Wide Load Range ZVS Three-level DC-DC Converter: Modular Structure, Redundancy Ability, and Reduced Filters Size

Abstract

In future dc distributed power systems, high performance high voltage dc-dc converters with redundancy ability are welcome. However, most existing high voltage dc-dc converters do not have redundancy ability. To solve this problem, a wide load range zero-voltage switching (ZVS) three-level (TL) dc-dc converter is proposed, which has some definitely good features. The primary switches have reduced voltage stress, which is only V_in/2. Moreover, no extra clamping component is needed, which results simple primary structure. Redundancy ability can be obtained by both primary and secondary sides, which means high system reliability. With proper designing of magnetizing inductance, all primary switches can obtain ZVS down to 0 output current, and in addition, the added conduction loss can be neglected. TL voltage waveform before the output inductor is obtained, which leads small volume of the output filter. Four secondary MOSFETs can be switched in zero-current switching (ZCS) condition over wide load range. Finally, both the primary and secondary power stages are modular architecture, which permits realizing any given system specifications by low voltage, standardized power modules. The operation principle, soft switching characteristics are presented in this paper, and the experimental results from a 1 kW prototype are also provided to validate the proposed converter.

1. Introduction

The dc distribution, with several good features, e.g., high system stability, high conversion and transmission efficiency, high flexibility and easy system control [1,2,3], seems to be the most attractive solution for future power systems with the increasing percentage of renewable energy sources, such as photovoltaic, wind power, and fuel cells. To improve the overall performance of a dc distribution, high dc input voltage is preferred. Therefore, dc-dc converters for high voltage dc distributions with good input and output characteristics, simple and compact circuit structure, good efficiency performance have already become hot issues in the power electronics society [4]. The main challenge caused by high dc input voltage is how to select proper power devices to fulfill power conversion task without system performance and reliability compensating [4]. Full bridge (FB) dc-dc topology with high voltage rating MOSFETs and IGBTs may be directly used in high voltage dc-dc conversion, but, high conduction loss and worse switching characteristics of these high voltage rating power devices may greatly degrade the conversion efficiency and power density. Moreover, high voltage dynamic transition would cause some electrical-magnetic compliable (EMC) problems, which is not preferred in the designing and producing procedure of the high input dc-dc power converters. Therefore, using series connected low voltage rating and high-performance power modules to sustain high dc bus voltage is still the best solution in high voltage dc-dc applications. Several good research papers have been published, and these solutions can be concluded into two kinds, which are TL dc-dc converters [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] and input series cells dc-dc converters [20,21,22,23,24,25,26,27,28,29,30,31,32]. The first TL dc-dc converter was proposed in [5], which is a diode clamped half bridge (HB) dc-dc converter. In [5], the voltage stress on each primary switch is only V_in/2, and the primary switches can obtain zero-voltage switching (ZVS) with limited load range. A series of zero-voltage and zero-current switching (ZVZCS) TL dc-dc converters were proposed in [6], and the primary switches in this converter can achieve ZVZCS operation over wide load range; furthermore, a simple switching scheme is used in these converters, which makes these topologies more convenient to industrial customers. Then, many other good research results have been reported in following main aspects: new topologies for special applications [8,9,10], wide range soft switching technologies [6,10,11,12,13,14,15,16], and converters with reduced volume of the input and output filters [16,17,18,19]. All above mentioned papers have made the TL dc-dc converters more applicable.

Input series cells dc-dc converter (ISCDC) is another solution for high voltage dc-dc conversion, which is composed of several series connected cells to reduce the voltage stress on the primary switches. Compared to TL dc-dc converters, ISCDCs have a simple and compact primary circuit due to its modular structure, which is attractive to high input industrial applications. In [20,21], ISCDCs based on forward or fly-back cells were proposed, which can reduce the voltage stress on the primary switches. The main drawback of these converters is hard switching operation, which results low power transferring efficiency. Some resonant ISCDCs were presented in [22,23], and these converters can achieve good soft switching characteristics, as well as low voltage stress on the primary switches. Half bridge (HB) based ISCDCs were reported and analyzed in [24,25,26], and some of these converters have input voltage auto-balance ability. Input-series output-parallel dc-dc converters (ISOPDCs) are new type ISCDCs, which are considered as the most promising choice due to its truly modular structure, which means normal two-level modules can be directly connected for special high voltage applications [27,28]. The main challenge of ISOPDCs is the input voltage balance problem, which can be solved by many control strategies [29,30,31] with increased cost and circuit complexity. In [32], a flying capacitor is added to achieve input voltage auto-balance ability, which makes the ISOPDC more applicable [32]. Figure 1 shows the ISOPDC in [32], which is composed of two two-level FB cells series connected in the primary side and parallel connected in the secondary side. Two FB cells are synchronously switched with the PS switching scheme, and a flying capacitor is used to obtain auto-voltage balance ability.

However, limitations still exist. As shown in Figure 1, the midpoint voltage is still highly dependent on the states of the input series and output parallel connected modules. Any errors occurring in each module, i.e., S₁ is broken, would cause the converter halting due to the voltage of the input capacitors cannot be balanced again, which means the primary and secondary sides of the converter in Figure 1 having no redundancy ability. In fact, this is a common problem of most ISCDCs. In addition, the converter in Figure 1 has some other disadvantages: the secondary rectifier voltage waveforms are still two-level, which needs a large output filter to minimize the output current ripple, and a large input EMI filter is also required; the ZVS load range is narrow, which results in high power loss especially under the light load condition. Therefore, it is still a worthy task to find new high voltage dc-dc converters with redundancy ability, modular structure, simple input voltage balance circuit, reduced volume of the output and input filters, and good soft switching characteristics.

