# Operation modes and design consideration for MMC with unipolar current full-bridge submodules

Martin Geske, Hatim Abbi, Duro Basic

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Martin Geske, Hatim Abbi, Duro Basic. Operation modes and design consideration for MMC with unipolar current full-bridge submodules. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0017. hal-05073967

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# Operation modes and design consideration for MMC with unipolar current full-bridge submodules

Martin GESKE*, Hatim ABBI**, Duro BASIC**

*GE Energy Power Conversion GmbH, Culemeyerstraße 1, 12277 Berlin, Germany

**GE Power Conversion SAS, 15 rue Jean Bart, 91300 Massy, France
martin.geske@gevernova.com, hatim.abbi@gevernova.com, duro basic@gevernova.com

URL: https://www.gevernova.com/power-conversion/

## Keywords

«Multilevel converters», «Modular Multilevel Converters (MMC)», «High voltage power converters», «Voltage Source Converter (VSC)»

## Abstract

The unipolar current full-bridge submodule (SM) for modular multilevel converters (MMC) operates with unipolar current and bipolar voltage. Two basic operating modes for unipolar arm currents are presented, described, and analyzed. The differences between the two idealized operating modes are further discussed regarding the system design of an MMC. The design factors for current and voltage in the DC-link differ, which leads, for example, to different numbers of SMs and power losses. These aspects are presented as examples and trade-offs are summarized.

## Introduction

MMCs were first considered for high-voltage DC power transmission [1], [2] and are increasingly adopted for other applications. For example, MMCs have been introduced for medium-voltage (MV) industrial drives [3]. Applications such as electrolysis, arc welding, data centers, and grid emulation are under research [4], [5]. The preferred SM is the half-bridge SM (HB-SM), which offers low power losses and low component efforts but lacks fault-blocking capability [6].

Janning and Salama invented the unipolar current full-bridge SM (UC FB-SM) illustrated in Fig. 1 (a) [7]. The quadrants chart in Fig. 1 (a) indicates that the UC FB-SM has unipolar current and bipolar voltage characteristics, which is the opposite of the HB-SM shown in Fig. 1 (b). The UC FB-SM has two switches in the diagonal configuration, providing fault-blocking in case of DC-side faults differentiating it from the HB-SM.

<figure><img src="image_2.png" /><figcaption>Fig. 1: (a) UC FB-SM and (b) HB-SM with quadrants chart</figcaption></figure>

Fault blocking is essential for transmission systems with overhead lines, as discussed in [8] for using UC-FB SMs. In addition, only one IGBT per phase leg is implemented in the UC FB-SM increasing reliability and reducing the likelihood of consequential IGBT faults. Consequential faults of IGBT failures can lead to so-called shoot-through faults [9], causing severe destruction. Additionally, full bridge based MMCs can operate with high modulation indices. Hence, for a UC FB-MMC the DC-link voltage can be set below the peak value of the phase voltage $v_{ac}$, which is depicted in Fig. 2 (a) and (b). The resulting high modulation index is advantageous for drive applications [10]. This voltage ratio is impossible with HB-SMs because the diode D2 limits the AC voltage versus the DC voltage. Finally, HB-MMC requires a DC-voltage level higher than $v_{ac}$, as shown in Fig. 2 (c).

<figure><img src="image_3.png" /><figcaption>Fig. 2: (a) MMC topology and AC/DC voltage ratios for MMC with (b) UC FB-SM, (c) HB-SM</figcaption></figure>
The omitted switch positions of the UC FB-SM restrict unipolar current flow for normal operation only, which is different for the HB-SM (cp. quadrants chart in Fig. 1 (b)). Nonetheless, it is noteworthy that derivatives using the UC FB-SM structure can achieve the output-voltage characteristics of a HB-SM [11]. The following sections deal with two idealized operating methods for UC FB-MMC.

## The unipolar current full-bridge submodule

Table I summarizes that the UC FB-SM holds two switches, T2 and T3, that can create four switch states and three output-voltage levels. The diodes D2 and D3 in Fig. 1 (a) are not involved in regular operation with unipolar current. IGBTs T2, T3, and diodes D1 and D4 are used for regular operation, which results in the same semiconductor expenditure for regular operation as for the HB-SM. The UC FB-SM without diodes D2 and D3 is considered in [7], [12]. The switch states 1 and 4 in Table I support bipolar voltage and balancing of the SM's stored energy. State 2 and 3 bypass the SM capacitor, create no output voltage, and can be used to balance power losses among both current paths.

