1. Introduction
With the emergence of energy crisis and environmental pollution problems, electric vehicles (EVs) are regarded as one of the essential methods to alleviate environmental concerns. The rapid growth of EVs has pushed the higher requirement for more reliable charging methods. Wireless power transfer (WPT), as one of the promising alternatives of traditional wired charging, can address the issues of easily broken power cables and electric shocks under the harsh environments of EVs [
1,
2]. DC microgrids, due to their higher efficiencies, easier integration into electric devices, and simpler control over their AC counterparts, have gained increasing attention in recent years [
3,
4,
5,
6,
7,
8]. Future WPT-based EV charging infrastructures have great potential to be integrated into DC microgrids. An imaginary diagram of WPT-based EV charging in DC microgrids is shown in
Figure 1. When WPT is adopted in high-power applications, large amplitudes of primary-side voltages and currents can lead to significant power loss on the driving circuits. Therefore, it is crucial to design coils, circuits, and controls of WPT systems to achieve optimal efficiencies while still maintaining accurate output regulations.
A typical WPT system for EV charging in DC microgrids comprises (i) a full-bridge inverter at the front end to convert DC voltage to high-frequency AC voltage, (ii) a coupled resonator with compensated circuits at both transmitter and receiver sides, (iii) a diode bridge rectifier and a filter capacitance, and (iv) a battery load, which can be modelled as pure resistance [
9,
10,
11]. The efficiency of the WPT system is mainly determined by the conduction loss on the equivalent series resistances (ESRs) of the resonators and switching loss on the full-bridge inverters. Thereinto, the conduction loss on the ESRs can be reduced by using high-quality resonator coils, while the switching loss on the inverters can be minimized by achieving zero voltage switching (ZVS).
There are four switches in the primary side of the circuit of the WPT system, and all of them have parasitic capacitance and internal resistance. When the switch tube is turned on, its voltage cannot instantly drop to 0, and its current cannot immediately rise to a stable value. Both voltage and current changes take a certain amount of time, and there will be an overlap between the voltage and current, resulting in conduction losses. The same happens when the switch is turned off. They are called hard-switching problems. Under the same circuit settings, the switch always produces the same loss in each switching period, and the loss is proportional to the switching frequency. The switching loss caused by hard switching limits the increase in the frequency of the inverter, thereby also limiting the miniaturization and weight reduction of the inverter. To reduce the size and weight of the inverter, it is necessary to increase the frequency [
12]. Therefore, soft-switching technology was born to solve the conduction loss problem caused by high frequency.
In WPT systems, a transformer or a coupled coil can transfer energy from the primary side to the secondary side of the circuit through the magnetic field. The coils are compensated with different circuits to achieve the maximum transfer efficiency at the resonant frequency. There are four compensation circuits in the WPT system that are most common, namely: series–series (S-S), series–parallel (S-P), parallel–parallel (P-P), and parallel–series (P-S) [
13,
14]. Soft-switching technology mainly uses the capacitance and inductance in the circuit to adjust the topology in order to avoid current and voltage overlapping as much as possible.
The development of soft-switching technology since the 1970s is shown in
Table 1 [
15].
In the early 1970s, soft-switching technology mainly used series or parallel resonance technology. The DC converter is also called a resonant converter. The resonant converter has three modes of operation defined by the switching frequency. f is the working frequency and fr is the resonant frequency. When f < 1/2fr, the resonator is in the current discontinuous working mode, and the switch tube works under the condition of ZCS. When 1/2fr < f < fr, the resonant tank is capacitive. Therefore, the current leads the voltage when the switch is turned off, and the overlap area becomes smaller. However, the current–voltage overlap area becomes more significant when the switch is turned on as hard switching. When fr < f, the resonant circuit is inductive, and the switch tube is turned on with ZVS, but the hard switching happens when turning off. Series or parallel resonance technology is used in some communication switching power supplies, and the switching frequency ranges from 180 to 450 kHz.
The active clamp ZVS technology proposed later is mainly used in single-ended converters. The authors of [
16] proposed an active clamp ZVS PWM converter design for satellite power supply. Such converters can be implemented with single-ended forward and fly back circuits and their combinations. Taking the active clamp single-ended fly back converter as an example, this converter adds a clamping capacitance and a MOSFET as a clamping switch on the basis of the PWM single-ended fly back circuit. The circuit also utilizes the resonance in the circuit. The parasitic capacitance of the MOSFET and the inductance in the transformer or coupling inductance resonate, so that the main switch can be turned on at zero voltage.
