Harmonic Currents of Semiconductor Pulse Switching Converters

doi:10.4236/epe.2013.54B214

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Energy and Power Engineering, 2013, 5, 1120-1125

doi:10.4236/epe.2013.54B214 Published Online July 2013 (http://www.scirp.org/journal/epe)

Harmonic Currents of Semiconductor Pulse Switching

Converters

Petr Bilik1, Jan Zidek1, Vaclav Kus2, Te r eza Josefova2

1Faculty of Electrical Engineering and Computer Science, VSB – Technical University of Ostrava, Czech Republic

2Department of Electromechanics and Power Electronics, University of West Bohemia, Pilsen, Czech Republic

Email: {petr.bilik, jan.zidek}@vsb.cz, [email protected], [email protected]

Received March, 2013

ABSTRACT

Due to the operation of power semiconductor switching converters, the content of harmonic currents, which these

switching converters take from the feed array, is still increasing. One of the possible ways of minimizing these currents

is the use of pulse switching converters. On one hand, the original, characteristic harmonic ones are minimized, but, on

the other hand, new frequencies caused by the modulation frequency appear in the current spectrum. The level of the

currents of these frequencies is small and is scarcely dependent on the load of the converter. It may happen that the

proportional value of the monitored harmonic one is high, although the absolute value is low. In the article presented,

there is a description of the activity of the pulse voltage rectifier and an analysis of the current taken. The other part

contains the results of the harmonic analysis of the stated current, including both the absolute and proportional values

according to the load. In the conclusion, there are results of measurements of pulsed switching converters taken from

the real measurement.

Keywords: Rectifiers; Harmonic Analysis; Harmonic Distortion; Power System Harmonics; Current Measurement

1. Introduction

Conventional controlled rectifiers designed for speed

regulation of DC motors were characterized by both the

consumption of harmonic currents and, especially, the

variable power factor (proportional to the steering angle

of the converter). There were mostly high power con-

verters, so the negative effects on the power network

were dealt with by experts. In the spectrum of the current,

there mostly occurred so called characteristic harmonic

ones and their level was computed using the amplitude

principle. When mentioning small power sources for the

use in electronics (charging of capacitors), there were, on

the contrary, very low powers and very small amount of

appliances, so that negative effects were ignored.

A significant increase of negative effects of the con-

verters on the power network occurs with the increase of

frequency converters with a DC voltage intermediate

circuit. These converters usually contain uncontrolled

rectifiers at the input. The converter thus works with a

negligible phase shift between the voltage and the current,

and the power factor (fundamental harmonic cos φ1) is

close to 1. However, the current harmonic ones become a

problem. The very first converters even worked without

sufficient circuits for limitation of the harmonic ones. In

principle, it is a rectifier working to capacitive load; the

values of harmonic currents are very high. In a simplified

calculation, there can be used a so-called "generalized

amplitude principle" (1) [1,2].

sin

II.

hsin 2

 (1)

where: h – harmonic order, I1 – magnitude of fundamen-

tal harmonic, d – diode conduction time.

Detailed information about calculations of characteristic

harmonics, non-characteristic harmonics and interharmonics

can be found in [2-5]. Topic of harmonics elimination

and power factor improvement of three-phase rectifier is

described in [6].

Equation (1) advantage is that it also applies to con-

ventional controlled rectifiers, to calculation of the har-

monic ones with intermittent currents, to calculation of

harmonic voltage converters as well as to frequency

converters or other rectifiers working to capacitive loads.

See the calculated shape of current in Figure 1.

The unambiguous result of this relation is the fact that

the values of harmonic ones depend on the time during

which the diode is open (the capacity is recharged). As

for large capacities, the time is very short and thus the

harmonic ones are even higher. This, paradoxically, re-

sults in a situation where the load requires large voltage

P. BILIK ET AL. 1121

smoothing (and thus a large capacitor) and the character

of the current consumption requires, on the contrary, a

capacitor as small as possible.

A large capacitor means low d factor in (1). The value

of the harmonic one then reaches up to 80-90% of the

value of the fundamental harmonic one of the current,

even for the nominal load.

With the increasing improvement of quality of the

components and control electronics, the number of con-

verters is increasing rapidly and thus the need to deal

with the limitations of harmonic currents. Besides the

methods consisting of deployment of filters, protected

compensation etc., solutions appear directly in the con-

struction and the control methods of converters. One of

the ways is the use of pulse rectifiers.

2. The Principle of Operation of Pulse

Rectifiers

The basic diagram of a pulse rectifier is shown in Figure

2. The connection does not practically differ from a sin-

gle-phase voltage inverter. The principle of operation

consists of suitable switching of transistors. Approxi-

mately sinusoidal current consumption (with very little

distortion) is achieved this way. At the same time, it is

necessary to guarantee current consumption of the first

harmonic one with a very good power factor. The phasor

diagram shows that it is necessary to ensure power sup-

ply voltage of the bridge Uv that is delayed behind the

consumed current Ia by the angle.

