An Inner Current Suppressing Method for Modular Multilevel Converters

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 11, NOVEMBER 2013 4873

Letters

An Inner Current Suppressing Method for Modular Multilevel ConvertersZixin Li, Member, IEEE, Ping Wang, Zunfang Chu, Haibin Zhu, Yongjie Luo, and Yaohua Li

AbstractIdeally, the inner (the upper or lower arm) current ofa modular multilevel converter (MMC) is ideally assumed to be thesum of a dc component and an ac component of the fundamentalfrequency. However, as ac current flows through the submodule(SM) capacitors, the capacitor voltages fluctuate with time. Conse-quently, the inner current is usually distorted and the peak/RMSvalue of it is increased compared with the theoretical value. Theincreased currents will increase power losses and may threatenthe safe operation of the power devices and capacitors. This paperproposes a closed-loop method for suppression of the inner currentin an MMC. This method is very simple and is implemented in astationary frame, and no harmonic extraction algorithm is needed.Hence, it can be applied to single-phase or three-phase MMCs.Besides, this method does not influence the balancing of the SMcapacitor voltages. Simulation and experimental results show thatthe proposed method can suppress the peak and RMS values of theinner currents dramatically.

Index TermsHarmonics, inner current, modular multilevelconverter (MMC).

I. INTRODUCTION

IN recent years, a modular multilevel converter (MMC),which is highly suitable for medium- to high-voltage applica-tions, has attracted many researchers interest. Compared withthe conventional multilevel converters, such as the cascaded,the diode-clamped, or the capacitor-clamped topologies [1][5],one of the advantages of an MMC may be its ability of di-rect connection to high-voltage networks without bulky trans-formers. Many academic papers have been published on theMMC [5][20]. These papers mainly focus on modeling, pulsewidth modulation (PWM), voltage balancing, digital control,loss analysis, and so forth.

As to the PWM of the MMC, there exist generally two typesof methods, i.e., the carrier-phase-shifted PWM (CPSPWM)method in [10] and [11] and the submodule (SM)-unified pulse-width-modulated (SUPWM) method in [12][15] (some otherscall it as direct modulation in [18] and [19]). The SUPWM

Manuscript received September 27, 2012; revised December 10, 2012;accepted January 15, 2013. Date of current version May 3, 2013. This workwas supported by the National Natural Science Foundation of China (ProjectNo. 51207151). Recommended for publication by Associate Editor C. C. Mi.

The authors are with the Key Laboratory of Power Electronics and ElectricDrive, Institute of Electrical Engineering, Chinese Academy of Sciences, Bei-jing 100190, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2242204

Fig. 1. One arm of an MMC-based inverter.

method can balance the SM capacitor voltages by sorting and se-lecting the different SMs without closed-loop voltage balancingcontrollers. On the other hand, the CPSPWM method modu-lates each SM separately and dedicated controllers for capacitorvoltage balancing are mandatory. This will not be an easy taskfor the processors when the number of the SM is great. Hence,the SUPWM method is more preferable in practice because ithas lower requirements on hardware.

Ideally, the voltages of the SM capacitors are assumed tobe constant. In fact, the current flowing through the upper andlower arms of the MMC is the sum of dc and ac components [6].Therefore, ac currents flow through the SM capacitors and theirvoltages will fluctuate with time. As shown in Fig. 1, the up-per arm voltage uU , the lower arm voltages uL , and the outputvoltage uan will all have low-order harmonics. The harmonicvoltages will be imposed on the buffer inductors LU and LL andinduce harmonics in the arm currents. On the other hand, the dis-torted arm currents will also influence the SM capacitor voltagesand introduce extra harmonic voltages. Consequently, a series ofharmonics will appear in the inner currents flowing through theupper and lower arms and the RMS value of these currents willbe increased compared with the ideal case. The increased cur-rents will do harm to the design and safe operation of the powerdevices in the converter. Besides, the power losses will be in-creased as well. To solve this problem, Angquist et al. [19], [20]proposed an open-loop method based on estimation of the stored

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energy in the arms. Angquist et al. [19], [20] showed that thismethod can suppress the inner currents in the MMC greatly.Anyway, the disadvantage of it may be its requirements on ac-curate parameters of the converter. Tu et al. [21] presented aclosed-loop method by suppressing the second-order harmoniccurrents in a negative rotating frame. This method is suitablefor the three-phase MMC under balanced conditions. But theanalytical expressions of the arm currents show that they con-tain not only second-order harmonics, but also all even-orderharmonics [22].

