# Analysis of a Multilevel Dual Active Bridge (ML-DAB) DC-DC Converter Using Symmetric Modulation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. ML-DAB Topologies with Symmetric Phase-Shift Modulation

**Figure 1.**Boost configuration (V

_{p}> V

_{s}) of a multilevel dual active bridge (ML-DAB), where the transformer primary voltage (v

_{AB}) is two-level (2L) and the secondary (v

_{ab}) of 5L.

**Figure 2.**Buck configuration (V

_{s}< V

_{p}) of the ML-DAB where the transformer primary voltage (v

_{ab}) is of 5L and the secondary (v

_{AB}) is of 2L.

#### 2.1. Neutral Point Diode Clamped Configuration

#### 2.2. Switching States of the 3L-NPC Bridge

Switching States | Status of the Switches in 3L-NPC Leg-a | 3-Level LEG Voltage, v_{ao} | |||
---|---|---|---|---|---|

S_{a1} | S_{a2} | S_{a3} | S_{a4} | ||

+ | ON | ON | OFF | OFF | + $\frac{{V}_{P}}{2}$ |

0 | OFF | ON | ON | OFF | 0 |

− | OFF | OFF | ON | ON | − $\frac{{V}_{P}}{2}$ |

**Figure 3.**Switching states and corresponding 3L voltage (v

_{ao}) synthesized from leg-a of a 3L-NPC bridge.

**Figure 4.**Switch pulses and corresponding voltage waveforms and primary current in a 2L-5L DAB boost topology.

#### 2.3. Symmetric Modulation

**Figure 5.**Voltage waveforms in a 5L-2L DAB for three different cases of buck topology when v

_{AB}is formed using $D=0.5$.

## 3. Power Flow Equations and Soft Switching in ML-DAB

#### 3.1. 2L-5L DAB Boost Topology

_{L}(θ) equation for each segment of v

_{L}from zero to π as shown in Figure 4, we get, $\text{for}0\theta \left(\varphi -\beta \right):\text{}$

**Figure 7.**ML-DAB output power ${P}_{{o}_{p.u.}}vs.\text{}\varphi \text{and}\beta \text{with}\alpha ={10}^{0}\text{}$for $m=0.5,\text{}1,\text{}1.5\text{and}2.$

#### 3.2. 5L-2L DAB Buck Topology

_{ab}is assumed to start at angle zero, and 2L v

_{AB}is lagging by the phase-shift angle ϕ. In this topology, based on the value of ϕ, there may be three cases, such as $\text{CaseI}:\text{}0\varphi \alpha ,\text{CaseII}:\text{}\alpha \varphi \beta \text{and}$$\text{CaseIII}:\text{}\beta \varphi \frac{\pi}{2}$. Each case has been analyzed to formulate a power flow equation using the same procedure described from (1) to (11).

**Figure 8.**Power flow through DAB for all three cases (12) to (14), with respect to phase-shift ϕ; here, $\alpha ={10}^{0}\text{}and\text{}{20}^{0},\text{}\beta ={40}^{0}$ are assumed for calculation.

#### 3.3. 3L-5L DAB Boost Topology

_{AB}is assumed to start at angle γ after the zero, and 5L v

_{ab}is lagging v

_{AB}by the phase-shift angle ϕ The pulse-width of 3L waveform is assumed symmetrically reduced by an angle of γ which actually results from switch duty cycles D < 5. Using the same sector-wise inductor current analysis, as shown in (1) to (10), the power flow equation for this topology has been derived as,

**Figure 9.**Primary 3L voltage v

_{AB}secondary 5L voltage v

_{ab}and current through the primary referred leakage inductance i

_{L}; where ${V}_{s}=290\text{V},\text{}{V}_{P}=1,868\text{V},\text{}\alpha ={10}^{0},\text{}\beta ={40}^{0},\text{}$$\text{\gamma}={20}^{0}\text{and}\varphi ={60}^{0}.$

#### 3.4. Soft Switching

**Figure 10.**Soft switching boundaries shown in three-dimensional power vs. $\varphi $-$\text{}\beta $ planes (where $\alpha ={15}^{0},\text{}0\beta {90}^{0}\text{and}0\varphi {90}^{0}$); the grey planes (15) show the power vs. phi-beta relations for m = 0.5, 1, 1.5, 2; the green plane (17) is for two-level bridge, and the zero voltage switching (ZVS) is possible while operating under this plane; the blue (18) and red (19) planes are for five-level bridge leg-a and leg-b, respectively.

