# Modular multilevel converter based on unipolar-current full-bridge submodules for medium voltage variable speed drive applications

Duro Basic, Hatim Abbi, Martin Geske

## ► To cite this version:

Duro Basic, Hatim Abbi, Martin Geske. Modular multilevel converter based on unipolar-current full-bridge submodules for medium voltage variable speed drive applications. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0037. hal-05075822

HAL Id: hal-05075822

https://utc.hal.science/hal-05075822v1

Submitted on 20 May 2025

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# Modular multilevel converter based on unipolar-current full-bridge submodules for medium voltage variable speed drive applications

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

*GE Power Conversion Vernova SAS, 15 Rue Jean Bart 91300 Massy, France

**GE Energy Power Conversion GmbH, Culemeyerstraße 1, 12277 Berlin, Germany
e-mail: duro basic@geveronva.com, hatim.abbi@gevernova.com, martin.geske@gevernova.com

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

## Keywords

«Multilevel converters», «Modular Multilevel Converters (MMC)», «Variable speed drive»

## Abstract

With the continuous development of Modular Multilevel Converters (MMC), the introduction of new Sub-Modules (SMs) and their operational characteristics has become favourable for optimizing the performance of many applications such as Variable Speed Drives (VSD), where the conventional ac/dc/ac MMC converters based on Half Bridge (HB) face challenges in low-frequency operation. This paper focuses on the main features of the Unipolar Current (UC) Full-Bridge (FB) SM (UC FB-SM) and benefits of its integration into the MMCs for VSD applications. Basic operation methods of the HB and UC FB based MMCs are analysed and compared, and the duality between their operational modes is highlighted. Main advantages of utilization of the UC FB MMCs in VSD applications are identified and illustrated in the simulation results presented.

## Introduction

The so-called double star MMC ac/dc converters, composed from chain links of HB SMs (converter arms), have been originally proposed for the network couplings at very high voltages [1]. Thanks to the modular design, readily available SM redundancy, simple scalability of the MMC converter voltages and powers via serialisation of SMs the HB MMC ac/dc converter topology has been rapidly adopted in the High Voltage Direct Current (HVDC) transmission where dc terminals of the ac/dc and dc/ac MMC converters are interconnected via constant voltage dc link. The constant dc link voltage operation requires only unipolar converter arm voltages which permits utilization of HB (chopper) SMs which are capable of producing only unipolar voltages. As

in HB MMC based converters only single power device is introduced into the converter arm per each SM, these converters are known for low losses and high efficiency which is extremely important in the HVDC transmission.

Due to the capability of the HB MMC ac/dc topology to produce multilevel voltages with low distortion, located at a relatively high effective switching frequency (requires small or no switching ripple filters), and readily implementable redundancy of the SMs, the topology has been considered for application for Medium Voltage (MV) VSDs [2]. However, due to arm power fluctuations at the first and second harmonic frequencies, excessive SM capacitor voltage ripple can be created in operation of HB MMC drives at lower frequencies. Thus, to operate the VSDs at low and medium frequencies, strong limitation of the converter ac currents is required. This constrains practical feasibility of the HB MMC drives to the loads with quadratic torque speed characteristics [2], [3]. To increase the drive torque capability at low frequencies (speeds) auxiliary ac common-mode voltage and differential-mode circulating current injections can be utilised [4]. In this way the SM capacitor voltage ripple can be constrained by the power flows created via controlled harmonic circulating currents injection at the cost of required increased converter current capability. A commercial MV HB MMC drive, based on auxiliary ac voltage/current harmonic injections, capable of starting from zero speed and operating at low frequencies, has been described in [5]. However, due to the high circulating ac harmonic current injection required to operate the drive at nominal torque in the low frequency region and related potentially harmful common mode harmonic voltage injection (bearing damages), alternative MMC topologies and capacitor ripple mitigation approaches have been proposed [6]-[12]. Considering that the dominant SM capacitor voltage ripple (at the first harmonic) is
proportional to a product of dc voltage and ac (motor) current, the focus is on the converter topologies permitting reduction of the dc voltage in proportion to the output frequency. To accomplish this a topology combining the classical HB MMC converter with a series dc bus switch has been proposed in [6] to control (in average) the dc voltage. For smooth dc voltage control, utilization of two MMC converters connected back-to-back which are based on FB SMs have been proposed in [7]. There, the reversible grid side ac/dc converter is capable of regulating dc bus voltage down to virtually zero. It should be noticed that utilization of the FB SMs at the grid side is required as the grid voltages are constant, and SMs must be able to produce bipolar voltage at reduced dc voltage. In the constant load torque applications, this drive effectively works with a constant intermediate dc current. However, at very low speeds and/or at zero frequency, the variable dc voltage and constant dc current operating mode [7] cannot ensure stable SM capacitor voltages and prevent their drifts. To enable permanent zero frequency operation, the intermediate bus voltage and current can be transferred from the dc to a low frequency bus operation [8]. However, with this operational mode the FB MMC converters must be used at the grid and motor sides. To reduce the drive cost, utilisation of 24-pulse rectifier equipped with an auxiliary diode/thyristor network, which enables dc bus voltage changes in discrete steps via series or parallel connections of the diode-bridge rectifiers, has been proposed in [9]. Variable dc voltage operation can be also achieved by using a mix of the FB and HB SMs in the MMC converter arms [9] or by combining the converter upper arms based on the FB SMs and the lower converter arms based on the HB SMs. In both cases, to control the overall dc voltage, the FB SMs produce variable positive or negative dc voltages which add to or subtracts from the constant dc voltages produced by the HB SMs. In non-reversible drives the grid side ac/dc MMC converter can be constructed using lower cost unidirectional half-controlled HB (chopper) SMs [12] (based on only one controllable switch).