This paper presents a closed-loop method for suppression ofthe inner currents in an MMC. This method does not requireaccurate parameters of the MMC and is implemented in thestationary frame, and thus, it is applicable to both single-phaseand three-phase topologies. Verification results show that thismethod can suppress the inner currents substantially comparedwith the conventional SUPWM method, while the balancing ofthe SM capacitor voltages is not affected.

II. MECHANISM OF HARMONICS IN THE INNER CURRENTFig. 1 shows one phase of an MMC-based inverter, in which

Udc is the dc-link voltage; SMU1SMUN and SML1SMLN arethe N SMs in the upper and lower arms, respectively; LU andLL are the two buffer inductors; uU and iU are the voltageand current of the upper arm; uL and iL are the voltage andcurrent of the lower arm; iac is the output current; and uac is theoutput voltage. Supposing that LU = LL = L and neglectingtheir inner resistance, the following equations exist [6]:

uU + uL + L(diU /dt + diL/dt) = Udc (1)iU = icir + iac/2 (2)iL = icir iac/2 (3)

where icir is the current circulating between the arms and the dcvoltage source. Obviously, the circulating current icir will de-liver active power from or to the dc link. Generally, the referencevoltage for this phase can be expressed as

uan ref = (Udc/2)m cos(0t) (4)where m(0m 1) is the modulation index and 0 is the fun-damental angular frequency. With the SUPWM for the MMC,the SM capacitor voltages are all supposed to be constant andthe voltage on the buffer inductors is zero, i.e.,

L(diU /dt + diL/dt) = Ld(iU + iL )/dt = 0. (5)From (1)(5) and according to Kirchhoffs law, one can obtain

uan =Udc2 uU = uL Udc2 . (6)

According to (4) and (6), the reference voltage for the upperand lower arms can be expressed as [6], [12], [13]

uU ref =Udc2 uan ref = Udc2 [1m cos(t)]

uL ref =Udc2

+ uan ref =Udc2

[1 + m cos(t)].(7)

However, the SM capacitor voltages are not constant andeven-order harmonic appears even in the ideal case because accurrent flow through them. So, the sum of uU and uL is in factcomprised of a dc component and a ripple component, i.e.,

{uU = uU + uUuL = uL + uL

(8)

where x denotes the dc component and x denotes the ripplecomponent of x. According to (1)(3), the voltage across thebuffer inductors can be expressed as

L(diU /dt + diL/dt) = 2Ldicir/dt

= Udc (uU + uU + uL + uL ). (9)With the SUPWM, there will always be half (N) of the SM

capacitors connected in between the dc link and the averagevalue of uU + uL or uU + uLL is approximately Udc [12][15].Therefore, (9) can be rewritten as

2Ldicir/dt = Udc Udc uU uL = uU uL . (10)The ideal waveform of the circulating current icir contains

only dc component [12][14], i.e.,icir = Idc (11)

where Idc is a constant and is determined by the phase numberof the MMC and the active power delivering from or to the dclink [12][14]. However, from (10), one can see that the ripplevoltages in uU and uL will introduce harmonic currents to thecirculating current icir through the buffer inductors. Conversely,the harmonics in icir will also flow through the SM capacitors.As a result of the interaction between the buffer inductor andthe SM capacitors, icir will be distorted and all even-order har-monics come in to being, even when the output ac current iac issinusoidal. In the steady state, icir can be expressed as [22]

icir = Idc +

k=2,4,6...

Ik cos(k0t + k ) (12)

where Ik is the peak value of the kth harmonic current and k isan positive even integer.

To prove the aforementioned analyses, computer simulation iscarried out first using MATLAB/Simulink software. The inverterfor simulation is a single-phase half-bridge topology as shownby the solid line in Fig. 1. The simulation results are shown inFigs. 24 using the parameters listed in Table I.