_{1}to S

_{4}with the condition of ${i}_{L}\left(0\right)<0$ as shown in Figure 12.

#### 3.4.1. Soft-Switching Conditions for the Two-Level (V_{s}) Bridge

_{s}) bridge (Figure 12), we can say that the condition for soft-switching in the primary bridge should be,

**Figure 12.**Voltage across the transformer v

_{AB}and v

_{ab}, inductor current i

_{L}and switch currents and voltages for S

_{1}to S

_{4}.

#### 3.4.2. Soft-Switching Conditions for the Leg-a of NPC (Five-Level) Bridge

_{a1}and S

_{a4}to be turned-on at ZVS: ${i}_{L}\left(\varphi +\beta \right)>0\text{}$

_{b1}and S

_{b4}to be turned-on at ZVS: ${i}_{L}\left(\varphi -\alpha \right)=0$

**Figure 13.**Voltage across the transformer ${v}_{AB}\text{and}{v}_{ab}$, inductor current ${i}_{L}$ and switch currents and voltages for ${S}_{a1}$ to ${S}_{a4}$.

**Figure 14.**Voltage across the transformer v

_{AB}v

_{ab}, inductor current i

_{L}and switch currents and voltages for S

_{b1}to S

_{b4}.

#### 3.5. Transformer Design

- ${V}_{1}\approx {V}_{s}=292\text{}V,\text{}{V}_{2}\approx {V}_{P}=1,667\text{}V,$ switching frequency ${f}_{s}=5\text{}kHz,\text{}$
- ${I}_{{1}_{rms}}=16.2\text{}A,\text{}{I}_{{2}_{rms}}=2.9\text{}A$ (RMS values calculated from simulation results),
- ${k}_{conv}=0.5$ (this factor value is chosen based on the converter topology),
- ${k}_{w}=0.4$ (this is the fill-factor having values usually within range of 0.3 to 0.6),
- ${B}_{mx}=1\text{}T$ (chosen based on the maximum saturation flux density being 1.56 T),
- ${J}_{mx}=6\text{}A/m{m}^{2}$ (peak current density with the use of litz wire).

## 4. Applications for ML-DAB

**Figure 16.**(From top to bottom) (

**a**) Change in PV output current I

_{pv}due to the change in light intensity from 800 W/m

^{2}to 1,000 W/m

^{2}; (

**b**) corresponding change in voltage V

_{pv}because of maximum power point tracking (MPPT) and (

**c**) power P

_{pv}.

**Figure 17.**(From top to bottom) (

**a**) Change in PV output current I

_{pv}due to the change in light intensity from 1,000 W/m

^{2}to 800 W/m

^{2}; (

**b**) corresponding change in voltage V

_{pv}because of MPPT and (

**c**) power P

_{pv}.

## 5. Simulation and Experimental Results

^{®}. The design parameters of the ML-DAB are listed in Table 2. Based on the soft-switching constraints for the ML-DAB switches, as shown in (16) to (19), a good choice for modulation parameters is used for simulation, which are $\alpha =10,\text{}\beta ={30}^{0}$ and $\varphi ={70}^{0}$. For the PV application explained in Section 4, 1,200-V or 1,700-V rated IGBTs are needed for ML-DAB. There are limitations in the switching characteristics of commercially available IGBTs when operated above 20 kHz. Hence, we have chosen 5 kHz for the proposed ML-DAB. The minimum input capacitor value has been theoretically calculated as 39 uF based on the ML-DAB parameters in Table 2. In the prototype, we have used a 100-uF polypropylene capacitor with a high ripple current carrying capacity.

Item Description | Nominal Value |
---|---|

V = _{s}V_{dc(2L)} | 292 V |

V = _{P}V_{dc(5L)} | 1,668 V |

ML-DAB high frequency transformer’s turns ratio, $\mathit{n}=\frac{{\mathit{V}}_{\mathit{P}}}{{\mathit{V}}_{\mathit{s}}}$ | 5.716 |

${\mathit{I}}_{{\mathit{L}}_{\mathit{2}\mathit{L}}}$ | 11.4 A |

${\mathit{I}}_{{\mathit{L}}_{\mathit{5}\mathit{L}}}$ | 2 A |

${\mathit{I}}_{{\mathit{L}}_{\mathit{2}\mathit{L}(\mathit{r}\mathit{m}\mathit{s})}}$ | 17 A |

