Reducing Harmonics and DC-Linl< Capacitors in Cascaded Multilevel Converters using Inter-Cell

Magnetic Couplings

Carlos R. Baier, Javier A. Munoz, Johan I. Guzman University of Talca

Department of Tndustrial Technologies Curic6, Chile

cbaier@utalca.cl, j amunoz@utalca.cl, j guzmand@utalca.cl

Abstract- The existence of single-phase inverters in cascaded

multilevel AC/DC/AC converters implies the use of large

capacitors in the DC links, because the H-bridge inverters

demand considerable second harmonic currents that must be

filtered out by the DC stage. If the filtering out is not strictly

performed, the AC input current of each module is affected with

the appearance of non-characteristic harmonics, sub-harmonics

or inter-harmonics; thus, the RMS currents in the multi-pulse

transformer secondaries increases. This problem may become

even more evident if the converter output frequency is lower than

the AC mains frequency, because the capacitor presents higher

impedance at low frequency, causing that part of the harmonic

currents demanded by the inverter is supplied directly by the

rectifier. This paper presents an alternative to eliminate the

unexpected harmonics and thus reduce the RMS values of the

power cells input current in cascaded multilevel converters. The

proposed solution uses magnetic couplings between the power

modules of the converter; such approach is presented as a low

cost solution compared to the conventional oversized DC-link

capacitors.

1. INTRODUCTION

For decades, power electronics has been a driving force for industrial development. One of its greatest achievements is the easy and inexpensive conversion of AC to DC power and vice versa. Tn fact, nowadays, energy conversion without the use of semiconductors is very hard to believe. However, the use of static converters has also been synonymous of harmonics in the AC mains, poor power quality and reduction of the system reliability [l ].

Tn this regard, since the very beginning, the use of medium voltage converters has been a concern, because the harmonic currents in the AC input lines of these equipments require large filters to avoid polluting the AC mains or affecting other loads [2]. Hence, the use of multi-pulse transformers in cascaded multilevel converters has become an adequate solution, because they allow feeding medium voltage loads, achieve low harmonic distortion in the demanded AC currents, provide high power quality to the load and operate with high reliability [3].

Although the successful operation of cascaded multilevel converters is mainly thanks to multi-pulse transformers, it is also due to the large DC-link capacitors of the power modules. Tn fact, if the size of these capacitors is not large enough, the

Jose R. Espinoza, Pedro E. Melin University of Concepci6n

Department of Electrical Engineering Concepci6n, Chile

jose.espinoza@udec.cl, pemelin@udec.cl

power modules would become highly non-linear and this would lead to "unexpected harmonics" (understood as the set of non characteristic harmonics, sub- and inter-harmonics) in the AC currents that bring disadvantages to the main power transformer [4].

Tn symmetrical cascaded multilevel converters, each power cell is fed from a multi-pulse transformer secondary, where it is expected that each of these modules draw currents with characteristic harmonic components (5th, 7th, 11th, 13th, etc). The relative amplitudes of these components depend upon the mode in which the rectifiers operate (continuous or discontinuous mode). These modes in tum, depend on the load power and the reactance in the rectifier AC input lines [5]. On the other hand, the operation of the multilevel converter at low output frequencies, in combination with an inappropriate design of the DC link capacitor, causes unexpected harmonics presence in the rectifier currents. Although, the multi-pulse transformers can supply currents with unexpected harmonic components, this reduces the transformer capacity to transfer useful energy [6],[7]. This is a good reason to use large DC link capacitors in the converters.

The problem may become more dramatic in cascaded multilevel converters with single-phase power cells, because some unexpected harmonic currents do not vanish in the transformer primary and consequently, they appear on the AC mains [4].

This paper shows that, as a result of reducing the DC link capacitors size in a symmetrical cascaded multilevel converter, there is an increased content of unexpected harmonics in the rectifiers AC input currents. With regard to this, it is proposed a solution that reduces the size of the capacitors, without affecting the input currents. The solution has been successfully implemented in a laboratory prototype.

