# A New Continuous Input Current Nonisolated Bidirectional Interleaved Buck-Boost DC-DC Converter

Authors: Yaser Babazadeh; Mehran Sabahi; Ebrahim Babaei; Sun Kai
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

In this paper, a new interleaved bidirectional buck-boost DC-DC converter is proposed. The input current of this converter is continuous and has a low ripple, that cause reduction in the size of the input filter of the converter. Because of these features, this converter is appropriate for renewable applications such as fuel cells and photovoltaic (PV) panels for obtaining maximum power in which the continuity of the input current is essential. The operation principle of this converter is detailed, and its power losses calculation shows the positive effects of the low input current ripple on its efficiency. The input current ripple of the proposed converter and conventional interleaved buck-boost converter has been calculated in detail. In addition, the comparison results of this converter with conventional interleaved buck-boost converters and other similar structures confirm that the proposed converter without utilizing extra components achieves continuous input current with low ripple. Compared with other buck-boost structures, the low input current ripple in the presented converter causes an improvement in its efficiency. An experimental prototype is implemented in the laboratory to confirm the correctness of theoretical analyses.


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## Body

## 1. Introduction

Today, bidirectional DC-DC converters are used in many applications, such as electric vehicles, solar panels, fuel cells, and other renewable energy sources. The used battery in renewable sources can be charged using a bidirectional converter and discharged in low and high loads, respectively [1–4]. In applications such as fuel cells, electric vehicles, and power factor correction, to increase the system’s life, it is necessary to have a converter with a continuous input current with a small ripple [5–7]. The DC-DC converter plays a vital role in tracking the maximum power of a photovoltaic source. If the input current of this converter has a ripple, the obtained power from PV will fluctuate around the maximum PowerPoint. The value of this oscillation is directly related to the input current ripple of the converter. Therefore, as the currents ripple increases, power oscillation will be higher around the maximum power point [8, 9]. In the conventional buck-boost converter, the converter’s input current has a pulse form, which reduces the life of the used components in the converter structure [10]. Usually, on the input side of the converter, an inductor can be used to reduce the ripple of the input current; because of the proper design of the inductor, the input current can be continuous. In converters such as Cuk, this method has been used to reduce the ripple of the current. However, the number of circuit elements is higher, and the resulting cost increases [11]. The interleaved converter is used to increase the power transferred, increasing the efficiency and reducing the current and voltage ripple [12–14]. The presented structure in [5] includes a two-phase interleaved buck converter and a two-phase boost converter that has been connected in series together. The input and output current ripple can be reduced by using the boost and buck converter. Therefore, the structure presented in [5] has a continuous input/output current with low ripple. However, due to the series connection of the two interleaved converters, the efficiency of the proposed converter in [5] decreases because the number of converter elements is high, and additional conductive losses in the converter are created [15]. In [16], a converter has been introduced in a hybrid source storage system with low input and outputs current ripple. This converter can only operate in step-up mode and is not applicable for both step-up and step-down applications. In [17, 18], additional elements are used to reduce the ripple of the converter’s current; however, due to the increase in the number of elements in the current path, the power losses and cost of the converter increase and the efficiency decreases. In [19], an interleaved buck-boost converter has been presented. The presented converter is constructed of two parallel conventional buck-boost converters, and the input current ripple of this converter is considerable, and this is in discontinuous mode. Also, this converter is not capable of operating as a bidirectional converter, and this issue makes it is not a suitable interface device between the battery port and other ports. The presented structure in [20] operates as an interleaved buck converter. In the structure of this converter to achieve soft switching for one of the switches, an inductor has been used, but the efficiency improvement is not considerable. Also, like other mentioned converters, this converter has a ripple in its input current. By switching the switches in the input side of the converter, the input current gets in discontinuous mode. The presented converter in [21] operates as a buck converter, and this converter has more elements in its structure and has five switches that cause the conduction losses, and the switching losses of the converter increase, so its efficiency decreases.An interleaved buck converter is presented in [22], in which the step-down ratio is improved. Still, the input current is discontinuous, and the input current ripple ratio is close to the conventional one. In [23], a ZCS interleaved bidirectional buck-boost DC-DC converter is presented, appropriate for energy storage applications. Although the conventional interleaved converter has been improved with the auxiliary resonant cells, the input current ripple is still not improved. In addition, the power loss of the converter is not much increased compared with similar structures. According to [24, 25], the large current ripple causes to increase in its RMS value, which produces extra power losses, so the low input current has a vital role in the converter losses. In [26], a SEPIC-based converter is proposed to increase the voltage gain without using any coupled inductors and isolated transformers. Nevertheless, this noncoupled inductor converter still has a low voltage gain, and its high number of passive components causes adverse effects on the dynamic response of the converter. A new buck-boost converter derived from conventional boost and buck-boost converter is proposed in [27], but the stress across one switch is high, and the voltage gain in the boost range is limited.In this paper, a new interleaved bidirectional buck-boost DC-DC converter is presented in which, without using the additional elements, the ripple of the input current is reduced. Due to the lack of an auxiliary circuit to reduce the current ripple, the number of converter elements is less, and the losses of the converter get low. Due to the bidirectional operation of this converter, it can be used in renewable energy sources. The applied batteries in these sources can be charged and discharged using this converter. Because the battery is sensitive to currents ripple, the high-current ripple will reduce its life. It should be noted that increasing the gain is not the contribution of this paper. The paper detailed the different operation modes for the proposed structure for both forward and reverse power flow directions. In addition, the design of converter elements has been done, the input current ripple is calculated, and the converter efficiency is fully analyzed. The small-signal model of the proposed converter has been obtained, and the converter stability has been investigated. In addition, a comparison has been made between the proposed converter and other structures, and finally, the experimental results have been presented.


## 2. Structure of the Proposed Converter and Its Steady-State Analysis

Figure1(a) shows the proposed bidirectional interleaved buck-boost DC-DC converter structure. This converter uses four switches with reverse-parallel diodes, two inductors, and a capacitor. The input and output voltages are shown, respectively, with Vin and Vo, and R represents the load resistance. The converter switches work with the duty cycle D, and the applied commands to the switches gate have a 180-degree phase difference with each other. The switches S1 and S2 and the reverse-parallel diodes of switches S3 and S4 are used to transmit the power from the input to the load. For power flow in the reverse direction, the switches S3 and S4 are used, and this power passes through the reverse-parallel diodes of switches S1 and S2. The operation of this converter in each direction of power flow has four modes; in the following, different modes are given.Figure 1
(a) Proposed converter and its equivalent circuits in different modes in forward operation: (b) mode 1, (c) modes 2 and 4, and (d) mode 3.
(a)(b)(c)(d)