Considering that operation of the MMC variable speed drive with a constant dc current has an advantage over the operation with constant dc voltage and that the FB SMs (at least in part) must be used to enable such mode of operation, the MV MMC drive based the half-controlled FB SMs which has been proposed in [13], is a potentially cost-effective option. The half-controlled FB

SMs have only two controllable switches (similarly as in HB SMs) and hence they are lower in cost than the classical FB SMs. Also, as in these SMs there are no two switches connected across the SM capacitors, there are no dead time and shoot through issues. In addition, by a proper selection of the ac and dc current and voltage ratios, the MMC converters equipped by such SMs can be operated with unipolar arm currents which permits full controllability of the SMs output voltages by only two controllable switches [13], [14]. In addition, with the ac/dc voltage/current ratios needed for the unipolar arm current operation, the required energy storage is reduced [14], [15] compared to the classical HB MMC converters. For this reason, this so called the Unipolar Current (UC) FB MMC (UC FB-MMC), is a viable MMC converter topology for constructing MV VSDs.

In this paper several salient features and benefits of utilization of the UC FB-MMC topology in MV VSDs are discussed. Duality between the unipolar arm current UC FB-MMC and classical unipolar arm voltage HB MMC is exposed and discussed. Preliminary simulation results illustrating the operation of the MV VSD based on UC FB-MMC are also presented.

## Stored energy ripple in HB MMC

In general, arm voltages and currents in the Double Star (DS) MMC converters (Fig. 1) are composed of the ac and dc components. For example, for two arms (1 and 2) supplying phase 1, the arm voltage and currents are:

$$ \left\{ \begin{aligned} v_{arm_{1,2}} &= \frac{V_{dc}}{2} \mp v_{m1} \\ i_{arm_{1,2}} &= \frac{I_{dc}}{3} \pm \frac{i_{m1}}{2} \end{aligned} \right. \qquad (1) $$

$$ \left\{ \begin{aligned} v_{m1} &= \hat{V}_m \sin(\omega_m t) \\ i_{m1} &= \hat{I}_m \sin(\omega_m t - \varphi) \end{aligned} \right. \qquad (2) $$

The instantaneous power of the converter arms 1 and 2 are:

$$ \begin{aligned} p_{arm_{1,2}}(t) &= v_{arm_{1,2}} i_{arm_{1,2}} \\ &= \frac{V_{dc}I_{dc}}{6} - \frac{\hat{V}_m \hat{I}_m \cos(\varphi)}{4} \\ &\quad \pm \frac{V_{dc}\hat{I}_m \sin(\omega_m t - \varphi)}{4} \\ &\quad - \frac{\hat{V}_m \hat{I}_m \cos(2\omega_m t - \varphi)}{4} \\ &\quad \mp \frac{\hat{V}_m I_{dc} \sin(\omega_m t)}{3} \end{aligned} \qquad (3) $$
In the HB MMC topology capable of producing only unipolar voltages, the ratio between the ac and dc voltage components must satisfy the following condition:

$$f_v = M_v = \frac{\hat{V}_m}{V_{dc}/2} \le 1 \quad (4)$$

This ratio can be viewed either as the ac modulation depth $M_v$ or as a dc to ac voltage transfer ratio $f_v$.