Switching frequency, f_{s} | 5 kHz |

Leakage Inductance for ML-DAB transformer, L (value calculated as per Equation 14) | 0.5 mH |

2-level PV side bridge IGBT’s V_{CE} | 600 V (49% of V_{s}) |

3-level NPC bridge IGBT’s V_{CE} | 1,200 V (70% of $\frac{{V}_{P}}{2}$) |

**Figure 18.**(From top to bottom) (

**a**) Primary 2L voltage v

_{AB}; (

**b**) secondary 5L voltage v

_{ab}; and (

**c**) current through the primary referred leakage inductor i

_{L}.

**Figure 19.**(From top to bottom) (

**a**) ML-DAB input current I

_{in}and its average; (

**b**) output current I

_{out}and its average; and (

**c**) average input and output power ${P}_{in}=AVG\left({I}_{in}*{V}_{s}\right)\text{and}{P}_{out}=AVG({I}_{o}*{V}_{P})$.

**Figure 21.**Gate pulses for the ML-DAB IGBTs (from top to bottom: ${S}_{1,4},{S}_{2,3}\text{and}{S}_{a1},{S}_{a2},{S}_{a3},{S}_{a4}\text{and}{S}_{b1},{S}_{b2},{S}_{b3},{S}_{b4})$.

V_{s} | V_{p} | P_{in} | P_{out} | ${P}_{los{s}_{trans}}$ | ${P}_{los{s}_{total}}$ | Eff_{trans} | Eff_{total} |
---|---|---|---|---|---|---|---|

(V) | (V) | (w) | (w) | (w) | (w) | (%) | (%) |

60 | 310 | 161 | 133 | 14 | 28 | 90 | 83 |

80 | 416 | 284 | 239 | 27 | 45 | 90 | 84 |

100 | 521 | 443 | 373 | 45 | 70 | 89 | 84 |

120 | 626 | 638 | 561 | 42 | 77 | 93 | 88 |

**Figure 22.**ML-DAB 2L voltage v

_{AB}, 5L voltage v

_{ab}and current through the 2L and 5L side of the transformers ${i}_{{L}_{pri}}\text{and}{i}_{{L}_{sec}}$; where ${V}_{s}=125\text{V},\text{}{V}_{P}=650\text{V},\text{}n=5.71,\text{}\alpha ={10}^{0},$$\beta ={30}^{0}\text{and}\varphi ={70}^{0}.$

**Figure 23.**ML-DAB input (2L bridge) and output (5L bridge) dc current waveforms ${I}_{d{c}_{2L}}$ and ${I}_{d{c}_{5L}}.$

**Figure 24.**Output voltage and current waveforms when the ML-DAB is connected to a full-bridge inverter and a resistive-inductive (R-L) load.