II. CHARACTERISTICS OF THE SYMMETRICAL CASCADED

MULTILEVEL CONVERTERS

A. Basic Design o{the Power Cells A symmetric cascaded multilevel converter, Fig.l (a), is

implemented starting from a multi-pulse transformer that

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(d)

Fig. 1. Traditional cascade multicell topology and a magnetically coupled version of this; (a) conventional 7-level arrangement (b) standard power cell, (c) proposed arrangement with power cells magnetically coupled (d) power cells using magnetic couplings

distributes power to an array of modules through its multiple secondaries. Each power cell or module takes a three-phase voltage which is rectified using a diode bridge, then this DC voltage is inverted through a single-phase inverter with a - in general - different frequency respect to the AC mains, supplying a controlled AC voltage to one phase of the load. Thus, a power cell is composed of a three-phase diode rectifier, a large capacitor as a DC link filter and a single-phase inverter, Fig I (b). These inverters connect their AC outputs in series to reach higher voltage magnitudes than a single module could withstand [3].

The basic SPWM modulating technique for these converters indicates that for nc power cells connected in a series way in one phase, the carriers must be 180o/nc shifted. If a converter with three power cells per phase is taken as an example, Fig.1 (a), the "expected" multilevel voltage is obtained in one of the output phases in the Fig. 2(a), where it can be seen that the waveform has 7 levels. For traditional cascaded multilevel converters, the maximum number of levels (Lmax) that the output voltage can reach depends on the number of cells nc connected in series (Lmax = 2nc + I) [3].

If oversized capacitors are considered in the DC-links of the power cells, it is expected that current harmonics in the rectifiers DC side will be of order 6k (k=1,2, .. ) with respect to AC mains frequency. On the other hand, (and consequently) harmonics of order 6k ± 1 (k = I, 2, .. ) appear in the rectifiers AC input currents, Fig.2 (c). Finally, the phase-shift technique in the multi-pulse transformer secondaries is used to remove

dominant low-order harmonics, so the low-order harmonic currents at the transformer primary will be 6nc·k ± 1 (k=l , 2, .. ).

If the design of the capacitor is not strict and the converter operates at a lower frequency than the one considered in the design, unexpected harmonic currents may appear in the AC input line of the power cells. The order of these harmonics depends on the AC output frequency [4].

B. Design a/the DC-link Capacitors in the Power Cells The DC link capacitor becomes a key component as besides

of providing a smooth DC voltage to the inverter, must filter out the harmonic currents demanded by the same inverter in order to avoid the rectifier to provide them.

Traditional design procedures select the DC capacitor size considering only the minimization of the second voltage harmonic. Particularly, this paper considers the following design expression,

c = __ l_O_O_I-,:vlll __ ,a:_xl,---:--:-8 -r VhO V;2nd ' 1[ J olminl cimini %1

(1)

where the DC link capacitor C is directly dependent on io[max] (maximum amplitude of load current) and inversely dependent on /')[min] , which is the minimum frequency imposed on the load side. The voltage V:i�illl is the minimum DC component expected in the rectifier output voltage and V �"d is the percentage of second voltage harmonic allowed on the capacitor. To ensure a minimal flow of second harmonic current from the load to the rectifier, this last percentage must be much smaller than I %. If this is not fulfilled, unexpected

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current hannonics will appear In the AC input line of the power cell.

Ill. UNEXPECTED HARMONICS ASSOCIATED TO POWER

CELLS OF THE CASCADED MULTILEVEL CONVERTERS

As stated previously, a relaxed design of the capacitors causes the appearance of sub-harmonics, inter-harmonics and non-characteristic hannonics in the AC input current of each rectifier of the converter.

When the DC stage of a power cell is analyzed, considering the rectifier output as a voltage source, the capacitor as a hannonic filter and the inverter input as a current source, it is possible to found the harmonics involved in the circuit. Taking this into account, the current imposed by the inverter is written as,

x

ii = liho + I1t2m cos(2mroj) , (2)

m=l where roo is the angular frequency of the load AC voltage, 1:'0 is the DC current component demanded by the inverter and

Ijh2m are the even hannonics also demanded by the inverter.

