# MMC-Autotransformer: Impact of the Control on the Design and Efficiency

Johan Boukhenfouf, Shabab Samimi, Michael Merlin, François Gruson, Philippe Delarue, Philippe Lemoigne, Frédéric Colas, Xavier Guillaud

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## To cite this version:

Johan Boukhenfouf, Shabab Samimi, Michael Merlin, François Gruson, Philippe Delarue, et al., MMC-Autotransformer: Impact of the Control on the Design and Efficiency. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0172. hal-05107600

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<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
MMC-Autotransformer : Impact of the Control on the Design and
Efficiency

Johan BOUKHENFOUF¹, Shabab SAMIMI², Michael MERLIN³, Francois GRUSON¹,
Philippe DELARUE¹, Philippe LEMOIGNE¹, Frédéric COLAS¹, Xavier GUILLAUD¹

1. Univ. Lille, Arts et Métiers Institute of Technology, Centrale Lille, Junia, ULR 2697 - L2EP
F-59000 Lille, France

2. ESME, ESME Research Lab, Campus de Lille, France

3. Institute for Energy Systems, School of Engineering, University of Edinburgh.

E-Mail: johan.boukhenfouf@ensam.eu, francois.gruson@ensam.eu

*Index Terms*—DC-DC converter, Modular Multilevel Converters (MMC), HVDC

***Abstract***—To increase flexibility and reliability of HVDC links and MTDC, it is likely that DC-DC converter will be employed. This paper specifically focuses on the DC-Auto-transformer. This study investigates its performance in relation to its parameters including: AC voltages, frequency and waveform characteristics. The analysis presented in this paper demonstrates that increasing the AC voltage within the converter reduces losses and minimizes capacitor size requirements. While, increasing the frequency reduces the losses as well as required size of capacitors. Furthermore, the results indicate that adopting a trapezoidal waveform improves both efficiency and capacitor size.

# I. INTRODUCTION

As the integration of renewable energy sources increases, there is a growing need for efficient transmission systems capable of delivering higher power over long distances, or from geographically dispersed generation sites to load centers. In this context, multi-terminal DC transmission systems are anticipated to emerge in the near future, likely through the interconnection of existing HVDC infrastructure. Due to the varying characteristics of these assets, such as voltage levels, converter technologies, and grounding methods, the integration of DC-DC converters becomes essential to ensure compatibility and efficient operation [1].

For this HVDC interconnection, various converters have already been proposed, studied and compared [2], [3]. They are usually represented in two categories : isolated and non-isolated [4]. The first are DC-AC-DC converters such as the front-to-front MMC (double-active-bridge MMC) [5], [6]. The second one includes the MMC-DC converter [7], [8] or MMC-Autotransformer.

<figure><img src="image_3.png" /><figcaption>Fig. 1: Topology of asymmetric DC-Autotransformer</figcaption></figure>

The latter was first introduced in [9], the authors
demonstrated its efficiency and reduced cost of this
converter. Controls aspects and fault-blocking capabil-
ities are deeper analyzed in [10], [11]. However, to the
authors knowledge, there is no study on the design or
control of such converter. The paper aim to fill this gap
by providing an analysis of the converter performance
according to the degrees of freedom of the converter.

To do so, the demonstration is structured in three
main parts : first, the operating principles and steady-
state model of the converter are recalled. The degrees of
freedom of the converter are then highlighted and their
influence on the converter performance is analysed. To
go further, the trapezoidal operation (also called quasi-
two-level) introduced in [12] for MMC-AT is also stud-
ied and compared to the original sinusoidal modulation.
<figure><img src="image_4.png" /><figcaption>Fig. 2: MMC</figcaption></figure>

## II. PRINCIPLE OF OPERATION OF MMC-AT

### A. Circuit Structure and Parameters

The DC-Autotransformer for is presented in fig.1. It is composed of two series-connected converter : DC terminals of VSCL are connected to $V_{dc2}$. As for VSCU, it is connected between the positive poles of $V_{dc2}$ and $V_{dc1}$. The AC terminals of both VSC are interconnected with a transformer. As the topic of interest is HVDC interconnection, the converters are Modular Multilevel Converter (MMC). The MMC topology (fig .2) consists of multiple submodules connected in series to form each phase leg, allowing for precise voltage control by switching these sub-modules on and off.

