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ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 55 (2007), Nr. 1
HARMONICS
POWER SYSTEMS
ANALYSIS
The analysis of separating harmonics from supplier and consumer
GEORGE CĂLIN SERIŢAN, COSTIN CEPIŞCĂ, PATRICK GUERIN∗
Analiza posibilităţii de separare a armonicilor
în relaţia producător – consumator de energie electrică
The more and more number of the use of non-liniar charges in electric networks leads to the coming out of electric
harmonics. We did the necessary measurements, they have been evaluated by using different methods for the
determination of the propagation sense of harmonics. The analysis of the harmonic behaviour of a usual converter
explains the difficulties to obtain significant results.
1. Introduction
With the development of power semi-conductors,
the number and the unit power of equipment using
power electronics don't stop increasing. Then,
harmonic currents generated by these non-linear
loads can produce overcurrents in lines and create
voltage disturbances due to the network impedance.
The harmonic effects on the power system are now
well known, particularly in industrial systems.
The standards [2, 3] give the limits of the harmonic
perturbations in the electrical distribution systems in
order to insure the electromagnetic compatibility of the
equipment connected to a same supply network. In
some cases, the power quality is defined by an
agreement between the supplier and the customer.
The application of these standards or contracts
assumes to distinguish both the harmonic background
level of the power system and the harmonic injection
of the consumer.
Fig. 1. Modelling of the system.
The harmonic voltages and currents can be
measured at the point of common coupling in the
same way than it can be done for energy
measurement. The harmonic currents are then
considered as the sum of those injected by the
disturbing load and those resulting of the harmonic
voltages derived from the power system through out
the consumer's loads (Fig. 1).
Several methods have been proposed [1, 4, 6] to
evaluate the harmonic emission level generated by an
individual non-linear load. The results are then
∗
Dr.ing. Seriţan George Călin – s.l. University Politehnica of
Bucharest; prof.dr.ing. Cepişcă Costin – s.l. University Politehnica
of Bucharest; conf.dr.ing. Guerin Patrick – IREENA – IUT de
St-Nazaire (France).
analysed, discussed and compared with the results of
converter’s simulation.
2. Application of evaluating techniques
Several methods have been proposed to
discriminate the harmonic injection of consumers of
those come from the supply system. Some of them
can be defined as intrusive method since they require
the switching of another special load or the
disconnection of the consumer load. These techniques
are not easy or impossible to be applied because of
the disturbances imposed on the consumer.
For these reasons the non-intrusive methods,
which are only based on of harmonic voltage and
current measurements at the PCC were preferred. The
advantage is then to be transparent for the supplier
and the consumer. In the following, two common
methods together with their variant are described.
2.1. Harmonic voltage versus harmonic current
This method consists in the correlation between the
harmonic voltage and the harmonic current injected by
the consumer's loads. In this case the harmonic
current can be independent of the fundamental one or
of the consumed power, like in the case of light
dimmers or some bridge rectifiers with a capacitive
filter.
Fig. 2. Harmonic voltage versus harmonic current.
The plot of the sampled data ( Vh ,
I h ) as shown in
Fig. 2, leads to a graphical representation of the
harmonic behaviour of the disturbing load: increasing
or decreasing effect on the resultant harmonic voltage.
The amplitude of the background harmonic level is
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ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 55 (2007), Nr. 1
deduced from an extrapolation for a null current
(I h = 0 ) .
It should be noticed that these results don't allow to
discriminating the individual contribution of the
consumer's loads from the power system, due to the
harmonic amplitudes that follow a vectorial summation
law.
2.2. Fluctuations of the harmonic voltage and
current
2.2.1. Principle
Considering the harmonic modelling of the
installation in Fig. 1, the harmonic voltage Vh can be
written as follows:
Vh = Z s .(I h 0 + I h )
(1)
Vh = Z c .(I hc − I h )
where every variable is in the complex form.
The following techniques are based on the principle
that the fluctuation of the harmonic current Ih is only
due to one side of the PCC: either the disturbing load
or the power system. The characteristics of the two
sub-systems can not vary simultaneously on the same
time interval. If the source and load impedances
(Z s , Z c ) and the fundamental voltage phase remain
constant during two successive measures, a current
variation modifies the resultant voltage in accordance
with two cases:
a) variation of I h 0 :
'
(
.(I
Vh = Z s . I h 0 + I h
'
Vh = Z c
− Ih
hc
'
'
)
)
(
'
)
'
)
(3)
= Z s . I h − I h = Z s .∆I h
where
∆I h is the measured variation of the current
I h . The source impedance is then deduced from (3):
∆Vh
Zs =
∆I h
(4)
'
(
= Z .(I
'
Vh
'
c
hc
− Ih
'
)
)
'
(5)
the fluctuation voltage is then:
(
'
'
)
∆Vh = Vh − Vh = Z c . I hc − I h − I hc + I h =
(
'
)
(6)
= Z c . − I h + I h = − Z c .∆I h
where
(7)
The real component of
Z s and Z c represents the
physical resistance of the two sub-circuits and their
values must be positive. In this way, the source and
load impedance can be alternatively determined by
the ratio of the harmonic voltage and current
fluctuations, called respectively ∆Vh and ∆I h , during
the time interval defined between two successive
measures:
 ∆V
If Re  h
 ∆I h

