Modeling of Power System Components
Paulo F. Ribeiro, PhD, PE
BWX Technologies, Inc.
Product Development Department
Lynchburg, VA 25502
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A Complex Environment:
A Philosophical Reflection
These things are so delicate and numerous that it takes a
sense of great delicacy and precision to perceive them and
judge them correctly and accurately: Most often it is not
possible to set it out logically as in mathematics, because
the necessary principles are not ready at hand, and it
would be an endless task to undertake. The thing must be
seen all at once, at a glance, and not as a result of
progressive reasoning, at least up to a point.
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Blaise Pascal, 1650
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Outline
Introduction
General Considerations
The Modeling of Linear Loads
Recommended Models
Other Considerations
Sensitivity Tests
Modeling of Other Elements
Distribution Lines and Cables
Transformers
Rotating Machines
Induction Motors
Supply System Equivalent
Distribution System Example
The Need for a Complete Load Representation
Conclusions
3
Introduction
One difficulty in calculating harmonic voltages and currents throughout a
transmission system is the need for an adequate equivalent to represent the
distribution system and consumers' loads fed radially from each busbar.
It has become evident that the use of equivalents without a comprehensive
check on the effect of all impedances actually present can lead to inaccurate
estimation of harmonic voltages and currents in the transmission system. On the
other hand, it is not practicable to obtain and represent all the system details.
A detailed analysis of distribution systems, loads and other linear system
elements is presented, models discussed and a simple but more realistic approach
adopted. It consists basically of representing the dominant characteristics of the
network using alternative configurations and models. Simpler equivalents for
extended networks are also suggested.
4
General Considerations
Although further considerations leading to simpler equivalents are given later, the basic
assumptions used in this paper are as follows:
(1)
Distribution lines and cables (say, 69-33kV, for example) should be represented by an
equivalent pi. For short lines, estimate the total capacitance at each voltage level and
connect it at the termination buses.
(2) Transformers between distribution voltage level should be represented by an equivalent
element.
(3) As the active power absorbed by rotating machines does not correspond to a damping
value, the active and reactive power demand at the fundamental frequency may not be
used straightforwardly. Alternative models for load representation should be used
according to their composition and characteristics.
(4) Power factor correction (PFC) capacitance should be estimated as accurately as
possible and allocated at the corresponding voltage level.
(5) Other elements such as transmission line inductors, filters and generators should be
represented according to their actual configuration and composition.
(6) The representation should be more detailed nearer the points of interest. Simpler
equivalents, either for the transmission or distribution systems should be used only for
remote points.
(7) For distribution system studies, all the elements may be assumed to be uncoupled
three-phase branches with no mutuals, but allowing unbalanced parameters per phase.
5
230kV
69kV
loads
69kV
identical circuits
13.8kV
13.8kV
380kV
p.f.c.
cap.
A distribution system comprises a
number of loads conveniently
supplied by circuits from the nearest
distribution point. The distribution
circuit configuration depends on the
particular load requirements. In
general, a considerable number of
loads are located so close together
and supplied from the main
distribution point, that they can be
considered as a whole. For the
majority of installations, whether
supplying a small factory,
domestic/commercial consumers, or
a large plant, a simple radial system
is used. A typical distribution
network is shown in Figure 3.1
Figure 3.1: Typical distribution system configuration
6
A simplified dominant configuration can be derived as illustrated in Figure 3.2, based
on the basic assumptions. This arrangement would represent the dominant
characteristics (impedances) of the supply circuit fed radially from each transmission
busbar.
230kV
69kV
69kV
13.8kV
Figure 3.2
7
In order to simplify the manipulation of the distribution system, load and other
elements data, the following procedure based on the configuration of Figure 3.2, is
suggested. The dotted lines in Figure 3.3 mean different possibilities of connecting
the load or other elements such as, compensator filters, generator, etc. The total
equivalent impedance is then calculated at each harmonic frequency and connected
to the transmission busbar as a shunt element. Consequently, there is no alteration
of the dimension of the transmission system matrix. See illustration in Figures 3.3
and 3.4. A composition of different arrangements can be represented at the same
busbar.
p.f.c. cap.