<table><caption>Table I: States of the UC FB-SM ($i_{SM} > 0$)</caption><thead><tr><th>State</th><th>T2</th><th>T3</th><th>v<sub>sm</sub></th><th>Δw<sub>c</sub></th></tr></thead><tbody><tr><td>1</td><td>0</td><td>0</td><td>-V<sub>C</sub></td><td>&gt; 0</td></tr><tr><td>2</td><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><td>3</td><td>0</td><td>1</td><td>0</td><td>0</td></tr><tr><td>4</td><td>1</td><td>1</td><td>+V<sub>C</sub></td><td>&lt; 0</td></tr></tbody></table>

A negative current $i_{SM}$ would create a negative output voltage, which is preferred for fault blocking, as shown by quadrant 3 in Fig. 1 (a). A UC FB-MMC can be modulated with a high modulation index $M_A = \hat{v}_{ac}/(V_{dc}/2) > 1$, as shown in Fig. 3 for the output-voltage characteristic.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Output-voltage curve of UC FB-SM</figcaption></figure>

The conventional modulation index is now defined as the AC/DC voltage factor

$$M_A = f_v = \frac{\hat{v}_{ac}}{v_{dc}/2}, \qquad (1)$$

A higher AC/DC voltage factor $f_v$ results in operation with lowered DC-link voltage, which reduces the maximum arm voltage. Fig. 4 shows again the simplified AC and DC voltages for a UC FB-MMC. For a phase voltage $v_{ac}$ higher than half the DC-link voltage, the respective SMs must provide bipolar voltage to reverse the output voltage (see encircled area in Fig. 4).

<figure><img src="image_5.png" /><figcaption>Fig. 4: Simplified principle for bipolar voltage operation of MMC with UC FB-SMs ($f_v=2$)</figcaption></figure>

## Continuous conduction mode

First, the operation of an MMC with UC FB-SM is considered for continuous conduction mode (CCM) as described in [12], [13]. CCM relates to the characteristics of the converter-arm current. The basic description is given by continuous time modeling using the equivalent circuit diagram in Fig. 5, which models one phase of an MMC (cp. Fig. 2 (a)). The converter arms are modeled as variable voltage sources, creating idealized voltage waveforms.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Generic single-phase equivalent circuit of an MMC (definition: $v_s=v_{ac}$, $i_s=i_{ac}$)</figcaption></figure>

The basic description starts with the power balance equation for the converter, given by

$$P_{ac} = P_{dc}, \qquad (2)$$

which can be rewritten as

$$\frac{3}{2} \cdot \hat{v}_S \cdot \hat{i}_S \cdot \cos\varphi = V_{dc} \cdot I_{dc}. \qquad (3)$$
The converter arm connected to the positive pole can be described as

$$v_{arm s,p}(t) = \frac{1}{2} \cdot V_{dc} - \hat{V}_s \cdot \sin(\omega_s t) \text{ and} \quad (4)$$

$$i_{arm s,p}(t) = \frac{1}{3} \cdot I_{dc} + \frac{1}{2} \cdot \hat{I}_s \cdot \sin(\omega_s t - \varphi_s). \quad (5)$$

The power equation for the converter arm is the product of Eqs. (4) and (5), which yields:

$$p_{arm s,p}(t) = \left( \frac{1}{2} V_{dc} - \hat{V}_s \cdot \sin(\omega_s t) \right) \cdot \left( \frac{1}{3} I_{dc} + \frac{1}{2} \hat{I}_s \cdot \sin(\omega_s t - \varphi_s) \right). \quad (6)$$

For idealized CCM operation, the magnitude of the AC current must be equal to or below the DC-link current $I_{dc}$. This relationship is expressed for the arm current as

$$\frac{1}{2} \cdot \hat{I}_s \le \frac{1}{3} \cdot I_{dc}. \quad (7)$$

For minimization of the DC-link current, the following assumption applies as a limiting case

$$I_{dc} = \frac{3}{2} \cdot \hat{I}_s. \quad (8)$$

This case is expressed as a current design factor

$$f_i = \frac{3 \cdot \hat{I}_s}{2 \cdot I_{dc}} = 1. \quad (9)$$

$0 \le f_i \le 1$ is valid for this operating mode while reducing $f_i$ to zero corresponds to $\hat{I}_s = 0$. Subsequently, a system simulation is used to verify the operation with idealized CCM. An MMC with UC FB-SMs, as shown in Fig. 6, is analyzed using the simulation software PLECS for the 20 MVA rated system in Table II.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Simulation model for UC FB-MMC</figcaption></figure>

