Analysis and Implementation of a Bidirectional Converter with Soft Switching Operation

Abstract

This paper presents a soft switching direct current (DC) converter, with the benefits of bidirectional power conversion and wide-ranging voltage operation for battery charging and discharging capability. A series resonant circuit with variable switching frequency modulation is used to achieve the advantages of soft switching turn-on or turn-off of semiconductor devices. Therefore, the switching power losses in power devices can be reduced. A symmetric resonant circuit topology with a capacitor–inductor–inductor–capacitor (CLLC) structure is adopted to achieve a bidirectional power conversion capability for battery storage units in electric vehicle applications. Due to the symmetric circuit structure on both input and output sides, the converter has similar voltage gains for each power flow operation. In order to overcome the drawback of narrow voltage range operation in conventional resonant converters, a variable transformer turns ratio is adopted in the circuit, to achieve wide output voltage operation (150–450 V) for battery charging applications. To demonstrate the converter performance, a 1-kW laboratory prototype was constructed and tested. Experimental results are provided, to verify the effectiveness of the studied circuit.

1. Introduction

Power converters with bidirectional power flow have been widely utilized between AC and DC grid systems and battery storage systems. Three-phase AC/DC bidirectional power factor correctors (PFC) [1,2] and DC/DC bidirectional converters [3,4,5] are adopted to realize forward and reverse power flow operations between AC grid and DC grid systems. The same circuit structures can be used for electric vehicle (EV) systems, to achieve vehicle-to-grid (V2G) and grid-to-vehicle (G2V) operations. The main advantages of AC/DC PFC are high power factor and low current harmonics. The bidirectional DC/DC converters can realize forward/reverse power operations between the different DC voltage buses, such as battery storage systems or EV battery units [6]. For renewable energy applications [7,8], wide voltage DC/DC and AC/DC converters are required in solar power and wind power conversion, respectively, due to unstable solar intensity and wind speed. The basic circuit topologies of a bidirectional AC/DC converter are based on four or six three-leg active switches. These AC/DC converters can be controlled in PFC operation under forward power flow, or inverter operation under reverse power flow. The buck/boost DC/DC converter is the basic topology for accomplishing bidirectional power conversion. Buck (boost) operation is controlled under forward (reverse) power flow. However, a buck/boost converter has no electric isolation.

In [9], a pulse-width modulation converter was presented, to realize a bidirectional power flow capability with voltage step-down/step-up features during forward/backward power flow. However, a PWM converter cannot achieve both voltage step up/down demands under both power flow directions. The same drawback can be found in bidirectional inductor–inductor–capacitor (LLC) resonant converters with synchronous switches on the secondary side. In references [10,11], symmetric PWM converters with two full bridge circuit structures were studied, to accomplish bidirectional power flow with PWM modulation and phase-shift angle control between two full bridge circuits with a load voltage range V_o = 300–450 V. However, two control variables (phase angle and duty cycle) are needed, so the control complexity is increased. In references [12,13,14], resonant converters with a capacitor–inductor–inductor–capacitor (CLLC) circuit structure were studied, to realize bidirectional power operation with pulse frequency modulation for electric EV or energy storage unit applications. The main advantage of this circuit topology is the symmetric circuit structure on the primary and secondary sides, to achieve voltage step up/down operations in both power flow directions. However, the CLLC converters has less voltage gain and the output voltage range is limited, such as to V_in = 400–600 V and V_o = 300–450 V. For the wide voltage variation conditions in solar power and wind power applications, the power converters are normally required to overcome wide solar intensity or wind speed variations. In references [15,16,17,18,19], two-stage converters and PWM or resonant converters with series-parallel connection were studied, to achieve wide voltage operation. However, these circuit topologies can only achieve forward power operation.

