WO2018059672A1

WO2018059672A1 - Power unbalance compensation in ac/ac mmc

Info

Publication number: WO2018059672A1
Application number: PCT/EP2016/073069
Authority: WO
Inventors: Michail VASILADIOTIS; Manfred Winkelnkemper
Original assignee: Abb Schweiz Ag
Priority date: 2016-09-28
Filing date: 2016-09-28
Publication date: 2018-04-05
Also published as: SE544016C2; SE1950287A1

Abstract

The present disclosure relates to a method of power unbalance compensation in a direct AC-to-AC Modular Multilevel Converter (MMC) (1) having a three- phase side connected to a three-phase AC network L having a first fundamental frequency, and having a single-phase side connected to a single-phase AC network R having a second fundamental frequency. The MMC has a double-star topology with a plurality of phase-legs (11), each phase having a first branch (12a) and a second branch (12b), each of the first and second branches comprising a plurality of series connected bipolar cells (13). The single-phase AC network contains voltage and/or current harmonic components of a frequency substantially the same as the first fundamental frequency. The method comprises circulating a current within the MMC, the circulating current having a frequency at least equal to the first fundamental frequency or higher.

Description

POWER UNBALANCE COMPENSATION IN AC/AC MMC

TECHNICAL FIELD

The present disclosure relates to compensation of active power unbalances in direct three-to-single-phase alternating current (AC) to AC Modular

Multilevel Converter (MMC).

BACKGROUND

An MMC is a power converter comprising series-connected cells (also known as modules or submodules), forming what is called a converter branch (also known as arm). These branches can be configured in several manners leading to dedicated converter topologies. According to whether this branch needs to provide only positive or also negative voltages, the cell can be implemented by means of a half-bridge or a full-bridge (also called bipolar or H-bridge) cell, respectively. A three-to-single-phase direct AC/AC MMC structure in double-star configuration may be used for interconnection of a three-phase utility grid, e.g., 50 Hz, with e.g. a single-phase railway supply, e.g., at 50/3 (synchronous) or 16.7 Hz (asynchronous).

SUMMARY

The present invention relates to the stability problem when direct AC/AC three-to-single-phase Modular Multilevel Converters (MMC), e.g. for railway applications, operate at equal or near equal input-output frequencies. In such a case, direct current (DC) power components or low frequency AC power components appear in the converter branches making it thus impossible to operate the converter without internal active power transfer between branches. In 50HZ/16.7HZ railway interties, third-order current harmonics appear in the single phase railway network as a result of old thyristor-based

locomotives. The 3rd harmonic on rail side coincides spectrally with the three-phase side voltage and causes active power in the MMC branches. In an MMC with balanced input-output power, the total energy inside the MMC is neither increased nor decreased at the end of the fundamental period. At the same time, same frequencies at input and output networks lead to unbalanced energies among branches. These are compensated by internal power transfer.

It is an objective of the present invention to compensate active power unbalances in direct three-to-single-phase AC/AC MMC by means of a circulating current of fundamental frequency (also called application frequency). For instance, in the case of 50 Hz three-phase to 16.7 Hz single- phase MMC, a 50 Hz circulating current is added for active power transfer between the branches of the MMC. By this, the energies of upper and lower branches of the same phase are changed in opposite direction.

According to an aspect of the present invention, there is provided a method of power unbalance compensation in a direct AC-to-AC MMC having a three- phase side connected to a three-phase AC network having a first fundamental frequency, and having a single-phase side connected to a single-phase AC network having a second fundamental frequency. The MMC has a double-star topology with a plurality of phase-legs, each phase-leg having a first branch and a second branch, each of the first and second branches comprising a plurality of series connected bipolar cells. The single-phase AC network contains voltage and/or current harmonic components of a frequency substantially the same as the first fundamental frequency. The method comprises circulating a current within the MMC, the circulating current having a frequency at least equal to the first fundamental frequency. According to another aspect of the present invention, there is provided a computer program product comprising computer-executable components for causing a controller of an MMC to perform an embodiment of a method of the present disclosure when the computer-executable components are run on processing circuitry comprised in the controller. According to another aspect of the present invention, there is provided a direct AC-to-AC MMC having a three-phase side configured to be connected to a three-phase AC network having a first fundamental frequency, and having a single-phase side configured to be connected to a single-phase AC network having a second fundamental frequency. The MMC has a double-star topology with a plurality of phase-legs, each phase-leg having a first branch and a second branch, each of the first and second branches comprising a plurality of series connected bipolar cells. The MMC further comprises a controller comprising processing circuitry, and storage storing instructions executable by said processor circuitry whereby said controller is operative to circulate a current within the MMC, the circulating current having a frequency at least equal to the first fundamental frequency when the single- phase AC network contains voltage and/or current harmonic components of a frequency substantially the same as the first fundamental frequency. It is to be noted that any feature of any of the aspects may be applied to any other aspect, wherever appropriate. Likewise, any advantage of any of the aspects may apply to any of the other aspects. Other objectives, features and advantages of the enclosed embodiments will be apparent from the following detailed disclosure, from the attached dependent claims as well as from the drawings.

Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/an/the element, apparatus, component, means, step, etc." are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated. The use of "first", "second" etc. for different features/components of the present disclosure are only intended to distinguish the features/components from other similar features/components and not to impart any order or hierarchy to the features/components. BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will be described, by way of example, with reference to the accompanying drawings, in which:

Fig l is a schematic circuit diagram of an embodiment of a three-phase-to- single-phase AC/ AC MMC in accordance with the present invention.

Fig 2 is a schematic circuit diagram of an embodiment of a bipolar cell of an MMC, in accordance with the present invention.

Fig 3 is a schematic block diagram of an embodiment of feed-forward power unbalance compensation, in accordance with the present invention. DETAILED DESCRIPTION

Embodiments will now be described more fully hereinafter with reference to the accompanying drawings, in which certain embodiments are shown.

However, other embodiments in many different forms are possible within the scope of the present disclosure. Rather, the following embodiments are provided by way of example so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Like numbers refer to like elements throughout the description.

Figure 1 is a schematic illustration of an MMC 1 in direct double-star configuration between a first AC network L, which is a three-phase network having currents iLi, 1L2 and 1L3, and the, and a second AC network R, which is a single-phase network having the current iR and the voltage uR. The first AC network may e.g. be a national power distribution network which may have a nominal utility frequency (power line/mains frequency) of for instance 50 or 60 Hz, herein called the first fundamental frequency. The second AC network R may e.g. be for a railway electrification system, and may have a nominal frequency of for instance 25 Hz, 50/3 Hz (synchronous) or 16.70 Hz (asynchronous), herein called the second fundamental frequency. The term "nominal" is herein used since the real frequency during operation may fluctuate or otherwise deviate slightly from the nominal frequency. The MMC l comprises a plurality of phase-legs n, here three (one per phase of the first AC network L), where each phase-leg n comprises a first (upper) branch (sometimes called arm) 12a and a second (lower) branch 12b. Each branch 12 comprises a plurality of series connected converter cells 13. In the figure, the currents and voltages relating to the first branches 12a are indexed "a" while the currents and voltages relating to the second branches 12b are indexed "b". Typically, each branch 12 comprises the same number of cells 13.

The MMC 1 also comprises a controller 14 which is schematically shown in figure 1. The controller may be a control system comprising a central unit and/or distributed units associated with respective phase-legs 11 or branches 12. The controller 14 may be configured, e.g. by means of computer

programming, to perform embodiments of the method of the present disclosure. Typically, the controller 14 comprises processing circuitry, enabling the controller to perform an embodiment of the method of the present disclosure. The processing circuitry may comprise one or more processing units, e.g. a Central Processing Unit (CPU) in the form of microprocessor(s) executing appropriate software stored in associated memory for procuring required functionality. However, other suitable devices with computing capabilities could be comprised in the processing circuitry, e.g. an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a complex programmable logic device (CPLD), etc., in order control the MMC 1 in accordance with embodiments of the method according of the present invention, while executing appropriate software stored in a suitable storage area, such as a RAM, a Flash memory or a hard disk in the controller 14.