<table><caption>Table II: Parameters of UC FB-MMC (CCM)</caption><thead><tr><th>Parameter</th><th>Value / Type</th></tr></thead><tbody><tr><td>Rated system power S<sub>ac</sub></td><td>20 MVA</td></tr><tr><td>Line-to-line voltage V<sub>ll</sub></td><td>13.8 kV</td></tr><tr><td>Angular frequency ω<sub>s</sub></td><td>314.16 rad/s</td></tr><tr><td>DC-link voltage V<sub>dc</sub></td><td>11.3 kV</td></tr><tr><td>SM voltage V&#773;<sub>SM</sub>, N<sub>SM</sub></td><td>1.1 kV, 16</td></tr><tr><td>L<sub>arm</sub>, L<sub>dc</sub>, L<sub>Tr</sub></td><td>0.75 mH, 2.5 mH, 1 mH</td></tr></tbody></table>

To achieve ideal conditions, the SM capacitance is increased to neglect the influence of circulating currents. Fig. 7 shows the simulated waveforms for a power-flow reversal starting at t=50 ms. The DC voltage is reversed within 40 ms, changing the power flow from inverting mode to rectifier operation. As indicated in the quadrants chart in Fig. 1 (a), quadrants 1 and 4 are used for normal operation and correspond to one power-flow direction each. The converter is operated with an almost constant DC current. The converter arm currents are nearly sinusoidal, which is close to the ideal case of CCM operation. In summary, the arm current is positive, sinusoidal, and can ideally reach zero.

<figure><img src="image_8.png" /><figcaption>Fig. 7: Simulated waveforms of UC FB-MMC for CCM operation (phase-shifted carrier PWM, carrier ratio = 7, cos(φ) = -1 to +1)</figcaption></figure>
## Discontinuous conduction mode

The discontinuous conduction mode (DCM) is characterized by non-conductive periods of the arm current. The peak currents in the arms can be higher than those CCM, whereas non-conductive periods are present. In this regard, current factors $f_i > 1$ are considered. Therefore, Eq. (7) for CCM changes for DCM to

$$ \frac{1}{2} \cdot \hat{I}_s > \frac{1}{3} \cdot I_{dc}. \qquad (10) $$

Fig. 8 shows simulated arm currents with non-conductive periods for about 180°. The resulting arm currents have similar shapes to those of half-wave rectifiers.

<figure><img src="image_9.png" /><figcaption>Fig. 8: Simulated arm currents for UC-FB MMC with DCM operation</figcaption></figure>

Accordingly, the arm currents of DCM are described here using formulas for conventional bridge rectifiers. Then, the converter-arm peak current is the peak value of the line-side current

$$ \hat{I}_{arm} = \hat{I}_s. \qquad (11) $$

Rectifier theory [14], [15] describes the DC-link current as

$$ I_{dc} = \frac{3}{\pi} \int_{-\pi/6}^{\pi/6} \hat{I}_s \cos(\omega_s t) \, d\omega_s t = \frac{3 \cdot \hat{I}_s}{\pi} \approx \hat{I}_s. \qquad (12) $$

Therefore, DCM is characterized by a different design factor $f_i$ compared to CCM with

$$ f_i = \frac{3 \cdot \hat{I}_s}{2 \cdot I_{dc}} = \frac{\pi}{2} > 1.5. \qquad (13) $$

The average arm current is formulated as

$$ I_{arm,av} = \frac{1}{2 \cdot \pi} \int_{0}^{\pi} \hat{I}_{s} \sin(\omega_{s} t) \, d\omega_{s} t = \frac{\hat{I}_{s}}{\pi}. \qquad (14) $$

For the discussed case, the root mean square (rms) value of the arm current is

$$ I_{arm,rms} = \sqrt{\frac{1}{2\pi} \int_{0}^{\pi} (\hat{I}_{s} \sin(\omega_{s} t))^{2} d\omega_{s} t} = \frac{\hat{I}_{s}}{2}. \qquad (15) $$

An ideal half-wave rectification would create a DC current $I_{dc}$ with a current ripple $I_{dc(ac)}$ overlaying the DC-link current $I_{dc}$

$$ I_{dc}(t) = I_{dc} + I_{dc(ac)}(t). \qquad (16) $$

For the operation of an MMC with UC FB-SMs, the DC-link current $I_{dc}$ should not contain the ripple current. To compensate for this undesirable AC current component, an additional current can be injected.

