An Enhanced Hybrid Switching-Frequency Modulation Strategy for Fuel Cell Vehicle Three-Level DC-DC Converters with Quasi-Z Source

Abstract

For fuel cell vehicles, the fuel cell stack has a soft output characteristic whereby the output voltage drops quickly with the increasing output current. In order to interface the dynamic low voltage of the fuel cell stack with the required constant high voltage (400 V) of the inverter DC link bus for fuel cell vehicles, an enhanced hybrid switching-frequency modulation strategy that can improve the voltage-gain range is proposed in this paper for the boost three-level DC-DC converter with a quasi-Z source (BTL-qZ) employed in fuel-cell vehicles. The proposed modulation strategy retains the same advantages of the original modulation strategy with more suitable duty cycles [1/3, 2/3) which avoids extreme duty cycles. Finally, the experimental results validate the feasibility of the proposed modulation strategy and the correctness of its operating principles. Therefore, the BTL-qZ converter is beneficial to interface the fuel cell stack and the DC bus for fuel cell vehicles by using the proposed modulation strategy.

1. Introduction

With the increase of the number of automobiles, more and more attention has been paid to the environmental pollution caused by automobile exhaust emissions. Almost all governments are increasing the research and development of renewable energy vehicles, including plug-in hybrid electric vehicles, blade electric vehicles with hybrid energy sources, and fuel cell vehicles [1,2,3].

Fuel cells are electrochemical devices that process hydrogen and oxygen to generate electric power, leaving water vapour as their only by-product. Fuel cell vehicles are an important contributor to those clean energy vehicles and have been applied widely in practice, due to the advantages of the environmental friendship, the reliability and the high efficiency [4,5,6,7]. However, the fuel cell has a “soft” output characteristic—its output voltage drops quickly with an increase of the output current [8,9,10,11,12,13]. Therefore, the fuel cell stack has to be interfaced with the inverter high voltage (400 V) DC link bus through a step-up DC-DC converter with a wide voltage-gain range [14,15].

Regarding the previously described characteristic of the fuel cell, many wide input-voltage range boost converters have been presented. Cascaded boost DC-DC converters were proposed in [16,17]. The interleaving structure was applied in the front-end of the converter for reducing the input current ripple [18], and interfacing the input side with the high voltage side (i.e., the DC link bus) by the second boost stage. Even though a high voltage-gain with a wide input-voltage range can be realized by such a structure, many disadvantages, such as a reduced efficiency, increased volume, a complex controller and low reliability still exist. In order to simplify the converter structure between the fuel cell stack and the DC link bus, and improve the operating performance of fuel cells [19,20], a non-isolated DC-DC converter with a coupled inductor was proposed in [21], where a high voltage-gain can be achieved by only one power stage. However, it suffers from the high voltage stress across the power semiconductors, due to the leakage inductance, which reduces the efficiency and the reliability of this converter [22]. Although the voltage stress can be reduced by an active-clamped circuit in [23], the active-clamped switch added and the floating gate driver increase both the circuit complexity and the cost. In addition, some optimized DC-DC converters are proposed for PV generation systems and the auxiliary power supply of fuel cell vehicles [24,25], with the synchronous rectification and zero voltage switching (ZVS) operations. As to the power interface between the fuel cells and the DC bus for fuel cell vehicles, a wide voltage-gain range is required.

Z source net has been applied in the traditional step-up DC-DC converters to achieve the higher voltage-gain [26], but this converter may introduce additional maintenance and safety issues for fuel-cell vehicles, due to the penalty of the discontinuous input current and the non-common grounds between the input and the load sides. To solve this issue, a quasi-Z source circuit was presented in [27,28,29]. It can be used in the step-up DC-DC converters with the merits of the lower capacitor voltages and the common ground [30]. For the better application of the step-up DC-DC converters with the quasi-Z source, a combination of the improved common ground three-level converter was applied in [31,32,33] and the quasi-Z network was proposed in [34], namely a wide input-voltage range Boost three-level DC-DC converter with a quasi-Z source (BTL-qZ) for fuel cell vehicles, as shown in Figure 1.

