A Family of Five-Level Pseudo-Totem Pole Dual Boost Converters

1. Introduction

With the development of power electronics technology, the neutral point clamped (NPC) multi-level converter has attracted more and more scholars' attention [1,2]. Multi-level NPC converters has the advantages of high efficiency, high power density, low total harmonic distortion (THD), low voltage and current stress [3,4,5]. Therefore, multi-level NPC converters are widely used in medium and high power, medium voltage applications [6,7,8,9], such as electric vehicles (EVs), motor drives, electrical railway traction, and DC-bus microgrids [10,11,12,1310-13].

Compared with IGBT, power MOSFET has some excellent characteristics such as high frequency operation, low switching loss, and low conduction loss. Therefore, power MOSFET is widely used in low-power converters to improve efficiency and reduce the volume. However, due to the poor reverse recovery characteristics of body diode, MOSFET-based have a risk of device failure, which is related to the phase-leg shoot, may cause false triggering of the gate voltage. Therefore, conventional H-bridge converters often used IGBTs [14,15,16,17]. The dual boost/buck converter can avoid the shoot-through problem effectively, and the freewheeling current flows through the independent diode to solve the MOSFET body diode reverse recovery problem [14,15,16,17,18,19,20,21]. However, due to the two inductance structure of the dual boost/buck converter, the volume and weight of the converter will increase. In this regard, in [16,17,22], the multi-level dual boost/buck converter is proposed to reduce the size and weight of this type of topology.

The bridgeless converter has high power factor (PF), low THD, and high efficiency. It usually includes the basic bridgeless converters, the bidirectional-switch bridgeless converters, the totem pole bridgeless converters, and the PTP bridgeless converters [22,23,24]. Among them, the PTP bridgeless converter has a simple structure, few semiconductor devices conducting in the series loop, and a natural dual boost structure. In order to increase the power density and reduce the THD, the PTP bridgeless converter must work at a higher frequency. Moreover, all the active devices in the circuit bear the DC voltage, which cause the high voltage stress [3].

Figure 1 shows two common five-level converter topologies. Figure 1a is conventional five-level converter (CFLC), which is widely used in bidirectional power flow scenario such as vehicle to gird (V2G). However, the number of switch is large, which can be further optimized for reduce the number of switch. Figure 1b is unidirectional five-level converter proposed in [25], which using only one NPC bridge arm in CFLC to reduce the number of switch. However, there is less topology derivation process. In [4], a new five-level converter with high power density is proposed and the current stress is analyzed, however, the number of active devices is large, and the cost is high. In [14,16], the PTP bridgeless structure is adopted to achieve five-level dual buck grid-connected inverter, and summarizes a topology structure method to expand the circuit. However, the utilization of two input inductors is low.

Based on the above analysis, the bridge arm of the topology proposed in [25] is used as the prototype to obtain new five-level bridge arms. By cascading five-level bridge arms with the three-level PTP circuit, a family of five-level PDBCs is proposed. The proposed PDBC optimizes the three-level PTP converter in terms of large volume and large switching loss, and retaining the dual boost structure, which have advantages of high reliability.

The structure of this paper is as follows. Section 2 derives the PDBC in detail and analyzes the working principle. Section 3 designs the control and modulation strategy of PDBC. In section 4, the voltage and current stress are analyzed. Section 5 conducts experimental verification on PDBC. Finally, section 6 concludes the paper.

2. Topological Derivation and Operating Principle

2.1. Topological Derivation

Figure 2 shows the three most commonly used clamping bridge arm structures in five-level converters. A new five-level converter can be obtained by cascading these three clamping bridge arm structures with a three-level circuit.

In this paper, the bridge arm shown in Figure 2b is used to generate a new bridge arm, as shown in Figure 3. For ease of description, the bridge arms are numbered below each bridge arms i.e. A1, A2. Firstly, the two diodes on the right side of A4 are replaced with MOSFETs to get A1*. Then removed S₂ and S₄ of A1*, and reconnected them to get a new bridge arm A2, as shown in Figure 3a. In the same way, remove S₁ and S₃ of A1*, and then reconnect them to obtain a new bridge arm A3, as shown in Figure 3b.