Transf. 1
Line/Cable
Different
possibilities of
connection
Fig. 3.3
Transmission
System 3-phase
Representation
Transf. 2
Load &
Other
Elements
Distribution system
and other elements
Fig. 3.4
8
The Modeling of Loads
In this section, the modeling of individual elements is discussed in detail.
Considering that there is some disagreement regarding which harmonic models are
best for loads, transformers, generators, etc, various proposed models are
discussed. Also simpler equivalents for distribution and transmission systems at
remote points of the area of interest are discussed.
Consumers' loads play a very important part in the harmonic network
characteristic. They constitute not only the main element of the damping
component, but may affect the resonance conditions, particularly at higher
frequencies. Indeed, measurements have shown that maximum plant conditions
resulted in a lowering of the impedance at the lower frequencies, but cause an
increase at higher frequencies. Simulations have shown that the addition of load
can result in either an increase or decrease in harmonic flow.
Consequently, an adequate representation of the system loads is needed. However,
it is very hard to obtain detailed information about this. Moreover, as the general
loads consist of an aggregate number of components, it is difficult to establish a
model based on theoretical analysis.
9
The necessity of practical measurements on distribution points, at 13.8kV for
example, together with detailed information of the network under study, is vital
for the understanding and establishment of a realistic model. Attempts to deduce
a model from measurements have been made. However, more comprehensive
measurements and system data are needed.
Although practical experience is still insufficient to guarantee the best model,
system studies have to proceed with whatever information is available. Thus,
load characteristics are looked at in detail and alternative models developed in the
following.
A typical composition of consumers' plant may be as shown in Table 3.1 . From
Table 3.1, it seems evident that there are basically two sorts of linear loads -resistive and motive. That would imply a simple combination of resistances and
inductances. However, the difficulty in obtaining detailed information about
composition, power and variation with time makes the task very hard.
Nevertheless, it is possible to approach the problem of representing loads for
harmonic studies by using alternative models according to the load characteristics
and information available.
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TABLE 3.1 Load Composition
Nature
Type of Load
Domestic
Incandescent
Lamp
Compact
Fluorescent
Small Motors
Computers
Home Electronics
Incandescent
Lamp
Air Conditioner
Resistive Heater
Refrigeration
Washing Machine
Fluorescent Lamp
(Std)
ASDs
Fluorescent
(Electronics)
Computers
Other Electronic
Loads
Fan
Pump
Compressor
Resistive Heater
Arc Furnace
ASDs
Other Electronic
Loads
Commercial
Small
industrial
Plants
(Low
Voltage)
Electrical
Characteristics
Passive Resistive
Non-linear
Passive Inductive
Non-linear
Non-linear(*)
Passive Resistive
Passive Inductive
Passive Resistive
Passive Inductive
Passive Inductive
Non-linear(*)
Non-linear(*)
Non-linear(*)
Non-linear(*)
Non-linear(*)
(*)These loads are harmonic producing.
Hence, they do not exhibit a constant R, L,
or C, ie. they are non-linear and therefore
cannot be included in an equivalent network
of impedances. Fortunately, there is every
reason to believe they have insignificant
effect (open circuit) on the harmonic
impedance.
Passive Inductive
Passive Inductive
Passive Inductive
Passive Resistive
Non-linear(*)
Non-linear(*)
Non-linear(*)
11
Recommended Models
Loads are generally expressed by their active and reactive power P
and Q, respectively, which are used to calculate the equivalent
impedance for load flow studies at fundamental frequency, assuming
the system voltage. However, at harmonic frequency, P and Q
cannot be used straightforwardly because the active power absorbed
by a rotating machine does not exactly correspond to a damping
value and so additional information is necessary.
The following alternative models can be used according to the load
characteristics and information available:
12
A.
