Resonant DC converter

Abstract

This disclosure describes a Modular Multilevel Resonant Direct Current, DC, converter. The Modular Multilevel Resonant DC converter comprises: two arms connected in series, each arm comprising a plurality of series connected sub-modules, SMs; a transformer Tr, a primary winding of the transformer Tr being connected to the mid- point of the two arms; and a resonant capacitor module, wherein the resonant capacitor module is connected either i) between the mid-point and the primary winding of the transformer, or ii) to the secondary winding of the transformer. The resonant capacitor module comprises: at least one resonant unit, each resonant unit comprising at least one switch and a resonant capacitor.

Description

[0001]SP3051 - 1 - RESONANT DC CONVERTER Field of the Invention This invention relates to electrical power systems. In particular, but non-exclusively, the disclosure herein relates to Resonant Direct Current (DC) converters, such as modular multilevel isolated DC converters (MMI-SRDC). Background of the invention The modular multilevel isolated direct current (DC) converter (MMI-SRDC) was introduced in the paper by S. Shao et al., "A Modular Multilevel Resonant DC–DC Converter," in IEEE Transactions on Power Electronics, vol. 35, no. 8, pp. 7921-7932, Aug. 2020; and can be used to connect medium-voltage and low-voltage buses. The structure of the MMI-SRDC is illustrated in Fig. 1 and comprises a plurality of submodules (SMs) 102, each submodule comprising a capacitor CSMijand associated switches Quij, Qdij. The SMs 102 are grouped in series into arms 104. The MMI-SRDC also comprises a diode rectifier (D1-D4), a transformer Tr, a resonant inductor Lr, and a resonant capacitor Cr. MMR-SDRCs are used in various applications, usually with Medium Voltage Direct Current (MVDC) input voltage (5-100 kV) and high power (0.1-100 MW). For example, some applications include but are not limited to: DC ship power supply systems, DC charging stations for Electric vehicles (EV), and renewable energy collection systems, where they serve as DC transformers and generate the Medium Voltage (MV) or Low Voltage (LV) DC bus within the DC distribution system. The converter also serves to provide controllability on the operating point of the connected load or source. Possible modulation waveforms of a conventional MMI- SRDC employing half-bridge modules (as illustrated in Fig. 1) are shown in Fig. 2. The switching frequency of the Modular Multi-level Converter (MMC), e.g. the structure 5 comprising the four arms 104 as illustrated in Fig. 1, is set to fs, and the duty cycle of the upper switch in each module is denoted by DQu. A phase-shifted angle is set between the driving signals of two adjacent half-bridge modules (e.g., between two submodules lying directly next 10 to one another in the same arm). The duty cycle in adjacent arms (arm_u1 and arm_u2; or arm_d1 and arm_d2) are therefore complementary and the phase shift can thus be observed when inspecting the driving signals of each submodule in an arm. 15 The modulation signals for armu1 and armd2 are the same, which leads the modulation signal armu2 and armd1 by Ts / 2, where Ts=1 / fs is the switching period. Summary of the Invention 20 Despite its numerous benefits, the MMI-SRDC illustrated in Figs 1 and 2 has a significant drawback of low power density. This is due to the large volume of submodule capacitors and the output filter capacitor. Current solutions to reduce the large volume of 25 submodule capacitors and the output filter capacitor involve increasing the switching frequency, fs, of the arms of the MMI-SRDC. By increasing the switching frequency of switches in MMI-SRDC, the frequencies of the input and output ripple currents can be improved and the filter30 capacitance is expected to be reduced. However, for MMI- SRDC, the switches in the modular multilevel converter are hard turned on and off. With the increase in operation frequency, there will therefore be higher switching losses, leading to low operation efficiency. Besides, the increase of switching frequency is limited by the poor high-frequency switching characteristic of high-power semiconductor switches and the manufacture of the isolation transformer. Thus, increasing fs to reduce the volume of capacitors comes with the drawback of increased losses and lower efficiency. It is thus an object of embodiments herein to provide an improved an MMI-SRDC that addresses this issue, amongst others. Thus, in embodiments herein, the resonant Capacitor Cr of the prior art MMI-SDRC arrangement, is replaced by a new resonant capacitor module Cra (which may otherwise be referred to herein as an “alternative resonant capacitor”). The resonant capacitor module Cra may be configured in various different ways, as described in more detail below, but generally comprises two or more resonant capacitors, where each resonant capacitor is controlled by at least one switch to regulate the insertion and bypassing of the respective resonant capacitor, so that the two or more resonant capacitors may individually be inserted into the circuit. For example, they may be inserted into the circuit in sequence, or in different combinations (e.g. in pairs or groups etc). Replacing the single resonant capacitor Crof Fig. 1 with a resonant capacitor module Cracomprising (e.g. two or more) smaller resonant capacitors that can be inserted (and / or bypassed) individually, enables the input and output current ripples to appear at higher frequencies which can be more easily filtered. In embodiments herein, a smaller filter can be employed to achieve a particular ripple level. Or put another way, with the same filter a smaller narrower ripple level can be achieved. This reduces the peak energy storage levels of the individual capacitors, while maintaining the same energy transfer in each time period. (Note that in embodiments herein, the capacitance of the resonant capacitor module Cra can be equal to the original