Comparative Analysis of PWM Techniques for Interleaved Full Bridge Converter in an AC Battery Application

Abstract

The AC battery utilizing second-life time batteries has gained great interest currently with the advantages of both power solutions and economic benefits. In this system, the power converters play a crucial role in the stable and effective operation of the system. This paper focused on the AC/DC stage with the chosen topology being the interleaved full bridge (IFB) converter due to its flexibility and the ability to increase the power rate of the system. For the sake of high-performance operation, various pulse width modulation (PWM) methods for this converter are analyzed. First, based on the theory of the traditional PWM methods for a full bridge inverter in combination with the interleaved technique, this paper proposed three interleaved PWM methods for the IFB converter. Secondly, the proposed methods are theoretically compared in terms of the output current, common-mode voltage, and power losses. Finally, the evaluation is carried out by both the simulation and the experimental prototype, in which the results are in good agreement with the theoretical analysis.

1. Introduction

Recently, along with the significant growth in the number of electric vehicles (EVs), EV batteries have become an interest of application. The capacity of these batteries after being discarded from EVs is approximately 70–80% of the initial value [1,2], corresponding to the impedance of the end-of-life lithium-ion battery, which normally is obtained from the battery manufacturers [3]. After that, they can be reused as second-life batteries (SLBs). These SLBs can store and deliver power in stationary applications [4] or energy storage systems [5]. Especially, the concept of the home battery storage system [6,7,8] has been concerned with consisting of multiple resources: renewable energy, the low voltage (LV) grid, domestic loads, and EVs and the SLBs from them. Among the two main structures for the home battery, the AC-coupled one is selected in this research because of its ability to retrofit the installed home PV system, its isolated battery system, and its flexibility with extended modules. To that extent, the AC battery, integrating both the battery and the power converters, has been introduced by many well-known companies.

To exchange power among all the sources in this resident application, the two-stage topology in Figure 1 is chosen as a suitable solution. This paper focuses on the power factor correction stage with the requirements of a multi-functional converter. First, in the US and some countries, while only the 1-phase grid power is allowed for the home, the 3-phase grid cord is acceptable for homes in many other countries for the higher power rate application. Therefore, the first function of the PFC stage is the ability to connect with both 1-phase and 3-phase grids. At the power rate of 6.6 kW for charging EVs, the TI prototype using a Totem-Pole converter is considered the best solution [9]. However, when the power rate increases, such as the 11 kW at level 2 of the charging standard, the high current stress and high current limit the advantage of the traditional Totem-Pole structure. A solution for this issue is using the interleaved converter, with the suggested one being the bridgeless interleaved boost [10]. The advantage of this converter is the significantly lower current ripple, which decreases the size of the electromagnetic interference (EMI) filter and improves the life of the systems. However, the disadvantage of this structure is that the upper switches are all four diodes, which means the power only can transfer in one direction and the system cannot supply the household loads. To ensure the second function of bidirectional power transfer for the home battery storage system, the IFB converter is chosen with the structure shown in Figure 2.

This converter achieves the reduction in current stress and current ripple, hence, lowering the EMI circuit. Furthermore, this converter has the flexibility to transform into the three-phase four-leg converter so that the PFC can operate with the three-phase grid power, as indicated in the first function. The modulation for the IFB converter is the main focus of this research. The basic knowledge of the modulation rule for a single H-Bridge and the comparison among various PWM methods is presented in [11]. The unipolar PWM gives a lower THD current but the leakage current is high, while the bipolar PWM method achieves a low leakage current but the current ripple is high [12,13,14,15]. The discontinuous PWM method helps reduce power losses [16,17,18]. Based on that, several PWM techniques for the IFB converter were studied in [19]. Unipolar double-frequency PWM modulation has a high-frequency circulation current, and its influence on split-filter elements can be minimized. Unipolar frequency–PWM modulation has a high-frequency circulating current, but its effect on split inductors cannot be minimized. In particular, bipolar–PWM modulation has been proven to have no high-frequency circulating currents in any operating mode of the converters [19]. However, this research mainly focuses on the circulation of current issues and their solutions.

Taking advantage of the interleaved technique with the fixed phase difference of 180° [10], three PWM methods, named the interleaved bipolar PWM (IB-PWM), the interleaved unipolar PWM (IU-PWM), and the interleaved discontinuous PWM (ID-PWM), are proposed for the IFB converter based on the corresponding traditional PWM methods. Furthermore, a comprehensive comparison among different PWM methods for the IFB converter is presented in this paper. In detail, three main standards for comparison consist of the THD current, the common-mode voltage, and the power losses.

