Implementation of a Parallel-Series Resonant Converter with Wide Input Voltage Range

Abstract

A new resonant converter is presented to have the advantages of soft switching operation on power devices, without reverse recovery current loss on power diodes and wide input voltage range operation. Resonant converter with frequency modulation is adopted in the proposed circuit to accomplish the low switching loss on power switches and possible zero current switching operation on fast recovery diodes. To improve the problem of limit voltage range operation in the conventional resonant converter, a new parallel-series structure resonant converter is studied to achieve wide input voltage operation capability, such as from V_in,min to 4V_in,min. A 1.8 kW laboratory circuit is implemented, and the measured results are provided to confirm the theoretical analysis and circuit performance.

1. Introduction

Modern power converters with high efficiency and high power density are important to achieve compact size and low power loss. To achieve the low switching loss and compact size, the soft switching circuit topologies with the high switching frequency using wide-band gap power devices, such as GaN power devices, have been developed in modern power electronics. The GaN devices have low switching loss characteristic at high switching frequency, so that the converter efficiency is increased. The main drawback of GaN power devices is high cost compared to power MOSFETs. For the past twenty years, the quasi-resonant (QR) flyback converter [1,2] with low turn-on switching loss, the active clamp dc/dc converters [3] with zero voltage switching operation, the resonant converters [4,5,6] with soft switching operation on power semiconductors, and pulse width modulation (PWM) converters [7,8,9] have been developed to implement high efficiency converters with power MOSFETs devices. QR flyback [1,2] is limited at low power applications, and active clamp dc/dc converters [3] have the problems of dc magnetizing current and unbalance voltage and current stresses on the rectifier diodes. For conventional resonant converters [4,5,6], the input voltage variation is limited due to the limited available voltage gain on the resonant tank. Conventional phase-shift PWM full bridge converters [7,8,9] have drawbacks of hard switching loss at light or low load condition, and high freewheeling current at low load or high input voltage condition. For solar photovoltaic systems, the output voltage of a solar panel is relative to geographical location and solar intensity, so that the solar cell panel has wide output voltage range. Therefore, the power converters with wide voltage operation and high circuit efficiency are demanded for solar power systems. The dc/dc converters with the widespread voltage operation have been proposed in [10,11,12,13,14,15] for fuel cell and solar power converters. In [10,11], the series-connected or parallel-connected structure has been studied to achieve wide input voltage operation on fuel cell power conversion. In [12,13,14,15], the phase-shift PWM dc/dc power converters have been presented to achieve wide voltage operation. In [16], the full-bridge resonant converter with one ac switch and two transformers is proposed to achieve wide input voltage operation. The main drawbacks in [16] are (1) transformer will be shorted suddenly when ac switch is turned on, which will result in serious problems at the transient voltage change and make system unstable, (2) the control scheme of this circuit topology is much more complicated with four equivalent operation topologies, and (3) some power switches will always be conducting at some specific circuit topologies that will increase the conduction loss.

A new parallel-series (full bridge resonant converters are parallel connection and diode rectifiers are series connection) based resonant circuit is developed to obtain the main benefits of the wide input voltage range operation (from v_in,min to 4V_in,min) and soft switching operation on power semiconductors. The variable frequency control is used to regulate load voltage over wide input voltage variation. The input impedance of the equivalent resonant tank in the proposed power converter is controlled under the inductive load characteristic. Therefore, the soft switching operation on power semiconductors is achieved. Since two diode rectifiers of the proposed converter are series-connected on the secondary sides, two resonant converters with the parallel-connection on the primary side are worked at the low voltage input (from 100 V to 200 V) to have high dc voltage gain. For high input voltage range (from 200 V to 400 V), only one resonant converter is operated on the primary side to reduce the conduction loss and obtain low dc voltage gain. Therefore, the developed resonant converter can be operated from V_in = 100 V to 400 V. At the low input voltage range, the parallel-series based resonant converter can provide 1.8 kW to output load. At the high input voltage range, only one resonant tank is operated (the other resonant tank is off) to provide 1 kW to output load. The main advantages of the proposed converter compared to [16] are a simple control scheme and low current rating of power switches. At the high input voltage, only four switches instead of eight power switches are operated to reduce power conduction losses. At the low input voltage range, eight power switches are operated to achieve high voltage gain and reduce current rating on each power switch for more power output. The circuit structure, the principle of operation, and design procedure are provided and discussed in this paper. Finally, the experimental waveforms with a 1.8 kW laboratory circuit are presented to show the theoretical examination and investigation of wide input voltage capability.