Figures 1 and 2 introduces the notation used in this work. $v_{dc1}, i_{dc1}$ are the DC voltage and current of the high voltage side and similarly $v_{dc2}, i_{dc2}$ correspond to the low voltage side. The arm current and modulated voltage of the MMCs are represented by $i$ and $v_m$, these notation are completed with the lower subscript $n,p,s$ and the upper subscript $A,...,M$ to describe the position of the quantities. $p$ and $n$ respectively represent the upper or lower arm while $s$ indicates the output filter. To complete these, the upper subscript $U$ and $L$ indicate whether the quantities belong to the upper MMC or lower one. For example, $v_{mp}^{AU}$ is the modulated voltage of the upper arm of leg A in the upper MMC.

The parameters of the case study are presented in table I. Voltages and power comes from [13]. MMCs arms inductance were calculated to limit the current

<table><caption>TABLE I: Caption</caption><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>P<sub>n</sub></td><td>Nominal power</td><td>600 MW</td></tr><tr><td>v<sub>dc1</sub></td><td>High-level voltage</td><td>320 kV</td></tr><tr><td>v<sub>dc2</sub></td><td>Low-level voltage</td><td>250 kV</td></tr><tr><td>L<sup>U</sup><sub>arm</sub></td><td>Upper MMC arm inductance</td><td>3.5 mH</td></tr><tr><td>R<sup>U</sup><sub>arm</sub></td><td>Upper MMC arm resistance</td><td>3.5 mΩ</td></tr><tr><td>L<sup>L</sup><sub>arm</sub></td><td>Lower MMC arm inductance</td><td>12.5 mH</td></tr><tr><td>R<sup>L</sup><sub>arm</sub></td><td>Lower MMC arm resistance</td><td>12.5 mΩ</td></tr><tr><td>L<sub>T</sub></td><td>Transformer leakage inductance</td><td>0.15 p.u</td></tr><tr><td>R<sub>T</sub></td><td>Transformer line resistance</td><td>0.015 p.u</td></tr><tr><td>M</td><td>Number of legs</td><td>2, 3 or 4</td></tr></tbody></table>

rise to the typical value of $10kA/ms$ [1]. As for the transformer, from the voltage level, it is supposed to be like HT-MT transformer with the traditional value of 0.15 p.u.

### B. Power flows in the converter

The converter structure and parameters were introduced. It is then possible to describe its operation. First, this part presents the power transfer in the converter as it can be found in [10]. Let $P$ be the power flowing from the HV side to the LV side, $\alpha$ the voltage ratio $V_{dc2}/V_{dc1}$ and $M$ the number of legs. By neglecting the converter losses, the approximated DC currents and voltages are given by :

$$i_{dc1} = \frac{P}{v_{dc1}} \qquad i_{dc2} = \frac{P}{v_{dc2}} \qquad (1)$$

$$i_{dc}^{U} = i_{dc1} \qquad i_{dc}^{L} = i_{dc1} - i_{dc2}$$

$$v_{dc}^{U} = v_{dc1} - v_{dc2} \qquad v_{dc}^{L} = v_{dc2}; \qquad (2)$$

From these elements, it is possible to establish the MMC powers :

$$P^{U} = v_{dc}^{U} \cdot i_{dc}^{U} = P(1 - \alpha) \qquad (3)$$

$$P^{L} = v_{dc}^{L} \cdot i_{dc}^{L} = -P(1 - \alpha)$$

These first equations means that, to transfer power with the DC-DC converter, the upper and the lower MMC will exchange $P(1 - \alpha)$ through their AC connection. This power transfer is, in fact, used to balance the energy within the converter. As evidence, by equation (3), the DC power transfer creates a power in the converter that, if not exchange between the two converters, will be reflected in the capacitor energy. If the power flows from the high-level to the low-level side, the upper capacitors will charge while the lowers will discharge: the operation would be unstable.