<figure><img src="image_2.png" /><figcaption>Fig. 1: MMC based on Half-Bridge SM</figcaption></figure>

The arm stored energy oscillates around some average value which is maintained via control of the balance of average power exchange between the dc and dc terminals:

$$I_{dc} V_{dc} = \frac{3}{2} \hat{I}_m \hat{V}_m \cos(\varphi) \quad (5)$$

The ripple in the stored energy can be derived via integration of the arm power ripple:

$$\tilde{w}_{arm_{1,2}} = \int \tilde{p}_{arm_{1,2}}(t)dt \quad (6)$$

The peak-to-peak stored energy variations in the HB MMC arms can be derived from (6), by integrating (6) between two angles of the arm current zero crossings [16].

$$\Delta W_{p-p} = \frac{2}{3} \frac{S_m}{f_v \omega_m} \left(1 - \left(\frac{f_v \cos(\varphi)}{2}\right)^2\right)^{3/2} \quad (7)$$

In (7), $S_m$ is the apparent power of the converter at its ac terminals. Generally, the positive and negative peak values of the arm stored energy ripples are not symmetrical with respect to average value of the stored energy. This offset is dependent on the PF:

$$\Delta W_{offset} = \frac{S_m}{12 \omega_m} \sin(\varphi) \left(1 + \frac{(f_v \cos(\varphi))^2}{2}\right) \quad (8)$$

## Issues in low-frequency operation of VSDs based on HB MMC

From (7), the stored energy ripple is inversely proportional to the machine supply frequency $\omega_m$ (defined by the rotational speed). Thus, as it will be shown in this section, excessive SM capacitor voltage ripple may be produced in VSDs based on HB MMCs when the machine frequency approaches zero.

In VSD applications, the machine current, under assumption of constant machine flux $\Phi$, is proportional to the machine electromagnetic torque:

$$T_{em} \propto \Phi \hat{I}_m \quad (9)$$

Hence, in the constant load torque applications, the machine current is virtually independent of the speed. Also, again under assumption of constant machine flux $\Phi$, the machine phase voltage is proportional to the frequency (speed):

$$\hat{V}_m \propto \Phi \omega_m \quad (10)$$

Consequently, the machine ac voltage and apparent and mechanical power ($\propto T_{em}\omega_m$) are all proportional to $\omega_m$ and, at low speeds, relatively low. Thus, considering that $f_v=M_v \propto \hat{V}_m \propto \omega_m$, the peak-to-peak ripple (7) is inversely proportional to the frequency $\Delta W_{p-p} \propto 1/\omega_m$. The major fluctuating term in the arm instantaneous power, which is dominantly contributing to the ripple (7) at low frequencies, can be identified from (3), if the terms depending on $\hat{V}_m$ are neglected:

$$\tilde{p}_{arm_{1,2}}(t) \approx \pm \frac{V_{dc} \hat{I}_m \sin(\omega_m t - \varphi)}{4} \quad (11)$$

The term (11) is proportional to a product of the dc bus voltage $V_{dc}$ and ac (motor) current. It produces fluctuations in the arms stored energies which can be approximated by (12):

$$\tilde{w}_{arm_{1,2}} \approx \mp \frac{V_{dc} \hat{I}_m}{4 \omega_m} \cos(\omega_m t - \varphi) \quad (12)$$

Obviously, in the constant torque applications, if the dc bus voltage is kept constant, the ripple component (12), which inversely proportional to the machine speed, is rapidly increased as the machine speed is reduced. This is the fundamental issue in low-speed operation of VSD based on HB MMCs which obviously can be effectively mitigated if the dc bus voltage $V_{dc}$ is changed proportionally to the machine frequency.
## Arm energy variations in UC FB MMCs

The UC FB SM is a reduced version of the FB SM (FBSM). It has smaller number of switching devices (two) compared to the FB SM (four) while retaining the benefits of dc fault blocking and bidirectional dc-link voltage capabilities. To ensure full controllability of the UC FB SM voltages, SM current must be maintained unipolar (or unidirectional). Fig. 2 shows the current paths and output voltages in operation of UC FB SMs when the arm current is maintained in unipolar in the positive direction. The available switching states are (summarized in Table 1) are effectively same is in the FB SMs.

