Tapped-inductor bi-directional Cuk converter with high step-up/down conversion ratio and its optimum design

Abstract

A bidirectional DC–DC converter is required for an energy storage system. High efficiency and a high step-up and step-down conversion ratio are the development trends. In this research, a series of bidirectional high-gain Cuk circuits was derived by combining tapped inductors and bidirectional Cuk. After analyzing and comparing the characteristics of each circuit, a bidirectional high-gain Cuk circuit with a tapped-inductor (reverse coupling) was proposed. The proposed converter has a simple structure and a high voltage gain in both the step-down (Buck) and step-up (Boost) operation modes. The voltage stress of S₂ was low. The voltage stress of S₁ was high, however, and this is a disadvantage of the proposed converter. The proposed circuit’s characteristics were thoroughly examined, including the voltage gain characteristics and the design of the main parameters. We established a power loss model of the new topology, and the tapped-inductor turn ratio was optimized for high efficiency. Finally, a 400 W experimental implementation of the converter was shown to achieve efficiencies of 93.5% and 92.4% in the step-up and step-down modes, respectively. These findings verified the validity of the proposed circuit’s theoretical analysis.

Introduction

Because of the scarcity of fossil fuels and serious environmental issues in recent years, significant effort has been focused on the development of environmentally friendly distributed generation (DG) technologies¹. Renewable energy, however, does not produce consistent energy because of weather conditions. Energy storage is required to provide stable power². Furthermore, the voltage of a storage battery is typically low, in the 12–48 V range, whereas the voltage of a DC bus is 400 V or higher to meet the requirements of an inverter or AC grid³. As a result, for energy storage systems to connect a low-voltage battery to a high-voltage DC bus, a bidirectional DC–DC converter with a high step-up/step-down voltage conversion ratio is required⁴. Furthermore, these converters have been researched extensively for a wide range of industrial applications, including uninterruptible power supply systems, electric vehicles, and aviation power supplies⁵. The traditional buck-boost converter can provide a high voltage gain with a large duty ratio, which will cause considerable conduction losses because of the large current ripples. Additionally, several bidirectional DC–DC converters based on isolated topologies have been presented in the literature. These topologies require a transformer and a high number of switching devices, which increases the cost and the switching losses, in addition to requiring more complicated control schemes.

Many bidirectional DC–DC converters with a high step-up/step-down conversion ratio have been proposed to improve the voltage gain and efficiency of a converter. The cascade method was used in reference ⁶ to broaden the ratio range of a bidirectional converter whose gain was calculated by multiplying the gains of each level converter. The efficiency was low, however, because of the cascade, and there was an issue of instability. The proposed converter in reference ⁷ improved a bidirectional DC-DC converter’s conversion ratio by connecting the low-voltage side in parallel and the high-voltage side in a series, but the structure of the converter was complex. Some appealing solutions, such as switched capacitors^8,9, switched inductors¹⁰, and coupled inductors¹¹, have been introduced for a basic bidirectional DC/DC converter to increase the voltage conversion ratio. The proposed bidirectional bridge modular switched-capacitor-based resonant DC–DC converter achieved a high step-up/step-down conversion ratio through a switched capacitor unit⁸. However, it employed a large number of switches, and the voltage and current stresses on the switches were high due to resonance. As a result, although the circuit proposed in ⁹ reduced the number of switches, its conversion ratio range was limited. Reference ¹⁰ employed the coupled-inductor technique to build a bidirectional DC–DC converter with a high step-up/step-down voltage gain. The current ripple was large because the current waveform on the low-voltage side of the topology was a square wave. In addition, reference ¹¹ discussed nonisolated bidirectional DC–DC converters based on dual-coupled inductors, which could achieve a high voltage gain and reduced switch voltage stresses by connecting the secondary windings of two coupled inductors in series. However, it necessitated a complex control.

In summary, these isolated converter structures usually have too many switches, so the conduction losses of the switches were very high. Additionally, the practical implementation is complicated and expensive. The existing nonisolated high-gain circuits are mainly switch capacitor converters and coupled inductor converters. The drawbacks of a switch capacitor converter include the switching loss and the current stress. The drawbacks of a coupled inductor converter include the complex circuit structure and the leakage inductance that results in spikes that need to be suppressed using snubber circuits.