This topology was controlled by the phase-shifted 180-degree modulation strategy as shown in Figure 2 [34]. The equivalent frequency of the inductor current in the BTL-qZ converter is twice the switching frequency, as shown in Figure 2l,m, which reduces the output current ripple of the fuel cell source. In addition, the voltage of the flying-capacitor can be clamped well at half of the output voltage by the total capacitor voltages of the quasi-Z source net, and the voltage stress across all power semiconductors is half of the output voltage. The step-up voltage-gain M₁ of the BTL-qZ DC-DC converter can be obtained as:

$$M_1=\frac{2}{3-4m}$$

(1)

where m is the modulation index for Q₁ and Q₂ in Figure 1, and 0.5 ≤ m < 0.75.

Because there are only three switching states (S₁S₂ = 01, S₁S₂ = 10, and S₁S₂ = 11, where “0” represents the turn-off of power switches Q₁, Q₂) existing for the BTL-qZ converter, when it is controlled by the phase-shift 180-degree modulation strategy, namely S₁S₂ = 00 is absent in [34]. In this paper, an enhanced hybrid switching-frequency modulation strategy without any extra hardware is proposed to further improve the voltage-gain range for the BTL-qZ DC-DC converter. Because it contains the switching state S₁S₂ = 00 in each switching period for the BTL-qZ converter. As a result, its voltage-gain range can be improved significantly, comparing with the phase-shifted 180-degree modulation strategy.

This paper is organized as follows: in Section 2, the operating principles of the converter controlled by the hybrid switching-frequency modulation strategy are analysed in detail, and the voltage-gain is deduced. The comparisons between the proposed modulation strategy and the original phase-shifted 180-degree modulation strategy from the aspects of voltage-gain and the stresses on the components are shown in Section 3. The application of the converter for fuel cell vehicles is presented in Section 4. In Section 5, the experimental results measured from the prototype controlled by the hybrid switching-frequency modulation strategy are shown and analysed finally, a summary of the proposed modulation strategy for the BTL-qZ converter is presented and the conclusion is delivered in Section 6.

2. Operating Principle of the Hybrid Switching-Frequency Modulation Strategy

2.1. Analysis of Operating States

There are two power switches in the topology as shown in Figure 1, and the corresponding gate signals can be modulated in theory by two carriers and two modulation waves. Therefore, there are four combination modes for two carriers: with the same frequency and the different phases, with the same frequency and the phase, with the different frequencies and the same phase, and with the different frequencies and phases. In addition, the modulation indices can also be different. Therefore, the modulation methods for the BTL-qZ converter are flexible and various in theory. The phase-shifted 180-degree modulation strategy in [34] is implemented by the two gate signals with the same duty cycles and the 180-degree phase difference. Under the control of the phase-shifted 180-degree modulation strategy, the switching state S₁S₂ = 00 (as shown in Figure 3c) is absent. In order to improve the operating performance by containing the switching state S₁S₂ = 00, the hybrid switching-frequency modulation strategy is proposed in this paper. The carrier frequency of Q₂ is twice the carrier frequency of Q₁. In addition, the gate signals of Q₁ and Q₂ have the same modulation index.

Figure 4 shows the key waveforms of the BTL-qZ converter controlled by the hybrid switching-frequency modulation strategy. According to Figure 4b,c, there are six switching processes in each switching period of Q₁, i.e., “S₁S₂ = 11→10→11→01→00→01”. Therefore, the inductors can charge and discharge twice in each switching period of Q₁ respectively. The currents of L₁ and L₂ are shown in Figure 4l,m. The energy flow paths of the BTL-qZ converter in different switching states are shown in Figure 3. The analysis of the different switching states are summarized as follows:

(1) S₁S₂ = 11: According to the equivalent circuit of this switching state in Figure 3a, and the key waveforms in Figure 4, Q₁ and Q₂ are both turned on, while diodes D₁–D₃ are all turned off. Therefore, the input voltage source U_in and the capacitor C₁ transfer the energy to the inductor L₁ through the diode D_FC and the power switches Q₁ and Q₂. C₂ transfers the energy to L₂ through Q₁ and Q₂. Due to the conduction of Q₁ and Q₂, and the turn-off of D₂ and D₃, the cathode of C_fly is connected to the ground, and the anode of C_fly is suspended. So the voltage across C_fly keeps invariant. Capacitor C₃ supplies the energy for the load.