Through the bridge arm transformation in Figure 3, new bridge arms A2 and A3 are derived. Figure 4 shows a family of five-level PTP dual boost converters, which named as PDBC-I, PDBC-II and PDBC-III, respectively. It can be seen in Figure 4, the PTP dual boost converter is cascaded with Figure 2(a), A2, and A3 to generate the PDBCs, respectively.

Compared with the traditional five-level converter, a family of PDBCs proposed in this paper reduces the number of MOSFETs by four, so it can effectively reduce the converter loss. It is worth mentioning that the three power flow converters proposed in this paper can all achieve bidirectional power flow after a slight circuit modification.

2.2. Operating Principle

Based on the above analysis, this paper takes the PDBC-II as an example for working mode analysis. Figure 5 shows the key waveforms of one power cycle, which are corresponding to the six working modes in Figure 6. For ease of analysis, it is assumed that the circuit works in continuous conduction mode (CCM), the inductances and capacitors are large enough, the capacitor voltage U_C1=U_C2=U_dc/2, and the DC voltage U_dc is remain constant. Figure 6 shows the six working modes of PDBC-II, which are corresponding to 0, ±0.5U_dc and ±U_dc, respectively. The six working modes are analyzed as follows.

Working mode 1: During [t₀, t₁] shown in Figure 5, the grid voltage u_g>0, u_aN=0, u_bN=u_g. In this mode, the current path is shown in Figure 6a. As shown in Figure 6a, the switch S₁ is ON, the diode D₄ is ON, and the other active components are OFF. The capacitors C₁ and C₂ are discharging to the load R_L.

Working mode 2: During [t₁, t₂] shown in Figure 5, the grid voltage u_g>0, u_aN=u_bN=U_dc/2. In this mode, the current path is shown in Figure 6b. As shown in Figure 6b, the switch S₃ is ON, the body diodes of S₂ and S₄ are ON, the diode D₁ is ON, and the other active components are OFF. The capacitor C₁ is charging and C₂ is discharging to the load R_L.

Working mode 3: During [t₂, t₃] shown in Figure 5, the grid voltage u_g>0, u_aN=u_bN=U_dc. In this mode, the current path is shown in Figure 6c. As shown in Figure 6c, the body diode of S₂ is ON, the diodes D₁ and D₄ are ON, and the other active components are OFF. The capacitors C₁ and C₂ are charging, and the AC power supplies to the load R_L.

Working mode 4: During [t₃, t₄] shown in Figure 5, the grid voltage u_g<0, u_bN=u_g, u_bN=0. In this mode, the current path is shown in Figure 6d. As shown in Figure 6d, the switch S₂ is ON, the body diode of S₃ is ON, the diode D₃ is ON, and the other active components are OFF. The capacitors C₁ and C₂ are discharging to the load R_L.

Working mode 5: During [t₄, t₅] shown in Figure 5, the grid voltage u_g<0, u_aN=u_bN=−U_dc/2. In this mode, the current path is shown in Figure 6e. As shown in Figure 6e, the switch S₄ is ON, the body diodes of S₁ and S₃ are ON, the diode D₂ is ON, and the other active components are OFF. The capacitor C₂ is charging and C₁ is discharging to the load R_L.

Working mode 6: During [t₅, t₆] shown in Figure 5, the grid voltage u_g<0, u_aN=u_bN=−U_dc. In this mode, the current path is shown in Figure 6f. As shown in Figure 6f, the body diodes of S₁ and S₃ are ON, the diodes D₂ and D₃ are ON, and the other active components are OFF. The capacitors C₁ and C₂ are charging, and the AC power supplies to the load R_L.

Based on the six working mode analysis above, the switching pulse distribution of PDBC-II is summarized, as shown in Table 1. Where "0" and "1" represent switching off and on, "↑" and "↓" represent capacitor charging and discharging, respectively. It can be seen from Table I that the PDBC-II has at most one switch ON in each mode, so the PDBC-II has a lower conduction loss.