More information about pulse rectifiers and its control

principles can be found in [7-9].

3. Harmonic Currents of Pulse Rectifiers

Figure 2 shows that this rectifier is supposed to meet the

basic requirement: consumption of a sinusoidal current

without a phase shift. To determine the harmonic cur-

rents, an analytical calculation of the shape of the current

that this converter takes from the power network was

performed (in Figure 3, it is the waveform in the lower

part, illustrated with the solid line). For simplicity,

modulation frequency fm=1kHz was selected. From this

simple figure and the low modulation frequency, it is

obvious that the shape of the current taken by the con-

verter from the power network is little distorted and the

power factor is very good as well. The determination of

the higher harmonic ones was then performed numeri-

cally.

Let observe the dependence of percentage values of

the harmonic currents as a function of the ε angle In fact,

ε triangle is therefore a relative unit of the load. For ε = 0,

the converter is close to the idle run and vice versa.

The unambiguous result from Figure 4 is that for the

frequencies near the modulation frequency, there are







Ism

d+k





Figure 1. Idealized shape of the current taken by the con-

verter fr om the power networ k.

T4T2

UVUv(1)

)1(1 a





Ia(1)



Figure 2. The block diagram of the pulse rectifier and the

corresponding phasor diagram.

u [V]

i [A]

t [s]

Figure 3. Voltage and current ratios of the pulse voltage

rectifier.

high percentage values of the harmonic currents. If this

graph is not complemented with comments on the size of

the absolute values of the current or dependence of the

fundamental harmonic current as a function of angle ε,

this result is highly misleading. The first impression may

be that the operation of this converter is construed as

inappropriate. Presentation of absolute values, which will

be dealt with in Chapter 4, is much more suitable.

P. BILIK ET AL.

1122

Figure 4. Percentage values of harmonic currents and THDi

(from the computed waveform).

4. Measurement of Pulse Rectifiers in the

Laboratory

The measurement was performed in the laboratories of

electric drive of Department of Electromechanics and

Power Electronics in The University of West Bohemia in

Pilsen. It was a single-phase pulse rectifier of the voltage

type with a rated current of 6A. The modulation fre-

quency was fm = 1kHz. As it was mentioned in the pre-

vious chapters, the characteristic harmonic ones that lie

closest to the modulation frequency appear. In our case,

they will be the 19th and the 21st harmonic ones. The

measurement was performed for various loads and for

the operation of both drive and brake. In order to conduct

the first assessment of the measured value, Figure 5

shows two types of current waveforms - one for the

nominal values and the other for values nearing the idle

run. As for the rated current, the waveform is of high

quality and low distortion can be expected. As for the

small load, the current is rippled, but the amplitude of the

current measured is very low.

In the Figure 6, can be seen an incorrectly represented

graph. Here is shown the percentage value of the current

of the 3rd and 5th harmonic ones and the current of the

modulation frequency depending on the load. From this

graph can be seen again that when the load is small, the

percentage values are high. Therefore, there is a risk that

the converter will be considered inappropriate from the

point of view of the harmonic content.

The graph in Figure 7 is much more apposite. There

were produced graphs for the waveforms from Figure 5

for the values of the harmonic ones, now in the absolute

values. In the graph, we can see that due to the rated in-

put current of the converter IN = 18A (the fundamental

harmonic), the values of the harmonic ones are negligible,

even in the mode of a very small load. For example, at

the load (on the DC side) of 1.4A, the value of the 19th

harmonic one is 0.25A, which is approximately 1.4% of

the rated current of the fundamental harmonic. There is

then a sharp contrast with Figure 6, which is technically

flawless, but otherwise unsuitable. Notice: beware of the

scale - in the headlines of the figures there are values of

the output current (the load of the converter), but the

graph shows the input currents.

5. Measurement of Pulsed Switching

Converters in Practice

The practical measurements were performed with a

measuring apparatus using the analyzer BK-ELCOM

ENA440, see Figure 8. As for the analyzer, there were

used input modules with A/D converters with the 24-bit

resolution. The currents higher than 5A (the photovoltaic

power plant and the converter) were measured by means

of current clamps while taking advantage of the com-

pensation of amplitude and phase errors. As for currents

of under 5A, the direct current input was used. The sam-

pling was the same in all channels and the sampling fre-

quency was 50kS/s for each channel.

Figure 5. Waveforms of the current measured for various

loads.

Figure 6. Percentage values of harmonics depending on the

load of the converter.

P. BILIK ET AL. 1123

Figure 7. A correctly used figure for documentation of

harmonic pulse converters.

Figure 8. Analyzer BK-ELCOM in version ENA440x.

As technical interest and for the notion of the dynamic

range of the input modules used with regard to the very

low system noise, there are also stated the minimum de-

tectable amplitudes of the harmonic ones:

 The voltage input of the range of 300Vrms is able

to evaluate correctly, in the band of 0-25kHz, the

signal of the minimum level of 300 µV (0.0001%

of the range).