At harmonic frequencies, the reactive power estimated may have a
negligible effect in some cases. Thus, the P is considered equivalent to a
resistance of value R=V2/P, V being the nominal voltage at fundamental
frequency (see Figure 3.5). This representation should be used when the
motor part is very small, i.e. for commercial and domestic loads in which
the motive part is so partitioned that the resistive effect is predominant.
R
resistive part only
Fig. 3.5
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B.
The equivalent resistance is estimated as above, but with an inductance in parallel. This should
be evaluated using an estimation of the number of motors in service, their installed unitary power, not
demand, and their negative sequence inductance. However, if precise information on the number of motors,
etc. in use at any given time is unavailable, a fraction K of the total MW demand must be used to represent
the motor part. This is then multiplied by a factor of, for example, 1.2 in order to consider the installed
power which should be used. To calculate the equivalent negative sequence inductance, a factor K1,
proportional to the severity of the starting condition should be used. Therefore, we will have:
R=
where
P
K
K
K1
w
V2 _
P(1-K)
L = V2 ____ ______
1.2 (K+KE) K1 Pw
=total MW demand
=motor fraction of the total MW
=electronic controlled load fraction of
total MW
=severity of starting condition
= radian frequency
R
L
R
I
Fig. 3.6
K assumes values around 0.80 for industrial loads and around 0.15 for commercial and domestic loads. K1 assumes values
between 4 and 7. KE can assumes values around 0. It may well be that it is sufficiently accurate to ignore the resistive
component of the motor part. However, an additional resistance representing the motor damping can be included as R1=L/K2,
where K2 is a fraction of the negative sequence inductance or locked-rotor inductance. K2 assumes values around 0.20.
14
C.
When a big induction motor or group of motors are connected directly at
intermediate voltage levels, which is the case in industrial plants, the motive part is better
represented by a resistance in series with the negative sequence inductance of the motor.
The model can be assessed as follows: -- The equivalent resistance, the resistive part, and
the negative sequence inductance of the motor is estimated as in B, and the series resistance
estimated by R1 = wL/K3, where
K3
=effective Q of the motor circuit ~ 8
w
=radian fundamental frequency
Alternatively, a series inductance LT to represent the equivalent leakage
reactance of the distribution transformers at lower voltage connecting the resistance
load can be incorporated (see Figure 3.7). A value of wLT = 0.1R can be
assumed.
LT
R
1
L
R
Fig. 3.7
resistiv
e par
t
motive part
part
15
D.
This model was developed from experiments performed on medium voltage
outputs using audio-frequency ripple-control generators at EDF. The circuit suggested was
an inductance in series with a resistance. This branch was connected in parallel with
another inductance. The estimated P and Q are used in empirical formulae to calculate the
equivalent impedances. Thus, R = V2/P; L1 = 0.073R/w; L2 = R/(6.7tg(phi)-0.74)w;
tg(phi) = Q/P
L1
resistive
part
R
L2
motive part
Fig. 38
(See Figure 3.8). Although this model was obtained based on two frequencies only, 175 and 495Hz, and the
information available is not clear enough on how the equivalent circuit was derived, the parameters do not
differ substantially from models B and C. L2 seems equivalent to the motor part inductance and R/L1 to the
resistive circuit.
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Other Considerations
When the harmonic number increases, it is
necessary to use larger values of R. As no
information is yet available, a factor of h1/2,
where h is the harmonic order, seems a
reasonable value as a first approximation.
linear
load
Z
C
P.F.C.
capacitance
Fig. 3.9
The harmonic impedance of distribution systems and loads has actually been measured on
many locations. The results could not be satisfactorily reproduced digitally until the
downstream system from 33kV and capacitance at 415V were represented. Measurements
showed that there is a strong indication of an effect of power factor correction capacitance
on the harmonic impedance of 11kV, 33kV, and 132kV systems. Therefore, there are reasons
to believe that PFC capacitance should be represented. The PFC MVAr could be up to half
of the MW numerically, depending on the local PFC policy and system conditions, i.e.
whether maximum or minimum plant. Hence, the overall load representation should be as
Figure 3.9. The PFC MVAr should be represented as a fraction of the total MW estimated.