In this paper, a wide load range ZVS high voltage dc-dc converter with redundancy ability, modular structure, simple input voltage balance circuit, reduced volume of the output and input inductors is proposed and investigated. The outline of this paper is concluded as follows. In Section 2, the configuration of the proposed converter is presented. Normal operation principle is discussed in Section 3. And in Section 4, module failure operation principle is analyzed to prove the redundancy ability. Some important technical issues are analyzed in Section 5. Experimental results are presented and discussed in Section 6. The main conclusions are given in the last section.

2. Circuit Configuration

Figure 2 shows the presented circuit. In the primary side, C_in1 and C_in2 are the input capacitors with the same value, which are used to split the input voltage. S₁-S₈ are the primary switches; D₁-D₈ are the anti-parallel diodes of S₁-S₈, and C₁-C₈ are corresponding parasitic capacitors of the primary switches. During the operation, OFF voltages across S₁-S₈ are directly clamped by C_in1 and C_in2, thus, no extra clamping component is needed. C_BL1 and C_BL2 are two dc blocking capacitors, which is series connected with N_1p and N_2p. L_lk1 and L_lk2 are the leakage inductors of the transformers; L_1m and L_2m are magnetic inductors of the transformers, which is designed to a specific value to help the ZVS of S₁-S₈. In the secondary side, two parallel-connected rectifier modules are included. The first rectifier module is built of S_s1-S_s2, D_o1-D_o6, L_o1 and C_o1; while, the secondary module is composed of S_s3-S_s4, D_o7-D_o12, L_o2 and C_o2.

3. Normal Operation

Before the discussion, some assumptions are concluded as follows: (1) the on-resistance of the primary switches are neglected; (2) the voltage ripple on C_in1, C_in2, C_BL1 and C_BL2 can be neglected due to high capacitance; (3) the output capacitance of the power devices is identical, and is represented by C_o; (4) L_lk1 and L_lk2 are identical, and are represented by L_lk; (5) L_1m and L_2m are identical, and are represented by L_m; (6) N_1p is identical to N_2p, and N_1s1 = N_1s2 = N_2s1 = N_2s2; (7) k_T = N_1p/N_1s1 = N_2p/N_2s1; (8) the current ripple of i_Lo1 and i_Lo2 is neglected; (9) With proper controlling, the output currents of the two paralleled connected modules can be identical, and the controlling method is not discussed in this paper. Therefore, i_Lo1 = i_Lo2. i_Lo1 and i_Lo2 are represented by I_o ; (10) i_in is identical to i_Vin + i_Cin, and its AC content is defined as ${\tilde{i}}_{\mathrm{in}}$. During the normal operation, the proposed converter can be controlled in the secondary side and primary side modulation modes. Figure 3 depicts the key waveforms,

Table 1. Switching scheme in the first half switching period (secondary side modulation mode).

Item	S1	S2	S3	S4	S5	S6	S7	S8	Ss1	Ss2	Ss3	Ss4
Stage 1	ON	OFF	OFF	ON	OFF	ON	ON	OFF	ON	OFF	ON	OFF
Stage 2	OFF	OFF	OFF	OFF	OFF	OFF	OFF	OFF	ON	OFF	OFF	ON
Stage 3	OFF	OFF	OFF	OFF	OFF	OFF	OFF	OFF	ON	OFF	OFF	ON
Stage 4	OFF	ON	ON	OFF	ON	OFF	OFF	ON	ON	OFF	OFF	ON
Stage 5	OFF	ON	ON	OFF	ON	OFF	OFF	ON	ON	OFF	OFF	ON
Stage 6	OFF	ON	ON	OFF	ON	OFF	OFF	ON	OFF	OFF	OFF	OFF

and

Table 2. Switching scheme in the first half switching period (secondary side modulation mode).

Item	S1	S2	S3	S4	S5	S6	S7	S8	Ss1	Ss2	Ss3	Ss4
Stage 1	ON	OFF	OFF	ON	OFF	ON	ON	OFF	OFF	OFF	OFF	OFF
Stage 2	OFF	OFF	OFF	ON	OFF	ON	OFF	OFF	OFF	OFF	OFF	OFF
Stage 3	OFF	OFF	OFF	ON	OFF	ON	OFF	OFF	OFF	OFF	OFF	OFF
Stage 4	OFF	ON	OFF	OFF	OFF	OFF	OFF	OFF	OFF	OFF	OFF	OFF
Stage 5	OFF	ON	OFF	OFF	OFF	OFF	OFF	ON	OFF	OFF	OFF	OFF
Stage 6	OFF	ON	ON	OFF	ON	OFF	OFF	ON	OFF	OFF	OFF	OFF

show the switching status in each stage.

3.1. Secondary Side Modulation

As shown in Figure 3a, the primary switches can be divided into two groups. The first group is S₁, S₄, S₆ and S₇; while another group is S₂, S₃, S₅ and S₈. The switches in each group are switched ON and OFF synchronously, and the switches in different groups are switched in the complementary mode. In the secondary side, S_s2 and S_s3 are switched ON and OFF synchronously; while S_s1 and S_s4 are switched ON and OFF synchronously. S_s1 and S_s3 are switched in the complementary mode with S_s2 and S_s4. V_o can be regulated by the phase angel between gate signals of S_s1 and S₁, S_s3 and S₅. When these angles equal 180°, V_o = V_in/(2k_T). There are 12 operation stages in one switching cycle, and the operation stages in the first half switching cycle are illustrated in Figure 4.

Stage 1 [Figure 4a]: before t₀, the circuit is stable. Input source powers the load. In the primary side, S₁, S₄, S₆ and S₇ are ON; v_CD = V_in/2, and v_AB = −V_in/2; i_1p = 2I_o/k_T, and i_2p = −2I_o/k_T. i_Llk1 and i_Llk2 are

$$i_{\mathrm{Llk}1}(t)=\frac{2{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+i_{1\mathrm{m}}(t_0)+\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_0)$$

(1)

$$i_{\mathrm{Llk}2}(t)=-\frac{2{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+i_{2\mathrm{m}}(t_0)-\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_0)$$

(2)

i_in = i_Vin + i_Cin1 with the value of i_Llk1. The DC content of i_in flows from the input source to the primary sides of the transformers directly. i_Cin1 is partial AC content of i_in depends on the reactance distribution of the input source and input capacitors. As i_Cin1 is identical to i_Cin2, the midpoint voltage of C_in1 and C_in2 is constant during this period. v_S2 and v_S5 are clamped by C_in1, and v_S3 and v_S8 are clamped by C_in2.