In order to overcome the drawbacks of the above circuit topologies, a new DC converter is provided, to implement soft switching operation, a wide voltage output capability (150~450 V), and bidirectional power flow for energy storage units, bidirectional DC nano-grid systems, and battery charge/discharge systems. A CLLC resonant converter is adopted in both input and output sides, to have bidirectional power conversion capability. The load voltage control is regulated by a frequency modulation scheme. Due to the resonant circuit characteristics, the power semiconductors are all turned on or turned off under zero voltage or zero current conditions, to achieve low switching loss. To extend the output voltage operating range, one additional power switch and a variable transformer turns ratio are adopted on the primary side. Thus, the proposed converter can be operated in two operation regions, with a low (high) transformer turns ratio for high (low) voltage output operation. Therefore, the studied circuit can overcome the narrow voltage range problem in conventional CLLC bidirectional converters. A laboratory prototype (1 kW power) was implemented to demonstrate the effectiveness of the proposed bidirectional resonant converter with the features of soft switching operation, bidirectional power flow, and wide voltage output. The circuit operations of basic bidirectional converters and the proposed converter are discussed and presented in Section 2. In Section 3, the circuit features and design example are provided. In Section 4, experiments are provided from on a laboratory prototype, to verify the theoretical discussions. A conclusion regarding the presented circuit is discussed in Section 5.

2. Circuit Diagram and the Principle of Operation

Figure 1 gives the circuit schematic of the bidirectional AC/DC circuit for electric vehicle charge/discharge. First, a bidirectional AC/DC converter with PFC function is required in the front stage, to achieve bidirectional power flow operation. The rear stage is a bidirectional DC/DC converter, to charge/discharge battery stacks. Therefore, G2V and V2G power flow operations can be achieved in a bidirectional AC/DC power converter (Figure 1). Due to high circuit-efficiency requirements, boost-type circuit topologies are normally adopted in PFC converters, to obtain low current harmonics and a high power factor (PF). Figure 2 shows the general four quadrature bidirectional PFC circuit topologies with a boost-type converter. In Figure 2a, a full bridge bridgeless PFC converter is used to achieve low current harmonics and high PF. Since a boost converter is adopted, the DC voltage V_dc > $\sqrt{2}{V}_{ac,rms}$ (peak voltage of AC source). A bidirectional half bridge bridgeless PFC converter is shown in Figure 2b. Two switches are employed to accomplish low current harmonics and high PF. However, the DC voltage V_dc > $2\sqrt{2}{V}_{ac,rms}$, when AC current i_ac is in phase with V_ac. Power flow is controlled from the AC mains to DC bus voltage V_dc. If the line current i_ac is out of phase with V_ac, then the power flow is from V_dc terminal to V_ac terminal.

Figure 3 gives the conventional circuit topologies of DC bidirectional converters for battery a charger/discharger. The conventional non-isolate converter with bidirectional power conversion is shown in Figure 3a. For forward power conversion, the circuit functions at voltage step-down, and power flow is from the V_in terminal to V_Bat terminal. If the circuit is used for reverse power conversion, voltage step-up operation is realized in this DC converter. The simple circuit structure and control scheme are the main advantages of this circuit topology. However, the lack of electric isolation is the main drawback of this DC converter. A full bridge resonant converter is provided in Figure 3b for battery charging and discharging operations. Compared to a conventional unidirectional resonant circuit, this circuit topology can achieve voltage step-up and step-down operations for power flow control. In Figure 3c, the symmetric half bridge structure has less circuit components and also achieves forward and backward power operation. The power switches in Figure 3b,c can turn on at zero voltage, to lessen the electromagnetic interference and switching loss. However, the disadvantage of the resonant converters in Figure 3b,c is low voltage gain (narrow voltage range) if a wide voltage output range is required for a battery charging station for universal electric vehicle charging applications.

