Phase shift control dual active bridge converter with integrated magnetics

Abstract

Traditional dual active bridge converters use transformer leakage inductance instead of energy storage inductors for magnetic integration, but this method cannot accurately control the leakage inductance. A phase shift control dual active bridge converter base on integrated magnetics is proposed, in which one transformer and one inductor are integrated in an EE core. The size of the inductance can be accurately controlled. The transformer and the inductor are decoupled and integrated so that the two operating states do not affect each other. The weight and volume of the magnetic elements are reduced accordingly. The finite element analysis and magnetic circuit simulation of the integrated magnetics are carried out. Finally, the integrated magnetics are designed and applied to the 600W prototype to realize bidirectional power transmission and a weight reduction is about 36.24% and a volume reduction is about 35.84%. The correctness of the design is verified by experimental results.

Keywords

Integrated magnetics dual active bridge gyrator-capacitor model the finite element method

1. Introduction

Power electronics technology is developing rapidly, DC/DC converters are used more and more widely in various fields. Nowadays, the converter are moving toward high power density and high frequency. However, according to statistics, magnetic components (including transformers, inductors) generally account for 30% to 40% of the weight of the converter, accounting for about 20% to 30% of the volume of the converter [1]. Therefore, the magnetic element is a major factor limiting the efficiency and power density of the converter. Integrated magnetics technology emerges as the times require, which can effectively reduce the size, cost and loss of magnetic core.

Figure 1.

DAB converter.

Dual active bridge (hereinafter referred to as DAB) has low voltage and current stress, which is suitable for high power applications and can realize soft switching of all devices after adding a clamp circuit. The advantage of DAB is that the control method is simple, and the power flow direction and size can be controlled under phase shift control. However, there are also some shortcomings: the complicated structure increases the product volume and design cost; the energy transfer of the transformer leakage inductance leads to a larger circulation energy [2]. Therefore, IM technology is introduced. The size of converter can be reduced by IM technology, thereby it can improve the power density and the efficiency of the converter.

Reference [3] uses a magnetic core to realize one transformer and three inductors of the ZVS full-bridge converter. All primary side H bridge switches are capable of zero voltage switching and the secondary side H bridge rectifier achieves a zero current switching state over the entire load range. However, the bidirectional transmission of energy is not achieved. Reference [4] proposes an optimal which combines the advantages of phase-shift with duty cycle modulation and traditional pure phase shift modulation. In this control method, soft switching in full power range and ensuring the maximum transmission power can be realized at the same time. But the IM is not realized. In summary, this paper proposes the IM of DAB, which realizes the increase of power density and the bidirectional transmission of energy.

Traditionally, the magnetic integration of DAB is to adjust the distance between the primary and secondary windings of the transformer to generate leakage inductance to achieve the energy storage inductance. The size of the energy storage inductor has a great impact on the energy transfer of the converter. Therefore, this paper presents a DAB magnetic integration with controllable inductance. The most typical control for DAB converters is Single-Phase-Shift (SPS) control, which changes the magnitude and direction of transmission power by adjusting the phase shift angle between the H-bridges on both sides of the converter [4]. The control methods of DAB include Dual-Phase-Shift (DPS) control [5, 6] and Triple-Phase-Shift (TPS) control [7, 8], which can improve the efficiency of DAB transmission. This paper mainly analyzes the operation of the IM in the SPS control mode. Figure 1a is the DAB discrete magnetics (DM), Fig. 1b is the DAB integrated magnetics (IM).

2. Principle analysis of IM internal magnetic flux

2.1 Analysis of DAB electric circuit-magnetic circuit coupling

Figure 2.

Integrated magnetics.

Figure 3.

Equivalent magnetic circuit of IM.