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3.3.3 Sensitivity Tests
In order to illustrate the sensitivity of the equivalent harmonic impedance with the load level
and composition, a set of examples is shown in Figures 3.10 to 3.12. Typical parameters for a
69 kV distribution system are used. The resistive, inductive, and capacitive parts of the load
are varied and the equivalent impedance calculated.
The examples show considerable variation in the equivalent impedance for variations of the
resistive and reactive components of the load. For instance, when the resistive part of the
load approximates the surge impedance of the line, the resonance effect is significantly
reduced (see Figure 3.10). Conversely, changes in the reactive part may affect considerably
the equivalent impedance. A general point is the magnitude of the peak impedance at
resonance.
These examples do show very clearly the importance of an accurate estimation and
representation of the distribution system and loads. Although the variations imposed seem
exaggerated, it is very likely that such deviations between the estimated and the actual
parameters may occur, as the information is not easily obtainable.
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Fig. 3.10
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Modeling of Other Elements
Distribution Lines and Cables
Distribution lines and cables are represented by their exact equivalent pi. An estimated
correction factor for skin effect is applied by increasing the line resistance with frequency
by:
0.646h2 )
192+0.518h2
R = R(0.187+0.532h1/2 )
R = R (1 +
lines
cables
Transformers
Complete representation of transformers, including capacitances, is not practical and cannot
be justified for harmonic frequencies. Experience has shown that capacitances start to have
some effect at 10KHz, i.e. well above the common harmonic frequencies present in power
systems, i.e. 2hkz. Transformer impedance is shown to be proportional to the leakage
reactance and linear with frequency. Various impedance representations have been
suggested. The following alternative models can be represented:-
20
A.
A resistance in series with the leakage inductance. Here a correction factor of
h1.15 can be used (See Figure 3.13).
R
L
Fig. 3.13
B.
The leakage reactance in parallel with a resistance. This is calculated by
multiplying a factor times the reactance. A factor of 80 has been suggested (See
Figure 3.14).
R
Fig. 3.14
L
C.
Pesonen et al suggested a resistance Rs in series with an assembly of inductance L
in parallel with a resistance Rp. Resistances Rs and Rp are constant whatever the frequency
and an estimate of their value can be obtained as provided by expressions:--
90<V2/SRs<110
13<SRp/V2<30
with S being the rated power of the transformer, (see Figure 3.15).
R1
R2
L
Fig. 3.15
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Rotating Machines
(a) Synchronous Generators
When non-linear currents/voltages appear in the stator of a synchronous machine, the fundamental component is
responsible for the energy conversion process and sets up a rotating mmf wave which reacts with the rotor mmf
to produce the resultant fundamental mmf gap flux. Conversely, the harmonic components set up mmf waves
rotating at different frequencies, but there is no armature reaction. Therefore, the reaction offered to harmonics
is not related to synchronous parameters but an equivalent impedance which should be a function of the leakage
path. Also, it may be assumed that synchronous machines produce no harmonic voltages, and they can be
represented by a shunt equivalent impedance.
However, the literature is not in agreement regarding appropriate impedances at harmonic frequencies.
Westinghouse, Williamson, and Pesonen et al suggest a reactance derived from either the subtransient or
negative sequence inductance:-X = 1/2(Xd"+Xq") =X2
Shilling suggest X = Xd", while Campbell and Murray suggest X =Xd'. Fresl suggests X =1/2(Xd"+X2), where
X2 = 1/2(Xd"+Xq"). Westinghouse suggests a correction of the equivalent inductance. This is because when
frequency increases, a smaller amount of flux penetrates the rotor. The amount is not known accurately but
normally taken as the unity for the fundamental and 0.8 at 1000Hz.
When using typical values of synchronous machine reactance to calculate the equivalent reactance X, it can be observed that the
subtransient reactance seems a reasonable value and should be used. A resistance representing the damping can be incorporated.