The output voltage reference is set as uac ref = 210 sin(100t)V in this simulation. According to Table I, the dc-link activepower current or the circulating current icir can be calculated as

icir = Pactive/Udc = [Rload U 2ac/[R2lo a d + (Lload)2 ]/Udc= 1.50 A. (13)

Thereby, from (2) and (3), the theoretical expressions for iUand iL are

iU = icir + iac/2 = 1.50 + 4.33 sin(100t 8.19) A (14)iL = icir iac/2 = 1.50 4.33 sin(100t 8.19) A. (15)


Fig. 2. Simulated iU , iL , and icir with the conventional SUPWM method.

Fig. 3. Simulated SM capacitor voltages with the conventional method.

Fig. 4. Simulated uac and 20 iac with the conventional SUPWM method.

TABLE IPARAMETERS OF THE MMC-BASED INVERTER FOR SIMULATION

AND EXPERIMENT

Fig. 5. Mathematical model of the circulating current icir .

Fig. 6. Proposed method for suppressing harmonic currents in icir .

Obviously, the positive and negative peak values of iU /iL are+5.83 and 2.83 A. Meanwhile, as the value of icir is ideally adc constant, the RMS values of iU and iL can be calculated as

iU RMS = iL RMS =

i2cir + (iac/

2/2)2 = 3.41 A. (16)However, it is seen from Fig. 2 that the actual waveform of

iU /iL is clearly distorted and differs from (14) or (15) a lot. Thepositive and negative peak values of iU /iL are around +9.1 and4.2 A, which are much greater than those in the ideal case.Meantime, the calculated RMS value of iU /iL is about 4.0 A,which is also greater than the ideal case. The increased and dis-torted inner currents appear because the SM capacitor voltagesare actually not constant as analyzed previously, which is alsoshown in Fig. 3. From Fig. 2, it is clear that icir contains harmon-ics. And it is just the harmonic components in the circulatingcurrents that make the peak/RMS value of iU /iL greater than itsideal value.

III. PROPOSED INNER CURRENT SUPPRESSION METHODTo suppress the increased and distorted arm currents in the

MMC with SUPWM mentioned previously, a novel closed-loopcontrol method is presented in this section. One can see from(10) that icir is determined by the ripple component of uU anduL . The mathematical model of the circulating current icir canjust be illustrated by Fig. 5.

Based on Fig. 5, a novel closed-loop method for suppressingthe harmonic currents in icir is proposed as displayed in Fig. 6where uU ref and uL ref are calculated by (7).

In Fig. 6, paralleled resonant controllers with the resonantfrequency at 20 , 40 , 60 , . . . are selected as the closed-loopcontrollers. This is because all even-order harmonic componentsexist in the circulating current as shown in (12). The transferfunctions of the resonant controllers are expressed as

Resh(s) =khs

s2 + (h0)2(h = 2, 4, 6, ...) (17)

where kh is the coefficient of the resonant controller.


From (6)(17) and Fig. 6, the transfer function from icir toits reference icir ref can be expressed as (the transfer functionfrom uU real /uL real to uU /uL is considered as 1 because thetime delay in these parts is usually negligible for applicationswith fundamental frequency of 50 Hz/60 Hz)

Hc(s) =icir(s)

icir ref (s)=

2Ls[

h=2,4,6,...kh s

s2 +(h0 )2]

1 + 2Ls[

h=2,4,6,...kh s

s2 +(h0 )2].

(18)In fact, icir can track its reference signal at the frequency of

h0 with zero error because the gain of Resh(j0) in (18) isinfinite at the frequency of h0 . In the proposed method, icir refis set as zero. So, there will be no even-order harmonics in icirin the steady state as with the conventional SUPWM shown in(12). Of course, this conclusion is true only when the system isstable.