∆Vh
 f 0 then Z s =
∆I h

 ∆V
If Re  h
 ∆I h

∆V
 p 0 then Z c = − h
∆I h

The determination of
(8)
Z s and Z c allows then
estimating the equivalent current sources:
I hc = I h +
Vh
Zc
and
I h0 = I h +
Vh
Zs
(9)
The current emission of the disturbing load is
defined [6] by:
Z
I
h
emis
=I
c
(10)
hc Z + Z
c
s
.
The effects of random variations of the impedance
can be minimised by average on the results of several
measures. According to the sign of the real
component of the fluctuation ratio, the recorded data
are split into two groups.
The load impedance is estimated during the N
time intervals, when the harmonic source of the supply
system varies:
1 N ∆Vhi
Z =
c N ∑ ∆I
i = 1 hi
(11)
The same assessment applies to the source
impedance during the M time intervals, when the
harmonic source of the consumer varies:
b) variation of I h 0 :
Vh = Z s . I h 0 − I h
∆Vh
∆I h
2.2.2. Estimation of the mean values
∆Vh = V h − Vh = Z s . I h 0 + I h − I h 0 − I h =
'
Zc = −
(2)
the fluctuation voltage is then:
(
I h . The load impedance is then deduced from (6):
∆I h is the measured variation of the current
∆V
hj
1 M
Z =
∑
s M
j = 1 ∆I hj
(12)
The average values obtained with the last
technique are theoretically the right estimates of the
impedances, if their variations are due to a random
and stationary process. However, a moving average
can be more convenient if the impedance values are
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ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 55 (2007), Nr. 1
dependant to the time evolution. Then, considering K
successive time intervals when only one current
source fluctuates, the impedance at time k can be
assessed from the last useful measures:
∆V
k
1
hi
Z =
∑
k K
i = k − K + 1 ∆I hi
Z =Z
+
k
k −1
 ∆V
∆V
h
1  hk
k − K +1
+ 
−
K  ∆I
∆I
h
h
k
k − K +1

(13)