Electra 32 suggests a skin effect correction factor of h0.96. Regarding the equivalent circuit, Personen et al suggest a parallel
combination of R and L. Here a series combination is more appropriate, as the equivalent circuit of a synchronous generator can
be visualized as an induction motor for harmonic frequency. However, regarding practical values, the skin effect representation
and the way to combine the impedances will not cause any significant difference on the equivalent impedance. In the program, a
series or parallel combination can be used. Skin effect and inductance correction can be represented too. A damping resistance
based on the losses can be added for both series or parallel combination.
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(b)
Induction Motor
The well known configuration of an equivalent circuit of an inducting motor is shown in Figure 3.17a. The
slip, s, at harmonic frequencies s(h) is approximately equal to 1 as
s(h) = h±(1-s(1)/h) ~ 1, where s(1) ~0.02
With Xm negligible, the equivalent circuit in Figure 3.17 is a reasonable approximation. Here L is the
locked-rotor inductance, which can be calculated from the severity of starting condition. R is the damping
resistance which is derived from the motor losses. Induction motors are generally present as part of the load
and in a group of different sizes.
R
R
‘‘
L
R
1
L
L
1
L
‘‘
Ld
R 2 / 5(h)
1
(a)
R
d
m
2
L
L-- locked rotor
inductance
(a)
(b)
(b)
FIGURE 3.16: Synchronous generator representation
(a) Series combination
(b) Parallel combination
Fig. 3.17
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3.5
Supply System Equivalent
In supergrid studies there is a need for an equivalent of the transmission system as the
representation of the whole network is not practicable. A simple inductance based on the fault level
contribution has been used in the past, but its representation is clearly unsatisfactory. The factors
influencing the equivalent impedance are discussed and a simple but more realistic model is
adopted.
The harmonic impedance of a transmission system is determined/affected by factors such as fault
level, system loads, capacitance of lines and cables, compensations, etc. In general, an increase in
fault level reduces the harmonic impedance at lower frequencies. However, the behavior for higher
frequencies is unpredictable as small capacitance may have a dominant effect producing
resonances. Measurements have shown that in some cases the minimum impedance at the higher
frequencies occurred at the minimum fault level.
The net effect of increasing the load is to reduce the impedance to both fundamental and harmonic
frequencies. The combined effect of increasing generation and load is to reduce system resonances
by increasing system inductive elements and increasing the damping by lower resistance paths to
ground.
The effect of the line capacitance is to reduce the harmonic impedance for higher frequencies.
However, the combined effect with inductances may cause parallel resonances and, thus, having the
opposite effect.
24
There is no typical equivalent that can be used in any system without question, but measurements have
shown similar characteristics in the harmonic impedance of a transmission system. A general point is
the prominence of the first two resonance frequencies, i.e. parallel (wp) and series (ws). This can be
observed from Figures 3.18 and 3.19 Inspection of the impedance characteristic shows that a T circuit
can be assumed as in Figure 3.20a. This produces an impedance as in figure 3.20b, which represents the
system impedance more accurately than the fault level inductance when the necessary data are
available. There are reasons to believe that the inductive part is inversely proportional to the fault level
contribution. That is:L = L1 + L2 = (nominal voltage in kV)2
(fault level in MVA). 2.pi.f.
The line capacitance is responsible for the capacitance C in the circuit of Figure 3.20a. Thus, the
impedance is given by:
Z(w)=wL1 -[wL2.(1/wC)]/[wL2 -(1/wC)]=
=wL1 - [wL2/(w2L2 C-1)]
(1)
In order to give more flexibility to the model, the parameters L1, L2, and C. as a function of wp
and ws can be assessed. That is because the transmission lines determine fundamentally the
behavior of the a.c. network and thus wp and ws could be estimated from the knowledge of the
lines, which would better approximate the system impedance.
