d6 transmission model parameter draft1-2_9!3!2010

7/28/2019 D6 Transmission Model Parameter Draft1-2_9!3!2010

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Rev 1.2

impedance is required for this analysis because the power system phases remain

balanced during these simulated conditions. Lumped series and shunt impedances

are typically included for this analysis because these conditions occur at or nearfull system voltage.

2.3. Relay setting/data

Transmission line impedances are commonly used to set phase and ground

distance relay reach settings and maximum torque angles. Positive- and zero-sequence lumped series impedances are used to determine settings for

underreaching and overreaching distance elements associated with step-distance

protection schemes or directional comparison schemes with communication

assistance.

Phase and ground distance element reach settings are generally set in terms of

positive-sequence line impedance. The operation of the ground distance elements

are compensated for the different loop impedance for ground fault conditionsby a residual or zero-sequence compensation factor that is computed using

positive- and zero-sequence line impedance information.

Lumped series line impedances are also used to set fault location parameters in

modern microprocessor based relays, although distributed line impedance datamay be used where different line construction, conductor size, and/or shielding

and to set directional element limits for relays using impedance based directional

elements.

Current values from short circuit calculations are used to set overcurrent element

pickup settings for distance and directional element current supervision elements

and to set overcurrent element pickup and time delay settings for non-directionalovercurrent relay elements.

2.4. Relay testing

Transmission line impedance data is commonly used to develop test data to verify

relay element performance and to verify proper relay distance element reach

settings. Test currents and voltages can be developed for various fault types usingsimplified calculation techniques. Test set vendors typically include software or

calculation techniques with their test set software or documentation to calculate

relay test quantities based on line impedance data.

Testing more sophisticated microprocessor based distance relays, source

impedance data may be needed to create proper test quantities. Strong, moderate,and weak source impedances can be estimated by applying a source-to-line

impedance ratio, otherwise referred to as SIR. The higher the SIR, the weaker the

source (larger the source impedance) when compared with the transmission line

impedance.


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Rev 1.2

3. System modeling issues

3.1. Effect of Modeling Assumptions (pi models, short line, long line, etc)(KevinJones)

3.2. Line Configuration (Norm Fischer)

There are four parameters that affect the ability of a transmission line to function as partof a power system, these are: Resistance (R), Inductance (L), Capacitance (C) and the

Conductance (G). Of these only two, the inductance and the capacitance are affected by

the configuration of the conductors that compose the transmission line.

Inductance:

From the theory we know that theself inductance for a conductor that is suspended above

the earth is given by:

[3.2.1]

[3.2.2]

[3.2.3]

(De is referred to in literature as conductor beneath the surface of the earth, this

parameter is dependent on the resistivity of the earth and is adjusted so that

inductance calculated with is configuration is equal to that measured by testing.

rx* is defined as the GMR (Geometric Mean Radius) and for a single round

conductor is equal to the radius of the conductor, however this is not the case for

bundled conductors)

The mutual inductance between two conductors suspended above the earth, is determined

as follows:


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Rev 1.2

[3.2.4]

Fig 3.2_1

From equation [3.2.1] we can see that the configuration of a transmission line does not

affect the self inductance of a conductor, but from equation [3.2.4] we can see that themutual impedance between two conductors is directly related to the distance between the

two conductors. The closer the conductors are the higher the mutual inductance between

them the further away the conductor is the lower the mutual inductance between them.Therefore the configuration of the transmission line directly impacts the inductance of a

transmission line.

Since we are mostly concerned with three phase transmission systems let us compute theinductance of the self and mutual inductance for the line shown in Fig 3.2_2:

Fig 3.2_2 Sketch of a single conductor 3 phase transmission line (without ground wire)

[3.2.5]

Equation [3.2.5] is the inductance matrix for a single conductor 3 phase transmission line

without a ground wire; however the matrix for a single conductor 3 phase transmission

line with asegmentedground wire would be identical to that given by equation [3.2.5].When dealing with segmented ground wire/s these are not includedin the in the

inductance matrix since the length of the segmented wire is much shorter than the

fundamental frequency wave length of the transmission line.