2. Circuit Diagram and Operating Principle

Figure 1a illustrates the presented resonant converter with wide input voltage operation. Two resonant converters are used in the studied circuit with parallel-series connection. V_in is the input voltage and V_o is the output voltage. L_r1 and L_r2 are resonant inductors, C_r1 and C_r2 are resonant capacitors, and L_m1 and L_m2 are the magnetizing inductors of transformers T₁ and T₂, respectively. In each resonant circuit, the primary side is a full bridge power converter for medium power rating, and the output side is a full-wave diode rectifier. The passive components (C_r1 and L_r1) and (C_r2 and L_r2) are naturally resonant in each resonant tank to allow the soft switching on power switches. In low input voltage range V_in = 100 V ~ 200 V (Figure 1b), two resonant converters are operated with primary-parallel and secondary-series structure. Each resonant converter provides power P to output load. Therefore, the total output power is 2P. Due to the series connection of two diode rectifiers, the load voltage V_o is the sum of two rectified voltages. Therefore, the voltage rating of diodes D₁ ~ D₈ equals V_o/2. The voltage gain G_each of each resonant circuit is controlled between 1 and 2. Therefore, the total voltage gain G_Total of the studied circuit operating at parallel-series connection is regulated at G_Total = 2 ~ 4 under the low input voltage range from V_in = 100 V ~ 200 V and V_o = 400 V. In the high input voltage operation (V_in = 200 V~400 V) as shown in Figure 1c, only one resonant converter (Q₁ ~ Q₄) is operated, and the other resonant converter (Q₅ ~ Q₈) is off. The diodes D₅ ~ D₈ are all conducting, and V_o equals the average rectified voltage of the diode rectifier by D₁ ~ D₄. Since the voltage gain of resonant circuit is controlled at G_Total = 1 ~ 2, the output voltage V_o can be regulated at 400 V under high input voltage range from V_in = 200 V ~ 400 V. Based on the circuit structures shown in Figure 1b,c for low and high voltage input, the wide input voltage operation and the soft switching characteristics are accomplished in the proposed power circuit.

2.1. Under Low Voltage Input Range (V_in = 100 V ~ 200 V)

For low voltage input range, two resonant circuits with parallel-series connection are operated to achieve the higher voltage gain. The dc voltage gain of each resonant converter is controlled between 1 and 2. Since two rectified voltages on the secondary-side are series-connected, the resultant voltage gain of the proposed parallel-series connected resonant converter is regulated between 2 and 4 under 100 V < V_in < 200 V. The proposed converter has six operating steps in every switching cycle. Under the condition of f_s (switching frequency) > f_r (resonant frequency), the main PWM waveforms are demonstrated in Figure 2a. The equivalent circuits of six operating steps are provided in Figure 2b–g.

Step 1 [t₀ ~ t₁]:D₁, D₄, D_5, and D₈ are conducting at t₀. Since Q₁, Q₄, Q_5, and Q₈ are conducting, the voltages v_ab = v_cd = V_in and v_Lm1 = v_Lm2 = nV_o, where n is the turns ratio of T₁ and T₂. Components C_r1 and L_r1 are naturally resonant in the first resonant converter, and components C_r2 and L_r2 are also naturally resonant in the second resonant converter. The resonant frequency $f_r=1/2\pi \sqrt{L_{r1}{C}_{r1}}$.

Step 2 [t₁ ~ t₂]:Q₁, Q₄, Q_5, and Q₈ turn off at time t₁. i_Lr1 and i_Lr2 are positive. Thus, C_Q2, C_Q3, C_Q6, and C_Q7 are discharged, and C_Q1, C_Q4, C_Q5, and C_Q8 are charged in this step. Due to i_Lr1 > i_Lm1 and i_Lr2 > i_Lm2, D₁, D₄, D_5, and D₈ are conducting.

Step 3 [t₂ ~ t₃]: At t₂, the voltages of C_Q2, C_Q3, C_Q6, and C_Q7 are decreased to zero voltage. Since i_Lr1 and i_Lr2 are still positive, D_Q2, D_Q3, D_Q6, and D_Q7 conduct. Thus, Q₂, Q₃, Q_6, and Q₇ can turn on after t₂ with soft switching operation. Since i_Lr1 > i_Lm1 and i_Lr2 > i_Lm2, diodes D₁ and D₄ in the first diode rectifier and D₅ and D₈ in the second diode rectifier are forward biased. Owing to v_ab = v_cd = –V_in and v_Lm1 = v_Lm2 = nV_o, i_Lr1 and i_Lr2 are decreased, and i_Lm1 and i_Lm2 are increased.