fixed passive capacitance Cr in Fig. 1). If less energy storage is required in the submodules, 5 the submodule capacitance needed in the MMI-SRDC can be reduced. Thus, the proposed MMI-SDRC designs described herein offer comparable performance to the prior art MMI- SRDC, while reducing the overall size and weight of the LV filter capacitor and the capacitors in the MMC. This means 10 that the MMI-SDRC designs herein can be applied to the same range of applications as the conventional MMI-SDRC (as shown in Fig, 1), but can additionally be applied in circumstances where size and weight of the converter are more important and thus the prior art MMI-SDRC might 15 otherwise have been disregarded. Another advantage associated with embodiments herein is that the newly proposed topologies increase the frequency of the harmonics in the current, (e.g. the resonant frequency of the current is increased), without 20 increasing the switching frequency of the submodules. This makes it easier to filter out the ripples or harmonics (in the form of the resonance), without substantially increasing the losses of the MMI-SDRC (or with minimal additional loss). Furthermore, if a filter is added to the 25 input or output of the converter for this purpose, then this filter can be smaller, while still achieving comparable ripple levels to prior art designs. Thus, according to an aspect of the invention, there is a Modular Multilevel Resonant DC converter (MMI-SRDC). 30 The resonant DC converter comprises: two arms connected in series, each arm comprising a plurality of series connected sub-modules, SMs; and a transformer Tr, a primary winding of the transformer Tr being connected to the mid-point of the two arms. The Modular Multilevel resonant DC converter further comprises a resonant capacitor module. The resonant capacitor module is connected either i) between the mid-point and the primary winding of the transformer, or ii) to the secondary 5 winding of the transformer. The resonant capacitor module comprises at least one resonant unit, each resonant unit comprising at least one switch and a resonant capacitor. In some embodiments, the MMI-SRDC may further comprise a resonant inductor Lr. The resonant inductor may 10 also be placed either i) between the mid-point and the primary winding of the transformer, or ii) to the secondary winding of the transformer (e.g. next to / in series with the resonant capacitor module). The resonant capacitor module may have various 15 different topologies. As an example, the one or more resonant units can be half-bridge resonant units. In other examples, there may be a single resonant unit that is full-bridge. In the embodiment where the resonant capacitor module is full-bridge, the resonant20 unit has two parallel-connected sets of four bi- directional switches (mutually connected in anti-series) and one resonant capacitor, connected in parallel to the two sets of anti-series connected switches. In another embodiment, each resonant unit comprises 25 two or more connected switches that are connected together in anti-series and the resonant capacitor is connected in parallel to the two or more anti-series connected switches. Thus, in some embodiments, the resonant capacitor 30 module comprises multiple series-connected half-bridge resonant units, with each half-bridge resonant unit comprising two anti-series-connected switches and a resonant capacitor. Put another way, the four switches are connected two by two in anti-series. In other embodiments, the MMI-SDRC comprises two or more resonant units that are connected together in parallel. In the embodiments where the resonant units are connected in parallel, there are various possible 5 configurations, as follows: In some embodiments, each resonant unit comprises a single switch (e.g. one switch) connected in series to the respective resonant capacitor. Thus, in some examples, there may be a plurality of parallel connected resonant 10 units, each resonant unit comprising a switch and a resonant capacitor connected together in series. In some embodiments, in each resonant unit, there are two or more connected switches that are connected in anti-series and the resonant capacitor is connected in 15 series with the two or more anti-series connected switches. Thus, put another way, the resonant capacitor module may be comprised of multiple parallel-connected resonant units, with each resonant unit comprising two anti-series-connected switches and a series-connected 20 resonant capacitor. As noted briefly above, the resonant DC converter described above may be configured to perform a modulation strategy whereby the on and off states of the two or more connected switches in each resonant capacitor module are 25 controlled, to insert or withdraw the resonant capacitors from the circuit(changing the resonance number) of the respective resonant capacitors in the respective resonant units at a frequency higher than a switching frequency associated with the two arms of the resonant DC converter. 30 In some embodiments, the frequency at which the on- off states of the resonant capacitor modules are turned on and off is twice the switching frequency of the two arms. The resonant capacitors in the resonant capacitor modules may be inserted individually, or two or more at a time (e.g. in groups) into the circuit. This provides further flexibility as to the possible frequencies and amplitudes of the modulation strategies that can be employed. 5 As noted above, this significantly reduces the required submodule capacitance in MMI-SRDC, offering good performance while minimizing the overall size and weight of the LV filter capacitor and the capacitors in the MMC (and thus the converter overall). 