## Characteristics of operating modes

As previously highlighted, the arm current waveforms of CCM and DCM differ with DCM having non-conducting periods. Fig. 9 shows a simplified graphical comparison of the operating modes, where the peak currents of the converter arms are identical for both modes. It is noted that idealized waveforms are presented that neglect circulating currents. The line voltages and arm current amplitudes are similar, but the AC/DC voltage factor $f_v$ differ. The design can be adapted for the two methods, or MMC operation can apply the optimal mode as needed. The AC/DC voltage factors for the idealized cases in Fig. 9 are different, whereby CCM uses $f_i=2$ (see red curve), and DCM considers $f_i=1.27$ (see blue curve). The reduced arm current for DCM implies a lower DC component, which is compensated by higher DC-link voltage. In this sense, the design for DCM will require more SMs per arm but a lower current rating.

<figure><img src="image_10.png" /><figcaption>Fig. 9: Comparison of CCM and DCM operation (red: CCM with $f_v=2.0$; blue DCM with $f_v=1.27$)</figcaption></figure>
Table III summarizes the analytically derived current parameters. Generally, the higher current design factor $f_i$ for DCM lowers the other current parameters for DCM.

<table><caption>**Table III: Factors for arm-current ratings for CCM and DCM operation**</caption><thead><tr><th>Parameter</th><th>CCM</th><th>DCM</th></tr></thead><tbody><tr><td>$I_{arm,av}$</td><td>$\hat{I}_S/2$</td><td>$\hat{I}_S/\pi$</td></tr><tr><td>$I_{arm,rms}$</td><td>$\sqrt{3/8} \cdot \hat{I}_S$</td><td>$\hat{I}_S/2$</td></tr><tr><td>$I_{dc}$</td><td>$3/2 \cdot \hat{I}_S$</td><td>$3/\pi \cdot \hat{I}_S$</td></tr><tr><td>$f_i$</td><td>$1.0$</td><td>$\pi/2$</td></tr></tbody></table>

For CCM, the limiting case from Eq. (8) is considered for the determination of the energy storage requirement. Fig. 10 shows calculated generalized waveforms indicating three zero crossings for the arm power $p_{arm s,p}$.

<figure><img src="image_11.png" /><figcaption>Fig. 10: Calculated waveforms for UC FB-SM with indicated zero crossings for arm power</figcaption></figure>

The voltage and current design factors are applied according to Lesnicar [16] as

$$f_v \cdot f_i = \frac{2}{\cos(\varphi)} \qquad (17)$$

with

$$f_i = \frac{3 \cdot \hat{I}_S}{2 \cdot I_{dc}} \quad \text{and} \quad f_v = \frac{2 \cdot \hat{V}_S}{V_{dc}}. \qquad (18)$$

Both factors are further combined with the arm power as per Eq. (6), which yields an equation for the determination of zero crossings. Zero crossings for CCM refer to the bipolar arm voltage. It is noted that zero crossings for HB MMC are considered for the arm current. The peak-to-peak energy fluctuations of $w_{arm s,p}$ occurring between two adjacent zero crossings are the basis for determining the energy storage requirement.

Mathematical transformations lead to a compact expression of the maximum energy delta $\Delta W_C$ per SM capacitor. The energy $\Delta W_C$ in Eq. (19) depends on the AC power $S_{ac}$, $\cos(\varphi)$, the frequency $\omega_S$, $N_{SM}$, and the factor $f_i$.

$$\Delta W_C = \frac{2}{3} \frac{S_{ac}}{f_i \omega_S N_{SM}} \left(1 - \left(\frac{f_i \cos(\varphi)}{2}\right)^2\right)^{\frac{3}{2}} \qquad (19)$$

DCM operates with a higher DC-link voltage for the same power and thus requires a higher number of submodules per arm. Furthermore, DCM applies lower arm currents, as indicated in Table III. Hence, the energy delta $\Delta W_C$ for CCM, according to Eq. (19), is higher than for DCM operation.