Step 4 [t₃ ~ t₄]: At time t₃, i_Lr1 is less than i_Lm1, and i_Lr2 is less than i_Lm2. D₂, D₃, D_6, and D₇ are conducting. The magnetizing voltages v_Lm1 and v_Lm2 are –nV_o so that i_Lm1 and i_Lm2 are decreased. L_r1 and C_r1 are naturally resonant with resonant frequency $f_r=1/2\pi \sqrt{L_{r1}{C}_{r1}}$ in the first resonant converter. Similarly, L_r2 and C_r2 are naturally resonant in the second resonant converter.

Step 5 [t₄ ~ t₅]: At t₄, switches Q₂, Q₃, Q_6, and Q₇ turn off. Owing to i_Lr1 < 0 and i_Lr2 < 0, C_Q1, C_Q4, C_Q5, and C_Q8 are discharged and C_Q2, C_Q3, C_Q6 and C_Q7 are charged in step 5. In this step, i_Lr1 < i_Lm1 and i_Lr2 < i_Lm2 so that D₂, D₃, D_6, and D₇ are conducting.

Step 6 [t₅ ~ T_s+t₀]: At time t₅, the capacitor voltages of C_Q1, C_Q4, C_Q5, and C_Q8 are decreased to zero voltage. Owing to i_Lr1 < 0 and i_Lr2 < 0, D_Q1, D_Q4, D_Q5, and D_Q8 conduct. Therefore, Q₁, Q₄, Q_5, and Q₈ turn on after t₅ with soft switching operation. Since i_Lr1 < i_Lm1 and i_Lr2 < i_Lm2, D₂, D₃, D_6, and D₇ are still conducting. Owing to v_ab = v_cd = V_in and v_Lm1 = v_Lm2 = –nV_o, the primary side currents i_Lr1 and i_Lr2 are increased, and i_Lm1 and i_Lm2 are decreased. At time T_s + t₀, i_Lr1 > i_Lm1, and i_Lr2 > i_Lm2 so that D₁, D₄, D_5, and D₈ conduct.

The main PWM waveforms and the equivalent step circuits at low voltage input range under f_s < f_r condition are provided in Figure 3. Under this condition, the presented circuit has six operation steps in every switching cycle. The circuit operations at f_s < f_r condition are discussed as follows.

Step 1 [t_{0 ~} t₁]:v_CQ1 = v_CQ4 = v_CQ5 = v_CQ8 = 0 at time t₀. Owing to i_Lr1(t₀) and i_Lr2(t₀) are negative, diodes D_Q1, D_Q4, D_Q5, and D_Q8 are conducting. Q₁, Q₄, Q_5, and Q₈ can turn on after t₀ with soft switching operation. In step 1, v_ab = v_cd = V_in and v_Lm1 = v_Lm2 = nV_o. C_r1 and L_r1 are naturally resonant in the first resonant tank, and C_r2 and L_r2 are naturally resonant in the second resonant tank.

Step 2 [t₁ ~ t₂]: Since f_s < f_r, i_Lr1 and i_Lr2 will equal i_Lm1 and i_Lm2 at time t₁ and D₁ ~ D₈ are reverse biased. On the primary-side, L_r1, L_m1, and C_r1 are naturally resonant in the first resonant converter and L_r2, L_m2, and C_r2 are naturally resonant in the second resonant converter.

Step 3 [t₂ ~ t₃]:Q₁, Q₄, Q_5, and Q₈ are turned off at time t₂. C_Q2, C_Q3, C_Q6, and C_Q7 are discharged due to i_Lr1(t₂) and i_Lr2(t₂) are both positive. Since the secondary-side currents of T₁ and T₂ are negative, D₂, D₃, D_6, and D₇ are forward biased. If the energy on L_r1, L_r1, L_m1, and L_m2 at time t₂ is large enough, then the voltages of C_Q2, C_Q3, C_Q6, and C_Q7 can decrease to zero at time t₃. The soft switching condition of power switches Q₂, Q₃, Q_6, and Q₇ are expressed as.

$$i_{Lm1}(t_2)=i_{Lm2}(t_2)=n{V}_o/(4L_m{f}_s)\ge V_{in}\sqrt{4C_e/(L_m+L_r)},$$

(1)

where L_m = L_m1 = L_m2, C_e = C_Q1 = ... = C_Q8 and L_r = L_r1 = L_r2.

Step 4 [t₃ ~ t₄]: At time t₃, v_CQ2 = v_CQ3 = v_CQ6 = v_CQ7 = 0. Since i_Lr1(t₃) and i_Lr2(t₃) are positive, D_Q2, D_Q3, D_Q6, and D_Q7 are conducting. Then Q₂, Q₃, Q_6, and Q₇ can turn on after time t₃ with zero-voltage switching. In this step, components C_r1 and L_r1 are naturally resonant in the first resonant tank and C_r2 and L_r2 are naturally resonant in the second resonant tank.