Cuk converters are gaining popularity because the input and output inductors reduce electromagnetic interference problems and the output ripple is small¹². In this research, tapped inductance and bidirectional Cuk are combined to create a series of bidirectional high-gain Cuk circuits. After analyzing and comparing the characteristics of each circuit, a bidirectional high-gain Cuk circuit with a tapped-inductor (reverse coupling) is proposed. The proposed converter has a simple structure and high voltage gain in both the step-down (Buck) and step-up (Boost) operation modes. The proposed circuit’s characteristics, including the voltage gain characteristics and the design of the main parameters, are thoroughly examined. Based on this examination, we established a power loss model of the new topology, and the tapped-inductor turn ratio was optimized for high efficiency. Finally, a 400 W 48 V/400 V prototype was created to verify the validity of the proposed circuit’s theoretical analysis.

A tapped-inductor bidirectional Cuk

The bidirectional Cuk circuit features low input and output ripple and low EMI interference, and the circuit diagram is shown in Fig. 1. Because of the influence of the parasitic parameters, the voltage gain of this circuit is limited, and it is not suitable for occasions with a large voltage transformation ratio. Therefore, a series of bidirectional high-gain Cuk circuits is created by combining tapped inductance and bidirectional Cuk to increase the voltage gain of bidirectional Cuk.

Figure 1

Bidirectional Cuk circuit.

The proposed series of circuits use coupled inductors to replace the inductors L₁ or L₂ in Fig. 1. Because of the different connection methods of the coupled inductor, four different circuits can be derived. Additionally, because the coupled inductor has two coupling modes (i.e., same-direction coupling and reverse-direction coupling), a total of eight circuits can be derived, as shown in Figs. 2 and 3. These converters with tapped inductors are formed by the same-direction coupling shown in Fig. 2. The reverse-direction coupling is shown in Fig. 3. The tapped inductor is composed of L₁ with the number of turns N₁ and L₂ with the number of turns N₂, where the tap ratio is n = N₂: N₁. Furthermore, D₁ is the parasitic body diode of S₁ and D₂ is the parasitic body diode of S₂. The same-direction coupling means that the currents all flow from the same-named end of the inductor and vice versa.

Figure 2

Bidirectional high-gain Cuk circuits are formed by the same-direction coupling, (a) S₁-tap, (b) S₂-tap, (c) C_B-tap 1, (d) C_B-tap 2.

Figure 3

Bidirectional high-gain Cuk circuits are formed by the reverse-direction coupling, (a) S₁-tap, (b) S₂-tap, (c) C_B-tap 1, (d) C_B-tap 2.

The voltage gain M of these converters versus the duty ratio D and the turn ratio n is obtained for the continuous current mode (CCM) mode by analyzing the working principles of the previously noted circuits, as shown in Table 1. S₁-tap means that the inductor L₁ of the bidirectional Cuk circuit is replaced by the tap inductor L_t, and the common terminal of the tapped inductor is connected to S₁, as shown in Fig. 2a and Fig. 3a. S₂-tap means that the inductor L₂ of the bidirectional Cuk circuit is replaced by the tap inductor L_t, and the common terminal of the tapped inductor is connected to S₂, as shown in Figs. 2b and 3b. C_B-tap 1 means that the inductor L₁ of the bidirectional Cuk circuit is replaced by the tap inductor L_t, and the common terminal of the tapped inductor is connected to C_B, as shown in Figs. 2c and 3c. C_B-tap 2 means that the inductor L₂ of the bidirectional Cuk circuit is replaced by the tap inductor L_t, and the common terminal of the tapped inductor is connected to C_B, as shown in Figs. 2d and 3d.

Table 1 The voltage gain M versus duty ratio D and the turn ratio n.