### 2.1. Forward Operation

The power transmission is through the switchesS1 and S2 and reverse-parallel diodes D3 and D4. In this case, the converter has four modes, all of which are listed in the following. The equivalent circuit for each mode and related key waveforms are shown in Figures 1 and 2(a), respectively.Figure 2
The key waveforms of the proposed converter elements in (a) forward buck operation and (b) reverse buck operation.
(a)(b)Mode 1 t0<t<t1: during this mode, the switch S1 and diode D3 are turned on, and the input voltage is applied to the L1 via the switch S1 and magnetized it, and the inductor current increases linearly. Also, the output voltage is inversely applied to L2, and its current decreases linearly. The currents of the inductors are given by (1) and (2) (Figure 1(b)):(1)iL1t=ViL1t+iL1t0,(2)iL2t=−VoL2t+iL2t0.The peak value ofiL1 occurs at t1; therefore, using (1), the value of the ripple of the iL1 is obtained as follows:(3)ΔIL1=VifsL1D.When the switchS1 is turned off at t1, this mode ends, and the next mode starts.Mode 2 t1<t<t2: in this mode, the switch S1 is turned off, and the reverse-parallel diodes D4 and D3 are directly biased, and the stored energy in the inductors is demagnetized to the load through these diodes. VL1 and VL2 are equal to −Vo, and the currents iL1 and iL2 decrease linearly. The voltage of the switches S1 and S2 is clamped to Vi + Vo (Figure 1(c)). When the switch S2 is turned on at t2, this mode ends, and the next mode starts.Mode 3 t2<t<t3: in this mode, the switch S2 is turned on, the reverse-parallel diode D4 is directly biased, the voltage of the inductor L1 is equal to −Vo, and the current iL1 decreases linearly according to (4).The input voltage is applied to the inductorL2 via the switch S2, and the current iL2 increases linearly according to (5) (Figure 1(d)):(4)iL1t=−VoL1t−t2+iL1t2,(5)iL2t=ViL2t−t2+iL2t2.The peak value ofiL2 occurs at t3. Therefore, using (5), the value of the ripple of iL2 is obtained as follows:(6)ΔIL2=VifsL2D.When the switchS2 is turned off at t3, this mode ends, and the next mode starts.Mode 4 t3<t<t4: at t3, the switch S2 is turned off, the reverse-parallel diode D3 is directly biased, and D4 still is in on state. Through these diodes, the inductors are demagnetized to the load. The voltages vL1 and vL2 are equal to −Vo, and the currents iL1 and iL2 are decreased linearly. In this mode, the voltage of the switches S1 and S2 is clamped to Vi + Vo (Figure 1(c)).


### 2.2. Reverse Operation

The load acts as an energy source in this mode, and the power is transferred from the output to the input source. For this purpose, the switchesS1 and S2 are turned off, and the command signals are applied to the switches S3 and S4. The power transmission is through switches S3 and S4 and reverse-parallel diodes D1 and D2. Like the forward operation, the converter has four modes in this mode. Figure 3(a) shows the circuit related to this operation with the elements used to transfer power in the reverse direction. The equivalent circuit for buck operation and their key waveforms are shown in Figures 3(b) and 3(c) and Figure 2(b), respectively.Figure 3
(a) The proposed converter and its equivalent circuit in different modes in reverse operation: (b) mode 1, (c) modes 2 and 4, and (d) mode 3.
(a)(b)(c)(d)Mode 1 t0<t<t1: during this mode, the switch S4 and the diode D2 are turned on and the voltage Vo is applied through the switch S4 to the inductor L1 and charges it. In this mode, the inductor current iL1 increases linearly according to (7). Also, the voltage Vi inversely is applied to the inductor L2 and discharges it, and its current decreases linearly according to (8) (Figure 3(b)):(7)iL1t=VoL1t+iL1t0,(8)iL2t=−ViL2t+iL2t0.The peak value ofiL1 occurs at t1. Therefore, using (7), the value of the ripple of iL1 is obtained as follows:(9)ΔiL1=VifsL1D.When the switchS4 is turned off at t1, this mode ends, and the next mode starts.Mode 2 t1<t<t2: the switch S4 is turned off in this mode, and the reverse-parallel diodes D1 and D2 are turned on. The energy stored in the inductors is discharged to the input source through these diodes. The voltages vL1 and vL2 are equal to −Vi, and the currents iL1 and iL2 decrease linearly. The voltages of the switches S3 and S4 are clamped to vi + vo (Figure 3(c)). When the switch S3 is turned on at t2, this mode ends, and the next mode starts.Mode 3 t2<t<t3: at t2, switch S3 turns on, and the diode D1 is still in on state. The voltage Vi through this diode is inversely applied to the inductor L1, and its current decreases linearly according (10). Applying the voltage Vo to the inductor L2, its current increases linearly according (11) (Figure 3(d)).(10)iL1t=−ViL1t−t2+iL1t2,(11)iL2t=VoL2t−t2+iL2t2.The peak value ofiL2 occurs at t3. Therefore, using (11), the value of the ripple of the iL2 is obtained as follows:(12)ΔiL2=VofsL2D.When the switchS3 is turned off at t3, this mode ends, and the next mode starts.Mode 4 t3<t<t4: at t3, the switch S3 is turned off, the reverse-parallel diode D2 is directly biased, and D1 is still in on state. The energy stored in the inductors discharges to the input source through these diodes. The voltages vL1 and vL2 equal −Vi, and the currents iL1 and iL2 decrease linearly. In this mode, the voltages of the switches S3 and S4 are clamped to Vi + Vo (Figure 3(c)).Also, in boost operation, the voltage and current of the inductors in each mode for forward and reverse operation are presented in Table1. The key waveforms for these operation modes can be obtained using this table.Table 1
Inductors applied voltage in forward and reverse boost operation.
CaseOperationMode 1Mode 2Mode 3Mode 4vL1ForwardViViVi−VoReverseVoVoVo−VivL2ForwardVi−VoViViReverseVo−ViVoVo


### 2.3. Voltage Conversion Ratio

The voltage conversion ratio of the proposed converter in both directions is similar to each other; therefore, in this section, voltage gain is obtained for one direction. In forward operation, using volt-second law for an inductor and taking into account thatt3-t2 = t1-t0 = D, the voltage conversion ratio of the converter is obtained as follows:(13)VoVi=D1−D.It can be seen from (13) that the voltage conversion ratio of the proposed converter is the same as a conventional buck-boost converter. Also, the voltage of the capacitor is obtained as follows:(14)vc=11−DVi.