Figure 4a gives the circuit structure of the proposed converter. The proposed circuit not only can achieve bidirectional power conversion, but also an extended output voltage range from 150–450 V for battery stacks. Four active switches S₁–S₄ and one ac switch Q are used on the input side, and two switches S₅ and S₆ are employed on the output side. S₅ and S₆ are inactive when the circuit is used for forward power conversion. The forward power conversion is controlled by switches S₁–S₄ and Q, to charge battery stacks. However, S₁–S₄ are off when reverse power conversion is required in the proposed circuit. The reverse power is controlled by switches S₅ and S₆, to realize battery discharging operations. The power semiconductors are all turned on or turned off at zero voltage or zero current conditions, for both power conversions. Therefore, the electromagnetic interference and switching loss can be reduced. The main drawback of a conventional bidirectional resonant converter is the limited input or output voltage operation. To implement a bidirectional converter with a wide voltage operation in universal battery charger/discharger units, two half bridge resonant circuit structures, (S₁, S₂, T, C_r1,1, L_r1,1, C₁ and C₂) and (S₃, S₄, T, C_r1,2, L_r1,2, Q, C_r1,1, L_r1,1, C₁ and C₂), are employed on the input side, to extend output voltage range. Figure 4b shows a circuit schematic operated for forward power conversion, with low voltage output range. The ac switch Q is on, and active switches S₁ and S₂ are turned off. Only S₃ and S₄ are activated with a frequency modulation scheme, to control the load voltage. The resonant components on the left-hand side include C_r1,2, L_r1,2, C_r1,1, and L_r1,1, and the turns ratio of transformer T in Figure 4b is 2n_p/n_s. When forward power conversion and high voltage output range are demanded, the high voltage gain is needed in the converter. Therefore, switches Q, S₃, and S₄ are turned off in Figure 4c. The equivalent resonant components on the left-hand side become C_r1,1 and L_r1,1, with the transformer turns ratio n_p/n_s, to achieve a higher voltage gain than the equivalent circuit in Figure 4b. In order to realize the same series resonant frequencies as in Figure 4b,c, the resonant components are selected as L_r1,1 = L_r1,2 and C_r1,1 = C_r1,2. For battery discharging operations (Figure 4d), the reverse power flow is controlled by switches S₅ and S₆. If the battery stack is in the full power condition, to transfer power from the V_bat side to V_in side, the ac switch Q is turned off and the half bridge diode rectifier with D_S1 and D_S2 is operated on the left-hand side. Therefore, the proposed converter can be controlled in three operating modes, to accomplish soft switching operation, a wide voltage output, and bidirectional power flow control. A comparison of the performance of the proposed converter and related past works in the literature is provided in

Table 1. Comparison between the presented circuit and the other bidirectional converters.

	Primary-Side	Secondary-Side	Input/Output Voltages	Power Flow Direction	Control Scheme
Proposed circuit	Half-bridge circuit	Half-bridge circuit	Vin = 400 V Vo = 150–450 V	Voltage step-up/step-down for bidirectional power flow	Frequency control
Circuit structure in [9]	Half-bridge circuit	Half-bridge circuit	Vin = 48 V Vo = 24–30 V	Voltage step-down for forward power flow and voltage step-up for reverse power flow	Phase shift + PWM control
Circuit structure in [11]	Full-bridge circuit	Full-bridge circuit	Vin = 400 V Vo =400 V	Voltage step-up/step-down for bidirectional power flow	Phase shift + PWM control
Circuit structure in [13]	Full-bridge circuit	Full-bridge circuit	Vin = 382–408 V Vo = 400 V	Voltage step-up/step-down for bidirectional power flow	Frequency control
Circuit structure in [15]	Cascade half-bridge circuit	Parallel center-tapped rectifier	Vin = 750–800 V Vo = 24 V	Voltage step-up/step-down for forward power flow	Frequency control

. The proposed bidirectional converter has a wider voltage operation capability compared to the other circuit topologies.

2.1. Forward Power Conversion and Low Voltage Output

When a battery stack has a low capacity or depleted condition, the converter is controlled in low voltage output mode (Figure 4b). Q turns on and S₁, S₂, S₅, and S₆ are off under low voltage output mode. S₃ and S₄ are operated with frequency modulation, to control the battery voltage or battery charging current. The transformer turns ratio in Figure 4b is n₁ = (n_p1 + n_p2)/n_s = 2n_p/n_s = 2n, where n_p1 = n_p2 = n_p and n = n_p/n_s. Figure 5a shows the main PWM signals of the proposed converter under a f_sw (switching frequency) < f_r (resonant frequency) condition. The circuit parameters are assumed as L_r1,1 = L_r1,2 = n²L_r2 and C_r1,1 = C_r1,2 = C_r2/n². Based on the above assumption, the resonant frequencies under forward and reverse power flow operations are identical. Figure 5b–i show the operating circuits for eight operating states.

State 1

[t₀ ≤ t < t₁]: For t = t₀, the output capacitor voltage v_CS3 is decreased to zero voltage and the diode D_S3 becomes forward biased, owing to i_Lr1(t₀) being negative. At this time, S₁ is turned on, to have zero voltage switching. Since i_Lr2 is positive, the antipallel diodes D_S5 and D_S6 are conducting.

