A Bi-Directional Dual-Input Dual-Output Converter for Voltage Balancer in Bipolar DC Microgrid

Abstract

Bipolar DC microgrids (BDCMGs) have several issues related to the voltage and require numerous converters to supply power to both poles. To solve these issues, a bidirectional dual-input dual-output (DIDO) converter is proposed for the voltage balancer in BDCMG. The DIDO converter has dual-input sources and a dual-output port connected to the grid. Additionally, the DIDO converter simultaneously performs independent bidirectional power control and voltage balancing control. Based on the input voltages, this paper proposes modulation methods for three cases. The modulation method of the second case has a wide operating range and low balancing current ripple without increasing the switching frequency. Moreover, only voltage balancer mode without active input sources is proposed, considering the intermittent source. Therefore, it can operate as a voltage balancer under all conditions. The voltage balancing performance of the three cases was analyzed. Finally, the proposed modulation and control method of the DIDO converter were verified through experimental results.

1. Introduction

Renewable energy sources such as photovoltaics (PV) and wind energy are used extensively, and microgrids (MGs) are an important research area in this regard. MGs are classified as AC and DC MG. In particular, the DC MG reduces power conversion losses and has simple control structures, because DC MGs do not have reactive power and synchronization issues [1,2,3,4,5].

DC MGs are classified into two types: unipolar and bipolar. In particular, bipolar DC microgrids (BDCMGs) use two voltage levels with three wires, as shown in Figure 1. Further, a BDCMG has higher reliability than unipolar DC microgrids, because BDCMG can use independent DC buses [6,7]. Grid-connected converters use a suitable voltage level in BDCMG. However, a BDCMG has several problems. The main issue is that a large number of converters are required for positive, negative and DC buses. Additionally, unbalanced voltage occurs depending on the load conditions in the positive and negative buses. The unbalanced voltage causes low reliability and reduces the quality of the BDCMG. Voltage balancers that control the voltage deviation of the bipolar DC bus are commonly used to solve unbalanced voltages in BDCMG [8,9,10].

To solve the aforementioned main issues, a combined converter with voltage balancer and various converter have been proposed previously [11,12,13,14,15,16,17,18,19,20]. A non-isolated SEPIK-Cuk converter combined SEPIC and Cuk converter [11]; however, these converters are unidirectional converters. The dual output boost converter combines two boost converters with independent voltage control loops [12]. A combined boost-SEPIC type interleaved DC–DC converter [13], and a voltage balancer with an EV charger [14], a non-isolated three-level converter for voltage balancer [15,16], and a bi-directional DC–DC boost converter with additional inductors [17] were proposed. These non-isolated conventional converters have a single input source and are used as voltage balancers. Moreover, isolated topologies in BDCMG have been proposed in [18,19]. In [18], a three-level dual active bridge (DAB) converter with a modulation balancing method was introduced. The DAB converter operates without additional passive elements. The DAB converter and interleaved buck-boost converter were combined in [19] as a voltage balancer.

To control voltage balancing, these conventional converters supply power from an input source to the unbalanced load of the bipolar bus with balancing control. Otherwise, balancing control is possible only when power is supplied to the load. However, grid-connected converters of DCMGs use several intermittent sources. As a result, if the input sources are inactive, the operation of the voltage balancer is limited in BDCMG.

The aforementioned study has only a single input source. Moreover, a non-isolated dual-input dual-output (DIDO) unidirectional DC–DC converter for BDCMG was proposed in [20]. This converter controls a dual input source and regulates one of the bipolar bus voltages with one active input source. However, this converter performs unidirectional power flow and has limitations in voltage balancing because it requires an active input source. A comparison of conventional converters and the proposed DIDO converter is presented in

Table 1. Comparison of conventional converters and proposed dual-input dual-output converter for BDCMG.