## 6. Conclusions

^{®}. A hardware prototype is built and tested to verify the proposed ML-DAB performance with the symmetric modulation scheme. Experimental results have been presented to validate the proposed modulation and power flow in the ML-DAB.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- De Doncker, R.W.A.A.; Divan, D.M.; Kheraluwala, M.H. A three-phase soft-switched high-power-density dc/dc converter for high-power applications. IEEE Trans. Ind. Appl.
**1991**, 27, 63–73. [Google Scholar] [CrossRef] - Krishnamurthy, H.K.; Ayyanar, R. Building block converter module for universal (ac-dc,dc-ac,dc-dc) fully modular power conversion architecture. In Proceedings of the Power Electronics Specialists Conference, 2007 (PESC 2007), Orlando, FL, USA, 17–21 June 2007; pp. 483–489.
- Qin, H.; Kimball, J.W. Solid-state transformer architecture using ac–ac dual-active-bridge converter. IEEE Trans. Ind. Electron.
**2013**, 60, 3720–3730. [Google Scholar] [CrossRef] - Bhattacharya, S.; Zhao, T.; Wang, G.; Dutta, S.; Baek, S.; Du, Y.; Parkhideh, B.; Zhou, X.; Huang, A.Q. Design and development of generation-i silicon based solid state transformer. In Proceedings of the 2010 Twenty-Fifth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Palm Springs, CA, USA, 21–25 February 2010; pp. 1666–1673.
- Krismer, F.; Kolar, J.W. Efficiency-optimized high-current dual active bridge converter for automotive applications. IEEE Trans. Ind. Electron.
**2012**, 59, 2745–2760. [Google Scholar] [CrossRef] - Tang, G.-J.S.L. A three-phase bidirectional dc-dc converter for automotive applications. In Proceedings of the Industry Applications Society Annual Meeting, 2008 (IAS’08), Edmonton, AB, Canada, 5–9 October 2008; pp. 1–7.
- Engel, S.; Stieneker, M.; Soltau, N.; Rabiee, S.; Stagge, H.; de Doncker, R. Comparison of the modular multilevel dc converter and the dual-active bridge converter for power conversion in HVDC and MVDC grids. IEEE Trans. Power Electron.
**2014**, 30, 124–137. [Google Scholar] [CrossRef] - Tripathi, A.; Mainali, K.; Patel, D.; Bhattacharya, S.; Hatua, K. Control and performance of a single-phase dual active half bridge converter based on 15 kv sic igbt and 1200 v sic MOSFET. In Proceedings of the Applied Power Electronics Conference and Exposition (APEC), 2014 Twenty-Ninth Annual IEEE, Fort Worth, TX, USA, 16–20 March 2014; pp. 2120–2125.
- Kouro, S.; Malinowski, M.; Gopakumar, K.; Pou, J.; Franquelo, L.G.; Bin, W.; Rodriguez, J.; Perez, M.A.; Leon, J.I. Recent advances and industrial applications of multilevel converters. IEEE Trans. Ind. Electron.
**2010**, 57, 2553–2580. [Google Scholar] [CrossRef] - Panagis, P.; Stergiopoulos, F.; Marabeas, P.; Manias, S. Comparison of state of the art multilevel inverters. In Proceedings of the Power Electronics Specialists Conference, 2008 (PESC 2008), Rhodes, Greece, 15–19 June 2008; pp. 4296–4301.
- Aggeler, D.; Biela, J.; Kolar, J. A compact, high voltage 25 kW, 50 kHz dc-dc converter based on SiC JFETS. In Proceedings of the IEEE Applied Power Electronics Conference (APEC), Austin, TX, USA, 24–28 February 2008; pp. 801–807.
- Kulasekaran, S.; Ayyanar, R. Analysis, design and experimental results of the semi-dual active bridge converter. IEEE Trans. Power Electron.
**2014**, 29, 5136–5147. [Google Scholar] [CrossRef] - Moonem, M.; Krishnaswami, H. Analysis and control of multi-level dual active bridge dc-dc converter. In Proceedings of the Energy Conversion Congress and Exposition (ECCE), 2012, Raleigh, NC, USA, 15–20 September 2012; pp. 1556–1561.
- Filba-Martinez, A.; Busquets-Monge, S.; Bordonau, J. Modulation and capacitor voltage balancing control of a three-level NPC dual-active-bridge dc-dc converter. In Proceedings of the IECON 2013–39th Annual Conference of the IEEE on Industrial Electronics Society, Vienna, Austria, 10–13 November 2013; pp. 6251–6256.
- Nabae, A.; Takahashi, I.; Akagi, H. A new neutral-point-clamped PWM inverter. IEEE Trans. Ind. Appl.
**1981**, IA-17, 518–523. [Google Scholar] [CrossRef] - Wu, B. High-Power Converters and ac Drives; Wiley-IEEE Press: Hoboken, NJ, USA, 2006. [Google Scholar]

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**MDPI and ACS Style**

Moonem, M.A.; Pechacek, C.L.; Hernandez, R.; Krishnaswami, H.
Analysis of a Multilevel Dual Active Bridge (ML-DAB) DC-DC Converter Using Symmetric Modulation. *Electronics* **2015**, *4*, 239-260.
https://doi.org/10.3390/electronics4020239

**AMA Style**

Moonem MA, Pechacek CL, Hernandez R, Krishnaswami H.
Analysis of a Multilevel Dual Active Bridge (ML-DAB) DC-DC Converter Using Symmetric Modulation. *Electronics*. 2015; 4(2):239-260.
https://doi.org/10.3390/electronics4020239

**Chicago/Turabian Style**

Moonem, M. A., C. L. Pechacek, R. Hernandez, and H. Krishnaswami.
2015. "Analysis of a Multilevel Dual Active Bridge (ML-DAB) DC-DC Converter Using Symmetric Modulation" *Electronics* 4, no. 2: 239-260.
https://doi.org/10.3390/electronics4020239