The output voltage of the six-pulse rectifier can be expressed as,

eN TThO "TTh6m . (6 ) Vr = Yr + L...Yr SIn mroJ , m=l

(3)

where v;.hO is the DC voltage component available at the

rectifier output, while v;.hom is the voltage hannonic

component, multiple of six, found in the same rectifier output. It is possible to use the superposition method to find the total

DC-link capacitor current, which can be written as,

ic = I[I;6m cos(6mm,t)-aJih2m cos(2mroot)] (4)

m=l where 1:'6m , are the harmonic currents, multiples of six,

excited in the capacitor by the rectifier voltage given in (3),

am is a filter factor of the harmonic current amplitude 1:'2m which is demanded by the inverter. This factor is necessary because the capacitor is not infinite, and therefore it cannot provide all the harmonic currents to the inverter. Regarding

am' it can be said that this factor is strongly dependent on the

size of the capacitor and its value is between 0 and 1. If the

TABLE 1

capacitor value C is equal to zero, it means that the factor

am = 0 and if the capacitor value C is very large then am tends to 1.

Using the Kirchhoff current law in the DC link node, (5)

it is possible to find that the current expression in the rectifier output can be written as,

ir = liho + f[ 1;6m cos(6mro)) + f3nJih2m cos(2mroot)] , (6) m=l

where f3m is the attenuation degree for the inverter harmonics

provided by the DC-link capacitor, saw from the rectifier. This attenuation degree corresponds to the complement of the

factor am and it is written as,

(7) Similarly to am' the attenuation degree f3m' is a factor that

depends strictly on the capacitor size and varies between 1 and o if the capacitor C varies between 0 and 00, respectively.

From (6), it is possible to consider a percentage of the second current harmonic, 1,�,2 , in the output of each rectifier, which is defined as,

(8)

where 1:'2 is the magnitude of the second current hannonic

demanded by the inverter, 1:'0 is the DC current component

demanded by the same inverter, and f32 is the attenuation

degree achieved by the capacitor for the second harmonic in the rectifier DC output.

The diode bridge could be represented as a switching function (sf), which can be written as,

ac

Al sin(mJ) + L Ac;n±l sin((6n ± l)mJ) n=l

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sf= Ajsin(ro,t-120)+ LAGn±lsin((6n±1)ro,t=t120) , (9) n=l

ac

A sin(mJ + 120) + L Ac;n±l sin((6n ± l)mJ ± 120) n=l

where the magnitudes of the Fourier coefficients (An) depend on the diode bridge load power, with A6n+I<A6n-l< AJ If this

MAIN NON-EXPECTED HARMONIC FREQUENCIES AT THE INPUT OF THE POWER CELLS WITH RELAXED CAPACITORS *

Item

2

3

4

5

6

roo

0,5

0,6

0,7

0,8

0,9

ill roOI

°

0,2

0,4

0,6

0,8

roih 02

roih 11

ill rol2

2 3 4 6 3 7

2,2 1,4 3,4 3,8 6,2 2,6 7,4

2,4 1,8 3,8 3,6 6,4 2,2 7,8

2,6 2,2 4,2 3,4 6,6 1,8 8,2

2,8 2,6 4,6 3,2 6,8 1,4 8,6

3 3 5 3 7 9

*without use of magnetic couplings between the power cells.

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roih 13

roih 21

2 8 6 8

1,4 8,6 5,8 8,2

0,8 9,2 5,6 8,4

0,2 9,8 5,4 8,6

0,4 10,4 5,2 8,8

II 5 9

function is multiplied with the rectifier output current (ir), from (6), the three-phase input currents of the power cells can be found, i.e.

is = [i� (10)

where is, are the rectifier AC input currents. Developing this

multiplication it is possible to identity the unexpected frequency components that are present in these currents. These frequencies may be written as,

ffi�;n =1(6n±1)ffi, ±2mffio l , (11)

where oo:::n are the frequencies of the unexpected components

in the rectifiers AC input lines; and m and n are the indexes of the sums in (6) and (9). Tn the same multiplication it is possible to determine the amplitudes of the unexpected current components, these are,

A 13 ]h2m /ih _ 6n±1 m i nm - 2 . (12)

As it can be seen in (12), these amplitudes depend on the harmonic amplitudes It2m demanded by the inverter, the attenuation degree 13m and the coefficients of the switching function �n±l that, in turn, depend on the power and system parameters.

