# Trapezoidal Wave Operation of High-power Non-isolated DC/DC Converter for Current Stress Reduction

Ning Wang, Binbin Li, Yingzong Jiao, Dianguo Xu

► To cite this version:

Ning Wang, Binbin Li, Yingzong Jiao, Dianguo Xu. Trapezoidal Wave Operation of High-power Non-isolated DC/DC Converter for Current Stress Reduction. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0263. hal-05085245

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# Trapezoidal Wave Operation of High-power Non-isolated DC/DC
## Converter for Current Stress Reduction

Ning Wang¹*, Binbin Li¹, Yingzong Jiao¹, Dianguo Xu¹

1. Harbin Institute of Technology, Harbin, China

E-Mail: wangning@stu.hit.edu.cn

URL: http://www.hit.edu.cn

## Acknowledgements

This work was supported in part by the National Key Research and Development Program of China under Grant 2023YFB2407200.

## Keywords

«Trapezoidal wave operation», «High-power», «Non-isolated DC/DC converter», «Modular multilevel converters (MMC)».

## Abstract

All-DC offshore wind farms are crucial for advancing large-scale offshore wind power in deep-sea applications. Overcoming the technical bottleneck of high-power DC/DC converters is essential for these farms. This paper presents a trapezoidal wave operation method for non-isolated DC/DC converters, introducing design constraints for minimum current stress and minimum root-mean-square (RMS) of current. These innovations significantly reduce converter current stress, enhancing the power capacity of DC/DC converter. The operation principle of two-phase and three-phase structures are introduced, and the effectiveness has been confirmed by simulation and experiment results.

## Introduction

Over the past few decades, high-voltage direct current (HVDC) transmission has rapidly advanced with the introduction of modular multilevel converter (MMC) technology based on voltage-source converters. However, as an AC/DC converter, MMC experiences high losses and is influenced by reactive power, frequency, phase, and positive and negative sequence components of the AC collection system, resulting in complex frequency and voltage stability issues with wind turbines. In recent years, all-DC offshore wind farm systems that utilize low-voltage DC (LVDC) collection and HVDC

transmission have garnered significant attention in both academia and industry [1]. To build up the LVDC distribution and HVDC transmission grids, high-voltage, high-power DC/DC converters serve as the core equipment in the all-DC offshore wind farm systems.

The classical high-power DC/DC converters are built connecting two MMC through an AC transformer in a front-to-front structure (FTF-MMC), at the expense of significant number of devices and losses [2]-[3]. A hybrid isolated DC/DC converter named HIT as an alternative to the traditional MMC-DCT is proposed [4]. Through the combination of half-bridge submodule (HBSM) based arms with thyristors and diodes, the HIT successfully combines the merits of low loss and low cost of the thyristor and diode. However, the cost, size and weight of hundred-hertz transformer cannot be ignored.

To eliminate the AC transformer in the isolated DC/DC converter, it is advisable to use a non-isolated DC/DC topology when the DC transformation ratio is low, particularly between 2 and 5. The modular multilevel DC/DC converter (MMDC) is presented in [5], utilizing a bulky filter inductor to filter the ac voltage and ac currents of MMC. The DC auto transformer (DC-AT) is another topology which has almost the same characteristics to MMDC [6]. However, these topologies still require bulky passive components to withstand high-amplitude AC voltages. References [7]-[8] proposed a high-power T-type non-isolated DC/DC converter topology. Compared to MMDC, this topology replaces the passive filter on the LVDC side with an arm created by cascading full-bridge submodule (FBSM). As a result, this topology eliminates bulky passive filters and transformers, and the number of SMs is also fewer than in FTF-MMC, possessing volume and cost advantages. In the traditional operational mode of the T-type non-isolated DC/DC converter, both the internal AC voltage and AC current are sinusoidal waves, which leads to high current stress and limits the
power of the DC/DC converter. References [9] introduce FBSMs in the middle arm to increase AC voltage amplitude and reduce AC current amplitude, which increases the number of devices. Existing literatures on T-type non-isolated DC/DC converter primarily addresses fault protection and parameter optimization design, and none of these approaches effectively address the issue of high current stress. This paper proposes a trapezoidal wave operation method, which significantly reduces the current stress and current RMS, improving the power capacity of DC/DC converter.