The question arises how we handle bundled conductors (more than one conductor perphase). There are two methods to deal with this issue; one may compute the GMR of the

bundle and use the value for GMR of the bundle in Equation [3.2.5] to replace ra*,rb

* and


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Rev 1.2

rc*. Following is a method on how to calculate the GMR for some typical bundle

conductors as shown in Fig 3.2_3.

Fig.3.2_3 Typical configuration for bundle conductors

For a double stranded bundled conductor:

[3.2.6]

For a triple stranded bundled conductor

[3.2.7]

For a Quad triple stranded bundled conductor

[3.2.8]

If the bundle contains more than 4 conductors the GMR for this configuration may be

obtained by following the method shown in equations [3.2.6] to [3.28].

Another method that can be used when a bundled conductor is present, is to treat eachconductor as an individual conductor and compute the mutual impedance between each

conductor. For example if you had a double stranded bundled conductor the inductance

matrix would be as given by equation 3.2.9.


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Rev 1.2

H/unit_length

[3.2.9]

The 6 x 6 matrix of equation [3.2.9] can be reduced to a 3 x 3 matrix by making use of

the fact that VA VA = 0, VB VB =0 and VC VC = 0 and IA_Total = IA1 + IA2.

(Appendix A3.2_2 includes an example) .

How do we treat a line that has a non segmented overhead ground wire?

You regard the ground wire or wires as an extra conductor and you calculate the mutualimpedance between each phase conductor and the ground conductor. Assume you have a

transmission configured as shown in Fig3.2_4.

Fig.3.2_4. Sketch of a single wire 3 phase transmission line with a ground wire.

The inductance matrix is as follows:

H/unit_length


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Rev 1.2

[3.2.10]

We then perform reduce this 4 x 4 matrix to a 3 x 3 matrix by eliminating the 4th row and

column, using a Kron reduction method.

[3.2.11]Once the matrix has been reduced to a 3 x 3 matrix, the series phase impedance for the

line can be calculated and from this the sequence series impedances can be calculated.

(Appendix A3.2_2 includes an example) .

Capacitance:

Consider the group of charged lines and their images as shown in Fig.3.2_5.

Fig.3.2_5

From theory we know that:


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Rev 1.2

[3.2.12]

Where: Vabcn = Voltage vector matrix

Pabcn = Potential coefficient matrix

Qabcn = Charge Vector matrix

The Potential coefficient matrix (P) is computed as follows:

, x = y

[3.2.13]

, x y

[3.2.14]Where:

F/m

But we know that :

Therefore

If we now calculate the potential coefficient matrix for a transmission line with a

configuration as shown in Fig.3.2_5, but ignoring the ground wire (conductor n) we

obtain a matrix as follows:

F-1/m

[3.2.15]

F/m


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Rev 1.2

The diagonal elements ofCabc are called the Maxwells coefficients or the capacitance

coefficients. The off diagonal elements are known as the electrostatic induction

coefficients. The off diagonal elements are negative due to the fact that all the elements(coefficients) in the potential coefficient matrix are positive. The Cabc matrix is obtained

by inverting the Pabc matrix.

F/m

Note that irrespective if the ground wire issegmentedornon- segmentedthe ground wireif present is considered in the potential coefficient (capacitance) matrix. The potential

coefficient matrix when a ground wire/s is present is similar than the inductance matrixand is reduced to a 3 x 3 matrix using Kron reduction similarly than what we did for the

inductance matrix. (Appendix A3.2_1 shows how the phase and sequence capacitance is

calculated for a specific line configuration.)

3.3. Transpositions(Ilia Voloh)

A transposition is a common technique to eliminate overhead line unbalance caused by

unsymmetrical placement of transmission line conductors above the ground and to each

other. Unbalance leads to generation of negative- and zero-sequence voltages andcurrents, which affect performance of many components of power system. This also has a

big impact on the protective relaying performance.

To reduce effect on unsymmetrical spacing of conductors to a minimum, the conductors

are transposed so that each conductor occupies successively same positions as the othertwo conductors in two successive line sections. For three such transposed sections, the

total voltage drop for each conductor is the same thus eliminating negative- and zero-

sequence voltages and currents. Double circuit lines create more challenges because ofthe effect of mutual inductance is not entirely eliminated by the transposition.