State 2

[t₁ ≤ t < t₂]: The primary current i_Lr1 becomes positive value after t₁. Therefore, i_Lr1 will flow through switch S₃ instead of diode D_S3. In this state, the forward power flow is from C₁ to C₃. The leg voltages are V_ac = V_C1 = V_in/2 and V_de = V_C3 = V_o/2. The series resonant frequency is $f_r=1/(2\pi \sqrt{(L_{r1,1}+L_{r1,2})(C_{r1,1}{C}_{r1,2})/(C_{r1,1}+C_{r1,2})})=1/(2\pi \sqrt{L_{r1,1}{C}_{r1,1}})$. If f_sw < (or >) f_r, then the next state operation of the proposed circuit will go to state 3 (or state 4).

State 3

[t₂ ≤ t < t₃]: At time t₂, i_Lr2 becomes zero at time t₂ and D_S5 becomes off. i_Lr1 flows through S₃, L_m,1, C_r1,1, L_r1,1, C_r1,2, L_r1,2, and C₁.

State 4

[t₃ ≤ t < t₄]: At time t₃, S₃ turns off. i_Lr1 charges C_S3 and discharges C_S4. V_CS4 = 0 at t₄.

State 5

[t₄ ≤ t < t₅]: v_CS4 = 0 at t₄ and D_S4 becomes forward biased due to i_Lr1(t₄) > 0. At this moment, S₄ turns on under zero voltage. In state 5, i_Lr2 < 0 and D_S6 is conducting to charge C₄.

State 6

[t₅ ≤ t < t₆]: Since V_ac = −V_C2 = −V_in/2, i_Lr1 is decreased and becomes negative at time t₅. Then, the primary current i_Lr1 will flow through S₄ instead of D_S4. Forward power flow is from C₂ to charge C₄.

State 7

[t₆ ≤ t < t₇]: i_Lr2 = 0 at t = t₆ and D_S6 turns off. The primary side current i_Lr1 flows through C₂, L_r1,1, C_r1,1, L_m,1, L_r1,2, C_r1,2, and S₄.

State 8

[t₇ ≤ t < T_sw+t₀]: S₄ turns off at t = t₇. Then, C_S3 is discharged and C_S4 is charged by current i_Lr1. This state is terminated at T_sw + t₀.

2.2. Forward Power Conversion and High Voltage Output

When the battery stack is in a high capacity condition, the proposed converter is operated at high voltage output mode (Figure 4c). To achieve high voltage output, switches S₃–S₆ and Q are turned off. S₁ and S₂ are triggered by variable frequency control. In Figure 4c, the circuit has a turns ratio n₂ = n_p1/n_s = n. The key PWM waveforms and state operations in every PWM period are shown in Figure 6. Due to the similar circuit operations in Figure 5 and Figure 6, the state operations in this mode are neglected in this section.

2.3. Reverse Power Conversion

If the battery stack is discharged, the proposed circuit is operated in reverse power conversion mode. The V_Bat terminal transfers power to V_in terminal (Figure 4d). All switches on the left-hand side of the converter are turned off. Only switches S₅ and S₆ are triggered by the frequency modulation scheme. The PWM signals and the operating circuits in every PWM period are provided in Figure 7.

State 1

[t₀ ≤ t < t₁]: The capacitor voltage v_CS5 is decreased to zero at t₅. Then, D_S5 becomes forward biased due to i_Lr2(t₀) being negative. At this moment, the zero voltage turn-on of S₅ can be achieved. Since i_Lr1 is positive, D_S1 is conducting to charge C₁.

State 2

[t₁ ≤ t < t₂]: Since V_de > 0 in this state, i_Lr2 is increased and has a positive value after time t₁. Therefore, i_Lr2 flows through S₅ instead of D_S5. Reverse power flow is from V_C3 to V_C1.

State 3

[t₂ ≤ t < t₃]: i_Lr1 = 0 at time t₂ and D_S1 turns off. Then, i_Lr2 is equal to the magnetizing current i_Lm2.

State 4

[t₃ ≤ t < t₄]: S₅ turns off at t = t₃ and i_Lr2(t₃) > 0. Thus, C_S5 (C_S6) is charged (discharged).

