HARMONIC MODELLING OF DISTORTING LOADS ON DISTRIBUTION

FEEDERS AND IN A LARGE POWER SYSTEM

M.Ghezelayagh V.J.Gosbell
(B.Sc,MS.c,Ph.D) (B.Sc,MS.c,Ph.D)
Power &Water Authority Electrical&Computer Engineering Dept
Darwin,Australia University of Wollongong, Australia
Tel : (08)89245086 Tel : (042)213402
E-mail:Maty.ghezelayagh/PAWA@PAWA E-mail : V.gosbell@UOW.edu.au

Abstract

In most of frequency response type program, it is common to assume that

all harmonic sources have the same phase angle. In this paper this
assumption is investigated for distorting loads with diode rectifier
front ends. Based on these investigation correct equivalent models of
distorting loads are proposed firstly on one distribution feeder and
secondly for distribution feeders in different subsystems of a large
network. For the purpose of these investigations a Power Electronic
Simulator (PES) with Time Domain solution has been used.

1. INTRODUCTION The assumption of equal phase

angle might seem reasonable for
Proposed installations of harmonic sources with diode
harmonic sources can be checked rectifiers such as AC derives but
to see if they will meet deserves closer investigation. In
standards by means of harmonic this paper this assumption is
analysis computer programs(1-2). investigated first for
Most cases can be conveniently representation of loads on one
and easily examined by a distribution feeder and secondly
frequency response type program for distribution feeders in
where harmonic sources are different subsystems. The first
represented by a parallel investigation is useful when
connection of ideal ac current harmonics analysis of a single
sources at each harmonic feeder is made by the frequency
frequency. Due to lack of data, domain computer program. The
it is common to assume that all second case is for calculation of
harmonic sources have the same harmonic distortion level in a
phase angle (normally zero). large interconnected network.
This gives a worst case result in
most cases. 2. METHODOLOGY

In an attempt at more realistic For investigation of the

results, some studies have assumption of equal phase angle of
assumed a random distribution of loads on one distribution feeder,
phase angles(3-4). This may be the phase angle at each harmonic
applicable where most of the order and variation of the phase
sources are SCR rectifiers (e.g angle of the harmonic current
DC drives) where the firing angle injected by the rectifier is
vary independently. However, it obtained with respect to the size
is expected in future that most of the rectifier and the condition
harmonic sources will have diode of its connection to the system
rectifier front ends where the (sensitivity analysis). If this
variations in the phase angle is variation is not significant, then
much more restricted. this assumption can be correct
provided correct equal phase angle
is assumed. For the purpose of flexibility in constructing models
the sensitivity analysis a Power for complex devices. These models
Electronic Simulator (PES)[5] has include switched mode power
been used. supplies, power converters,ac and
dc motors.
The results of obtained
sensitivity analysis is verified 3)The output is shown on the
by studying a typical screen graphically . A harmonic
distribution feeder with two spectrum facility is available.
rectifiers. In this study first
the harmonic current and voltage 4. INVESTIGATION ON THE ACCURACY
distortion level of a feeder with OF ASSUMPTION OF EQUAL PHASE ANGLE
two rectifiers for different FOR HARMONIC SOURCES
system conditions are obtained by
PES. Then the rectifiers are The assumption of equal phase
replaced with two equivalent angle is investigated first for
harmonic sources with equal phase representation of loads on one
angles as obtained before and distribution feeder and secondly
harmonic current and voltage for distribution feeders in
distortion levels are obtained different subsystems.
for the same system conditions.
Comparison between the two cases 4.1 Loads On One Distribution
gives the accuracy of the Feeder
assumption of equal phase angles
for the harmonic sources with Assume a distribution feeder
rectifiers. supplies “n” harmonic sources
connected at different locations
For representation of as shown in Figure 1. The phase
distribution feeders in different angle of the nth harmonic current
subsystem with ideal current source is assumed to be (θn)h for
sources, the results obtained harmonic order h with respect to
from the first case is used to absolute reference. The harmonic
give the required phase angles of sources can be modelled with equal
the equivalent harmonic current phase angle for harmonic current
sources. only if the difference of the
phase angle of the sources are
3.POWER ELECTRONIC SIMULATION negligible. One method to
PROGRAM investigate is to find the
variation of the harmonic current
In all of system studies in this phase angle of one diode rectifier
paper, Power Electronic with respect to system parameters
Simulation Program [5] has been at each harmonic order .
used to obtain current and
voltage in time domain. By the Pcc xd (θ1)h
aide of spectrum analysis which xs
is part of the simulator,
harmonic current and voltage can
be calculated. Generally (PES)
calculates circuits in which (θn)h
electronic devices are used as
switches. It has some advantages
over existing methods in harmonic Figure 1: A Typical Distribution
studies. The main features of Feeder
PES are :
4.1.1 Sensitivity Analysis
1)The circuit input is by means
of a circuit schematic drawn on For sensitivity analysis first it
the screen. is assumed that only one rectifier
has been connected to the system.
2)The built in models have been With this condition the effect of
chosen to give a lot of the following system parameters on
the phase angle is investigated.
-Size of the rectifier Table 2 : Harmonic level at PCC
-Fault level at the PCC
-Reactance of distribution line Harmonic Harmonic Harmonic
-Combination of above cases. order Current(A) Voltage(V)
1 73.4 19480
Table 1 shows different cases for 5 49 231
7 31.3 207
the performance of the
11 7 62
sensitivity analysis. The studied 13 5.4 61
cases represent weak and strong 17 3.3 58
power systems, light and heavy 19 1.9 38
loaded feeder. In all cases a 23 1.5 30
capacitor filtered diode 25 0.9 23
rectifier as shown in Figure 2
has been considered. Each 4.1.2 Calculation of the Harmonic
rectifier capacitor in the model Current Phase Angle of the
has been connected in series with Rectifier at Each Harmonic Order
a DC voltage (equal to L-L
voltage of the transformer To obtain the phase angle of the
secondary (5.6KV) for initial rectifier, the rectifier is
capacitor charging and the replaced by a two phase equivalent
damping of the initial transient harmonic current source as shown
waveshapes. The current in Table in Figure 3. A two phase
1 is the magnitude of the current equivalent source is sufficient to
source IA as shown in Figure 2. represent three phase system under
It is assumed that the system balanced system conditions. Each
primary voltage is 13.8KV line- harmonic current source is
line and the rectifier is controlled by a voltage probe. The
connected to the system by delta- voltage probe is connected across
delta transformer with a ratio of a series of harmonic voltage
3.3. The other parameters on sources.
Table 1 have been defined in
Figure 1. In order to obtain the same system
condition with the equivalent
Table 2 gives the magnitude of harmonic source as the rectifier,
the harmonic current and voltage two factors should be considered.
distortion level. Note that PES First the harmonic current
gives peak current and voltage. injection level by the equivalent
current source should be the same
Va Vb Vc as the replaced rectifier. This is
achieved with a suitable selection