### 2.4. Discontinuous Conduction Mode

The presented converter’s operation is divided into four modes in this mode. Mode 1 and mode 3 in DCM, respectively, are the same as that of mode 2 and mode 4 in CCM, and in mode 2, the currents of switchesS1 and S2 and diode D3 are zero. In addition, in mode 4, the currents of semiconductors (except D3) are zero. These modes and the related typical waveforms are shown in Figures 4 and 5, respectively. The current ripple of the inductors still is according to (9) and (12). If the average value of the inductor current is greater than half of its current ripple (according to equation (15)), then the current of the inductor would be continuous.(15)IL=Io21−D>ΔiL2=ViD2Lfs,in which IL = IL1 = IL2 and L = L1 = L2. By replacing (12) in (15), the relationship between duty cycle (D) and constant parameters (L, fs, and Ro) is obtained as follows:(16)1−D2<LfsRo.Figure 4
Different modes of the proposed converter in DCM: (a) mode 1, (b) modes 2, (c) mode 3, and (d) mode 4.
(a)(b)(c)(d)Figure 5
Typical waveforms of the proposed converter in DCM.By considering the normalized inductor time constant asτb = Lfs/Ro, according to equation (16), τ is a function of the duty cycle. If the value of τ is lower than its critical value (τb), the operation of the converter will be in discontinuous mode; otherwise, it will be in continuous mode. In Figure 6, the curve τb is shown. According to this figure, the operation region of the proposed converter in CCM is larger than DCM.Figure 6
Normalized inductor time constant versus duty cycle D.From Figure6, it can be concluded that the boundary normalized inductor time constant (τb) for the presented converter is the same as the conventional interleaved buck-boost converter.In order to calculate the voltage gain in discontinuous conduction mode, the volt-second balance principle of inductors is used. This principle for inductorL1 can be expressed as follows.(17)1Ts∫0TVL1dt=D1Vi+D2Vo+D30=0.Thus, the voltage conversion ratio is obtained as follows:(18)VoVi=D1D2.According to Figure5, in time interval D2Ts, the capacitor, respectively, is charged and discharged by the inductor and load. The DC output current is calculated as follows:(19)Io=1Ts∫0TsiD3t+iD4tdt=2×D2ΔiL2=VoRo.Hence, by substituting (15) and (18) in (19), duty cycle D2 in the second mode can be obtained as follows:(20)ViD1D2Lfs=D1ViD2Ro,(21)D2=LfsRo=τb,where τb = Lfs/Ro. Using (18) and (21), the voltage conversion ratio can be derived as follows:(22)VoVi=D1τb.Thus, the voltage conversion ratio of the presented converter is the same gain as that of the conventional interleaved buck-boost converter in DCM.


### 2.5. Switches Voltage Stress

As shown in Figures1 and 3, in forward and reverse operations, the voltage stress of switches S1–S4 is calculated as follows:(23)Vsw=VoD.According to (23), it concluded that the voltage across switches in the proposed converter and the conventional buck-boost converter are equal.


## 2.1. Forward Operation

The power transmission is through the switchesS1 and S2 and reverse-parallel diodes D3 and D4. In this case, the converter has four modes, all of which are listed in the following. The equivalent circuit for each mode and related key waveforms are shown in Figures 1 and 2(a), respectively.Figure 2
The key waveforms of the proposed converter elements in (a) forward buck operation and (b) reverse buck operation.
(a)(b)Mode 1 t0<t<t1: during this mode, the switch S1 and diode D3 are turned on, and the input voltage is applied to the L1 via the switch S1 and magnetized it, and the inductor current increases linearly. Also, the output voltage is inversely applied to L2, and its current decreases linearly. The currents of the inductors are given by (1) and (2) (Figure 1(b)):(1)iL1t=ViL1t+iL1t0,(2)iL2t=−VoL2t+iL2t0.The peak value ofiL1 occurs at t1; therefore, using (1), the value of the ripple of the iL1 is obtained as follows:(3)ΔIL1=VifsL1D.When the switchS1 is turned off at t1, this mode ends, and the next mode starts.Mode 2 t1<t<t2: in this mode, the switch S1 is turned off, and the reverse-parallel diodes D4 and D3 are directly biased, and the stored energy in the inductors is demagnetized to the load through these diodes. VL1 and VL2 are equal to −Vo, and the currents iL1 and iL2 decrease linearly. The voltage of the switches S1 and S2 is clamped to Vi + Vo (Figure 1(c)). When the switch S2 is turned on at t2, this mode ends, and the next mode starts.Mode 3 t2<t<t3: in this mode, the switch S2 is turned on, the reverse-parallel diode D4 is directly biased, the voltage of the inductor L1 is equal to −Vo, and the current iL1 decreases linearly according to (4).The input voltage is applied to the inductorL2 via the switch S2, and the current iL2 increases linearly according to (5) (Figure 1(d)):(4)iL1t=−VoL1t−t2+iL1t2,(5)iL2t=ViL2t−t2+iL2t2.The peak value ofiL2 occurs at t3. Therefore, using (5), the value of the ripple of iL2 is obtained as follows:(6)ΔIL2=VifsL2D.When the switchS2 is turned off at t3, this mode ends, and the next mode starts.Mode 4 t3<t<t4: at t3, the switch S2 is turned off, the reverse-parallel diode D3 is directly biased, and D4 still is in on state. Through these diodes, the inductors are demagnetized to the load. The voltages vL1 and vL2 are equal to −Vo, and the currents iL1 and iL2 are decreased linearly. In this mode, the voltage of the switches S1 and S2 is clamped to Vi + Vo (Figure 1(c)).


## 2.2. Reverse Operation

The load acts as an energy source in this mode, and the power is transferred from the output to the input source. For this purpose, the switchesS1 and S2 are turned off, and the command signals are applied to the switches S3 and S4. The power transmission is through switches S3 and S4 and reverse-parallel diodes D1 and D2. Like the forward operation, the converter has four modes in this mode. Figure 3(a) shows the circuit related to this operation with the elements used to transfer power in the reverse direction. The equivalent circuit for buck operation and their key waveforms are shown in Figures 3(b) and 3(c) and Figure 2(b), respectively.Figure 3
(a) The proposed converter and its equivalent circuit in different modes in reverse operation: (b) mode 1, (c) modes 2 and 4, and (d) mode 3.
(a)(b)(c)(d)Mode 1 t0<t<t1: during this mode, the switch S4 and the diode D2 are turned on and the voltage Vo is applied through the switch S4 to the inductor L1 and charges it. In this mode, the inductor current iL1 increases linearly according to (7). Also, the voltage Vi inversely is applied to the inductor L2 and discharges it, and its current decreases linearly according to (8) (Figure 3(b)):(7)iL1t=VoL1t+iL1t0,(8)iL2t=−ViL2t+iL2t0.The peak value ofiL1 occurs at t1. Therefore, using (7), the value of the ripple of iL1 is obtained as follows:(9)ΔiL1=VifsL1D.When the switchS4 is turned off at t1, this mode ends, and the next mode starts.Mode 2 t1<t<t2: the switch S4 is turned off in this mode, and the reverse-parallel diodes D1 and D2 are turned on. The energy stored in the inductors is discharged to the input source through these diodes. The voltages vL1 and vL2 are equal to −Vi, and the currents iL1 and iL2 decrease linearly. The voltages of the switches S3 and S4 are clamped to vi + vo (Figure 3(c)). When the switch S3 is turned on at t2, this mode ends, and the next mode starts.Mode 3 t2<t<t3: at t2, switch S3 turns on, and the diode D1 is still in on state. The voltage Vi through this diode is inversely applied to the inductor L1, and its current decreases linearly according (10). Applying the voltage Vo to the inductor L2, its current increases linearly according (11) (Figure 3(d)).(10)iL1t=−ViL1t−t2+iL1t2,(11)iL2t=VoL2t−t2+iL2t2.The peak value ofiL2 occurs at t3. Therefore, using (11), the value of the ripple of the iL2 is obtained as follows:(12)ΔiL2=VofsL2D.When the switchS3 is turned off at t3, this mode ends, and the next mode starts.Mode 4 t3<t<t4: at t3, the switch S3 is turned off, the reverse-parallel diode D2 is directly biased, and D1 is still in on state. The energy stored in the inductors discharges to the input source through these diodes. The voltages vL1 and vL2 equal −Vi, and the currents iL1 and iL2 decrease linearly. In this mode, the voltages of the switches S3 and S4 are clamped to Vi + Vo (Figure 3(c)).Also, in boost operation, the voltage and current of the inductors in each mode for forward and reverse operation are presented in Table1. The key waveforms for these operation modes can be obtained using this table.Table 1
Inductors applied voltage in forward and reverse boost operation.
CaseOperationMode 1Mode 2Mode 3Mode 4vL1ForwardViViVi−VoReverseVoVoVo−VivL2ForwardVi−VoViViReverseVo−ViVoVo