10 In some examples, the resonant capacitors are inserted into the circuit in sequence, one after another. E.g. creating several consecutive resonances. In some embodiments, the Modular Multilevel Resonant DC converter comprises two further series-connected arms, 15 the two further arms being connected in parallel to the two arms. In such embodiments, the secondary winding of the transformer is connected to the midpoint between the two further arms. It will be appreciated that other designs comprising further pairs of arms are also 20 possible. Generally, the Modular Multilevel Resonant DC converters described herein may have a resonant frequency greater than the switching frequency associated with the two arms of the resonant DC converter. 25 In a second aspect, there is multi-phase Modular Multilevel Resonant DC converter, comprising two or more Modular Multilevel Resonant DC converters as in the first aspect. In such embodiments, the two or more resonant DC converters are mutually connected in parallel. 30 In some embodiments of the multi-phase Modular Multilevel Resonant DC converter, the frequency at which the on-off states of the resonant capacitor modules are turned on and off is three times the switching frequency associated with the arms of the resonant DC converter. Thus, according to a third aspect, there is a method of operating the Modular Multilevel Resonant DC converter, MMI-SDRC, of the first or second aspects. The method comprises: inserting each arm in the MMI-SDRC into the converter circuit at a first frequency, fs, and inserting each resonant capacitor in the two or more resonant units into the circuit, in sequence, at a second frequency fscr, wherein fscr> fs. As described in more detail below, in some embodiments, fscr = a*fs. Brief Description of the Drawings Fig. 1 illustrates a prior art topology of a conventional single-phase Modular Multilevel Resonant DC converter; Fig. 2 illustrates prior art modulation and operation waveforms of the conventional (prior art) Modular Multilevel Resonant DC converter shown in Fig. 1; Fig. 3 illustrates an example single-phase Modular Multilevel Resonant DC converter according to some embodiments herein; Fig. 4 illustrates example modulation and operation waveforms for the Modular Multilevel Resonant DC converter shown in Fig. 3; Fig. 5a illustrates example drive signals for the arms of the Modular Multilevel Resonant DC converter sub- modules shown in Fig. 3; Fig. 5b illustrates an example modulation of the resonant capacitors in the resonant capacitor module illustrated in Fig. 3; Fig. 6 shows an example topology of an N-phase Modular Multilevel Resonant DC converter and an example topology for a resonant capacitor module suitable therefore; Figs. 7a and b show further example topologies of the resonant capacitor module according to some embodiments; Fig. 8 shows an example modulation strategy for the 5 topologies illustrated in Figs. 7a and 7b; Fig. 9 illustrates a further example topology of a full-bridge resonant capacitor module; Fig. 10 shows a modulation strategy for the topology of Fig. 9; 10 Fig. 11 illustrates simulation results; Fig. 12 shows an Enlarged view of the HBSM capacitor voltages under the maximum transmission power according to the simulation of Fig 11; and Fig. 13 shows an enlarged view of the LV output 15 voltage under the maximum transmission power according to the simulation of Fig 11. These drawings depict one or more implementations in accordance with the present teachings, by way of example only, not by way of limitation. In the figures, like 20 reference numerals refer to the same or similar elements. Detailed Description of the Drawings As noted above, embodiments herein relate to power systems, and particularly to a modified version of the modular multi-level isolated DC converter (MMI-SRDC) 25 illustrated in Fig 1 (as described in the background section). It is noted that an MMI-SRDC may alternatively be called a Modular Multilevel Resonant DC–DC Converter and is generally described in the paper by Shao et al. (2020) cited in the Background section above. 30 Fig. 3 schematically illustrates a topology of a single-phase modular multilevel isolated dc converter 300 according to some embodiments herein. In this embodiment, compared to the prior-art MMI-SDRC Fig. 1 topology, the resonant capacitor, Cr in Fig. 1 is replaced with a resonant capacitor module Cra(otherwise referred to herein as an alternative resonant capacitor), as described below. The resonant capacitor, Cr in Fig. 1 is a fixed passive capacitor, whereas, in embodiments herein, the resonant capacitor module Cra is a variable active capacitor. The MMI-SDRC 300 in the example of Fig. 3 comprises two arms, armu1and armd1, connected in series. Each arm comprises a plurality of series connected submodules (corresponding to submodules SM1N-SM1N in armu1 and submodules SM21-SM2N in armd1). MMI-SDRC 300 comprises two further arms, armu2 and armd2, however the skilled person will appreciate that this is merely an example, and that the further two arms armu2and armd2 could equally be omitted. Equally, in other examples, there may be more than four arms, for example, MMI-SDRC 300 may comprise 6 arms, 8 arms etc. Generally, there are different possible configurations of the submodules SMs 102. For example, the submodules may i) all be half-bridge modules; ii) all be full-bridge modules; or iii) be a hybrid utilisation of half-bridge and full-bridge modules. The skilled person will be familiar with the terms half-bridge and full bridge, but in brief, the term half bridge module refers to the circuit shown as 102 in Fig. 1, which comprises a leg consisting of two series- connected switches and a capacitor. The leg and capacitor are connected in parallel. The midpoint of the leg and the negative pole of the capacitor form the output terminals. A full bridge module comprises two parallel- connected legs and a capacitor. Each leg comprises two series-connected switches. The capacitor and legs are connected in parallel. The midpoints of the two respective legs constitute the output terminals. The internal topology of submodule SMijis also illustrated in Fig. 3. The MMI-SRDC further comprises a transformer Tr. The primary winding of the transformer Tr is