Step 5 [t₄ ~ t₅]: At time t₄, i_Lm1 equals i_Lr1 and i_Lm2 equals i_Lr2. Thus, D₁ ~ D₈ are all reverse biased. In the first converter, L_r1, L_m1, and C_r1 are resonant, and L_r2, L_m2, and C_r2 are naturally resonant in the second converter with input voltage v_ab = v_cd = –V_in.

Step 6 [t₅ ~T_s + t₀]:Q₂, Q₃, Q_6, and Q₇ turn off at t₅. Since i_Lr1(t₅) and i_Lr2(t₅) are negative, C_Q1, C_Q4, C_Q5, and C_Q8 are discharged from t₅. At time T_s + t₀, v_CQ1, v_CQ4, v_CQ5, and v_CQ8 are decreased to zero voltage.

2.2. Under High Voltage Input Range (V_in = 200 V ~ 400 V)

For high input voltage case, only one resonant converter (Q₁ ~ Q₄) is operated and the other resonant converter (Q₅ ~ Q₈) is off. The rectifier diodes D₅ ~ D₈ are all conducting and the output voltage of T₁ is connected to the output load (Figure 1c). The voltage gain of the proposed resonant converter is regulated between 1 and 2 under 200 V < V_in < 400 V. The proposed converter under high voltage input case has six operating steps for every switching cycle. Figure 4a gives the PWM waveforms under the condition of f_s > f_r. Figure 4b–g demonstrate the equivalent circuits of six operating steps. The circuit operations under high input voltage range and f_s > f_r are presented below.

Step 1 [t₀ ~ t₁]:D₁ and D₄ are conducting after time t₀. Since Q₁, Q₄, D₁, D_4, and D₅ ~ D₈ are conducting, it can obtain the voltages v_ab = V_in and v_Lm1 = nV_o. Components C_r1 and L_r1 are resonant.

Step 2 [t₁ ~ t₂]:Q₁ and Q₄ turn off at t₁. Due to i_Lr1(t₁) is positive, C_Q2 and C_Q3 are charged. Owing to i_Lr1(t₁) > i_Lm1(t₁), D₁, D_4, and D₅ ~ D₈ are conducting.

Step 3 [t₂ ~ t₃]: At time t₂, v_CQ2 = v_CQ3 = 0. Since i_Lr1(t₂) > 0, D_Q2 and D_Q3 are forward biased and Q₂ and Q₃ turn on at zero voltage after t₂. Since i_Lr1(t₂) > i_Lm1(t₂), D₁, D_4, and D₅ ~ D₈ conduct. In this step, v_ab = –V_in and v_Lm1 = nV_o so that i_Lr1 decreases and i_Lm1 increases.

Step 4 [t₃ ~ t₄]: At t₃, i_Lr1 < i_Lm1, and D₂ and D₃ are conducting. In step 4, v_Lm1 = –nV_o and i_Lm1 decreases. C_r1 and L_r1 are naturally resonant with resonant frequency $f_r=1/2\pi \sqrt{L_{r1}{C}_{r1}}$.

Step 5 [t₄ ~ t₅]: At t₄, Q₂ and Q₃ are turned off. Since i_Lr1(t₄) < 0, C_Q1 and C_Q4 are discharged. In this step, i_Lr1 < i_Lm1 so that D₂, D_3, and D₆ ~ D₈ are conducting.

Step 6 [t₅ ~ T_s+t₀]: At time t₅, v_CQ1 = v_CQ4 = 0. Since i_Lr1(t₅) < 0, D_Q1 and D_Q4 are conducting and Q₁ and Q₄ turn on at zero voltage after t₅. Owing to i_Lr1 < i_Lm1, D₂, D_3, and D₆ ~ D₈ are conducting. In this step, v_ab = V_in and v_Lm1 = –nV_o so that i_Lr1 increases and i_Lm1 decreases. At time T_s+t₀, i_Lr1 > i_Lm1. Then, D₁, D_4, and D₅ ~ D₈ are conducting.

The PWM waveforms under f_s < f_r condition are given in Figure 5a and the equivalent circuits in every cycle under high voltage input range are provided in Figure 5b–g. The operation principles under high voltage input and f_s < f_r condition are discussed as follows.