State 5

[t₄ ≤ t < t₅]: The capacitor voltage v_CS6 is decreased to zero at t = t₄. Then, D_S6 becomes forward biased due to i_Lr2(t₄) being positive. After time t₄, the zero voltage turn-on of S₆ can be realized. In state 5, i_Lr1(t) is negative and D_S2 becomes forward biased. Since the leg voltage V_de = −V_C4, i_Lr2 decreases in this state.

State 6

[t₅ ≤ t < t₆]: After time t₅, i_Lr2 < 0. Then, i_Lr,2 flows through switch S₆ instead of diode D_S6. Reverse power conversion is achieved from the V_C4 terminal to V_C2 terminal.

State 7

[t₆ ≤ t < t₇]: The left-hand side current i_Lr1 = 0 at time t₆ and D_S2 becomes reverse biased.

State 8

[t₇ ≤ t < T_sw+t₀]: S₆ turns off at time t₇ and i_Lr,2 charges (discharges) C_S6 (C_S5). At time T_sw + t₀, the switching cycle is completed.

3. Circuit Properties and Design Example

The proposed bidirectional converter has three operating modes (Figure 4b–d). The output voltage is controlled using a variable switching frequency. The fundamental switching frequency approach [20] is selected to control the voltage gain of the resonant circuit. According to the on-off states of the power semiconductors, the leg voltages are obtained as V_ac (or V_bc) = V_in/2 or −V_in/2 and V_de = V_o/2 or −V_o/2. The equivalent resonant tank circuits of Figure 4b–d can be obtained in Figure 8. In Figure 4b, the turns ratio is n₁ = 2n. However, the effective transformer turns ratio in Figure 4c,d is n₂ = n. The voltage gain of the proposed circuit can be obtained from the root mean square (rms) values of the input and output voltages at fundamental switching frequency. The rms leg voltages of input and output terminals are calculated as $V_{ac,f}=\sqrt{2}{V}_{in}/\pi$ in Figure 4b, $V_{bc,f}=\sqrt{2}{V}_{in}/\pi$ in Figure 4c,d, and $V_{de,f}=\sqrt{2}{V}_o/\pi$. The equivalent resonant tanks at fundamental switching frequency are provided in Figure 9. For forward power operation, the equivalent load resistance $R_{o,e}=\frac{2n_1{}^2}{{\pi }^2}{R}_o$ for low voltage output, $R_{o,e}=\frac{2n_2{}^2}{{\pi }^2}{R}_o$ for high voltage output, and $R_{in,e}=\frac{2R_{in}}{{\pi }^2{n}_2{}^2}$ for reverse power operation.

Based on the equivalent resonant circuit in Figure 9, the transfer functions of the proposed converter for the three operating modes are obtained and expressed as.

$$\begin{array}{ll}{G}_{F,L}\left(s\right)& =\frac{n_1{V}_{de,f}}{V_{ac,f}}=\frac{n_1{V}_o}{V_{in}}\\ & =\frac{s{L}_{m,1\_n_1}//\left(s{n}_1^2{L}_{r2}+\frac{1}{s{C}_{r2}/n_1^2}+R_{o,e}\right)}{2s{L}_{r1,1}+\frac{2}{s{C}_{r1,1}}+\left[s{L}_{m,1\_n_1}//\left(s{n}_1^2{L}_{r2}+\frac{1}{s{C}_{r2}/n_1^2}+R_{o,e}\right)\right]}\times \frac{R_{o,e}}{s{n}_1^2{L}_{r2}+\frac{1}{s{C}_{r2}/n_1^2}+R_{o,e}}\end{array}$$

(1)

$$\begin{array}{ll}{G}_{F,H}\left(s\right)& =\frac{n_2{V}_{de,f}}{V_{bc,f}}=\frac{n_2{V}_o}{V_{in}}\\ & =\frac{s{L}_{m,1\_n_2}//\left(s{n}_2^2{L}_{r2}+\frac{1}{s{C}_{r2}/n_2^2}+R_{o,e}\right)}{s{L}_{r1,1}+\frac{1}{s{C}_{r1,1}}+\left[s{L}_{m,1\_n_2}//\left(s{n}_2^2{L}_{r2}+\frac{1}{s{C}_{r2}/n_2^2}+R_{o,e}\right)\right]}\times \frac{R_{o,e}}{s{n}_2^2{L}_{r2}+\frac{1}{s{C}_{r2}/n_2^2}+R_{o,e}}\end{array}$$