Based on S-P resonance technology, quasi-resonant conversion technology and multi-resonance conversion technology became popular in the next decade [
17,
18]. Initially, it was to realize the soft-switching of the converter composed of a single tube. Still, the push–pull converter, the half-bridge converter, and the full-bridge converter can also participate in the quasi-resonant converter and the multi-resonant converter. The difference between the quasi-resonant converter and the series–parallel resonance technology proposed in the 1970s is that it adds a resonant inductance and a resonant capacitance to the DC converter in the resonant converter. This resonant inductance and resonant capacitance reconstitute a resonant tank. According to the different combinations of series and parallel of inductance and capacitance in the resonant tank, the switch tube can realize ZVS or ZCS [
19]. The resonant tank of a multi-resonant converter is different from that of a quasi-resonant converter. The resonant tank of the multi-resonant converter is composed of the general resonant tank, the leakage inductance of the transformer, and the parasitic capacitance in the circuit [
20]. According to the working principle of the multi-resonant converter and quasi-resonant converter, it can be seen that they also use frequency modulation. This is also a disadvantage because it is challenging to design the output filter for the system using frequency modulation. Therefore, quasi-resonant converters and multi-resonant converters are generally used with low power and low voltage, and with strict requirements on volume and weight.
Since the early resonant circuits all required frequency modulation control, which brought great difficulty to the design of the filter, the converter based on constant frequency control was proposed in the later period. This kind of converter is also called the ZVS PWM converter. The ZVS PWM converter adds an auxiliary switch tube to the quasi-resonant converter in the circuit structure. It controls the resonant tank by controlling the conduction of the auxiliary switch tube. In the ZVS PWM converter, the resonant tank does not always participate in the resonance as before but only works in resonance at the moment when the switch tube is switching [
21]. Therefore, the working time of the resonant tank occupies only a small part of the switching period.
Full-bridge converters are generally used in medium and high-power occasions such as electric vehicle charging. In particular, the primary-side phase-shifted (PPS) full-bridge (FB) DC-DC converter is widely used [
22,
23,
24,
25,
26,
27]. It adopts the phase shift control method, uses the circuit’s own parameters to resonate to achieve soft switching, and maintains the PWM technology’s characteristics of an adjustable duty cycle based on constant frequency [
28].
The main contributions of this paper include
a new passive auxiliary circuit method for WPT systems in achieving both ZVS and accurate output regulations with conventional phase shift control;
an investigation of the soft switching for primary-side inverters in WPT systems with a wide range of load conditions;
a systematic design procedure and parameter selection method for the passive auxiliary circuit.
2. Analysis and Control of Wireless Power Transmission Systems
The main circuit of the wireless charging system used in this paper is shown in
Figure 2. The full-bridge inverter consists of a DC source and four MOSFETs which are
Q1 to
Q4.
D1 to
D4 are the intrinsic diodes of
Q1 to
Q4 and
C1 to
C4 are the corresponding capacitances. The resonant tank circuit adopts the S-S compensation circuit.
Lp and
Ls represent the inductances on the primary and secondary side coils, respectively, and
M is the mutual inductance.
Cp and
Cs are the compensated capacitances. Meanwhile
ip and
is denote the currents of the primary and secondary circuits, respectively.
DR1 to
DR4 represent the four diodes in the full-bridge rectifier.
Cf is the filter capacitance and
RLd is the load resistor in the secondary circuit.
The wireless charging system uses the phase-shifted full-bridge control mode.
Q1 and
Q3 are called leading legs, and
Q2 and
Q4 are called lagging legs.
Figure 3 shows a possible switching signal waveform for MOSFETs.
is the phase shift angle. Fully compensated resonance occurs at the same operating frequency on both the primary and secondary side of the circuit.
A stable output voltage is essential for wireless charging systems. Therefore, the system needs a control circuit to realize the closed-loop control of the circuit. The flow chart of the control circuit is shown in
Figure 4. The proportional–integral (PI) controller will output a phase angle between the leading and the lagging leg. The control loop then generates two sine waves with the phase difference and converts the sine waves into square waves with the same frequency through the comparator. These square waves are the input conduction signals for MOSFETs. Thus, a wireless charging system loop with controllable output voltage is obtained.
However, when the system is at the light load condition, the switching tube will have apparent conduction loss due to the large phase shift, which is called hard switching. The following article analyzes in detail the process of hard switching in the WPT system. The different switching modes for the WPT system are shown in
Figure 5.
Some assumptions are made before the analysis:
All switching devices are ideal;
All capacitances and inductances are ideal regardless of their internal resistance;
The intrinsic capacitances of the four MOSFETs are all equal in value.
At
t1,
Q1 is turned off. The primary current
ip begins to charge
C1 and discharge
C3. When the voltage of
C1 increases to
Vin and the voltage of
C3 decreases to 0, this makes
D3 conduct at
t1. Then
D3 clamps the voltage of
C3 at 0. Therefore,
Q3 can achieve ZVS. At
t2,
Q4 is turned off. The primary current
ip still does not reach 0, charging
C4 and discharging
C2. However, when the system is at light load condition,
ip is already very small. Therefore, although
ip can charge and discharge
Q2 and
Q4, it cannot complete the charge and discharge process. As a result,
Q2 and
Q4 cannot achieve ZVS, as shown in
Figure 6. At
t3,
Q2 is turned on.
ip flows from B to A in reverse.
