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STUDY OF HARMONIC CURRENTS INTRODUCED BY
THREE-PHASE PWM-CONVERTERS CONNECTED TO
THE GRID
Philippe Delarue *, Patrick Bartholomeus *,
Frank Minne **, Emmanuel De Jaeger **
presented by: Bruno FRANCOIS *
Slide 1
Mr. chairman, ladies and gentleman, the work I will present you is about HARMONIC
CURRENTS INTRODUCED BY THREE-PHASE PWM-CONVERTERS CONNECTED
TO THE GRID . This study has been done by Laborelec Belgium and our laboratory the L2eP
through the CNRT a French Research National Center in Electrical network.
The input stages of the static converters connected to the three-phase network are frequently
rectifiers with diodes or thyristors. These converters cause significant harmonic pollution and do
not readily make the converter power-reversible. This harmonic pollution adds losses on lines
and in distribution transformers and also make distortions in the voltage waveform at the point of
connection.
The present trend is to replace these converters by fully controlled structures that operate under
PWM. PWM converters ensure power reversibility and improve the harmonic content of the
currents absorbed into the network.
These power converters produce harmonic currents not at low frequencies (except from the
fundamental current) but at frequencies around the commutation frequency (of some kHz) and its
multiples. Although these currents are generally of low magnitude. If a large number of thes
converrters appears in the electrical network they will increase the level of harmonics which are
injected. It is therefore important to be able to assess the effect of this new type of disturbances
on the network.
The aim of the work is to determine the harmonic content of the currents absorbed by these PWM
rectifiers.
Slide 2
This study takes account of various parameters for the converter, few network parameters and the
required operating power point.
The harmonics of the current depend on a number of factors:
- the impedance of the distribution network and the impedance of the filter;
- the structure of the installation used (three-leg bridge, multi-level, associations, etc.);
- the type of the used filter (1st order, 3rd order, etc.);
- the modulation strategy (regular symmetrical, space vector, hysteresis, etc.);
- the DC bus voltage and rms distribution network;
- the quality of the network voltage and of the DC bus voltage.
An academic study with justified simplifications has been done in order to generalize obtained
results with the help of easily used abaci.
Slide 3
Hypothesis for the simplifications are:
- The network is modeled by a balanced three-phase voltage and balanced line inductances
- A first order filter is used
- The three phase converter is fully controllable.
- The DC bus voltage E is constant.
- The modulation strategy is a carrier-based PWM (sinus-triangle comparison).
These hypotheses correspond to the most of industrial PWM rectifiers.
It must be noticed that the results can extended to other specific modulation techniques as space
vector modulation.
Slide 4
This slide illustrates the principle of the studied pulse width modulation.
This modulation technique requires a sinusoidal reference voltage of magnitude r and frequency f
which intersects with a triangular carrier wave of unit amplitude and frequency fc. When the
modulating wave is greater than the carrier wave, the upper switch is closed and the lower switch
opened. When the modulating wave is less than the carrier wave, the upper switch is opened and
the lower switch closed.
The obtained modulated voltages v have two levels +E/2 and -E/2. These voltages are referenced
to the middle point of the DC voltage.
Relations between these voltages and the network voltages lead to 5 level voltages for va, vb , vc
For m=20, r=0.8 the figure gives the waveform for a line voltage on the converter side (v’a) and
the waveform for a line network voltage (va).
It is therefore shown that the voltage v has its fundamental at frequency f of amplitude r.E/2 (r is
termed the voltage regulation coefficient).
The harmonics are grouped into families around frequencies mf, 2mf, 3mf, etc., where m=fc/f is
called the modulation index.
If m is high, these families will be distinct from each other and the harmonics are easier to filter.
The current is then very nearly sinusoidal.
Slide 5
The remaining dominant harmonics in voltages and currents due to PWM switching are those of
the frequency (m±2)f and (2m±1)f centered around fc and 2fc.
These figures shows the fundamental and the main harmonics for voltages and currents according
to the regulation coefficient r.
Graduation of abacus will require knowledge of the internal characteristics of the system (E, Lg,
Lf, m). Reading of these same abaci requires the knowledge of the regulation coefficient r.
It is obvious possible to obtain such abacus for other types of PWM modulation.
Slide 6
To determine the regulation coefficient r, only the fundamental magnitudes are used.
P and Q are respectively the active and reactive powers at the converter connection point. And Pu
and Qu are those same powers at reduced magnitude.
The knowledge of k, allows us to draw on the level Qu, Pu .
A first network of constant production curves r and a second network of curves with Vpu
constant.
This second network or curves will only exist if k is different from 0. These two curve networks
will make up an abacus that allows us, if we begin from the point of function characterized by P
and Q, to determine the regulation coefficient for the converter and the effective value for the
voltage at the converter connection point.
It should be noted that this abacus does not depend on the used PWM technique. It has been
constructed on the basis of relations that link the fundamental magnitudes.
Figures gives abaci for two values of k (k=0 and k=0.2).
Slide 7
We illustrate now the use of the abaci
The line inductance value Lg is deducted from the short-circuit power
The value of the parameter can therefore be determined from DC bus voltage E
The coefficient k can be calculated from Lf and Lg
The switching frequency of 1,000 Hz allows the modulation ratio value m to be determined
The procedure for using the abaci is therefore as follows:
- knowing k, one can draw the abacus from theoretical relations given in the paper,
- the operation power point for Pu and Qu is located on the abacus;
- the value of the parameter r is obtained (in our case, r = 1.5);
- knowing , one can deduce the value of r (here we have r = 0.56);
- knowing r, one can obtain on the second abacus the rms value and frequency of the harmonics
due to PWM.
In our example, the current will show two components of about 130 A rms at 1,950 and 2,050 Hz
and two components of about 80 A rms at 900 and 1,100 Hz.
Slide 8
The abaci has been compared with experimental results. The test conditions were as follows: E =
60V, Lg = 2mH, k = 0.02, fc = 2,000 Hz.
Figure shows the waveforms of a line voltage and line current. It will be noted that they are in
phase. Both current and voltage show a wave linked to the PWM, based around the fundamental.
Slide 9
These figures show the frequency spectrum of the measured line current (in maximum values) for
three values of the regulation coefficient r.
The first two families of harmonics, centered around 2mf (equals 2 kHz) and 4mf (equals 4 kHz)
can be clearly seen. The presence of low-frequency harmonics, linked to imperfections in the
network voltages. Imperfections are caused by the use of an autotransformer.
A good accuracy of the predicted values from the abaci has been noted.
In the same way the knowledge of the line inductance (about 50 μH in our case) allows the
voltage harmonics. Figure shows, for r=0.4, the spectrum for a voltage at the connection point.
The abacus shows the validity of this pre-determination.
Slide 10
In this communication a method for predicting the current and voltage harmonics generated by
PWM rectifiers is presented. This has been done thanks to a few parameters of the system and a
few relations which can be presented in the form of an easily used abaci. The results of this study
have been verified thanks to experimental tests which give a good precision.
This study can be extend to other modulation techniques and to other converter topologies as
multilevel rectifiers.