<figure><img src="image_3.png" /><figcaption>Fig. 2: Current paths of UC FB-MMC cell. (a) Positively inserted. (b) negatively inserted. (c)&(d) bypassed</figcaption></figure>

<table><caption>Table 1: UC FB-MMC SM states ($i_{arm}>0$).</caption><thead><tr><th>State</th><th>S2</th><th>S3</th><th>Vsm</th></tr></thead><tbody><tr><td>(a)</td><td>0</td><td>0</td><td>Vc</td></tr><tr><td>(b)</td><td>1</td><td>1</td><td>-Vc</td></tr><tr><td>(c)</td><td>0</td><td>1</td><td>0</td></tr><tr><td>(d)</td><td>1</td><td>0</td><td>0</td></tr></tbody></table>

From (1), to achieve unidirectional or unipolar arm currents, the dc current must be kept at a level defined by (13):

$$I_{dc} \geq \frac{3}{2} \hat{I}_m \qquad (13)$$

The dc bus voltage must be adjusted to satisfy the power balance equation (3):

$$V_{dc} \leq \hat{V}_m \cos \varphi \qquad (14)$$

The stored energy ripple in this operational mode can be derived in a similar manner as in case with the HB MMC while considering new constraints. For further analysis it is convenient to introduce

the ac to dc current conversion factor $f_i$ (based on (13)) [17]:

$$f_i = \frac{3}{2} \frac{\hat{I}_m}{I_{dc}} \geq 1 \qquad (15)$$

Unlike the conventional HB MMC, the arm instantaneous power of the UC FB MMC changes its sign correspondingly to the arm voltage. Thus, the arm peak-to-peak energy fluctuation is calculated between the angles which correspond to instants when the arm voltage changes its sign:

$$v_{arm1} = 0, \quad \sin(\theta) = \frac{1}{M_v} = \frac{1}{f_v} \qquad (16)$$

The energy variation of an arm is equal to:

$$\Delta W_{UC_{p-p}} = \frac{2}{3} \frac{S_m}{f_i \omega_m} \left( 1 - \left( \frac{f_i \cos(\varphi)}{2} \right)^2 \right)^{3/2} \qquad (17)$$

An offset in the arm peak-to-peak energy variation also exists and for UC FB-MMC it is equal to:

$$\Delta W_{UC_{offset}} = -\frac{S_m}{12 \omega_m} \sin(\varphi) \left( 1 + \frac{(f_i \cos(\varphi))^2}{2} \right) \qquad (18)$$

By inspection of the expressions (17) - (18) and (7) - (8) a full duality between two operational modes [17] of SMs, with unipolar voltage in HB MMC and unipolar current in UC FB MMC topologies, can be observed if the voltage conversion factor $f_v$ is swapped by the current conversion factor $f_i$.

In VSD applications the operational mode used in UC FB MMC has some important advantages. At low speeds, the dominant ripple component can be expressed by (19), when variable dc bus voltage defined by (14) is introduced into (12):

$$\tilde{w}_{arm_i} = \mp \frac{1}{6} \frac{P_m}{\omega_m} \cos(\omega_m t - \varphi) \qquad (19)$$

As the ratio $P_m/\omega_m$ is constant in the constant torque application, the dominant ripple component (19) remains virtually constant at any machine frequency.

In summary, if the MMC converter is equipped with the UC FB SMs and thus operated with the constant dc current (proportional to ac current peak value), the dc bus $V_{dc}$ voltage must be adapted to satisfy the average power balance between the dc and ac terminals. In the constant load torque applications this operational mode naturally varies the dc bus voltage proportionally to the machine speed. This feature is essential in
the VSD applications at medium and low frequencies as then peak-to-peak ripple in the stored energy is essentially maintained at a constant level at any machine speed. In this way, from the stored energy ripple point of view, the machine can be driven by a UC FB MMC converter in a broad range of speeds, down to very low speeds, in the natural operating mode for this type of the converters.