3. Control and Modulation Strategy

3.1. Control Strategy

In this paper, a double closed loop control system suit for PDBCs is designed, both the voltage outer loop and the current inner loop adopt PI controller. The control block diagram of the PDBCs is shown in Figure 7. The transfer function of the PI link in Figure 7 can be expressed as (1), where k_p and k_i are the proportional and integral coefficient, respectively.

$$G_{\mathrm{pi}}=(k_{\mathrm{p}}\cdot s+k_{\mathrm{i}})/s$$

(1)

The voltage outer loop is used to keep the output voltage U_dc stable, whose output is the reference value of the current inner loop. Firstly, the difference between the DC side voltage U_dc and its reference value U_dc* is send into the PI controller to obtain an error signal. Then, the error signal is multiply with the phase information of the grid voltage u_g. As a result, the input reference signal i_g* of the current inner loop is obtained.

The current inner loop is used to ensure that the waveform of i_g is sinusoidal and control the power factor close to 1. Firstly, the difference between the AC side current i_g and the reference signal i_g* (the output of the voltage outer loop) is sent to the PI controller. Then, the output of the PI controller is multiply with kU_dc*. Finally, its output is taken the difference with the grid voltage ug to get PWM reference signal v_ref.

The neutral point (NP) balance of the DC side capacitor is attained by the phase delay control method in this paper. Firstly, the difference between the voltage signals of the capacitors C₁ and C₂ is compared with the reference value. Then, the result is sent to the PI controller to obtain correction signal, which is added to the modulation wave after limiting the amplitude. Therefore, the NP voltage balance is achieved by adjusting the capacitor charging and discharging time.

3.2. Modulation Strategy

In this paper, the multi-carrier PWM modulation strategy is used to generate switching pulse distribution for proposed PDBCs. The PDBC-II is taken as an example to illustrate the switching pulse distribution and bridge arm voltage u_aN, u_bN of multi-carrier PWM modulation strategy, as shown in Figure 8, where v_c1(t), v_c2(t), v_c3(t), v_c4(t), and v_ref(t) represent four carrier signals and reference signal, respectively. The reference signal v_ref(t) is compared with v_c1(t), v_c2(t), v_c3(t), v_c4(t) to obtain the switching pulse waveform of the switches S₁, S₂, S₃, and S₄.

In the positive half-cycle the PWM modulation strategy, the duty cycle can be derived from (2) to (6). Where U_g,max, T_on, and T_off is the amplitude of AC voltage, the turn on and off time of the switch, respectively. The modulation ratio M and duty ratio D can be defined as follows:

$$M=U_{\mathrm{g},\max }/U_{\mathrm{dc}}$$

(2)

$$D=T_{\mathrm{on}}/\left(T_{\mathrm{on}}+T_{\mathrm{off}}\right)$$

(3)

When 0<v_ref(t)<0.5, the PDBCs operate alternately in working mode 1 and working mode 2. At this time, the inductance volt-second balance has the following relationship:

$$\left(u_{\mathrm{g}}-0.5U_{\mathrm{dc}}\right)\cdot T_{\mathrm{on}}=\left(U_{\mathrm{dc}}-u_{\mathrm{g}}\right)\cdot T_{\mathrm{off}}$$

(4)

The duty cycle D₁ is derived from (2) to (4):

$$D_1=1-2M\sin \left(wt\right)$$

(5)

Similarly, when 0.5<v_ref(t)<1, the PDBCs operate alternately in working mode 2 and working mode 3. The duty cycle D₂ can be obtained as follows:

$$D_2=2-2M\sin \left(wt\right)$$

(6)

Based on (5) and (6), when PDBCs operates in the positive half-cycle, the duty cycle change curve is shown in Figure 9. Where the green curve represents the duty cycle D₁, the yellow curve represents the duty cycle D₂, θ₁ and θ₂ are the two angles of alternation between v_c1(t) and v_c2(t).

It is assumed that, the amplitude of v_ref(t) is 1 (after normalization), the θ₁ and θ₂ can be calculated as follows:

$${\mathsf{\theta }}_1=\arcsin 0.5=\frac{\pi }{6}$$

(7)

$$D_2=2-2M\sin \left(wt\right)$$

(8)

4. Performance Analysis

4.1. Voltage Stress Analysis

Based on the working mode analysis of Figure 6, the switches and diodes voltage stress of three PDBCs are summarized, as shown in Table 2. It can be seen from Table 2 that part of the components voltage stress on the three level bridge is reduced by half. In addition, the PDBC-II and PDBC-III have three components voltage stress reduced by half, while PDBC-I only have two components voltage stress reduced by half. Therefore, in terms of cost, PDBC-II and PDBC-III have the lower cost compared with PDBC-I.