2. PWM Method Principle

2.1. Interleaved Bipolar PWM

• Pulse pattern analysis

In the IB-PWM method, the modulation indexes m_1, and m₂ are applied for H-Bridge 1 (H₁) and H-Bridge 2 (H₂), as shown in Figure 3, and they are assumed to be equal in the ideal case. Due to the rule of the traditional Bipolar PWM, in terms of the H₁, a sawtooth carrier-based signal is compared to the modulation index m₁ to create the control signal for switches S₁ and S₆, while inverted signals are used for S₂ and S₅. With regard to the H₂, the phase of the sawtooth signal is shifted by 180° from that of H₁, so-called the “Interleaved Bipolar PWM”, and the control signals for switches S₃, S₈, S₄, and S₇ are created similarly. The pulse diagram for this modulation method is presented in Figure 4.

• Common-mode voltage analysis

Due to the 180° out of phase between the two carriers, the control signals for S₁ and S₃ are interleaved. In addition, assuming that the modulation indexes of two bridges are the same, the turn-on interval in a switching period of S₁ is equal to that of S₃. Therefore, the output voltages of two inverters are shifted by 180° in phase.

Defining that s₁, s₂, s₃, s₄ are the switching states of the switches S₁, S₂, S₃, S₄, correspondingly, the voltage $v_{AN},v_{BN},v_{CN},v_{DN}$ can be written in terms of switching states, as follows:

$$\left\{\begin{array}{l}{v}_{AN}=s_1{V}_{AN}+(1-s_1)V_{ON}=s_1{V}_{dc}+V_{ON}\\ v_{BN}=s_2{V}_{dc}+V_{ON}\\ v_{CN}=s_3{V}_{dc}+V_{ON}\\ v_{DN}=s_4{V}_{dc}+V_{ON}\end{array}\right.$$

(1)

By applying Kirchhoff’s voltage law at the output of the inverter:

$$\left\{\begin{array}{l}{v}_{AN}=L_1\frac{d{i}_{L1}}{2}+v_s\\ v_{BN}=-L_3\frac{d{i}_{L3}}{2}\\ v_{CN}=L_2\frac{d{i}_{L2}}{2}+v_s\\ v_{DN}=-L_4\frac{d{i}_{L4}}{2}\end{array}\right.$$

(2)

Assuming that the split-inductor currents are balanced: $i_{L1}=i_{L3},i_{L2}=i_{L4}$, the common-mode voltage can be calculated from Equations (1) and (2) as follows:

$$v_{ON}=\frac{-(s_1+s_2+s_3+s_4)V_{dc}}{4}+\frac{v_s}{2}$$

(3)

Each phase voltage takes the value of +V_dc when the upper switch is on and 0 V when this switch is off. According to the pulse diagram in Figure 4, in a switching period, there are always two turned-on upper switches and two turned-off upper switches, which means the common voltage can be defined as

$$v_{CM\text{\_}IBPWM}=\frac{v_s}{2}-\frac{V_{dc}}{2}$$

(4)

Because $-\frac{V_{dc}}{2}$ is the constant component, the leakage current with the IB-PWM method only depends on the sinusoidal output voltage at the fundamental frequency of 50 Hz.

• Ripple of the split-inductor current and the output current

According to the traditional bipolar PWM, each bridge has two operation modes. In mode 1, taking H₁ for instance, as depicted in Figure 4, switches S₁ and S₆ are on, the output voltage of H₁ is +V_dc, and the inductor currents i_L1 and i_L3 increase, while in mode 2, switches S₂ and S₅ are on, the output voltage of H₁ is −V_dc, and the inductor currents i_L1 and i_L3 decrease. Because of the interleaved feature of the IB-PWM method, the two bridges of the IFB converter operate independently; therefore, the IFB converter with the IB-PWM method has four operation modes.

Table 1. Operation modes of IFB converter with different PWM methods.

Mode	H-Bridge 1	H-Bridge 2	Method
1	S1 on, S2 off, S5 off, S6 on	S3 on, S4 off, S7 off, S8 on	IB-PWM 1,2, IU-PWM 1
2	S1 on, S2 off, S5 off, S6 on	S3 off, S4 on, S7 on, S8 off	IB-PWM 1,2
3	S1 off, S2 on, S5 on, S6 off	S3 on, S4 off, S7 off, S8 on	IB-PWM 1,2
4	S1 off, S2 on, S5 on, S6 off	S3 off, S4 on, S7 on, S8 off	IB-PWM 1,2, IU-PWM 2
5	S1 on, S2 on, S5 off, S6 off	S3 off, S4 off, S7 on, S8 on	IU-PWM 1,2,ID-PWM 2
6	S1 off, S2 off, S5 on, S6 on	S3 on, S4 on, S7 off, S8 off	IU-PWM 1, ID-PWM 2
7	S1 on, S2 on, S5 off, S6 off	S3 on, S4 on, S7 off, S8 off	ID-PWM 1
8	S1 off, S2 off, S5 on, S6 on	S3 off, S4 off, S7 on, S8 on	ID-PWM 2

¹ D > 0.5, ² D < 0.5.

synthesizes the comprehensive operation modes, along with the switching states of all switches of the IFB converter, applying various PWM techniques: the IB-PWM, the IU-PWM, and the ID-PWM. In this section, the equivalent circuit of each operation mode and the current ripple with the IB-PWM in each case are focused. The time intervals of mode 1, 2, 3, 4, 5, 6, 7, and 8 in a switching period T_s are defined as D₁T_s, D₂T_s, D₃T_s, D₄T_s, D₅T_s, D₆T_s, D₇T_s, and D₈T_s, respectively.