In the secondary side, S_s1 and S_s4 are ON; D_o1, D_o6, D_o8 and D_o11 are conducted; v_rect1 = v_rect2 = V_in/k_T.

Stage 2 [Figure 4b, t₀-t₁]: At t₀, S₁, S₄, S₆ and S₇ are switched OFF. In the primary side, the slope rates of i_1m and i_2m are very slow, and the absolute value of these currents is constant value I_m. Therefore, the absolute value of i_Llk1 and i_Llk2 during this period is

$$\left|i_{\mathrm{Llk}1}(t)\right|=\left|i_{\mathrm{Llk}2}(t)\right|={\mathrm{I}}_m+\frac{2{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}$$

(3)

i_Llk1 charges C₁ and C₄, discharges C₂ and C₃; while i_Llk2 charges C₆ and C₇, discharges C₅ and C₈. v_S1, v_S4, v_S6 and v_S7 are

$$v_{\mathrm{S}i}(t)=\frac{I_m{k}_{\mathrm{T}}+2{\mathrm{I}}_{\mathrm{o}}}{2k_{\mathrm{T}}{\mathrm{C}}_{\mathrm{o}}}t, i=1, 4, 6, 7$$

(4)

v_S2, v_S3, v_S5 and v_S8 are

$$v_{\mathrm{S}k}(t)=\frac{{\mathrm{V}}_{\mathrm{in}}}{2}-\frac{{\mathrm{I}}_m{k}_{\mathrm{T}}+2{\mathrm{I}}_{\mathrm{o}}}{2k_{\mathrm{T}}{\mathrm{C}}_{\mathrm{o}}}t, k=2, 3, 5, 8$$

(5)

According to (4) and (5), the voltage of S₁-S₈ is lower than V_in/2, before the end of this stage.

This stage lasts until v_S1 is V_in/2, and the interval is

$${\mathrm{T}}_{10}=\frac{{\mathrm{V}}_{\mathrm{in}}{\mathrm{C}}_{\mathrm{o}}{k}_{\mathrm{T}}}{({\mathrm{I}}_m{k}_{\mathrm{T}}+2{\mathrm{I}}_{\mathrm{o}})}$$

(6)

i_Cin1 is identical to i_Cin2, which is i_Llk1−i_Llk2, and under ideal condition, this value is zero. Therefore, the midpoint voltage of C_in1 and C_in2 can also be stabled during this period.

In the secondary side, S_s1 and S_s4 are ON; D_o1, D_o6, D_o8 and D_o11 are conducted; v_rect1 = v_rect2 = 2v_CD(t)/k_T = 2|v_AB (t)|/k_T.

Stage 3 [Figure 4c, t₁-t₂]: At t₁, D₂, D₃, D₅ and D₈ are ON. In the primary side, v_CD = −V_in/2, and v_AB = V_in/2; L_1m and L_2m sustain negative voltage, and i_1m and i_2m are

$$i_{1\mathrm{m}}(t)={\mathrm{I}}_m-\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_1)$$

(7)

$$i_{2\mathrm{m}}(t)=-{\mathrm{I}}_m+\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_1)$$

(8)

i_Llk1 and i_Llk2 are

$$i_{\mathrm{Llk}1}(t)=(\frac{2{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+{\mathrm{I}}_m)-\frac{{\mathrm{V}}_{\mathrm{in}}}{2}\frac{{\mathrm{L}}_{\mathrm{m}}+{\mathrm{L}}_{\mathrm{lk}}}{{\mathrm{L}}_{\mathrm{m}}{\mathrm{L}}_{\mathrm{lk}}}(t-t_1)$$

(9)

$$i_{\mathrm{Llk}2}(t)=-(\frac{2{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+{\mathrm{I}}_m)+\frac{{\mathrm{V}}_{\mathrm{in}}}{2}\frac{{\mathrm{L}}_{\mathrm{m}}+{\mathrm{L}}_{\mathrm{lk}}}{{\mathrm{L}}_{\mathrm{m}}{\mathrm{L}}_{\mathrm{lk}}}(t-t_1)$$

(10)

i_in = i_Vin + i_Cin1 with the value of i_Llk2. The DC content of i_in will flow from the input source to the primary sides of the transformers directly. i_Cin1 is partial AC content of i_in depends on the reactance distribution of the input source and input capacitors. As i_Cin1 is identical to i_Cin2, the midpoint voltage of C_in1 and C_in2 is constant during this period. v_S1 and v_S6 are clamped by C_in1, and v_S4 and v_S7 are clamped by C_in2. S₂, S₃, S₅ and S₈ should be gated after t₁ to achieve ZVS operation.

In the secondary side, D_o3-D_o6 and D_o9-D_o12 are ON to free-wheel the secondary currents. v_rect1 = v_rect2 = 0.

Stage 4 [Figure 4d, t₂-t₃]: At t₂, S₂, S₃, S₅ and S₈ are switched ON with ZVS. In the primary side, i_1m, i_2m, i_1p and i_2p keep increasing in the reverse direction, and the increasing slope are defined as (13) to (16). i_in = i_Vin + i_Cin1 with the value of i_Llk2. i_Cin1 is partial AC content of i_in depends on the reactance distribution of the input source and input capacitors. As i_Cin1 is identical to i_Cin2, the midpoint voltage of C_in1 and C_in2 is constant during this period. v_S1 and v_S6 are clamped by C_in1, and v_S4 and v_S7 are clamped by C_in2.