An interesting feature about the DC-auto-transformer is that the MMC nominal power is only part $((1 - \alpha))$ of
the converter power. So, it works better for low voltage ratio ($\alpha > 0.5$) which is often the case for HVDCs interconnection.

### C. AC steady-state modeling

To study AC power exchange, the traditional model of MMC is used. In particular, the decoupling (4) of [14] is employed. With this decoupling, it is possible to draw the equivalent AC circuit of the converter from the upper MMC of figure.3. (It is recalled that from an AC point of view, DC voltage sources are considered short-circuits). Note that, in this section, the resistances are neglected against the inductances.

$$ 
\begin{aligned}
i_{diffj} &= \frac{i_{pj} + i_{nj}}{2} \qquad i_{sj} = i_{pj} - i_{nj} \\
v_{diffj} &= \frac{v_{mpj} + v_{mnj}}{2} \qquad v_{sj} = \frac{-v_{mpj} + v_{mnj}}{2}
\end{aligned}
\qquad (4) $$

The AC steady-state operation is described using the phasor representation. The sinusoidal quantity $x(t) = \sqrt{2}X\cos(2\pi ft+\theta)$ are represented with by $X = X\angle\theta = Xe^{j\theta}$. With this notation, (5) describes the AC modulated voltages by the MMCs. The upper MMC is chosen as a reference for the angle and the lower one is phase-shifted by $\delta$ to enable the power transfer. From the AC equivalent circuit of fig.3, the current (6) and power (7) can be obtained. As mentioned in the previous part, $P_{AC}$ must be equal to $P(1 - \alpha)$ in order to keep the energy balanced within the converter.

$$ 
\begin{aligned}
\mathbf{V}_{\mathrm{s}}^{\mathrm{U}} &= V_{\mathrm{s}}^{\mathrm{U}} = \frac{V_{\mathrm{peak}}^{\mathrm{U}}}{\sqrt{2}} \\
\mathbf{V}_{\mathrm{s}}^{\mathrm{L}} &= V_{\mathrm{s}}^{\mathrm{L}} \angle \delta = \frac{V_{\mathrm{peak}}^{\mathrm{L}}}{\sqrt{2}} \angle \delta
\end{aligned}
\qquad (5) $$

$$ \mathbf{I}_{\mathrm{s}}^{\mathrm{U}} = \frac{\mathbf{V}_{\mathrm{s}}^{\mathrm{U}} - \mathbf{V}_{\mathrm{s}}^{\mathrm{L}}}{X_{\mathrm{eq}}} \qquad (6) $$

where $X_{eq} = 2\pi f(L_{arm}^{U} + m^{2}L_{arm}^{L} + L_{T})$

$$ P_{AC} = \Re(3V_s^U I_s^{U*}) = 3 \frac{m V_s^L V_s^U \sin(\delta)}{X_{eq}} \qquad (7) $$

(7) highlights four parameters that can be chosen: the AC voltages in the upper and lower MMCs, the operating frequency and the phase shift between the AC voltages. However, there is only on constraint: the energy balance. This means that there are three degrees of freedom to analyse. In this work, $f$, $V_s^L, V_s^U$ are chosen and $\phi$ is deduced.

<figure><img src="image_5.png" /><figcaption>Fig. 3: AC equivalent circuit from upper MMC side</figcaption></figure>

### III. IMPACT OF THE DEGREES OF FREEDOM

The objective is to study the impact on the aforementioned degrees of freedom. First, the performance indicators to the design are presented. Then, they are evaluated by varying the degrees of freedom in order to find an optimal operating point.

#### A. Performance Indicators

The performance is analyzed by looking at the currents, the capacitor size and the efficiency as determined with the methods described in this section.

**Steady state values of the current** : For the current, the maximum value and RMS value are observed. They can be obtained directly from (1) and (6).