 The direct current input of the range of 5Arms is

able to evaluate correctly, in the band of 0-25

kHz, the signal of the minimum level of 70 µA

(0.0001% of the range)

5.1. The First Measurement

The first measurement was performed at the photovoltaic

power plant (PVPP) with a nominal output of 20kW, see

Figures 9 and Figure 10. The measurement at the PVPP

was performed on a sunny day in the middle of Septem-

ber, at about 09:30. The PVPP uses several single-phase

converters for each phase. The non-equivalent load of the

individual phases may be caused by the malfunction of

one of the converters. The most distorted waveform of

the current appeared in phase L3 where there were found

out the following parameters: U=226V, I=7,12A, P=

1596W, PF=0,992, cos φ = 0.998. From the waveforms

in Figure 9 as well as from the basic data of the meas-

urement, it is obvious that the converter works with a

very good power factor. The distortion of the current is

minimal. Although there is used the pulse modulation of

the inverter, the current is also (perhaps by means of the

influence of the high modulation frequency) at the fre-

quency of the modulation frequency very low. It is con-

firmed by the results of the harmonic analysis shown in

Figure 10. More about disturbing impact of grid con-

nected converters can be found in [10].

5.2. The Second Measurement

The second measurement was carried out on a frequency

converter with so called "Active Front End" in a labora-

tory at VSB-TU Ostrava (see Figure 11 to 14). Therefore,

it is also a pulse rectifier connected to the power network.

The maximum load of approximately 3kW, which could

have been reached, was limited by the equipment of the

laboratory. When the converter was loaded, the following

parameters were obtained in phase L3: U=228 V, I=4.9 A,

P=963W, PF=0.85, cosφ=0.865.

When the converter was iddle, the following parame-

ters were obtained in phase L3: U=224 V, I=7.15 A,

P=384W, PF=0.24, cosφ=0.26.

From the current waveforms and the results of the

harmonic analysis, it is obvious that the distortion of the

input current is low due to the activity of the pulse recti-

fier. When the load is small, a wide spectrum of har-

monic of the input current appears due to the activity of

Figure 9. Left: Currents in PVPP. Right: relation of U and I

of phase L3.

Figure 10. The spectrum of the current of phase L3. Left:

graph in Amps. right: graph in per cent.

Figure 11. Left: Currents of the converter under a load.

Right: relation of voltage and current of phase L3.

P. BILIK ET AL.

1124

Figure 12. The spectrum of the current of phase L3. Left:

graph in Amps. Right: graph in percentage.

Figure 13. Left: Currents of the converter at the idle run.

Right: relation of voltage and current of phase L3.

Figure 14. The spectrum of the current of phase L3. Left:

graph in Amps. Right: graph in percentage.

the pulse rectifier. However, the absolute value of the

harmonic ones is low, especially if a comparison is done

with the fundamental harmonic of the current at the no-

minal load.

5.3. The Third Measurement

The third measurement was performed on a typical

household appliance - a television, as a demonstration of

the fact that producers of consumer electronics try to

improve the parameters of their products with respect to

the reverse impact on the feed array. The measurement

was carried out on a plasma TV with a diagonal of 42'',

model 2010, see Figures 15 and 16. The following pa-

rameters were obtained: U= 230 V, I=0.85 A, P=182 W,

PF= 0.932, cosφ= 0.959. Despite the fact that the dia-

gram of the connection of the feed source of the televi-

sion was not available, the result of the measured courses

of the current and its harmonic analysis is that there is no

occurrence of higher harmonic ones that would have a

dangerous impact on the power network.

6. Conclusions

The article shows the development of semiconductor

converters with respect to higher harmonic currents taken

by the converter from the feed array. If modern methods

Figure 15. The waveform of the current of a plasma TV.

Right: relation of voltage and current.

Figure 16. The spectrum of the current. Left: graph in

Amps. Right: graph in percentage.

of pulse switching are used elimination of these currents,

the characteristic harmonic ones of these currents are low.

Currents of higher harmonic ones, that are identical to

the frequencies of modulation frequencies, newly appear

in the spectrum. However, these currents are not signifi-

cant in their absolute values. The graphs show that when

the loads are small, the percentage values of the currents

of modulation frequencies can be high, but with respect

to the low current consumption (in relation to the nomi-

nal values), the absolute values are low. The article also

presents results of several practical measurements. The

article does not feature the aspects of largeness, i.e. con-

currence of a high number of small household appliances,

including modern sources of light, on the feed array.

Generally, there is no need to be afraid of converters with

pulse modulation. From the point of view of their effect

on the power network, the use of these converters can

even be considered beneficial.

7. Acknowledgements

This paper was supported by the project No. GACR

102/09/1164, by the European Regional Development

Fund and the Ministry of Education, Youth and Sports of

the Czech Republic under the Regional Innovation Cen-

tre for Electrical Engineering (RICE), project No.

CZ.1.05/2.1.00 /03.0094. This work was supported in

part by The Ministry of Education, Youth and Sports of

Czech Republic under the project KONTAKT II registra-

tion number LH12183.

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