## Basic circuit and principle

<figure><img src="image_2.png" /><figcaption>Fig. 1: Basic circuit of single phase non-isolated DC/DC converter.</figcaption></figure>

The non-isolated DC/DC converter has j phases ($j \ge 2$), and each phase consists of three arms: H-arm, M-arm and L-arm. The H-arm and M-arm together support $U_H$, while the M-arm and L-arm jointly support $U_L$. The arms contain both AC voltage/current and DC voltage/current components, with the AC power utilized to balance the DC power. When designing converter parameters, the DC voltage component in the M-arm $U_{dc}=U_L$ is specified. In this way, the device utilization of the DC/DC converter is maximized, with L-arm is consisted of FBSMs [9]. The AC voltage amplitude $U_{ac}$ in each arm is kept equal. While $U_{ac}$ is typically maximized to reduce current stress. However, considering that when the $U_{ac}$ is greater than $U_{dc}$, the M-arm must use the FBSMs, leading to an increase in cost. It is usually designed to be $0.95U_{dc}$ to avoid the increased costs associated with introducing FBSMs in the M-arm.

To prevent the AC voltage/current of the arms in the DC/DC converter from appearing on the DC side, the voltage and current of each arm must meet the following conditions:

1. The internal AC currents between phases should be staggered and offset.

2. The AC voltages between arm and arm in each phase should also be offset in opposite phases.

Therefore, based on the above operating characteristics, the voltages and currents of the arms in phase j can be expressed as follows:

$$ 
\left\{
\begin{aligned}
u_{Hj} &= U_H - U_{dc} - U_{ac}f(t) + L \frac{dI_{Hacj}f(t)}{dt} \\
u_{Mj} &= U_{dc} + U_{ac}f(t) + L \frac{dI_{Macj}f(t)}{dt} \\
u_{Lj} &= U_{dc} - U_L + U_{ac}f(t) + L \frac{dI_{Lacj}f(t)}{dt}
\end{aligned}
\right.
\quad (1). $$

$$ 
\left\{
\begin{aligned}
i_{Hj} &= I_{Hj} + I_{Hacj}f(t) \\
i_{Mj} &= I_{Mj} + I_{Macj}f(t) \\
i_{Lj} &= I_{Lj} - I_{Lacj}f(t)
\end{aligned}
\right.
\quad (2). $$

where $f(t)$ is the AC waveform function, and the arm generates an AC current by applying the voltage to the arm inductor $L$.

## Two-phase structure operation

The non-isolated DC/DC converter topology shown in Fig. 1 typically employs a two-phase or three-phase structure. Increasing the number of phases (more than 3) leads to more components and is not cost-effective. The following section first analyzes the operational principles of the trapezoidal wave in the two-phase structure.

In the traditional sinusoidal operation mode, the utilization of the arm voltage and current waveforms is low, leading to a high peak current in the arm. When the trapezoidal wave operation mode is adopted, the AC voltage of the arm takes the form of a square wave, resulting in the highest voltage utilization. Take AC current $i_a(t)$ of phase a as an example to introduce waveform design. Based on the symmetry of the AC current waveform and the AC and DC power balance within the arm shown in (3), we can derive the expression for the average value of the half-cycle current in the arm shown in (4).

$$ 
\left\{
\begin{aligned}
i_a(t) &= -i_a\left(t + \frac{T}{2}\right) \\
\frac{2}{T} \int_0^T U_{ac} i_a(t) dt &= \frac{(U_H - U_{dc}) I_H}{2}
\end{aligned}
\right.
\quad (3) $$

$$ \frac{2}{T} \int_{0}^{T} i_{a}(t) dt = \frac{(U_{H} - U_{dc}) I_{H}}{2U_{ac}} \quad (4) $$

When the AC current $i_a(t)$ consistently equals the average value over half a cycle, the AC current amplitude $I_{ac}$ is minimized, resulting in
the lowest current stress on the arm. In this case, $I_{ac}$ is equal to the average value, indicating that the ideal AC current also forms a square wave.