4.2. Current Stress Analysis

To estimate the conduction loss of the switches and diodes, it is necessary to calculate the average value and the root mean square (RMS) value of the current flowing through the switches and diodes. In this section, PDBC-II is taken as an example to conduct the current stress analysis. Figure 10 shows the current stress simulation waveform of PDBC-II in the Matlab/Simulink environment. It is easy to know from Figure 9, the switching times of two duty cycle D₁, D₂ in Figure 10 are T_g/12 and 5T_g/12 (T_g is one power frequency cycle), respectively. Based on Figure 10, the theoretical derivation of the average value and RMS value of the current flowing through the semiconductor device can be shown as (9) to (18). For the following calculations, it is assumed that the AC side current is a sine wave, the DC side voltage remains unchanged, and the switching frequency f_s is much greater than the grid frequency f_g.

The RMS and average value of diode D₁, D₂ current is calculated by (9):

$$\left\{\begin{array}{l}{I}_{{}_{\mathrm{D}1,2,\mathrm{rms}}}^{{}^2}=\frac{2}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}\left(1-D_1\right)\cdot i_{\mathrm{g}}{}^2}dt+{{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{12}}^{\frac{T_{\mathrm{g}}}{4}}\left(\frac{i_{\mathrm{g}}+0.5I_{\mathrm{g},\max }}{2}\right)}}^{2}dt\right]\\ I_{\mathrm{D}1,2,\mathrm{avg}}=\frac{2}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}\left(1-D_1\right)\cdot i_{\mathrm{g}}}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{12}}^{\frac{T_{\mathrm{g}}}{4}}\left(\frac{i_{\mathrm{g}}+0.5I_{\mathrm{g},\max }}{2}\right)}dt\right]\end{array}\right.$$

(9)

Substituting (5) into (9), the RMS and average values of diodes D₁, D₂ can be obtained:

$$\left\{\begin{array}{l}{I}_{\mathrm{D}1,2,\mathrm{rms}}=\frac{\sqrt{6}{I}_{\mathrm{g},\max }}{24\sqrt{\pi }}\cdot \sqrt{6\pi +15\sqrt{3}+\left(128-72\sqrt{3}\right)M}\\ I_{\mathrm{D}1,2,\mathrm{avg}}=\frac{I_{\mathrm{g},\max }}{12\pi }\cdot \left[\pi +3\sqrt{3}+\left(2\pi -3\sqrt{3}\right)M\right]\end{array}\right.$$

(10)

The RMS and average value of MOSFET S₁, S₂ current is calculated by (11):

$$\left\{\begin{array}{l}{I}_{{}_{\mathrm{S}1,2,\mathrm{rms}}}^{{}^2}=\frac{2}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}{D}_1\cdot i_{\mathrm{g}}{}^2}dt+{{\displaystyle {\int }_{\frac{7T_{\mathrm{g}}}{12}}^{\frac{3T_{\mathrm{g}}}{4}}\left(\frac{i_{\mathrm{g}}+0.5I_{\mathrm{g},\max }}{2}\right)}}^{2}dt\right]\\ I_{\mathrm{S}1,2,avg}=\frac{2}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}{D}_1\cdot i_{\mathrm{g}}}dt+{\displaystyle {\int }_{\frac{7T_{\mathrm{g}}}{12}}^{\frac{3T_{\mathrm{g}}}{4}}\left|\frac{i_{\mathrm{g}}+I_{\mathrm{g},\max }}{2}\right|}dt\right]\end{array}\right.$$

(11)

Substituting (5) into (11), the RMS and average values of MOSFET S₁, S₂ can be obtained:

$$\left\{\begin{array}{l}{I}_{\mathrm{S}1,2,\mathrm{rms}}=\frac{\sqrt{6}{I}_{\mathrm{g},\max }}{24\sqrt{\pi }}\cdot \sqrt{14\pi -21\sqrt{3}+\left(72\sqrt{3}-128\right)M}\\ I_{\mathrm{S}1,2\mathrm{avg}}=\frac{I_{\mathrm{g},\max }}{12\pi }\cdot \left[12-\pi -3\sqrt{3}+\left(3\sqrt{3}-2\pi \right)M\right]\end{array}\right.$$