+ Vp1 -
IA
Va Vb Vc

~ ~

I1 I2 Vp2
~ ~
Figure 2 :Distorting Load Model
Figure 3 : Harmonic source as
modelled in PES
Table 1 :System Parameters
of voltage magnitude at each
Sys Base Case Case Case
param case (i) (ii) (iii)
harmonic in harmonic voltage
IA 0.014 0.036 0.036 0.072 source circuit. Secondly the
(xd) 0.047 0.047 0.047 0.148 waveshape of the harmonic current
(xs) 0.28 0.28 0.84 0.28 distortion level at the PCC should
be the same for the two cases.
All values in PU on 100MVA, 13.8KV This is achieved by adjustment of
the phase angles of the harmonic system. The power system is
voltage source at each harmonic. assumed to be balanced and is
Table 3 gives the required phase modelled by its equivalent
angles for equivalent harmonic Thevenin model reactance derived
source at each harmonic. Hence from short circuit studies. The
the obtained phase angles are system voltage level and other
with respect to the fundamental parameters are the same as in
system voltage at the PCC (zero Section 4.
for phase “a”).
For investigation of the
Table 3 : phase angle and assumption of equal phase angle of
Magnitude of the harmonic current two rectifiers, two stages are
considered. In Stage 1 the
Harmonic Angle Mag(A) magnitude of the harmonic current
order (phase a) and voltage distortion level of a
1 -10 73.4 feeder with two rectifiers are
5 120 49
7 -90 31.3
obtained for different system
11 -120 7 conditions. Then in Stage 2 the
13 60 5.4 rectifiers are replaced with two
17 90 3.3 harmonic sources with equal phase
19 30 1.9 angles with the same system
23 180 1.5
conditions as the two rectifiers.
25 180 0.9
The assumed equal phase angle at
each harmonic order is according
Similar procedure was performed to phase angles as shown on Table
to obtain the phase angle of the 3. The comparison between the
rectifier for other cases as results of the two stages gives
shown in Table 1. It was found the accuracy of the assumption of
that the variation of the phase the equal phase angles. Different
angle up to the 13th harmonic is cases regarding to the size of
less than 15% as compared with rectifier and system parameters as
the base case. This indicated shown in Table 4 have been
that harmonic sources with diode considered. Table 5 shows the
rectifier can be represented with harmonic current and voltage
ideal current sources and equal distortion level for Case (i).
phase angles in computer programs Similar results were obtained for
for harmonic order up to 13th other cases. The results are the
provided the assumed phase angle bench-mark for the subsequent
for each harmonic order to be comparisons.
according to Table 3. It is
important to notice that the
Table 4 : System Parameters
assumption of equal zero phase
angle (normal practice) gives
Sys- Base Case Case Case Case
significant error. param case (i) (ii) (iii) (iv)
(IA)1 0.014 0.036 0.014 0.014 0.036
In the next section this (IA)2 0.021 0.072 0.021 0.021 0.072
conclusion is verified for a xs 0.28 0.28 0.28 0.84 0.28
typical distribution feeder with xd 0.047 0.047 0.148 0.047 0.148
All values in PU on 100 MVA and 13.8 KV
two harmonic sources with diode base
rectifiers.
Table 5 :Harmonics for case (i)
4.1.3 : Accuracy on the
Assumption of Equal Phase Angle
Harm- I1(A) I2(A) Ipcc(A Vpcc(V)
on A Distribution Feeder with Two order )
Rectifiers 1 166 331 498 19460
5 65 98 164 765
The distribution feeder selected 7 25 30 49 330
for investigation of the 11 13 22 33 335
13 6 13 15 192
assumption of equal phase angle 17 6 9 12 176
for harmonic sources is as shown 19 3 8 8 139
in Figure 1 but with only two 23 3 5 5 101
rectifiers connected to the 25 2 5 4 99
In order to validate the buses(PCCs) for each harmonic by
assumption of equal phase angle, I1∠α1, I2∠α2... Ir∠αr...and
the two rectifiers are replaced In∠αn where αr is the phase
with two equivalent harmonic angle with respect to the phase
sources and equal phase angles. angle of the fundamental system
The harmonic current is obtained voltages at the PCC. If the
for various cases as shown in feeders supply only harmonic
Table 4. Table 6 shows the error sources with diode rectifiers,
of the magnitude of harmonic then all angles of the harmonic
current at the PCC if rectifiers current sources at each harmonic
are replaced with equivalent with respect to the fundamental
harmonic sources. It is observed system voltages can be assumed
that up to 13the harmonic the
equal to ‘α’ for example :
error is less than 15%. This is
consistent with results obtained
in Section 4. α1=α2=.....=αn=α