The corresponding curve can be drawn using the data from Table 1, as shown in Fig. 4. The voltage-gain characteristic curve of the circuits formed by same-direction coupling is shown in Fig. 4a. The curves of the S₁-tap circuit and capacitor-tap circuit 2 are overlapped, and the curves of the S₂-tap circuit and capacitor-tap circuit 1 are overlapped. As shown in Fig. 4a, the bidirectional Cuk circuit with the tapped inductor derived from S₂-tap and capacitor-tap circuit 1 can achieve a high voltage gain. The voltage conversion ratio characteristic curve of the circuits formed by the reverse-direction coupling is shown in Fig. 4b. The curves of the S₁-tap circuit and capacitor-tap circuit 2 are overlapped, and the curves of the S₂-tap circuit and capacitor-tap circuit 1 are overlapped. As shown in Fig. 4b, the bidirectional Cuk circuit with the tapped inductor derived from S₁-tap and capacitor-tap circuit 2 can achieve a high voltage gain.

Figure 4

The voltage gain characteristic curves of the eight circuits in the step-up mode, (a) the same-direction coupling, (b) the reverse-direction coupling.

The voltage conversion ratio characteristic curves of the circuits in Figs. 3d and 2b are plotted, as shown in Fig. 5, to obtain the circuit with a larger step-up ratio from the previously noted circuits. As a result, it is determined that the circuit in Fig. 3d is the best of the previously noted circuits.

Figure 5

The voltage gain characteristic curves of the 4 circuits in step-up mode.

Because the analysis of these converters in the step-down mode is similar to the analysis in the step-up mode, it is not repeated here.

The feasibility analysis of the topologies’ large ratio is shown in Table 2 based on the preceding analysis. In the table, the term “inapplicable” means that the conversion ratio of this circuit is less than that of the bidirectional Cuk circuit, and the term “available” means that the conversion ratio of this circuit is greater than that of the bidirectional Cuk circuit.

Table 2 The feasibility analysis of the topologies’ large ratio.

A tapped-inductor bidirectional high gain Cuk converter

The circuit topology

According to this analysis, we proposed a tapped-inductor bidirectional Cuk converter with a high step-up/step-down conversion ratio, as shown in Fig. 6. The proposed converter is made up of the following components: the low-side voltage V₂, the high-side voltage V₁, the inductor L₃, the tapped inductor L_t, the capacitor C_B, and the two switches S₁–S₂. The tapped inductor L_t is composed of L₁ and L₂ coupled in the opposite direction, and the turns of the inductor are N₁ and N₂(N₁ > N₂). The equivalent circuits of these stages are shown in Fig. 7.

Figure 6

A reverse coupling tapped-inductor high gain bidirectional Cuk converter.

Figure 7

A reverse coupling tapped-inductor high gain bidirectional Cuk equivalent circuit, (a) step-up mode, (b) step-down mode.

The effective turn ratio of the tapped inductor is expressed as follows.

$$ \lambda = \frac{{N_{1} - N_{2} }}{{N_{1} }} $$

(1)

The coupling coefficient of the tapped inductor is:

$$ k = \frac{{L_{m} }}{{L_{m} + L_{k} }} $$

(2)

where L_m is the equivalent magnetizing inductance on the N₂ side; and L_k is the leakage inductance on the N₂ side.

Operational principles

When using the proposed circuit in energy storage systems, the battery voltage V₂ is on the low-voltage side and the DC-bus voltage V₁ is on the high-voltage side. The proposed converter can operate in both step-up mode and step-down mode with bidirectional power flow. Reference ¹³ contains the operating principles and steady-state analysis. Hence, the simple results are discussed in the following, but the detailed analysis is not repeated.

As shown in Fig. 8, one switching period of the step-up mode has two switching stages. In Fig. 8, v_gs2 is the driving signal of S₂, the currents flowing through the L₁, L₂, and L₃ inductors are i_Ls, i_Lp, and i_L3, and i_D1, i_S2, and i_CB are the currents flowing through D₁, S₂, and C_B. The equivalent circuits of these stages are shown in Fig. 9.

Figure 8

The main operation waveforms of the key components in the step-up mode.

Figure 9

The equivalent circuit of the operation modes in the step-up mode, (a) S₂ on, (b) S₂ off.

The gain of the proposed circuit in the step-up mode can be derived as follows.

$$ M_{up} = \frac{{V_{1} }}{{V_{2} }} = \frac{\lambda + (1 - \lambda )D}{{\lambda (1 - D)}} - \frac{D(1 - k)}{{\lambda (1 - D)}} $$

(3)

Ideally, the leakage inductor can be ignored, and the M_up can be derived as follows.

$$ M_{up} = \frac{{V_{1} }}{{V_{2} }} = \frac{\lambda + (1 - \lambda )D}{{\lambda (1 - D)}} $$

(4)

where M_up is the step-up conversion ratio of the proposed converter and D is the duty cycle of S₂.