Figure 2 illustrates an example of a bipolar cell 13. The cell comprises an energy storing device 5, here in the form of a capacitor. The energy storing device 5 may comprise a capacitor arrangement with any number of capacitors in series and/or parallel connection with each other. The cell 13 also comprises four semiconductor switches S, forming the full-bridge (H- bridge) topology in the cell. Any number of semiconductor switches may be used as long as the cell is still bipolar, and the cell with four switches shown in the figure is only an example. The semiconductor switches of the bipolar cell are conventionally named in the figure as Si switch, S2 switch, S3 switch and S4 switch. When the switches Si and S4 are closed and S2 and S3 are open, the cell is in a +1 state in which a positive voltage will be applied. By opening Si and S4 switches and closing S2 and S3 switches, this voltage is reversed whereby the cell is in a -1 state and a negative voltage will be applied. Each of the S switches may comprise e.g. an insulated-gate bipolar transistor (IGBT) or a gate commutated thyristor GCT (in which case a snubber circuit may also be needed), for instance an integrated gate commutated thyristor (IGCT), a reverse-conducting IGCT (RC-IGCT) or a bi- mode GCT (BGCT), possibly in combination with an antiparallel one- direction conducting/blocking component such as a diode. In the example of figure 2, each S switch comprises an IGCT and antiparallel diode.

The active power unbalance in the MMC 1 is caused by interactions of voltage and current of the same (or close to/essentially the same) frequency generally described by the following equation: p(t) = u cos(a)t)^■ i cos(a)t + ψ) = COSOP) + cos(2o)t + ψ) (l)

In 50Hz to 16.7Hz railway interties, the 3rd harmonic current has the same (or almost the same) frequency as the fundamental frequency of the three- phase grid L. A branchi2 is then charged/discharged by active power or features a low frequency power oscillation because of the interaction between the three-phase voltage component and the 3rd harmonic of the single-phase current.

The undesirable DC or low frequency power is compensated by three-phase fundamental currents (here: 50 Hz). Preferably, these currents are controlled to be circulating only internally and not appearing at the MMC terminals. However, in special cases, these currents can also add up to non-zero terminal currents. The amplitudes of the currents are driven by an outer branch voltage controller (could alternatively be called an energy controller) of the MMC controller 14. The power coming from the original 50 Hz voltage component and the added circulating 50 Hz current preferably cancel the undesirable power completely.

Voltage controller performance may be improved by estimation and measurement, respectively, of the 3rd harmonic current in the single-phase grid R and feed-forward of this current to the voltage controller output.

Further, in some embodiments, an additional voltage may be applied to all branches and having the same frequency as the circulating current. The current is circulated internally only and, by this, shifting active power from one branch to the other. The additional voltage preferably cancel on the single-phase side of the MMC and preferably appears as a common-mode

(CM) voltage on the three-phase side of the MMC, which may be blocked by a transformer.

In the 50 to 16.7 Hz railway MMC case, a strong third-order railway current harmonic is expected to be sourced by the converter 1 as a result of old locomotives in the single-phase network R. The latter can reach up to 30% of the nominal current. Considering a balanced three-phase network L, the branch power equations are therefore given by:

where k=i,2,3 correspond to the different phases, i_{R 3} and <p '³ denote the amplitude and phase of the railway current third-order harmonic, and represents the initial phase-shift between the two network voltages.

Expanding the above equations gives naturally the following individual terms revealing the interaction of the different frequency elements in the branch (br): Ptr = P_br + Vl + P_b ²? + Γ ^Ω + ,Τ^Ω + ³ + Ptr ³ + Ρ ³ + ΡΓ ³ (4)

The last term ρ^Γ^Ω3 is due to the interaction between the three-phase converter voltages with the single-phase third-order harmonic current. Due to the fact that the single-phase frequency is about one third of the three- phase one, this term can become either DC or very low frequency one, depending on whether the two networks L and R operate synchronously (single-phase side at exactly 50/3 Hz) or asynchronously (single-phase side at 16.70 Hz).

By examining the analytical expressions of the branch power, it may be found that they appear with different signs in the upper and lower branches 12a and 12b of the same phase-leg 11. Therefore, they may be compensated for through the injection of proper circulating currents of the three-phase grid frequency (typically 50 Hz).

Assuming an injection of a three-phase circulating current of the first fundamental frequency i ^Lc^ki-rc ¾_rc cos (o;t - ^p^) , fc = 1,2,3 (5) the branch current will now become

By solving the power equation and setting the sum of constant or low- frequency power terms to zero as u_Lt^k _circ + -u_Ll_Ri3 cos ((ω - n₃)t - φ* '³ - ^p^) = 0 (7) the following solution is obtained: ^Lcirc _k = _1>2>3 (8)

It may not be allowed to change the single-phase side output current in terms of amplitude and phase. Therefore, the compensation algorithm may have to ensure that all circulating currents remain within the converter branches 12. This may be done by injecting additional symmetrizing currents associated with the compensating actions.