## 2.3. Voltage Conversion Ratio

The voltage conversion ratio of the proposed converter in both directions is similar to each other; therefore, in this section, voltage gain is obtained for one direction. In forward operation, using volt-second law for an inductor and taking into account thatt3-t2 = t1-t0 = D, the voltage conversion ratio of the converter is obtained as follows:(13)VoVi=D1−D.It can be seen from (13) that the voltage conversion ratio of the proposed converter is the same as a conventional buck-boost converter. Also, the voltage of the capacitor is obtained as follows:(14)vc=11−DVi.


## 2.4. Discontinuous Conduction Mode

The presented converter’s operation is divided into four modes in this mode. Mode 1 and mode 3 in DCM, respectively, are the same as that of mode 2 and mode 4 in CCM, and in mode 2, the currents of switchesS1 and S2 and diode D3 are zero. In addition, in mode 4, the currents of semiconductors (except D3) are zero. These modes and the related typical waveforms are shown in Figures 4 and 5, respectively. The current ripple of the inductors still is according to (9) and (12). If the average value of the inductor current is greater than half of its current ripple (according to equation (15)), then the current of the inductor would be continuous.(15)IL=Io21−D>ΔiL2=ViD2Lfs,in which IL = IL1 = IL2 and L = L1 = L2. By replacing (12) in (15), the relationship between duty cycle (D) and constant parameters (L, fs, and Ro) is obtained as follows:(16)1−D2<LfsRo.Figure 4
Different modes of the proposed converter in DCM: (a) mode 1, (b) modes 2, (c) mode 3, and (d) mode 4.
(a)(b)(c)(d)Figure 5
Typical waveforms of the proposed converter in DCM.By considering the normalized inductor time constant asτb = Lfs/Ro, according to equation (16), τ is a function of the duty cycle. If the value of τ is lower than its critical value (τb), the operation of the converter will be in discontinuous mode; otherwise, it will be in continuous mode. In Figure 6, the curve τb is shown. According to this figure, the operation region of the proposed converter in CCM is larger than DCM.Figure 6
Normalized inductor time constant versus duty cycle D.From Figure6, it can be concluded that the boundary normalized inductor time constant (τb) for the presented converter is the same as the conventional interleaved buck-boost converter.In order to calculate the voltage gain in discontinuous conduction mode, the volt-second balance principle of inductors is used. This principle for inductorL1 can be expressed as follows.(17)1Ts∫0TVL1dt=D1Vi+D2Vo+D30=0.Thus, the voltage conversion ratio is obtained as follows:(18)VoVi=D1D2.According to Figure5, in time interval D2Ts, the capacitor, respectively, is charged and discharged by the inductor and load. The DC output current is calculated as follows:(19)Io=1Ts∫0TsiD3t+iD4tdt=2×D2ΔiL2=VoRo.Hence, by substituting (15) and (18) in (19), duty cycle D2 in the second mode can be obtained as follows:(20)ViD1D2Lfs=D1ViD2Ro,(21)D2=LfsRo=τb,where τb = Lfs/Ro. Using (18) and (21), the voltage conversion ratio can be derived as follows:(22)VoVi=D1τb.Thus, the voltage conversion ratio of the presented converter is the same gain as that of the conventional interleaved buck-boost converter in DCM.


## 2.5. Switches Voltage Stress

As shown in Figures1 and 3, in forward and reverse operations, the voltage stress of switches S1–S4 is calculated as follows:(23)Vsw=VoD.According to (23), it concluded that the voltage across switches in the proposed converter and the conventional buck-boost converter are equal.


## 3. Converter Design

### 3.1. Inductor Design

Since the average current of the inductorsL1 and L2 are equal, the design for L1 is given and the design of the L2 is similar to L1. In Figure 7, the waveform of the current of inductor L1 is shown in a critical condition. By using this waveform, the minimum values of the inductors L1 and L2 can be obtained. As shown in Figure 7, the inductor current reaches its maximum value in time interval DTs. Therefore, the maximum value of the current ripple of inductor L1 will be equal to(24)ΔIL1,max=Vo1−DminfsL1,min.Figure 7
Current waveform of the inductorL1 in boundary mode.As shown in (25), in the critical condition, the current of the inductor L1 is equal to half of the current ripple.(25)IL1,B=Vo1−Dmin2fsL1,min.Since the average current of the inductors is equal and the average current of the capacitorC is zero,(26)Ii+Io=IL1+IL2.The average currents ofIL1 and IL2 can be calculated as follows:(27)IL1=IL2=Io21−D.Using (25) and (27), the critical output current Io,B is obtained by(28)Io,B=Vo1−Dmin2fsL1,min.According to (28), the minimum values of the inductors L1 and L2 are given by(29)L1,min=L2,min=Ro,max1−Dmin2fs.


### 3.2. Capacitor Design

The design of capacitorC is based on the value of the voltage ripple of this capacitor so that the ripple does not exceed its maximum permissible value. Using (27) and (28), in the first mode of forward operation, the capacitor current is given by(30)ict=Io−iL2t=Io+VoL2t−iL2t0.The ac component of the output voltage is the sum of the voltage across the capacitor ESR (rC) and the capacitance C. Using (6), (27), and (30), vo can be calculated.Using the derivative of the voltagevo with respect to time, the minimum value of vo is obtained. This occurs at a minimum capacitance, given by(31)C≥2Ro1−D2−fsL21−2D2rcRofs1−D.


## 3.1. Inductor Design

Since the average current of the inductorsL1 and L2 are equal, the design for L1 is given and the design of the L2 is similar to L1. In Figure 7, the waveform of the current of inductor L1 is shown in a critical condition. By using this waveform, the minimum values of the inductors L1 and L2 can be obtained. As shown in Figure 7, the inductor current reaches its maximum value in time interval DTs. Therefore, the maximum value of the current ripple of inductor L1 will be equal to(24)ΔIL1,max=Vo1−DminfsL1,min.Figure 7
Current waveform of the inductorL1 in boundary mode.As shown in (25), in the critical condition, the current of the inductor L1 is equal to half of the current ripple.(25)IL1,B=Vo1−Dmin2fsL1,min.Since the average current of the inductors is equal and the average current of the capacitorC is zero,(26)Ii+Io=IL1+IL2.The average currents ofIL1 and IL2 can be calculated as follows:(27)IL1=IL2=Io21−D.Using (25) and (27), the critical output current Io,B is obtained by(28)Io,B=Vo1−Dmin2fsL1,min.According to (28), the minimum values of the inductors L1 and L2 are given by(29)L1,min=L2,min=Ro,max1−Dmin2fs.