Value of unbalance depends on few factors, such as geometry of the conductors and

ground wires on the tower, spacing, capacitance to ground of conductors etc. Value of

unbalance is characterized by the unbalance factor, which can vary significantly. Thismay affects results of protective relay study if not accounted for.

Not every transmission line model can be used for studies involving untransposed lines.

For example, lumped parameters or PI segments models are not appropriate for protective

relaying studies. Modeling involving representation of transmission lines in physicalparameters are likely to be most accurate followed by distributed parameters or travelling

wave models.


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Rev 1.2

3.4. Effects of Non-Homogeneous lines(George Bartok)

For typical transmission lines, the impedance is not a linear function of distance. All

transmission lines have, to varying degrees, some non-homogeneity; that is, theimpedance per unit length is not constant over the length of the line. This can be a source

of error in distance relay and fault location applications.

Sources of non-homogeneity in overhead lines include:

Substation entrance/exit structures may differ from line structures

Angle structures may be of a different design than tangent structures

River/highway crossings may have longer spans, wider spacings and larger

conductors

Regulatory agencies may require compact or low profile tower designs in

sensitive areas

On upgrade or reconductoring projects, it may not be necessary or feasible to

rebuild the entire line

Interim or temporary line designs may be used during construction

Tower spacing and effective conductor sag will differ in hilly or uneven terrain

Soil characteristics and thus ground resistivity may vary along line length

Mutual impedances may be present over portions of the line

Transmission line constants programs generally allow the line impedance to be calculated

in segments, with the ability to sum the characteristics of individual segments into a

terminal-to-terminal total. The individual using these programs must exercise judgmentregarding which identifiable line characteristic changes are significant enough to warrant

calculation as a separate line segment. Typically, single line sections, such as river and

highway crossings are ignored if they are not a significant fraction of the entire line

length. In addition, the line sections that transition from one line construction type toanother are ignored, since they cannot be modeled with conventional transmission line

constants programs because of the variable geometry.

Distance relays and fault locating algorithms generally assume that the line is

homogeneous from terminal to terminal. The total line impedance and line length are

entered as setting parameters. This assumption can introduce error in the distance-to-fault calculation if the line has significant non-homogeneity. Figure XX gives an

example of a transmission line having three construction types over its length from

Terminal A to Terminal B. The error in distance is most significant near the transitionpoints between line construction types. An impedance table or graph can be used to

correct the distance calculation for this error.


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Rev 1.2

Figure XX

3.4.1. Conductors(George Bartok)

3.4.2. Changes in structure or spacing(George Bartok)3.4.3. Segmented/ Insulated Shield wires(Don Lukach)

Segmented or insulated shield wires provide a discontinuity in the ground paths, thus

impact the zero sequence networks. The first question is how this type of shield wire istreated in the zero-sequence line impedance calculation.

In the EMTP theory book by Hermann Dommel, the ground wires are ignored whencalculating the series impedance matrix but are taken into account for the shunt

impedance matrix. Thus, for lines that have segmented ground wires, the ground wires

do not affect the inductance of the line. The reason Dommel gives for this reasoning isthat the ground wires do not carry any significant fundamental current because the wave

length of the fundamental frequency is much larger than the segmented span. However,

this not true for transients such as lightning strikes. Some utilities follow the practice of

not including segmented/insulated shield wires in the series inductance calculations for

the line constants. Also, a line constants programs contain the option to select segmentedversus continuous shield wires.

In the paper by Gerez and Balakrishnan entitled,Zero-sequence Impedance of Overhead

Transmission Lines with Discontinuous Ground Wire, the authors give a method to

calculate the zero-sequence impedance of a transmission line having ground wires thatare not continuous or are not connected to the station grounds at the end of the line. The

calculated values are compared with the measured zero-sequence impedance of a line.

TERMINAL

A

Distance (Miles or Kilometers)

Impedance

()

Actual impedance ofline consisting ofthree sections withdiffering impedancecharacteristics.

Line impedanceassuminghomogeneousimpedancecharacteristics.