connected to the mid-point 106 of the two arms, armu1 and armd1. In the MMI-SDRC illustrated in Fig 3, each arm has an associated inductor Larm1, Larm2, connected in series between the respective arm and the mid-point 106 of the two arms. As noted above, compared to the topology of Fig. 1, the MMI-SRDC comprises resonant capacitor module Cra (e.g. in place of the resonant capacitor Cr). Although placed between the mid-point 106 and the resonant inductor Lr on the primary winding of Transformer Tr in Fig 3, it will be appreciated that this is merely an example, and that the resonant capacitor module Cra can be placed at other locations, for example, the resonant indictor Lrand / or the resonant capacitor module Cramay equally be connected to the secondary winding of the transformer. Furthermore, it will be appreciated that in some designs, the resonant inductor Lr may be omitted. For example, it is possible to design the leakage inductor of the transformer in such a way that the additional inductance provided by Lris not needed. An example structure of the resonant capacitor module Cra is illustrated in box 302 in Fig. 3 and comprises two or more (e.g. potentially multiple) series- connected half-bridge resonant units 304, with each half- bridge resonant unit comprising two anti-series-connected switches (e.g. Q11and Q12) and a resonant capacitor, Cr1. This is merely an example, and there are other resonant capacitor module structures that may equally be used, as described below. Turning back to the full MMI-SRDC 300, the secondary winding of the transformer Tr is further connected to a diode rectifier comprising diodes D1-D4. However, it will be appreciated that this is merely an example, and that 5 the rectifier can also adopt other types of switches such as, for example, IGBT, IGCT, thyristors, or any other type of switch. As described above, the use of the resonant capacitor module allows the size of the respective 10 capacitors to be reduced. The reduction of the submodule capacitance or LV-side capacitance CLV is proportional to the number of resonant units in the resonant capacitor module (for the topologies in Figs. 3 and 7), or proportional to the switching frequency of the resonant 15 capacitor module in Fig. 9. In other words, the reduction is proportional to the number of half-sine waveforms during each half operation period (t0~Ts / 2 in Fig. 4). For example, if there are N half-sine waveforms during t0 and Ts / 2, the submodule and LV-terminal capacitances will be 20 reduced to 1 / N of the original topology (in Fig. 1). Thus, generally, the reduction in capacitance is proportional to the number of resonant units 304. Example Modulation Strategy for the MMI-SRDC 300 The main motivation of controlling the proposed MMI- 25 SRDC with the resonant capacitor module Crais to be able to change the resonant capacitances during each switching period (e.g. in a more granular manner). A possible realization method is to control the on and off-state of switches in resonant units to regulate 30 the insertion and bypassing of resonant capacitors. The main difference between the control of the proposed and conventional MMI-SRDCs is the modulation strategy for the resonant capacitors in the resonant capacitor module. An example modulation strategy for the MMI-SRDC topology 300 described in Fig. 3, is illustrated in Fig. 4. In this example, during the positive / negative half- 5 operation period of MMI-SRDC, the left switch Qi1 (i=1, 2, …, m) of one resonant unit is turned on to insert one resonant capacitor Cri into the circuit, and the resonance between Cri and inductor (including resonant inductor Lr and four arm inductors) starts. When the resonance ceases, 10 this resonant capacitor is cut off by switching off the left switch Qi1. And then another resonant capacitor is inserted to start resonance with resonant inductor Lr and four arm inductors again. This process is conducted again and again, causing repetitive resonance (e.g. a ripple 15 current). Hence, the frequency of the ripple current through submodule capacitors is upward by multiple, leading to a dramatic reduction of the required submodule capacitance, while still meeting the voltage ripple requirement of the MMC capacitor. The frequencies of the 20 input and output ripple currents also increases due to the repetitive resonance, and the input filter inductance and output filter capacitance can be also decreased. Note that as described above, it is also permitted to insert two or more resonant capacitors at the same 25 time, to change the resonant capacitance in the circuit. Generally, there are three different frequencies that can be defined with respect to the examples in Figs 3 and 4: The switching frequency (fs) of the converter, refers 30 to the frequency with which the switches in the submodules 102 are turned ON and OFF. For example, in Fig. 4: if Ts= 1ms, then the fs=1kHz. In embodiments herein, the switching frequency can generally be the same as in the prior art design of Fig. 1. In other words, the capacitors in the submodules may “operate” (e.g., switch) the in the same way. A second frequency is the frequency at which the switches that are in the resonant capacitor modules are switched ON and OFF. This may be denoted fsCr herein. In the example shown in Fig. 4, fscris double the switching frequency of the arm submodules, e.g. fsCr= 2*fs. In Figs. 3 and 4, a resonant capacitor module is illustrated comprising three resonant capacitors. Each of the capacitors are inserted into the circuit in sequence, in the periods T1, T2 and T3 respectively, as illustrated on the irp plot in Fig 4. irpcorresponds to the current that goes into the transformer. The current irp goes through resonant- capacitor 1 only part of the time, because the first resonant capacitor in the resonant capacitor module is not inserted for the full period Ts. The current in capacitor 1 corresponds to the curve in time periods T1and T1’in this example. So during T1 the first resonant