# Design Guidelines for a DAB Converter Incorporating a Multilevel Bridge with Quasi-2-Level Operation

José Andrés Aguilar Croston, Jean-Yves Gauthier, Cyril Buttay, Maryam Saeedifard, Besar Asllani, Piotr Dworakowski

## ► To cite this version:

José Andrés Aguilar Croston, Jean-Yves Gauthier, Cyril Buttay, Maryam Saeedifard, Besar Asllani, et al.. Design Guidelines for a DAB Converter Incorporating a Multilevel Bridge with Quasi-2-Level Operation. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0186. hal-05105964

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# Design Guidelines for a DAB Converter Incorporating a Multilevel Bridge with Quasi-2-Level Operation

José Andrés Aguilar Croston¹,², Jean-Yves Gauthier², Cyril Buttay², Maryam Saeedifard³, Besar Asllani¹, Piotr Dworakowski¹

¹SUPERGRID INSTITUTE

Villeurbanne, France

jose-andres.aguilar@supergrid-institute.com

https://www.supergrid-institute.com/

²INSA Lyon, CNRS, Universite Claude

Bernard Lyon 1, Ecole Centrale de Lyon,
Ampère, UMR5005

Villeurbanne, France

http://www.ampere-lab.fr/

³GEORGIA INSTITUTE OF TECHNOLOGY

School of Electrical and Computer Engineering
Atlanta, USA

https://ece.gatech.edu/

## Acknowledgements

This work was supported by the French Government under the program Investissements d'Avenir (ANE-ITE-002-01).

## Keywords

«Dual Active Bridge Converter», «Medium voltage converter», «Power transmission», «Bi-directional converters».

## Abstract

The development of medium voltage DC networks requires efficient DC-DC converters. In this context, the Dual Active Bridge (DAB) with quasi-2-level (Q2L) operation is analyzed as a potential candidate. Power transfer equations, conduction losses and zero voltage switching conditions are derived using Fourier series approximations. Operating principles for multilevel converters are also provided. It is determined that 25° is the boundary of the transition time at which 2L design equations remain valid for Q2L operation. Furthermore, Q2L operation demonstrates superior efficiency during medium to high load operation, due to reduced switching losses, provided the transition time is chosen optimally.

## I. Introduction

The rising interest in renewable energy, electric vehicles, energy storage and data centers results in renaissance of DC networks [1], [2], enabled by fast-switching semiconductors [3]. One of the

remaining obstacles to the growth of DC networks is the development of an isolated, high conversion ratio, bidirectional DC-DC converter: indeed, recent medium voltage DC (MVDC) research [4] and industrial interest [5] demand a suitable MVDC-LVDC (low voltage DC) converter, comparable in its function to the ubiquitous distribution transformer for AC networks. The Dual Active Bridge (DAB) [6] converter, shown in Fig. 1, is a possible candidate, offering galvanic isolation, bidirectional power flow, high power density, and energy efficiency thanks to soft switching. Resonant topologies, like the series resonant converter (SRC), offer improved efficiency [7], [8] but have a limited voltage range due to limited switching frequency variation.

In its 2-level (2L) implementation, the operating voltage of a DAB converter is restricted by the voltage ratings of its switches. Given the lack of commercially available high-voltage semiconductors for a 2L medium-voltage DAB converter, various workarounds have been proposed for MVDC applications. A common approach is the modular input-series, output-parallel (ISOP) arrangement of individual converters [9]. However, this cascading approach requires multiple medium-frequency transformers, terminals and connections, isolated at medium voltage level, which may be suboptimal on an industrial scale. Another option is the series connection of multiple switching devices [10], such as SiC MOSFETs [11] or SiC JFETs in a SuperCascode [12], [13], though issues like voltage sharing and high $dV/dt$ arise.
A more recent approach uses multilevel voltage-source inverters such as the Flying Capacitor Converter (FCC) [10] or the Modular Multilevel Converter (MMC) [14], with the goal of scaling up the bridge voltage rather than improving the harmonic spectrum. The quasi-2-level (Q2L) or quasi-square-wave (QSW) operation enables trapezoidal voltage waveforms with controllable and steep transitions. The key operating parameter is the transition time, which defines the duration of these steep transitions. Q2L operation [15] has been studied in the context of MMC, FCC, and Neutral-Point-Clamped (NPC) [16], [17] topologies.