A conventional controller (such as proportional, proportional-integral etc.) acting on the difference between the energies/voltages of the upper and lower branches of the same converter branch is usually sufficient to stabilize the system without further implementation actions. However, this control loop has to be dimensioned with very low gain, in order not to track reactive power fluctuation reflected on the capacitor voltage ripples. The latter can lead to significant performance deterioration in the presence of high third-order railway current harmonics.

The control performance may, in accordance with embodiments of the present invention, be increased by means of dynamic identification of the third-order harmonic in the single-phase network L current and feed- forwarding of the value of this identified harmonic to the circulating current references. In this way, control speed may be improved and the risks for overvoltage or instabilities related to operating point changes may be avoided. Further system improvement in terms of capacitor voltage and branch current peak values may be reached. The feed-forward concept, performed by the controller 14, is illustrated in figure 3.

"Identification" here means extracting a specific harmonic content of a measured waveform, in this case the third harmonic of the measured railway current. It could be also done by estimation. "Calculation" here means to calculate the required circulating current injection according to equations (5) and (8). t_{R 3} and < ^,3of figure 3 have been explained above. ¾rc ,FF is the feed-forward reference of the required circulating current. ^larc,bai is the required balancing circulating current coming from the MMC 1 inner closed- loop voltage controller. ^Lcirc IS the final resulted circulating current control reference.

Thus, in some embodiments of the present invention, the amplitude of the circulating current is controlled by, for each branch 12, controlling a sum of energies of capacitors 5 of the cells 13 in the branch. Additionally or alternatively, in some embodiments of the present invention, the amplitude of the circulating current is controlled by, for each branch 12, controlling a sum of voltages of capacitors 5 of the cells 13 in the branch. Additionally or alternatively, in some embodiments of the present invention, the amplitude of the circulating current is controlled by, for each phase-leg 11, controlling the difference of the sum of voltages of capacitors 5 of the cells 13 between the second (lower) branch 12b and the first (upper) branch 12a of the phase- leg 11. In some embodiments, the controlling (of the capacitor energies and/or voltages) is done based on a measured or estimated third-order voltage harmonic in the single-phase AC network R.

From simulations it has been observed that the MMC 1 is stable even in the presence of large single-phase side third-order harmonic currents when compensated with a circulating current, whose amplitude is defined by a superposed closed-loop controller. However, big steady state errors and/or low frequency deviations may occur, leading to risk of potential overvoltages. Increasing the balancing control bandwidth is a straightforward task, however, the steady state errors may remain. In addition, the bandwidth increase may be limited by the fact that unwanted current frequencies may also be injected. In a specific example, the maximum branch root mean square (rms) current increase was in the order of 4.3%. In contrast, using feed-forward control seems to give excellent performance, featuring no steady state errors and even reducing the low-frequency oscillation magnitude in the asynchronous case. Moreover, lower maximum branch current increase is observed (3.4% rms in this case). In addition to the circulating current, an additional voltage may be used for handling imbalance among branch 12 voltages. This may be done by spectrally separating the imposed circulating current from the three-phase side L and using additional common-mode (CM) voltage of the same frequency as the circulating current (e.g. 50 Hz) to create the necessary compensating terms. The injected components are described by the following equations:

Ucm = U_cm COs(<y_cmt + (p_cm) (9) ^circ = ¾rc C0s(0⁾ _cmt + <p_circ) (lO)

By solving the power equation and setting the sum of constant or low- frequency power terms to zero, the following solution is obtained assumin fixed pre-calculated amplitude u_cm of the imposed common-mode voltage _tk ₌ ! H_{. COS}

^ClrC 3Z_cm cos((p_cm-(p_circ) (( ) - Ω₃)ί - ^'³ -≥¾=^) , k = 1,2,3 (11)

It follows that both the amplitudes of the common-mode voltage and the circulating currents can be freely selected by the user, as long as it fulfils the power equation. Preferable phase shifts are equal (p_cm = <p_circ for minimum amplitudes.

Thus, in some embodiments of the present invention, an additional voltage is applied to the MMC 1, the additional voltage appearing as a common-mode voltage on the three-phase side of the MMC. In some embodiments, the additional voltage cancels out on the single-phase side of the MMC. Thus, no power is injected into the single-phase network R from the MMC terminals due to the additional CM voltage. Typically, the additional voltage is applied such that it has the same frequency as the circulating current.