## 3.2. Capacitor Design

The design of capacitorC is based on the value of the voltage ripple of this capacitor so that the ripple does not exceed its maximum permissible value. Using (27) and (28), in the first mode of forward operation, the capacitor current is given by(30)ict=Io−iL2t=Io+VoL2t−iL2t0.The ac component of the output voltage is the sum of the voltage across the capacitor ESR (rC) and the capacitance C. Using (6), (27), and (30), vo can be calculated.Using the derivative of the voltagevo with respect to time, the minimum value of vo is obtained. This occurs at a minimum capacitance, given by(31)C≥2Ro1−D2−fsL21−2D2rcRofs1−D.


## 4. Input Current Ripple

ForD < 0.5, in forward operation, the input current in different modes is a function of the current of the inductors and the load as described as follows:(32)ii=iL1+iL2−io.By using the currents equations of inductorsL1 and L2 in various modes, the following equation is obtained:(33)ii=ViL1−VoL2t+iL1t0+iL2t0−io,t0<t<t1,−VoL1+VoL2t−t1+iL1t1+iL2t1−io,t1<t<t2,ViL2−VoL1t−t2+iL1t2+iL2t2−io,t2<t<t3,−VoL1+VoL2t−t3+iL1t3+iL2t3−io,t3<t<t4.Using (33), the value of the input current ripple can be calculated as follows:(34)ΔIi,proposed=iiDTS−ii0=VofsL21−D−DL1L1L2.IfL1 = L2 = L, (26) can be simplified as follows:(35)ΔIi,proposed=VoLfs1−2D.ForD > 0.5, in the case where the proposed converter acts as a step-up in the forward operation, the inductor L1 and L2 currents are given by the following equations, respectively:(36)iL1=VoL1t+iL1t0,t0<t<t3,−ViL1t−t3+iL1t3,t3<t<t4,(37)iL2=VoL2t+iL2t0,t0<t<t1,−ViL2t−t1+iL2t1,t1<t<t2,VoL2t+iL2t2,t2<t<t4.IfL1 = L2 = L, then using (36) and (37), in one switching period, the input current equations can be calculated in all modes as follows:(38)ii=2VoLt+iL1t0+iL2t0−io,t0<t<t1&t2<t<t3,Vi−VoLt−t1+iL1t1+iL2t1−io,t1<t<t2&t3<t<t4.For the proposed converter in step-up mode, by using (38), the input current ripple is obtained as follows:(39)ΔIi,proposed=21−DD−0.5VoDLfs.In a conventional two-phase interleaved buck-boost converter, assumingL1 = L2 = L, the input current ripple for D < 0.5 and D > 0.5 is calculated according to the following equations:(40)ΔIi,conv=Vo1Ro1−D+1−D2fsL,forD<0.5,(41)ΔIi,conv=VifsLD,forD>0.5.Using (35), (39), (40), and (41), the ratio of the input current ripple of the proposed converter to the input current ripple of the conventional interleaved buck-boost converter for D < 0.5 and D > 0.5 is obtained as (42) and (43), respectively. According to (42), in step-down mode, by increasing the power and frequency, the ratio of the input current ripple of the proposed converter decreases with respect to the conventional converter.(42)ΔIi,proposedΔIi,conv=1−2DLfs/Ro1−D+1−D/2,(43)ΔIi,proposedΔIi,conv=2D−1D.The curve of the input current ripple ratio of the proposed converter to the input current ripple of the conventional interleaved buck-boost converter is shown in Figure8. According to this figure, this ratio is less than 1 for all duty cycles, and the input current ripple of the proposed converter in buck mode is less than the conventional interleaved buck-boost converter.Figure 8
The ratio of the input current ripple of the proposed converter to the input current ripple of the conventional interleaved buck-boost converter.According to the analyzes performed in Sections2.5 and 4 and using equations (3), (15), (16), (42), and (43), the three-dimensional curve of normalized inductor time constant (τb) with respect to duty cycle (D) and input current ripple ratio (∆iProposed/∆iConventional) for the buck and boost operation modes is provided as shown in Figure 9. The upper and lower level of the surface corresponds to continuous conduction mode (CCM) and discontinuous mode (DCM), respectively. As can be seen, for different values of duty cycle and τb, the input current ripple ratio (∆iProposed/∆iConventional) is less than 1, representing that the presented converter’s input current ripple is less than the conventional interleaved buck-boost converter.Figure 9
Normalized inductor time constant with respect to duty cycle and input current ripple ratio: (a) buck operation and (b) boost operation.
(a)(b)


## 5. Power Losses Calculation

The operation of the proposed converter in the forward mode is similar to the reverse mode. In other words, the currents of the elements are the same in two operations, and the same voltage is applied to the elements. Therefore, to calculate the losses of the converter and its efficiency, the equivalent circuit of the forward operation is used as shown in Figure10. In this circuit, the parasitic components of all elements are shown. In this figure, RF is equal to the resistance of the diode in conduction mode, VF is the diode conduction threshold voltage, rL is the equivalent series resistance of inductor L, rc is the equivalent series resistance of capacitor C, and rDS stands for the total resistance between the drain and source in a switch when the switch is on. Using definitions of the RMS and average values, the power losses of the switch, diode, inductor, and capacitor are obtained as listed in Table 2.Figure 10
The equivalent circuit of the proposed converter with parasitic resistances and diodes conduction threshold voltage.Table 2
Calculated losses of components.
SymbolLossesPSwitchPorDS1D/4Ro1−D2+fsCs1Ro/D2PDPoRF,D4/4Ro1−D+VF/2VoPr,L1rL1Po/4Ro1−D2Pr,CD1−2DrcPo/2Ro1−D2According to Figure10, the total power loss is calculated as follows:(44)Ploss=2PSwitch+PD+PrL+Prc.Using (44) and Table 2, the converter efficiency is equal to(45)η=PoPo+Ploss.The efficiency curves versus output power of the proposed converter in boost and buck modes are illustrated in Figure11. As can be seen from this figure, the measured efficiency is a little lower than the calculated losses. For boost and buck operation modes, this converter at 50 W load has a maximum efficiency of 95.6% and 95.4%, respectively. For smaller and larger loads than 50 W, the converter’s efficiency decreases because for loads less than 50 W and the switching losses are high. For loads greater than 50 W, the conduction losses increase, and efficiency decreases. In the rated power, the efficiency in boost and buck modes is equal to 93.9% and 93.4%, respectively. According to Figure 11, the efficiency of the theoretical is slightly different with experimental one. In practice, due to conduction losses and differences in the performance of practical elements, different efficiencies will be obtained. In general, the value of this difference is not so great and for the presented converter is equal to 0.5%. For example, the performance of the same power components (diode and switch) cannot be exactly the same. This is related to the internal structure and factory production of the component. As a result of conduction losses, differences in the internal structure of exactly the same power components and errors due to measuring devices (such as internal resistances or some external conditions of the environment, such as pressure, temperature, humidity, or magnetic field) are the most important factors that cause differences between the experimental and simulation efficiency values.Figure 11
Converter efficiency curve versus output power.