Studies have analyzed Q2L-MMC leg design [18] and compared flying capacitor sizing in Q2L-FCC to classic FCC designs [19]. Q2L operation is a growing area of research, with prototypes of FCC [20], [21] and MMC [22], [23] utilizing trapezoidal modulation. However, a comprehensive study on Q2L voltage-source converters is still lacking. Recent studies have explored QSW operation [24] and the impact of trapezoidal modulation on Isolated Modular Multilevel DC-DC Converters (IM2DC) [25], [26], but they do not address the transition time requirements for MVDC-LVDC converter operations. A clear limit for the transition time in Q2L voltage-source inverters used in isolated MVDC-LVDC converters has yet to be established.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Circuit diagram of a single-phase DAB converter.</figcaption></figure>

This paper uses Fourier series of current and voltage waveforms to provide design equations for a DAB converter with a Q2L bridge. Power transfer equations, conduction losses and zero voltage switching conditions are derived. Based on the findings of this paper, the guidelines provided are applicable to FCC, MMC and any other multilevel topology operated in Q2L. The novelty of this work lies in defining the boundary of the transition time at which 2L design equations remain valid for Q2L operation.

The paper is structured as follows: Section II defines 2L, Q2L, and multilevel operation and specifies the converter requirements; Section III

details Q2L operation; Section IV presents a power transfer characterization and conduction loss analysis, Section V examines zero voltage switching conditions; Section VI compares efficiency across different operational modes; Section VII provides guidelines for Q2L operation; and the final section presents the conclusions.

## II. Monolithic high ratio isolated bidirectional DC-DC converter specifications

In this paper, an isolated bidirectional DC-DC converter for MVDC to LVDC interconnection is considered. The key parameters used in the analysis are listed in Table I. Silicon carbide (SiC) MOSFETs are selected for their high efficiency and fast-switching performance.

The main aspects for the development of a Q2L bridge in a DC-DC converter are:

* Higher achievable bridge voltage compared to voltages sustained by single-transistor-per-switch 2L bridges.

* Limited and controllable average $dV/dt$.

* Design and control similar to 2L operation.

* Small passive components compared to multilevel operation.

<table><caption>Table I: Parameters of the study system</caption><thead><tr><th>Parameter of the two case studies</th><th>1st</th><th>2nd</th></tr></thead><tbody><tr><td>Medium voltage (V<sub>MV</sub>)</td><td>40 kV<br>±10%</td><td>10 kV<br>±10%</td></tr><tr><td>Low voltage (V<sub>LV</sub>)</td><td colspan="2">1.5 kV ±10%</td></tr><tr><td>Nominal power (P<sub>n</sub>)</td><td>4 MW</td><td>1 MW</td></tr><tr><td>Switching frequency (F<sub>sw</sub>)</td><td colspan="2">10 kHz</td></tr><tr><td>Transition time angle (θ)</td><td>17°</td><td>4°</td></tr><tr><td>MOSFET voltage rating</td><td colspan="2">3.3 kV</td></tr></tbody></table>

Here, “2L operation” refers to the use of two single switches in an inverter leg, where each switch can consist of either a single transistor or series-connected transistors that operate simultaneously. “Q2L operation” involves
generating trapezoidal voltage waveforms using multi-level topologies. From a converter control perspective, the resulting waveforms in Q2L operation are equivalent to those produced by a 2L inverter. On the other hand, “multi-level operation” refers to a multi-level leg generating voltages waveforms that differ significantly from those of a 2L leg, such as a sinewave.

The DC-DC converter topology considered here is a single-phase DAB with a multilevel bridge with Q2L operation for the medium voltage, as shown in Fig. 2.

<figure><img src="image_3.png" /><figcaption>Fig. 2: An MVDC-LVDC DAB converter. Q2L leg can be a multilevel topology such as FCC or MMC.</figcaption></figure>

The selected modulation strategy is the so-called single-phase shift (SPS), with the primary waveforms for a 2L reference bridge shown in Fig. 3 (a). The phase shift, denoted as $\delta_{2L}$, is used to control the power flow. For the Q2L bridge, the voltage waveform $V_{AB}$ is illustrated in Fig. 3 (b), where the transition time angle $\theta$ is defined. This angle depends on the number of levels ($n$) and the duration of each stair ($t_{delay}$) in the staircase shape transition. It can be calculated following (1). To maintain consistent control and design across both 2L and Q2L operation modes, $\theta$ must remain small relative to the fundamental period $T=1/F_{sw}$. The Q2L waveforms are depicted in Fig. 3 (c), with the phase shift $\delta_{Q2L}$ measured from the midpoint of the staircase transition to ensure that its behavior and power flow are equivalent to the 2L counterpart.

$$ \theta = (n - 2) \times t_{delay} \times 360 \times F_{sw} \quad (1) $$

$$ \delta_{2L} = \delta_{Q2L} + \theta/2 \quad (2) $$

Although the overall converter behavior is expected to be nearly identical for both 2L and Q2L operation, there are structural differences between the two approaches. These distinctions are discussed in the following section.