(12)

The RMS and average value of MOSFET S₃ current is calculated by (13):

$$\left\{\begin{array}{l}{I}_{{}_{\mathrm{S}3,\mathrm{rms}}}^{{}^2}=\frac{4}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}{D}_1\cdot i_{\mathrm{g}}{}^2}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{12}}^{\frac{T_{\mathrm{g}}}{4}}{D}_2\cdot i_{\mathrm{g}}{}^2}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{2}}^{\frac{3T_{\mathrm{g}}}{4}}{i}_{\mathrm{g}}{}^{2}dt}\right]\\ I_{\mathrm{S}3,\mathrm{avg}}=\frac{2}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}{D}_1\cdot i_{\mathrm{g}}}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{12}}^{\frac{T_{\mathrm{g}}}{4}}{D}_2\cdot i_{\mathrm{g}}}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{2}}^{\frac{3T_{\mathrm{g}}}{4}}\left|i_{\mathrm{g}}\right|dt}\right]\end{array}\right.$$

(13)

Substituting (5) and (6) into (13), the RMS and average values of MOSFET S₃ can be obtained:

$$\left\{\begin{array}{l}{I}_{\mathrm{S}3,\mathrm{rms}}=\frac{I_{\mathrm{g},\max }}{2\sqrt{3\pi }}\cdot \sqrt{3\sqrt{3}+10\pi -32M}\\ I_{\mathrm{S}3,\mathrm{avg}}=\frac{I_{\mathrm{g},\max }}{\pi }\cdot \left(\sqrt{3}+2-\pi M\right)\end{array}\right.$$

(14)

The RMS and average value of MOSFET S₄ current is calculated by (15):

$$\left\{\begin{array}{l}{I}_{{}_{\mathrm{S}4,\mathrm{rms}}}^{{}^2}=\frac{4}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}{D}_1\cdot i_{\mathrm{g}}{}^2}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{12}}^{\frac{T_{\mathrm{g}}}{4}}{D}_2\cdot i_{\mathrm{g}}{}^2}dt\right]\\ I_{\mathrm{S}4,\mathrm{avg}}=\frac{4}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}{D}_1\cdot i_{\mathrm{g}}}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{12}}^{\frac{T_{\mathrm{g}}}{4}}{D}_2\cdot i_{\mathrm{g}}}dt\right]\end{array}\right.$$

(15)

Substituting (5) and (6) into (15), the RMS and average values of MOSFET S₄ can be obtained:

$$\left\{\begin{array}{l}{I}_{\mathrm{S}4,\mathrm{rms}}=\frac{I_{\mathrm{g},\max }}{2\sqrt{3\pi }}\cdot \sqrt{3\sqrt{3}+10\pi -32M}\\ I_{\mathrm{S}4,\mathrm{avg}}=\frac{I_{\mathrm{g},\max }}{\pi }\cdot \left(\sqrt{3}+2-\pi M\right)\end{array}\right.$$

(16)

The RMS and average value of diode D₃, D₄ current is calculated by (17):

$$\left\{\begin{array}{l}{I}_{{}_{\mathrm{D}3,4,\mathrm{rms}}}^{{}^2}=\frac{2}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}\left(1-D_1\right)\cdot i_{\mathrm{g}}{}^2}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{12}}^{\frac{T_{\mathrm{g}}}{4}}\left(1-D_2\right)\cdot i_{\mathrm{g}}{}^2}dt\right]\\ I_{\mathrm{D}3,4,\mathrm{avg}}=\frac{4}{T_{\mathrm{g}}}\left[{\displaystyle {\int }_0^{\frac{T_{\mathrm{g}}}{12}}\left(1-D_1\right)\cdot i_{\mathrm{g}}}dt+{\displaystyle {\int }_{\frac{T_{\mathrm{g}}}{12}}^{\frac{T_{\mathrm{g}}}{4}}\left(1-D_2\right)\cdot i_{\mathrm{g}}}dt\right]\end{array}\right.$$