According to the above analysis, it can be concluded that under the light load condition, the phase shift of the feedback system output is very large. Hence the lagging leg cannot achieve ZVS and results in a significant loss, while the leading leg does not have such a hard-switching problem. Therefore, although the system can realize the controllable output voltage, it needs to solve the conduction loss problem of the lagging leg.
3. Solutions and Analysis to Improve Hard Switching in WPT Systems
In
Section 2,
ip drops to 0 before charging and discharging of the lagging leg is completed. If
ip is large enough to finish the charging and discharging,
Q2 can achieve ZVS. Hence it is considered to place a current source at point B, as shown in
Figure 7a. The current source is used to increase the charging current for the lagging leg to complete the charging and discharging process, and it is typically modelled with a large inductance. The circuit topology after replacing the current source with an inductance is shown in
Figure 7b and
La is the auxiliary inductance.
The control circuit in the WPT system has not changed. The control circuit still feeds back the load voltage mentioned in
Section 2 and controls the output voltage by adjusting the phase shift. The auxiliary inductance in the full-bridge inverter is only to solve the hard-switching problem. The following article analyzes the working process of the improved circuit. After adding the auxiliary inductance, the signal for the MOSFETs and the waveform of current and voltage between points A and B are shown in
Figure 8.
In order to better analyze this circuit, the following assumptions are made:
All switching devices are ideal;
All capacitances and inductances are ideal regardless of their internal resistance;
The intrinsic capacitances of the MOSFETs are all equal in value.
The current flow diagram at different time periods is shown in
Figure 9.
- 1.
Both Q1 and Q4 are on. UAB = Vin. The primary current ip goes from point A to point B.
- 2.
At
t1,
Q1 is turned off. The primary current
ip begins to charge
C1 and discharge
C3, as shown in
Figure 9b. The voltage of the two capacitances gradually changes. When the voltage of
C1 increases to
Vin and the voltage of
C3 decreases to 0, this makes
D3 conduct, clamping the voltage of
C3 at 0, as shown in
Figure 9c. Therefore, if
Q3 turns on after that time, it can achieve ZVS.
- 3.
At
t2,
Q4 is turned off. The primary current
ip charges
C4 and discharges
C2. Since the primary side of the circuit is now inductive, the time for the current to drop to 0 can be greatly increased, providing additional time for the charging and discharging process. As a result,
C2 can successfully end the discharge process until
D2 turns on and clamps the voltage of
Q2 to 0, as shown in
Figure 10. This provides a prerequisite for
Q2 to realize ZVS conduction.
- 4.
The charging and discharging process is completed at t3. If Q2 turns on after t3, it can achieve ZVS. After t3, Q2 and Q3 have already turned on. UAB = −Vin. ip goes down linearly to 0 and then begins to increase reversely.
- 5.
ip still increases during this period. At t6, Q3 is turned off and the circuit operates similarly to Mode 1, which is the beginning of the second switching period. The second half-switching period is similar to the first half period.
As can be seen from
Figure 9, the auxiliary inductance can solve the hard-switching problem of the lagging leg. After adding the auxiliary inductance, the current and voltage overlapping area disappear, resulting in almost no conduction loss. Hence, the efficiency is improved compared to the previous one. Moreover, the added inductance does not affect the work of the control loop, so the improved WPT system can realize soft-switching conduction while controlling the output voltage.
In order to simplify the circuit and reduce the EMI brought by the auxiliary inductance, it can be considered making the primary side circuit inductive without auxiliary inductance. Since the operating frequency of the resonant tank is inconvenient to adjust, the resonant capacitance on the primary side can be changed. Increasing the capacitance value can make the primary side circuit inductive rather than resistive at the original resonant frequency. The resonator on the secondary side still works as a fully compensated mode at the initial operating frequency, so it remains resistive. This improvement method just replaces the auxiliary inductance by adjusting the circuit parameters to make the circuit inductive. It does not affect the control circuit.
4. Simulation Results
Three simulations were performed as follows:
1. First, the experiment observes whether the control circuit can stabilize the system output voltage at the reference value. At the same time, the current and voltage waveform of the lagging leg in the circuit is observed to determine whether ZVS can be achieved.
2. Then, according to the increase in the auxiliary inductance, the switch tubes can all work in the conduction state of the soft switch so that the loss of the circuit can be significantly reduced.
3. Finally, when the power supply voltage fluctuates, and the load resistance fluctuates, the system can still output an ideal voltage to ensure the soft-switching working state.
The parameter values of the switch tube are unchanged in the three simulations and they are shown in
Table 2.