Ref	Topology	Input Sources of Converter	Control and Voltage Balancing Method	Voltage Balancing without Input Source
[11]	SEPIC-Cuk Combination Converter	Single source	Unidirectional control with voltage balancing	No
[12]	Dual Output Boost Converter	Single source	Independent voltage control loops	No
[13]	Boost-SEPIC Interleaved Converter	Single source	Bidirectional control with voltage balancing	Yes
[14]	Modified Series-capacitor Converter	Single source	Bidirectional control with voltage balancing	No
[15]	Buck three-level Converter	Single source	Balancing control with modulation method	No
[16]	Full-bridge three-level Converter	Single source	Balancing control with modulation method	No
[17]	Integrated three-level Boost Converter	Single source	Independent voltage control loops	Not considered
[18]	Three-level DAB Converter	Single source	Balancing control with modulation method	No
[19]	Enhanced Two-level DAB Converter	Single source	Bidirectional control with voltage balancing	Not considered
[20]	DIDO Unidirectional DC–DC Converter	Dual sources	Unidirectional control with single bus voltage control	No
This paper	DIDO Bidirectional DC–DC Converter	Dual sources	1. Bidirectional and voltage balancing control with modulation method 2. Only voltage balancer mode without input sources	Yes

.

This paper proposes a combined bidirectional DIDO DC–DC converter that is used as a voltage balancer under all conditions with two input sources. Additionally, three types of modulation methods for voltage balancing in a BDCMG are proposed. The major contributions of this paper are summarized as follows:

(1)

The DIDO converter simultaneously performs voltage balancing and bidirectional power controls with dual inputs and outputs. Independent bidirectional power control and balancing control are realized under all load conditions.

(2)

Three types of modulation methods are performed. All three modulations can compensate for unbalanced power. Among the three types of modulation methods, the second modulation method reduces the current ripple in the voltage balancer without increasing the switching frequency.

(3)

To maintain voltage balancing without active input sources, additional modulation and control methods are required. Unlike conventional converters, this paper proposes a voltage balancer mode without active input sources.

The performances of the bidirectional control and voltage balancing were experimentally verified.

2. Proposed DIDO Converter

2.1. Configuration of the DIDO Converter

Figure 2 shows the bidirectional DIDO DC–DC converter. This converter has six power switches (S₁, S₂, S₃, S₄, S₅ and S₆), three inductors (L₁, L₂ and L₃), and four capacitors (C_in1, C_in2, C_out1 and C_out2). The output is connected to the BDCMG. P, O, and N are the nodes of the positive bus V_out1 and negative bus V_out2. The boost inductors L₁ and L₂ are connected to each input V_in1 and V_in2. R₁ and R₂ are the equivalent loads of the bipolar bus. C_in1 and C_in2 are the input capacitors, C_out1 and C_out2 are the output capacitors. i_L1 and i_L2 are the inductor currents, and i_L3 is the balancing current. To perform voltage balancing without active input sources, the balancing inductor L₃ is connected directly to the neutral line of the BDCMG. A theoretical analysis of the inductor currents and capacitors in the DIDO converter is presented in

Table 2. Theoretical analysis of the DIDO converter.

-	Theoretical Analysis
$\Delta i_{L1}$	$\frac{V_{in1}{D}_{1}T}{L_1}$$\mathrm{and} \frac{(V_{in1}-V_{out})(1-D_1)T}{L_1}$
$\Delta i_{L2}$	$\frac{V_{in2}{D}_{2}T}{L_2}$$\mathrm{and} \frac{(V_{in2}-V_{out})(1-D_2)T}{L_2}$
$\Delta v_{out}$	$\frac{C_{out1}\cdot C_{out2}}{(C_{out1}+C_{out2})}(\frac{V_{out}}{R_1+R_2})D_{1}T$
$\Delta v_{in1}$	$\frac{1}{L_1{C}_{in1}}\frac{V_{out}(1-D_1)D_1{T}^2}{8}$
$\Delta v_{in2}$	$\frac{1}{L_2{C}_{in2}}\frac{V_{out}(1-D_2)D_2{T}^2}{8}$

. First duty ratio is D₁, second duty ratio is D₂ and sampling time is T. The passive elements of each converter are designed based on Table 2 and the balancing inductor L₃ is designed for the modulation methods described in the next section.

2.2. Modulation Methods of DIDO Converter for Voltage Balancing in BDCMG

To simultaneously control voltage balancing and dual input sources, there are three possible operating cases: A, B and C. Three cases are defined based on d₁ and d₂, and an appropriate modulation method is proposed for each case. In every case, all switches switch only once, and the converter implements independent control loops with the same carrier waveform and switching frequencies.