As shown in Fig. 10, one switching period of the step-down mode has two switching stages. In Fig. 10, v_gs1 is the driving signal of S₁, the currents flowing through the L₁, L₂, and L₃ inductors are i_L1, i_L2, and i_L3, and i_D2, i_S1, and i_CB are the currents flowing through D₂, S₁, and C_B. The equivalent circuits of these stages are shown in Fig. 11.

Figure 10

The main operation waveforms of the key components in the step-down mode.

Figure 11

The equivalent circuit of the operation modes in the step-down mode, (a) S₁ on, (b) S₁ off.

The gain of the proposed circuit in the step-down mode can be derived as follows.

$$ M_{{{\varvec{down}}}} = \frac{{V_{2} }}{{V_{1} }} = \frac{\lambda D}{{1 + (\lambda - 1)D}} + \frac{\lambda D(1 - D)(1 - k)}{{(1 + \lambda D - D)(k + \lambda D - kD)}} $$

(5)

Ideally, the leakage inductor can be ignored, and M_down can be derived as follows.

$$ M_{{{\varvec{down}}}} = \frac{{V_{2} }}{{V_{1} }} = \frac{\lambda D}{{1 + (\lambda - 1)D}} $$

(6)

where M_down is the step-down conversion ratio of the proposed converter and D is the duty cycle of S₁.

Comparison analysis of the proposed converter

The characteristic comparison of the proposed converter with the counterparts is shown in Table 3 (NS is the number of power switches, NCI is the number of coupled inductors, NI is the number of inductors, and NC is the number of capacitors). The conventional buck/boost converter can achieve bidirectional power flows while employing the fewest number of power switches, but the converter’s conversion ratio range is limited. The converter in reference ¹⁴ has a high step-up/step-down conversion ratio, but it is complex and inefficient. Compared with the converters in reference ¹⁴, the converter’s efficiency in reference ¹⁵ has been improved by using soft switching technology, but the circuit structure is still complex. It can be seen that the proposed converter achieves a high and wide voltage-gain range by employing two power switches. Additionally, it has a simple structure.

Table 3 Characteristic comparison of the proposed converter with the main competitors.

The feasibly control strategy for the proposed converter

To improve the dynamic performance and antidisturbance ability of the proposed converter, we proposed an improved fuzzy control strategy based on the Takagi–Sugeno-Kang fuzzy control technique, as shown in Fig. 12. The operating principle and a detailed analysis of the control strategy can be obtained from reference ¹³. Therefore, the detailed analysis is not repeated in this paper.

Figure 12

The improved fuzzy control schematic.

Analysis and design of the key parameters

Optimized design of turn ratio

Power loss model

A power loss model of the new topology is established in the step-up mode. The loss of the proposed converter is composed of the losses of S₂, L_t, L₃, and D₁. The specific analysis is given as follows.

• (1) The loss of S₂.

  The conduction loss is expressed as follows

  $$ P_{con\_S} = I_{rms\_S}^{2} \cdot R_{ds(on)\_S} $$

  (7)

  where I_{rms_S2} is the effective value of the current across S₂, and R_ds(on) is the forward conduction resistance of S₂ at a certain temperature, which can be estimated from the datasheet and the ambient temperature.

  The switching loss is found as follows

  $$ P_{sw} = \frac{1}{2} \cdot f_{s} V_{ds} \cdot \left[ \begin{gathered} I_{d01} \cdot (t_{ri} + t_{fv} ) \hfill \\ { + }I_{d02} \cdot (t_{rv} + t_{fi} ) \hfill \\ \end{gathered} \right] $$

  (8)

  where t_ri, t_fv, t_r, and t_fi are the equivalent times of the four phases with the loss during the switching process, which can be calculated from the datasheet.

