Duty ratio control ofthree port isolated bidirectional asymmetrical triple active bridge DC-DC converter

Received Jan 2, 2021 Revised Feb 25, 2021 Accepted Mar 19, 2021 Multiport converters are used in interfacing of distributed energy sources with grid/load. Isolated converters are needed in applications where converter gain is high and there is a requirement of isolation. Dual transformer asymmetric triple active bridge offers the advantage of reduced circulating current. However, the operating range is low for variation in load and source voltage. In this paper duty ratio modulation technique is proposed to regulate the load voltage and control the power flow in both the directions. As a result of the new gating scheme, the converter switches operate with ZVS, irrespective of variations in load power and source voltage. The converter is designed to ensure high switch utilization. The control technique is validatedthrough simulation of a 1kW three port DC-DC converter. It was observerd that the load voltage was regulated for wide range of variation in load power and source port voltages. The single input dual output mode was also verified.


INTRODUCTION
Multiport converters (MPC) are used in systems where more than two sources and loads are interfaced.The multiport converter has lower number of components compared to multiple two port converters; hence it is compact [1]- [3]. Multiport converters can be classified into three types based on the isolation of ports. They are, isolated, non-isolated and partially isolated MPC [2], [3]. In non-isolated MPC there is no galvanic isolation between any ports. Some ports of partially isolated MPC are isolated and all the ports are galvanically isolated in the case of Isolated MPC.
Isolated MPC is used in applications where there is a requirement of transformer isolation. It can also be used in applications demanding high converter gain and high power. Usually high frequency (HF) transformers are used in MPC, due to high switching frequency. This reduces the size of the transformer and other magnetic components [2]- [4]. Isolated MPC topologies have been derived from corresponding two port topologies, such as, forward converters, push-pull converters and flyback converters [2], [3].
Among the topologies reported in the literature, triple active bridge (TAB) has been researched extensively. It facilitates bidirectional power flow in all the ports [5]- [12]. The phase shift was optimized to minimize switching loses and mitigate electromagnetic issues [13]. Power flow was controlled using phase shift control method. The soft switching operating region with phase shift control was very narrow, hence duty ratio technique was utilized to increase the range of ZVS for variation of input voltage and load [14]- [18]. It also helped to reduce the switch voltage and current stresses. The topology is also scalable to higher ports. [19]- [21] had demonstrated the scalability by extending the number of ports to four. However control of power flow in the topology involved cross coupling of control loops, this problem was rectified by the decoupling network implemented in [18]. LC, LLC and CLLC resonant tank circuits respectively were added to TAB converter, thereby reducing the switching losses and enabling the operation at 100 kHz, hence increasing the power density [22]- [24]. Two modules of TAB wereused to interface four ports, consisting of two energy storage devices. There was one energy storage device for each module and the source and loads were shared by both modules [25]. Distributed transformers were usedto reduce the input current ripples and included a decoupling networkin the control system to overcome the cross coupling [25]. Modified TAB with DCM operation ensured the decoupling operation by average current control, without the decoupling network [26]. Altering the geometry ofthe transformer core andwindings to obtain four quadrant integrated transformer structure resulted in decoupled control [27].
The topologies discussed earlier used three winding transformer, which is susceptible to magnetic short circuit [28]. To overcome this problem, dual transformer based topologies were implemented. They were multiport CLL resonant converter and Dual transformer asymmetrical triple active bridge (DTATAB). Multiport CLL resonant converter reduced the voltage stress in the switches; however, the load port was not bidirectional [29]. DTATAB ensured bidirectional power flow in all its ports, however its switch current and voltage stress were high [28]. Since only phase shift control was used to control the power flow, the switches did not operate with ZVS for the entire range of load and supply voltage. Hence, a new modulation technique (Duty ratio control) is proposed in this paper, to regulate load voltage, control power flow in both the directions and operate the switches with ZVS for the entire range of variation in the load and supply voltage.
The paper is organized as follows: working principle of duty ratio control applied to DTATAB topology is explained in Section 2. Steady state analysis is explained in Section 3. The converter design is given in Section 4 and the simulation results are discussed in Section 5. The conclusions are drawn in Section 6.

