CHAPTER 3

DISTRIBUTION SYSTEM AND OTHER ELEMENTS MODELING

Paulo F. Ribeiro

BWX Technologies, Inc.

Naval Nuclear Fuel Division

Lynchburg, VA 24505-0785

3.1 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 system elements is carried out, 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. Also

simpler equivalents for extended networks are suggested.

3.2 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 and 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.

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.1

A typical distribution network is shown in Figure 3.1

Figure 3.1: Typical distribution system configuration

A simplified dominant configuration can be derived

as illustrated in Figure 3.2, based on the basic assumptions.

This arrangement would represent the dominant

13.8kV

380kV

13.8kV

69kV identical circuits

loads p.f.c.

cap.

230kV

69kV

230 kV

69 kV

p.f.c.

cap.

identical circuits 69kV

13.8 kV

380 V

characteristics (impedances) of the supply circuit fed radially

from each transmission busbar.

Figure 3.2: Dominant arrangement

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 in star-grounded 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.

Figure 3.3: Distribution system, loads and other elements

3.3 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., 2 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 3 have shown that maximum plant

conditions resulted in a lowering of the impedance at the

lower frequencies, but cause an increase at higher

frequencies. Mahmoud and Shultz4 observed in simulations

that the addition of load can result in either an increase or

decrease in harmonic flow.

Figure 3.4: Overall System representation

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.

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. See Bergeal et al5 and Baker

6. 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 load

composition may be as shown in Table 3.1 . From Table 3.1,

it seems evident that there are basically two sorts of 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.

3.3.1 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.

230kV 69kV 69kV 13.8kV

p.f.c. cap.

Transf. 1 Line/Cable Transf. 2

Load &

Other

Elements

Different

possibilities of

connection

Trans.

system

busbar

Transmission

System 3-phase

Representation

Distribution system

and other elements

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:

TABLE 3.1 Load Composition

Nature Type of Load Electrical

Characteristics

Domestic Incandescent

Lamp

Compact

Fluorescent

Small Motors

Computers

Home Electronics

Passive Resistive

Non-linear

Passive Inductive

Non-linear (*)

Non-linear(*)

Commercial Incandescent

Lamp

Air Conditioner

Resistive Heater

Refrigeration

Washing Machine

Fluorescent Lamp

ASDs

Fluorescent

(Electronics)

Computers

Other Elect. Loads

Passive Resistive

Passive Inductive

Passive Resistive

Passive Inductive

Passive Inductive

Non-linear(*)

Non-linear(*)

Non-linear(*)

Non-linear(*)

Non-linear(*)

Non-linear(*)

Small

industrial

Plants

(Low

Voltage)

Fan

Pump

Compressor

Resistive Heater

Arc Furnace

ASDs

Other Electronic

Loads

Passive Inductive

Passive Inductive

Passive Inductive

Passive Resistive

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 and may be neglected.

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 rotating machinery part is so

partitioned that the resistive effect s predominant.

Figure 3.5: Load model A

Figure 3.6: Load model B

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, as 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. This

model is a combination of common practices.

Therefore, one can have:

R = V2 ____ L = V

2 ____

P(1-K-KE) 1.2 K1 PK

where P = total MW demand

K = motor fraction of the total MW

KE = electronic controlled load fraction of

total MW

K1 = severity of starting condition

= radian frequency

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 assume values

between 0.1 and 0.4. It may well be that it is sufficiently

R

resistive part

only

resistive

part motor part

I R

R L

accurate to ignore the resistive component of the motor part.

However, an additional resistance representing the motor

damping can be included as R1=Lw/K2, where K2 is a

fraction of the negative sequence inductance or locked-rotor

inductance. K2 assumes values around 0.20.

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 rotating

machinery 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 R = L/K3, where

K3 = effective Q of the motor circuit ~ 8

= 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 LT = 0.1R can be

assumed.

D. This model (also called CIGRE Model) was

developed from experiments performed on medium

voltage outputs using audio-frequency ripple-

control generators at EDF7. 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/; L2 = R/(6.7tg(phi)-0.74)

;

tg(phi) = Q/P (See Figure 3.8).