(2) S₁S₂ = 01: There are four energy flow loops in this switching state as shown in Figure 3b. L₂ is discharging, at the same time C₁ is charging through D₁. The inductor current i_L2 and the capacitor voltage U_C1 are shown in Figure 4m,f. L₁ and U_in connected in series are discharging, while C₂ is charging through D_FC and D₁. Thus the inductor current i_L1 and the capacitor voltage U_C2 can be illustrated in Figure 4l,g. L₁, L₂ and U_in in series are discharging, while the flying-capacitor C_fly is charging through D_FC, D₁, D₂, and Q₂. Capacitor C₃ supplies the energy for the load.

(3) S₁S₂ = 00: From the equivalent circuit in Figure 3c, and the key waveforms in Figure 4, diodes D₁ and D₂ are turned on, while Q₁ and Q₂ are both turned off. Hence, U_in and L₁ transfer the energy to C₂ through the diode D_FC and D₁, L₂ transfers energy to C₁ through D₁, and capacitor C₃ supplies the energy for the load. In addition, due to the turn-off of Q₁ and Q₂, the anode of C_fly is suspended. So the voltage across C_fly keeps invariant, which is similar to the switching state S₁S₂ = 11.

(4) S₁S₂ = 10: D₂ is turned off due to the reverse voltage across C_fly, and Q₂ is turned off. At the same time, D₁, D₃ and Q₁ are turned on. As a result, there are three energy flow paths left, as shown in Figure 3d. C_fly, U_in, L₁, and L₂ connected in series are discharging to supply the energy for the load and C₃ through D_FC, D₁, Q₁ and D₃. U_in and L₁ transfer energy to C₂ through D_FC and D₁. L₂ transfers energy to C₂ through D₁.

When S₁S₂ = 01, as shown in Figure 3b, Q₂ is turned on, namely U_Q2 = 0. By means of Kirchhoff’s Voltage Laws (KVL), U_Cfly can be obtained as follows:

$$U_{\mathrm{Cfly}}=U_{\mathrm{C}1}+U_{\mathrm{C}2}$$

(2)

Based on Figure 3c and KVL, when the switching state changes from “S₁S₂ = 01” to “S₁S₂ = 00”, U_Cfly can be described as follows:

$$U_{\mathrm{Q}2}=U_{\mathrm{C}1}+U_{\mathrm{C}2}-U_{\mathrm{Cfly}}$$

(3)

According to (2) and (3), when S₁S₂ = 00, the voltage stress across Q₂ is also equal to zero, namely U_Q2 = 0. Therefore, when the switching state changes from “S₁S₂ = 01” to “S₁S₂ = 00”, Q₂ can be turned off in the zero voltage switching. When the switching state changes from “S₁S₂ = 00” to “S₁S₂ = 01”, Q₂ can be turned on in the zero voltage switching. According to the gate signal and the corresponding voltage stress across Q₂ in Figure 4c,e, the frequency of the voltage across Q₂ is half the frequency of the gate signal of Q₂. Therefore, the switching losses of power switches can be reduced due to this special characteristic of hybrid switching-frequency modulation strategy.

2.2. Voltage-Gain

In order to simplify the analysis, the operating conditions are assumed as follows:

(1)

The capacitance of the capacitors in Figure 1 is infinite, as well as the inductance of the inductors. Therefore, capacitors are regarded as constant voltage sources, and inductors can be considered as constant current sources.

(2)

All the power semiconductors and energy storage components are in the ideal conditions, namely the on-state resistances of the power semiconductors, the forward voltage drops of the diodes, and the equivalent series resistances (ESRs) of the inductors and capacitors are ignored.