Step 1 [t₀ ~ t₁]: When t < t₀, Q₁ ~ Q₄ are all off and C_Q1 and C_Q4 are discharged due to i_Lr1 < 0. At time t₀, v_CQ1 = v_CQ4 = 0, and D_Q1 and D_Q4 are conducting. Thus, Q₁ and Q₄ can turn on after t₀ with soft switching operation. The load current flows through the components D₁, C_o, R_o, D₅ ~ D_8, and D₄ so that the magnetizing inductor voltage v_Lm1 = nV_o and i_Lm1 increases. C_r1 and L_r1 are naturally resonant with v_ab = V_in and v_Lm1 = nV_o.

Step 2 [t₁ ~ t₂]: At t₁, i_Lm1 = i_Lr1 and D₁ ~ D₈ are all off. L_r1, L_m1, and C_r1 are naturally resonant with V_ab = V_in.

Step 3 [t₂ ~ t₃]: At t₂, Q_1, and Q₄ turn off. Owing to i_Lr1(t₂) > 0, C_Q2 and C_Q3 are discharged. Since i_Lr1 < i_Lm1 after t₂, D₂, D_3, and D₅ ~ D₈ conduct.

Step 4 [t₃ ~ t₄]: At t = t₃, v_CQ2 = v_CQ3 = 0. Since i_Lr1(t₃) is positive, D_Q2 and D_Q3 are conducting and Q₂ and Q₃ turn on with zero-voltage switching after time t₃. Since Q₂, Q₃, D_2, and D₃ are conducting, v_ab = –V_in and v_Lm1 = –nV_o. C_r1 and L_r1 are naturally resonant with v_ab = –V_in and v_Lm1 = –nV_o. In step 4, i_Lr1 and i_Lm1 both decrease.

Step 5 [t₄ ~ t₅]: At time t₄, i_Lm1 = i_Lr1, and D₁ ~ D₈ are off. Therefore, L_r1, C_r1, and L_m1 are naturally resonant with v_ab = –V_in.

Step 6 [t₅ ~ T_s + t₀]:Q₂ and Q₃ turn off at t₅. Owing to i_Lr1(t₅) < 0, C_Q1 and C_Q4 are discharged. At time T_s + t₀, v_CQ1 = v_CQ4 = 0. Then, the circuit operations in a switching cycle are completed.

3. Circuit Analysis and Design Procedures

Variable frequency control is used to generate the PWM signals of power switches and regulate output voltage at V_o = 400 V under wide voltage variation from V_in = 100 V to 400 V. Then, a dc/ac inverter can be adopted as the second stage for PV inverter applications. The fundamental harmonic analysis is adopted to derive the voltage transfer function of the proposed converter. For low voltage input range from V_in = 100V to 200V, two resonant converters are operated, and the output voltages of two diode rectifiers are series connection to achieve high voltage gain (Figure 1b). For high voltage input range from V_in = 200 V to 400 V, only one resonant converter is operated on the primary side to regulate load voltage (Figure 1c). Since the frequency modulation is used in the presented circuit, it can obtain that the waveforms on v_ab and v_cd are square voltage waveforms. Based on the Fourier Series Analysis (FSA), the fundamental root-mean-square (rms) voltages V_ab,rms and V_cd,rms are obtained as.

$$V_{ab,rms}=2\sqrt{2}{V}_{in}/\pi ,$$

(2)

$$V_{cd,rms}=\{\begin{array}{cc}\hfill 2\sqrt{2}{V}_{in}/\pi ,& 100\mathrm{V}\le V_{in}<200\mathrm{V}\hfill \\ \hfill 0,& 200\mathrm{V}<V_{in}\le 400\mathrm{V}\hfill \end{array},$$

(3)

For low input voltage range (V_in = 100 V ~ 200 V), the magnetizing voltages v_Lm1 = v_Lm2 = ±nV_o/2. On the other hand, the magnetizing voltage v_Lm1 = ±nV_o and v_Lm2 = 0 for high input voltage range (V_in = 200 V ~ 400 V). Therefore, the fundamental rms magnetizing voltages are derived as.

$$V_{Lm1,rms}=\{\begin{array}{c}\sqrt{2}n{V}_o/\pi ,100\mathrm{V}\le V_{in}<200\mathrm{V}\\ 2\sqrt{2}n{V}_o/\pi ,200\mathrm{V}<V_{in}\le 400\mathrm{V}\end{array},$$

(4)

$$V_{Lm2,rms}=\{\begin{array}{cc}\hfill \sqrt{2}n{V}_o/\pi ,& 100\mathrm{V}\le V_{in}<200\mathrm{V}\hfill \\ \hfill 0,& 200\mathrm{V}<V_{in}\le 400\mathrm{V}\hfill \end{array},$$

(5)