(17)

Substituting (5) and (6) into (17), the RMS and average values of diodes D₃, D₄ can be obtained:

$$\left\{\begin{array}{l}{I}_{\mathrm{D}3,4,\mathrm{rms}}=\frac{I_{\mathrm{g},\max }}{2\sqrt{6\pi }}\cdot \sqrt{32M-3\sqrt{3}-4\pi }\\ I_{\mathrm{D}3,4,\mathrm{avg}}=\frac{I_{\mathrm{g},\max }}{2\pi }\cdot \left(\pi M-\sqrt{3}\right)\end{array}\right.$$

(18)

Figure 11 shows the change curve of the average value and RMS value of the switches and diodes with the modulation ratio M after normalization of I_g,max. It can be seen from Figure 11 that the current RMS value and average value of each components have the same trend. Since I_g,max are normalized, the trend shown in Figure 11 is also applicable under different power levels, which is of great significance for studying the working principle of the rectifier.

To verify the correctness of the current stress formula deduced in this paper, the current stress value of the switches and diodes is measured in Matlab/Simulink environment under 1kW power rate. Figure 12 shows the comparison between the calculated value and the simulated value of the current stress. It can be seen from Figure 12, the calculated current stress in this paper is consistent with the simulated value, which verifies the correctness of the current stress formula.

4.3. Loss Analysis

Based on the above current stress analysis, this section analyzes the loss and efficiency of the proposed PDBCs. The losses of MOSFET mainly include conduction losses and switching losses. When the MOSFET is on-state, the on-state resistance r_ds resulting the conduction losses. The conduction losses P_con can be calculated as (19), where I_S,rms is the RMS value of the current flowing through the MOSFET, which can be obtained from the current stress analysis.

$$P_{\mathrm{con}}=I_{\mathrm{S},\mathrm{rms}}{}^2\cdot r_{\mathrm{ds}}$$

(19)

During the drain current and voltage conversion process of the MOSFET, the switching losses is generated. The switching losses which can be calculated by (20), where U_in, I_o, t_on, t_off, and f_s are the RMS value of the input voltage, the output current, the switching process drain current and voltage conversion crossover time, and the switching frequency, respectively.

$$P_{\mathrm{sw}}=0.5U_{\mathrm{in}}\cdot I_{\mathrm{o}}\cdot \left(t_{\mathrm{on}}+t_{off}\right)f_{\mathrm{s}}$$

(20)

Similarly, the power losses of the diode in a cycle consists mainly of static losses and dynamic losses. For the static losses, since the fast recovery diode is employed in this paper, there is only the on-state losses are considered. The dynamic losses of the diode can be calculated with (21), where U_f is the forward conduction voltage, I_D,avg is the average value of the diode.

$$P_{\mathrm{Son}}={\displaystyle {\int }_0^{T_{\mathrm{g}}}u\cdot idt}/T_{\mathrm{g}}=U_{\mathrm{f}}\cdot I_{\mathrm{D},\mathrm{avg}}$$

(21)

Compared with the reverse recovery time t_r, the forward recovery time t_f is negligible, therefore the turn-on losses can be ignored. The turn-off losses can be calculated with (22), where U_rp and I_rp are the reverse peak voltage and current, t_b is the reverse current fall time.

$$P_{\mathrm{Doff}}={\displaystyle {\int }_{t_0}^{t_2}{u}_{\mathrm{F}}\left(t\right)\cdot i_{\mathrm{F}}\left(t\right)}dt/T_{\mathrm{S}}=0.5U_{\mathrm{rp}}{I}_{\mathrm{rp}}{t}_{\mathrm{b}}{f}_{\mathrm{s}}$$

(22)

In this paper, the MOSFETs and diodes employ IRFP450 and RHRP3060, respectively. According to the data sheet, the parameters for IRFP450 and RHRP3060 are shown in Table 3. The switching frequency f_s=20kHz.

Based on (9) to (22), the losses of the proposed three PDBCs and CFLC at different output power are calculated respectively. According to the results of the losses calculation, the efficiency diagram at different output power rate is generated, as shown in Figure 13. It can be seen from Figure 13, the four circuits reach peak efficiency around 300W. However, when the output power is over 300W, the efficiency declines slowly as the output power increase. The peak efficiency of PDBC-I is 98.27%, which is the highest in the four circuits. In addition, as the output power level increases, the efficiency of the PDBC-I reaches the highest of the four circuits. Therefore, PDBC-I is more suitable at higher power rate.