The first duty ratio d₁ and second duty ratio d₂ have independent voltage gain, expressed as follows:

$$\frac{V_{out}}{V_{in1}}=\frac{1}{(1-d_1)}$$

(1)

$$\frac{V_{out}}{V_{in2}}=\frac{1}{(1-d_2)}.$$

(2)

The main switches are connected in a series, and the duty ratio d₁ is limited depending on d₂.

$$d_1\le d_2.$$

(3)

The voltage gain of the voltage balancer is expressed as follows:

$$\frac{V_{out2}}{V_{out1}}=\frac{d_3}{(1-d_3)}.$$

(4)

Based on the d₁ and d₂ values, the operating cases are defined as shown in

Table 3. The operating range of duty ratio and used switches for balancing modulations.

Case	Operating Range of Duty Ratio	Used Switches for Voltage Balancing
A	$d_1\le d_2<0.5$	S2 or S3
B	$d_1<0.5$$\mathrm{and} d_1\le d_2$	S1, S2 or S3, S4
C	$d_2-d_1>0.5$	S1 or S4

. Accordingly, Figure 3 shows the typical waveforms of the proposed modulations methods with the voltage balancing method when the equivalent load of the ON bus is a heavy load. In all cases, voltage balancing and bidirectional control are performed simultaneously. Values d₁ and d₂ are controlled independently; however, d₃ changes depending on the case. In particular, in case B, the balancing current ripple decreases without increasing the number of switching in the main switches.

The modulation methods use PI controller. The simple control loops for the grid-connected mode are shown in Figure 4. PI₁ and PI₂ are the outputs of the PI controller in the control loops, and PI₃ is the output of balancing control. Based on the master-slave control of BDCMG, current command references are selected by the master control with communication. To generate the balancing modulation, a flow chart of the balancing modulation is shown in Figure 5. If V_out1 is larger than V_out2, the balancing current is supplied to the ON pole using Out1. Conversely, if V_out2 is larger than V_out1, the balancing current is supplied to the PN pole using Out2. The modulation methods of the three cases are analyzed below.

2.2.1. Case A: $d_1\le d_2<0.5$

Figure 3a shows the typical waveforms of the modulation method in case A. Only one switch (S₂ or S₃) is used for voltage balancing; therefore, the modulation method is simple, as shown in Figure 6. The balancing factors Out1 or Out2 is added to the PWM reference of the switch (S₂ or S₃) for voltage balancing. If V_out1 is larger than V_out2, Out1 is used; alternatively, if V_out2 is larger than V_out1, Out2 is used. Consequently, the current ripple of the balancing inductor in the steady-state can be calculated as

$$\Delta i_{L3}=\frac{V_{out1}}{L_3}{d}_{3}T \mathit{or} \Delta i_{L3}=\frac{-V_{out2}}{L_3}(1-d_3)T$$

(5)

There is no limit to compensate for unbalanced loads because the balancing inductor is controlled similar to a buck-boost converter.

2.2.2. Case B: $d_1<0.5$ and $d_1\le d_2$

The second typical waveform of the modulation method in case B is shown in Figure 3b. The modulation method in case B is more complex than those in cases A and C, as shown in Figure 7. However, case B has a wide operation range and lower current ripple, because the voltage of L₃ is supplied twice during one switching period by the switch (S₁, S₂ or S₃, S₄). As a result, the current ripple of L₃ is reduced without increasing the switching frequency. The balancing factors Out1 or Out2 are added to the PWM reference of a switch (S₂ or S₃) and subtracted from the PWM reference of the other switch (S₁ or S₄). The operating modes in case B are shown in Figure 7.

Mode 1 (t₀–t₁) (Figure 8a): S₁, S₂, S₃, S₅, and S₆ are turned on, and S₄ is turned off. The inductor current i_L1 is the negative current slope, and i_L2 is the positive current slope because inductor voltage V_L1 is V_in1–V_out and V_L2 is equal to V_in2. The balancing current i_L3 is the positive current slope generated by V_out1.