DCM does not have continuous arm currents, and the determination of the zero crossings is different from that of CCM. Comparisons for various $\cos(\varphi)$ in [13] have shown that $\Delta W_C$ can vary by a factor of two and more depending on the operating mode and the system design. In this sense, the SM storage for DCM may then be significantly smaller. Accordingly, factor $f_i$ is furthermore a design parameter for the installed SM capacitance and the MMC's stored energy.

The formulated energy storage requirement is compared here to a HB-MMC as initially described in [16]. Table IV summarizes the current and voltage design factors for a UC FB-MMC and a HB-MMC. The duality between both MMC variants is given by the interpretation of the voltage and current factors, which in each case must be viewed in the opposite sense. In the same way, this can be seen for the energy delta $\Delta W_C$, where both design factors ultimately swapped the positions in the energy equation.

<table><caption>**Table IV: Duality consideration between UC FB-MMC and HB-MMC, cp. [13], [16]**</caption><thead><tr><th>UC FB-MMC (CCM)</th><th>HB-MMC</th></tr></thead><tbody><tr><td>$f_i = \frac{3 \cdot \hat{I}_S}{2 \cdot I_{dc}}$; $0 \le f_i \le 1$</td><td>$f_v = \frac{2 \cdot \hat{V}_S}{V_{dc}}$; $0 \le f_v \le 1$</td></tr><tr><td>$\Delta W_C = \frac{2}{3} \frac{S_{ac}}{f_i \omega_S N_{SM}} \cdot \left(1 - \left(\frac{f_i \cos(\varphi)}{2}\right)^2\right)^{\frac{3}{2}}$</td><td>$\Delta W_C = \frac{2}{3} \frac{S_{ac}}{f_v \omega_S N_{SM}} \cdot \left(1 - \left(\frac{f_v \cos(\varphi)}{2}\right)^2\right)^{\frac{3}{2}}$</td></tr></tbody></table>
## System design aspects

The discussed operating modes influence the system design. In summary, more SMs are necessary for operation with DCM, but the arm currents and SM currents are lower. In this respect, the number of SMs and the power losses of an MMC will be different for the same system power and AC voltage. This chapter deals with these relationships based on the design example for the UC-FB MMC specified in Table II.

Table V summarizes a relative comparison for an MMC design based on ideal factors as per Table III, whereas a system design for CCM is set as the reference with 100%. The DC-link current and voltage are referred to the same power rating, showing a 36% lower DC-link current for DCM, resulting in an 18% lower arm current. The higher DC-link voltage for DCM of +57% results in a higher peak voltage of the arm, ideally increasing by 19%. It is noted that the idealized comparison may deviate from a system design that considers criteria for other components and efforts. Nevertheless, generally, it is a good estimate that the number of SMs per arm for DCM will be around 20% higher.

<table><caption>Table V: Idealized, relative design factors for UC-FB MMC with CCM and DCM operation</caption><thead><tr><td>Parameter</td><td>CCM</td><td>DCM</td></tr></thead><tbody><tr><td>I<sub>dc</sub></td><td>100%</td><td>64%</td></tr><tr><td>V<sub>dc</sub></td><td>100%</td><td>157%</td></tr><tr><td>I<sub>arm,rms</sub></td><td>100%</td><td>82%</td></tr><tr><td>V̂<sub>arm</sub></td><td>100%</td><td>119%</td></tr></tbody></table>

Below, a loss analysis based on a simulation compares the operating modes relative to one another. The semiconductor power losses are determined using a switched model for phase-shifted carrier PWM. The modeling uses AC and DC current sources, the total current of which flows through one SM, as shown in Fig. 11.

<figure><img src="image_12.png" /><figcaption>Fig. 11: Simulation of average power losses with single SM for phase-shifted carrier PWM</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 12: Characteristics of IGBT module FF1800R17IP5: diode (top), IGBT (bottom), V<sub>CE</sub>=900V, cp. [17]</figcaption></figure>

The switching frequency of the simulation has been increased by a factor of 10, whereas the models for switching losses are divided by 10. This factor is introduced to consider a sufficiently high number of switching instants for a real carrier ratio of 7. In summary, this approach achieves average losses with 10 times more different switching times.