25
FIG. 3.18: Harmonic impedance of 132kV system
FIG. 3.19: Harmonic impedance of 132kV cable system
without local generation, minimum plant condition
26
FIG. 3.20:Transmission system equivalent model
27
L - fault level inductance -
p, s - frequencies of resonance
Equation (3.1) above is a second-order equation. Therefore, considering the two
frequencies where the parallel and series resonances occur, the equations can be solved
in terms of L1, L2, and C.
1. Z(wp) = infinite, therefore wp2L2C=1
C = 1/wpL2 = 1/wp2(L-L1)
2. Z(wS) = 0, therefore wSL1 = wSL2/(wS2L2C-1)
L1 = L2/(w22L2C-1), wS2L2C = 1+L2/L1 = L/L1
C = (L/L1)×(1/wS2L2)
Comparing C from (1) and (2), it will result:L1 = L(wp/ws)2 , and the equivalent circuit is completely determined .
Resistances in series with the inductances can be incorporated to provide a damping
component to attenuate resonance peak. In order to illustrate the accuracy of the model,
the measured impedances of Figures 3.18 and 3.19 are reconstructed in Figures 3.21 and
3.22, respectively.
28
FIG. 3.21 Calculated harmonic impedance 132kV system corresponding to measurements of Figure 3.23
FIG. 3.22: Calculated harmonic impedance 132 kV system corresponding to measurements of Figure 3.24
29
Distribution System Example
A simple, but typical 11 kV distribution
system, was modeled, as shown in
Figure 3.23. In the diagram the
consumer has a connected load of 865
kVA at a power factor of 0.8 lagging
and a power factor correction capacitor
of 250 kVA. The consumer wishes to
connect an adjustable speed drive using
a 6-pulse converter at the 11kV busbar.
The system fault level at the busbar,
including the transformer, is 30MVA
and the source impedance may be
considered as purely inductive. The
maximum harmonic currents (5th, 7th,
11th, and 13th) injected are specified
and typical for 6 pulse drives.
Figure 3.23 - System Schematic Diagram
30
In order to illustrate the influence of the load modeling in harmonic studies, Figures
3.24 to 3.26 show the equivalent harmonic impedance viewed from the 11 kV bus using
different load models. The dominant parallel resonance harmonic frequency is
estimated commonly by:
h
MVA sc
MVAr cap
which can be derived by finding the unity power-factor frequency of the system. This
calculation assuming no load indicates that the resonance frequency is around 10.95
times the fundamental frequency. At the resonance frequency, the impedance of the 11
kV bus becomes very large as it can be seen on Figure 3.24, when load model 1 is used.
Thus, significant voltage distortion may result at the 11th harmonic. The high
harmonic voltages will also result in high harmonic currents both in the capacitor bank
and the system reactance. A more detailed analysis, however, reveals that the
resonance frequency varies with the resistance of the system, and the amplitude of
equivalent harmonic impedance or the output voltage is not necessarily maximum at the
resonant frequency, and is also a function of the damping (resistance) of the circuit.
However, since current is only injected at the 11th harmonic, one does not need to
consider other frequencies, but rather remember the sensitivity of the system harmonic
impedance (around the resonance frequencies) to parameters variations.
31
Figure 3.24 - Equivalent 11 kV Frequency
Response Impedance - Load Represented by Series
Model 1
Figure 3.25 - Equivalent 11 kV Frequency Response
Impedance - Load Represented by Parallel Model 2
Figure 3.26 - Equivalent 11 kV Frequency
Response Impedance - Load Represented by
EdF/CIGRE Model 7
32
When the harmonic currents are injected, it can be observed that at the 11th harmonic the resultant
voltage obtained with a parallel representation(model 2) is 66 V or 1.04%, whereas with the series
representation (model 1), the 11th harmonic voltage on the 11kV bus was 332 V or 3.23%. Thus,
near the resonance parallel frequency, the impact of the load representation can be very significant.