  The loss of the equivalent output capacitance of S₂ is found as follows:

  $$ P_{{{\text{Co}} \_S}} = \frac{1}{2} \cdot C_{oss} \cdot V_{ds\_S2}^{2} \cdot f_{S} $$

  (9)

  Therefore, the overall loss of S₂ is given by the following:

  $$ P_{s} = P_{con\_S} + P_{sw} + P_{{{\text{Co}} \_S}} $$

  (10)

• (2) The loss of D₁

  $$ P_{D} = V_{F} \cdot I_{D} + V_{off\_D} \cdot Q_{rr} \cdot f_{S} $$

  (11)

  where V_F is the forward voltage drop of D₁, I_D is the average value of the current across D₁, V_{off_D} is the reverse voltage of D₁, and Q_rr is the reverse recovery charge of D₁.

• (3) The loss of the inductor

  The core loss is found as follows:

  $$ P_{core} = f_{s} \cdot Kf_{eq}^{{{{\alpha - 1}}}} B^{\beta } \left( {C_{0} + C_{1} T + C_{2} T^{2} } \right) $$

  (12)
  $$ f_{eq} (D) = \frac{2}{{B^{2} \pi^{2} }}\int\limits_{0}^{T} {(\frac{dB}{{dt}})^{2} dt = } \frac{{2f_{s} }}{{\pi^{2} D(1 - D)}} $$

  (13)

The winding loss is found as follows

$$ P_{winding} = I_{L\_rms}^{2} \cdot R_{dc} $$

(14)

Therefore, the overall loss of inductor is given by the following:

$$ P_{core} = P_{core} \cdot V_{core} + P_{winding} $$

(15)

where the parameters K, α, β, C₀, C₁, and C₂ can be obtained from the datasheet provided by the core manufacturer; T is the operating temperature of the magnetic core; V_core is the volume of the magnetic core; I_{L_rms} is the effective value of the current through the inductor; and R_dc is the equivalent resistance of the inductor.

The power loss models of L_t and L₃ are similar to each other. Therefore, the description of the power loss model of L_t is not repeated here.

To summarize, the overall loss of the proposed converter in the step-up mode is given by the following:

$$ P_{total\_up} = P_{S2} + P_{D1} + P_{L3} + P_{Lt} $$

(16)

Hence, the efficiency of the proposed converter in the step-up mode is given as follows

$$ \eta_{up} = \frac{{P_{o} }}{{P_{o} + P_{total\_up} }} $$

(17)

Similarly, the overall loss of the proposed converter in the step-down mode is given by the following:

$$ P_{total\_down} = P_{S1} + P_{D2} + P_{L3} + P_{Lt} $$

(18)

Hence, the efficiency of the proposed converter in the step-down mode is given as follows

$$ \eta_{down} = \frac{{P_{o} }}{{P_{o} + P_{total\_down} }} $$

(19)

The optimization selection of turn ratio

The loss characteristics of the proposed circuit are analyzed using Mathcad and the power loss model from the previous section. The following are the converter’s main simulation parameters: V₂ = 48 V, V₁ = 400 V, P_o = 400 W, L₃ = 1.5 mH, L₁ = 0.9 mH, switching frequency: fs = 50 kHz.

According to Formula (16), the curves for the loss of the proposed circuit and the turn ratio under different loads can be drawn using Mathcad, as shown in Fig. 13.

Figure 13

The curves between the loss of the proposed circuit and the turn ratio under different loads.

From Fig. 13, when the output power is constant, the total loss of the circuit decreases at first and then increases as the turn ratio increases. As a result, a minimum loss point serves as the foundation for selecting the appropriate turn ratio in this research.

The calculation curve for the efficiency of the proposed circuit in the step-up mode can be drawn using Formula (17), as shown in Fig. 14a. Figure 14b depicts the calculation curve for the efficiency of the proposed circuit in the step-down mode, according to Formula (19).

Figure 14

The calculation curve for λ, D, and the efficiency: (a) step-up mode, (b) step-down mode.

As shown in Fig. 14, the circuit’s efficiency increases at first and then decreases as the turn ratio increases. There is a maximum level of efficiency. As a result, to achieve the expected output and high efficiency, an appropriate turn ratio and steady-state duty ratio should be chosen. The turn ratio should be around 0.4, and the duty cycle should be around 0.75, according to Fig. 14.