**Capacitor Size** : The value of an arm capacitor is determined in order to limit the voltage ripple to ±10%. To calculate it, the fluctuating power is first calculated. It is then possible to estimate the energy fluctuation in an arm. Knowing this fluctuation, the capacitor value is determined to limit the voltage ripple by using (8).($\Delta V$ is given in per unit of $V_{ctot}$).

$$ C_{tot} = \frac{\Delta E}{2V_{ctot}^{2}\Delta V} \qquad (8) $$

Finally, it is usual to represent the energy stored in capacitors in relation to the rated power, as shown in (9). Each arm is rated to the $P_{nom} = P_n/M$.

$$ H_c = \frac{1}{2} \frac{C_{tot} V_{ctot}^2}{P_{nom}} \qquad (9) $$

**Losses estimation** : To calculate the efficiency, the method described in [15] is employed. It consists of four steps :

1) Waveforms of the voltages and currents are determined using the steady-state equations (1)-(6).

2) These are fed to the switching model of one leg that generates the instants of commutation and the sub-module voltages. To do so, the reduced switching frequency balancing algorithm [16] is employed because it generates less switchings.
<table><caption>TABLE II: Considered Infineon IGBT Modules</caption><thead><tr><th>Module</th><th><i>I</i><sub>cnom</sub> (A)</th><th><i>I</i><sub>CRM</sub> (A)</th><th><i>V</i><sub>CES</sub> (V)</th></tr></thead><tbody><tr><td>FZ1400R33HE4</td><td>1400</td><td>2800</td><td>3300</td></tr><tr><td>FZ1600R33HE4</td><td>1600</td><td>3200</td><td>3300</td></tr><tr><td>FZ2000R33HE4</td><td>2000</td><td>4000</td><td>3300</td></tr><tr><td>FZ2400R33HE4</td><td>2400</td><td>4800</td><td>3300</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Fig. 4: Influence of the chosen AC voltages on the indicators ()</figcaption></figure>

3) From the previous information, the conduction and commutation losses are retrieved thanks to the datasheet. For this work, data from IGBT Infineon sub-modules is used. The latter was adapted according to the currents, the smallest one possible in tab.II is chosen.

4) Finally, the losses of the passive elements are calculated and added for each resistance in the system ($L_R = R \cdot I_{Eff}^2$).

So, the total losses is composed of the passive losses, the conduction losses and the switching losses.

## B. Influence of AC voltages

Figure.4 shows the influence of the AC peak voltage of MMCU ($V_{peak}^U$) and MMCL ($V_{peak}^L$) on the chosen indicators. For each MMC, the maximum voltage possible is $V_{peak} = v_{dc}/2$ as not to employ more SM nor full-bridges [17]. Moreover, note that, the transformer is supposed to be adapted for each case but its parameters are kept as $L_T = 0.15$ p.u and $R_T = 0.015$ p.u which are typical values for this voltage levels.

<figure><img src="image_7.png" /><figcaption>Fig. 5: Influence of the frequency</figcaption></figure>

From fig.4, it can be concluded than the higher voltage, the better the performances as the capacitor size decreases and the efficiency increases. Both this behavior can be explained by the reduction of the AC current. Less current leads to less passive and conduction losses. For the commutation losses, the analysis is less straight forward because, although the switching losses decrease with current, higher voltages means more switching. So the commutation losses are less impacted by the voltage variation.

## C. Influence of the operating frequency

As for the frequency, the results are displayed in fig.

5. The frequency was varied from 50 to 300Hz.

The conclusion for frequency is less straightforward than for the voltages although quite typical for power electronics. Here, the use of higher frequency decreases the size of the capacitor that is needed to limit the voltage
<figure><img src="image_8.png" /><figcaption>(a) Modulated voltages</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(b) Arm currents</figcaption></figure>

Fig. 6: MMCs Lower arm quantities with sinusoidal and trapezoidal operation for a 2-legs MMC-AT

ripple. But by increasing the frequency, the switching losses also increased which leads to less efficiency. The passive and conduction losses are almost not impacted here. The designer must chose between the footprint (capacitor and transformer size) and efficiency. For the following of this work, a frequency of 100 Hz has been chosen as a trade-off.

## IV. DESIGN ANALYSIS WITH TRAPEZOIDAL MODULATION

### A. Trapezoidal operation

On the MMC-DAB, the quasi-two-level operation proved to be efficient for both efficiency and capacitor size [5], [6]. Moreover, its application on a similar topology to the MMC-AT was tested in [12]. The waveform of the trapezoidal operation are presented in fig.6.