Figure 2 is the schematic diagram of IM, $N_{\text{P}}$ and $N_{\text{S}}$ are primary and secondary windings of transformer respectively. The winding turns of inductor $L_{\text{A}}$ and inductor $L_{\text{B}}$ are $N_{\text{L}_{\text{A}}}$ and $N_{\text{L}_{\text{B}}}$ respectively. $\Phi_{\text{L}_{\text{A}}}$ , $\Phi_{\text{L}_{\text{B}}}$ and $\Phi_{\text{T}}$ are the flux generated by the inductor $L_{\text{A}}$ , inductor $L_{\text{B}}$ and transformer winding respectively. Figure 3 is equivalent magnetic circuit of IM, $R_{m1}$ , $R_{m2}$ and $R_{m3}$ are the magnetic reluctance of the left column, right column and center column of the core respectively. $N_{\text{P}}i_{\text{P}}$ and $N_{\text{S}}i_{\text{S}}$ are MMF of primary winding and secondary winding of transformer, and $N_{\text{L}_{\text{A}}}i_{\text{L}_{\text{A}}}$ and $N_{\text{L}_{\text{B}}}i_{\text{L}_{\text{B}}}$ are MMF of column inductance on both sides. $\Phi_{1}$ , $\Phi_{2}$ and $\Phi_{3}$ are the magnetic flux of the left column, the right column and the center column respectively [9].

To facilitate the design of EE cores, the air gap is opened at the same time in three magnetic columns, in which the cross-sectional area of the middle column is twice as large as that of the side column, so it can be obtained:

$\displaystyle R_{m1}=R_{m2}=2R_{m3}$ (1)

According to the equivalent magnetic circuit of IM as shown in Fig. 3, $\Phi_{\text{L}_{\text{A}}}$ , $\Phi_{\text{L}_{\text{B}}}$ and $\Phi_{\text{T}}$ can be expressed as:

$\displaystyle\left\{{\begin{array}[]{l}\Phi_{\text{L}_{\text{A}}}=\frac{N_{% \text{L}_{\text{A}}}i_{\text{L}_{\text{A}}}}{R_{m1}+R_{m2}//R_{m3}}=\frac{3N_{% \text{L}_{\text{A}}}i_{\text{P}}}{8R_{m3}}\\ \\ \Phi_{\text{L}_{\text{B}}}=\frac{N_{\text{L}_{\text{B}}}i_{\text{L}_{\text{B}}% }}{R_{m2}+R_{m1}//R_{m3}}=\frac{3N_{\text{L}_{\text{B}}}i_{\text{P}}}{8R_{m3}}% \\ \\ \Phi_{\text{T}}=\frac{N_{\text{P}}i_{\text{P}}-N_{\text{S}}i_{\text{S}}}{R_{m3% }+R_{m1}//R_{m2}}=\frac{N_{\text{P}}i_{\text{P}}-N_{\text{S}}i_{\text{S}}}{2R_% {m3}}\\ \end{array}}\right.$ (2)

Then the flux $\Phi_{1}$ , $\Phi_{2}$ and $\Phi_{3}$ of each magnetic column can be expressed as:

$\displaystyle\left\{{\begin{array}[]{l}\Phi_{1}=\Phi_{\text{L}_{\text{A}}}+% \Phi_{\text{T}}\frac{R_{m2}}{R_{m1}+R_{m2}}+\Phi_{\text{L}_{\text{B}}}\frac{R_% {m3}}{R_{m1}+R_{m3}}\\ \\ \Phi_{2}=\Phi_{\text{L}_{\text{B}}}-\Phi_{\text{T}}\frac{R_{m1}}{R_{m1}+R_{m2}% }+\Phi_{\text{L}_{\text{A}}}\frac{R_{m3}}{R_{m1}+R_{m3}}\\ \\ \Phi_{3}=\Phi_{\text{T}}+\Phi_{\text{L}_{\text{A}}}\frac{R_{m2}}{R_{m2}+R_{m3}% }-\Phi_{\text{L}_{\text{B}}}\frac{R_{m1}}{R_{m1}+R_{m3}}\\ \end{array}}\right.$ (3)

Because the inductor voltage $U_{\text{L}}=U_{\text{L}_{\text{A}}}+U_{\text{L}_{\text{B}}}$ and inductor current $i_{\text{L}}=i_{\text{L}_{\text{A}}}+i_{\text{L}_{\text{B}}}$ , the primary voltage $U_{\text{P}}$ , secondary voltage $U_{\text{S}}$ , and inductor voltage $U_{\text{L}}$ can be expressed as:

$\displaystyle\left\{{\begin{array}[]{l}U_{\text{P}}=N_{\text{P}}\frac{\text{d}% \Phi_{3}}{\text{d}t}\\ \\ U_{\text{S}}=-N_{\text{S}}\frac{\text{d}\Phi_{3}}{\text{d}t}\\ \\ U_{\text{L}}=U_{\text{L}_{\text{A}}}+U_{\text{L}_{\text{B}}}=N_{\text{L}_{% \text{A}}}\frac{\text{d}\Phi_{1}}{\text{d}t}+N_{\text{L}_{\text{B}}}\frac{% \text{d}\Phi_{2}}{\text{d}t}\\ \end{array}}\right.$ (4)

Substituting Eqs (2) and (3) into Eq. (4), the voltage and current relationship of the magnetic element can be written as:

$\displaystyle\left[{{\begin{array}[]{*{20}c}{U_{\text{P}}}\\ {U_{\text{S}}}\\ {U_{\text{L}}}\\ \end{array}}}\right]=\left[{{\begin{array}[]{*{20}c}{L_{\text{P}}}&{-M_{\text{% PS}}}&{M_{\text{PL}}}\\ {-M_{\text{PS}}}&{L_{\text{S}}}&{M_{\text{SL}}}\\ {M_{\text{PL}}}&{M_{\text{SL}}}&{L_{\text{L}}}\\ \end{array}}}\right]\left[{{\begin{array}[]{*{20}c}{\frac{\text{d}i_{\text{P}}% }{\text{d}t}}\\ \\ {\frac{\text{d}i_{\text{S}}}{\text{d}t}}\\ \\ {\frac{\text{d}i_{\text{L}}}{\text{d}t}}\\ \end{array}}}\right]$ (5)

The parameters of Eq. (5) are shown in Eq. (6):

$\displaystyle\left\{{\begin{array}[]{l}L_{\text{P}}=\frac{N_{\text{P}}^{2}}{2R% _{m3}}\\ \\ L_{\text{S}}=\frac{N_{\text{S}}^{2}}{2R_{m3}}\\ \\ L_{\text{L}}=\frac{3N_{\text{L}_{\text{A}}}^{\text{2}}}{8R_{m3}}+\frac{3N_{% \text{L}_{\text{B}}}^{2}}{8R_{m3}}+\frac{3N_{\text{L}_{\text{A}}}N_{\text{L}_{% \text{B}}}}{4R_{m3}}\\ \\ M_{\text{PS}}=\frac{N_{\text{P}}N_{\text{S}}}{2R_{m3}}\\ \\ M_{\text{PL}}=\frac{N_{\text{P}}(N_{\text{L}_{\text{A}}}-N_{\text{L}_{\text{B}% }})}{4R_{m3}}\\ \\ M_{\text{SL}}=\frac{N_{\text{S}}(N_{\text{L}_{\text{B}}}-N_{\text{L}_{\text{A}% }})}{4R_{m3}}\\ \end{array}}\right.$ (6)

Then the coupling coefficient can be simplified as follows:

$\displaystyle\left\{{\begin{array}[]{l}k_{\text{PS}}=-\frac{M_{\text{PS}}}{% \sqrt{L_{\text{P}}L_{\text{S}}}}=-1\\ \\ k_{\text{PL}}=-\frac{M_{\text{PL}}}{\sqrt{L_{\text{P}}L_{\text{L}}}}=\frac{N_{% \text{L}_{\text{A}}}-N_{\text{L}_{\text{B}}}}{\sqrt{3N_{\text{L}_{\text{A}}}^{% \text{2}}+3N_{\text{L}_{\text{B}}}^{\text{2}}+2N_{\text{L}_{\text{A}}}N_{\text% {L}_{\text{B}}}}}\\ \\ k_{\text{SL}}=\frac{M_{\text{SL}}}{\sqrt{L_{\text{S}}L_{\text{L}}}}=\frac{N_{% \text{L}_{\text{B}}}-N_{\text{L}_{\text{A}}}}{\sqrt{3N_{\text{L}_{\text{A}}}^{% 2}+3N_{\text{L}_{\text{B}}}^{2}+2N_{\text{L}_{\text{A}}}N_{\text{L}_{\text{B}}% }}}\\ \end{array}}\right.$ (7)

In Eq. (7), $k_{\text{PS}}$ is the coupling coefficients between the primary side and the secondary side of the transformer, $k_{\text{PL}}$ is the coupling coefficients between the inductor and the primary side of the transformer, $k_{\text{SL}}$ is the coupling coefficients between the inductor and the secondary side of the transformer.