To determine the current ripple, the modulation indexes for the two bridges are equal, and the effect of deadtime is neglected. In this case, the turn-on interval in one switching period of two switches S₁ and S₃ are the same, which is defined as DT_s.

-

With D > 0.5 (Vs > 0): The IFB converter works in modes 1, 2, and 3.

In mode 1, both the split-inductor current i_L1, i_L2, and the output current i_L increase. For the sake of intuition, the current ripple of i_L is calculated in this case.

Because two bridges operate separately with the IB-PWM, based on the equivalent circuit in Figure 5a–c, all the split-inductor currents increase in the interval of DT_s. Hence, the ripple of each inductor current is given as

$$\left\{\begin{array}{l}\Delta i_{L1\text{\_}IB}=\Delta i_{L3\text{\_}IB}=\frac{V_{dc}-v_s}{L_1+L_3}DT=\frac{V_{dc}-v_s}{2L}D{T}_s\\ \Delta i_{L2\text{\_}IB}=\Delta i_{L4\text{\_}IB}=\frac{V_{dc}-v_s}{L_2+L_4}D{T}_s=\frac{V_{dc}-v_s}{2L}D{T}_s\end{array}\right.$$

(5)

The time interval for the increase in the output current in a switching period is determined in the Figure 4a: $D_s{T}_s=(D-0.5)T_s$. Therefore, the output current ripple when D > 0.5 is determined as

$$\begin{array}{ll}\Delta i_{L\text{\_}IB}& =(\frac{\Delta i_{L1\text{\_}IB}}{D{T}_s}+\frac{\Delta i_{L2\text{\_}IB}}{D{T}_s})D_s{T}_s=\frac{V_{DC}-v_s}{2L}\times 2\times (D-0.5)T_s\\ & =\frac{V_{DC}-v_s}{2L}\times (2D-1)T_s\end{array}$$

(6)

Inherently, $\Delta i_{L\text{\_}IB}<\Delta i_{L1\text{\_}IB}$ when D < 1, which means the interleaved PWM method has the ability to reduce the output current ripple. The decrease in the current ripple significantly reduces the THD of the output current, which is the advantage of the interleaved PWM method in general and the IB-PWM in particular.

-

With D < 0.5 (Vs < 0): the IFB converter operates in modes 2, 3, and 4.

In mode 4, both the split-inductor current i_L1, i_L2, and the output current i_L decrease. For the intuitive approach, the ripple of i_L is calculated in this case.

Because two bridges operate separately with the IB-PWM, based on the equivalent circuit in Figure 5b–d, the split-current increases in the interval of (1 - D)T_s. Hence, the ripple of each inductor current is given as

$$\left\{\begin{array}{l}\Delta i_{L1\text{\_}IB}=\Delta i_{L3\text{\_}IB}=\frac{-V_{dc}-v_s}{L_1+L_3}(1-D)T_s=\frac{-V_{dc}-v_s}{2L}(1-D)T_s\\ \Delta i_{L2\text{\_}IB}=\Delta i_{L4\text{\_}IB}=\frac{-V_{dc}-v_s}{L_2+L_4}(1-D)T=\frac{-V_{dc}-v_s}{2L}(1-D)T_s\end{array}\right.$$

(7)

The time interval for the decrease in the output current in a switching period is determined from the Figure 4b: $D_s=0.5-D$. Therefore, the output current ripple when D < 0.5 is calculated as:

$$\begin{array}{ll}\Delta i_{L\text{\_}IB}& =(\frac{\Delta i_{L1\text{\_}IB}}{D{T}_s}+\frac{\Delta i_{L3\text{\_}IB}}{D{T}_s})D_s{T}_s=\frac{-V_{DC}-v_s}{2L}\times 2\times (0.5-D)T_s\\ & =\frac{-V_{DC}-v_s}{2L}\times (1-2D)T_s\end{array}$$

(8)

Here, we have $\Delta i_{L\text{\_}IB}<\Delta i_{L1\text{\_}IB}$ since D > 0, which means the ripple of the output current is smaller than that of the split-inductor current.