Mode 2 (t₁–t₂) (Figure 8b): S₁, S₂, S₃, and S₄ are turned on, S₅ and S₆ are turned off. All the main switches are turned on. The inductor currents i_L1 and i_L2 have a positive current slope because the inductor voltage V_L1 is V_in1 and V_L2 is equal to V_in2. The balancing current i_L3 is the negative current slope generated by −V_out2. This mode determines the maximum inductor current ripple of L₃.

Mode 3 (t₂–t₃) (Figure 8c): S₁, S₂, S₄, S₅, and S₆ are turned on, and S₃ is turned off. The inductor currents i_L1 and i_L2 are negative current slopes because the inductor voltage V_L1 is V_in1–V_out and V_L2 is V_in2–V_out. The balancing current i_L3 is the positive current slope once again, like Mode 1. In case B, the current ripple is reduced because this positive current slope is repeated twice.

Mode 4 (t₃–t₄) (Figure 8d): S₁, S₄, S₅, and S₆ are turned on, and S₂, S₃ are turned off. The inductor current i_L1 and i_L2 are negative currents as in Mode 3. The balancing current i_L3 is the negative current slope.

Mode 5 (t₄–t₅) (Figure 8e): S₂, S₄, S₅, and S₆ are turned on, and S₁, S₄ are turned off. The inductor current i_L1 and i_L2 are the same as those in mode 1. The balancing current i_L3 is still the negative current slope. In addition, the maximum current ripple of L₃ changes according to d₁ and d₂. Therefore, an analysis is required for inductor design. The current ripple of L₃ in the steady-state is calculated as follows:

$$\Delta i_{L3}=\{\begin{array}{cc}\frac{V_{out1}}{L_3}{d}_{3}T& t_0<t\le t_1\\ \frac{-V_{out2}}{L_3}{d}_{1}T& t_1<t\le t_2\\ \frac{V_{out1}}{L_3}{d}_{3}T& t_2<t\le t_3\\ \frac{-V_{out2}}{L_3}(1-d_1-2d_3)T& t_3<t\le t_5\end{array}$$

(6)

Based on Equation (6), the positive current slopes are determined by d₃, but the value of d₃ is equal in the first and third current slopes. Therefore, the maximum current ripple of L₃ is determined by the second and fourth current slope as d₁.

When d₁ < 0.25, the maximum current ripple of L₃ is

$$\frac{-V_{out2}}{L_3}{d}_{1}T<\frac{-V_{out2}}{L_3}(1-d_1-2d_3)T; \mathrm{as} d_1<0.25$$

(7)

When d₁ > 0.25, the maximum current ripple of L₃ is

$$\frac{-V_{out2}}{L_3}{d}_{1}T>\frac{-V_{out2}}{L_3}(1-d_1-2d_3)T; \mathrm{as} d_1>0.25.$$

(8)

Based on Equations (7) and (8), the maximum current ripple of L₃ is calculated based on d₁. When d₁ is 0.25 and V_PN is 190 V, the minimum current ripple is half the current ripples of the other cases, as shown in Figure 9.

2.2.3. Case C: $d_2-d_1>0.5$

The modulation method for case C is shown in Figure 3c. Only one switch (S₁ or S₄) is used in the balancing modulation to have a sufficient voltage gain for the balancer. The balancing factors Out1 or Out2 are subtracted from the PWM reference of the switch (S₁ or S₄) as shown in Figure 10. The modulation method is simple and uses the same voltage gain similar to case A. The current ripples of the buck-boost converter in a steady-state can be calculated as follows:

$$\Delta i_{L3}=\frac{V_{out1}}{L_3}{d}_{3}T \mathrm{or} \Delta i_{L3}=\frac{-V_{out2}}{L_3}(1-d_3)T.$$

(9)

The three modulation methods simultaneously perform dual bidirectional power control and voltage balancing control. The duty ratios are independently controlled and voltage balancing is implemented regardless of the unbalanced power.

Figure 9. Current ripple of L₃ in case B.

Figure 9. Current ripple of L₃ in case B.

Figure 10. The modulation method of case C.

Figure 10. The modulation method of case C.