From (11), Table 1 can be computed and it is possible to see the unexpected frequencies (of low-order) that can be found in the power cells AC input currents. These unexpected frequencies are normalized in p.u .. It is also worth mentioning that from (12) it is possible to deduce that if the attenuation degrees are minimal, then the unexpected harmonic components are not perceived in the power cell AC input current.

An imperfect attenuation performed by the capacitor, causes sub-harmonic, inter-harmonics and/or non-characteristic harmonics in the rectifiers AC input currents, which may include a DC value, even harmonics and/or zero sequence components as the third or ninth harmonics (Note item I and 6 in Table 1).

As it can be deducted, the solution to reduce these unwanted harmonics is to design the capacitor C as large as possible, and then Pm should become small enough to

minimize the harmonic amplitudes given in (12). However, there is a different approach that is presented hereafter.

IV. ELIMINATION OF HARMONICS IN THE DC-LINK BY USE

OF MAGNETIC COUPLING BETWEEN POWER CELLS

A solution that can relax the capacitor design while avoiding the occurrence of unexpected harmonics in the modules AC input currents is the use of magnetic couplings in the rectifiers output, as shown in Fig 1 ( c) and Fig.1 (d). As a consequence of the arrangement, each magnetic coupling rejects its DC flux and allows equalizing the voltage harmonic components on each DC-link; thus, each module shares its harmonics with the adjacent power cells. This equalization eliminates harmonics of positive or negative sequence

between the DC links, which will be explained in the following.

Tf we write the equations of the voltage loop at the output of each rectifier in Fig.l (d), we have,

(13)

(14)

(15)

where v:,l' , v:�' and v;lI are the common harmonic voltages

shared by the couplings. Moreover, the unfiltered rectified voltages are equal, because the rectifiers are fed from the same types of secondary of the transformer, i.e.

(16)

From (13) to (16), a new DC filtered voltage v; can be obtained for every output rectifier loop, which is given by,

* 1 (u " w) vr ='3 Vc +vc +vc . (17)

If the system is completely balanced, the voltages on the capacitors v:� , v: and v:' in each cell of Fig. 1 (d) mainly reflect a second harmonic and other even harmonics voltages that can be written as,

�

u = vhO + "" uh2m sin(2 OJ t) Vc c L re m 0 ' m=l

sin(2mOJot - 120m) , m=!

CL

w VhO "" Vh2m • (2 120 ) Vc =

c + L.." c sin mOJj + m , m=l

(18)

(19)

(20)

since each capacitor has a continuous voltage component Vtl , and even harmonic amplitudes �'2m caused by the currents of

each inverter, considered in (2), but 1200 phase shifted, due to the power cells feed different load phases. The result is that the new DC filtered voltage, seen from the rectifier output, in the coupled system will be,

if)

* VhO "Vh6m • (6 ) vr = c + L.. c sm mOJi . (21 )

It is important to note that this voltage does not have a second harmonic component, not because of the capacitor but rather by the cancellation caused by the magnetic couplings. Another deductible fact is that in a system like Fig.l (d) (considering ideal magnetic couplings), the DC-link currents

of the cells are equal to i,�, i.e. .* 'u 'v ."It'

Ir = Ir = Ir = Ir '

therefore, it is also possible to find that,

i; = � (i; +i; +in .