(2)

$$\begin{array}{ll}{G}_R\left(s\right)& =\frac{V_{bc,f}/n_2}{V_{de,f}}=\frac{V_{in}}{n_2{V}_o}\\ & =\frac{s{L}_{m,2}//\left(s{L}_{r1,1}/n_2^2+\frac{1}{s{n}_2^2{C}_{r1,1}}+R_{in,e}\right)}{s{L}_{r2}+\frac{1}{s{C}_{r2}}+\left[s{L}_{m,2}//\left(s{L}_{r1,1}/n_2^2+\frac{1}{s{n}_2^2{C}_{r1,1}}+R_{in,e}\right)\right]}\times \frac{R_{in,e}}{s{L}_{r1,1}/n_2^2+\frac{1}{s{n}_2^2{C}_{r1,1}}+R_{in,e}}\end{array}$$

(3)

where G_F,L(s), G_F,H(s), and G_R(s) are the transfer functions of Figure 4b–d, respectively. To further simplify the transfer function Equations in (1)–(3), the circuit parameters are defined as C_r1,1 = C_r1,2 = C_r2/n², L_r1,1 = L_r1,2 = n²L_r2, $Q_{F,L}=\sqrt{4L_{r1,1}/C_{r,1}}/R_{o,e}$, $Q_{F,H}=\sqrt{L_{r1,1}/C_{r,1}}/R_{o,e}$ $Q_R=\sqrt{L_{r2}/C_{r2}}/R_{in,e}$, $K_{F,L}=L_{m,1\_n1}/2L_{r1,1}$, $K_{F,H}=L_{m,1\_n2}/L_{r1,1}$, $K_R=L_{m,2}/L_{r2}$ and $F_F=F_R=f_{sw}/f_r$. Then the voltage gains for the three operating modes are expressed as:

$$|G_{F,L}|=\frac{n_1{V}_o}{V_{in}}=\frac{1}{\sqrt{{[1+\frac{1}{K_{F,L}}-\frac{1}{K_{F,L}{F}_F^2}]}^2+Q_{F,L}^2{[F_F(2+\frac{1}{K_{F,L}})-\frac{1}{F_F}(2+\frac{2}{K_{F,L}}-\frac{1}{K_{F,L}{F}_F^2})]}^2}}$$

(4)

$$|G_{F,H}|=\frac{n_2{V}_o}{V_{in}}=\frac{1}{\sqrt{{[1+\frac{1}{K_{F,H}}-\frac{1}{K_{F,H}{F}_F^2}]}^2+Q_{F,H}^2{[F_F(2+\frac{1}{K_{F,H}})-\frac{1}{F_F}(2+\frac{2}{K_{F,H}}-\frac{1}{K_{F,H}{F}_F^2})]}^2}}$$

(5)

$$|G_R|=\frac{V_{in}}{n_2{V}_o}=\frac{1}{\sqrt{{[1+\frac{1}{K_R}-\frac{1}{K_R{F}_F^2}]}^2+Q_R^2{[F_R(2+\frac{1}{K_R})-\frac{1}{F_R}(2+\frac{2}{K_R}-\frac{1}{K_R{F}_R^2})]}^2}}$$

(6)

These three voltage gains have similar equations with different circuit parameters and transformer turns ratios. According to Equations (4)–(6), Figure 10 illustrates the curves of voltage gain under K = 5.

The electric parameters of the circuit prototype are V_in = 400 V, V_o = 150 V–450 V, P_o,max = 1kW at V_o = 450 V condition and f_r = 80 kHz. When V_o = 150–300 V, a half bridge resonant circuit with transformer turns ratio 2n is used in Figure 4b, to control the load voltage. If V_o = 300–450 V, then the half bridge resonant circuit with transformer turns ratio n is adopted in Figure 4c to control output voltage. When reverse power flow is required, the half bridge resonant circuit on the right-hand side is adopted (Figure 4d), to transfer power flow from the low side to input side. Since the three operating modes in Figure 4 have similar voltage transfer functions, the circuit parameters of the prototype circuit are obtained from Figure 4c with V_o = 300–450 V in this design example. First, the unity gain of M_F,H| is designed at V_o = 300 V. From Equation (5), the turn ratio n = n_p1/n_s is obtained in Equation (7).