According to Figure 3a–d, there are four switching states in a switching period of Q₁. The durations of the corresponding states can be expressed as t₁, t₂, t₃ and t₄ respectively. The carrier frequencies for the gate signals of Q₁ and Q₂ are f and 2f respectively, and the modulation index (m) for Q₁ and Q₂ is equal. The durations of the four switching states in a switching period of Q₁ can be obtained as follows by means of Figure 4a–c:

$$\{\begin{array}{l}{t}_1=(3m-1)/f\\ t_2=(1-m)/f\\ t_3=(1-m)/f\\ t_4=(1-m)/f\end{array}$$

(4)

In addition, the BTL-qZ converter operates within the range 1/3 < m < 1 to guarantee the existence of the switching state sequence “11→10→11→01→00→01”.

When the BTL-qZ converter operates in the continuous conduction mode, the voltage-second balance equations can be obtained as follows:

$$\{\begin{array}{c}（U_{\mathrm{C}2}-U_{\mathrm{in}}）\times （t_2+t_3+t_4）=（U_{\mathrm{in}}+U_{\mathrm{C}1}）\times t_1\\ U_{\mathrm{C}1}\times （t_2+t_3+t_4）=U_{\mathrm{C}2}\times t_1\end{array}$$

(5)

The capacitor voltages across C₁, C₂ and C_fly can also be obtained by Equations (4) and(5):

$$\{\begin{array}{c}{U}_{\mathrm{C}1}=\frac{3m-1}{4-6m}{U}_{\mathrm{in}}\\ \begin{array}{l}{U}_{\mathrm{C}2}=\frac{3-3m}{4-6m}{U}_{\mathrm{in}}\\ \begin{array}{c}{U}_{\mathrm{Cfly}}=U_{\mathrm{C}1}+U_{\mathrm{C}2}\\ U_{\mathrm{Cfly}}=\frac{U_{\mathrm{O}}}{2}\end{array}\end{array}\end{array}$$

(6)

As a result, the step-up voltage-gain M₂ of the BTL-qZ converter controlled by the proposed modulation strategy can be obtained by means of (4)–(6) as follows:

$$M_2=\frac{2}{2-3m}$$

(7)

where 1/3 < m < 2/3.

3. Comparisons between Proposed and Original Modulation Strategies

3.1. Comparisons of Voltage Gain

In Figure 5, the comparison of voltage gain M versus modulation index m between the proposed and the original modulation strategies is obtained by means of (1) and (7). According to Figure 5, the relationship between the voltage gains is M₂ > M₁, when m > 0.5 and the modulation indices for the proposed and the original modulation strategies are both equal. Therefore, compared with the original modulation strategy in [34], the BTL-qZ converter controlled by the proposed modulation strategy benefits from the higher voltage-gain. In addition, the maximum effective modulation index for the proposed modulation strategy is less than 2/3, which is much closer to 0.5 than that for the original modulation strategy which is “0.75”. Hence, when the same high voltage-gain is required, comparing with the original modulation strategy in [34], the modulation index of the proposed modulation strategy is closer to 0.5, namely the proposed modulation strategy benefits from avoiding the extreme duty cycle better.

3.2. Comparisons of Voltage and Current Stresses

In

Table 1. Comparisons of voltage stress for components in BTL-qZ converter controlled by proposed and original modulation strategies respectively.

Modulation Strategy	C1	C2	Cfly	Q1	Q2	D1	D2	D3
Phase shifted 180-degree	$\frac{M-2}{4M}{U}_{\mathrm{O}}$	$\frac{M+2}{4M}{U}_{\mathrm{O}}$	UO/2	UO/2	UO/2	UO/2	UO/2	UO/2
hybrid switching-frequency	$\frac{M-2}{4M}{U}_{\mathrm{O}}$	$\frac{M+2}{4M}{U}_{\mathrm{O}}$	UO/2	UO/2	UO/2	UO/2	UO/2	UO/2

, the voltage stress across the components in BTL-qZ converter controlled by the proposed and the original modulation strategies is compared, when the voltage gain M and the output voltage U_O are under the same conditions, respectively. According to Table 1, the theoretical voltage stress across the corresponding capacitors and the power semiconductors in BTL-qZ converter controlled by the two modulation strategies are all equal. Hence, the proposed modulation strategy still retains the advantage of the low component voltage stress for the BTL-qZ converter.