Although this model was obtained based on two

frequencies only, 175 and 495Hz, and the

information available is not clear enough8 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.

Figure 3.7: Load model C

Obs. With the approach adopted, a composite load model at

the transmission system substation can be represented. The

expected effect is a better representation of the load. Since

most supply electricity companies have not thoroughly

studied their own loads, a comprehensive investigation of the

load composition is necessary to enable the engineer to

choose a better model or composition of models based on an

estimate of the system load.

Figure 3.8: Load model D (CIGRE Model)

3.3.2 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. Pesonen

et al(2)

have suggested a factor of approximately 0.6h1/2

.

The harmonic impedance of distribution systems and loads

has actually been measured on a few sites in the U.K. The

results could not be satisfactorily reproduced digitally until

the downstream system from 33kV and capacitance at 415V

were represented9. Measurements, Baker

6 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

R

L 1

L 2

resistive

part motor part

resistive

part motor part part

L T 1

R L

R

representation should be as Figure 3.9. The PFC MVAr

should be represented as a fraction of the total MW

estimated.

Figure 3.9: Overall load representation

3.3.3 Sensitivity Tests

In order to illustrate the sensitivity of the equivalent

harmonic impedance with the load level and composition

several examples were simulated using typical parameters for

a 69 kV distribution system. The resistive, inductive, and

capacitive parts of the load are varied and the equivalent

impedance calculated.

The results 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.

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.

3.4 Modeling of Other Elements

3.4.1 Distribution Lines and Cables

Distribution lines and cables are represented by their exact

equivalent pi11

. An estimated correction factor for skin effect

is applied by increasing the line resistance with frequency

by:

R = R (1 + 0.646h2 ) lines

192+0.518h2

R = R(0.187+0.532h1/2

) cables

3.4.2 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 an linear with

frequency. Various impedance representations have been

suggested. The following alternative models can be

represented:-

A. A resistance in series with the leakage inductance.

Here a correction factor of h1.15

can be used10

(See

Figure 3.10).

FIG. 3.10 Transformer model A

B. The leakage reactance in parallel with a resistance.

This is calculated by multiplying a factor times the

reactance. A factor of 80 is suggested in the CEGB

program11

(See Figure 3.11).

FIG. 3.11 Transformer model B

C. Pesonen et al2

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

FIG. 3.12 Transformer model C

3.4.3 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, 12

Williamson,13

and

Pesonen et al2 suggest a reactance derived from

either the subtransient or negative sequence

inductance:--

X = 1/2(Xd"+Xq") =X2

Shilling14

suggest X = Xd", while Campbell and

Murray15

suggest X = Xd'. Fresl16

suggests X

=1/2(Xd"+X2), where X2 = 1/2(Xd"+Xq").

Westinghouse12

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 3211

suggests a skin effect

correction factor of h0.96

. Regarding the equivalent

circuit, Personen et al2 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.

(b) Induction Motor

The well known configuration of an

equivalent circuit of an inducting motor is shown in

Figure 3.14a. 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

3.14b 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. For detailed analysis, see

Chalmers17

and Klingshirn and Jordan18

. Induction motors

are generally present as part of the load and in a group of

R

L

R R 2 R 2 R 1

R

R

R L d

L d

L d

(a) (b) (a)

FIGURE 3.13: Synchronous generator representation

(a) Series combination

(b) Parallel combination

FIG. 3.14 Induction motor representation

(a) Complete representation

(b) Equivalent harmonic model

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.

Measurements3 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, have the opposite effect.

3.5 Distribution System Example A simple, but typical distribution system was

modeled with the following characterisitcs: A customer load

of 865 kVA at a power factor of 0.8 lagging and a power

factor correction capacitor of 250 kVA is connected to a 11

kV bus. The customer 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.

The dominant parallel resonance harmonic

frequency is estimated commonly by:

hMVA

MVAr

sc

cap

and which can be derived by finding the unity power-factor

frequency of the system. This calculation reveals 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. 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.