(22)

(23)

Using the superposition method in the DC link of each power cell (without considering the magnetic couplings), it can be found that the currents at the output of each rectifier are,

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Fig. 2. Test 1 - Behavior of the Cascaded Multilevel Converter using capacitors of 22[mF] in the DC·links, (a) Output voltaje converter (b) A line primary current of the transformec (c) AC input current to a rectifiec (d) Output current of a rectifieL (e) spectra of (c), (1) spectra of (d),

i� = J,hO + ! [J,h6m cos( 6mwJ) + f3mJ,h2m cos(2mwJ) ] ' (24) m=l i; = JtO + ! [J,h6m cos(6mwJ) + f3mJ,h2m cos(2mwJ - 120m) J, (25) m=l i;' = l,ho + ! [1;6m cos(6mm,t) + f3ml,h2m cos(2mwot + 120m) J. (26) m=l Nevertheless, if we replace (24) to (26) into (23), it can be

found that,

i; = J,hO + ! [J;6m cos(6mw,t) ] . (27) m=l This means that current harmonic components ± 1200 phase

shifted are canceled in the DC-link, allowing a rectifier output current without frequency components from the load, which implies rectifier AC input currents without unexpected harmonics. The use of magnetic couplings between power cells can significantly reduce the size of the DC link capacitors, since the magnetic couplings are responsible for filtering out the harmonic currents that a standard capacitor cannot reduce or eliminate.

V. EXPERIMENTAL RESULTS

For this paper three experimental tests were performed using a cascaded multilevel converter prototype of 3k VA, which allows the use of magnetic couplings. The first two tests (test 1 and 2) have the intention to assess the AC input current of the power cells using two different sizes of DC link capacitor in the cells (oversized capacitor in test 1 and standard size in test 2). In the last test, the prototype of Fig. 1 (c) and Fig. 1 (d) with magnetic couplings is implemented, in

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Fig. 4. Test 3 - Behavior of the cascaded multilevel converter using capacitors of 2[mF] in the DC·links and magnetic couplings. (a) Output voltaje converter, (b) a line primary current of the transformer, (c) AC input current to a rectifiec (d) Output current of a rectifier. (e) spectra of (c). (f) spectra of (d).

order to verity the improvements in the power cells AC input current when capacitors of standard size are used.

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All tests were performed with 30 Hz at the converter output, i.e. a frequency of 0.6 in p.u. in order to verity the occurrence of unexpected harmonics, as shown in Table 1.

The first test (see Table 11 - Test 1 and Fig.2), allows evaluating the converter using 22 [mF] DC link capacitors, where it is expected to achieve a 0.2% of second harmonic voltage on each link. On the other hand, the percentage of second current harmonic from the inverter (in the rectifier output) turns out to be 9.5%, which is hardly noticeable in Figs. 2 (d) and (t). Finally, in order to compare with the next test, the true RMS value of the AC input current is taken as base (1 [pu]), where its harmonic distortion is 52%.

For the next test, Test 2, a new design is used, where the size of the capacitance decreases 10 times, i.e. 2.2 [mF] in each cell. Now, it is expected to achieve 2% of second voltage harmonic on the capacitor. For this new test, the same power load and output frequency (of 0.6[p.u]) is considered. The results are shown in Table IT - Test 2 and Fig. 3, where one can see the occurrence of unexpected harmonics.

Tn Fig. 3 (d) and Fig. 3 (t), it is possible to see the second current harmonic demanded by the inverter from the rectifier output, which is almost 68%. The analysis shows that this problem causes a total harmonic distortion of 66% in the rectifiers AC input currents (see also Fig. 3 (c) and Fig. 3(e)). These new harmonic content in the rectifiers AC input currents do increase their RMS values in a 10% (with respect to Test I), i.e. 1.1 [p.u].

Finally, using the same DC link capacitances of Test 2, the last test (Test 3) evaluates the performance of the converter with magnetic coupling between cells, as proposed in Fig.1 ( c) and Fig.1 (d). Tn this last test (see Table IT - Test 3 and Fig. 4), it is possible to see that the percentage of second current harmonic demanded by the inverter from the rectifier output current improves to a 5%, resulting in a reduction of the RMS value in the rectifiers AC input currents to a 0.96 [p.u].