## 6. Relation between Input Current Ripple and Converter Efficiency

In addition, in the following, the effects of the input current ripple on the converter efficiency are discussed, and the relation between these two parameters is derived. The current of inductorL1, switch S, diode D, and capacitor C in different time intervals is as follows:(46)iL=ΔiLDTst+iL1t0,0<t<DTs,−ΔiL1−DTst−DTs+iLDTs,DTs<t<1−DTs,(47)iS=ΔiLDTst+iL1t0,0<t<DTs,0,DTs<t<1−DTs,(48)iD=0,0<t<DTs,−ΔiL1−DTst−DTs+iLDTs,DTs<t<1−DTs,in which the amplitude of iL(0) and iL(DTs) is obtained using(49)iLt0=Io21−D−ΔiL2,(50)iLDTs=Io21−D+ΔiL2.Using (47), (49), and (50), the effective currents of the switches S1 and S2 are obtained as follows:(51)IS1,rms=IS2,rms=DΔiL212−DIoΔiL21−D+DI0241−D2.The switch losses of the converter include two components, including conduction losses and switching losses. The component losses of Figure2 are calculated and then multiplied in 2 to obtain the proposed converter losses. The conduction losses of the switches can be calculated by the following:(52)PrDS1=rDS1DΔiL212−DIoΔiL21−D+DI0241−D2.The switching losses are also obtained as follows:(53)PSWS1==fsCs1PoRoD2.The losses of the switch are equal to the sum of the conduction and switching losses; therefore, the total losses associated with the switches are equal to the following:(54)PSwitch=2rDS1DΔiL212−DIoΔiL21−D+DIo241−D2+fsCs1PoRoD2.Using (47), (49), and (50), the effective currents of diodes D3 and D4 are obtained as follows:(55)ID3,rms=ID4,rms=ΔiL25D−212+ΔiL1−Io2+Io21−D.The average currents of the diodesD3 and D4 are obtained as follows:(56)ID3=ID4=Io2.The power losses inRF of diodes are equal to the following:(57)PRF=RF,D4ΔiL25D−212+ΔiL1−Io2+Io21−D.Using (55), the power losses associated with the diode conduction threshold voltage can be calculated as follows:(58)PVF==VFPo2Vo.The diode losses are equal to the sum of (57) and (58). Therefore, the overall loss of diodes is equal to the following:(59)PD=2RF,D4ΔiL25D−212+ΔiL1−Io2+Io21−D+VFPo2Vo.Equation (60) is used to calculate the power losses of the equivalent series resistance of the inductance:(60)IL1,rms=ΔiL26D−212+ΔiL1−D−Io21−D+DIo241−D2+Io21−D,(61)PrL1=rL1ΔiL26D−212+ΔiL1−D−Io21−D+DIo241−D2+Io21−D.In order to calculate the equal series resistance losses of the capacitorC and the effective current of capacitor C, equation (62) is used, and this loss is calculated as (63).(62)Ic,rms=Io2−ΔiL25D−26+ΔiL1−Io+Io1−D,(63)Prc=rcIo2−ΔiL25D−26+ΔiL1−Io+Io1−D.The total power losses of the converter are obtained using the following:(64)Ploss=PSwitch+PD+PrL+Prc.Using (54), (59), (61), (63), and (64), the converter efficiency is equal to the following:(65)η=PoPo+Ploss=PoPo+aΔiL2+bΔiL+c,where(66)a=rDS1D6+RF,D45D−26+rL16D−212−rc5D−26,(67)b=−rDS1DIo1−D+RF,D41−Io+rL11−D−Io21−D+rc1−Io,(68)c=DIo221−D2rDS1+rL12+Io1−DRF,D4+rL12+rc+2fsCs1PoRoD2+VFPo2Vo+rcIo2.Using (33), the relation between input current ripple and inductor current ripple is obtained as follows:(69)Δii=iit1−iit0=iL1t1+iL2t1−iL1t0−iL2t0=ΔiL1+iL2t1−iL2t0.According to Figure2, iL2(t1) − iL2(t0) has a negative value, so the input current is less than the value of the inductor current ripple. Also, according to equation (69), the input current ripple is directly related to the inductor current ripple. Therefore, with the increase in the input current ripple, the inductor current ripple also increases. The effective value of the component current increases, and as proved in equations (54), (59), (61), and (63), the converter losses increase, and according to (65), the converter efficiency decreases.


## 7. Dynamic Modeling

In this section, the dynamic model of the proposed converter is presented. Since the input current is divided equally between phases, the equivalent circuit is used to model the proposed converter [18]. Modeling for the equivalent circuit of the converter in forward operation is performed. For this purpose, according to Figure 12, a phase has been used in which the actual model of the inductor and capacitor is used. In Figure 12, L = L1/2 and rL = rL1/2 and the switch S1 is in on state for DTs during a switching period and for (1 − D)Ts is in off state. In these intervals, the equations for the inductor voltages and capacitor currents are given by(70)vLt=Vi−rLiL,0<t<DTs,−Vo−rLiL,DTs<t<Ts,(71)ict=Io,0<t<DTs,Io−iL,DTs<t<Ts.Figure 12
Single-phase equivalent circuit of the proposed converter with parasitic elements.In order to achieve the average model of the converter, an average method for states variables is used. By applying this method on (70) and (71), the average model of the proposed converter is obtained as follows:(72)f1x=diLdt=ViL−rLLiL−1−dLvc,(73)f2x=dvcdt=1RoCvc−ViRoC−1−dCiL.The relationship between the output voltage and the states variables is also in a steady state and is given by(74)Vo=vc−Vi.To analyze the system’s dynamic behavior, a small-signal model is used. To obtain the small-signal model, the following states space equations are used:(75)x˜˙=Ax˜+Bu˜=fx,u,y˜=Cx˜+Du˜=hx,u,where x, u, and y denote states variables, input, and output, respectively, and A, B, C, and D are matrices and calculated by(76)ABCD=∂fx,u∂xxe,ue∂fx,u∂uxe,ue∂hx,u∂xxe,ue∂hx,u∂uxe,ue.In (76), ue and xe represent the equilibrium points for state variables and inputs, respectively. Using (72)–(76), the following equations are obtained:(77)di^Ldtdv^Cdt=−rLL−1−DL−1−DC1RoCi^Lv^C+1LVcL−1RoCILCv^id^,(78)Vo=01000010i^Lv^C+−10v^id^.Considering (75), the output-to-input transfer function is obtained as follows:(79)G=CSI−A−1B+D.Using (77)–(79) and Laplace transforms, the output voltage transfer functions to the input voltage and the output voltage to the duty cycle are obtained as follows, respectively:(80)GVoVis=L2Cs+RoL2C2−1−DRoLC−rLRoLC1−D2s2+Ro1−D2rcC−1s−rL1−D2,(81)GVods=RoCILs+RoCrLIL−RoVC1−DRoLC1−D2s2+Ro1−D2rcC−1s−rL1−D2.The amplitudes of the variables in equations (80) and (81) and the ESR of inductors L1 and L2 and capacitor C are listed in Table 3. The Bode diagram for transfer functions (56) and (57) is shown in Figure 13(a) and Figure 13(b), respectively. This figure shows that proposed converter has a positive phase margin and gain margin for all transfer functions that approve the proposed converter’s stability.Table 3
Used parameters in experimental prototype.
ParametersValuesInput voltage (Vin)50 VOutput voltage (Vo)Buck 35 VBoost 75 VOutput power (Po)200 WSwitching frequency (fs)30 kHzSeri capacitanceC(rC)100µF (79mΩ)InductorL1, L2 (rL)450µH (100mΩ)Duty cycle (Buck),D0.41Duty cycle (Boost),D0.6SwitchesIRFP260nFigure 13
Bode diagram of the proposed converter for the output voltage transfer function to the (a) input voltage; (b) duty cycle.
(a)(b)