When the harmonic currents are injected, it can be

observed that at the 11th harmonic, the resultant voltage

obtained with a parallel representation(Model B) is 66 V or

1.04%, whereas with the series representation (Model A), 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

or CIGRE Model), the frequency response of the equivalent

impedance is slightly altered. 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

R1 L 2 L1

L m R2 /s(h)

R L

L - locked rotor

inductance

(a

)

(b

)

Figure 3.15- Harmonic Voltage (%) for Different Load

Model

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 3.15 illustrates the amplitude of the 5th and 11th

harmonic voltage (%) at the 11 kV bus for all models used.

Case

3 Case

4 Case

5 Case

6 Case

7 Case

8 Case

9 Case

10V5 (%)

V11(%)

0

0.5

1

1.5

2

2.5

3

3.5

4

V5 (%)

V11(%)

Figure 3.16- Harmonic Voltage (%) at the 11kV Bus for

Different Load Models

Figure 3.16 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, as far as the harmonic voltages are concerned, 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.

3.6 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, 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

correction 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

3.17 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 3.17.

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

Case

1 Case

2 Case

3 Case

4 Case

5 Case

6 Case

7 Case

8 Case

9 Case

10V5 (%)

V11(%)

0.1

1

10

100

V5 (%)

V11(%)

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.

Figure 3.17 - General Load Representation for Harmonic

Studies

R

V

P K KEh1

1

2

, XL

V

KmKK Ph2

1

2

.

RXL

K2

2

2

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).

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.

3.7 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.

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. Never forget that the accuracy

of any calculation cannot be better than the data on which it

is based.

References

1 ROLLS, T.B., Power Distribution in Industrial Installations,

IEE Monograph Series 10, 1972. 2 PERSONEN, M.A., Harmonics, Characteristic Parameters,

Methods of Study, Estimates of Existing Values in the Network,

Electra, Vol. 77, pp. 35-54, 1981. 3 HUDDART, K.W., and BREWER, G.L., Factors Influencing the

Harmonic Impedance of a Power System, Conference on High

Voltage DC Transmission, IEE No. 22, pp. 450-452, 1966. 4 MAHMOUD, A.A. and SHULTZ, R.D., A Method for Analyzing

Harmonic Distribution in a.c. Power Systems, IEEE Trans., PAS-

101, No. 6, pp. 1815-1824, 1982. 5 BERGEAL, J. and MOLLER, L., Influence des Charges sur la

propagation des perturbations de type harmoniques - principales

consequences, Internal Report E.D.F., HR/22-1034, 31.12.80. 6 BAKER, W.P., Measured Impedances of Power Systems,

International Conference on Harmonics in Power Systems, UMIST,

1981. 7 BERGEAL, J. and MOLLER, L., Influence of Load

Characteristic on the Propagation of Disturbances, CIRED 1981. 8 MEYNAUD, P., E.D.F., Direction des Etudes et Recherches,

Private communication, 25 Fevrier, 1983. 9 HOWROYD, D.C., CEBG Technology Planning and Research

Division, Private communication 29.12.83. 10 Electra, Vol. 32 11 HARPO 3 - Harmonic Impedance and Penetration Program.

CEGB Report CS/C/P300. 12 Westinghouse Electric Corporation, Electrical Transmission and

Distribution Refrence Book, 1950. 13 WILLIAMSON, A.C., The Effects of System Harmonics upon

Machines, International Conference on Harmonics in Power

Systems, UMIST, 1981. 14SHILLING, W.J., Exciter armature reaction and excitation

requirements in a brushless rotating-rectifier aircraft alternator,

Trans.Am.Inst.Elect.Eng. 1960, 79, pt. II. 15 CAMPBELL, L.C. and MURRAY, N.S., Harmonic Penetration

into Power Systems, 5th Universities Power Engineering

Conferences, Swansea, Wales, 1970 16 FRESL, V.: Sistermi uzbude generatora HE Derap, Inf. Rade KONCAR, 1974, 60-63, pp. 67-77. 17CHALMERS, B.J., Induction-motor losses due to non-sinusidal

supply waveforms, Proc. IEE, Vol. 115, No. 12, 1968. 18 KLINGHRIRN, E.A and JORDON, H.E., Polyphase induction

motor performance and losses on nonsinusoidal voltage sources,

IEEE Trans., 1968, PAS-87.