However, due to the influence of the arm inductor $L$, the AC current experiences a current change time $T_c$. This change in current is facilitated by applying a voltage $U_T$ across the arm inductor, where $U_T$ can be calculated as

$$U_T = L \frac{2I_{ac}}{T_c} \qquad (5)$$

Furthermore, based on the AC current offset constraint shown in (6) between phase and phase, the current and voltage waveforms of the arm under two-phase trapezoidal wave operation can be derived, as illustrated in Fig. 2.

$$i_a(t)+i_b(t)=0 \qquad (6)$$

<figure><img src="image_3.png" /><figcaption>Fig. 2: Two-phase operation waveforms of non-isolated DC/DC converter.</figcaption></figure>

The duration $T_c$ influences the amplitude of the AC current $I_{ac}$ and $U_T$. By analyzing the relationship among $T_c$, $I_{ac}$ and $U_T$, we can determine the value of $T_c$ that minimizes the AC current amplitude. As illustrated in Fig. 2, at $T_c=1.4$ms, the voltage $U_T$ is 26.6% of $U_{ac}$, resulting in an acceptable voltage stress.

<figure><img src="image_4.png" /><figcaption>Fig. 3: The relationship between $I_{ac}$, $U_T$ and $T_c$.</figcaption></figure>

## Three-phase structure operation

For applications requiring higher power transmission, the DC/DC converter can utilize a three-phase structure. Similar to the two-phase structure, we can derive (7) and (8) based on the symmetry of the AC current waveform, combined with the relationship of AC current between the three phases (staggered $T/3$).

$$i_a(t)=-i_a\left(t+\frac{T}{2}\right) \qquad (7)$$

$$\left\{ \begin{array}{l} i_b(t)=i_a\left(t+\frac{T}{3}\right)=i_a\left(t-\frac{T}{6}+\frac{T}{2}\right) \\ i_c(t)=i_a\left(t+\frac{2T}{3}\right)=i_a\left(t+\frac{T}{6}+\frac{T}{2}\right) \end{array} \right. \qquad (8)$$

Therefore, based on equations (7) and (8), the characteristics of the AC current waveform during half a cycle under three-phase operation can be further analyzed. Specifically, the waveform of $(0 \sim T/6)$ is equal to the algebraic sum of the waveforms from the $(-T/6 \sim 0)$ and $(T/6 \sim 2T/3)$, as shown in (9).

$$i_a(t)=i_a\left(t-\frac{T}{6}\right)+i_a\left(t+\frac{T}{6}\right) \qquad (9)$$

By combining equation (9) with the arm AC and DC power balance equation (10), we can derive the expression for the average value of the bridge arm current over one period $(0 \sim T/6)$ as shown in (11):

$$\frac{2}{T} \int_{0}^{\frac{T}{2}} U_{ac} i_{a}(t) dt = \frac{(U_{H} - U_{dc}) I_{H}}{3} \qquad (10)$$

$$\frac{6}{T} \int_{0}^{\frac{T}{6}} i_{a}(t) dt = \frac{(U_{H} - U_{dc}) I_{H}}{2U_{ac}} \qquad (11)$$

It can be seen that the average value of the AC current $i_a(t)$ remains constant within the time interval $(0 \sim T/6)$. When $i_a(t)$ is consistently equal to this average value during $(0 \sim T/6)$, the AC current amplitude $I_{ac}$ is minimized, resulting in the lowest current stress on the arm, where $I_{ac}$ is equal to the average value. However, it is still impossible to determine the AC current waveform under three-phase operation.