2.3. Modulation Methods of DIDO Converter for Voltage Balancing in BDCMG

The previous balancing methods are implemented with an active input source; i.e., converters supply power from an input source to an unbalanced load of the bipolar bus with balancing control, or balancing control is possible only when power from the input source is supplied to the load. Because the combined converters simultaneously perform balancing and power control with modulation, the voltage balancing operation is limited by the condition of input sources, for example, PV, battery application, and fuel cell. However, as BDCMG always maintain voltage balancing, an additional balancing method is required. Therefore, the DIDO converter circuit has buck-boost-based voltage balancer for only voltage balancer mode. The only voltage balancer mode implements the voltage balancer and modulation method, such as a buck-boost converter, as shown in Figure 11. As shown in Figure 12, if the switches (S₁, S₂, S₅ or S₃, S₄ and S₆) are turned on simultaneously, the voltage is only supplied to L₃. The voltage gain in only voltage balancer mode is expressed as follows:

$$\frac{V_{out2}}{V_{out1}}=\frac{d_3}{(1-d_3)}.$$

(10)

Based on the only voltage balancer mode, the DIDO converter always performs balancing control without active input sources in BDCMG. This mode also controls voltage balancing regardless of the unbalanced power.

2.4. Modeling of DIDO Converter

This converter has independent control loops based on d₁, d₂ and d₃. Control operations based on two boost converters and one buck-boost converter are performed. Based on each operation mode, the small-signal model can be calculated.

$$\frac{{\widehat{i}}_{L_1}}{{\widehat{d}}_1}=\frac{V_{PN}(C_{out1}+C_{out2})s+\frac{V_{PN}}{(R_1+R_2)}+(1-D_1)I_{L1}}{L_1(C_{out1}+C_{out2})s^2+(\frac{L_1}{(R_1+R_2)}+R_{L_1}(C_{out1}+C_{out2}))s+\frac{R_{L_1}}{(R_1+R_2)}+{(1-D_1)}^2}.$$

(11)

$$\frac{{\widehat{i}}_{L_2}}{{\widehat{d}}_2}=\frac{V_{PN}(C_{out1}+C_{out2})s+\frac{V_{PN}}{(R_1+R_2)}+(1-D_2)I_{L_2}}{L_2(C_{out1}+C_{out2})s^2+(\frac{L_2}{(R_1+R_2)}+R_{L_2}(C_{out1}+C_{out2}))s+\frac{R_{L_2}}{(R_1+R_2)}+{(1-D_2)}^2}.$$

(12)

$$\frac{{\widehat{v}}_{on}}{{\widehat{d}}_3}=\frac{V_{PO}[\frac{D_3{L}_3}{R_2}s-{(1-D_3)}^2]}{{(1-D_3)}^2[L_3(C_{out2})s^2+\frac{L_3}{R_2}s+{(1-D_3)}^2]}.$$

(13)

Based on small-signal model, the PI controllers are designed within the stable region. The parameters of the PI controller are as follows: K_p1 and K_p2 are 0.3, K_i1 and K_i2 are 30, K_p3 is 3 and K_i3 is 10.

3. Experimental Results

The experimental results were obtained using a prototype converter to verify the DIDO converter and control methods, as shown in Figure 13. The parameters of the prototype are listed in

Table 4. Parameters of the prototype.

Parameter	Value
Input voltage #1 (Vin1)	150 – 170 V
Input voltage #2 (Vin2)	55 – 130 V
DC link voltage (Vout)	190 V
Inductor (L1, L2, L3)	500 μH
Capacitor (Cin1, Cin2, Cout1, Cout2)	280 μF
Switching frequency (fs)	20 kHz

. The power switches are used as FCH060N80. In this paper, the control of the DB-BB DIDO converter is implemented using TMS320F28377s.

3.1. Experimental Result of the DIDO Converter without Voltage Balancing Method

Figure 14 shows the experimental waveforms under an unbalanced load without balancing control, when R₁ and R₂ are 62.3 and 18.7 Ω, respectively. The gate-source voltages of S₁, S₂, and S₅, and inductor current i_L1 are shown in Figure 14a. In these waveforms, the input voltage conditions are V_in1 = 150 V and V_in2 = 130 V and the output current i_L1 increases when V_gs1 and V_gs2 overlap. In Figure 14b, the output voltages V_out1 and V_out2 and inductor currents i_L1 and i_L2 are shown. The input voltage conditions are V_in1 = 160 V and V_in2 = 80 V. V_out1 and V_out2 are unbalanced without balancing control and the duty ratios d₁ and d₂ are different depending on the input voltages.