In the secondary side, D_o3-D_o6 and D_o9-D_o12 are conducted to free-wheel the secondary currents. S_s1 and S_s4 are ON. As the currents through S_s1 and S_s4 are 0, thus, S_s1 and S_s4 can achieve ZCS turned on after this period. v_rect1 and v_rect2 are zero.

Stage 5 [Figure 4e) t₃-t₄]: At t₃, the absolute value of i_1p and i_2p is I_o/k_T. In the primary side, S₂, S₃, S₅ and S₈ are ON; v_CD =−V_in/2, and v_AB = V_in/2; i_1p = −I_o/k_T, and i_2p = I_o/k_T. i_1m and i_2m are

$$i_{1\mathrm{m}}(t)=i_{1\mathrm{m}}(t_3)-\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_3)$$

(11)

$$i_{2\mathrm{m}}(t)=i_{2\mathrm{m}}(t_3)+\frac{{\mathrm{V}}_{\mathrm{in}}}{2L_{\mathrm{m}}}(t-t_3)$$

(12)

i_Llk1 and i_Llk2 are

$$i_{\mathrm{Llk}1}(t)=-\frac{{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+i_{1\mathrm{m}}(t_3)-\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_3)$$

(13)

$$i_{\mathrm{Llk}2}(t)=\frac{{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+i_{2\mathrm{m}}(t_3)+\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_3)$$

(14)

i_in = i_Vin + i_Cin1 with the value of i_Llk2. i_Cin1 is partial AC content of i_in depends on the reactance distribution of the input source and input capacitors. As i_Cin1 is identical to i_Cin2, the midpoint voltage of C_in1 and C_in2 is constant during this period. v_S1 and v_S6 are clamped by C_in1, and v_S4 and v_S7 are clamped by C_in2.

In the secondary side, D_o4, D_o5, D_o9 and D_o12 are conducted; v_rect1 = v_rect2 = V_in/(2k_T).

Stage 6 [Figure 4f, t₄-t₅]: At t₄, S_s1 and S_s4 are OFF with zero-current switching (ZCS). After t₅, the circuit will be operated into the secondary switching period, and detail analyses are not provided here for the sake of simplicity.

The ideal output-input voltage ratio in this mode is

$$\frac{{\mathrm{V}}_{\mathrm{o}}}{{\mathrm{V}}_{\mathrm{in}}}=\frac{(1+\mathrm{D})}{2k_{\mathrm{T}}}$$

(15)

3.2. Primary Side Modulation

When the phase angle between S_s1 and S₁ is 180°, the secondary side modulation mode cannot further change the output voltage. To regulate output voltage down to zero, the converter must be controlled into the primary side modulation mode. In this mode, the secondary switches S_s1-S_s4 are OFF; the primary switches are divided into two groups, which are S₁ to S₄ and S₅ to S₈. As shown in Figure 3b, the primary switches in each group are switched in the PS switching scheme, and S₁ and S₆ are switched with the same phase angle. D₁ and D₂ are duty ratios of S₁-S₄ and S₅-S₈, and with symmetrical switching pattern, D₁ = D₂. The output voltage is varied with the value of D₁ and D₂, when D₁ = D₂ = 0, the output voltage is zero. The key waveforms of this mode are depicted in Figure 3b, and the operation stages in the first half switching cycle are illustrated in Figure 6.

Stage 1 [Figure 5a]: before t₁, the circuit is operated in steady condition. Input source powers the load. In the primary side, S₁, S₄, S₆ and S₇ are ON; v_CD = V_in/2, and v_AB =−V_in/2; i_1p = −I_o/k_T, and i_2p = I_o/k_T.

i_Llk1 and i_Llk2 are

$$i_{\mathrm{Llk}1}(t)=-\frac{{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}-{\mathrm{I}}_m+\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_0)$$

(16)

$$i_{\mathrm{Llk}2}(t)=\frac{{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+{\mathrm{I}}_m-\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_0)$$

(17)

i_in = i_Vin + i_Cin1 with the value of i_Llk1. i_Cin1 is formed by partial AC content of i_in depends on the reactance distribution of the input source and input capacitors. As i_Cin1 is identical to i_Cin2, the midpoint voltage of C_in1 and C_in2 is constant during this period. v_S2 and v_S5 are clamped by C_in1, and v_S3 and v_S8 are clamped by C_in2.

In the secondary side, S_s1-S_s4 are OFF; D_o3, D_o6, D_o10 and D_o11 are conducted; v_rect1 = v_rect2 = V_in/(2k_T).

Stage 2 [Figure 5b, t₁-t₂]: At t₁, S₁ and S₇ are switched OFF. In the primary side, S₁ and S₇ can obtain zero-voltage turned OFF due to existence of C₁ and C₇. i_1m and i_2m reach their maximum absolute value I_m. Therefore, the absolute values of i_Llk1 and i_Llk2 are

$$\left|i_{\mathrm{Llk}1}(t)\right|=\left|i_{\mathrm{Llk}2}(t)\right|=I_m+\frac{I_{\mathrm{o}}}{k_{\mathrm{T}}}$$

(18)

i_Llk1 charges C₁, discharges C₂; while i_Llk2 charges C₇, discharges C₈. v_S1 and v_S7 are

$$v_{\mathrm{S}i}(t)=\frac{I_m{k}_{\mathrm{T}}+I_{\mathrm{o}}}{2k_{\mathrm{T}}{C}_{\mathrm{o}}}t, i=1, 7$$

(19)

v_S2 and v_S8 are

$$v_{\mathrm{S}k}(t)=\frac{V_{\mathrm{in}}}{2}-\frac{I_m{k}_{\mathrm{T}}+I_{\mathrm{o}}}{2k_{\mathrm{T}}{C}_{\mathrm{o}}}t, k=2, 8$$

(20)

According to (19) and (20), v_S1, v_S2, v_S7 and v_S8 is lower than V_in/2 before the end of this stage.