Further, the RMS expression for the arm current can be written as follows:

$$I_{a,RMS} = \sqrt{\frac{2}{T} \int_{0}^{T/2} i_{a}^{2}(t) dt} \qquad (12)$$

Substituting equation (9) into equation (12), and (13) is get finally. We can find that when the AC current is always equal to $I_{ac}/2$ during the time interval $(-T/6 \sim 0)$, the AC current RMS is minimized. At this point, the AC current remains
equal to $I_{ac}/2$ during the time interval $(T/6 \sim 2T/3)$ as well.

$$I_{a,RMS} = \sqrt{\frac{2}{T} \left\{ \begin{aligned} & \int_{0}^{\frac{T}{6}} i_{a}^{2} \left(t - \frac{T}{6}\right) dt + \int_{0}^{T} (I_{ac})^{2} dt \\ & + \int_{0}^{\frac{T}{6}} \left[I_{ac} - i_{a}\left(t - \frac{T}{6}\right)\right]^{2} dt \end{aligned} \right\}} \quad (13)$$

$$I_{a,RMS} = \sqrt{\frac{4}{T} \left\{ \int_{0}^{\frac{T}{6}} \left[ i_{a} \left(t - \frac{T}{6}\right) - \frac{I_{ac}}{2} \right]^{2} dt + \frac{I_{ac}^{2}}{8} T \right\}} \quad (14)$$

Based on the minimum current stress condition from equation (11) and the minimum current RMS condition from equation (14), we can establish the optimal waveform for the AC current half-cycle, as depicted in Fig. 4.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Half-cycle optimal AC current waveform.</figcaption></figure>

Fig. 4 illustrates an ideal AC current waveform. However, there will still be a change time $T_c$ during the actual current transition process. Under three-phase operation, $T_c$ affects only the current RMS. In the optimal AC current waveform, the range for $T_c$ is (0~$T/12$). Based on the current waveform expression shown in (15), the current RMS expression of the AC current, taking $T_c$ into account, can be derived as (16). When $T_c$ reaches its maximum value, the difference from the ideal current RMS is 5.6%. Considering the value of $U_T$, $T_c$ can be designed to be $T/24$.

$$i_a = \begin{cases} \frac{I_{ac}}{2T_c} t & 0 \le t < T_c \\ \frac{I_{ac}}{2} & T_c \le t < \frac{T}{6} - T_c \\ \frac{I_{ac}}{2} + \frac{I_{ac}}{2T_c} \left(t - \frac{T}{6} + T_c\right) & \frac{T}{6} - T_c \le t < \frac{T}{6} \\ I_{ac} & \frac{T}{6} \le t < \frac{T}{3} \\ I_{ac} - \frac{I_{ac}}{2T_c} \left(t - \frac{T}{3}\right) & \frac{T}{3} \le t < \frac{T}{3} + T_c \\ \frac{I_{ac}}{2} & \frac{T}{3} + T_c \le t < \frac{T}{2} - T_c \\ \frac{I_{ac}}{2} - \frac{I_{ac}}{2T_c} \left(t - \frac{T}{2} + T_c\right) & \frac{T}{2} - T_c \le t < \frac{T}{2} \end{cases} \quad (15)$$

$$I_{a,RMS} = \sqrt{\frac{1}{2} \left(1 + \frac{4T_c}{3T}\right)} I_{ac} \quad (16)$$

The final optimal AC current waveforms are presented in Fig. 5.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Final optimal AC current waveforms of three phases.</figcaption></figure>

## Simulation results

<table><caption>Table I: Simulation parameters.</caption><thead><tr><td>Parameters</td><td>Simulation</td></tr></thead><tbody><tr><td>Power rating P</td><td>480MW</td></tr><tr><td>HVDC voltage U<sub>H</sub></td><td>320kV</td></tr><tr><td>LVDC voltage U<sub>L</sub></td><td>100kV</td></tr><tr><td>Operation frequency f(=1/T)</td><td>100Hz</td></tr><tr><td>SM capacitor voltage U<sub>C</sub></td><td>2.5kV</td></tr><tr><td>SM capacitor C<sub>SM</sub></td><td>10mF</td></tr><tr><td>SM number of H-arm</td><td>160</td></tr><tr><td>SM number of M-arm</td><td>120</td></tr><tr><td>SM number of L-arm</td><td>50</td></tr><tr><td>Arm inductor L</td><td>5mH</td></tr></tbody></table>

In order to verify the effectiveness of the proposed operation method, a three-phase simulation was built to convert 100kV LVDC to 320kV HVDC with rated 480MW power. The rated SM capacitor voltage is 2.5kV. More detailed parameters are summarized in Table I.