Assuming $k=k_{\text{PL}}=-k_{\text{SL}}$ , we can easily get $-1<k<1$ . It can be seen from the above derivation that the coupling coefficient of the inductor and the transformer can be adjusted by the number of turns of the inductor on both sides of the column. According to different values of $k$ , it can be divided into $-1<k\leqslant 0$ and $0<k<1$ integration modes. Therefore, the expression of IM based on the coupling coefficient can be obtained as follows:

$\displaystyle\left[{{\begin{array}[]{*{20}c}{U_{\text{P}}}\\ {U_{\text{S}}}\\ {U_{\text{L}}}\\ \end{array}}}\right]=\left[{{\begin{array}[]{*{20}c}{L_{\text{P}}}&{-\sqrt{L_{% \text{P}}L_{\text{S}}}}&{-k\sqrt{L_{\text{P}}L_{\text{L}}}}\\ {-\sqrt{L_{\text{P}}L_{\text{S}}}}&{L_{\text{S}}}&{k\sqrt{L_{\text{S}}L_{\text% {L}}}}\\ {-k\sqrt{L_{\text{P}}L_{\text{L}}}}&{k\sqrt{L_{\text{S}}L_{\text{L}}}}&{L_{% \text{L}}}\\ \end{array}}}\right]\left[{{\begin{array}[]{*{20}c}{\frac{\text{d}i_{\text{P}}% }{\text{d}t}}\\ \\ {\frac{\text{d}i_{\text{S}}}{\text{d}t}}\\ \\ {\frac{\text{d}i_{\text{L}}}{\text{d}t}}\\ \end{array}}}\right]$ (8)

When the coupling coefficient of the inductor and the transformer $k=0$ . That is, the number of turns $N_{\text{L}_{\text{A}}}=N_{\text{L}_{\text{B}}}$ of the inductor, we can get Eq. (9). It can be clearly seen from Eq. (9) that the inductance and the transformer operation do not affect each other, and the decoupling and integration of the two are realized.

$\displaystyle\left[{{\begin{array}[]{*{20}c}{U_{\text{P}}}\\ {U_{\text{S}}}\\ {U_{\text{L}}}\\ \end{array}}}\right]=\left[{{\begin{array}[]{*{20}c}{L_{\text{P}}}&{-\sqrt{L_{% \text{P}}L_{\text{S}}}}&0\\ {-\sqrt{L_{\text{P}}L_{\text{S}}}}&{L_{\text{S}}}&0\\ 0&0&{L_{\text{L}}}\\ \end{array}}}\right]\left[{{\begin{array}[]{*{20}c}{\frac{\text{d}i_{\text{P}}% }{\text{d}t}}\\ \\ {\frac{\text{d}i_{\text{S}}}{\text{d}t}}\\ \\ {\frac{\text{d}i_{\text{L}}}{\text{d}t}}\\ \end{array}}}\right]$ (9)

2.2 Analysis of AC flux with DAB energy forward transmission

Figure 4.

DAB-IM operation waveforms under SPS control.

Figure 5.

DAB-IM operation modals.

The DAB-IM AC magnetic circuit [10] is shown in Fig. 6, in which $R_{m1}$ , $R_{m2}$ and $R_{m3}$ are equivalent reluctance of magnetic column respectively. According to Faraday law of electromagnetic induction, the AC flux of each magnetic column is determined by the volt-second product of the winding. The equivalent AC current sources of each magnetic column are $\Phi_{\text{AC1}}(t)$ , $\Phi_{\text{AC2}}(t)$ and $\Phi_{\text{AC3}}(t)$ .

Figure 6.

Equivalent AC magnetic circuit.