2.2. Interleaved Unipolar PWM

• Pulse pattern analysis

The modulation rule for each H-Bridge is based on the traditional Unipolar PWM as shown in Figure 6. Taking the H-Bridge 1, for example, the modulation indexes m₁ and -m₁ are compared to the carrier sw₁ to generate the control signals for S₁ and S₂, respectively. By inverting the logic of control signals S₁ and S₂, the signals for S₅ and S₆ are achieved, respectively. In terms of H-Bridge 2, the control signals for S₃, S₄, S₇, and S₈ are generated by a similar rule with the modulation index m₂ (m₂ is chosen to be equal to m₁ in the ideal case), and the carrier sw₂ shifted 180° in phase with the sw₁ of H₁.

The pulse pattern of the IB-PWM method is shown in Figure 7. An important feature that should be noted is that due to the symmetric feature, for example, when D > 0.5 (D is defined as in Section 2.1), the turn-on interval of both switches S₁ and S₂ overlaps the turn-off interval of both switches S₃ and S₄. As a result, at a moment in a switching period, there are two turn-on upper switches and two turn-off upper switches. Therefore, similar to the IB-PWM method, the common voltage of the IFB converter with the IU-PWM method can be defined from Equation (3):

$$v_{CM\text{\_}IUPWM}=\frac{v_s}{2}-\frac{V_{DC}}{2}$$

(9)

As a result, the common-mode voltage with the IU-PWM is high-frequency pulse-free and only depends on the sinusoidal output voltage at the fundamental frequency of 50 Hz.

• Ripple of the split-inductor current and the output current

  -

  With D > 0.5 (Vs > 0): The IFB converter operates in modes 1, 5, and 6.

Different from the IB-PWM method, there is a current loop flowing through one branch of the H₁ and another branch of the H₂, as shown in mode 5 and mode 6 in Figure 8.

Hence, the current ripple with the IU-PWM should be calculated in each mode instead of the whole DT_S interval with the IB-PWM. The split-inductor current ripple in mode 1 is given by

$$\left\{\begin{array}{l}\Delta i_{L1\text{\_}IU}=\Delta i_{L3\text{\_}IU}=\frac{V_{dc}-v_s}{L_1+L_3}{D}_1{T}_s=\frac{V_{dc}-v_s}{2L}(D-0.5)T_s\\ \Delta i_{L2\text{\_}IU}=\Delta i_{L4\text{\_}IU}=\frac{V_{dc}-v_s}{L_2+L_4}{D}_1{T}_s=\frac{V_{dc}-v_s}{2L}(D-0.5)T_s\end{array}\right.$$

(10)

The split-inductor current ripple in mode 5 is given by

$$\left\{\begin{array}{l}\Delta i_{L1\text{\_}IU}=\Delta i_{L4\text{\_}IU}=\frac{V_{dc}-v_s}{L_1+L_4}{D}_5{T}_s=\frac{V_{dc}-v_s}{2L}(1-D)T_s\\ \Delta i_{L2\text{\_}IU}=\Delta i_{L3\text{\_}IU}=\frac{-V_{dc}-v_s}{L_2+L_3}{D}_5{T}_s=\frac{-V_{dc}-v_s}{2L}(1-D)T_s\end{array}\right.$$

(11)

The split-inductor current ripple in mode 6 is given by

$$\left\{\begin{array}{l}\Delta i_{L1\text{\_}IU}=\Delta i_{L4\text{\_}IU}=\frac{-V_{dc}-v_s}{L_1+L_4}{D}_6{T}_s=\frac{-V_{dc}-v_s}{2L}(D-0.5)T_s\\ \Delta i_{L2\text{\_}IU}=\Delta i_{L3\text{\_}IU}=\frac{V_{dc}-v_s}{L_2+L_3}{D}_6{T}_s=\frac{V_{dc}-v_s}{2L}(D-0.5)T_s\end{array}\right.$$

(12)

Because all the currents flowing through the four split-inductors are balanced, the current ripple $\Delta i_{L1\text{\_}IU}$ of split-inductor L₁ is chosen. The split-inductor current ripple is determined from Equations (10) and (11):

$$\Delta i_{L1\text{\_}IU}=\frac{V_{dc}-v_s}{2L}(2D_1+D_5)T_s=\frac{V_{dc}-v_s}{2L}(2(D-0.5)+1-D)T_s=\frac{V_{dc}-v_s}{2L}D{T}_s$$

(13)

In mode 1, both the split-inductor current i_L1, i_L2 and the output current i_L increase. For the intuitive approach, the output current ripple is determined in this mode:

$$\Delta i_{L\text{\_}IU}=(\frac{\Delta i_{L1\text{\_}IU}}{D{T}_s}+\frac{\Delta i_{L2\text{\_}IU}}{D{T}_s})D_s{T}_s=\frac{V_{dc}-v_s}{2L}\times 2\times (D-0.5)T_s=\frac{V_{dc}-v_s}{2L}\times (2D-1)T_s$$

(14)

Compared to Equations (4) and (6), $\Delta i_{L\text{\_}IB}=\Delta i_{L\text{\_}IU}$ and $\Delta i_{L1\text{\_}IB}=\Delta i_{L1\text{\_}IU}$. It can be noted that even though the pulse patterns of the IB-PWM and IU-PWM techniques are different when D > 0.5, the inductor current ripple and the output current ripple of the two modulation methods are the same.