capacitor in the resonant capacitor module is charged, and during T1’the first resonant capacitor in the resonant capacitor module is discharged. But in any case, the first resonant capacitor is switched to ON. When the current is zero, that is when the first resonant capacitor is not inserted in the circuit. Thus, it can be seen that the switching frequency of the first resonant capacitor in the resonant capacitor module is twice that of the switching frequency of the submodules in the arms, or that Ts= 2 * TsCrwhich means that: fsCr= 2*fs. It will be appreciated that this is merely an example, and that the ratio of the frequencies fsCr and fs may change depending on the topology used. A third frequency of note is the resonant frequency (fres). When a resonant capacitor from the resonant module is inserted into the circuit (e.g. when associated switch is turned on) this creates a resonant circuit with the resonant inductor. The resonant frequency (e.g. frequency of the resonance between the resonant capacitor and resonant inductor) is given by the value of the resonant capacitor module (Cra) and the resonant inductor (Lr). In embodiments where the resonant capacitor module comprises three resonant capacitors, then this frequency may be a3 times higher than the switching frequency of the submodules: fres = 3*fs. In some embodiments, fres> 3*fs, if a margin (indicated by Tmin Fig 4) is This is in contrast to the topology of Fig. 1 fres is approximately equal to fs (as can be seen from . Thus, noted that in embodiments herein: - fscan be the same as in the prior art solution - however, the proposed changes in topology enable fres > N *fs. Thus, embodiments herein increase the resonant without increasing the switching frequency of the submodules. This means that the RIPPLE that appears in the voltage / current signals appears at higher frequency (which is easier to filter). Generally, for two current / voltage ripples of the same amplitude, the one with higher frequency demands smaller filter capacitance, which is why this is advantageous. Note that, in the topology of Fig. 1, fres can be increased (thereby reducing the size of the passive components in the system (e.g., capacitors in submodules)) by increasing fs. However, this is sub-optimal as increasing fs can lead to a lot of losses and thus low efficiency. Thus, in embodiments herein, the ripple can be filtered efficiently without increasing fs, thereby avoiding potentially large reductions in efficiency of the MMI-SDRC (associated with solutions that increase fs). 5 Turning back to Fig. 4, an example operating principle will now be described, for a single-phase MMI- SRDC with three half-bridge resonant units as illustrated in Fig. 3. In this example there are nine operation modes during the half-operation period, and the waveforms are 10 shown in Fig. 4. In the following description, the reference variables are the same as those in Fig. 3. (1) Mode 1 [t0, t1]: In this mode, SM11~ SM1N and SM41~SM4N keep bypassed, while SM21~SM2N and SM31~SM3N are inserted sequentially. At t1, the arm voltages varm_u1 and 15 varm_d2 remain zero, and varm_d1 and varm_u2 change to NVCSM. During this interval, all resonant capacitors Cr1~Cr3 are bypassed. Since varm_u2−varm_u1 (or varm_d1−varm_d12) is lower than KVLV, the rectifier diodes D1~D4 are blocked and the primary current irp keeps zero. 20 (2) Mode 2 [t1, t2]: At t1, Q11 is turned on and Q12 is turned off with zero current, and the resonant capacitor Cr1 is inserted and begins resonance with the resonant inductor Lr and arm inductors Larm1~Larm4. (3) Mode 3 [t2, t3]: At t2, the resonance among 25 Larm1~Larm4 and Cr1 ceases, and D1 and D4 are cut off. During this mode, irp keeps zero and vCr1 remains unchanged. When turning off Q11 and Q22 at t3, zero- current-switching (ZCS) can be achieved to reduce switching losses. 30 (4) Mode 4 [t3, t4]: With the turn-on of Q12 and Q21 at t3, Cr2 is inserted and starts to resonate with Larm1~Larm4. Since the resonant inductor Lr limits the rising rate of irp, quasi-ZCS turn-on can be achieved for Q12 and Q22. The operation in this mode is similar to Mode 2. (5) Mode 5 [t4, t5]: The operation in this mode is similar to Mode 3. The resonance between Larm1~Larm4 and 5 Cr2 stops at t4, and irp keeps zero during this mode. (6) Mode 6 [t5, t6]: With ZCS turn-on of Q31 and ZCS turn-off of Q32 at t5, the last capacitor Cr3 is inserted and resonates with arm inductors. At t6, irp varies to zero. 10 (7) Mode 7 [t6, t7]: In this mode, the resonance ceases, and irp keeps zero. Hence, Q31 is turned off with ZCS. (8) Mode 8 [t7, t8]: At t7, SM21~ SM2N and SM31~SM3N are bypassed sequentially. In this mode, rectifier diodes are reversely blocked, and irp still keeps zero. 15 (9) Mode 9 [t8, Ts / 2]: During this mode, all MMC arms are bypassed and irp remains zero. In the next half- operation period, Cr1, Cr2, and Cr3 resonate with arm inductors sequentially, similar to the first half- operation period. 20 An example modulation strategy that may be used for the MMI-SRDC (of Fig. 3) includes submodules in the MMC and the series-connected half-bridge resonant units, as depicted in Figs. 5(a) and 5(b), respectively. The MMI- SRDC with three half-bridge resonant units is still taken 25 as an example to introduce the modulation strategy, however it will be appreciated that this is merely an example and that other strategies are possible for other topologies. In this example, for the submodules in the MMC, the 30 duty cycle for the upper switch Qu is set to DQu, and a phase delay is inserted into the carrier waves of two adjacent driving channels. The duty cycle can be obtained through voltage / current closed-loop control or can be directly fixed by the controller. The switching frequency for MMC is denoted as fs(as described above0), and the phase delay is set to φ. In this example, the phase of triangle carrier waves for armu2 and armd1 is shifted by π relative to the waves 5 for armu1 and armd2. To achieve