The operational characteristics of the UC-FB MMC from Fig. 6 and Table II are modeled by current sources (see Fig. 11) and corresponding AC/DC voltage factors. The definition of SMs per arm is based on Eq. (4) for the maximum arm voltage. $N_{SM}$ is increased by three additional SMs per arm for DCM compared to Table II for CCM. The power semiconductors are modeled based on datasheet values of the IGBT module type FF1800R17IP5 (1800 A, 1.7 kV) [17]. The conduction and switching losses of the IGBT and diode in Fig. 12 and the transient thermal impedances in Fig. 13 are modeled in simulation software PLECS.

<figure><img src="image_14.png" /><figcaption>Fig. 13: Thermal impedances of modeled 1.7-kV IGBT module FF1800R17IP5, cp. [17]</figcaption></figure>
The thermal resistance from case to heatsink is not considered, and the case temperature of the power module is set to 80°C. The loss simulation holds the mentioned factor of 10 for the increase in the switching frequency and as divider factor for the modeled switching losses in Fig. 12. The loss study is carried out for averaged inverter losses in rectifying mode and inverting mode ($cos(φ) = -1, +1$).

For DCM, the semiconductor power losses were simulated to be 0.7% for one inverter, which would result in a semiconductor-based efficiency of 99.3%. In contrast, the CCM operation creates semiconductor losses for one inverter of 0.94% with fewer SMs per arm. In this regard, it is noted that 16% fewer SMs for CCM are used here - but the increase in arm current causes about 0.24% higher semiconductor losses. This result shows that the system design of a UC FB-MMC has a trade-off in terms of losses and the number of SMs according to the operating modes. Even if idealized arm currents for CCM and DCM are assumed in this work, limits for the trade-off's range are shown. Finally, the semiconductor losses are in the order of magnitude of a FB-MMC, cp. [8]. The expense for semiconductors in conducting mode for normal operation is halved compared to FB-SMs and identical to HB-SMs. Nevertheless, the design of a UC FB-MMC has a lower arm voltage than HB MMC as per Eq. (4) with the same AC voltage and rated power. UC-FB SMs provide bipolar voltage, allowing operation with a lower half DC-link voltage than AC peak voltage (cp. Fig. 2 (b)). This aspect requires a higher DC-link voltage for a HB-MMC and therefore approximately 30% higher number of SMs, cp. [13].

## Conclusion

Modular multilevel converters (MMC) are deployed for high-voltage DC power transmission and variable speed drives (VSD). The selected type of submodule (SM) plays an essential role in defining the properties of the respective MMC. The unipolar current full-bridge SM (UC FB-SM) is characterized by bipolar voltage and unipolar current operation, opposite to that of the half-bridge SM (HB-SM). The UC FB-SM provides fault blocking on the system level and operation with high modulation indices that are beneficial for VSD applications.

In this work, two idealized operating modes for the arm current are introduced and investigated. First, continuous conduction mode (CCM) uses a sinusoidal unipolar arm current with a relatively low DC-link voltage. The CCM creates a high utilization of the arm current with a relatively small number of submodules. The second approach uses discontinuous conduction mode (DCM) that ideally only carries arm current for half a period. The arm current is lower at this point, which requires a higher DC-link voltage and therefore more SMs per arm. The trade-off for an idealized DCM arm current is about 10% to 20% higher number of SMs but a lower arm current of the same order of magnitude compared to CCM.

Semiconductor power losses for a UC FB-MMC with 13.8 kV$_{ac}$, 20 MVA, and DCM are simulated for one inverter stage with 0.7%. Applying CCM operation would increase the power loss to about 0.94%, with three SMs less per arm. For this example, CCM requires 16% fewer SMs than a design for DCM, which in turn causes about 0.24% more semiconductor losses. This result outlines the design scope for a UC-FB MMC concerning the operating mode. Furthermore, the stored energy of the SM capacitor and the MMC presents another criterion that must be evaluated with a focus on the selected application.

Finally, the bipolar voltage capability of the UC-FB SM supports lower DC-link voltage at same AC voltage compared with the HB-SM. In this case, a UC-FB MMC can be built with about 20% to 30% fewer submodules at a slightly higher current per submodule.

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