## UC FB MMC arm current shaping by the second harmonic circulating current injection

The UC FB MMC converter can be operated in so called discontinuous current conduction mode, which is permitting the following operation point of the UC FB MMC [17]:

$$I_{dc} \approx \hat{I}_m \qquad f_i \approx \frac{3}{2} \qquad (20)$$

Reduction of the $I_{dc}$ compared to a level defined by (13) and consequent increase of the current transfer factor $f_i$ to 3/2 is beneficial as the peak-to-peak ripple in the stored energy can be significantly reduced by the factor $f_i$ increase. From (7) and (17), ratio of the energy peak-to-peak ripples in the unipolar current and unipolar voltage operational modes can be found (shown Fig. 3 for different PF assuming values for $f_i=1.1$ and $f_i=1.5$):

$$\frac{\Delta W_{UC FB MMC p-p}}{\Delta W_{HB MMC p-p}} = \frac{f_v}{f_i} \left( \frac{1 - \left( \frac{f_i \cos(\varphi)}{2} \right)^2}{1 - \left( \frac{f_v \cos(\varphi)}{2} \right)^2} \right)^{3/2} \quad (21)$$

<figure><img src="image_4.png" /><figcaption>Fig. 3: Ratio of $\Delta W_{UC FB MMC p-p}$ to $\Delta W_{HB MMC p-p}$ in percentage as a function of power factor</figcaption></figure>

At higher power factors, for the same peak-to-peak ripple, the required stored energy in the UC FB-MMC can be as low as 50% of that required in the classical HB-MMC. This means that, due to duality and when $f_i>f_v$, the UC FB MMC allows for lower capacitance value and reduced capacitor size compared to HB-MMC. This is a major factor benefit since the SM capacitor volume has great impact on the size and cost of the whole converter.

The UC FB MMC converter can be operated in the continuous current conduction mode with the $f_i$ factor close to 3/2 (achievable in the discontinuous conduction mode (20)). To achieve this, a circulating current injection at the 2nd harmonic can be added to asymmetrically shape the arm currents to reduce their minimum peaks [14]. For example, if the 2nd harmonic circulating currents with magnitude $I_{2h}$:

$$I_{2h} = \frac{2}{3} \frac{1}{\pi} \hat{I}_m \qquad (22)$$

is injected into the UC FB MMC arms, the unipolar current operation can be achieved with the dc current only marginally higher than the ac current peak [14]:

$$I_{dc} = \sqrt{\frac{9}{8}} \hat{I}_m \approx 1.06 \hat{I}_m \qquad (23)$$

This effect of the second harmonic circulating current injection is illustrated in Fig. 4.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Arm current in UC FB-MMC with the second harmonic current injection</figcaption></figure>

In summary, the second harmonic injection allows to simultaneously reduce the semiconductor current peaks and required energy storage requirements in UC FB MMCs, comparable to these achievable in the discontinuous conduction mode. At the same time, the converter is operated in the continuously conducting mode, like that in the classical HB MMCs.
UC FB MMC VSD

Considering that the UC FB MMC topology has
reduced stored energy storage requirements and
that the peak-to-peak energy ripple remains
nearly constant at different operational
frequencies, it is well suited for the VSD
applications. An example of a fully reversible
VSD topology based on the back-to-back
connection of two DS UC FB MMC converters is
shown in Fig. 5.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Back-to-back UC FB MMC topology for variable speed drives</figcaption></figure>

The grid side converter can be replaced with any
other converter capable of regulating the required
constant dc current, like thyristor rectifier, diode
or rectifier + chopper. This type of the drive is
analogous to the classical ‘current source’ drive.
The classical HB MMC back-to-back converter

topology, which operates with constant dc bus
voltage, resembles the classical ‘voltage source’
converters.

Simulation results

A simplified control block diagram of the ac/dc/ac drive converter system based on UC FB MMC used in the simulations is shown in Fig.6. The intermediate dc current level is not kept fixed, it is dynamically adjusted according to magnitude of the ac currents on both ends. In this way an optimal margin in the dc current and unidirectional arm currents can be secured with minimised converter losses at partial loads. The dc link voltage is adjusted by the grid side stored energy control to meet the power demand of the machine side converter.

The fundamental difference in operations the HB
MMC and UC FB MMC based VSD is illustrated
by the simulation results shown in Fig.7 (a) and
Fig.7 (b). The simulated system parameters are
summarized in Table 2.

The UC FB SM have lower capacitance (only 60% of the HB SM capacitance), Also, the UC FB MMC has only 8 SMs while the HB MMC has 9 SMs (in total the UC FB MMC VSD has reduced energy storage for about 47%).