Using an alternative series/parallel load representation (EdF model 7), the frequency response of the
equivalent impedance is shown below in Figure 3.26. Two important facts can be noted. First the
resultant voltage on the 11kV bus was now 48 V or 0.69%. Second the resonant frequency shifted
slightly higher (from 11th harmonic to near the 13th harmonic). Table 2 shows a summary of the
cases simulated where the model and load and composition were varied.
Table 2 - Load Modeling and Conditions Simulated
Case
Linear Load Model
Case 1
No Load Representation
Case 2
P, Q - Basic Load Flow
Case 3
P, Q - Basic Load Flow
Case 4
50% Induction Motor
Case 5
25 % Induction Motor
Case 6
50% Induction Motor
Case 7
75% Induction Motor
Case 8
90% Induction Motor
Case 9
25% Ind. Motor + Skin Effect
Case 10
75% Ind. Motor + Skin Effect
33
Skin effect was included in cases 9 and 10 to account for the impact on the system
impedance of the frequency dependence of the resistive component of the load. Figure
3.28 illustrates the amplitude of the 5th and 11th harmonic voltage (%) at the 11 kV bus
for all models used.
Figure 3.29 demonstrates more clearly how much the resultant voltage can vary depending
on the model and load composition used. When comparing to standards such as the
IEEE 519, it becomes clear that the violation of the standard may depend on the load
model used for the calculation of the resultant distortion.
Modeling loads using just the economic model (P and Q only) is inadequate for harmonic
studies. No load (case 1) representation should not be used for harmonic studies. The load
models suggested in the literature can not be used indiscriminately without a
comprehensive check of the actual load characteristics and composition. The appropriate
representation is particularly crucial near the parallel resonant frequencies of the system,
exactly where an accurate estimation of the system behavior is most necessary. Frequency
response of the system impedance is sensitive to both the methodology
(modeling/topology) and the actual load composition. A comprehensive list of linear load
models for harmonic studies found in the literature is illustrated in Annex 1
34
Figure 3.28- Harmonic Voltage (%) for Different Load Model
100
V5 (% )
V1 1 (% )
10
1
C a se
1 C a se C a se
2
3 C a se C a se
4
5 C a se
C a se
6
C a se
7
8
0 .1
C a se
9
C a se
10
V 5 (% )
V 1 1 (% )
4
3.5
3
V5 (%)
V11(%)
2.5
2
1.5
1
Case
3 Case
4 Case
5 Case
6 Case
Case
7
8
0.5
Figure 3.29- Harmonic Voltage (%) at the 11kV Bus
for Different Load Models
0
Case
9
Case
10
V11(%)
V5 (%)
35
The Need for a Complete Load Representation
General loads in a transmission or distribution
system are generally expressed by their active and
reactive power P and Q, respectively, which are
used to calculate the equivalent impedance
for load flow studies at the fundamental frequency,
assuming the system voltage. However, at harmonic
frequencies, P and Q cannot be used directly because,
for example, the power absorbed by rotating machines
does not exactly correspond to a damping value,
Fig. 3.30
neither does the motor equivalent inductance bear any
direct or simple relationship to the reactive power
estimated at the fundamental frequency. In addition a measurable percentage of any general load nowadays is electronically
controlled and needs to be properly represented. Electronic loads are harmonic producing and consequently do not exhibit a
constant R, L or C. Therefore, they cannot be included as part of the passive component of the equivalent impedance.
They should be represented by a harmonic source at all frequencies of importance. With the proliferation of the utilization
of power electronics, a progressive conversion of traditionally linear loads to electronically controlled will happen.
Another component normally overlooked in harmonic studies is the Power Factor Correction capacitance of distribution
systems. Measurements have shown that there is a strong correlation of the effect of power factor connection capacitance on
the harmonic impedance of distribution systems. The PFC MVAr could be up to half of the MW numerically, depending on
the local PFC policy and system conditions.
Therefore, the proposed model shown in Figure 3.30 makes an attempt to incorporate all these aspects in the modeling
general loads for harmonic studies, and consequently make the so called general, normal or "linear" load representation for
harmonic studies much more realistic. Detailed research should be carried out to assess the actual load composition and
determine the proper representation and parameters of each load or aggregate of loads.