$$n_2=n=n_{p1}/n_s=|G_{F,H}{|}_{}\times \frac{V_{in}}{V_{o,\min }}=1\times \frac{400}{300}\approx 1.333$$

(7)

The magnetic core PC40/EE55 with primary turns n_p1 = n_p2 = 26 and secondary turns n_s = 20 is adopted to implement transformer T. Therefore, the turns ratio n₂ becomes 26/20 = 1.3. Then, the voltage gains at V_o = 300 V and V_o = 450 V conditions are expressed as

$$|G_{F,H}{|}_{\min }=\frac{n_2{V}_{o,\min }}{V_{in}}=\frac{1.3\times 300}{400}\approx 0.975$$

(8)

$$|G_{F,H}{|}_{\max }=\frac{n_2{V}_{o,\max }}{V_{in}}=\frac{1.3\times 450}{400}\approx 1.46$$

(9)

Similarly, the voltage gains at V_o = 150 V and V_o = 300 V conditions under low voltage output range operation in Figure 4b are expressed as.

$$|G_{F,L}{|}_{\min }=\frac{n_1{V}_{o,\min }}{V_{in}}=\frac{2\times 1.3\times 150}{400}\approx 0.975$$

(10)

$$|G_{F,L}{|}_{\max }=\frac{n_1{V}_{o,\max }}{V_{in}}=\frac{2\times 1.3\times 300}{400}\approx 1.95$$

(11)

To obtain a voltage gain of more than 1.95 at V_o = 300 V under low voltage output range ($|G_{F,L}{|}_{\max }\approx 1.95$), the quality factors Q = 0.2 and K = 5 are selected. For forward power flow and high voltage output range (300–450 V), the quality factor $Q_{F,H}=\sqrt{L_{r1,1}/C_{r,1}}/R_{o,e}$ and the inductor ratio $K_{F,H}=L_{m,1\_n2}/L_{r1,1}$. The resistance R_o,e at full load is calculated as:

$$R_{o,e}=\frac{2n_2{}^2}{{\pi }^2}{R}_o=\frac{2\times {1.3}^2}{{3.14159}^2}\times \frac{{450}^2}{1000}\approx 69 \Omega$$

(12)

Then, the resonant components can be calculated as:

$$L_{r1,1}=L_{r1,2}=Q_{F,H}{R}_{o,e}/(2\pi f_r)=0.2\times 69/(2\times 3.14159\times 80000)\approx 27.45 \mathsf{\mu }\mathrm{H}$$

(13)

$$L_{r2}=L_{r1,1}/n_2^2=27.45/{1.3}^2\approx 16.24 \mathsf{\mu }\mathrm{H}$$

(14)

$$L_{m,1}=K_{F,H}L{}_{r1,1}=5\times 27.45\approx 137.25 \mathsf{\mu }\mathrm{H}$$

(15)

$$C_{r1,1}=C_{r1,2}=1/(2\pi Q_{F,H}{f}_r{R}_{o,e})=1/(2\times 3.14159\times 0.2\times 80000\times 69)\approx 144 \mathrm{nF}$$

(16)

$$C_{r2}=n_2^2{C}_{r1,1}={1.3}^2\times 144\approx 243 \mathrm{nF}$$

(17)

Table 2. Circuit components in the laboratory prototype.

Items	Parameter
C1, C2	660 μF
C3, C4	660 μF
Cr1,1, Cr1,2	144 nF
Cr2	243 nF
Lr1,1, Lr1,2	27.45 μH
Lr2	16.24 μH
Lm,1	137.25 μH
S1–S6	GP50B60PD1 (600 V/33 A)
Q	6R125P6 (650 V/19 A)
Transformer np1:np2:ns	26:26:20

shows the circuit components in the laboratory prototype.