OPERATING PRINCIPLE 2.1. Circuit description
DTATAB is a dual transformer fully isolated three port converter. This configuration was initially implemented by Jakka et. al. to overcome the problems of magnetic short circuiting in the triple active bridge three port converter [28].
In this topology two voltage source ports are connected across two single phase H bridge inverters. The resistive load port is connected across a three phase inverter bridge. The transformers are connected to the bridge conFigureurations as shown in Figure 1. The switches of the individual inverters are gated in such a way as to control the phase shift between the inverter output voltages. By adjusting the phase shift between the transformer winding input voltages (inverter output voltages) the power delivered by the ports can be controlled and the load port voltage V 3 can also be regulated. This is called phase shift control. The process of controlling the pulse width of the transformer winding voltage waveforms (inverter output) is called duty ratio control. Using duty ratio control combined with phase shift control, it is possible to operate the converter switches with ZVS. Hence this work is aimed at applying a gating scheme in the switches to enable duty ratio control.

Gating scheme
V 1 and V 2 are DC voltage sources connected across port 1 and port 2 respectively, R is a resistive load connected across port 3. The capacitor C 3 is assumed to be large enough to obtain a DC voltage V 3 across R, with minimum ripple. The switches are gated as shown in Figure 2. The waveforms of inverter output voltages due to this gating scheme are as shown in Figure 2. The transformer winding currents are also shown in Figure 3.

Operation modes
There are six operating modes for half the switching cycle. The proposed modulation technique is symmetric. a. Mode 1:0wt1 S 11 , S 14 , S 22 , S 23 , S 33 , S 32 , S 36 are the switches gated during this mode. The path of current flow is shown in Figure 4 3 . The winding currents are as shown in Figure 4 (a). The switch currents i s11 and i s14 are equal to i A . Currents i s23 and i s22 are equal to -i C . The currentsi A and i C are transformed as i A and i C in the secondary side of the transformer.The switch current i s32 is equal to i A , is i s36 is equal to i C and i s33 is equal to i A' +i C. b. Mode 2 1 <wt< 2 S 11 , S 14 , S 22 , S 24 , S 33 , S 32 , S 36 are the switches gated during this mode. The path of current flow is shown in Figure 4

(a). The voltage across A and B is (v AB ) is V 1 , voltage across C and D is (v CD ) is V 2 , the voltage across E and O (v EO ) and the voltage across F and O is (v FO ) is V
The switch currents i s11 and i s14 are equal to i A . Currenti s22 is equal to -i C and i s24 is equal to i C . The switch current i s32 is equal to i A , is i s36 is equal to i C' and i s33 is equal to i A' +i C. c. Mode 3:  2 <wt< 3 S 11 , S 14 , S 22 , S 24 , S 32 , S 34 , S 36 are the switches gated during this mode. The path of current flow is shown in Figure 4 (c). The voltage v AB is V 1 , vCD is 0, v EO is 0 and v FO is 0. The switch currents i s11 and i s14 are equal to i A . Currents i s22 is equal to -i C and i s24 is equal to i C . The switch current i s32 is equal to i A , i s36 is equal to i C' and i s34 is equal to -(i A' +i C' ).
d. Mode 4:  3 <wt< 4 S 11 , S 14 , S 21 , S 24 , S 32 , S 34 , S 36 are the switches gated during this mode. The path of current flow is shown in Figure 4 The switch currents i s11 and i s14 are equal to i A . Currents i s21 and i s24 are equal to i B . The switch current i s32 is equal to i A' , is 36 is equal to i C and i s34 is equal to -(i A' +i C' ). e. Mode 5:  4 <wt< 5 S 11 , S 14 , S 21 , S 24 , S 31 , S 34 , S 35 are the switches gated during this mode. The path of current flow is shown in Figure 4 (e). The voltage v AB is V 1 , vCD is V 2 , v EO is V 3 and v FO is V 3 . The switch currents i s11 and i s14 are equal to i A . Currents i s21 and i s24 are equal to i C . The switch current i s31 is equal to -i A , is 35 is equal to -i C' and i s34 is equal to -(i A' +i C' ). f. Mode 6:  5 <wt< 6 S 11 , S 13 , S 21 , S 24 , S 31 , S 34 , S 35 are the switches gated during this mode. The path of current flow is shown in Figure 4 3 and v FO is V 3 . The switch current i s11 is equal to i A and i s13 is equal to -i A . Currents i s21 and i s24 are equal to i C . The switch current i s31 is equal to -i A , is 35 is equal to -i C' and i s34 is equal to -(i A' +i C' ).