-

With D < 0.5 (Vs < 0): The IFB converter operates in modes 4, 5, and 6.

The current ripple through split-inductor L₁ is determined from Equations (12) and (13):

$$\Delta i_{L1\text{\_}IU}=\frac{-V_{dc}-v_s}{2L}(2D_4+D_6)T_s=\frac{-V_{dc}-v_s}{2L}(1-2D+D)T_s=\frac{-V_{dc}-v_s}{2L}(1-D)T_s$$

(15)

The output current ripple is determined as

$$\Delta i_s=\frac{V_{dc}-v_s}{2L}\times 2\times (0.5-D)T_s=\frac{V_{dc}-v_s}{2L}\times (1-2D)T_s$$

(16)

2.3. Interleaved Discontinuous PWM

• Pulse pattern analysis

The discontinuous PWM method consists of two types: the DPWM1P method and the DPWM2P method [16], as shown in Figure 9, which is applied for a single H-Bridge converter. Because of the similar features of these types, this paper chooses the DPWM1P in combination with the interleaved technique, the so-called “Interleaved Discontinuous PWM”, for the IFB converter to compare the other interleaved PWM methods. In the ID-PWM method, a clamp signal V_c, which is synchronous with the AC voltage Vs, is created. The double modulation index is added with the clamp signal, which is saturated from −1 to 1 to obtain the discontinuous signal V_DIS. This signal is compared to the carrier, taking the H₁, for instance, to generate control signals for switches S₁ and S₃, while those for switches S₅ and S₆ are inverted. Similarly, the control signal for the switches S₃, S₄, S₇, and S₈ is generated with the carrier being shifted 180° in phase from that of H₁.

• Common-mode voltage analysis

The pulse pattern of the IU-PWM is shown in Figure 10. As can be seen, in a switching period, there are two or no turn-on upper switches when D < 0.5, while there are two or four turned-on upper switches when D > 0.5. Therefore, unlike the IB-PWM and IU-PWM, the common mode voltage of the IFB converter can take one of these values: 0, V_dc/2, and V_dc. This high-frequency voltage component increases the leakage current of the converter [20]:

$$i_{lk}=C_p\frac{d{v}_{CMV}}{dt}$$

(17)

In which the parasitic capacitor C_p consists of several parasitic capacitors C_p1, C_p2, and C_p3, as shown in Figure 2.

• Ripple of the split-inductor current and output current

The current ripple with the IU-PWM is analyzed in two intervals: non-switching interval (accounts for half of the Vs cycle) and switching interval (accounts for the other half of the Vs cycle).

• Non-switching interval: Due to the discontinuous PWM rule, all the upper switches S₁, S₂, S₃, and S₄ are on or off in this interval, hence, the currents through the four split-inductors are in phase and the current ripples seem to be zero.
• Switching interval: In some modes of this interval, the currents only flow through the inductor and Vs. Therefore, the sign of Vs decides whether the current increases or decreases. In this section, the current ripples are analyzed when Vs < 0, while the analysis when Vs > 0 is similar. Unlike the previous interleaved PWM method, the inductor currents with the ID-PWM increase or decrease with the different rates in the different modes.

-

With D > 0.5: The IFB converter operates in modes 5, 6, and 7.

Similar to the IU-PWM, there is a current loop flowing through one branch of the H₁ and another branch of the H₂, as shown in mode 5 and mode 6 in Figure 10.

The split-inductor current ripple in mode 5 is given by

$$\left\{\begin{array}{l}\Delta i_{L1\text{\_}ID}=\Delta i_{L4\text{\_}ID}=\frac{V_{dc}-v_s}{L_1+L_4}{D}_5{T}_s=\frac{V_{dc}-v_s}{2L}(1-D)T_s\\ \Delta i_{L2\text{\_}ID}=\Delta i_{L3\text{\_}ID}=\frac{-V_{dc}-v_s}{L_2+L_3}{D}_5{T}_s=\frac{-V_{dc}-v_s}{2L}(1-D)T_s\end{array}\right.$$

(18)

The split-inductor current ripple in mode 6 is given by

$$\left\{\begin{array}{l}\Delta i_{L1\text{\_}ID}=\Delta i_{L4\text{\_}ID}=\frac{-V_{dc}-v_s}{L_1+L_4}{D}_6{T}_s=\frac{-V_{dc}-v_s}{2L}(1-D)T_s\\ \Delta i_{L2\text{\_}ID}=\Delta i_{L3\text{\_}ID}=\frac{V_{dc}-v_s}{L_2+L_3}{D}_6{T}_s=\frac{V_{dc}-v_s}{2L}(1-D)T_s\end{array}\right.$$