4. Experimental Verifications

The output voltage V_o between 150 V and 450 V and the switching signals of switches Q, S₁, and S₃ are provided in Figure 11a. If V_o is between 150 V and 300 V, S₁ is off and Q is on. The half bridge circuit with switches S₃ and S₄, as shown in Figure 4b, is controlled to regulate load voltage. If V_o is between 300 V and 450 V, Q and S₃ are off, and switches S₁ and S₂ are operated to control load voltage. The constant voltage (CV) and constant current (CC) modes are used to charge the battery. If the battery voltage is less that 450 V, then the battery charge current is controlled at CC mode with I_o = 2.3 A. If the battery voltage is close to 450 V, then CV mode with V_o = 450 V is selected to charge the battery. Therefore, the load current I_o will be decreased from 2.3 A. In Figure 12, Figure 13, Figure 14 and Figure 15, the experimental waveforms operated at constant current mode with V_o = 150 V, 310 V and 450 V are provided, to show the circuit characteristics under a forward power flow condition. Figure 12a–c shows the measured waveforms of input voltage, load current, load voltage, and switch signal under V_in = 400 V, I_o = 2.3 A, and V_o = 150, 310, and 450 V, respectively, with CC mode control. When V_o = 150 V, the converter is controlled in low voltage output mode (Figure 4b). Therefore, switch S₃ is controlled with variable switching frequency, to regulate load voltage, as shown in Figure 12a. When V_o = 310 V and 450 V, the proposed circuit is operated in high voltage output mode (Figure 4c). Thus, switch S₁ is controlled to adjust the load voltage, as shown in Figure 12b,c. Figure 13 provides the test results of the leg voltage and the primary current and voltage under V_o = 150 V, 310 V, and 450 V outputs. The square voltage with ±200 V is generated on the leg voltage V_ac at V_o = 150 V condition or V_bc at V_o = 310 V and 450 V conditions. The resonant voltage v_Cr1,1 is almost a sinusoidal voltage. In low voltage output mode, the voltage gain at V_o = 150 V output is close to unity. Therefore, f_sw (switching frequency) is close to 80 kHz (series resonant frequency) and i_Lr1 resembles a sinusoidal waveform. In high voltage output mode, the proposed converter has a high (or low) voltage gain under V_o = 450 V (or 310 V) output. Thus, f_sw < f_r at V_o = 450 V condition. Therefore, the primary current i_Lr1 resembles a quasi-sinusoidal waveform at V_o = 450 V output. The measured secondary side waveforms are shown in Figure 14. Since f_sw > f_r at V_o = 150 V and 310 V conditions are more than series resonant frequency, the diode currents i_DS5 and i_DS6 are turned off at hard switching, as shown in Figure 14a,b. However, D_S5 and D_S6 turn off at zero current under V_o = 450 V output (Figure 14c), due to f_sw < f_r. Figure 15 provides the experimental waveforms of the active switch for different output voltage conditions. The switch waveforms at full rated current and 150 V output case are shown in Figure 15a. The switch S₃ is tuned on with zero voltage switching, due to the collect-to-emitter voltage being reduced to zero voltage before S₃ turns on. In the same way, S₁ also turns on at zero voltage switching under 310 V output (Figure 15b) and 450 V output (Figure 15c,d). Figure 16 shows the experimental results under reverse power conversion at V_in = 400 V, V_o = 450 V, and full power condition. Only switches S₅ and S₆ are controlled to realize reverse power flow operation. Figure 16a gives the measured waveforms V_o, V_in, I_in, and v_S5,g. The measured right hand side waveforms are given in Figure 16b, and the measured left hand side waveforms are given in Figure 16c. Since the voltage gain under the reverse power flow operation is close to unity, f_sw is almost equal to f_r. Thus, the resonant voltage and current waveforms are almost sinusoidal waveforms, as shown in Figure 16b. Figure 16d,e show the test results of switch S₅ at 100% and 50% rated power conditions. S₅ turns on at zero voltage switching. The measured circuit efficiencies are 90.7%, 92.5%, and 91.7% at V_o = 150 V, 310 V, and 450 V under CC mode control.

5. Conclusions

A frequency control DC/DC converter with the advantages of bidirectional power conversion, soft switching operation, and wide voltage operation is presented and implemented for battery charging and discharging applications. Symmetric half bridge resonant circuits are used to achieve bidirectional power flow action and voltage step up/down operation. By using a variable transformer turns ratio, the proposed converter has a wide voltage output capability, to overcome the drawback of wide frequency variation in traditional resonant converters. The presented circuit is controlled at inductive load characteristics, so that power semiconductors are turned on (or off) at zero voltage (or zero current) switching. Thus, the electromagnetic interference and switching losses can be reduced. The circuit schematic, system operation, and design procedures of the proposed circuit are discussed and provided in detail. The circuit effectiveness was confirmed and verified by the experimental results with a 1-kW power scaled down prototype.