Given the possibility of errors during the design and winding processes, the best turn ratio is ${\lambda }_{opt}$ = 0.375–0.412. The efficiency calculation curves are shown in Fig. 15. When the proposed converter operates under rated conditions, the best turn ratio is ${\lambda }_{opt}$ = 0.394. Figure 15a depicts the efficiency curve in the step-up mode, and Fig. 15b shows the efficiency curve in the step-down mode.

Figure 15

The calculation curve of the efficiency, (a)step-up mode, (b) step-down mode.

Other parameters design

The selection of the inductor

To ensure that the circuit works in CCM mode, the values of L₁, L₂, and L₃ must be greater than the inductance value with critical continuity. These values are given as follows:

$$ L_{1} \ge \frac{1}{{\frac{{2\lambda f_{s} I_{1} }}{{(V_{1} - V_{2} )(1 - D)}} - \frac{1 - \lambda }{{L_{3} }}}} $$

(20)

$$ L_{2} = L_{1} (1 - \lambda )^{2} $$

(21)

$$ L_{3} \ge \frac{{V_{1} - V_{2} }}{{f_{{\text{s}}} (2 \cdot I_{L3} )}} = \frac{{V_{1} - V_{2} }}{{2I_{{1}} f_{{\text{s}}} }} $$

(22)

The selection of capacitor

The selection of the capacitor mainly includes consideration of the voltage stress and the voltage ripple within a certain range. The value of C_B is found as follows:

$$ C = \frac{{|i_{CB} | \cdot DT_{{\text{s}}} }}{{\Delta V_{C} }} $$

(23)

Simulation and experimental verification

Simulation results

We performed detailed simulations in Matlab/Simulink to verify the correctness of the aforementioned theoretical analysis. The proposed converter operation is verified at V₂ = 48 V, V₁ = 400 V, P_o = 400 W, L₃ = 1.5 mH, L₁ = 0.9 mH, L₂ = 0.33 mH, L_k = 0.92 uH, C_B = 2.2 uF, C_o1 = 47 uF, C_o2 = 47 uF, and the switching frequency fs = 50 kHz.

The simulation results in the step-up mode at full load are shown in Fig. 16. In Fig. 16, v_gs2 is the driving signal for S₂, the currents flowing through the L₁, L₂, and L₃ inductors are i_Ls, i_Lp, and i_L3, and i_D1, i_S2, and i_CB are the currents flowing through D₁, S₂, and C_B, respectively.

Figure 16

The stable waveforms of the key components in the step-up mode.

The simulation results in the step-down mode at full load are shown in Fig. 17. v_gs1 is the driving signal for S₁, the currents flowing through the L₁, L₂, and L₃ inductors are i_Ls, i_Lp, and i_L3, and i_D2, i_S1, and i_CB are the currents flowing through D₂, S₁, and C_B separately.

Figure 17

The stable waveforms of the key components in the step-down mode.

In the step-up mode, the output voltage is stable at 400 V, as shown in Fig. 16. The duty cycle of S₂ is 0.74. The voltage stresses of S₂ and D₁ are 457 V and 472 V. Similarly, Fig. 17 shows that the output voltage is stable at 48 V in the step-down mode. The duty cycle of S₁ is 0.26. The voltage stresses of S₁ and D₂ are 987 V and 180 V. The voltage and current spikes of S₁, S₂, and the inductor are caused by the leakage inductance of the coupled inductor. Thus, the results in Figs. 16 and 17 show that the simulation results closely match the theoretical analysis.

Experimental results

To validate the theoretical analysis, we built a laboratory prototype of the proposed converter. First, based on typical applications, we selected the operating conditions of the proposed converter as V₂ = 48 V, V₁ = 400 V, and P_o = 400 W. Second, according to Formulas (20)–(23), L₃ = 1.5 mH, L₁ = 0.9 mH, L₂ = 0.33 mH, C_B = 2.2 uF, C_o1 = 100 uF, and C_o2 = 100 uF. Then the voltage-current stress of the semiconductor device can be obtained by analyzing the specific operating principle of the converter. The voltage-current stress of S₁ is as follows:

$$ \left\{ {\begin{array}{*{20}c} {v_{{{\varvec{S}}1.\max }} = V_{1} + \frac{1 - \lambda }{\lambda }V_{2} = \frac{1}{1 + (\lambda - 1)D}V_{1} } \\ {i_{{{\varvec{S}}1.\max }} = \frac{\lambda }{1 - (1 - \lambda )D}I_{2} + \frac{{D(V_{1} - V_{2} )(L_{1} + L_{3} )}}{{2f_{{\varvec{s}}} L_{1} L_{3} }}} \\ \end{array} } \right. $$