In

Table 2. Comparisons of current stress for components in BTL-qZ converter controlled by proposed and original modulation strategies respectively.

Modulation Strategy	Q1	Q2	D1	D2	D3
Phase-shifted 180-degree	2MIO	2MIO	$(2M-\frac{4M}{M+2})\times I_{\mathrm{O}}$	$\frac{4M}{M+2}{I}_{\mathrm{O}}$	$\frac{4M}{M+2}{I}_{\mathrm{O}}$
hybrid switching-frequency	2MIO	2MIO	2MIO	$\frac{6M}{M+2}{I}_{\mathrm{O}}$	$\frac{6M}{M+2}{I}_{\mathrm{O}}$

, the current stress on the components for BTL-qZ converter controlled by the proposed and the original modulation strategies is compared, when the voltage gain M and the output current I_O are under the same conditions, respectively. According to Table 2, the theoretical current stresses on the corresponding power switches for BTL-qZ converter controlled by the two modulation strategies are equal to 2MI_O. However, the theoretical current stress on D₁ under the proposed modulation strategy is 2MI_O, which is higher than the original modulation strategy. In addition, the corresponding theoretical current stresses on D₂ and D₃ under the two modulation strategies can also be obtained, which are equal respectively. Therefore, it is easy to choose the diodes with the same rated parameters. However, the theoretical current stress for the proposed modulation strategy is higher than that of the original modulation strategy. Hence, the current stresses on diodes under the proposed modulation strategy are all greater than those of the original modulation strategy.

4. Application of the Converter for Fuel Cell Vehicles

On the basis of the output characteristic of the fuel cell presented previously, the powertrain of fuel cell vehicles with the required converters is shown in Figure 6. The energy sources consist of the fuel-cell source and the super capacitor. The low voltage of the fuel-cell source is boosted to match the high voltage of the DC bus by a wide voltage-gain range DC-DC converter. At the same time, the fuel-cell source provides the average power (PFC) for the DC bus. The super capacitor is deployed to supply the instantaneous peak power (PSC) required due to the slow dynamic response of the fuel-cell source, and to absorb the power recovery from the DC bus by the bidirectional DC-DC converter (BDC). Accordingly, the power interface between the fuel-cell source and the DC bus should have a wide voltage-gain range characteristic, as well as a high voltage-gain feature. When the fuel cell vehicle operates at a constant speed, the fuel-cell source provides the stable energy for the load (P_load), and charges the super capacitor if it is needed. When the fuel cell vehicle accelerates, the super capacitor supplies the instantaneous power required from the motor. Then the fuel-cell source can increase its output power gradually, and ensure the vehicle still has the fast dynamic response. When the fuel cell vehicle decelerates or brakes, the fuel-cell source decreases its output power, and the super capacitor absorbs the regenerative energy.

5. Experimental Results and Analysis

In order to validate the operating performance of the BTL-qZ converter controlled by the proposed modulation strategy, a BTL-qZ experimental prototype is developed as shown in Figure 7. The parameters of this prototype are the same as those in [34], which are listed in

Table 3. Main experimental parameters of the BTL-qZ converter in [34].

Parameters and Components	Values (units)
Input voltage Uin	40~150 V
Output voltage UO	400 V
Inductor L1	228 μH
Inductor L2	225 μH
Capacitors C1, C2 and Cfly	450 V/660 μF
Capacitor C3	450 V/440 μF
Rated power P	400 W
Load R	400 Ω
MOSFETs Q1 and Q2	IXTK102N30P
Diodes DFC, D1, D2 and D3	DSEC60-03A

.