Fig. 6 shows the DC voltage and current waveforms. There is no AC component on the DC side, which means that the AC current between phases is offset, and the AC voltage between two arms in one phase is also offset. In the simulation, the power increases from 0.5pu. to 1pu., and the DC/DC converter can still operate stably.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Current waveforms of the arms.</figcaption></figure>
Fig.7 shows the current waveforms of the three-phase arms. There are DC and AC current components in H-arm and M-arm. The AC current is the optimal AC current waveform considering the minimum current stress and the minimum current RMS, as shown in (11) and (14). In the simulation, the DC voltage component in M-arm $U_{dc}=U_L$, so there is no AC current component in L-arm, only a DC current component of 1.6kA.

<figure><img src="image_8.png" /><figcaption>Fig. 7: Current waveforms of the arms.</figcaption></figure>

Fig.8 shows the SM capacitor voltage of the three-phase arms. The average value of the SM capacitor voltages of all arms is stable near the rated voltage of 2.5kV. It should be noted that the SM capacitor voltage fluctuations of H-arm, M-arm and L-arm are different. The reason is that the energy storage of the three arms is different. When capacitors of the same capacitance are selected for three arms, the capacitor voltage fluctuations are different.

<figure><img src="image_9.png" /><figcaption>Fig. 8: Current waveforms of the arms.</figcaption></figure>

## Experimental prototype

To further verify the validation of proposed operation method, a downscaled prototype has been built as shown in Fig. 9 and the experiment parameter is shown in Table II.

<figure><img src="image_10.png" /><figcaption>Fig. 9: Downscaled prototype.</figcaption></figure>

<table><caption>**Table II: Simulation parameters.**</caption><thead><tr><td>Parameters</td><td>Simulation</td></tr></thead><tbody><tr><td>Power rating <i>P</i></td><td>2.4kW</td></tr><tr><td>HVDC voltage <i>U</i><sub>H</sub></td><td>320V</td></tr><tr><td>LVDC voltage <i>U</i><sub>L</sub></td><td>100V</td></tr><tr><td>Operation frequency <i>f</i> (=1/T)</td><td>150Hz</td></tr><tr><td>SM capacitor voltage <i>U</i><sub>C</sub></td><td>50V</td></tr><tr><td>SM capacitor <i>C</i><sub>SM</sub></td><td>3.88mF</td></tr><tr><td>SM number of H-arm</td><td>8</td></tr><tr><td>SM number of M-arm</td><td>5</td></tr><tr><td>SM number of L-arm</td><td>3</td></tr><tr><td>Arm inductor <i>L</i></td><td>2mH</td></tr></tbody></table>

Fig. 10(a) and (b) shows the DC voltage and current waveforms, and no AC component accrued on the DC side, which means that the AC current between phases is offset, and the AC voltage between two arms in one phase is also offset.

Fig. 10(c) presents the current waveforms of the three bridge arms in phase a. Evidently, the AC current components in the H-arm and M-arm
are trapezoidal waves, whereas the low-voltage bridge arm has no AC current component.

Fig. 10(d) depicts the voltages of the three arms in phase a. It shows that the AC voltage components in the three arm voltages are offset, thus preventing the AC voltage from influencing the DC side. The L-arm contains no DC voltage component but only an AC voltage component, which is in line with the theoretical analysis. The DC voltage components in the H-arm and M-arm are 220 V and 100 V, respectively.