DistanceMeasureme

nt Error

TERMINAL

B


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Rev 1.2

The authors observe that for transmission lines having discontinuous ground wires, the

actual zero-sequence impedance is different from the zero-sequence impedance of the

line calculated with the classical methods and considering either no ground wire orcontinuous ground wire. This difference is significant if the ground wire is of ACSR

conductor. The method given for calculating the zero-sequence impedance of a

transmission line with discontinuous ground wire gives more accurate results, which areclose to the measured values. While the paper does not directly address

segmented/insulated ground wires, it does discuss the implications of missing shield

spans and the affect of not connecting shields to the substation ground grid.

Refs:Thapar, B.; Gerez, V.; Balakrishnan, A., Zero-sequence Impedance of Overhead

Transmission Lines with Discontinuous Ground Wire, Power Symposium, 1990.

Proceedings of the Twenty-Second Annual North American, Volume , Issue , 15-16 Oct

1990 Page(s):190 192, Digital Object Identifier 10.1109/NAPS.1990.151371

3.5. Earth Resistivity(Don Lukach)

A basic understanding of the factors that influence earth resistivity is required for the

protection engineer to accurately model a given system or line.

3.5.1. Variation in soilsFirst and foremost is the soil material and its physical conditions, like moisture content

and temperature. For example, soil with quartz grains have a thermal resistivity of 11C-

cm/W, water is 165, organic can be from 400 wet to 700 dry, and air is 4000. Thus, it isgenerally concluded that soil with the lowest thermal resistivity has a maximum amount

of soil grains and water while having a minimum amount of air. Simply stated, the

resistivity of sandy dry soil such as in Nevada will be very different from Illinois silty-clay-organic soil. Also, river-bottom soil will be vastly different than the soil on top of a

ridge, or bluff within the same general area.

Resistivity is measured in ohm-cm. Variations in soil compositions are as vast as theranges of published soil resistivity. Generally, clay-silty-loam soils have much lower

values (e.g., 4000 ohm-cm average per one data source) than sandy soils (e.g., 94,000

ohm-cm average per the same data source). The very nature of the soil and the factorsthat determine resistivity equate to a dynamically changing value of resistivity. The

transmission line in Nevada will have a different local resistivity during a major

precipitation event, than during a drought.

To emphasize the affect that resistivity can have on a given line, a 138Kv line was

arbitrarily chosen within a line constant program. The line was modeled at 100 miles

long with 10 ohm-meter and 100 ohm-meter resistivity value. All other line parameters


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Rev 1.2

were held constant. The difference in zero-sequence impedance was over 10%. Note

that this was utilized for demonstration purposes and additional cases may have different

results.

The important point to the system protection engineer is that the physical characteristics

of a transmission line must be known to accurately model it, resistivity notwithstanding.If certain factors are not addressed the model will be inaccurate, perhaps at the most

inopportune time. For example, the season of the year, like when the soil is saturated, or

if a company that encompasses different geological areas uses a standard resistivityvalue, the model accuracy can be compromised.

A good check against the system model, including resistivity, are right-of-way

measurements and fault data review. Both topics are also covered in this report.

Refs:

IEEE STD 442 Guide for soil thermal resistivity measurements

AVO, Getting Down to Earth testing guide"Reference Data for Radio Engineers", (book), Howard W. Sams and Co., Inc.

FCC published soil conductivity map showing in millisiemens, which, when invertedand multiplied by 1000 becomes ohm-meters.

http://www.fcc.gov/mb/audio/m3/index.html

3.5.2. Other conducting paths to ground

I think this should be in another sectionnot really part of earth resistivity

Line constant programs typically contain configurations that share multiple conductors onthe same pole structure and the same right-of-way. What may not be addressed are other

conductors that follow the same path. Examples include railroad track, railroad

communication and control lines, pipelines, etc. These other conductors can be buried orbe on pole structures that run parallel to the power lines. The difficulty is in modeling

these other conductors.

While railroad control lines look like an adjacent line, obtaining grounding information

or pole structure characteristics is not readily available. For the other structures the

question becomes how to approximate their properties within the confines of the line

constant programs. Simply put, what approximates a railroad track with a certain rail andcommunication systems or the pipeline?

Regardless of the methods used for approximating the zero sequence networks forsituations that have these other conductors, the fault analysis studies of such areas would

be beneficial to revise the model.