Equivalent circuit
Referring to the operation stages explained in Section II C, the circuit can be approximated to an equivalent circuit as shown in Figure 5. The following assumptions are made to obtain the equivalent circuit. L 1 and L 2 are the sum of the leakage inductance of the respective transformers referred to the secondary side and the inductors L A and L C respectively. a. The switches and diodes are assumed to be ideal b. The transformer can be replaced by a T equivalent circuit with all quantities referred to the secondary side c. The transformer loses are neglected d. The magnetizing inductance of the transformer can be neglected as its effect on the currents obtained will be minimum due to high switching frequency e. All the switches in the converter are switched at the same switching frequency.

STEADY STATE ANALYSIS
The current expressions for i A' and i C' are derived from the equivalent circuit using superposition theorem. There are 6 operating modes based on the values of phase shifts f 12 , f 23 and duty ratios D 1 , D 2 and D 3 . The voltage across port 3 can be expressed as shown in (1). (1) the power at the three ports P 1 , P 2 and P 3 can be expressed as shown in (2).
Where f is the switching frequency M 13 and M 23 depend on the phase shifts and duty ratios. Table 1 and Table 2 shows the expression of M 13 and M 23 respectively. For negative value of f 13 andf 23 respectivelyM 13 and M 23 can be obtained by negating the corresponding expressions in Tables 1 and 2. The plots of M 13 versus phase shift is shown in Figure 6. It can be observed from Figure 6 that M 13 is maximum for phase shift of 90 o . Hence powertransferred is maximum at a phase shift of 90 o . Hence the phase shift is fixed at 90 o and the power flow is controlled by varying the duty ratio D 1 , D 2 and D 3 . If D 3 is fixed at 1 and phase shift f 13 and f 23 are fixed at 0.5p c , the value of M 13 and M 23 will depend on D 1 and D 2 alone, respectively. Since P 1 is proportional to M 13 it can be controlled using D 1 and P 2 can be controlled using D 2 as it is proportional to M 23 .Hence the technique is easy to implement.   The plot of M 13 versus D 1 is shown in Figure 7. The graph of M 23 versus D 2 is same as Figure 7.

Figure 7. Gain vs Duty Ratio at Phase Shift 90o and -90o
For both the cases the expression of current in the switches during turn on is given by (7).
Since (7) is negative irrespective of V x and D x it can be inferred that the converter switches operate with ZVS irrespective of load power and source voltage variations. However, in the case of standalone phase shift control, ZVS can occur only when the condition specified in (8) is satisfied. Hence when the range of ZVS is taken into consideration, duty ratio control is better than phase shift control.

DESIGN
In this section an isolated DTATAB DC to DC Converter is designed for the specifications given in Table 3, the converter is designed for worst case operating conditions of minimum voltage in port 1, port 2 and maximum load of 1KW. It is a desirable quality to design the converter in such a way as to increase the switch utilization. Switch utilization defined by (9). = 3 (9) where P 3 is the maximum power at port 3 (Load power) and S is the switch stress given by (10).  (Right). It is observed in the plot that utilization increases with increase in transformer turns ratio and reduction in inductance. Hence n=n 1 =n 2 is chosen as 5 and n/ (w*L) is chosen as 0.1768. Hence the inductance L 1 =L 2 =L is 45µH. In (1) can be modified as shown in (12).
D1 and D2 are deduced from Figure 7.
The converter parameter design values are displayed in Table 4