5. Experimental Verification

In order to verify the feasibility of the PDBC proposed in this paper and the correctness of the theoretical analysis, PDBC-II [shown in Figure 4(b)] is selected for corresponding experimental verification, as shown in Figure 14. The experimental circuit design mainly includes EMI circuit, auxiliary power supply, main power circuit, signal sampling circuit, MOSFET drive circuit, and protection control circuit. The circuit experimental parameters are shown in Table 4, the controller employ DSP28335, the MOSFETs and diodes employ IRFP450 and RHRP3060, respectively.

Figure 15 shows the PDBC-II steady-state experimental waveforms of the input and output sides at 1kW rated power. Figure 15a shows the voltage waveforms of the single-phase AC power supply voltage u_g, the input side current i_g, and the DC side voltage U_dc, U_C1, U_C2. As seen from Figure 15a, the input power supply voltage u_g is in phase with the input side current i_g, and it is consistent to achieve power factor correction. The DC side voltage U_dc is stable at 400V, and the capacitor voltage U_C1, U_C2 remains dynamically balanced at 200V. Figure 15b shows the bridge arm voltage u_aN, u_bN waveform and the input inductor current i_L1, i_L2 waveform. As can be seen from Figure 15b, the waveform of inductor current i_L1 phase ahead 180° of inductor current i_L2. Similarly, the bridge arm voltage u_aN, u_bN waveform changes in positive and negative half-cycles alternately, which is consistent with Figure 6 and Table 1.

Figure 16 shows the PDBC-II switching pulse distribution experimental waveform. As can be seen from Figure 16, the switches S₁-S₄ has a short high-frequency switching time. As a result, the switching losses of PDBC-II is relatively low. In addition, the switches S₃ and S₄ symmetrically action in positive and negative half-cycle, which is consistent with the switching pulse distribution of Table 1.

Figure 17 shows the PDBC-II voltage and current stress experimental waveforms of the switches at 1kW rated power. Figure 17a shows the voltage stress waveform of the switches S₁-S₄. It can be seen from Figure 17a that the maximum voltage stress of the four switches U_S1=U_S2≈400V, U_S3=U_S4≈200V, i.e. the partial voltage stress is halved, which is consistent with the voltage stress analysis in Table 2. Figure 17b shows the waveform of the inductor current, diode D₁ current i_D1, the switch S₁ current i_S1. As can be seen from Figure 17b, the switch current i_S1 waveform is enveloped by the inductor L₁ current i_L1 waveform in the positive half cycle. In addition, the current i_D1, i_S1 changes at high frequencies during the [0, T_g/12] and [5T_g/12, T_g/2] (where T_g is the grid period), which is the same as the simulation waveforms in Figure 10.

Figure 18 shows the THD test results of PDBC-II at 1kW rated power. As can be seen from Figure 18, at the switching frequency of 20kHz, the THD of PDBC-II is 3.2%, which meets the IEC 6100-3-2 standard.

6. Conclusions

In this paper, combining the three-level PTP circuit and the five-level NPC bridge arm, a family of PDBCs is proposed by transforming the NPC bridge arm. The proposed circuit reduces the volume of the filter inductor to increase the power density of the circuit and improves the working efficiency of the circuit. Through comparative analysis of voltage and current stress, loss, the following conclusions are drawn.

1) The experimental results show that the PDBCs proposed in this paper has a good input and output waveform at low switching frequency. Therefore, the PDBCs can improve overall efficiency by reducing switching losses.

2) The efficiency of the five PDBCs proposed in this paper is higher than CFLC. The PDBC-I has the smallest loss and the highest efficiency, with a peak efficiency of 98.27%, and its overall performance is the best.

3) Compared with the conventional three-level PTP circuit, the five PDBCs proposed in this paper have higher power density, and the voltage stress of some devices is reduced by half. In addition, the PDBC-II and PDBC-III more devices have the voltage stress halved, so their cost is lower.