## 8. Comparison of the Proposed Converter with Other Structures

To confirm the advantage of the proposed converter, it has been compared with the conventional interleaved buck-boost converter (CIBBC) and other structures. Different indexes such as the number of components, input current ripple, and continuity or discontinuity of the input current are used for comparison, and the results are listed in Table4.Table 4
Comparison of the proposed converter with other similar structures.
CaseNo. of componentMaximumefficiency (%)Normalized input current ripple (ΔIi/Ii)Input currentSwitchDiodeCapacitorInductorTotalD > 0.5D < 0.5Proposed converter4012795.621−D2D−0.5Ro/D2LfsRo2D2−3D+1/DLfsContinuousCIBBC4012888.6Ro1−D2/DfsL2fsL+Ro1−D2/2DfsLDiscontinuous[19]2213897.72−D/2DfsL2−D+Ro1−D2/2DfsLDiscontinuous[20]2213794.7fsL1−D+Ro2D2−3D+1/2DfsLDiscontinuous[21]50321091.5Ro2D2−5D+3/3DfsLDiscontinuous[22]2222893fsL1−D+Ro1−D2/2DfsLDiscontinuous[23]60341390.321−D2/DfsLContinuous[26]136414949DfsL1R+1−D2/9DfsL1RoContinuous[27]23321093.91−D4+4DfsL1Ro/4DfsL1RoContinuousAs shown in Table4, the proposed converter in all operation modes has a continuous input current. However, the input current of the conventional interleaved buck-boost converter and presented structure in [19] for buck operation is discontinuous, and the presented structures in [20–22] have a discontinuous input current for all duty cycles. In addition, the ratio of the input current ripple of the proposed converter versus other structures (Δi,proposed/Δi,x {x = CIBBC, [19, 20]}) is provided in Figure 14, in which Figures 14(a) and 14(b) refer to the buck and boost mode, respectively.Figure 14
Input current ripple ratio in (a) buck operation and (b) boost operation.
(a)(b)A ratio of less than 1 indicates that the input current of the proposed converter is less than that of other converters. According to Figure14(a), in the proposed converter, the input current ripple for D < 0.5 is minimal compared with other structures. As the duty cycle increases, the input current ripple ratio decreases so that the converter’s input current ripple canceling capability occurs in the duty cycle equal to 50%. A ripple less current has been drawn from the power source in this duty cycle.According to Figure14(b), for D > 0.5, the input current of the proposed converter is minimal and close to zero in comparison with the structure [19], and this ratio of the input current compared with the conventional interleaved buck-boost converter is less than 1. Therefore, for all duty cycles, the input current ripple of the proposed converter is less than that of other converters. All components used in converters structures have internal resistance, which contributes to the losses and efficiency of the converter.The higher the RMS values of current passing through the resistor, the greater the losses because the power loss in a resistor is directly related to the square of the current passed through it. As mentioned in [24, 25], the large current ripple causes the RMS value of the current to increase, which produces extra power losses. In structures presented in [21–23], the input current is discontinuous, and the RMS value of current passing through the components increases. Since the number of components in the current path in structures [21–23] is more than the proposed converter and because of the high value of their RMS input current, the efficiency of the proposed converter is higher than that of the structures [21–23] and others except [19]. In the converter presented in [19], an additional inductor is used for soft switching, which reduces the switching losses and increases the converter’s efficiency. However, the presented converter in [19] has a discontinuous input current for duty cycles less than 50%. The practical applications of the proposed converter are as follows: power supply for portable devices where the battery is discharging, obtaining the I-V curve in PV panels. In addition, the proposed converter can be used for renewable energy applications because of drawing continuous current from the DC source. Large current ripple causes, as a result, the RMS value of the current to increase that produces extra power losses and higher temperatures that advance the degradation of the renewable energy source. Furthermore, the maximum renewable source power can be extracted using a converter with a continuous input current [24, 25].Figure15 illustrates the normalized input current ripple with respect to the average value of the input current for all the converters. According to this figure, converter [21] has the highest input current ripple. For D < 0.5, the input current ripple of the proposed converter is lower than the converters [19–23] and CIBBC. Also, for D > 0.5, the input current ripple of the converter [26] gets higher than the presented converter and the presented converter acts better than others. In other words, as shown in Figure 15, the curve of the presented converter is placed lower than others; this illustrates that the presented converter has low input current ripple in comparison with [19–23] and CIBBC. The input current ripple ratio of the converter [27] in comparison with the proposed converter is less; however, the voltage conversion ratio of this converter in comparison with the presented converter and the conventional one for buck operation mode is not improved. Also, the high voltage stress in the components of the converter [27] causes a decrease in its efficiency.Figure 15
Normalized input current ripple to the average value of the input current.In order to analyze the harmonic oscillation in the case of the presented converter and conventional interleaved buck-boost converter, the time-domain waveforms ofii, proposed and ii, CIBBC for the same condition are shown in Figure 16. One large DC component and the other smaller AC components from the provided frequency spectrums exist at the switching frequency and other frequencies. This indicates that except for switching frequency, more than one harmonic are distorted the waveforms. According to Figure 16(a), in the presented converter, besides fs, three new harmonics appear in the frequency spectrum, i.e., f1 = 953 Hz and f2 = 2f1 = 1906 Hz, and in frequency spectrum of the conventional converter as shown in Figure 16(b), f1 = 714 Hz, f2 = 2f1 = 1428 Hz, f3 = f1 + f2 = 2142, and f4 = f1 + fs = 30714 Hz. Among these harmonics, in the presented converter, f1 and fs have the most dominate role in the harmonic oscillation, whereas other harmonics do negligible role. However, in conventional interleaved buck-boost converter, the magnitude of harmonics in f1, f2, and fs is more than the presented one. Besides, two new harmonics at f3 and f4 appeared in the frequency spectrum of the conventional converter. The asymmetric waveform distortion in the conventional converter mainly results from f3 and f4 (the interactions between harmonics at frequencies f1, f2, and f1, fs). It is obvious that the harmonics f1 and f2 in waveform of ii ,proposed are dominated by both even and odd signal components. In the conventional converter, harmonics of ii,CIBBC are dominated by odd signal components.Figure 16
Frequency spectrum of input current in (a) proposed converter and (b) conventional interleaved buck-boost converter.
(a)(b)Total harmonic distortion (THD) for the input current is defined as the effective value of all harmonics divided by the effective value of its fundamental current.Distortion is defined as follows:(82)THD=I22+I32+I42+…+Ih2I1,where Ih is the effective current of the hth harmonics and I1 is the effective value of the current in the fundamental frequency. In the case of harmonic absence, the THD will be equal to “0”. Using (82) and the harmonics of Figure 16, the THD amplitudes for the presented converter and conventional interleaved buck-boost converter are obtained as 0.12 and 0.277, respectively. So, the proposed converter’s low THD amplitude compared with the conventional one confirms its better performance.The practical THD value of the input current was obtained as 0.127. The slight difference in the practical and theoretical THD is because more numbers of harmonics are considered in the practical calculation.