According to the dc load resistor R_o, the equivalent ac resistors R_ac1 and R_ac2 on the primary-side of T₁ and T₂ can be obtained as:

$$R_{ac1}=\{\begin{array}{c}\frac{4n^2{R}_o}{{\pi }^2},100\mathrm{V}\le V_{in}<200\mathrm{V}\\ \frac{8n^2{R}_o}{{\pi }^2},200\mathrm{V}<V_{in}\le 400\mathrm{V}\end{array},$$

(6)

$$R_{ac2}=\frac{4n^2{R}_o}{{\pi }^2},100\mathrm{V}\le V_{in}<200\mathrm{V},$$

(7)

According to the resonant components L_r1, C_r1, R_ac1, and L_m1, the voltage gain of the presented resonant converter is derived in (8).

$$|G|=\frac{V_{Lm1,rms}}{V_{ab,rms}}=1/\sqrt{{[1+\frac{1}{l_n}\frac{f_n^2-1}{f_n^2}]}^2+x^2{(\frac{f_n^2-1}{f_n})}^2}=\{\begin{array}{l}\frac{n{V}_o}{2V_{in}},100\mathrm{V}\le V_{in}<200\mathrm{V}\\ \frac{n{V}_o}{V_{in}},200\mathrm{V}<V_{in}\le 400V\end{array},$$

(8)

where $x=\sqrt{L_{r1}/C_{r1}}/R_{ac1}$ is the quality factor, l_n = L_m1/L_r1 is the inductor ratio, and f_n = f_s/f_r is the frequency ratio. The output voltage can be obtained in (9).

$$V_o=\{\begin{array}{l}\frac{2V_{in}}{n\sqrt{{[1+\frac{1}{l_n}\frac{f_n^2-1}{f_n^2}]}^2+x^2{(\frac{f_n^2-1}{f_n})}^2}},100\mathrm{V}\le V_{in}<200V\\ \frac{V_{in}}{n\sqrt{{[1+\frac{1}{l_n}\frac{f_n^2-1}{f_n^2}]}^2+x^2{(\frac{f_n^2-1}{f_n})}^2}},200\mathrm{V}<V_{in}\le 400V\end{array}$$

(9)

According to the input and output voltage conditions, the switching frequency of power switches Q₁ ~ Q₈ are regulated according to the input voltage variation. Since the input impedance of the proposed resonant circuit is controlled at the inductive load, Q₁ ~ Q₈ can be turned on under zero voltage switching. The power loss analysis of the resonant converter or inverters has been discussed in [17,18] for fixed switching frequency. However, the switching frequency of the resonant converter is variable. Therefore, it is very difficult to predict and calculate the actual power losses. In the proposed converter, the main power losses are conduction losses on power switches Q₁ ~ Q₈, copper and core losses on the resonant inductors L_r1 and L_r2 and transformers T₁ and T₂, conduction losses on the resonant capacitors C_r1 and C_r2, and the conduction losses on the rectifier diodes Q₁ ~ Q₈. The rms currents of the resonant capacitors C_r1 and C_r2 at the series resonant frequency are calculated as:

$$i_{Cr1,rms}=i_{Cr2,rms}=i_{Lr1,rms}=i_{Lr2,rms}\approx \sqrt{{(\frac{\pi I_o}{2n\sqrt{2}})}^2+{(\frac{V_{Lm1}}{4\sqrt{3}{L}_{m1}{f}_{sw}})}^2},$$

(10)

It is clear that the primary currents are related to the switching frequency f_sw and the magnetizing voltage V_Lm1. In the same input voltage range such as V_in = 100 V ~ 200 V, the low input voltage (V_in = 100 V) will result in low switching frequency. The low switching frequency will increase the primary current and conduction loss on power switches, inductors, and resonant capacitors. Therefore, the proposed converter efficiency at V_in = 100 V is less than the efficiency at V_in = 200 V. For low input voltage range (V_in = 100 V ~ 200 V), two resonant circuits are operated, and the magnetizing voltages V_Lm1 = V_Lm2 = nV_o/2 instead of V_Lm1 = nV_o under high input voltage range (V_in = 200 V ~ 400 V). Therefore, the circuit efficiency operated at low input voltage range is better than the circuit efficiency operated at high input voltage range.