<figure><img src="image_7.png" /><figcaption>Fig.6: Principal block diagram of the drive control.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig.7: Simulation results illustrating voltage and current waveforms in the: (a) HB MMC VSD and (b) UC FB MMC VSD during the frequency ramping down from 50Hz to 0Hz.</figcaption></figure>

In the simulations it is assumed that the nominal power of the machine is about 36MW (at nominal frequency of 50Hz) and that the machine is controlled to produce constant torque at all frequencies (speeds).

<table><caption>Table 2: Simulated system parameters.</caption><thead><tr><th>Variable</th><th>Unit</th><th>HB SM</th><th>UC FB SM</th></tr></thead><tbody><tr><td>Vm line-line</td><td>kV rms</td><td>14.5</td><td>16</td></tr><tr><td>Sm</td><td>MVA</td><td>42.5</td><td>42.5</td></tr><tr><td>PF</td><td>-</td><td>0.847</td><td>0.847</td></tr><tr><td>Im</td><td>kA rms</td><td>1.7</td><td>1.54</td></tr><tr><td>Pm</td><td>MW</td><td>36</td><td>36</td></tr><tr><td>Idc</td><td>kA</td><td>1.6</td><td>2.4</td></tr><tr><td>Vdc</td><td>kV</td><td>22.5</td><td>15</td></tr><tr><td>C sub-module</td><td>mF</td><td>15</td><td>9</td></tr><tr><td>Vc sub-module</td><td>kV</td><td>2.5</td><td>2.5</td></tr><tr><td>N sub-modules</td><td>-</td><td>9</td><td>8</td></tr></tbody></table>

The simulation result in Fig.7 (a) shows characteristic voltage and current waveforms of the HB MMC VSD. It can be seen in Fig.7 (a) that the arm capacitor voltages are rapidly increased when the frequency is reduced. The main driving source of this ripple is linked to the constant dc bus voltage operation with $V_{dc}=22.5kV$. The SM capacitor capacitance of 15mF have been adopted to keep the capacitor voltage ripple at acceptable level at medium frequencies. With this SM capacitance, at about 25Hz, the arm capacitor voltage ripple reaches critically high values (500V or 20% peak-peak). Below this frequency the machine torque/current must be reduced and/or employed some auxiliary method for the capacitor voltage ripple mitigation.

In case of the VSD based on the UC FB SM (Fig.7 (b)), the dc current is maintained constant at about 2.4kA while the dc bus voltage is changed proportionally to the power transmitted through
the dc bus. Thanks to the natural variable dc bus voltage operation mode, the arm capacitor voltage ripple remains basically constant in a broad frequency range spanning from 50Hz down to 2.5Hz (5% of the nominal frequency). Its value can be estimated from the energy ripple as will be shown in the further text.

The UC FB SM system parameters listed in Table 2 are selected according to simplified calculations presented in this section. The starting point was the maximum current of the switching device of 2400A. In the UC FB topology this defines maximum value of the dc current $I_{dc}=2400A$. The required dc voltage is defined by the maximum power which needs to be transferred through the dc link by this dc current value:

$$V_{dc} = \frac{P_{dc}}{I_{dc}} = \frac{36 \times 10^{6}}{2400} = 15kV \quad (24)$$

Considering that the ac current peak should be slightly lower than the dc current peak (selected reduction factor is 1.1, slightly higher than the minimum value in (23)) the maximum ac current peak is:

$$\hat{I}_m = \frac{I_{dc}}{1.1} = \frac{2400}{1.1} = 2180A \quad (25)$$

or its rms value:

$$I_{m \text{ rms}} = \frac{\hat{I}_m}{\sqrt{2}} = \frac{2180}{\sqrt{2}} = 1540A \quad (26)$$

With the known ac current value and requested apparent power, it is possible to calculate the line-to-line ac voltage level:

$$\begin{aligned} V_{m \text{ line-line rms}} &= \frac{S_m}{\sqrt{3} I_{m \text{ rms}}} \\ &= \frac{42.5 \times 10^6}{\sqrt{3} \times 1540} = 16kV \end{aligned} \quad (27)$$

and the phase voltage peak value:

$$\hat{V}_m = \sqrt{2} \frac{V_{m \text{ line-line rms}}}{\sqrt{3}} = 13kV \quad (28)$$

If the SM capacitor voltage is $V_c=2.5kV$ and if the 3rd harmonic injection is used to reduce the ac voltage peak by a factor of 1.155, The estimated minimum number of modules is equal to the ceiling of the arm peak voltage divided by the cell capacitor voltage, as follows:

$$\begin{aligned} N &\ge \text{ceil}\left(\frac{V_{dc}}{2} + \hat{V}_m\right) \\ &= \text{ceil}\left(\frac{\frac{15}{2} + 13 \times \frac{\sqrt{3}}{2}}{2.5}\right) = 8 \end{aligned} \quad (29)$$

The adopted number of SMs is (N=8).