(24)

The voltage-current stress of S₂ is as follows:

$$ \left\{ {\begin{array}{*{20}c} {v_{{{\varvec{S}}2.\max }} = \lambda V_{1} + (1 - \lambda )V_{2} = \frac{\lambda }{1 + (\lambda - 1)D}V_{1} } \\ {i_{{{\varvec{S}}2.\max }} = \frac{{I_{1} }}{\lambda (1 - D)} + \frac{{(1 - D)(V_{1} - V_{2} )(L_{1} + L_{3} )}}{{2\lambda f_{{\varvec{s}}} L_{1} L_{3} }}} \\ \end{array} } \right. $$

(25)

where I₁ is the average value of the high-voltage side current and I₂ is the average value of the low-voltage side current.

The maximum voltage and the current stress values of S₁ and S₂ are obtained by incorporating the corresponding parameters. Then, based on a certain margin, the specific type of switching tube that is required can be selected. The specific parameters of the proposed converter are listed in Table 4, and the prototype is shown in Fig. 18.

Table 4 The parameters of the proposed circuit.

Figure 18

Prototype of the converters.

When v₂ = 48 V, we obtain the experimental results in the step-up mode at a full load as shown in Fig. 19. Figure 19a shows the waveforms of v_gs2, v_ds2, and i_ds2, and the duty cycle of S₂ is 0.75. The voltage stress of S₂ is 325 V. Figure 19b shows the waveforms of v_gs2, v_D1, and i_D1, and the voltage stress of D₁ is 675 V. Figure 19c shows the waveforms of v_gs2, v₁, i_L1, and i_L3, and the output voltage of the proposed converter in step-up mode is 400.8 V.

Figure 19

The experiment results of the proposed converter in the step-up mode when v₂ = 48 V: (a) v_gs2, v_ds2, i_ds2, (b) v_gs2, v_D1, i_D1, (c) v_gs2, v₁, i_L1, i_L3.

When v₂ = 36 V, we obtain the experimental results in the step-up mode at full load as shown in Fig. 20. As illustrated in Fig. 20, the duty cycle of S₂ is 0.81, and the output voltage of the proposed converter in the step-up mode is 400.4 V. The voltage stresses of S₂ and D₁ are 362 V and 669 V.

Figure 20

The experiment results of the proposed converter in the step-up mode when v₂ = 36 V: (a) v_gs2, v_ds2, i_ds2, (b) v_gs2, v_D1, i_D1, (c) v_gs2, v₁, i_L1, i_L3.

When v₂ = 60 V, we obtain the experimental results in the step-up mode at full load as shown in Fig. 21. As illustrated in Fig. 21, the duty cycle of S₂ is 0.69, and the output voltage of the proposed converter in the step-up mode is 400.1 V. The voltage stresses of S₂ and D₁ are 315 V and 725 V.

Figure 21

The experiment results of the proposed converter in the step-up mode when v₂ = 60 V: (a) v_gs2, v_ds2, i_ds2, (b) v_gs2, v_D1, i_D1, (c) v_gs2, v₁, i_L1, i_L3.

Compare with the simulation results in Fig. 16, the experimental results in the step-up mode are consistent with it. Both of them are then consistent with the theoretical analysis. The voltage and current spikes are caused by the leakage inductance.

When v₁ = 400 V, we obtain the experimental results in the step-up mode at full load as shown in Fig. 22. Figure 22a shows the waveforms of v_gs1, v_ds1, and i_ds1, and the voltage stress of S₁ is 731 V. Figure 22b shows the waveforms of v_gs1, v_D2, and i_D2, and the voltage stress of D₂ is 225 V. Figure 22c shows the waveforms of v_gs2, v_o, i_L1, and i_L3, and the output voltage of the proposed converter is 47.9 V.

Figure 22

The experiment results of the proposed converter in the step-down mode when v₁ = 400 V: (a) v_gs1, v_ds1, i_ds1, (b) v_gs1, v_D2, i_D2, (c) v_gs, v₂, i_L1, i_L3.