To confirm the theoretical analysis, a design example of a laboratory circuit is provided with the electric specifications V_in = 100 V ~ 400 V and V_o = 400 V. The rated power is 1800 W (by two resonant circuits) for low input voltage range and 1 kW (by one resonant circuit) for high input voltage range. The series resonant frequency of the resonant tank is designed at 100 kHz. For low input voltage range V_in = 100 V ~ 200 V, two resonant circuits with parallel-series connection are operated in the studied circuit to obtain high voltage gain. However, one only resonant circuit is operated under high voltage input V_in = 200 V ~ 400 V. Figure 6 provides the voltage gain of the studied converter with wide input voltage operation. The transient voltage (V_in,tran) between low input voltage range and high input voltage range is selected at 200 V with ±4 V voltage tolerance. From equation (8), it is clear that the voltage gain of the presented resonant converter under high input voltage range is two times of voltage gain under low input voltage range. Therefore, the design considerations for two resonant converters operation (Figure 1b) for low voltage input and one resonant converter operation (Figure 1c) for high voltage input are identical. To simplify the design consideration, only one resonant converter under high voltage range is discussed to design circuit components. Under high voltage range, the minimum voltage gain G_min is designed as unity at V_in,max = 400 V. From equation (8), the turn-ratio n₁ is obtained as:

$$n=n_1=n_2=\frac{G_{\min }{V}_{in,\max }}{V_o}=\frac{1\times 400}{400}=1,$$

(11)

Magnetic cores EE-55 with flux density ΔB = 0.4 tesla and window area A_e = 3.54 cm² are used to build the isolated transformers T₁ and T₂. The minimum switching frequency of the resonant converter is designed at 55 kHz and 200 V input. Therefore, the minimum primary turns at 200 V input are calculated as:

$$N_{p1,\min }\ge \frac{n{V}_o}{f_{s,\min }\Delta B{A}_e}=\frac{1\times 400}{55000\times 0.4\times 3.54\times {10}^{-4}}\approx 51.4,$$

(12)

The actual primary turns and secondary turns of transformers T₁ and T₂ are N_p1 = N_p2 = N_s1 = N_s2 = 52 turns. From equation (6), the equivalent resistance R_ac1 under P_o = 1 kW and V_o = 400 V is obtained as:

$$R_{ac1}=\frac{8n^2}{{\pi }^2}{R}_{o,rated}=\frac{8\times 1^2}{{\pi }^2}\times \frac{{400}^2}{1000}\approx 130\mathsf{\Omega },$$

(13)

The selected inductor ratio l_n is equal to 5, and the selected quality factor x is equal to 0.2. Based on the l_n, R_ac1, x, and f_r, the theoretical resonant components are derived as:

$$L_{r1}=L_{r2}=\frac{x{R}_{ac1}}{2\pi f_r}=\frac{0.2\times 130}{2\pi \times 100\times {10}^3}\approx 41.4\mu H,$$

(14)

$$C_{r1}=C_{r2}=\frac{1}{4{\pi }^2{L}_{r1}{f}_r^2}=\frac{1}{4{\pi }^2\times 41.4\times {10}^{-6}\times {(100\times {10}^3)}^2}\approx 61nF,$$

(15)

$$L_{m1}=L_{m2}=l_n{L}_{r1}=41.4\times 5=207\mu H,$$

(16)

In the prototype circuit, the actual resonant components are L_r1 = L_r2 = 40 μH, L_m1 = L_m2 = 200 μH and C_r1 = C_r2 = 63 nF. The voltage stress of Q₁ ~ Q₈ equals V_in,max = 400 V and power MOSFETs STW48N60M2 with 600 V/26 A rating are used for Q₁ ~ Q₈. The voltage stress of D₁ ~ D₈ equals V_o = 400 V and STTH8R06FP with 600 V/8 A are used for D₁ ~ D₈. The selected output capacitance C_o = 810 μF (three 270 μF in parallel).