4.1. Simulation of WPT Systems without Auxiliary Circuits
The circuit does not contain the auxiliary inductance and the resonator operates at the resonant frequency. The full-bridge inverter works in the phase shift mode, and the four switches are controlled by the PS modulation.
Table 3 and
Table 4 show the values of various parameters in the circuit. In
Table 4,
Kp and
KI are the parameters of the PI controller.
Kp represents the proportional control coefficient, and
KI represents the integral control coefficient.
Under light load conditions, the phase of the control circuit output reaches more than 160°. As shown in
Figure 11, the output phase reaches 178.6°. When the circuit reaches a stable state, the output voltage is consistent at 48.13 V, which is very similar to the reference voltage.
The voltage and current waveforms when the leading leg
Q1 is turned on and off are shown in
Figure 12. It can be seen that when
Q1 is turned on, there is no overlap area between the voltage and current, indicating that
Q1 can realize ZVS conduction and
Q1 has no conduction loss. The voltage and current waveform of
Q3 is exactly the same as that of
Q1, so there is no hard-switching problem in the leading leg in the WPT system. The upper part of
Figure 12 is an overview of the waveforms, and the lower part shows the details of the voltage and current waveforms when
Q1 conducts.
Figure 13 shows the voltage and current relationship of
Q2 during operation. It can be seen that when
Q2 is turned on, the current increases, while the voltage decreases, and the two have an overlapping area. The part covered by the dotted line in the black circle in
Figure 13 is the conduction loss generated by
Q2.
Q4 works the same as
Q2. The lagging leg cannot achieve soft switching when turning on, resulting in conduction loss. These losses reduce the overall efficiency of the circuit.
According to the simulation results, it can be concluded that the control circuit in the WPT system can make the circuit output an ideal voltage. However, in the full-bridge converter, there is conduction loss in the lagging leg, so the efficiency of the circuit decreases.
4.2. Simulation of WPT Systems with Auxiliary Circuits
According to the theory in
Section 3, an inductance is added to the resonant tank in this simulation. The inductance is 20 μH, and the rest of the circuit remains the same. The simulation verifies whether the conduction loss can be reduced, while the output voltage is still controllable under the original circuit parameters. Therefore the circuit is the same as the first simulation except that inductance is added. The structure and parameters of the control circuit are also completely unchanged.
Figure 14 shows the output voltage when the system is stable and the phase difference. The simulation time is set to 0.15 s. It can be seen that the system output voltage can quickly reach 48.2 V within 0.15 s. When the system reaches the steady state, the phase difference between the leading leg and the lagging leg is different. However, both can output the ideal voltage in time so that the control circuit can work well in the improved system.
Figure 15 shows the current–voltage waveforms of
Q1 at the turning on stage.
Q1 can still achieve soft switching. The voltage and current waveforms of
Q3 are the same as those of
Q1. The added auxiliary inductance does not affect the working state of the leading leg.
Figure 16 shows the current and voltage waveforms when
Q2 is turned on. In the black circle, the current and voltage have no overlapping area. The current of
Q2 shows the same trend as
Q1. It increases in the negative direction and then rises again. This is because the discharge current does not decrease to 0 before
Q2 turns on. The current direction is opposite to
Q2’s voltage direction, which means that
Q2 has completed the discharge process before turning on. Therefore, ZVS can be turned on. The conduction process of
Q4 is the same as that of
Q2. The lagging leg can achieve ZVS conduction with the help of the auxiliary inductance.
4.3. Simulation of WPT System with Auxiliary Inductance in Special Cases
In order to verify the stability of the system, the input of the DC power supply is fluctuated by ±10% and the load resistance is adjusted at another moment. In the simulation, the load resistance is set to abruptly change at 0.1 s. The power supply voltage is set to have the maximum voltage fluctuation at 0.2 s in this simulation. The circuit parameters of the circuit are completely consistent with the former simulation, and the parameters of the control circuit also remain unchanged.
According to
Figure 17, at 0.1 s, the load suddenly changed from 120 Ω to 20 Ω at 0.1 s. The power supply voltage changed from 380 V to 418 V at 0.2 s. The two areas inside the black circle are the fluctuation of the output voltage, but the output voltage recovered to the reference voltage of 48 V quickly. At the moment of 0.2 s, the power supply voltage fluctuated to the greatest extent, and the output voltage was immediately affected, resulting in a slight fluctuation. However, the voltage also recovered to 48.2 V within 0.5 s and then slowly returned to the exact 48 V.
Figure 18a shows the waveform of the voltage and current of the lagging leg when the load changes.
Figure 18b shows the waveform of the lagging leg when the input voltage changes. Both of the two waveforms are obtained when the system becomes stable again. After changes, the voltage can always return to the referenced value and there were still no hard-switching issues in the circuit.