Fig. 10(e) presents the current waveforms of the three phase H-arms. Evidently, the AC current components in the three phase current waveforms are staggered by 120 degrees. As a result, the AC components cancel each other out, preventing them from affecting the DC current.

Fig. 10(f) shows the capacitor voltage of the submodule in the H-arm of phase a. The voltages all remain stable around the rated value of 50 V, verifying the stable operation of the converter.

<figure><img src="image_11.png" /><figcaption>Fig. 10: Experiment waveforms.</figcaption></figure>

## Comparison with sinusoidal wave operation method

For comparison of the proposed trapezoidal wave operation with traditional sinusoidal wave operation, the simulation parameters in Table I are selected as a specific case study.

The expression of AC current amplitude and current RMS under two-phase sinusoidal wave operation are

$$ \left\{ \begin{aligned} & \frac{I_H - U_{dc}}{2} = \frac{U_{ac} I_{ac}}{2} \\ & U_{dc} \frac{I_L - I_H}{2} = \frac{U_{ac} I_{ac}}{2} \end{aligned} \right. \Rightarrow I_{ac} = \frac{P - U_{dc} I_H}{U_{ac}} \quad (17) $$

$$ I_{\text{RMS}} = \sqrt{\left(\frac{I_L - I_H}{2}\right)^2 + \frac{I_{ac}^2}{2}} \quad (18) $$

The expression of AC current amplitude and current RMS under three-phase sinusoidal wave operation are

$$ \left\{ \begin{aligned} & \frac{I_H - U_{dc}}{3} = \frac{U_{ac} I_{ac}}{2} \\ & U_{dc} \frac{I_L - I_H}{3} = \frac{U_{ac} I_{ac}}{2} \end{aligned} \right. \quad (19) $$

$$ I_{\text{RMS}} = \sqrt{\left(\frac{I_L - I_H}{3}\right)^2 + \frac{I_{ac}^2}{3}} \quad (20) $$

The expression of AC current amplitude and current RMS under two-phase trapezoidal wave operation are

$$ \left\{ \begin{aligned} & \frac{I_H - U_{dc}}{2} = I_{ac} U_{ac} \frac{T - T_c}{T} \\ & U_{dc} \frac{I_L - I_H}{2} = I_{ac} U_{ac} \frac{T - T_c}{T} \end{aligned} \right. \quad (21) $$
$$ \Rightarrow I_{ac} = \frac{(P - U_{dc} I_H)T}{2U_{ac}(T - T_c)} $$

$$ I_{\text{RMS}} = \sqrt{\left(\frac{I_L - I_H}{2}\right)^2 + \frac{2}{T} \left[ \int_0^{T_c} \left(\frac{I_{ac}}{T_c} t\right)^2 dt + \int_{T_c}^{T} (I_{ac})^2 dt \right]} \quad (22) $$
$$ = \sqrt{\left(\frac{I_L - I_H}{2}\right)^2 + I_{ac}^2 \left(1 - \frac{4T_c}{3T}\right)} $$

The expressions of AC current amplitude and current RMS under three-phase trapezoidal wave operation are
$$ egin{cases} 
(U_H - U_{dc}) \frac{I_H}{3} = \frac{2I_{ac}U_{ac}}{3} \\ 
U_{dc} \frac{(I_L - I_H)}{3} = \frac{2I_{ac}U_{ac}}{3} 
\end{cases} 
\quad (23) 
$$ 
$$ \Rightarrow I_{ac} = \frac{(P - U_{dc}I_H)}{2U_{ac}} $$

$$ I_{\text{RMS}} = \sqrt{\left(\frac{I_L - I_H}{3}\right)^2 + \left(\sqrt{\frac{1}{2}\left(1 + \frac{4T_c}{3T}\right)} I_{ac}\right)^2} \quad (24) $$

According to (17) to (27), the calculated results are listed in Table III. The proposed operation method can reduce 32% current stress and 20% current RMS in two-phase, and 17% current stress and 16.7% current RMS in three-phase compared to traditional sinusoidal waves operation. The comparison results indicate that, when using the same devices, trapezoidal wave operation can significantly enhance the power capacity of the non-isolated DC/DC converter while also reducing losses.