<figure><img src="image_4.png" /><figcaption>Fig. 3: DAB converter waveforms within one switching period with (a) 2L and (c) Q2L operation along with (b) the definition of transition time angle $\theta$.</figcaption></figure>

### III. Q2L Operation of a DAB Converter

A primary difference between 2L and Q2L operation is related to $dV/dt$ values during transitions. In 2L operation, $dV/dt$ increases linearly with the bus voltage $V_{MV}$ [10], while in Q2L operation, $dV/dt$ is independent of $V_{MV}$.

In Q2L operation, the average $dV/dt$ is influenced by the transition time angle ($\theta$) and can be adjusted using $t_{delay}$. However, the instantaneous $dV/dt$ during each intermediate voltage transition is fixed and relatively high due to the fast switching of SiC MOSFETs. Importantly, this $dV/dt$ is limited to the voltage of a single voltage step, making it significantly lower than the $dV/dt$ observed in a series-connected MOSFET string operating in 2L mode [11].

Another key difference between 2L and Q2L is the value of the current at the switching instant. In Q2L operation, the staircase-shaped voltage results in different switching instants for each switching device in a Q2L leg, as shown in Fig. 3 (c). In contrast, in 2L operation, all switches
$$V_{ab}(t) = \sum_{h=1,3,5...} \frac{4V_{LV}}{h\pi} \sin(h(\omega_0 t - \delta)) = \sum_{h=1,3,5...} \beta_h \sin(h(\omega_0 t - \delta)) \quad (3)$$

$$V_{ab,rms} = V_{LV}$$

$$V_{AB}(t) = \sum_{h=1,3,5...} \frac{4V_{MV}}{hN\pi} \frac{\sin\left(\frac{N h\theta}{2(N-1)}\right)}{\sin\left(\frac{h\theta}{2(N-1)}\right)} \sin\left(h\left(\omega_0 t - \frac{\theta}{2}\right)\right) = \sum_{h=1,3,5...} \alpha_h \sin\left(h\left(\omega_0 t - \frac{\theta}{2}\right)\right) \quad (4)$$

$$V_{AB,rms} = \sqrt{\sum_{h=1,3,5...} \frac{\alpha_h^2}{2}}$$

$$I_{AC}(t) - I_{AC}(0) = \int_{0}^{t} \frac{V_{AB}(t) - V_{ab}(t)}{L} dt$$

$$I_{AC}\left(\frac{\pi}{\omega_0}\right) = -I_{AC}(0)$$

$$I_{AC}(t) = \sum_{h=1,3,5...} \frac{1}{Lh\omega_0} \left\{ \left[ -\alpha_h \sin\left(h\frac{\theta}{2}\right) + \frac{\beta_h}{m} \sin(h\delta) \right] \sin(h\omega_0 t) - \left[ \alpha_h \cos\left(h\frac{\theta}{2}\right) - \frac{\beta_h}{m} \cos(h\delta) \right] \cos(h\omega_0 t) \right\} \quad (5)$$

$$I_{AC}(t) = \sum_{h=1,3,5...} \alpha_{1h} \sin(h\omega_0 t) - \beta_{1h} \cos(h\omega_0 t) = \sum_{h=1,3,5...} \sqrt{\alpha_{1h}^2 + \beta_{1h}^2} \sin\left(h\omega_0 t - \arctan\left(\frac{\beta_{1h}}{\alpha_{1h}}\right)\right)$$

$$I_{AC,rms} = \sqrt{\sum_{h=1,3,5...} \frac{\alpha_{1h}^2 + \beta_{1h}^2}{2}}$$

change state simultaneously under the same operating current, as shown in Fig. 3 (a).