RESULTS
In this section, the simulation results of a 1KW DTATAB DC-DC converter designed in Section 4 is shown. The worst case operating condition is V 1 =48V, V 2 =24V and the load R=10Ω. Both the ports 1 and 2 deliver equal power to port 3. For changes in load connected to port 3, V 3 is regulated to 100V by adjusting the duty ratios D 1 and D 2 .
The converter is simulated in PSIMto verify load voltage regulation (port 3) and ZVS in all the converter switches for different values of load (R, connected at port 3) and voltages at port 1(V 1 ) and port 2(V 2 ) .The value of load voltage, calculatedtheoriticaly (Th) and obtained through simulation (Sim) is tabulated in Table 5 and average current delivered by port 1 is tabulated in Table 6, forvarying valuesof load and source voltages in port1 and port 2. The average current delivered by port 2 is same as port 1. From Table 5, it is evident that the load voltage (V 3 ) is regulated at 100V, irrespective of variations in source voltage V 1 , V 2 and load R. The ratio of P 2 to P 1 ismaintained at V 2 /V 1, to maximise the switch utilisation. Figure 9 and Figure 10 show the waveforms of switch currents through all the converter switches, for full load. It can be observed from the waveformsthat every switch is turned on with ZVS. Hence, the switching losses are reduced in the converter due to soft switching. As the load reduces, the duty ratio D 1 and D 2 are reduced to regulate the load voltage V 3 , keeping D 3 , f13 and f23 constant. Hence the converter operates with mode 3 or mode 4. In mode 3 or mode 4 the switch operates with ZVS irrespective of port voltages or load value. To demonstrate ZVS at a lower value of load, the switch current waveforms for 10% of full load are shown in Figure 11 and Figure 12. It is evident from the switch current waveforms in Figure 11 and Figure 12 that all the converter switches turn on with ZVS.
The results mentioned earlier in this section correspond to the dual input single output case. The waveforms of load voltage, source currents and transformer winding voltages at 50% of full load are shown in Figure 13 (a).The figure shows that the load voltage is regulated at 100V and the source currents I 1 and I 2 are equal, which indicates that the ratio of P 2 to P 1 ismaintained at V 2 /V 1 .As the converter has bidirectional capability, it can operate in single input dual output mode, with port 1 being the input port and port 2, port 3 being the load ports.The simulation is performed to verify whether V 2 is regulated at 24V and V 3 is regulated at 100V, when port 3 and port 2 are loaded to 500W and 100W respectively. The voltages at port 2 and port 3 are regulated by adjusting D 1 at 0.7764, D 2 at 0.3873, f 13 at 0.5*p and f 23 at -0.5*p. The waveforms of load voltage, source currents and transformer winding voltages in the single input dual output mode are shown in Figure 13 (b). The figure shows that the value of V 2 and V 3 are 24V and 100V respectively, hence the voltage regulation is verified.
The results demonstrate the capability of duty ratio control to regulate the load voltage effectively for wide range of variation in load and source voltages. It is also shown that the converter switches operate with ZVS irrespective of the load and source voltage value. The bidirectional operation is verified from a case of single input dual output operation.

CONCLUSION
DTATAB topology was proposed to overcome the disadvantages of isolated TAB topology. Phase shift control was used for the topology. In this paper duty ratio control is proposed to increase the range of soft switching for wide variation of load power as well as the source port voltage. Duty ratios D 1 and D 2 are adjusted to regulate the load voltage V 3 and control the port powers P 1 and P 2 , keeping the phase shift (f 13 and f 23 ) fixed at 0.5p, for change in load or source voltage V 1 and V 2 or both. The direction of power flow P 1 can be reversed by fixing f 13 at -0.5p, P 2 can be reversed by fixing f 23 at -0.5p. The converter was designed to maximize the switch utilisation.
A 100V, 1KW ,3 port converter was simulated to verify the proposed method and it was observed that the load voltage is regulated with soft switching in all its switches for changes in the load and supply voltage.The bidirectional capability of the converter is demonstrated by loading port 2 and 3 at 100W and 500W, respectively. The load voltages at port 2 and 3 were regulated at 24V and 100V. The effectiveness of duty ratio control over phase shift controlin ZVS operation, with respect to the range of port voltage and load was mathematically demonstrated in section 3. The proposed duty ratio control is an effective and easy way to control the magnitude and direction of the port powers in a dual transformer isolated three port converter. Since operation with ZVS is achieved for all possible values of load and source voltages, the switching losses in the converter with the proposed modulation technique will be lesser compared to other modulation techniques reported in the literature. The technique can be conveniently scaled up for increase in the number of ports. However, thepeak value of switch current decreases at a low rate for decrease in the load. Hence future work may be onreducing the peak current with reduction in load and further increase the switch utilisation.