When v₁ = 250 V, we obtain the experimental results in the step-down mode at full load as shown in Fig. 23. As illustrated in Fig. 23, the duty cycle of S₁ is 0.4, and the output voltage of the proposed converter in the step-up mode is 47.9 V. The voltage stresses of S₁ and D₂ are 640 V and 173 V.

Figure 23

The experiment results of the proposed converter in the step-down mode when v₁ = 250 V: (a) v_gs1, v_ds1, i_ds1, (b) v_gs1, v_D2, i_D2, (c) v_gs, v₂, i_L1, i_L3.

When v₁ = 250 V, we obtain the experimental results in the step-down mode at full load as shown in Fig. 24. As illustrated in Fig. 24, the duty cycle of S₁ is 0.253 and the output voltage of the proposed converter in the step-up mode is 47.9 V. The voltage stresses of S₁ and D₂ are 785.5 V and 245 V.

Figure 24

The experiment results of the proposed converter in the step-down mode when v₁ = 430 V: (a) v_gs1, v_ds1, i_ds1, (b) v_gs1, v_D2, i_D2, (c) v_gs, v₂, i_L1, i_L3.

Similarly, compare with the simulation results in Fig. 17, the experimental results in the step-down mode are consistent with it. Both of them are then consistent with the theoretical analysis.

We obtain the input and output current waveforms in the step-up/step-down mode at full load as shown in Fig. 25. Figure 25a shows the current waveforms in the step-up mode, and Fig. 25b shows the current waveforms in the step-down mode. As illustrated in Fig. 25, the input and output current ripple of the proposed converter is low.

Figure 25

The input and output current waveforms of the proposed converter, (a) step-up mode, (b) step-down mode.

The measured efficiency curve of the experimental circuit in the step-up mode is shown in Fig. 26a. Figure 26b shows the measured efficiency curve of the experimental circuit in the step-down mode. Compare with Fig. 14, it can be seen that the proposed circuit’s measured efficiency curve agrees with the calculation curve. The trends of the curves are increased firstly and then decreased. Furthermore, because the actual total loss is not taken into account in the calculation, the maximum measured efficiency is less than the theoretical calculation value.

Figure 26

The efficiency curves of $\lambda$, (a) step-up mode, (b) step-down mode.

When the proposed converter operates under rated conditions and the best turn ratio is ${\lambda }_{opt}$ = 0.394, we obtain the experimental loss of the proposed converter as shown in Fig. 27. As illustrated in Fig. 27, the loss is mainly concentrated on the switching and the coupled inductor in the step-up/step-down mode.

Figure 27

The experimental loss of the proposed converter, (a) step-up mode, (b) step-down mode.

The conversion efficiency versus the output power in the step-up mode and step-down mode is plotted in Fig. 28.In the step-up mode, the maximum efficiency of the proposed converter is 93.5%. In the step-down mode, the proposed converter has a maximum efficiency of 92.2%.

Figure 28

The efficiency curves with the load, (a) step-up mode, (b) step-down mode.

Comparing Figs. 28 and 15, we found that the trends of the measured efficiency curve and the calculation curve ere consistent in the step-up/step-down mode. The trends increased at first and then decreased as the output power increased. Similarly, because the actual total loss was not taken into account, the maximum measured efficiency was less than the theoretical calculation value.

Conclusion

The use of a tapped inductor in this research improved the bidirectional DC-DC converter’s conversion ratio and overcame the shortcomings of the nonisolated bidirectional DC–DC converter’s low conversion ratio. Furthermore, a series of bidirectional high-gain Cuk circuits was derived by summarizing and analyzing the various forms of the proposed coupled inductor. The best circuit was obtained by analyzing and comparing the characteristics of each circuit, and we proposed a bidirectional high-gain Cuk circuit with a capacitor-tapped inductor (reverse coupling). In both the step-down and step-up operation modes, this converter had a simple structure and a high voltage gain. Following this, the proposed circuit’s operational principles and characteristics were thoroughly examined. In addition, the efficiency of the proposed converter was improved further after the optimal selection of the coupled inductor’s turn ratio. Finally, we created a 400 W 48 V/400 V prototype to verify the validity of the proposed circuit’s theoretical analysis.