It is also possible to compare the converters output voltages used in Test I, Test 2 and Test 3 (Fig. 2 (a), Fig. 3 (a) and FigA (a)), where it can be seen that the multilevel voltage reached in the last two tests are irregular compared to Test I. This happened because the DC link capacitors (used in test 2 and 3) are considerably smaller. However, this irregularity is barely perceptible in the harmonic distortion.

Likewise, if one compares the total harmonic distortion of a line current in the transformer primary in the three tests (Fig. 2 (b), Fig 3 (b) and FigA (b)), it is possible to see that there are

ahnost no differences, except for its RMS value where the analysis shows a higher RMS current in the primary of Test 2.

VI. CONCLUSIONS

This paper shows a decreased quality in the shape of currents in the transformer secondary when standard sized capacitors are used to achieve a 2% of second harmonic voltage on the DC link. As seen in the experimental results, a classic way to achieve AC input currents without unexpected harmonics in the rectifiers, is the use of DC link oversized capacitors designed to achieve levels of second harmonic much lower than 1%.

The use of magnetic coupling between the power cells in the cascaded multilevel converters encourages the use of relaxed capacitors in the power cells, without worrying about the increase of the RMS value in the rectifiers AC input currents. The use of these magnetic couplings prevents that the transformer secondary deliver inter-harmonic, sub-harmonic or non-characteristic harmonic currents to the power cells.

ACKNOWLEDGMENT

The authors wish to thank the financial support from the Chilean Fund for Scientific and Technological Development (FONDECYT) through project 1111 0292 and I I I 0794 and the technical support provided by the Applied Digital Control Laboratory, University of Concepcion, Chile.

REFERENCES

[1] Bimal K. Bose "Power Electronics and Motor Drives Recent Progress and Perspective" IEEE Trans. on Industrial Electronics. Vol 56, No. 2. Feb. 2009. pp. 581-588.

[2] Robert A. Hanna and Shiva Prabhu "Medium-Voltage Adjustable-Speed Drives - Users' and Manufactures' Experiences" IEEE Trans. on Industry Applications, Vol 33, NO. 6. Nov/Dec 1997. pp. 1407-1415.

[3] Malinowski, M. Gopakumar, K. Rodriguez, 1. Perez, M.A. "A Survey on Cascaded Multilevel Inverters" IEEE Trans. on Industrial Electronics, 2010, Vol. 57, No 7, pp 2197-2206.

[4] Baier, c.R.; Munoz, 1.; Espinoza, 1.R.; Melin, P.; Guzman, 1.; Moran, L.; "Improving power quality in cascade multilevel converters based on single-phase non-regenerative power cells," IECON 2011 , pp.4192-4197, 7-10 Nov. 2011.

[5] Ertl, H.; Kolar, J.W.; , "A constant output current three-phase diode bridge rectifier employing a novel "Electronic Smoothing Inductor"" IEEE Transactions on Industrial Electronics, vo1.52, no.2, pp. 454- 461, April 2005.

[6] "Transformer Design and Application Considerations for Nonsinusoidal Load Currents" IEEE Trans. on Industry Applications, Vol 32, NO. 3. May/Jun 1996. pp. 633-645.

[7] IEEE Recommended Practice for Establishing Liquid-Filled and Dry Type Power and Distribution Transformer Capability When Supplying Nonsinusoidal Load Currents, IEEE Standard C.57.11 0-2008.

TABLE II

PARAMETERS AND RESULTS OF THE EXPERIMENTAL TESTS TO DIFFERENT CONDITION OF DESIGN IN THE CONVERTER

Test C v.,h2 1"2 I,.RMs THDis THDl'o % %

Test 1 22[mF] 0.15[%] 9.5[%] 1 [p.u] 52[%] 26.6[%] Test 2 2.2[mF] 1.7[%] 67.5[%] 1.1 [p.u] 66[%] 26.7[%]

Test 3* 2.2[mF] 2[%] 5[%] 0.96[p.u] 50.1[%] 26.8[%]

J;=50Hz;j,=30Hz; *using magnetic couplings

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