(19)

The split-inductor current ripple in mode 7 is given by

$$\left\{\begin{array}{l}\Delta i_{L1}=\Delta i_{L3}=\frac{-v_s}{L_1+L_3}(D-0.5)T_s=\frac{-v_s}{2L}(D-0.5)T_s\\ \Delta i_{L2}=\Delta i_{L4}=\frac{-v_s}{L_2+L_4}(D-0.5)T_s=\frac{-v_s}{2L}(D-0.5)T_s\end{array}\right.$$

(20)

In mode 8, both the split-inductor currents i_L1, i_L2 and the output current i_L decrease as shown in Figure 11. For the intuitive approach, the output current ripple is determined in this mode.

Because all the currents flowing through the four split-inductors are balanced, the current ripple of split-inductor L₁ is chosen. The split-inductor current ripple is determined from Equations (18) and (19):

$$\begin{array}{ll}\Delta i_{L1\text{\_}ID}& =\frac{V_{dc}-v_s}{2L}\times D_5{T}_s+\frac{-v_s}{2L}\times 2D_7{T}_s=\frac{V_{dc}-v_s}{2L}\times (1-D)T_s+\frac{-v_s}{2L}\times (2D-1)T_s\\ & =\frac{V_{dc}-v_s}{2L}\times D{T}_s+\frac{v_s}{2L}\times (2D-1)T_s\end{array}$$

(21)

The output current ripple is determined as

$$\Delta i_L=\Delta i_{L1}+\Delta i_{L2}=\frac{v_s}{2L}\times 2D_7{T}_s=\frac{-v_s}{2L}\times (2D-1)T_s$$

(22)

-

With D < 0.5: The IFB converter operates in modes 5, 6, and 8.

The split-inductor current ripple in mode 8 is given by

$$\left\{\begin{array}{l}\Delta i_{L1}=\Delta i_{L3}=\frac{v_s}{L_1+L_3}(0.5-D)T_s=\frac{v_s}{2L}(0.5-D)T_s\\ \Delta i_{L2}=\Delta i_{L4}=\frac{v_s}{L_2+L_4}(0.5-D)T_s=\frac{v_s}{2L}(0.5-D)T_s\end{array}\right.$$

(23)

The split-inductor current ripple is determined from Equations (19) and (20):

$$\Delta i_{L1\text{\_}ID}=\frac{-V_{dc}-v_s}{2L}\times D_6{T}_s=\frac{-V_{dc}-v_s}{2L}\times D{T}_s$$

(24)

The output current ripple is determined as

$$\Delta i_L=\Delta i_{L1}+\Delta i_{L2}=\frac{v_s}{2L}\times 2D_8{T}_s=\frac{-v_s}{2L}\times (1-2D)T_s$$

(25)

2.4. Theorectical Comparion among Three Interleaved PWM Methods for the IFB Converter

To begin with, the stress voltage on the switches of the IFB converter is the same for all PWM methods. In terms of current, the current stress on each switch depends on the form of the corresponding split-inductor current, which was analyzed in each PWM method. The inductor current ripple $\Delta i_{L1}$, output current ripple $\Delta i_L$, and the high-frequency component of the common voltage $v_{CM}$ of the IFB converter, applying three PWM techniques, are synthesized in

Table 2. The performance of three proposed PWM methods.

		Pulse Width Modulation Method
Criteria		IB-PWM	IU-PWM	ID-PWM
$\Delta i_{L1}$	$D>0.5$	$\frac{V_{dc}-v_s}{2L}D{T}_s$	$\frac{V_{dc}-v_s}{2L}D{T}_s$	$\frac{V_{dc}-v_s}{2L}\times D{T}_s+\frac{v_s}{2L}\times (2D-1)T_s$
	$D<0.5$	$\frac{-V_{dc}-v_s}{2L}(1-D)T_s$	$\frac{-V_{dc}-v_s}{2L}(1-D)T_s$	$\frac{-V_{dc}-v_s}{2L}D{T}_s$
$\Delta i_L$	$D>0.5$	$\frac{V_{DC}-v_s}{2L}\times (2D-1)T$	$\frac{V_{dc}-v_s}{2L}\times (2D-1)T_s$	$\frac{-v_s}{2L}\times (2D-1)T_s$
	$D<0.5$	$\frac{-V_{DC}-v_s}{2L}\times (1-2D)T_s$	$\frac{-V_{DC}-v_s}{2L}\times (1-2D)T_s$	$\frac{-v_s}{2L}\times (1-2D)T_s$
$\frac{(s_1+s_2+s_3+s_4)V_{dc}}{4}$		$\frac{V_{dc}}{2}$	$\frac{V_{dc}}{2}$	$0,\frac{V_{dc}}{2},\frac{V_4}{2}$

. As can be seen in Table 2, first, the output current ripple is always smaller than the inductor current ripple for all methods, proving the effectiveness of the proposed interleaved modulation technique for the IFB converter particularly. In addition, even though the pulse patterns of the IB-PWM method and the IU-PWM method are different, the ripple of their inductor currents and output currents are the same.