The additional common-mode voltage may be used to compensate for unbalances also in a converter 1 where the single-phase network R has a fundamental frequency which is close to or the same as the fundamental frequency of the three-phase network L, e.g. 50 Hz, but then the frequency of both the circulating current and current of the additional CM voltage is preferably the same and substantially higher than the fundamental frequency of the three-phase network L, e.g. 200 Hz. For instance, the nominal frequency of the circulating current, as well as any additional (CM) voltage, is an integer multiple of the nominal first fundamental frequency, e.g. two, three, four or five times the nominal first fundamental frequency.

When the CM mode voltage is applied to a 50/50 Hz railway intertie operation, the power equation may be solved and the sum of constant or low- frequency power terms are set to zero as

the following solution is obtained, assuming a fixed pre-calculated amplitude u_cm of the imposed common-mode voltage:

In the simplest case, (p_cm = (p_circ = o is chosen.

Regardless of the respective frequencies of the three-phase network L and the single-phase network R, a certain amount of common-mode voltage may be added without requiring additional voltage margin in the converter 1. A key is an amplitude modulation of the common-mode voltage.

It is noted that the peak branch voltage defines the required minimum DC blocking capability of the MMC 1. It is defined by the sum of the input and output peak voltages.

Adding a common-mode voltage with constant amplitude (= constant envelope) may require additional voltage margin, i.e. additional cells 13 in the MMC phase 11. In three-to-single-phase applications the difference between the single-phase voltage and its peak value can be used for common-mode voltage. The envelope of the common-mode voltage is defined by envelope(t) = u_R — abs[u_R (t)] (14) In case of an existing voltage margin, the envelope can be increased by a DC component matching the margin.

Other possible envelopes are not exactly u_R - abs[u_R(t)] but similar. For example a sinusoidal envelope with 0.75^■ u_R leads to a spectrum with less harmonics. As previously mentioned, the circulating current preferably has the same frequency and zero degrees phase shift compared to any additional common- mode voltage. Of course the phase-shift may alternatively be not zero, but zero results in minimum amplitude.

The circulating current may have constant amplitude. On the other hand, it produces losses also when circulated power is low or even zero. Therefore it may be beneficial to apply the same shape of envelope to the circulating current as the additional CM voltage. As a result, the losses are lower while the circulated power does not decrease too much.

Another option is to apply a sinusoidal envelope to both the additional CM voltage and the circulating current. This leads to a spectrum with lower number of harmonics. The sinusoidal envelope may be designed such that it does not require too much voltage margin. On the other hand it helps reducing the current amplitude.

Also when using an additional CM voltage, feed-forward compensation may be used. The branch voltage controller of the converter controller 14 controls the amplitudes of the circulating currents and the common-mode voltage, respectively. A deviation between the target voltage and the measured (or estimated) voltage creates an output reference value for the circulating currents and common-mode voltages. Typically, the common-mode voltage amplitude may be pre-set to a value defined by the user and the application respectively. For example, the amplitude may be a constant amplitude which is the overall maximum for all possible operation points. Alternatively, it can be the maximum of each individual operating point. Further, it can be an amplitude modulated as described earlier.

With the common-mode voltage amplitude defined, the energy controller may control the circulating current and its amplitude respectively.

Similar to the feed-forward compensation discussed above for the circulating current relating to figure 3, the performance of the voltage controller may be improved by feed forward of the current matching the power imbalance. The power imbalance may be determined in many ways. It may be measured directly or calculated from measured voltages and currents. Or it may be estimated from measured voltages and currents in the combination with reference voltages and currents.

The controller 14 may additionally or alternatively comprise a branch voltage controller for the sum of the cell DC voltages.

The present invention has mainly been discussed in relation to an MMC 1 acting as a railway intertie. Typically, the nominal fundamental frequency of the three-phase side is about 50 Hz, and the nominal fundamental frequency of the single-phase side is 50/3 Hz (synchronous) or 16.70 Hz

(asynchronous), whereby the third-order harmonic on the single-phase side has a frequency equal to or close to the fundamental frequency of the three- phase side. However, embodiments of the present invention may also be used for other cases, e.g. where the first fundamental frequency (of the three-phase side) is essentially an integer multiple (e.g. two, three, four or five) of the second fundamental frequency (of the single-phase side), whereby a harmonic on the single-phase side may have a frequency equal to or close to the fundamental frequency of the three-phase side. As discussed above, embodiments of the present invention may also be beneficial when the nominal fundamental frequency of the single-phase network R is the same, e.g. 50 Hz, as the nominal fundamental frequency of the three-phase network L. However, then the frequency of the circulating current, as well as of any additional CM voltage, should preferably have a substantially higher frequency than the first fundamental frequency. Thus, in some embodiments, the nominal frequency of the circulating current is an integer multiple of the nominal first fundamental frequency, e.g. two, three, four or five times the nominal first fundamental frequency.