The equivalent impedance should consist of a combination of series and parallel combination of resistances, inductances,
capacitances, and harmonic current source as indicated in Figure 3.30.
36
Since the reactive power of the load estimated at the fundamental frequency has little to do with the
equivalent impedance of the load at harmonic frequencies, it is suggested that Q (estimated for the load
without any PFC) should be totally disregarded for the estimation of the equivalent harmonic impedance
of the load. Thus, starting with the total active power P and additional information about the load
composition, the following procedure is suggested for calculating parameters for harmonic studies.
V = System Voltage
XL1 = Transformer Reactance
C1 = Estimated Capacitance of the Load
I1 = Estimated Harmonic Current Source
where
P
=
Total Active Power
K
=
Fraction of Induction Motors
KE
=
Fraction of Electronic Loads
R1
=
Equivalent resistance representing the purely resistive component
of the load factor for skin effect correction
XL2
=
Equivalent inductance representing the induction motors
R2
=
Damping factor for the induction motor representation
K1
=
Severity of Starting Condition
Km
=
Installed Motor Factor
K2
=
Fraction of the locked-rotor (or negative sequence) inductance
h
=
Harmonic order
XL1
=
Leakage inductance of transformers at lower voltages connecting
the resistive load
I1
=
Ideal harmonic current source (use typical values according to type
of load feeder).
37
The resistance R1 is estimated from the actual resistive load connected to the
bus, that is, discounting the induction motor and electronic load part. The skin
effect can be incorporated in the equivalent resistance by choosing an
appropriate factor as indicated. The inductance of the induction motors should
be evaluated using an estimation of the fraction of the total load that represents
induction motors and their installed unitary power (not the demand). Also a
factor K1 representing the severity of the starting condition should be used to
calculate the equivalent inductance. R2 represents the damping component of
the equivalent induction motor impedance. Also background distortion should
not be neglected. Harmonic simulation studies will have to include background
distortion if they are to be become more accurate. Background distortion can
increase or decrease the resultant distortion depending on phase relationship. A
harmonic current or voltage source representing the harmonic contribution of
the non-linear component of the load must be modeled.
38
Conclusions
This document demonstrates that the representation of the power system loads and extended
networks can be improved by using alternative models. The distribution system, loads,
other elements and equivalents of extended networks have been considered in detail. The
models developed allow a more realistic representation of the system and, consequently, a
more accurate assessment of the harmonic currents and voltages throughout the
transmission network. Guidance has been provided on modeling of individual loads and on
typical load composition. System tests are necessary to provide verification of the
modeling methodology developed, as well as adding to the knowledge of system load
characteristics.
This paper demonstrates that the representation of linear elements is very important for
harmonic studies and should not be neglected or represented without full consideration of
the load characteristics and composition. Guidance has been provided on modeling of
individual loads and on typical load composition. System tests are necessary to provide
verification of the modeling methodology developed, as well as adding to the knowledge of
system load characteristics.
Consequences regarding system predictions: Wrong indication of excessive high harmonic
distortion. And don't be fooled: utilization of sophisticated harmonic penetration programs
with inaccurate basic information, and or inadequate modeling is a waste of money, and the
consequences of the interpretation of the results might cost even more. Remember: that the
accuracy of any calculation cannot be better than the data on which it is based.
39
Model 4
Parallel
Combination
Model
Description
Model 1
Series
Combination
(Common
Practice)
From P and Q
Model 2
Parallel
Combination 1
(Common
Practice)
From P and Q
plus skin effect
Model 3
Parallel
Combination 2
From Pand
fraction of
induction
motors
Equivalent Circuit
From P and
fraction of
motors
Model 5
Series/Parallel
Combination 1
(CIGRE/EdF
Model)
Model 6
Series/Parallel
Combination 2
Error! Bookmark not
defined.
Model 7
Series/Parallel
Combination 2
From P,
inductance of
distributioon
transformers
and induction
motors
40