This stage ends until v_S1 and v_S7 is V_in/2, and the time is

$${\mathrm{T}}_{21}=\frac{{\mathrm{V}}_{\mathrm{in}}{\mathrm{C}}_{\mathrm{o}}{k}_{\mathrm{T}}}{({\mathrm{I}}_m{k}_{\mathrm{T}}+{\mathrm{I}}_{\mathrm{o}})}$$

(21)

i_Cin1 is identical to i_Cin2, which is i_Llk1-i_Llk2, and with symmetrical switching sequence i_Cin1 is zero. Therefore, the midpoint voltage of C_in1 and C_in2 is constant during this period.

In the secondary side, D_o3, D_o6, D_o10 and D_o11 are conducted; v_rect1 = v_rect2 = v_CD(t)/k_T = |v_AB (t)|/k_T.

Stage 3 [Figure 5c, t₂-t₄]: At t₂, D₂ and D₈ are on. In the primary side, v_CD = v_AB = 0; i_1m and i_2m keep constant value I_m; i_1p and i_2p are with the same absolute value |I_o/k_T|, During this period, i_Llk1 and i_Llk2 are

$$i_{\mathrm{Llk}1}(t)=\frac{{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+{\mathrm{I}}_m$$

(22)

$$i_{\mathrm{Llk}2}(t)=-(\frac{{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+{\mathrm{I}}_m)$$

(23)

i_Cin1 is identical to i_Cin2 with the value of i_Llk1-i_Llk2, thus, with symmetrical switching cycle, i_Cin1 and i_Cin2 are zero, which means stable midpoint voltage of input capacitors can be achieved. Therefore, the midpoint voltage of C_in1 and C_in2 is constant during this period. v_S1 and v_S5 are clamped by C_in1, and v_S3 and v_S7 are clamped by C_in2. S₂ and S₈ should be gated after t₂ to achieve ZVS operation, and according to Figure 3b, S₂ and S₈ are switched at t₃.

In the secondary side, D_o3-D_o6 and D_o9-D_o12 are ON to free-wheel the secondary currents. v_rect1 = v_rect2 = 0.

Stage 4 [Figure 5d, t₄-t₅]: At t₄, S₄ and S₆ are switched OFF. In the primary side, S₄ and S₆ can obtain zero-voltage turned OFF due to C₄ and C₆. The primary currents keep constant during this stage. i_Llk1 charges C₄, discharges C₃; while i_Llk2 charges C₆, discharges C₅. v_S4 and v_S5 are

$$v_{\mathrm{S}i}(t)=\frac{{\mathrm{I}}_m{k}_{\mathrm{T}}+{\mathrm{I}}_{\mathrm{o}}}{2k_{\mathrm{T}}{\mathrm{C}}_{\mathrm{o}}}t, i=4, 5$$

(24)

v_S3 and v_S6 are

$$v_{\mathrm{S}k}(t)=\frac{{\mathrm{V}}_{\mathrm{in}}}{2}-\frac{{\mathrm{I}}_m{k}_{\mathrm{T}}+{\mathrm{I}}_{\mathrm{o}}}{2k_{\mathrm{T}}{\mathrm{C}}_{\mathrm{o}}}t, k=3, 6$$

(25)

This stage ends until v_S4 and v_S6 are V_in/2, and the time is

$${\mathrm{T}}_{54}=\frac{{\mathrm{V}}_{\mathrm{in}}{\mathrm{C}}_{\mathrm{o}}{k}_{\mathrm{T}}}{2({\mathrm{I}}_m{k}_{\mathrm{T}}+{\mathrm{I}}_{\mathrm{o}})}$$

(26)

i_Cin1 is identical to i_Cin2 with the value of i_Llk1-i_Llk2, thus, with symmetrical switching cycle, the currents flowing through C_in1 and C_in2 are zero, which means stable midpoint voltage of input capacitors can be achieved. Therefore, the midpoint voltage of C_in1 and C_in2 is constant during this period.

In the secondary side, D_o3-D_o6 and D_o9-D_o12 are ON to free-wheel the secondary currents. v_rect1= v_rect2 = 0.

Stage 5 [Figure 5e, t₅-t₆]: At t₅, D₃ and D₅ are ON. In the primary side, v_CD = −V_in/2, and v_AB = V_in/2; negative voltage is applied on magnetic inductors, and i_1m and i_2m are

$$i_{1\mathrm{m}}(t)={\mathrm{I}}_m-\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_5)$$

(27)

$$i_{2\mathrm{m}}(t)=-{\mathrm{I}}_m+\frac{{\mathrm{V}}_{\mathrm{in}}}{2{\mathrm{L}}_{\mathrm{m}}}(t-t_5)$$

(28)

i_Llk1 and i_Llk2 are

$$i_{\mathrm{Llk}1}(t)=(\frac{{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+{\mathrm{I}}_m)-\frac{{\mathrm{V}}_{\mathrm{in}}}{2}\frac{{\mathrm{L}}_{\mathrm{m}}+{\mathrm{L}}_{\mathrm{lk}}}{{\mathrm{L}}_{\mathrm{m}}{\mathrm{L}}_{\mathrm{lk}}}(t-t_5)$$

(29)

$$i_{\mathrm{Llk}2}(t)=-(\frac{{\mathrm{I}}_{\mathrm{o}}}{k_{\mathrm{T}}}+{\mathrm{I}}_m)+\frac{{\mathrm{V}}_{\mathrm{in}}}{2}\frac{{\mathrm{L}}_{\mathrm{m}}+{\mathrm{L}}_{\mathrm{lk}}}{L_{\mathrm{m}}{L}_{\mathrm{lk}}}(t-t_5)$$

(30)

i_in = i_Vin + i_Cin1 with the value of i_Llk2. i_Cin1 is partial AC content of i_in depends on the reactance distribution of the input source and input capacitors. As i_Cin1 is identical to i_Cin2, the midpoint voltage of C_in1 and C_in2 is constant during this period. v_S1 and v_S6 is clamped by C_in1, and v_S4 and v_S7 is clamped by C_in2. S₃ and S₅ should be gated after t₅ to achieve ZVS operation, and according to Figure 3b, S₃ and S₅ are switched at t₆.