The present disclosure has mainly been described above with reference to a few embodiments. However, as is readily appreciated by a person skilled in the art, other embodiments than the ones disclosed above are equally possible within the scope of the present disclosure, as defined by the appended claims.

Claims

CLAIMS l. A method of power unbalance compensation in a direct AC-to-AC Modular Multilevel Converter, MMC, (l) having a three-phase side connected to a three-phase AC network (L) having a first fundamental frequency, and having a single-phase side connected to a single-phase AC network (R) having a second fundamental frequency, wherein the MMC has a double-star topology with a plurality of phase-legs (n), each phase-leg having a first branch (12a) and a second branch (12b), each of the first and second branches (12) comprising a plurality of series connected bipolar cells (13), the single-phase AC network containing current and/or voltage harmonic components of a frequency substantially the same as the first fundamental frequency, wherein the method comprises circulating a current within the MMC, the circulating current having a frequency at least equal to the first fundamental frequency.

2. The method of claim 1, wherein the nominal frequency of the circulating current is the same as the nominal first fundamental frequency.

3. The method of claim 1, wherein the nominal frequency of the circulating current is an integer multiple of the nominal first fundamental frequency, e.g. two, three, four or five times the nominal first fundamental frequency.

4. The method of any preceding claim, wherein the nominal first fundamental frequency is the same as the nominal second fundamental frequency.

5. The method of any claim 1-3, wherein the nominal first fundamental frequency is essentially an integer multiple of the nominal second

fundamental frequency, e.g. two, three, four or five times the nominal first fundamental frequency.

6. The method of any preceding claim, wherein the nominal first fundamental frequency is 50 Hz.

7. The method of any preceding claim, wherein the nominal second fundamental frequency is 50 Hz, 50/3 Hz or 16.70 Hz.

8. The method of any preceding claim, wherein the single-phase AC network (R) is a railway electrification network.

9. The method of any preceding claim, wherein the circulating current has a phase shift equal to zero to the voltage of the three-phase AC network (L).

10. The method of any preceding claim, wherein the circulating current in the respective branches (12) of the MMC (1) add up to zero.

11. The method of any preceding claim, wherein the amplitude of the circulating current is controlled by, for each branch (12), controlling a sum of voltages of capacitors (5) of the cells (13) in the branch.

12. The method of any preceding claim, wherein the amplitude of the circulating current is controlled by, for each phase-leg (11), controlling the difference between the sum of voltages of capacitors (5) of the cells (13) in the second branch (12b) and the sum of voltages of capacitors (5) of the cells (13) in the first branch (12a) of each phase-leg (11).

13. The method of claim 11 or 12, wherein the controlling is done based on a measured or estimated third-order current harmonic in the single-phase AC network (R).

14. The method of any preceding claim, wherein the method further comprises applying an additional voltage to the MMC (1), the additional voltage appearing as a common-mode voltage on the three-phase side of the MMC.

15. The method of claim 14, wherein the additional voltage cancels out on the single-phase side of the MMC.

16. The method of claim 14 or 15, wherein the additional voltage is applied such that it has the same frequency as the circulating current.

17. A computer program product comprising computer-executable components for causing a controller (14) of an MMC (1) to perform the method of any preceding claim when the computer-executable components are run on processing circuitry comprised in the controller.

18. A direct AC-to-AC Modular Multilevel Converter, MMC, (1) having a three-phase side configured to be connected to a three-phase AC network (L) having a first fundamental frequency, and having a single-phase side configured to be connected to a single-phase AC network (R) having a second fundamental frequency, the MMC having a double-star topology with a plurality of phase-legs (11), each phase-leg having a first branch (12a) and a second branch (12b), each of the first and second branches (12) comprising a plurality of series connected bipolar cells (13), the MMC further comprising a controller (14) comprising: processing circuitry; and storage storing instructions executable by said processor circuitry whereby said controller is operative to: circulate a current within the MMC, the circulating current having a frequency at least equal to the first fundamental frequency, when the single- phase AC network contains voltage and/or current harmonic components of a frequency substantially the same as the first fundamental frequency.