4. Test Results

Experiments based on a prototype circuit shown in Figure 7 are demonstrated to confirm the circuit performance. The test results at low input voltage range are shown in Figure 8 and Figure 9 with V_in = 100 V and 190 V, respectively. For low voltage range, two resonant circuits are operated with parallel-input and series-output structure to achieve high voltage gain. Figure 8 are the test waveforms under V_in = 100 V, V_o = 400 V and P_o = 1.8 kW. Figure 8a provides the measured waveforms of v_Q1,g ~ v_Q8,g. The test switching frequency at V_in = 100 V shown in Figure 8a is about 51 kHz. Figure 8b gives the experimental waveforms of the resonant currents and voltages. Due to f_s (51 kHz) < f_r (100 kHz), the resonant currents i_Lr1 and i_Lr2 are quasi-sinusoidal waveforms. Figure 8c,d provide the current waveforms of the rectifier diodes. Owing to f_s < f_r, the rectifier diodes D₁ ~ D₈ are all reverse biased without reverse recovery current loss. Figure 8e demonstrates the experimental waveforms under V_in = 100 V, V_o = 400 V and I_o = 4.5 A (P_o = 1.8 kW). Figure 8f demonstrates the experimental waveforms of power switch Q₁ at full load. Before Q₁ turns on, the drain voltage v_Q1,d is already zero voltage. Therefore, the zero voltage turn-on of Q₁ is achieved. Q₂ ~ Q₈ have the same turn-on characteristic as Q₁ with soft switching operation. Figure 9 provides the test waveform under V_in = 190 V, V_o = 400 V and P_o = 1.8 kW. The switch signals of Q₁ ~ Q₈ are provided in Figure 9a. The measured resonant current and voltages are given in Figure 9b. Since f_s ≈ f_r, the resonant currents are sinusoidal waveforms. The measured diode currents are provided in Figure 9c,d. The measured waveforms of input voltage V_in = 190 V, load voltage V_o = 400 V and load current I_o = 4.5 A are provided in Figure 9e. The test waveforms of switch Q₁ are given in Figure 9f. For high input voltage range, Figure 10 and Figure 11 shows the experimental results of the studied circuit at V_in = 210 V and 400 V, respectively. For high input voltage range, only one resonant converter (Q₁ ~ Q₄) is controlled to regulate load voltage. The rectifier diodes D₅ ~ D₈ are bypassed at high voltage range operation. The measured waveforms at V_in = 210 V, V_o = 400 V and P_o = 1 kW are provided in Figure 10. Due to the voltage gain at V_in = 210 V is close to 2 (under high input voltage range), it is obtained that f_s < f_r. From Figure 10b, the resonant current i_Lr1 is a quais-sinusoidal waveform. From Figure 10c,d, D₁ ~ D₈ turn off under zero current switching. Since the diodes D₅ ~ D₈ are bypassed for high input voltage range, the secondary-side rectified current is distributed on D₅ ~ D₈. Therefore, the diode currents i_D5 ~ i_D8 are balanced and the amplitude of i_D5 ~ i_D8 is only one-half of amplitude of i_D1 ~ i_D4. From test results in Figure 10f, it can observe that the soft switching turn-on of Q₁ is achieved. Figure 11 provides the test waveforms under V_in = 400 V, V_o = 400 V and P_o = 1 kW. The voltage gain at V_in = 400 V is 1 (Figure 6). The resonant current i_Lr1 is a sinusoidal waveform (Figure 11b). Similarly, the secondary-side rectified current is distributed on D₅ ~ D₈ and the amplitude of i_D5 ~ i_D8 (Figure 11d) is equal to one-half of amplitude of i_D1 ~ i_D4 (Figure 11c). From the experimental waveforms in Figure 11f, Q₁ is turned on at zero voltage switching. The measured circuit efficiencies of the proposed converter are 92.55% at V_in = 100 V and P_o = 1.8 kW, 94.1% at V_in = 190 V and P_o = 1.8 kW, 90.8% at V_in = 210 V and P_o = 1 kW, and 91.8% at V_in = 400 V and P_o = 1 kW. It is clear that the proposed converter has better circuit efficiency at low input voltage case. Because the magnetizing current loss is depended on the output voltage instead of input voltage. For high voltage input, only one resonant converter is operated to provide 1 kW output. However, 1.8 kW is provided by two resonant converters at low voltage input case. Therefore, the proposed converter has better circuit efficiency at low input voltage case. Figure 12 provides the test circuit efficiencies of the proposed resonant converter for 50% and 100% rated power under different input voltages.

5. Conclusions

A new resonant converter is proposed, discussed, and implemented to have low switching losses on power devices and wide input voltage operation from V_in = 100 V to 400 V. To overcome the drawback of the limit range of input voltage operation on conventional resonant converter, two resonant circuits with parallel-series connection are used in the proposed converter. For low voltage input, the output voltages of two diode rectifiers are series-connected to have higher voltage gain. On the other hand, only one resonant circuit is operated and the other circuit is off under high input voltage range. Because the presented resonant circuit is operated at the inductive input impedance, the soft switching operation of all active devices is achieved. The proposed resonant converter can be implemented by the general integrated circuit with the frequency modulation and a voltage comparator. The applications of the studied circuit are front stage of solar power conversion with wide input voltage variation and high voltage output. Although two independent resonant converters working for each voltage range can also be adopted to achieve wide input voltage operation, the current rating of active and passive power components in the proposed converter is much lower (half current rating) than two converters working for low input voltage case. Finally, a 1.8 kW laboratory circuit was constructed and measured. Experiments are demonstrated to confirm the circuit performance and usefulness of the studied resonant converter with wide voltage range capability.