The phase angle of each harmonic

Table 6: % Error for Cases source with respect to common
reference for each harmonic source
Harm- Case Case Case Case
order (i) (ii) (iii) (iv) is obtained as: φr=θr-α. The
1 0 0 0 0 harmonic voltage distortion level
5 0 0 2 0.8 is calculated from :
7 12 3 3 20
11 6 9 8 13 Vh=Zh.Ih
13 25 10 9 50
17 23 18 20 50
19 31 21 20 64 By writing the equation in terms
23 69 28 28 160 of the magnitude and the phase
25 56 34 33 130 angle , it can be shown that the
magnitude of the harmonic voltage
5. MODELLING OF THE DISTRIBUTION is independent of the phase angle
FEEDERS IN DIFFERENT SUBSYSTEMS ‘α’. Consequently each harmonic
source (distribution feeder) can
In Section 4, it has been shown be modelled as an ideal current
that the harmonic sources with source with the phase angle equal
diode rectifiers in one to the phase angle of the
distribution feeder can be fundamental system voltages at its
represented by ideal current PCC.
source with equal phase angles
for only low order harmonics. In 6. CONCLUSIONS
this section this assumption is
investigated for distribution In most of the frequency domain
feeders in different subsystems. harmonic analysis program, it is
Based on this investigation the common to represent all harmonic
required phase angle of the ideal current sources with ideal ac
ac current source for current sources and zero phase
representation of distribution angle with respect to the absolute
feeders in the computer programs reference. This is due to lack of
are given. sufficient data regarding the
phase angles. In this paper this
Assume that the phase angles of assumption was investigated
the fundamental system voltage at firstly for the loads on one
the PCCs(where the distribution distribution feeder and secondly
feeders are connected) with for distribution feeders in
respect to the system common different subsystems. It has been
reference are θ1,θ2 , ..,θr...and assumed that the loads have diode
θn. These angles can be obtained rectifier front ends.
from normal load flow. Let us
assume the distribution feeders For modelling of harmonic sources
are represented as harmonic on one distribution feeder it has
current sources at different been found that the assumption of
equal phase angle for harmonic [1] ‘Harmonic Analysis Program’.
sources can be used only for VHARM, Power Technologies Inc,
harmonics up to the 13th provided U.S.A
the correct phase angle is [2] ‘Frequency Analysis Program’,
assumed FREESCA-386, ABB Network Control
at each harmonic order(e.g 120° LTD, TURGI/Switzerland.
for 5th harmonic).
[3] CARPIELLI, G, GAGLIARDI,P :
For modelling of distribution ‘Probabilistic Modelling for
feeders in different subsystems Harmonic Penetration Studies in
with ideal current sources, it Power Systems’, ICHPS V, 1992,
was found that the phase angle of PP.35-40.
the equivalent source should be
equal to the phase angle of the [4] EMANUEL A.E, KAPRIELIAN S.R :’
fundamental system voltage at the Contribution to the Theory of
PCC where the distribution feeder Statistically Periodic Harmonics
has been connected otherwise an in Power Systems, IEEE Trans on
error of up to 20% may occur. Power Delivery, Vol.PWRD,
No.3,1986, PP 285-292.
The obtained results in this
paper can be used in the [5] GOSBEOLL V.J, SCOTT J.D :
frequency domain computer program ‘Simulation of Power Electronic
for harmonic modelling of Circuits’. National Energy
distorting loads. Research Development and
Demonstration Council, Australian
7. REFERNCES Report 1185, 1991.