In the secondary side, D_o3-D_o6 and D_o9-D_o12 are ON to free-wheel the secondary currents. v_rect1 = v_rect2 = 0.

Stage 6 [Figure 5f, t₆-t₇]: At t₇, i_1p equals −I_o/k_T, and i_2p equals I_o/k_T; the free-wheeling mode is over. Input source powers the load. In the primary side, S₂, S₃, S₅ and S₈ are ON; v_CD =−V_in/2, and v_AB = V_in/2. i_in = i_Vin + i_Cin1 with the value of i_Llk1. i_Cin1 is partial AC content of i_in depends on the reactance distribution of the input source and input capacitors. As i_Cin1 is identical to i_Cin2, the midpoint voltage of C_in1 and C_in2 is constant during this period. v_S1 and v_S3 are clamped by C_in1, and v_S4 and v_S7 are clamped by C_in2.

In the secondary side, S_s1-S_s4 are OFF; D_o4, D_o5, D_o9 and D_o12 are conducted; v_rect1 = v_rect2 = V_in/(2k_T).

The ideal output-input voltage ratio in this mode is

$$\frac{{\mathrm{V}}_{\mathrm{o}}}{{\mathrm{V}}_{\mathrm{in}}}=\frac{\mathrm{D}}{2k_{\mathrm{T}}}$$

(31)

4. Module Failure Operation

The most important feature of the proposed converter is the redundancy ability for the primary and secondary sides. In this part, the operation principle of module failure operation is briefly described to illustrate the redundancy ability. To simplified the description, S₆ is set to be broken, which causes a primary module failure. It should be pointed out that the proposed converter can also be operated with a secondary module failure. During the module failure operation, the proposed converter can also be operated in the secondary and primary side modulation switching schemes according to the output voltage, and key waveforms are given in Figure 6. The switching scheme of the secondary side modulation is illustrated in

Table 3. Switching scheme in the first half switching period (secondary side modulation mode).

Item	S1	S2	S3	S4	Ss1	Ss2
Stage 1	ON	OFF	OFF	ON	ON	OFF
Stage 2	OFF	OFF	OFF	OFF	ON	OFF
Stage 3	OFF	OFF	OFF	OFF	ON	OFF
Stage 4	OFF	ON	ON	OFF	ON	OFF
Stage 5	OFF	ON	ON	OFF	OFF	OFF
Stage 6	OFF	ON	ON	OFF	OFF	OFF

.

4.1. Secondary Side Modulation

Figure 6a and Figure 7 show the key waveforms and operation stages of the secondary side modulation. As shown in Figure 6a, S₆ is broken due to some unknown reasons. In the primary side, S₅-S₈ are stop, and S₁-S₄ are switched in the mode which is identical to the secondary operation mode of normal operation. According to Figure 7, the input capacitor currents remain zero during stages 3 to 6, the mid-point voltage of the input capacitors are balanced during these stages. In addition, during stages 1 and 2, the input capacitor currents are identical to partial AC content of i_in, thus, the mid-point voltage of the input capacitors are also balance during stages 1 and 2. Therefore, a stable mid-point voltage can be obtained during the first switching cycle, and in the secondary half switching cycle, the same conclusion can also be achieved. The primary waveforms of v_CD, i_Llk1, i_1m and i_1p are quite similar to that of the normal operation, which is not analyzed here for the sake of simplicity. The OFF voltage of the primary switches is clamped by C_in1 and C_in2, which is not higher than V_in/2.

In the secondary side, the down cell is stop, and the up cell operates in the same pattern with that of the normal operation, and detail analysis is not provided here for the sake of simplicity.

4.2. Primary Side Modulation

During the primary side operation, the proposed converter can be treated as a conventional TLDC in [8]. Figure 6b illustrates key waveforms. The output can be regulated down to zero by switching scheme in Figure 6b. The operation principle about this procedure is not provided here for the sake of simplicity and detail information can reference [8].

4.3. Output Range of the Module Failure Operation

The output voltage of the module failure mode is quite similar to that of the normal operation. When V_in/k_T ≥ V_o > V_in/2k_T, the proposed converter is operated in the secondary side modulation, the output voltage is varied from V_in/k_T to V_in/2k_T with the duty ratio D; When V_in/2k_T ≥ V_o > 0, the proposed converter is operated in the primary side modulation, the output voltage is varied V_in/2k_T to 0 with the duty ratio D.

5. Technical Analysis

5.1. ZVS of the Primary Switches

The soft switching characteristics of the normal and module failure operation are quite similar, thus, only the soft switching characteristics of the normal operation are analyzed in the following parts.

5.1.1. Secondary Side Modulation

When the converter is operated in the secondary side modulation mode, the primary switches can obtain ZVS down to zero load current with proper designing of i_im, I = 1 and 2. And the L_m should observe following equation [19]

$${\mathrm{L}}_{\mathrm{m}}\le \frac{\sqrt{3}{\mathrm{T}}_{\mathrm{s}}}{8}\sqrt{\frac{{\mathrm{L}}_{\mathrm{lk}}}{C_{\mathrm{o}}}}$$

(32)

Figure 8 shows the required magnetizing inductance versus C_o, L_lk and T_s. It should be pointed out that I_m is irrelevant to the load current and increased with input voltage, hence, there is still enough energy stored in the leakage inductance to ensure ZVS for all primary switches under no loads or high input condition. Consequently, the proposed converter will have higher efficiency compared to its competitors under light loads and high input applications.

