Energy and Power Engineering, 2013, 5, 1120-1125
doi:10.4236/epe.2013.54B214 Published Online July 2013 (
Harmonic Currents of Semiconductor Pulse Switching
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},,
Received March, 2013
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].
hsin 2
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
Copyright © 2013 SciRes. EPE
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
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-
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
Figure 1. Idealized shape of the current taken by the con-
verter fr om the power networ k.
)1(1 a
Figure 2. The block diagram of the pulse rectifier and the
corresponding phasor diagram.
u [V]
i [A]
t [s]
t [s]
Figure 3. Voltage and current ratios of the pulse voltage
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.
Copyright © 2013 SciRes. EPE
Figure 4. Percentage values of harmonic currents and THDi
(from the computed waveform).
4. Measurement of Pulse Rectifiers in the
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
Figure 6. Percentage values of harmonics depending on the
load of the converter.
Copyright © 2013 SciRes. EPE
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.
Copyright © 2013 SciRes. EPE
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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