voltage balancing among these MMC submodules, a simple method can be used whereby the generated driving signals are rotated in turn and then given to the MMC submodules. It should be noted that a capacitor voltage-balancing strategy based on regulating 10 the duty cycle is not generally appropriate for MMI-SRDC, since this can change the output ac voltage and lead to operational failure. It is noted that other modulation methods can also be utilized for the modular multilevel converter, such as 15 the nearest-level modulation strategy. Fig. 5 shows an example modulation strategy for the resonant capacitor module resonant units. The duty cycle of the left switches Qi1 (i=1, 2, …, m) in half-bridge resonant units is denoted as Da, which can be calculated 20 as 2(DQu-Da) / m. m is the number of the half-bridge resonant units in the resonant capacitor module circuit. Dt denotes the duty cycle of the rising / decreasing stage, calculated by nφ, where n is the number of submodules in each MMC arm. Furthermore, the frequency of the carrier 25 wave for the resonant capacitor module is twice that of the MMC, and both waves are synchronized in phase. There is a time delay of DaTs / 3 between each two adjacent driving channels for the resonant units. Similarly, to realize voltage balancing among the 30 resonant capacitors, the driving signals are rotated in turn and then given to the switches Qi1, whose reverse signals are given to switches Qi2 (i=1, 2, …, m). An example rotating procedure is given as follows, using m=3 as an example. (1) During the first half-operation period, G1, G2, and G3 are given to GQ11, GQ21, and GQ31, respectively. (2) During the second half-operation period, the sequence changes to G3, G1 and G2. 5 (3) During the third positive half-operation period, the sequence changes to G2, G3 and G1. (4) During the next half-operation period, the sequence changes back to G1, G2 and G3. Turning now to Fig. 6, which shows an example 10 topology of a multi-phase MMI-SRDC according to some embodiments herein. The topology of multi-phase MMI-SRC with resonant capacitor modules Cr1, Cr2and Crnis depicted in Fig. 6, which is comprised of n phases of modular multilevel 15 converters, resonant inductors, resonant capacitor module(s), transformers, rectifiers, an input filter inductor, and two bus capacitors. Put another way, the multi-phase Modular Multilevel Resonant DC converter, comprises two or more Modular 20 Multilevel Resonant DC converters as described above (e.g. with respect to Figs 3 and 4). As can be seen in Fig. 6, in this embodiment of the multi-phase MMI-SDRC, the two or more resonant DC converters are mutually connected in parallel. 25 The structures of the resonant capacitor modules Cr1, Cr2 and Crn can be the same as introduced with respect to Figs 3 and 4, for example, the multi-phase MMI-SDRC may comprise multiple series-connected half-bridge resonant units, with each half-bridge resonant unit comprising two 30 anti-series-connected switches and a resonant capacitor (as illustrated in Fig. 6). In this example, each modular multilevel converter comprises two series-connected legs, and each leg comprises N submodules and an arm inductor. The DC ports of these modular multilevel converters are connected in parallel with two series-connected bus capacitors. The mid-point of the modular multilevel converter is connected to the resonant capacitor module, resonant inductor, and 5 primary winding of the transformer. The other terminals of transformers are connected together to the mid-point of two series-connected bus capacitors. The transformer’s secondary winding is connected to the rectifier’s AC port, and the rectifiers’ DC ports are connected together to 10 form the output terminal. It is also noted that variations on the topology shown in Fig. 6 are equally possible. For example, compared to Fig. 6, the resonant inductor and the resonant capacitor modules, Crn, can be put on the transformer’s 15 secondary side. As another example, other types of switches, such as IGBT, IGCT, or thyristor, could be utilized in the rectifier. In the N-phase MMI-SRC of Fig. 6, all phases can be controlled separately, even with different switching 20 frequencies and resonant frequencies. In each phase of MMI-SRC, a possible modulation strategy is given as follows: (1) The duty cycles of switches in modular multilevel are fixed at 50%, with the switching frequency set to fs. 25 And a small phase delay is inserted into the carrier waves of two adjacent driving channels to reduce the rising / decreasing rate of the medium-frequency ac voltage. (2) Assuming that there are m half-bridge resonant units in each phase of the resonant capacitor module, the duty 30 cycles of Qi1 (i=1, 2, …, m) are set to 1 / m and their switching frequencies are set to 2fs. The driving signal of Qi2(i=1, 2, …, m) is the opposite of Qi1’s driving signal, respectively. Turning now to Figs 7a and 7b, in the preceding examples, the resonant capacitor modules comprised series- connected resonant units. However, other topologies of the resonant units in the resonant capacitor module(s) of Figs 5 3 and 6 are also possible, for example, in some embodiments, the resonant units are parallel-connected. Fig. 7a shows an example resonant capacitor module 700 where the resonant units 702 are parallel connected. In the embodiment in Fig. 7a, each resonant capacitor 10 module comprises a plurality of resonant units 702, each resonant unit comprising two or more connected switches connected in anti-series and a resonant capacitor connected in series to the two or more anti-series connected switches. 