Mode 1 ( $t_{0}\sim t_{1}$ ): Before $t_{0}$ moment, the converter has run steady state. The switching tubes S ${}_{2}$ , S ${}_{3}$ are in an on state and the inductor current flows $i_{\text{L}}$ is in a reverse direction with a negative value. The equivalent circuit diagram of working mode is shown in Fig. 5a. At time $t_{0}$ , switch S ${}_{1}$ and S ${}_{4}$ open simultaneously, switch S ${}_{2}$ and S ${}_{3}$ disconnect simultaneously. Since the inductance current cannot be abruptly changed, its magnitude is still negative, so the primary inductor current flows through D ${}_{1}$ and D ${}_{4}$ , and the secondary current flows through D ${}_{6}$ and D ${}_{7}$ to provide energy for the converter input and output. Under the action of forward voltage, the inductance current decreases gradually. Transformer ratio is $n={N_{\text{P}}}/{N_{\text{S}}}$ , and the magnetic flux of the side column and middle column are respectively:

$\displaystyle\Phi_{\text{AC1}}(t)=\Phi_{\text{AC2}}(t)=\frac{U_{\text{AB}}+U_{% \text{P}}}{N_{\text{L}}}(t-t_{0})$ (10) $\displaystyle\Phi_{\text{AC3}}(t)=\left(-\frac{U_{\text{P}}}{N_{\text{P}}}+% \frac{U_{\text{CD}}}{N_{\text{S}}}\right)(t-t_{0})$ (11)

Mode 2 ( $t_{1}\sim t_{2}$ ): The equivalent circuit diagram of working mode is shown in Fig. 5b. The switches S ${}_{1}$ , S ${}_{4}$ , S ${}_{6}$ and S ${}_{7}$ are forward-conducting. At the same time, both V1 and V2 charge the inductor. After that, the inductor current is positive and increases rapidly. At this time, the flux of the side column and the middle column is the same as that of mode 1.

$\displaystyle\Phi_{\text{AC1}}(t)=\Phi_{\text{AC2}}(t)=\frac{U_{\text{AB}}+U_{% \text{P}}}{N_{\text{L}}}(t-t_{1})$ (12) $\displaystyle\Phi_{\text{AC3}}(t)=\left(-\frac{U_{\text{P}}}{N_{\text{P}}}+% \frac{U_{\text{CD}}}{N_{\text{S}}}\right)(t-t_{1})$ (13)

Mode 3 ( $t_{2}\sim t_{3}$ ): The equivalent circuit diagram of working mode is shown in Fig. 5c. The switches S ${}_{5}$ and S ${}_{8}$ are opened, S ${}_{6}$ and S ${}_{7}$ are disconnected. The primary side H bridge runs in the same way as mode 2, and the secondary side H bridge charges the V2 through D ${}_{5}$ and D ${}_{8}$ . At this time, the power is forwardly transmitted, and the inductor current is gradually increased. The rate of growth is slowed due to the reduced inductor voltage. The magnetic flux of the side column and middle column are respectively:

$\displaystyle\Phi_{\text{AC1}}(t)=\Phi_{\text{AC2}}(t)=\frac{U_{\text{AB}}-U_{% \text{P}}}{N_{\text{L}}}(t-t_{2})$ (14) $\displaystyle\Phi_{\text{AC3}}(t)=\left(\frac{U_{\text{P}}}{N_{\text{P}}}-% \frac{U_{\text{CD}}}{N_{\text{S}}}\right)(t-t_{2})$ (15)

Mode 4 ( $t_{3}\sim t_{4}$ ): The equivalent circuit diagram of working mode is shown in Fig. 5d. At time $t_{3}$ , the switches S ${}_{1}$ , S ${}_{4}$ open simultaneously, and S ${}_{2}$ , S ${}_{3}$ disconnect simultaneously. Because $i_{\text{L}}$ can not change abruptly, the inductance current can continue through the diodes D ${}_{3}$ and D ${}_{4}$ , and it will decrease to zero at $t_{4}$ . The secondary H bridge operates in the same state as mode 3 and charges V2 through D ${}_{5}$ and D ${}_{8}$ . The magnetic flux of the side column and middle column are respectively:

$\displaystyle\Phi_{\text{AC1}}(t)=\Phi_{\text{AC2}}(t)=\frac{-U_{\text{AB}}-U_% {\text{P}}}{N_{\text{L}}}(t-t_{3})$ (16) $\displaystyle\Phi_{\text{AC3}}(t)=\left(\frac{U_{\text{P}}}{N_{\text{P}}}-% \frac{U_{\text{CD}}}{N_{\text{S}}}\right)(t-t_{3})$ (17)

Mode 5 ( $t_{4}\sim t_{5}$ ): The equivalent circuit diagram of working mode is shown in Fig. 5e. The inductor current is zero at time $t_{4}$ , and the switches S ${}_{2}$ , S ${}_{3}$ and S ${}_{5}$ , S ${}_{8}$ are turned on at the same time. When the primary and secondary power supplies charge the inductor at this time, the inductor current becomes zero-crossing negative and increases rapidly. During this period, the flux in the middle column of the side column is the same as that in mode 4.

$\displaystyle\Phi_{\text{AC1}}(t)=\Phi_{\text{AC2}}(t)=\frac{-U_{\text{AB}}-U_% {\text{P}}}{N_{\text{L}}}(t-t_{4})$ (18) $\displaystyle\Phi_{\text{AC3}}(t)=\left(-\frac{U_{\text{P}}}{N_{\text{P}}}+% \frac{U_{\text{CD}}}{N_{\text{S}}}\right)(t-t_{4})$ (19)

Mode 6 ( $t_{5}\sim t_{6}$ ): The equivalent circuit diagram of working mode is shown in Fig. 5f. At time $t_{5}$ , the switches S ${}_{2}$ , S ${}_{3}$ and S ${}_{6}$ , S ${}_{7}$ are turned on. The primary side operates in the same mode as modal 5, and the secondary side charges V2 via diodes D ${}_{6}$ and D ${}_{7}$ . At this time, the power is forwardly transmitted, and the inductor current is gradually increased, but the growth rate of $i_{\text{L}}$ is slowed down due to the reduction of inductance voltage. The magnetic flux of the side column and middle column are respectively:

$\displaystyle\Phi_{\text{AC1}}(t)=\Phi_{\text{AC2}}(t)=\frac{-U_{\text{AB}}+U_% {\text{P}}}{N_{\text{L}}}(t-t_{5})$ (20) $\displaystyle\Phi_{\text{AC3}}(t)=\left(-\frac{U_{\text{P}}}{N_{\text{P}}}+% \frac{U_{\text{CD}}}{N_{\text{S}}}\right)(t-t_{5})$ (21)

From the above analysis, the internal magnetic flux waveform of the integrated magnetics piece can be obtained, as shown in Fig. 4. The principle of the reverse operation mode is similar to that of the forward operation simply by changing the full bridge phase shift angle of the secondary H side is advanced to the full bridge phase-shifting angle of the primary H side. The magnetic flux analyzed by the internal magnetic flux of the IM core has zero variation in one cycle, which is the same as the DM.

2.3 Analysis of DC flux with DAB energy forward transmission

Figure 7.

Equivalent DC magnetic circuit.

The IM-DAB DC magnetic circuit is shown in Fig. 7. According to Ampere circuital theorem, the DC flux of each magnetic column is determined by the DC ampere turn and reluctance of the winding, so each magnetic column has an equivalent DC voltage source $0.5N_{\text{L}}i_{\text{L}}$ , $0.5N_{\text{L}}i_{\text{L}}$ , $N_{\text{P}}i_{\text{P}}-N_{\text{S}}i_{\text{P}}$ .