Meanwhile, in this aspect, the ID-PWM method offers the smallest output current ripple, although its inductor current ripple could be smaller than that of other methods in the non-switching interval and be larger in the switching interval. As a result, the THD of the output current with the ID-PWM achieves the smallest value, while those of the IB-PWM and IU-PWM are equal. Second, while the common mode voltage with the IB-PWM and IU-PWM methods are free of high-frequency pulse, that of the ID-PWM additionally depends on the high-frequency pulse, which results in higher leakage current. Third, the reduction of the switching loss is the essential advantage of the ID-PWM compared to other methods. Obviously, the number of the commutations in one switching period is the same in the case of the IB-PWM and the IU-PWM method, while that of the ID-PWM is lower because its modulation index is clamped at the value of −1 or 1. Hence, the ID-PWM method has the smallest switching losses.

In the following sections, the power losses of three PWM methods are verified by simulation results, while the comparison of the current performance and common-mode voltage are verified by the experimental results.

3. Simulation Verification

3.1. Power Losses Evaluation

To determine the Mosfet power loss and thermal analysis, a thermal model of the IFB converter was built along with the thermal model using PLECS. The print screen of the simulated circuit is shown in Figure 12. PLECS allows researchers to provide the necessary parameters for the loss estimation of power semiconductors as the threshold voltage, thermal impedance, and drain-source on-state resistance. These are and can be used for the numerical estimation of losses using equations or implemented in the form of lookup tables for the turn-on loss, the turn-off loss, and conduction loss [16,20]. The simulation parameters are presented in

Table 3. Key specifications of the IFB converter.

Parameter	Unit	Value
Nominal power	kW	10
AC voltage	V	220
AC frequency	Hz	50
DC voltage	V	400
Switching frequency	kHz	30
L filter	μH	330
DC-link capacitor	μF	1000

. The power loss is compared among three PWM methods with 2 scenarios in the open-loop mode: variable switching frequency and variable power rate.

• Scenario 1:

In this scenario, while the power rate is set up at 1.5 kW, which is similar to the experimental scenario, the switching frequency varies among 10 kHz, 30 kHz, 50 kHz, and 100 kHz.

As shown in Figure 13, the conduction losses of all three PWM methods for the IFB converter are similar with multiple chosen switching frequencies. Whereas, the switching losses increases significantly when the switching frequency increases. Moreover, at the low frequency of 10 kHz, the switching loss in three PWM methods is almost the same; however, that of the ID-PWM is significantly smaller than those of other interleaved methods. In detail, the reductions of around 23%, 30% and 27% in the switching loss of the IU-PWM are achieved in comparison with other methods at the switching frequency of 30 kHz, 50 kHz and 100 kHz, respectively.

• Scenario 2:

In this scenario, while the switching frequency is set up at 30 kHz, which is similar to the experimental scenario, the power rate varies among 1.5 kW, 5 kW, 7.5 kW, and 10 kW. As shown in Figure 14, while the conduction losses of all three PWM methods for the IFB converter are still similar at any specific power rate, there is a difference among the switching losses. In detail, the reductions of around 25%, 24.8%, 25%, and 28% in the switching loss of the IU-PWM are achieved in comparison with those of other methods at the power rate of 1.5 kW, 5 kW, 7.5 kW, and 10 kW, respectively.

3.2. Leakage Current Comparisons

The parasitic capacitors normally have a small value; however, the accurate value is difficult to determine in a practical product. In this research, for simulation verification, the parameter of a parasitic RC branch is taken, as in [11] (R = 5 Ohms and C = 800 pF), which connects point O and point N, as in Figure 2. The high-frequency component in the common-mode voltage in the previous theoretical analysis leads to the different results among the leakage current of three methods, as shown in Figure 15.

In detail, the root mean square (RMS) values of the leakage current with the IB-PWM and IU-PWM methods are relatively small at 2.29 mA and 2.39 mA, and the statistics for peak value are just 7.2 mA and 6.7 mA, respectively. Additionally, the RMS value and peak value of the leakage current in the case of the IU-PWM are much higher, at 470 mA and 980 mA. These values are out of standard IEC/EN 60335-1 [21] for leakage current in the domestic applications, which results in safety problems and electromagnetic emissions.