One should also note that the dc component exists in icir ,but the reference value for icir is set as zero with the proposedmethod as shown in Fig. 8. However, this inner current suppres-sion controller will not influence the dc component in icir as longas the controller parameters are properly designed. Actually, atzero frequency, the Fourier form of (18) can be expressed as

Hc(j0) = lim0

2Lj[

h=2,4,6,...jkh

2 +(h0 )2 ]

1 + 2Lj[

h=2,4,6,...jkh

2 +(h0 )2 ]= 0.

(19)

Equation (19) means that the inner current suppression con-troller has no influence on the dc component in icir . Of course,this conclusion is only true for steady-state analysis. Anyway,this controller will introduce little impact on the dc componentdynamically, if the bandwidth of the paralleled resonant con-trollers is not wide enough. This will not be a difficult taskbecause the resonant controller can be seen as a bandpass filterwith a very narrow bandwidth.

It should be pointed out that not all even-order harmonic res-onant controllers are needed because the harmonic current de-creases as the order of it increases. The second- and fourth-orderharmonic resonant controllers are usually necessary. Meantime,the parameter design of the parallel operated resonant controllersin this paper is based on the frequency-domain method presentedin [23]. For the MMC-based inverter in this paper, the second-and fourth-order harmonic resonant controllers are adopted. Thecoefficients for the resonant controllers are selected as k2 = 400and k4 = 200, i.e., the transfer function of this controller isexpressed as

Res2(s) + Res4(s) =400s

s2 + (200)2+

200ss2 + (400)2

. (20)

The frequency characteristic of (20) is displayed in Fig. 7.Obviously, this controller has a very narrow bandwidth. Outsidethe region of 100/200 Hz, the gain of it decreases quickly. So,this controller only affects the harmonic currents of icir around100/200 Hz. At the frequency of 0.01 Hz, the gain of it is muchbelow 60 dB, i.e., very trivial influence on the dc componentin icir . As the dc component in icir is responsible for delivering

Fig. 7. Frequency characteristic of the designed controller.

Fig. 8. Simulated iU , iL , and icir with the proposed method.

active power from the dc to the ac side, the proposed controllerwill introduce little effect on the ac-side current/power.

In many applications, closed-loop control of the output cur-rent is often needed. From (2) and (3), it is clear that the outputcurrent iac and the inner circulating current icir can be controlledindependently. However, from Fig. 6, one can see that the innercurrent suppression controller actually adds ripple componentsto the upper and lower arm reference voltages [ideally com-prised of a dc and a sinusoidal component as expressed in (7)].So, this inner current suppression controller may need higherdc voltage, compared with the case without this controller. Be-sides, the parameters of the inner current suppression controllerand the output current controller should be designed with careso that both the two controllers are stable.

IV. SIMULATION RESULTSIn order to test the proposed method for suppressing the inner

current of the MMC, computer simulation is carried out first.The circuit topology of the MMC-based inverter and the param-eters for simulation are the same as the conventional method, aslisted in Table I. Figs. 812 show the simulation results. In thesimulation, the modulation index of this inverter is 0.7 (uac ref= 210sin(100t) V) when t < 0.25 s and the inverter is with no


Fig. 9. Simulated SM capacitor voltages with the proposed method.

Fig. 10. Simulated uac and 20 iac with the proposed method.

Fig. 11. Simulated iU and iL with the proposed method under load changeand modulation index change.

Fig. 12. Simulated uac and 20 iac with the proposed method under loadchange and modulation index change.

Fig. 13. Experimental results of uac (the upper yellow line), iac (the uppergreen line), 2 icir (the middle pink line), iU (the lower purple line), and iL(the lower red line) with the conventional SUPWM method.

load when t < 0.15 s. At the instant of t = 0.15 s, the RL load,as listed in Table I, is connected to the inverter, while at theinstant of t = 0.25 s, the modulation index suddenly changesfrom 0.7(uac ref = 210sin(100t) V) to 0.3(uac ref = 120sin(100t) V).

Figs. 810 show the steady-state results. Comparing Fig. 8with Fig. 2, it is clear that the proposed method in this pa-per can improve the quality of iU and iL . With the proposedmethod, the positive and negative peak values of iU /iL are about+5.9 and2.9 A (ignoring the ripple component caused by the2-kHz switching), which are almost the same as their theoreticalvalues +5.83 and 2.83 A. The RMS value of iU /iL is about3.4 A, which is also almost the same as the theoretical value3.41 A and greatly decreased compared with the conventionalSUPWM method. What is more, the proposed method almosthas no visible influence on the balance of the SM capacitorvoltages, which is clear from Figs. 3 and 9.