As a result with Q2L operation, most switches change state under lower current. Finally, there is a distinction in power flow between 2L and Q2L operation under the SPS modulation. Due to the transition time angle θ, a Q2L converter delivers slightly less power compared to a 2L converter under the same phase shift and conditions. This difference can be quantified with power transfer equations. Using the same approach as in [27] and [28], the voltages shown in Fig. 3 (c) can be transformed based on Fourier series following (3) and (4) where root mean square (RMS) values are also derived. Here, $ω_0 = 2πF_{sw}$, m is the transformer turns ratio $N_{LV}/N_{MV}$, for simplicity $δ = δ_{2L}$, calculated in (2) from θ and $δ_{Q2L}$, and N is half the number of switching devices per leg. From Fig. 2, the DAB converter can be modeled as two AC voltage sources connected across an inductor. Given the symmetry of operation in one switching cycle and the fact that the average steady-state AC current is zero, the AC current and its RMS value can be calculated following (5).

The DAB AC-link inductor is designed for 2L operation at a nominal power flow with $δ_{2L}=30°$ ($δ_{Pn}$) following the guidelines provided in [29]. The same inductor value is used for all subsequent cases.

## IV. Power Transfer Characterization

The average power (P) transferred by a lossless DAB converter over one switching period is calculated by:

$$P = \frac{1}{T} \int_{0}^{T} V_{AB}(t) \cdot I_{AC}(t) dt$$ $$P = \sum_{h=1,3,5...} \frac{\alpha_h}{2} \left[ \alpha_{1h} \cos\left(h\frac{\theta}{2}\right) - \beta_{1h} \sin\left(h\frac{\theta}{2}\right) \right] \quad (6)$$ $$P = \sum_{h=1,3,5...} \frac{\alpha_h}{2} \sqrt{\alpha_{1h}^2 + \beta_{1h}^2} \cos\left(h\frac{\theta}{2} + \arctan\left(\frac{\beta_{1h}}{\alpha_{1h}}\right)\right)$$

Where $α_h$ is defined in (4) and, $α_{1h}$ with $β_{1h}$ are defined in (5). Due to the existence of the AC link in the DAB, the reactive power (Q) can be defined following $Q = \sqrt{S^2 - P^2}$ where the apparent power is defined as $S = V_{AB,rms} \times I_{AC,rms}$. Normalized active and reactive powers as functions of phase shift for different θ values are shown in Fig. 4. It can be noted that to achieve the same active power output, systems with a higher θ will need a higher phase shift $δ_{Q2L}$. It can be observed the converter with θ = 45° requires a $δ_{Q2L}=32°$ to reach the nominal power flow.

The power factors $pf$, calculated by $pf = P/S$, as a function of normalized active power for different θ values are shown in Fig. 5. From these
results, it can be noted that a higher θ improves the power factor at nominal power.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Active (left) and reactive (right) powers varied with δQ2L and θ.</figcaption></figure>

To evaluate the impact of operating with a high θ, the square RMS values of currents are calculated and compared in Fig. 6. The square RMS value of the current is an indicator of conduction losses. The results in Fig. 6 show that with high θ, even if the power factor is higher at nominal power, the increased reactive power leads to higher RMS currents, which in turn reduces efficiency. Consequently, in order to minimize conduction losses, it is preferred to keep θ as small as possible.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Power factor variations with active power and θ with δPn = 30°.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6: Relative square RMS values of current varied with active power and θ. 2L operation is used as reference with δPn = 30°.</figcaption></figure>

## V. Zero-voltage switching zones

As discussed in Section III, the staircase-shaped voltage waveform impacts the switching current of the individual transistors. This also has an impact on the zero-voltage switching (ZVS) conditions in the DAB converter.

A typical Q2L waveform is shown in Fig. 7. When the current changes sign, the remaining transistors can no longer benefit from ZVS. One can conclude that depending on the AC current zero crossing instant, the number of switches in the Q2L leg benefiting from ZVS will vary. The ZVS conditions depend on the voltage ratio k, defined in (7), θ, δQ2L and N:

$$k = V_{LV} / (V_{MV} \times m) \qquad (7)$$

Piecewise analysis using the Heaviside step function for the Q2L voltage waveform [18] allows for the calculation of the ZVS conditions similar to those in [28]. For this analysis, only the cases with δQ2L ≥ 0 are considered since the opposite sign cases are equivalent due to the DAB’s bidirectionality.