## 9. Experimental Results

In order to confirm the theoretical analyses of the proposed converter, a 200 W prototype is built in the laboratory. This prototype is shown in Figure17. The specifications of the circuit and components are presented in Table 3.Figure 17
The experimental prototype of the proposed converter.To calculate the practical value of inductances according to equation (29), the maximum value of load resistance and the minimum value of duty cycle are 35 ohms and 0.385, respectively. The operating frequency of the converter is also equal to 30 kHz. By substituting these values in equation (2), the minimum value of inductors is obtained as 440 µH, of which 450µH has been selected for the experimental prototype.(83)L1,min=L2,min=35×1−0.385230000≃440μH.The value of capacitorC is obtained based on the minimum value of load resistance, which can be calculated using equation (31). Using this equation and the value of the parameters provided in Table 3, the minimum value of the capacitor C is equal to 86 µF.(84)C≥2×6.125×1−0.3852−30000×450×10−6×1−2×0.3852×79×10−3×6.125×30000×1−0.385≃86μF.Therefore, for the implemented prototype, a 100µF capacitor has been selected.Figure18(a) shows the PWM gate signals of the switches S1 and S2, and these switches operate with the duty cycle of 0.41.Figure 18
The experimental waveform for (a)VGS1 and VGS2 in buck mode; (b) the input and output voltages in buck mode; (c) VGS1 and VGS2 in boost mode; (d) the input and output voltages in boost mode.
(a)(b)(c)(d)The switchesS3 and S4 are in the off state in forward buck operation, and their reverse-parallel diodes transfer the power to the load. Command signals for the gates of the switches S1 and S2 are shown in Figure 18(a). According to (13), for input voltage 50 V and duty cycle 0.41, the output voltage should be 35 V. The correctness of this analysis is confirmed in Figure 18(b). In addition, boost operation mode with 75 V output voltage is provided by the duty cycle of 0.6 of power switches. The experimental waveforms are given in Figures 18(c) and 18(d) that confirm the mentioned values.As mentioned in previous sections, this converter has a continuous input current with low ripple. For duty cycle equal to 0.41, the input current ripple of this converter according to (35) is about 1 A which this ripple agrees with the experimental input current ripple at Figure 19. The conventional interleaved buck-boost converter has a closer input current ripple to the proposed one among the compared converters. The practical value of the input current ripple of conventional interleaved buck-boost converter is obtained as a coefficient of the proposed converter input current ripple. In the same condition, the ripple ratio of the input current in the conventional converter to the proposed converter is 2.5, which indicates that the proposed converter has less ripple than it. Also, the experimental results for forward boost, reverse buck, and reverse boost operation have been presented, respectively, in Figures 19(b)–19(d). In forward boost operation, the switches S1 and S2 operate with D = 0.6, and in reverse buck and reverse boost operation, the switches S3 and S4 operate with D = 0.41 and D = 0.6, respectively.Figure 19
The experimental waveform of the input current for (a) forward buck operation, (b) forward boost operation, (c) reverse buck operation, and (d) reverse boost operation.
(a)(b)(c)(d)In forward buck operation, the current of the inductorsL1 and L2 is equal to each other and, according to (27), is about 4.87 A, and the experimental results of Figure 20(a) reconfirm these amounts. As shown in this figure, the current iL1 increases and decreases linearly when switch S1 is turned on and turned off, respectively, and the current iL2 vice versa. In boost operation mode, according to equation (27), the average value of inductor L1 and L2 should be equal to 3.3 A; the correctness of this current is demonstrated in Figure 20(c). In time intervals that switches are turned on, the currents of inductors increase, and in the off state of switches, the inductors’ currents decrease (Figures 20(a) and 20(c)). The applied voltage to the inductors L1 and L2 in buck and boost operation modes is shown in Figures 20(b) and 19(d), respectively. The applied voltages to the inductors L1 and L2 are shown in Figure 20(b). According to theoretical analyses, when switch S1 is turned on, the voltage applied to L1 is vL1 = 50 V; otherwise, vL1 = 35 V. When S2 is turned on, the voltage applied to L2 is vL2 = 50 V, and in off-state time intervals of the mentioned switch, vL2 is equal to 35 V. Figure 20(b) confirms the correctness of these analyses.Figure 20
The experimental waveform of (a) inductors current in buck mode; (b) inductors voltage in buck mode; (c) inductors current in boost mode; (d) inductors voltage in boost mode.
(a)(b)(c)(d)According to equations (1) and (2), the proposed converter in the duty cycle of 0.5 has the property of eliminating the input current ripple. The switch’s duty cycle has been set to the mentioned value to demonstrate this capability in the experimental prototype. Experimental waveforms of the switch’s command and input current are shown in Figure 21. As can be seen, in this duty cycle, the input current ripple is zero, which confirms the theoretical analysis.Figure 21
Input current ripple cancelation in selected duty cycle.In order to observe the dynamic behavior of the proposed converter, the step response of the system is shown in Figure22. This step response is obtained by changing the duty cycle suddenly from 0.4 to 0.55. It can be seen that the recovery time for the proposed converter is 35 ms.Figure 22
Output voltage changing in case of sudden changes of the duty cycle from 0.4 to 0.55.


## 10. Conclusion

In this paper, an interleaved nonisolated bidirectional buck-boost DC-DC converter is proposed. The operation principle of this converter, design consideration, and its dynamic modeling are detailed completely. Unlike conventional interleaved buck-boost converter that has discontinuous current for buck mode, the input current of this converter is continuous. It has a low ripple for both buck and boost modes. The analyses showed that the ratio of the input current ripple of the proposed converter to the conventional interleaved converter and other similar interleaved converters for all duty cycles is much less than 1. Also, this converter has low components in comparison with similar converters. Other properties of the proposed converter are low current stress of the components, the small size of the input filter, power flow in two directions, improved efficiency, and increased life of the component. This structure has a maximum efficiency of 95.6%, and finally, a prototype approved the theoretical analysis.



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*Source: 9453913-2022-06-01.xml*