Figs. 11 and 12 display the dynamic state results with load andmodulation index step change. When t = 0.15 s, the load changeoccurs, while the modulation index step change happens at t =0.25 s. One can see that this inner current controller is stableunder step change of load and modulation index. When the loador modulation index change occurs, distortion and overshootappear in the waveforms of iU and iL . But these waveformssettle within about two fundamental cycles.

V. EXPERIMENTAL RESULTS

After computer simulation, experiments on an MMC-basedsingle-phase inverter are also carried out to further prove theproposed approach. The topology and the parameters of theinverter for experiments are the same as those for simulation.

The experimental results are shown in Figs. 1318. In theexperiments, the currents are measured by current clamps andthe ac voltages are measured by differential probes. The eightSM capacitor voltages are measured through optical fiber-based


Fig. 14. Experimental results of all the eight SM capacitor voltages with theconventional SUPWM method.

Fig. 15. Experimental results of uac (the upper yellow line), iac (the uppergreen line), 2 icir (the middle pink line), iU (the lower purple line), and iL(the lower red line) with the proposed suppression method.

Fig. 16. Experimental results of all the eight SM capacitor voltages with theproposed suppression method.

series communication interface and the sampling frequency is2 kHz. The circulating current multiplied by 2, i.e., 2 iciris obtained by the math function of addition (iU + iL ) on theoscilloscope.

Figs. 13 and 14 show the experimental results with the con-ventional SUPWM method. As shown in Fig. 13, it is clear that

Fig. 17. Experimental results of uac (the upper yellow line), iac (the uppergreen line), iU (the lower purple line), and iL (the lower red line) with theproposed suppression method when the inverter operates from no load to theRL load listed in Table I.

Fig. 18. Experimental results of uac (the upper yellow line), iac (the uppergreen line), iU (the lower purple line), and iL (the lower red line) with theproposed suppression method when the modulation index changes from 0.7 to0.3 under the RL load listed in Table I.

iU and iL are clearly distorted, while the circulating current icircontains obviously second-order harmonics (note that the timescale is 5 ms/div). Meantime, the RMS values of iU , iL , and2 icir are 4.08, 4.00, and 5.448 A, respectively, which matchthe simulation results well.

Figs. 15 and 16 show the experimental results with the pro-posed suppression method. Comparing Fig. 15 with Fig. 13, itis seen that the peak values and distortions of iU and iL areboth reduced. Meanwhile, the circulating current icir containsno obvious second-order harmonics any more (note that the timescale is 5 ms/div). What is more, the RMS values of iU , iL , and2 icir are decreased to 3.378, 3.329, and 2.913 A respectively,showing great improvement with the proposed method and very


similar to the simulation. Besides, the voltages of the SMs arewell balanced in both cases as shown in Figs. 14 and 16.

Besides, the stability of this inner current suppression con-troller is also tested by experiments. Fig. 17 shows the resultswith load change from no load, while Fig. 18 shows the resultswith the modulation index change from 0.7 to 0.3, which are alsothe same as the simulation. It is clear that the inner current sup-pression controller is stable under these step changes. It shouldalso be pointed out that the experimental waveforms are not asgood as those in the simulation because the implementation is-sues, such as the dead time effect, current measurement errors,etc., will influence the performance of this inverter, especiallywhen the current is low.

VI. CONCLUSIONThis paper proposed a closed-loop control method for sup-

pressing inner currents of the MMC. This method is simple andcan substantially reduce the peak and the RMS value of the in-ner current compared with the existing SUPWM method, whilethe voltages of the SM capacitors are kept well balanced. Thismethod is very helpful for reducing power losses of the MMC inreal applications. Both simulation and experimental results haveshown the validity and effectiveness of the proposed method.

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An Inner Current Suppressing Method for Modular Multilevel Converters