5.1.2. Primary Side Modulation

During the primary side modulation, the primary switches are switched in the PS mode, S₁, S₄, S₆ and S₇ are controlled as the leading leg switches; while S₂, S₃, S₅ and S₈ are switched as the lagging leg switches. Just as traditional PS FB converter, the leading leg switches can be switched with ZVS easily, and the ZVS criteria is

$$\frac{1}{2}{{\mathrm{L}}_{i\mathrm{p}}}^{\prime }{\mathrm{I}}_{\mathrm{Llk}i}{}^2\ge \frac{{\mathrm{C}}_{\mathrm{o}}{\mathrm{V}}_{\mathrm{in}}{}^2}{4}, i=1,2$$

(33)

where L_ip^’ is the sum of L_lki and k_T²L_oi, with the help of the output inductance and magnetic inductance, these switches can be achieved ZVS down to no-load easily.

S₂, S₃, S₅ and S₈ are lagging leg switches, and with proper designing of L_im, i = 1 and 2, these switches can also be achieved ZVS down to no-load.

5.1.3. ZVS Load Range

The minimum ZVS load currents for the two operation modes are concluded in

Table 4. Zero-voltage switching (ZVS) load range of the secondary and primary side modulation (I_m = 60%I_{p, rate}).

Mode	Switches	Minimum ZVS Load Current	Added Conduction Loss (Ratio of Primary Side Rate Conduction Loss) [19]
Secondary side modulation	S1 to S8	0	12%
Primary side modulation	S1, S4, S6 and S7	0	112.8%
	S2, S3, S5 and S8	0

.

As illustrated in Table 4, with the help of the magnetizing currents, all the primary switches can obtain ZVS down to 0 load currents, furthermore the added conduction loss in the secondary side modulation are quite smaller than that of the primary side modulation. Therefore, it is recommended that the proposed converter should be designed to operate into the secondary side modulation mode during most operation situations, and only to operate into the primary side modulation mode in some abnormal situation, such as overload, to regulated output down to zero.

5.2. ZCS of the Secondary Switches

During the secondary side modulation, all secondary switches can obtain ZCS independent of the load condition [19]. S_s1 is selected as an example. As shown in Figure 3a, S_s1 is on at this stage. But, the current flowing through S_s1 is zero due to the reverse voltage applied to D_o1. As shown in Figure 3b, S_se1 is switched off at zero current. Therefore, the switching loss of the secondary switches can be minimized.

5.3. Output Inductance

The reduction of the output inductance with TL secondary rectified voltage waveform has been discussed in [19]. According to these references, the required output inductance of the converters with TL secondary rectified voltage waveform is about one-third of that of conventional two-level converters. Therefore, the volume of the output filter in the proposed converter can be significantly reduced.

5.4. Voltage Balance Principle of the Input Capacitors

The initial voltage across the input capacitors is V_in/2 due to the configuration of the proposed converter. During the operation, the voltage across the input capacitors can be maintained if this capacitor can observe charge balance principle over each switching cycle.

Table 5. Currents of the input capacitors during the secondary side modulation.

Item	Normal Operation		Module Failure Operation
	icin1	icin2	icin1	icin2
Stage 1	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 2	iLlk1 − iLlk2 = 0		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 3	Partial of ${\tilde{i}}_{\mathrm{in}}$		0
Stage 4	Partial of ${\tilde{i}}_{\mathrm{in}}$		0
Stage 5	Partial of ${\tilde{i}}_{\mathrm{in}}$		0
Stage 6	Partial of ${\tilde{i}}_{\mathrm{in}}$		0
Stage 7	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 8	iLlk1 − iLlk2 = 0		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 9	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 10	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 11	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 12	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$

and

Table 6. Currents of the input capacitors during the primary side modulation.

Item	Normal Operation		Module Failure Operation
	icin1	icin2	icin1	icin2
Stage 1	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 2	iLlk1 − iLlk2 = 0		iLlk1	−iLlk1
Stage 3	iLlk1 − iLlk2 = 0		iLlk1	−iLlk1
Stage 4	iLlk1 − iLlk2 = 0		iLlk1	−iLlk1
Stage 5	Partial of ${\tilde{i}}_{\mathrm{in}}$		0
Stage 6	Partial of ${\tilde{i}}_{\mathrm{in}}$		0
Stage 7	Partial of ${\tilde{i}}_{\mathrm{in}}$		0
Stage 8	iLlk1 − iLlk2 = 0		−iLlk1	iLlk1
Stage 9	iLlk1 − iLlk2 = 0		−iLlk1	iLlk1
Stage 10	iLlk1 − iLlk2 = 0		−iLlk1	iLlk1
Stage 11	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$
Stage 12	Partial of ${\tilde{i}}_{\mathrm{in}}$		Partial of ${\tilde{i}}_{\mathrm{in}}$

show the currents of the input capacitors, as proved in Table 5 and Table 6, with symmetrical switching scheme, the input capacitors voltage can be stable properly. Detail descriptions have been provided in Section 3.

5.5. Comparison

The circuit and performance of the proposed converter and the converter in [32] are compared in this part, and the circuit of the converter for comparison is provided in Figure 1, and the detail operation principle about this converter can reference [32].

Table 7. Components comparison.

Item	Proposed	Figure 1
Primary side components
Switches	8	8
Flying capacitors	0	1
Blocking capacitors	2	2
Input capacitors	2	2
Primary coils	2	2
Secondary side components
Rectifier diodes	12	8
Secondary coils	4	2
Switches	4	0

and

Table 8. Performance comparison.

Item	Proposed	Figure 1
Voltage stress of the primary switches	Vin/2	Vin/2
Primary side redundancy ability	Yes	No
Secondary side redundancy ability	Yes	No
TL secondary rectified voltage waveform	Yes	No
Soft switching characteristics of the primary switches	Good	Normal
System dynamic response	Fast	Normal

illustrate the components and performance comparison.

5.5.1. Redundancy Ability

Compared to the converter in Figure 1, the redundancy ability is an obvious advantage of the proposed converter, which ensures higher system reliability. As shown in Figure 1, the primary side is built of two series connected modules, and the converter must be shut down when one primary switch is broken due to the remained switches would suffer higher voltage stress. However, as shown in Figure 6 and Figure 7, the proposed converter can still be operated safely when one primary switch is broken.