15 The topology of an example resonant capacitor module with parallel-connected resonant units is shown in Fig. 7(a). When m = 2 (e.g. when the resonant capacitor module has two resonant capacitors therein), this resonant unit can be simplified to the topology shown in Fig. 7(b). In 20 Fig. 7(b), the resonant capacitor module comprises two resonant units 702’that each comprise a single switch connected in series to a respective resonant capacitor. For 702', the voltage across Cr1 is the reverse to that across Cr2, and this contributes to them both achieving ZCS. 25 This arrangement utilizes fewer switches and helps reduces the cost and power losses. An example modulation strategy for the resonant capacitor modules in Figs 7(a) and 7(b) is shown in Fig. 8. As for the bypassed switch Qb in Fig. 7, its driving 30 signal can be the reverse of all other driving signals, namely, GQb = not(GQ1 or GQ2 or … or GQm). Qb is utilized to provide a conducting path for the transformer’s magnetizing current during the dead zone of Q1~Qm. The rotating method of driving signals can be the same as illustrated in Figs 4 and 5 (described above). Turning now to Fig. 9 which illustrates another example topology of the resonant capacitor module 5 according to some embodiments herein. In this embodiment, the resonant capacitor module comprises a full-bridge resonant unit 902. Resonant unit 902 has two parallel- connected sets of four bi-directional switches (connected in anti-series) and one resonant capacitor, connected in 10 parallel to the two sets of anti-series connected switches. An example modulation strategy for the topology in Fig. 9 is illustrated in Fig. 10. It is noted that the variable m in Fig. 9 does not mean the number of resonant 15 units. In Fig. 9, m refers to the number of resonances in one operation period. (For example, according to the waveforms shown in Fig. 4, three half-sine waveforms exist in the current irpduring half operation period, so the number m is three.) With this modulation strategy, it is 20 possible to use only one full-bridge resonant capacitor module in the MMI-SRDC to achieve the same current irp as shown in Fig. 4, while the switching frequency of switches in the full-bridge resonant capacitor module will be three times fs(instead of 2fsfor half-bridge resonant capacitor 25 module shown in Fig. 4). Experimental Data Based on the parameters given below, the proposed MMI-SRDC shown in Fig. 3 was tested with the PLECS simulation software (see, for example, the PLECS User 30 Manual v. 4.7 entitled: “THE SIMULATION PLATFORM FOR POWER ELECTRONIC SYSTEMS” © 2002–2023 by Plexim GmbH). The simulation results are shown in Figs 11-13. Parameters: MV terminal voltage VM = 35kV LV terminal voltage VL = 0.9~1.1kV Transmission power Pt = 0~10MW Switching frequency of modular multilevel converter fs = 1kHz 5 Transformer ratio K:1 = 39:1 Half-bridge sub-module (HBSM) number in each arm N = 16 HBSM capacitor CSM = 600μF HBRSM capacitor Cr = 20μF Arm inductor Larm = 46μH 10 Resonant inductance Lr = 40μH LV-side magnetic inductance 1mH LV output capacitor CLV = 120mF As shown in Figure 11, VLV_ref is set as 1100V before 15 0.15s, and DQu is regulated to 0.407. The HBSM capacitor voltages keep stable at 2682V, and its enlarged view is shown in Fig. 12. All HBSM capacitor voltages can keep balanced and the voltage ripple vCSMpp is measured as 13.15V. The enlarged view of vLV under the maximum 20 transmission power is shown in Figure 13, and the voltage ripple vLVpp is measured as 10.1V, corresponding to the design. At 0.25s, the reference voltage VLV_ref steps down to 1000V and the transmission power drops to 4.55MW. After 25 a short regulation, DQu varies to 0.448 and vLV stays balanced at 1000V, with HBSM capacitor voltages changing to 2438V. At 0.5s, with VLV_ref decreasing to 925V, the transmission power falls to 1.05MW. After 75ms regulation, 30 vLV keeps stable at 925V and HBSM capacitor voltages keep balanced at 2255V. From the enlarged view in Fig. 11, switches in HBRSMs can realize ZCS turn-off over the whole transmission power, which helps reduce the switching losses. Noticeably, the peak currents in three resonances are nearly the same, due to the rotating modulation strategy. For a conventional resonant MMI-SRDC (without a resonant capacitor module) with the same operating 5 conditions shown in Table. I, its resonant inductor (Larm+Lr), is designed as 774μH. To achieve the same voltage ripples of HBSM capacitors and LV output voltage, HSBM capacitor CSM and LV output filter capacitor CLV should be designed as 1300μF and 165mF, respectively, 10 which are 2.17 and 1.375 times those in the proposed MMDC with the resonant capacitor module. Otherwise, another option is to increase the switching frequency, which will lead to high switching losses for the modular multilevel converter. It is known 15 that the switches in the modular multilevel converter are hard turned on and off, which results in about approximately 0.5% power consumption of rated power in medium-frequency operation. In order to achieve the same submodule capacitance and filter capacitance as in the 20 proposed MMI-SRDC, the switching frequency of conventional MMI-SRDC needs to be increased to three times that of the proposed MMI-SRDC, resulting in triple switching losses and an extra reduction of 1% on operating efficiency. Thus, in summary, the resonant capacitor module 25 structures described herein comprise several resonant capacitors, and the resonance occurs several times during half of a switching period. With the proposed resonant capacitor modules, the frequencies of input and output are increased, leading to the reduction of the demanded input 30 and output filter inductors and capacitors. Furthermore, the submodule capacitors in modular multilevel converter are also reduced. Therefore, compared with the modular multilevel dc converter in Shao et al. (2020), the size and weight of the converter in this disclosure are reduced. There is thus provided an improved Modular Multilevel Isolated dc Converter with resonant capacitor module(s). While many possible variations of the MMI-SDRC 5 converter have been described above, it will be clear to the skilled person that additional variations and modifications can be made without departing from the scope of the invention as claimed in the appended claims. 10