It should be noted that for this non-isolated DC/DC converter, current stress becomes more significant with a higher transformation ratio. Therefore, compared to traditional sinusoidal operation, the trapezoidal wave operation method can increase the voltage transformation ratio of the converter without the need for an isolation transformer, providing significant technical and economic advantages.

<table><caption>Table III: Comparison of current stress and current RMS between sinusoidal waves operation and trapezoidal wave operation.</caption><thead><tr><th></th><th>Sin-2</th><th>Sin-3</th><th>Tra-2</th><th>Tra-3</th></tr></thead><tbody><tr><th>Current Stress</th><td>4.4kA</td><td>2.93kA</td><td>2.69kA</td><td>2.33kA</td></tr><tr><th>Current Stress</th><td>5.34kA</td><td>3.56kA</td><td>3.62kA</td><td>2.95kA</td></tr><tr><th>Current RMS</th><td>2.68kA</td><td>1.78kA</td><td>2kA</td><td>1.42kA</td></tr><tr><th>Current RMS</th><td>3.1kA</td><td>2.1kA</td><td>2.5kA</td><td>1.75kA</td></tr></tbody></table>

## Conclusion

A trapezoidal wave operation method of high-power non-isolated DC/DC converter for current stress reduction is proposed in this paper. The minimum current stress and minimum current RMS constraints are proposed for two-phase and three-phase structure respectively, and the

optimal trapezoidal AC current waveforms are designed. The effectiveness is confirmed by simulation results. According to the comparison results, the proposed operation method can reduce 32% current stress and 20% current RMS in two-phase, and 17% current stress and 16.7% current RMS in three-phase compared to traditional sinusoidal waves operation. The experimental results and more detailed analysis will be included in the final paper.

## References

[1]. I. Alhurayyis: Isolated and nonisolated DC-to-DC converters for medium voltage DC networks: A review, IEEE J. Emerg. Sel. Topics Power Electron., vol. 9, no. 6, pp. 7486-7500, Dec. 2021.

[2]. J. D. Páez: Overview of DC-DC converters dedicated to HVDC grids, IEEE Trans. Power Del., vol. 34, no. 1, pp. 119-128, Feb. 2019.

[3]. S. Kenzelmann: Isolated dc/dc structure based on modular multilevel converter, IEEE Trans. Power Electron., vol. 30, no. 1, pp. 89-98, Jan. 2015.

[4]. X. Zhao: A high-power step-up DC-DC converter dedicated to DC offshore wind farms, IEEE Trans. Power Electron., vol. 37, no. 1, pp. 65-69, Jan. 2022.

[5]. G. J. Kish: A modular multilevel DC/DC converter with fault blocking capability for HVDC interconnects, IEEE Trans. Power Electron., vol. 30, no. 1, pp. 148-162, Jan. 2015.

[6]. W. Lin: DC-DC autotransformer with bidirectional DC fault isolating capability, IEEE Trans. Power Electron., vol. 31, no. 8, pp. 5400-5410, Aug. 2016.

[7]. S. Dey: A Modular DC-DC Converter as a Hybrid Interlink Between Monopolar VSC and Bipolar LCC-Based HVDC Links and Fault Management, in IEEE Trans. Ind. Appl., vol. 59, no. 4, pp. 4342-4352, Aug. 2023.

[8]. S. Dey: A Modular DC-DC Converter as a Hybrid Interlink Between Monopolar VSC and Bipolar LCC-Based HVDC Links and Fault Management, in IEEE Trans. Ind. Appl., vol. 59, no. 4, pp. 4342-4352, Aug. 2023.

[9]. R. Vidal-Albalate: Sizing and Short-Circuit Capability of a Transformerless HVDC DC-DC Converter, in IEEE Trans. Power Del., vol. 35, no. 5, pp. 2363-2377, Oct. 2020.