$\displaystyle\left\{{\begin{array}[]{l}\Phi_{\text{DC1}}=\frac{0.5N_{\text{L}}% i_{\text{L}}(R_{m2}+R_{m3})+0.5N_{\text{L}}i_{\text{L}}R_{m3}}{R_{1}R_{2}+R_{1% }R_{3}+R_{2}R_{3}}+\frac{(N_{\text{P}}i_{\text{P}}-N_{\text{S}}i_{\text{S}})R_% {m2}}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}\\ \\ \Phi_{\text{DC2}}=\frac{0.5N_{\text{L}}i_{\text{L}}(R_{m1}+R_{m3})+0.5N_{\text% {L}}i_{\text{L}}R_{m3}}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}-\frac{(N_{\text{P}}i% _{\text{P}}-N_{\text{S}}i_{\text{S}})R_{m1}}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}% \\ \\ \Phi_{\text{DC3}}=\frac{(N_{\text{P}}i_{\text{P}}-N_{\text{S}}i_{\text{S}})(R_% {m1}+R_{m2})}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}+\frac{0.5N_{\text{L}}i_{\text{% L}}R_{m2}-0.5N_{\text{L}}i_{\text{L}}R_{m1}}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}% \\ \end{array}}\right.$ (22)

In Eq. (22), $i_{\text{P}}$ is equal to $i_{\text{L}}$ , assume $R=R_{m3}=0.5R_{m1}=0.5R_{m2}$ . We can easily get Eq. (23):

$\displaystyle\left\{{\begin{array}[]{l}\Phi_{\text{DC}1}=\frac{N_{\text{L}}i_{% \text{L}}+(N_{\text{P}}i_{\text{P}}-N_{\text{S}}i_{\text{S}})}{4R}\\ \\ \Phi_{\text{DC2}}=\frac{N_{\text{L}}i_{\text{L}}-(N_{\text{P}}i_{\text{P}}-N_{% \text{S}}i_{\text{S}})}{4R}\\ \\ \Phi_{\text{DC3}}=\frac{N_{\text{P}}i_{\text{P}}-N_{\text{S}}i_{\text{S}}}{2R}% \\ \end{array}}\right.$ (23)

It can be seen from Eq. (23) that the DC component of the inductor core is $\Phi_{\text{DC1}}+\Phi_{\text{DC2}}\text{ = }{N_{\text{L}}i_{\text{L}}}/{2R}$ , so the DC component of the inductor is not affected by the transformer. Similarly, the DC component of the transformer is not affected by the inductance [11].

3. Gyrator-capacitor model of IM

Figure 8.

G-C model of inductance/transformer IM.

The gyrator-capacitor model has many advantages in simulating magnetic core nonlinearity and circuit-magnetic circuit hybrid simulation. In Fig. 8, the gyrator-capacitor model (hereinafter referred to as G-C model) [12] of DAB-IM is established in Spice software to test the accuracy of the design. $C_{\text{1}}$ , $C_{2}$ , $C_{3}$ simulate core side column and middle column reluctance, their values are 0.975 uF, 0.975 uF and 1.95 uF [13], respectively. The capacitor and EVALUE module are connected in parallel to realize the hysteresis characteristic of the nonlinear capacitor analog core. $C_{\text{L1}}$ , $C_{\text{L2}}$ analog transformer leakage inductance, its value is 1% of primary and secondary inductance divided by the square of turns, respectively. In Fig. 8, the current-controlled voltage source (CCVS) is used to simulate the gyrator capacitor, and its internal settings are shown in Fig. 9. The EE65 core is selected by the AP method, and the material is MnZn ferrite PC40.

Figure 9.

CCVS circuit diagram of G-C model.

Figure 10.

G-C model simulation waveform diagram.

Table 1

IM prototype parameters

Parameter	Value
Transformer primary turns	65
Transformer secondary turns	13
Inductor turns in the left column	21
Inductor turns in the right column	21

4. Result analysis

4.1 Simulation analysis of gyrator-capacitor model

The above analysis is verified by simulation. Switch tube selects IXFB60N80P, switching frequency is 20 kHz. The transformer ratio is 5:1, and inductance is 860 uH. Input voltage is 400 V, output voltage is 75 V. Figure 10a is a simulation waveform diagram of the DAB discrete magnetics. Figure 10b is a simulation waveform diagram of the DAB integrated magnetics. The simulation results show that the waveforms of $U_{\text{AB}}$ , $U_{\text{CD}}$ , the inductance voltage $U_{\text{L}}$ and the inductance current $i_{\text{L}}$ are the same after the integration. Simulation results by G-C model show that the design meets the requirements.

4.2 IM electric circuit-magnetic coupling calculation and analysis

Figure 11.

Flux density distribution in IM core.