3.2. Experimental Results with the Proposed Method in Case A

Figure 15 shows the experimental waveforms of the DIDO converter with balancing modulation in case A. In case A, the switch that implements balancing control uses only S₂. In Figure 15a–c, V_in1 is 150 V, V_in2 is 130 V, R₁ is 62.3 Ω, and R₂ is 18.7 Ω. Experimental result of the balancing duty ratio d₃ is approximately 0.5 based on Equation (5), and the inductor current i_L3 is 3.65 A with unbalanced loads. The gate-source voltages, S₁, S₂, and S₅, and inductor current i_L3 are shown in Figure 15a. The turn-on time of S₂ is increased by d₃, and S₂ is used for the balancing control because the ON bus is a heavier load than the PO bus. V_out2, i_L1, i_L2, and i_L3 are shown in Figure 15b; i_L1 is 1.2 A, i_L2 is 1.75 A, i_L3 is 3.65 A and V_out2 is 95.2 V. As a result, the performance of the modulation method in case A is confirmed under the unbalanced load conditions. Additionally, independent power control and balancing control are performed simultaneously. In Figure 15c, the DIDO converters output a positive output current and simultaneously implement balancing control. The conditions are the same as those in Figure 15b. Likewise, V_out1 and V_out2 have a balanced voltage, and the error of the balancing voltage is 0.2 V. In Figure 15d, the boost converters output negative inductor currents and control balancing control; i_L2 is −1.67 A and i_L3 is 3.6 A. Based on Figure 15, the proposed modulation and control method of case A are verified with bidirectional and balancing control.

3.3. Experimental Results with the Proposed Method in Case B

Figure 16 shows the experimental waveforms of the DIDO converter for case B. In case B, the two switches (S₁ and S₂) perform the balancing control. This case reduces the current ripple of i_L3 without increasing the switching frequency. In Figure 16a,b, the input voltage conditions are V_in1 = 160 V and V_in2 = 80 V, with unbalanced load R₁ = 62.3 Ω and R₂ = 37.3 Ω. The balancing duty ratio d₃ is almost 0.25 in the steady state. In the other cases, the maximum current ripple is 4.7 A; however, the proposed control method in case B reduces to 3 A, as shown in Figure 16. As a result, the theoretical balancing current and experimental balancing current of L₃ are similar.

Figure 16a shows the gate-source voltages of S₁, S₂, and S₅ and inductor current i_L3. The turn-on times for S₁ and S₂ increase with d₃. In Figure 16b,c, the boost converters implement positive and negative outputs with balancing control. In Figure 16b, i_L1 is 1.25 A, and i_L3 is 1 A. In Figure 16c, i_L2 is −2 A, and i_L3 is 1 A. Bidirectional control and balancing control are performed independently. The proposed modulation method for case B is experimentally verified.

3.4. Experimental Results with the Proposed Method in Case C

Figure 17 shows the experimental waveforms of the DIDO converter for case C. In case C, only one switch (S₁) performs balancing control. The input voltage conditions are V_in1 = 170 V and V_in2 = 55 V. The unbalanced loads are R₁ = 62.3 Ω and R₂ = 18.7 Ω as shown in Figure 17a. In Figure 17a, the turn-on time of S₁ is increased by d₃. The balancing current of L₃ is 3.55 A. The balancing current of L₃ in case C is similar to that of L₃ in case A. In Figure 17b, the unbalanced load R₁ is 31.2 Ω and R₂ is 18.7 Ω. In Figure 17b, the DIDE converters control the negative current with balancing; further, i_L2 is −1.6 A, and i_L3 is 2.13 A.

3.5. Experimental Result of the Only Voltage Balancer Mode

Figure 18 shows the experimental waveforms of the only voltage balancer mode. The only voltage balancer mode controls V_out1 and V_out2 without active input sources. In Figure 18a, R₂ is changed from 37.3 to 18.8 Ω, and V_out2 is 95 V under the variable unbalanced load with positive balancing currents i_L3. Figure 18b shows that the balancing currents i_L3 is changed from positive to negative under the following changing loads: R₁ changes from 62.4 Ω to 31.2 and R₁ from 18.8 to 37.3 Ω. This mode operates as a voltage balancer without active input sources, but stable voltage balancing is performed.

