of capacitor C3:
in:
4. Simulation Results Analysis
The output power Pout, the current value of the secondary compensation capacitor C2, and the voltage value of C3 in the S/SP compensation topology were simulated and analyzed using Matlab simulation software. Table 1 shows the designed simulation parameters; Figure 8 shows the relationship between the output power Pout of the S/SP compensation topology and the horizontal distance c between the primary and secondary sides; Figure 9 shows the relationship between the current of the secondary compensation capacitor C2 and the horizontal distance c between the primary and secondary sides; Figure 10 shows the relationship between the voltage of the secondary compensation capacitor C3 and the horizontal distance c between the primary and secondary sides.
As can be seen from Figures 8, 9, and 10, as the horizontal distance c increases, the larger KC becomes, the greater the output power Pout exceeds the rated output power. Furthermore, the current value of the secondary compensation capacitor C2 and the voltage value of the capacitor C3 also increase significantly, increasing the capacitor voltage and current values, which is detrimental to the safe and reliable operation of the system.
Combining Figures 8, 9, and 10, it can be concluded that when KC=0.35, when the relative horizontal positions of the primary and secondary windings of the loosely coupled transformer change, it not only has rated power transmission, but also the current value of the secondary compensation capacitor C2 and the voltage value of the capacitor C3 remain basically unchanged, thus enhancing the stable operation of the secondary side.
5. Conclusion
To address the problems existing in the four basic compensation topologies, this paper analyzes the S/SP compensation topology. By changing the value of the secondary compensation capacitor, as the horizontal distance c between the primary and secondary coils increases, the larger KC becomes, the greater the output power Pout exceeds the rated output power. Furthermore, the current value of the secondary compensation capacitor C2 and the voltage value of capacitor C3 also increase significantly, increasing capacitor voltage and current values, which is detrimental to the safe and reliable operation of the system. By selecting a coefficient KC of 0.35, when the relative horizontal positions of the primary and secondary coils change, the S/SP compensation topology can not only transmit the rated power, but also maintain the current value of the secondary compensation capacitor C2 and the voltage value of capacitor C3 essentially unchanged, enhancing the stable operation of the secondary side voltage and current.