The gate signals of Q₁ and Q₂ and inductor currents of L₁ and L₂ with the two modulation strategies are shown in Figure 8, when the voltage gain is M = 10 and the output voltage is U_O = 400 V. For the original modulation strategy, as shown in Figure 8a, the frequencies of the gate signals for both Q₁ and Q₂ are 10 kHz. As to the proposed modulation strategy, as shown in Figure 8b, the frequencies of the gate signal for Q₂ is 20 kHz. According to Figure 8, the duty cycles of Q₁ and Q₂ are both the same with the two modulation strategies, but different duty cycles are needed for achieving the voltage gain 10. As a result, the duty cycles 0.7 for the original modulation strategy, and the duty cycles 0.6 for the proposed modulation strategy are required respectively, which agree with the theoretical analysis. Comparing with these duty cycles, the conclusion that the proposed modulation strategy can avoid extreme duty cycles better than the original modulation strategy, under the same condition of the high step-up voltage-gain can be achieved.

Inductor currents of L₁ and L₂ with the two modulation strategies are shown in Figure 8c,d, when the output voltage is U_O = 400 V and the load is R = 400 Ω. From Figure 8c, the current ripple rates and the frequencies of i_L1 and i_L2 are about 62.07% and 20 kHz, respectively. Therefore, the equivalent frequency of the inductor current is double the switching frequency. According to Figure 8d, the current ripple rates of i_L1 and i_L2 are about 66.67%. Although the frequency of i_L1 and i_L2 are 10 kHz, the inductor can charge and discharge twice in each switching period of Q₁, respectively. In addition, the charging time is identical, but the discharging time is different. So the approximate current ripple can be achieved under the proposed modulation strategy, comparing with the original modulation strategy.

The gate signal and the voltage stress across Q₂ are shown in Figure 9a, when the voltage gain is M = 10 and the output voltage is U_O = 400 V. According to Figure 9a, although the frequency of the gate signal for Q₂ is 20 kHz, the frequency of the voltage stress across Q₂ is still 10 kHz, which agrees with the theoretical analysis of the hybrid switching-frequency modulation strategy mentioned in Figure 4c,e.

The voltage stress across the power semiconductors and the capacitors with the two modulation strategies are shown in Figure 9 and Figure 10, when the output voltage is U_O = 400 V and the voltage gain is M = 10. From Figure 9b–d, it can be observed that the voltage stress across all the power semiconductors is 200 V. According to Figure 10a, the voltage stresses across C₁ and C₂ are 80 V and 120 V respectively. From Figure 10b, the voltage stress across C_fly is 200 V (i.e., half of the output voltage) approximately. Therefore, these experimental results validate the correctness of the theoretical analysis of the voltage stress across the power semiconductors and the corresponding capacitors with the two modulation strategies respectively. When the output voltage is U_O = 400 V and the load resistance is R = 400 Ω, the efficiency η measured by a power analyser (WT3000, Yokogawa, Tokyo, Japan) for different input voltages varying from 150 V to 60 V under the two modulation strategies is shown in Figure 11. It is noticed that when the input voltage declines, the efficiency decreases correspondingly due to the increasing losses caused by the increasing input current. The maximum measured efficiencies of the BTL-qZ converter controlled by the original and proposed modulation strategies are 95.1% and 94.7% respectively, which are approximately equal. However, the minimum measured efficiencies of the BTL-qZ converter controlled by the proposed modulation strategy is 86.3% which is 1.7% higher than that with the original modulation strategy in [34].

6. Conclusions

An enhanced hybrid switching-frequency modulation strategy is proposed for the boost three-level DC-DC converter with a quasi-Z source (BTL-qZ) employed in fuel cell vehicles. The proposed modulation strategy retains many advantages of the phase-shifted 180-degree modulation strategy, such as the low input current ripple, the low voltage stress across the power semiconductors, and the controllable voltage across the flying capacitor. In addition, compared with the phase-shifted 180-degree modulation strategy, the BTL-qZ converter controlled by the proposed modulation strategy can achieve a higher voltage gain range, with the more proper duty cycles [1/3, 2/3) for the power switches rather than [1/2, 3/4), which can avoid the extreme duty cycles better than the original modulation strategy. Therefore, it is beneficial for the BTL-qZ converter to interface the wide voltage range fuel cell source and the high voltage DC bus in fuel cell vehicles.