3.6. Comparison of Conventional Converters and the DIDO Converter in BDCMG

Table 5. Comparison between conventional converter and DIDO converter for voltage balancer in BDCMG.

Topology	No. of Power Switches (MOSFET + Diode)	No. of Inductors + Capacitor (Input and Output)	Power Flow	Controllable Port (Input + Output Source)	Peak Efficiency (Power)
[11]	1 + 2	4 + 5	Unidirectional	1 + 2	88.1% (450 W)
[12]	2 + 2	2 + 3	Unidirectional	1 + 2	89.6% (53.5 W)
[13]	4 + 0	3 + 4	Bidirectional	1 + 2	96.1% (200 W)
[14]	4 + 0	2 + 3	Bidirectional	1 + 2	96.39% (60 kW)
[17]	4 + 2	2 + 3	Bidirectional	1 + 2	-
[20]	2 + 4	1 + 4	Unidirectional	2 + 2	93% (200 W)
This paper	6 + 0	3 + 4	Bidirectional	2 + 2	94.8% (1 kW)

shows a comparison between the conventional combined converter and DIDO converter for BDCMG. The DIDO converter performs bidirectional control of both input sources and voltage balancing. Balancing control is realized without active input sources, and the DIDO converter controls voltage balancing regardless of the unbalanced power. Therefore, voltage balancing of the DIDO converter is possible under all conditions of a BDCMG. However, voltage balancing of conventional converters is limited, owing to the modulation methods, active input sources, and configuration. Conventional converters perform voltage balancing with an active input source. The proposed control enables voltage balancing even when the input source is not activated. In addition, dual input and voltage balancing control can be controlled independently. Moreover, the converter in [20] controls dual inputs and dual outputs for BDCMG, but it performs unidirectional control. However, the proposed converter controls voltage balancer and dual bidirectional power.

Figure 19 shows the efficiency analysis based on unbalanced loads with WT3000. When the unbalanced power is 760 W and converters #1 and #2 control positive output current, the efficiency of the DIDO converter based on the position of the unbalanced load is analyzed. Under this condition, the ON pole is a heavy load, and the efficiency is high as the current of the switch decreases because i_L3 is a positive balancing current and i_L1 and i_L2 are a positive output current. Furthermore, the PO pole is a heavy load, and the current of the switch increases, because i_L3 is a negative balancing current. As a result, i_L1 and i_L2 are a positive output current.

Figure 20 shows the performance of voltage balancing for cases A, B and C. The unbalanced load condition is R₁ = 62.3 Ω and R₂ = 18.7 Ω. The Three cases show a voltage deviation of less than 0.5 V. Therefore, it is confirmed that three cases have proper voltage balancing performance.

4. Conclusions

This paper proposes a bidirectional DIDO converter for voltage balancer in BDCMG. The DIDO converter has two input sources and two output ports connected to the BDCMG, and it simultaneously performs independent bidirectional power control and voltage balancing control. Based on d₁ and d₂, modulation methods are proposed for three cases. Cases A and C have a simple control structure because only one switch is used for the balancing control. In case B, two switches are used for the balancing control, which has a wide operating range, and the current ripple of L₃ is reduced by up to 50% without increasing the switching frequency. The proposed modulations can be used by optimizing for each condition. Since the control loop operates independently, this converter has a simple control structure. Furthermore, only a voltage balancer mode is proposed to perform voltage balancer without an active input source. Voltage balancing is possible by using only two output ports without input sources. As a result, The DIDO converter operates as a voltage balancer under all conditions in BDCMG. Additionally, voltage balancing can be controlled regardless of the unbalanced power. The bidirectional control and voltage balancing performance of the three cases are verified through the experimental results. From the experimental results, the bipolar voltage has a voltage deviation of less than 0.5 V. The bidirectional current control operated stably. Therefore, three cases have proper voltage balancing and bidirectional control performance. As MGs become more popular, this paper will be used in the study of grid-connected converters considering the characteristics of MG.