3.6. Mutual effects (Mutual coupling)

In this part we concentrate on the mutual coupling between transmission lines, similarly

as the different phases of a transmission line influence each others volt drop, the phases
http://www.fcc.gov/mb/audio/m3/index.htmlhttp://www.fcc.gov/mb/audio/m3/index.html


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Rev 1.2

of a line sharing the same right of way or the same tower will also influence the voltage

drop of the phase.

Assume a transmission system as shown in Fig 3.6_1 where two transmission lines are a

distance Dd from each other.

Fig 3.6_1 simple sketch showing conductors of a two transmission line system

The mutual coupling between all the conductors and the A-phase of circuit 1 are shown

in Fig 3.6_2

Section 3.2, line configuration, discusses how to compute the mutual impedance between

two conductors from a common circuit. To calculate the mutual impedance between twoconductors from two different circuits is done in exactly the same manner. Therefore

equation 3.2.4 is still applicable.

If we now consider the voltage drop for a section of circuit 1, A-phase we get the

following relationship [3.6.1]

[3.6.1]

Where:

ZAA = Self impedance of the conductor

ZAB = Mutual impedance between conductor A and B (circuit 1)ZAC = Mutual impedance between conductor A and C (circuit 1)

ZAa = Mutual impedance between conductor A (circuit 1) and

conductor a (circuit 2)


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Rev 1.2

ZAb = Mutual impedance between conductor A (circuit 1) and

conductor b (circuit 2)

ZAc = Mutual impedance between conductor A (circuit 1) andconductor c (circuit 2)

For simplicity let us assume that mutual impedance between the phases of circuit 1 are

equal ( ZAB = ZAB = ZM ) and lets also assume that the distance Dd is large enough thatthe mutual impedance between the conductors of circuit two are also approximately equal

(ZAa ZAb ZAc Zmp). , using these assumptions we can now rewrite equation 3.6_1 as

follows:

[3.6_2]

If we now analyze the second half of equation [3.6_2] we will ready see that for allpositive and negative sequence currents that flow in circuit 2 the effective mutual

coupling is zero since , however this is not true if the ciruit2 contains

zero sequence current, so we can say that the mutual coupling between

circuits 1 and 2 is mainly due only due to zero sequence current. We can say that Zmp

is the zero sequence mutual coupling between circuit 1 and 2, and can be computed by

taking the average mutual impedance between circuit 1 and 2 [3.6.3].

[3.6_3]

In reality there is some mutual coupling between the circuits due to positive and negative

sequence current but in general these are less than 5% and for all practical purposes can

be ignored. This small coupling is due to the mutual impedances between the conductorsin circuit 1 and circuit 2 not being exactly equal to one another.

3.7. Special concerns with modeling cable (Steve Turner)

3.8. Special concerns with modeling cable (Steve Turner)

3.9. Other Considerations affecting use of the Model (may be Appendix?)( JoeUchiyama)

3.9.1. Transient and subtransient reactances

3.9.2. Sources

3.9.3. Transformers3.9.4. Device effects

3.9.4.1. Wind generators

3.9.4.2. Large motors


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Rev 1.2

3.9.4.3. Dynamic VAR controls

3.9.4.4. HVDC

3.9.4.5. Capacitors3.9.4.6. Reactors

3.9.5. Geomagnetic concerns

3.9.6. Loads, Prefault voltages, Power flow3.10. Six Wire Lines( Rick Cornelison)Six wire lines as defined in this report are single circuit three phase lines with two non-bundledconductors per phase. The separation of the two wires making up each phase is typically greater

than distance between the phases. These single circuit lines look like double circuit lines.

Figure 3.9.1 Typical six wire circuit

Where bundled conductors can be considered continuously connected, the two wires per phase on

six wire lines may only be connected at the beginning and ending points, and possibly, but not

necessarily at tap points. If the two wires per phase are not connected at tap points, then the only

way to model six wire lines is as two separate circuits. If, however, the two wires per phase are

connected at every tap point, then the six wires can be reasonably represented with one set of

impedances.