Claims

SP3051 - 26 - C L A I M S 1. A Modular Multilevel Resonant Direct Current, DC, converter, comprising: two arms connected in series, each arm comprising a plurality of series connected sub- 5 modules, SMs; a transformer Tr, a primary winding of the transformer Tr being connected to the mid-point of the two arms; a resonant capacitor module, Cra, wherein the 10 resonant capacitor module is connected either i) between the mid-point and the primary winding of the transformer, or ii) to the secondary winding of the transformer; and wherein the resonant capacitor module 15 comprises: at least one resonant unit, each resonant unit comprising at least one switch and a resonant capacitor. 20 2. The Modular Multilevel Resonant DC converter of claim 1 wherein: the one or more resonant units are half-bridge resonant units or full-bridge resonant units. 25 3. The Modular Multilevel Resonant DC converter of claim 1 or 2 comprising two or more resonant units; and wherein - the two or more resonant units are connected together in series.

304. The Modular Multilevel Resonant DC converter of claim 3, wherein each resonant unit: - comprises two or more connected switches that are mutually connected in anti-series; and 5 wherein the resonant capacitor is connected in parallel to the two or more anti-series connected switches.

5. The Modular Multilevel Resonant DC converter of 10 claim 1 or 2 comprising two or more resonant units; and wherein: - the two or more resonant units are connected together in parallel. 15 6. The Modular Multilevel Resonant DC converter of claim 5 wherein each resonant unit comprises a single switch connected in series to the respective resonant capacitor. 20 7. The Modular Multilevel Resonant DC converter of claim 5 wherein, each resonant unit comprises two or more connected switches that are connected in anti-series; and wherein the resonant capacitor is connected in 25 series to the two or more anti-series connected switches.

8. The Modular Multilevel Resonant DC converter of claim 1 or 2 having a single resonant unit, the 30 resonant unit comprising: - two or more connected switches that are connected in anti-series; andwherein the resonant capacitor is connected in parallel to the two or more anti-series connected switches. 5 9. The Modular Multilevel Resonant DC converter of any one of the preceding claims, configured to perform a modulation strategy whereby the on and off states of the two or more connected switches in each resonant capacitor module are controlled, to change the 10 resonant capacitances or the resonance number of the respective resonant capacitors in the respective resonant units at a frequency higher than a switching frequency associated with the two arms of the Modular Multilevel Resonant DC converter. 15 10. The Modular Multilevel Resonant DC converter of claim 9 wherein the frequency at which the on-off states of the resonant capacitor modules are turned on and off is twice the switching frequency of the 20 two arms of the resonant DC converter.

11. The Modular Multilevel Resonant DC converter of claim 9 or 10 wherein the modulation strategy comprises inserting more than one of the resonant 25 capacitors in the two or more resonant units at a time.

12. The Modular Multilevel Resonant DC converter of any one of the preceding claims wherein a resonant 30 frequency of the Modular Multilevel Resonant DC converter is greater than the switching frequency associated with the two arms of the resonant DC converter.

13. A multi-phase Modular Multilevel Resonant DC converter, comprising two or more Modular Multilevel Resonant DC converters as in any one of claims 1 to 12, wherein the two or more resonant DC converters 5 are mutually connected in parallel.

14. The multi-phase Modular Multilevel Resonant DC converter of claim 13 wherein the frequency at which the on-off states of the resonant capacitor modules 10 are turned on and off is three times the switching frequency of the two arms of the resonant DC converter.

15. A method of operating the Modular Multilevel 15 Resonant DC converter, MMI-SDRC, of any one of the preceding claims, the method comprising: inserting each arm in the MMI-SDRC into the converter circuit at a first frequency, fs; and inserting each resonant capacitor in the two or 20 more resonant units into the circuit, in sequence, at a second frequency fscr, wherein fscr> fs.

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