So, to complete the present analysis, a trapezoidal waveform is also considered and analysed. In the following subsections, the voltages, frequency and transition time (time to go from the lower level to the upper level of the trapeze) are studied.

<figure><img src="image_10.png" /><figcaption>(a) Current in upper MMC
$H_c$ (ms)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>(c) Capacitor energy</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(d) Efficiency</figcaption></figure>

Fig. 7: Influence of the chosen AC voltages on the indicators for trapezoidal operation ($f = 100$ Hz, $T_r = 1$ ms)

### B. Influence of voltages

Fig.7 displays the performances of the converter according to the AC voltages with a trapezoidal waveform. The observed tendency are the same than with sinusoidal signal, that is to say, the voltages needs to be maximize in order to enhance the converter.

### C. Influence of frequency and transition time

Fig.7 displays the performances of the converter according to the frequency and transition time for a trapezoidal waveform.

For the frequency, the results are similar than for sinusoidal operation. The higher the frequency, the lower the efficiency and the lower the capacitor size.

For the transition time, the smaller it is, the smaller are the currents. Indeed, a small transition time leads to a square voltage with high RMS and fundamental value. So, to transfer the AC power, less currents are needed. The reduction of the these leads to lower capacitor size and higher efficiency.

The parameter chosen as optimal are $f = 100$ Hz and $T_r = 1$ ms. This frequency is a compromise between
<figure><img src="image_13.png" /><figcaption>Fig. 8: Influence of frequency and transition time on the converter for trapezoidal operation</figcaption></figure>

capacitor size and efficiency. The transition time could be decreased to enhance both $H$ and $\eta$, however it would present a higher $\frac{dv}{dt}$ to the transformer. This value of 1 ms gives an efficiency of 99.75% and $H_c = 1.6$ ms which are already satisfying values.

## D. Comparison with sinusoidal operation

In this part, the design and operation of the converter are compared for sinusoidal and trapezoidal modulation. This analysis is realized using the optimal point found in the previous subsections. To complete this study, the number of legs was also varied, the sinusoidal operation with two legs and the trapezoidal operation with four legs were studied with the same set of parameters as there three-legs and two-legs counterparts. Results for losses and capacitor energy are displayed in fig. 9.

On the converter capacitor size, the use of quasi-two-level reduces it by a factor of 3. This results is coherent with the previous studies on Q2L operation of MMC-DAB. The energy variations are much more limiter as they only happens during the transition times [18].

On the efficiency, the trapezoidal operation increases the efficiency from 99.62% for the two-legs sinusoidal operation to 99.71% for the two-legs trapezoidal one.

<figure><img src="image_14.png" /><figcaption>Fig. 9: Comparison of operation for sinusoidal and trapezoidal modulation</figcaption></figure>

Passive losses, conduction and switching losses are all reduced thanks to the reduced current. As for the number of legs, it seems that two is the best solution. More legs introduces more semi-conductor that generate losses. However, as these legs carry less current, these losses are reduced. A balance is seek between the current reduction and the number of submodule. In this converter, the MMCs have partial power rating, therefor the current are lower compared to F2F-MMC, so the addition of legs (and sub-modules) is not beneficial.

## V. CONCLUSIONS

This paper provides a design analysis of the MMC-AT which is an attractive non-isolated topology for HVDC interconnections. From the steady-state analysis, three degrees of freedom were identified : the AC voltages of the upper and lower MMC and the frequency. The analysis of converter performances showed that the voltages should be as high as possible and the frequency should be around 100Hz. Then, the quasi-two-level operation was introduced and studied, it proved to be more efficient than the sinusoidal modulation.

But, the conclusions of this paper have to be nuanced with one element that has been considered perfect : the transformer. In the DC-autotransformer, the transformer has a lot of design constraint and the main one is the
DC voltage biased between the primary and secondary coil. To add to this unusual constraint, it has to handle harmonics of the trapeze. At least, at low frequencies, the $\frac{dv}{dt}$ can be well controlled without conceding efficiency.

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