If δQ2L ≥ θ/2 the obtained conditions for ZVS are shown in (8) for the first switch in the Q2L operation, (9) for the last switch in the Q2L operation and (10) for the switches in the LV bridge with 2L operation:

$$\delta_{Q2L} \geq \frac{1}{2k} [(\pi - \theta)(k - 1)] \qquad (8)$$

$$\delta_{Q2L} \geq \frac{1}{2k} [\pi(k - 1) + \theta(k + 1)] \qquad (9)$$

$$\delta_{Q2L} \geq \frac{\pi}{2}(1 - k) \qquad (10)$$

Under nominal operation with a voltage ratio (k) of 1, the condition to ensure ZVS in all switches is δQ2L ≥ θ.

If δQ2L < θ/2 the obtained conditions are shown in (11) for the first switch in the Q2L operation, (12) for the last switch in the Q2L operation and (13) for the switches in the LV bridge with 2L.

<figure><img src="image_8.png" /><figcaption>Fig. 7: ZVS analysis example for Q2L operation.</figcaption></figure>
$$k \ge \frac{\lambda + \lambda^* + \frac{2(\gamma - 1)}{N} \left(\frac{\theta}{2} - \delta_{Q2L}\right) + \pi - 2\theta}{\pi - \theta - 2\delta_{Q2L}} \quad (11)$$

$$k \ge \frac{1}{\pi} \left[ -\lambda + \lambda^* + \frac{2(\gamma-1)}{N} \left( \frac{\theta}{2} - \delta_{Q2L} \right) + \pi - \theta + 2\delta_{Q2L} \right] \quad (12)$$

$$k \ge \frac{\lambda + \lambda^* + \frac{2(\gamma - 1)}{N} \left(\frac{\theta}{2} - \delta_{Q2L}\right) - \pi}{-\pi + \theta - 2\delta_{Q2L}} \quad (13)$$

$$\text{with } \lambda = \frac{2\gamma}{N} \left[ \frac{\theta}{2} + \delta_{Q2L} - \frac{\theta}{2} \left( \frac{\gamma-1}{N-1} \right) \right],$$

$$\lambda^* = \frac{2(N-1-\gamma)}{N} \left[ \theta + \frac{\theta}{2} \left( \frac{4-\gamma-N}{N-1} \right) \right]$$

$$\text{and } \gamma = \text{floor} \left[ \left( \frac{2\delta_{Q2L}}{\theta} + 1 \right)^{\frac{N-1}{2}} + 1 \right]$$

Assuming that the Q2L power calculation can be approximated using the single-phase DAB formula in (14) when $\theta$ is sufficiently small, it is possible to determine the ZVS operation zones for classic 2L operation as well as for the presented case studies. The results of this analysis are shown in Fig. 8.

$$P \approx \frac{kV_{MV}^2}{\omega_0 L} \times \delta_{Q2L} \left(1 - \frac{\delta_{Q2L}}{\pi}\right) \quad (14)$$

Q2L operation results in a gray zone where only some of the switches achieve ZVS. To minimize this gray zone and ensure that as many switches as possible benefit from ZVS, $\theta$ must be kept as small as possible.

In addition, when parasitic capacitors are considered, $t_{delay}$ must be longer than the discharge time of $C_{ds}$ to achieve ZVS [30].

For the results shown in Fig. 8 (b) and (c), corresponding to the two case studies mentioned in Section II, an operating voltage of 1.7 kV per transistor and a $t_{delay}$ of 200 ns were considered. It is important to note that specifications such as the voltage level will constrain the value of $\theta$.

## VI. Efficiency comparison

Bridge losses are calculated, for $k=1$, following a similar method to the one in [31] with adaptations to consider Q2L operation. An analytical model of Q2L-MMC was implemented for these calculations. Efficiency as a function of phase shift is shown in Fig. 9 for the whole range of values of $\theta$.

It is shown that high $\theta$ values result in lower efficiency compared to 2L operation for low phase shift ($\delta_{Q2L} < 15^{\circ}$). This is attributed to the

elevated RMS current and the hard switching under these conditions.

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8: ZVS zones (in white) for three different values of $\theta$. (a) 2L operation, (b) 10 kV case study, and (c) 40 kV case study.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 9: Overall efficiency of the MV bridge for different $\delta_{Q2L}$ and $\theta$.</figcaption></figure>
In the scenario where nominal power is achieved at $\delta_{Pn} = 30^\circ$ with a 2L DAB design, the case with $\theta = 10^\circ$ demonstrates better efficiency than 2L for the highest power range among the Q2L cases. This constraint highlights the importance of limiting the transition time angle to avoid decreasing efficiency at reduced load.