To proceed with the stored energy ripple calculations, firstly the current conversion factor $f_i$ is calculated:

$$f_i = \frac{31500\sqrt{2}}{22400} = 1.325 \quad (30)$$

The stored energy ripple in the arms is then found from (17):

$$\begin{aligned} \Delta W_{UC_{p-p}} &= \frac{2}{3} \frac{42.5 \times 10^6}{1.325 \times 2\pi 50} \times \\ &\quad \left(1 - \left(\frac{1.325 \times 0.845}{2}\right)^2\right)^{3/2} = 38.6kJ \end{aligned} \quad (31)$$

The energy peak to peak ripple can be further approximately linked to the per unit capacitor voltage ripple:

$$\delta V_{p-p} \approx \frac{\Delta W_{UC_{p-p}}}{N C V_c^2} \quad (32)$$

If it is assumed that the peak-to-peak voltage ripple is to be limited to $\delta V_{p-p} < 0.1$ p.u., the lowest SM capacitor value is:

$$C \ge \frac{38.6 \times 10^3}{8 \times 0.1 \times 2500^2} = 7.7mF \quad (33)$$

In the simulated case, the SM capacitance of 9mF has been adopted. With this SM capacitance, the capacitor peak to peak voltage ripple is reduced to about 8.5% or 214V:

$$\begin{aligned} \Delta V_{p-p} &\approx \frac{\Delta W_{UC_{p-p}}}{N C V_c} = \\ &= \frac{38.6 \times 10^3}{8 \times 9 \times 10^{-3} \times 2500} = 214 V \end{aligned} \quad (34)$$

The capacitor voltage ripple remains essentially constant at any machine speed with the constant load torque. This theoretical result is in full agreement with simulation results shown in Fig.7 b.
## Future Work

In this paper the MV VSD MMC topology is introduced and, due to length limitations, it was not possible to discuss in details some aspects which are important for the practical implementation of the system. For example, at extremely low frequencies (at and around zero, in the simulated case below 2.5Hz) the classical balancing control of the arm capacitor voltages may not be reliable. At around zero frequency these balancing mechanisms based on the fundamental frequency and dc circulating current control are not effective due diminishing arm voltages and increased effect of the resistive voltage drops (which are not reduced proportionally with the frequency). The operational frequency range of the VSDs based on UC FB MMCs can be still extended down to zero frequency with a much lower effort (compared to that required with HB MMC drives) using the harmonic voltage and relatively small current injections.

In addition, as the proposed converter topology is based on FB SMs, the semiconductor losses are somewhat increased compared to that in HB MMC topology. Further work is required to make a fair comparison between the semiconductor stresses and losses in both topologies considering the most critical operational points (including the harmonic current injection).

## Conclusions

The VSDs based on the classical HB MMCs operated with constant dc bus voltage have limited torque capability at low speeds due to excessive peak-to-peak voltage ripple in the SM capacitive energy storages. The major source of this excessive ripple at low frequencies is the term in the arm power oscillations proportional to the dc bus voltage and machine current.

To address this problem, utilisation of UC FB MMC has been proposed for MV VSDs. The first major advantage of the UC FB MMC is that it requires approximately ½ of the energy storage required by the classical HB MMCs. The second major advantage is that the UC FB MMC converter, by its principle of operation, works naturally with constant dc current and variable dc bus voltage which is proportional to the machine

power (i.e. frequency in the constant torque applications). Due to this frequency dependant variable dc bus operation, the stored energy ripple remains essentially constant at any frequency. These two major advantages of the UC FB MMC when used in VSD applications have been illustrated by the simulation results presented.

The UC FB MMC permits operation at zero frequency due to ability of its FB SM to generate voltages with both polarities. However, special control mode is required to prevent drifts of the arm capacitor voltages at extremely low frequencies (including zero). This type of operation will be discussed in a future paper.

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