4. Experiment Verification

To clarify the comparison among the three proposed PWM methods, a 1.5 kW experimental prototype for the IFB converter was implemented. The experimental system shown in Figure 16 includes the IFB converter inverter, filtered inductor, a programmable electronic load ITECH IT8617, and a DC power supply model ITECH IT6018C-1500-40. The control algorithm is programmed in control kit Launchpad TMS320F28379D. To display and collect the data, a GW INSTEK GDS-2104A Digital Oscilloscopes is utilized with the current probe Micsig CP2100A and the isolated voltage probe Micsig DP10013. Except for a lower power rate of 1.5 kW, the two experimental scenarios in open-loop mode are carried out with similar parameters of the PLECS simulation in Table 3.

• Output current performance evaluation

The current responses are shown in Figure 17, Figure 18 and Figure 19. Overall, the currents through the split inductor L₁ and L₂ are interleaved, which leads to the output current ripple being smaller than the inductor current ripple. In detail, the largest peak-to-peak current ripples of the split-inductor with the IB-PWM, IU-PWM, and ID-PWM are approximately 3 A, 3 A, and 5 A, respectively. These results show good agreement with the theoretical analysis in Section 2. In addition, the output current ripples with these three PWM methods are 2.5 A, 2.5 A and 1.8A, respectively, which proves the effectiveness of the interleaved technique for reducing the output current ripple. Moreover, the ID-PWM gives the smallest output current ripple as the aforementioned theory.

To that extent, the THD of the output currents with three methods are compared in Figure 20. The part highlighted in red indicates the portion used for THD analysis. The harmonic spectrum is displayed as a bar graph relative to the fundamental frequency. While the THD current of the IB-PWM and the IU-PWM are equal at 9.76%, that of the IU-PWM is significantly smaller at 5.85%. To achieve a similar THD current as the ID-PWM, the switching frequency has to increase by 1.7 times or the inductance increases by 1.7 times. This produces higher switching loss, which decreases the total efficiency or increases the volume of the passive component, as well as reduces the power density. This also inherently illustrates the economic benefit of the IU-PWM for the IFB converter.

Notably, the experimental and simulation results have proven the theoretical analysis. The advantage of lower power losses is achieved with the ID-PWM method for the IFB converter. Moreover, while the traditional discontinuous PWM does not improve the performance of the output current of the full bridge converter, the proposed ID-PWM offers a significant reduction in the THD current of the IFB converter compared to other interleaved PWM methods.

• Common-mode voltage discussion

In the experimental prototype, an open-frame IFB inverter is tested in which the parasitic capacitor is not taken into consideration due to the lack of the product chassis. Therefore, the leakage current responses are evaluated through the common-mode voltage. It can be seen that the common-mode voltage in Figure 21a for the IB-PWM method and in Figure 21b for the IU-PWM method are free of high-frequency pulses and they have the sinusoidal waveform for half of the grid voltage, with the offset being half of the DC voltage. However, high-frequency noise superimposes on a sinusoidal voltage in the measured negative poles of DC bus-to-ground voltage with IU-PWM in Figure 21c. In this case, high dv/dt could inject a spiky current with large di/dt through the parasitic capacitances and exceed the safety limitation for the leakage current in a household appliance in the IEC/EN 60335-1 standard [21]. To maintain the advantage of the ID-PWM method for the IFB converter, some hardware solutions could be considered.

An EMI filter [22] is a traditional solution for the leakage current. In [23,24], the DC–bus midpoint is connected to the LCL filter capacitor midpoint in order to effectively reduce the DC–side leakage current. An integrated common-mode (CM) and different-mode filter with passive damping is proposed in [25] for grid-connected single-phase power converters for PV systems. Furthermore, an active CM filter is proposed in [26] for reducing the ground leakage current, but additional magnetic components and computational burden are required. Additionally, some modifications in structure by adding extra devices are applied in much of the research concerning full bridge converters. The H6 converter in [27] uses two additional switches, which would be turned off during the freewheeling period to disconnect the inverter from the DC source. The improvement of this structure can be mentioned in [28], with two additional diodes in the FB-DCBP inverter. Similarly, the AC side could also be bypassed with the HERIC inverter with two extra switching devices at the AC side [29].

5. Conclusions

This paper proposes three PWM methods, along with a comprehensive comparison of the interleaved full bridge converter in an AC Battery application. These PWM methods are IB-PWM, IU-PWM, and ID-PWM, namely, based on the traditional PWM method and the interleaved techniques method. The theoretical comparison among these PWM methods is also presented, and then, the simulation and experimental prototype are carried out to verify. The results prove that the IB-PWM and IU-PWM give a similar performance in output current ripple and THD, common-mode voltage, and power loss. The ID-PWM method not only achieves a reduction in the switching loss but also the lowest THD output current. However, different from the IB-PWM and IU-PWM, the common-mode voltage of the IFB converter using the ID-PWM consists of a high-frequency component, which results in a higher leakage current. This issue could be handled in a future work by hardware solutions, which allows this method to be the most suitable PWM method for the IFB converter.