To account for the increased phase shift required to achieve the same power in Q2L, as illustrated in Fig. 4, Fig. 10 presents efficiency as a function of normalized active power. This complements the results in Fig. 9, which focus solely on the phase shift. The results in Fig. 10 align with the studies in Section IV and Section V. At reduced load operation, 2L operation exhibits the lowest RMS current and achieves ZVS at $k=1$, resulting in the best efficiency. As power increases, and consequently $\delta_{Q2L}$ also increases, more transistors in the Q2L leg meet the ZVS conditions. Eventually during medium to high load operation, an operation region is reached where Q2L becomes more efficient. This typically occurs when $\delta_{Q2L}$ approaches $\theta$, the condition required to achieve ZVS across the entire MV bridge.

In this operating region, conduction losses are independent of $\theta$ when $\theta$ is sufficiently small. Consequently, efficiency differences are primarily influenced by variations in switching losses. At this point in Q2L operation, most transistors either achieve ZVS or switch under significantly lower currents than their nominal values, which explains why Q2L efficiencies surpass those of 2L.

<figure><img src="image_13.png" /><figcaption>Fig. 10: Overall efficiency of MV bridge for different active power values and $\theta$ for a 2L design with $\delta_{Pn}=30^\circ$.</figcaption></figure>

## VII. Guidelines

In a DAB converter with a multilevel Q2L bridge, the transition time angle $\theta$ can range from $0^\circ$ to $180^\circ$, however Q2L operation requires a short transition time. As demonstrated in Section IV,

minimizing conduction losses requires favoring smaller $\theta$ values. Furthermore, to optimize the number of transistors achieving ZVS under nominal conditions, $\theta$ must remain smaller than the phase shift $\delta_{Q2L}$ needed for nominal power flow, as detailed in Section V.

In most cases, $\theta$ is constrained by semiconductor device switching limitations, control delay constraints, and the medium voltage level. The minimum number of 3.3 kV SiC MOSFET pairs required per Q2L leg, and the corresponding minimum transition time angle ($\theta$) are depicted in Fig. 11 as a function of the medium voltage level. For this analysis, an operating voltage of 1.7 kV per MOSFET, a switching frequency of 10 kHz, and a $t_{delay}$ of 200 ns were considered. The results indicate that the maximum $\theta$ is $25^\circ$ for a medium voltage level of 60 kV. Additionally, the choice of $t_{delay}$ affects the average $dV/dt$, as shown in Fig. 12, where Q2L and 2L $dV/dt$ are compared, with a transistor switching time of 50 ns consistently assumed.

<figure><img src="image_14.png" /><figcaption>Fig. 11: Pair of minimum required components per leg (blue) and $\theta$ (red) evolution for different voltage levels.</figcaption></figure>

Assuming $\theta$ is fixed during the converter predesign phase, an optimal value can be chosen based on the load profile to optimize efficiency.

<figure><img src="image_15.png" /><figcaption>Fig. 12: $dV/dt$ as a function of $V_{MV}$ values for 2L and Q2L topologies.</figcaption></figure>

Finally, the value of $\theta$ impacts the size of passive components used in different Q2L topologies. A smaller $\theta$ allows for smaller passive components
in multilevel converter topologies, such as the
Flying Capacitor Converter [19] and the Modular
Multilevel Converter [18].

Conclusion

Recent research underscores the significance of Q2L operation in DC-DC converters, yet comprehensive requirements for a voltage-source Q2L bridge have not been established. This paper investigates Q2L operation within a DAB converter, focusing on voltage, current, power transfer and efficiency. Fourier series analysis was employed to assess conduction losses, while piecewise analysis provided insights into zero voltage switching (ZVS) conditions and switching losses. Power factor and bridge efficiencies were analyzed, revealing that while a higher transition time enhances the power factor near nominal power, overall efficiency does not exhibit the same trend. Compared to 2L bridges, Q2L bridges with high transition times demonstrate better efficiency at specific power levels close to nominal power. However, under low-load conditions, shorter transition times should be prioritized to improve efficiency. The study concludes that a Q2L bridge with a transition time angle up to 25° can achieve efficiency comparable to that of a 2L bridge. Guidelines are presented to optimize both the efficiency and design of the Q2L bridge in a DAB converter. The results demonstrate that maintaining a transition time angle below 25° is feasible for Q2L bridges operating at voltages up to 60 kV.

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