Figure 12.

IM core loss density distribution.

Figure 13.

Prototype experimental system.

Figure 14.

Physical comparison before and after integrated magnetics.

Figure 15.

Phase-shifted 30 ${}^{\circ}$ waveform.

Figure 16.

Phase-shifted 60 ${}^{\circ}$ waveform.

Figure 17.

Phase-shifted 90 ${}^{\circ}$ waveform.

Figure 18.

Reverse transmission phase-shifted 30 ${}^{\circ}$ waveform.

Figure 19.

Efficiency comparison between DM and IM.

Figure 20.

Comparison of output power of IM with different coupling degrees.

The finite element [14, 15, 16] analysis software is used to establish the IM electric circuit-magnetic field finite element model, so as to verify whether the internal magnetic flux density of the design meets the requirements. Figure 11 shows the flux density distribution of IM core under the control of SPS. Figure 12 shows the loss density distribution of IM core under SPS control. Under the control of SPS, the operating magnetic density of the core is about 0.14 T, and the maximum magnetic density is about 0.18 T, which is far less than the saturation magnetic density of 0.35 T of ferrite. In this case, the core is unsaturated and the loss is low. Therefore, the EE65 core selected under the control of SPS meets the design requirements [17, 18].

4.3 Experimental verification

A integrated magnetics DAB experimental prototype of 600 W, 400 V input, 75 V/8 A output, and 20 kHz was fabricated to test the previous analysis. The IM parameters are shown in Table 1. Figure 13 is the experimental prototype, Fig. 14 is the physical comparison of the magnetic parts before and after the integrated magnetics. Experiments were carried out on the DAB-IM under the SPS control phase shift angle 30 ${}^{\circ}$ , 60 ${}^{\circ}$ and 90 ${}^{\circ}$ and the reverse phase shift angle of 30 ${}^{\circ}$ .

It can be clearly seen in Fig. 14 that when discrete magnetic parts are used, the design of the inductor core and transformer core are EE65 and EE55 respectively. Integrated magnetics can still use EE65. In this way, the volume and weight of the integrated magnetic core can be reduced by 35.84% and 36.24% respectively. Figures 15–17 are the phase shift waveform of 30 ${}^{\circ}$ , 60 ${}^{\circ}$ and 90 ${}^{\circ}$ in SPS control under energy forward transmission respectively. $U_{\text{AB}}$ is the primary input voltage waveform, $U_{\text{CD}}$ is the secondary output voltage waveform, $i_{\text{L}}$ is the inductor current waveform. Figure 18 shows the SPS controlled phase-shifting 30 ${}^{\circ}$ waveform under reverse energy transmission. The experimental results verify that the design can operate in a DAB system and enable bidirectional transmission of energy.

Figure 19 is a comparison of the operating efficiency of DM and IM under the same output current. When the output current is less than 4A, the efficiency of IM is greater than DM, but when the current is greater than 4A, the efficiency of DM is greater than IM. With the increase of the output current [19], the saturation of the integrated magnetics component will increase, which will lead to increased losses and increased temperature, and the decrease of the efficiency. Figure 20 is a comparison of the output power of different coupling degrees under the same input voltage. It can be clearly seen that the output power is maximum when the coupling coefficient $k=$ 0 under the same input voltage. When the coupling coefficient is not zero, it will lead to the coupling operation of the transformer and affect the operation effect [20].

5. Summary

A new integrated magnetics DAB is proposed. The proposed integration method is used to realize the decoupling integration of DAB inductor and transformer with a EE magnetic core. Compared with the discrete magnetics, the volume and weight of the integrated magnetic core can be reduced by 35.84% and 36.24% respectively. Simulation and experimental results verify the integrated magnetics can realize the bidirectional transmission of DAB power under phase shift control. The advantages of the method proposed in this paper are: (1) The power density of the converter is improved; (2) The energy storage inductance of the converter can be controlled; (3) The bidirectional energy flow of the converter can be realized.

Footnotes

Acknowledgments

Fundings: National Natural Science Foundation of China (51337001), National Natural Science Foundation of China (51777136), Joint Fund of State Key Laboratories of New Energy and Power Systems (LAPS 16017).

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