The advantage of this averaging technique is to
take into account the possible time variation of the
impedances and to give information about their
evolution.
Fig. 4. Fundamental voltage
and current versus time.
3. Applications
In order to apply the different existing methods,
measurements have been carried out on a mechanical
entreprise installation and his supply substation. At the
point of common coupling, harmonic voltages and
currents have been recorded during 24 hours (start at
0H00).
Amplitude and phase of each harmonic
component have been sampled every one second, on
the three lines, with a power analyser.
The 20kV/400V substation supplies alone this
mechanical enterprise, where the main disturbing load
is a laser device. As illustrated in Fig. 3, harmonic
currents and voltages are measured at the secondary
of the transformer. The specifications of the installation
allow us to estimate the equivalent source impedance:
Z s (mΩ ) = 4.46 + j ⋅ 11.1 at 50Hz
The recorded data are displayed in Fig. 4 and
rd
Fig. 5 for the fundamental and 3 harmonic of voltage
and current. The non-activity (0H – 6H) and operating
periods are clearly identified.
rd
Fig. 5. voltage and current versus time (3 harmonic).
4. Harmonic analysis of a rectifier
The goal of simulating the behavior of a charge
depending on injected power is performed in order to
clarify why the methods don’t give satisfactory results.
Using Matlab for calculating the parameters which
are interesed and based on the simulation scheme’s
(Fig. 6), we analyzed the active power depending on
the harmonics number (Fig. 7), phase and amplitude
of the voltage of the obtained power were calculated
as well. It can be seen that the third degree harmonic
has a negative sign.
Fig. 3. Electrical diagram of the mechanical enterprise.
Fig. 6. Simulation scheme PSIM.
17
By calculating for each harmonic and drawing the
graphs the equivalent impedance for different values
of harmonic tension we obtained the impedance’s
graph depending on the harmonic order (Fig. 8), from
which we can come to the conclusion that for negative
values the inverter is injecting power into the circuit.
ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 55 (2007), Nr. 1
Fig. 7. Harmonic power.
Simulations has been performed whithin the limits
of EN50160 standard, that stipulate for example, that
the limit for the third harmonic is 5%. Simulation have
been performed for scenarious on which the third
order harmonic is below and over 5% as well.
Fig. 8. The impedance’s graph depending on
the harmonic order.
Tab. 1.
h=3
2% U h
5% U h
8 %U h
P3
- 12,38
- 10,48
+ 14,15
5. Conclusion
Results were identical in scenarious in which the
limit was 2% U h and 5% U h , for those scenarious
whith a bigger than 5% limit: 8 % U h , the sign of the
third degree harmonic was positive (Tab. 1).
For a source nonlinear load at the same power, the
sign of the third harmonic can be change according to
the harmonic voltage of the supply. It can be noticed
that the others harmonic can change too.
We calculate the equivalent impedance for (each
measurement with harmonic - h ):
U
ch =  s
U
G
s  h
G
where: G
ch
=
2

P
 ⋅ h

P

s
(14)
1
Z
c
Different methods have been applied to an
industrial installation, in order to assess the harmonic
contribution of both the supplier and the consumer.
This paper presents the difficulties to evaluate the
impedance and then the harmonic emission of the
disturbing load.
Values for Z c and Gc vary with Vh , so the
conclusion is that we cannot get a constant voltage or
current variation. If the Z c p 0 the method which
determine the sign of
Re (∆Vh ∆I h ) cannot be
applied.
The simulations for a non-linear load reveals that
the sign of harmonic power changes according to the
harmonic voltage of the supply. Also it can be
observed that different voltage amplitudes change the
sense of that harmonic and also had impact on the
others harmonics ( U 3 modify I 5 ).
U s [V] – the RMS value of the nominal grid voltage;
The conclusion is then in accordance with the one
in [4]: In the present state of the art, no universal
method exits. Thus, further researches must be
carried on.
Ps [W] – the nominal delivered or dissipated active
References
G s - the conductance that let a current flow;
power (P ref is different for the operating modus of a
device);
U h [V] – the RMS value of the harmonic voltage
[1]
(h-th harmonic);
Ph [W] - the delivered or dissipated active power of
[2]
the h-th harmonic;
h – the harmonic number.
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1992.
18
[4]
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ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 55 (2007), Nr. 1
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