5.5.2. Components Comparison

The primary side components number of the proposed converter is similar to that of the converter in Figure 1, and as proved in pervious sections, OFF voltage across each primary switch is directly clamped by the input capacitors, thus no added clamping device is required. The secondary structure of the proposed converter is a little complex than that of the converter in Figure 1 to achieve TL secondary rectified waveforms, which would result reduced volume of input and output filter. In addition, according to Table 8, the system dynamic response of the proposed converter is higher than that of the converter in Figure 1. As shown in Table 8, the voltage stress on the primary switches of the proposed converter and the converter in Figure 1 are identical with the value of V_in/2, thus, these two converters are well suitable for high input voltage dc-dc power conversion.

5.5.3. Soft Switching Characteristics

With proper designing, the ZVS load range of the primary switches in the proposed converter is down to zero, which is better for wide load range applications. Furthermore, the turn-off switching loss can be reduced by increasing output capacitance of the primary switches. However, as depicted in [32], the lagging switches in Figure 1 cannot achieve wide ZVS load range due to only the energy stored in the leakage inductance can be used [32]. And the turn-off switching loss cannot be optimized due to limited ZVS load range of the lagging switches. As illustrated in Table 8, the proposed converter features have better soft switching characteristics, which means higher power conversion efficiency especially under light load and high input voltage operation.

5.5.4. Power Loss

The power loss distributions of the proposed converter and the converter in Figure 1 are compared in Figure 9. The data is obtained by power analyzer (PW60001), and the converters for comparison are operated with V_in = 600 V and I_o = 2 A. As shown in Figure 9, the proposed converter has lower power loss due to good switching loss of MOSFETs, which is an attractive characteristic of the proposed converter. As illustrated in Figure 9, the conduction loss of the proposed converter is a little higher than that of Figure 1 due to higher magnetizing current and extra secondary MOSFETs. Therefore, the expected efficiency of the proposed converter is better.

6. Experimental Results

The performance of the proposed converter is verified by a 1kW prototype, and the main parameters of the prototype are provided in

Table 9. Parameters of the prototype.

Item	Parameters
Input voltage	500–600 V
Output Voltage	250 V
Power rating	1 kW
fs	100 kHz
Primary switches	IRFP460
kT	3
L1m and L2m	300 μH
Lo1 and Lo2	30 μH
Co1 and Co2	220 μF
Secondary switches	IPP600N25N3G
Rectifier diodes	IDP18E120

. Figure 10 and Figure 11 give some experimental results. Figure 12 illustrated the prototype, and the control signals for the switches are generated by two UCC 3895s in synchronized mode. In the efficiency experiment, the power loss of control circuit and cooler system are considered. The proposed converter has several operation modes, and some key waveforms of these operation modes are quite similar. Therefore, only some typical experimental results are selected to validate the proposed converter for the sake of simplicity.

As shown in Figure 10a, OFF voltage across the primary switches in the proposed converter is even in the secondary side modulation mode, and the midpoint voltage of the input capacitors is stable and equals V_in/2. Figure 10b proves the voltage stress across the primary switches and the midpoint voltage of the input capacitors is also even and stable in the primary side modulation mode.

As proved in Figure 10c, the voltage applied to the primary coils is V_in/2, and i_Llk1 is not a constant value because i_1m is enlarged to help ZVS of the primary switches. As i_1m is not in phase with load current, the added primary RMS current is smaller. Thus, the added conduction loss is also smaller. As proved in Figure 10d, the duty ratio of v_BC is 100% and uncontrolled during the whole operation stages, which means zero primary circulating current.

As depicted in Figure 10e, the secondary rectified voltage is a TL waveform, which significantly reduces the volume of the output filter. The output voltage is adjusted by changing the time of high output voltage level. As there is no free-wheeling time, the input current ripple is also smaller. The voltages across the rectifier diodes are shown in Figure 10f,g.

The waveforms of the drain-source voltage and current of S_s1 are shown in Figure 10h, and it is clearly that S_s1 can obtain ZCS. The ZVS characteristics of the primary switches in the proposed converter are test with zero load current. The waveforms of the gate signals and the drain-source voltage of switch S₁ is depicted in Figure 10i. In Figure 10i, the gate-source voltage of S₁ is much lower than the threshold voltage when the drain-source voltage of S₁ decreases to zero, thus, S₁ can obtain ZVS.

Figure 10j gives some experimental results of the failure mode operation, and it is similar to that of normal operation. From Figure 10j, we can conclude the proposed converter can be operated into the failure mode operation. Other waveforms in the failure mode operation is not provided in this paper for the sake of simplicity.

Figure 11a shows the efficiency comparison under different load current with 600V input voltage, and the comparison is carried out under the same base line. As all primary switches can obtain ZVS in wide load range, the proposed converter has higher efficiency with smaller load. In Figure 11b, the efficiency results under constant I_o and variable V_in condition are shown, and the proposed converter can obtain more optimum high input efficiency owing to the ZVS operation can still be assured with increasing of the input voltage.

7. Conclusions

A wide load range ZVS high voltage dc-dc converter is proposed and analyzed in this paper. From above theoretical and experimental analysis, the advantages of the proposed converter can be concluded as follows: Low voltage stress on the primary switches with auto-balanced ability; Redundancy ability for the primary and secondary sides, which ensures high system reliability; Modular structure for the primary and secondary sides; Full ZVS load range for the primary switches, and less primary conduction loss is added; TL secondary rectified voltage waveform can be obtained, which reduce the volume of input and output filter size. The added secondary switches can obtain ZCS independent of the load current.

The main disadvantage of the proposed converter is that the VA rating of the transformers in the proposed converter is a little higher than that of Figure 1 under variable input and constant output condition.