4. Model verification methods

4.1. Required Accuracy

4.2. Comparison with measured results(Steve Turner)4.2.1. Measured points

4.2.2. Fault location

4.2.2.1. Accuracy of location4.2.2.2. Performance of relaying

4.3. Direct measurement(Hyder Do Carmo/Mukesh Nagapal)

Validation of transmission circuit parameters can be validated from direct measurementsfrom load unbalances and short circuit tests. The load unbalance technique requiressynchronized measurements from each line terminal. Even with synchronized

measurements, the zero sequence impedance validation can be challenging because

transmission circuits experience low load unbalance. Staging of short circuit tests areexpensive and are not liked due to undesirable stress and on the equipment. Under certain

configurations, relay records from actual short circuits on transmission circuit can be

helpful in validating its parameters.


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Rev 1.2

A frequency injection signal injection is an alternative method to stage short circuit faults

on live circuits. However, this method requires that the circuit be taken out-of-service forthe test and isolated from sources at both ends. Figure X.1 shows experimental step-up.

It consists of single generator, amplifier and dynamic signal analyser. Typically, signal

generator and analyser functions are available in a single piece of equipment. Tomeasure series parameters of line, all three three-phases of the receiving terminal are

short to the ground as in shown in Figure X.1. Measurements of shunt parameters,

mainly for the cable circuits, require terminal left open circuited.

Figure 1.x Test set-up for measuring series self impedance of Phase A.

Single generator injects low voltage signal via amplified into the isolated circuit. The

signal can be white noise or sweep from low frequency about 10 Hz to 200 Hz in smallsteps. The applied voltage and current measured using Pearson coil CT are applied to

dynamic signal analyser. Dynamic Signal analyser performs spectrum analysis on the

measured signals. It then uses auto (voltage) and cross (voltage and current) correlations

to determine impedance of the transmission circuit over the frequency range using the

following relationship:

Zaa(f) = Va(f)*ConjVa(f)/Ia(f)*ConjVa(f)

Where:

Va(f) voltage phasor of frequency f extracted from applied voltage on Phase A


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Rev 1.2

I(f) current phasor of frequency f extracted from measured current into Phase

A

Zaa(f) series self impedance of Phase A of transmission circuit

These measurements averaged over several measurements to improve the accuracy of

measurements.

The impedance measurement obtained using the set-up in Figure X.1 provides self

impedance of Phase A. The mutual impedance between Phase A and B be measuredrepeating the experiment except Phase B voltage from the transmission circuit applied

is signal analyser while signal generator injected the voltage into Phase A as follows:

Zab(f) = Vb(f)*ConjVb(f)/Ia(f)*ConjVb(f)

Where:

Vb(f) voltage phasor of frequency f extracted from voltage measured on Phase Awhile signal injected on Phase A

I(f) current phasor of frequency f extracted from measured current into PhaseA

Zab(f) series mutual impedance between Phases A and B

These two measurements are sufficient to calculate ositive and zero sequence

impedances. Similar measurements on each phase can be averaged to obtain better

estimates of self and mutual impedances by averaging:

Zs(f) = (Zaa(f) + Zbb(f) + Zcc(f))/3

Zm(f) = (Zab(f) + Zac(f) + Zba(f) + Zbc(f) +Zca(f) + Zcb(f))/6

Average values of self and mutual impedance values can positive and zero sequence

impedances of a symmetrical or transposed line as:

Z1(f) = Zs(f) Zm(f)

Zo(f) = Zs(f) + 2 Zm(f)

In case of un-transposed or non-symmetrical lines, the measurement provide full 3x3matrix of line impedances, which can be converted into sequence component matrix

using symmetrical component transformations. In case of long lines and cable, shunt

impedance can also be obtained with similar tests but keeping receiving terminal opencircuited instead of short circuited.

Figure 2.x and 3x shows magnitude and phase angle of series self and mutual impedancesmeasured for a short cable circuit. Since applied is low-voltage signal, measurements

near 60 Hz are corrupted due stray signal from adjacent equipment. These corrupted

estimates are rejected. Curve fitting or interpolation technique from estimates at non-60

Hz frequencies are then used to determine impedance parameters at 60-Hz.


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Rev 1.2

Figure 2.x Magnitude and phase angle of the cables self-impedance during the short-

circuit tests.


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Rev 1.2

4.4. Use of Synchrophasors (Jim OBrien) (Norm Fisher)4.5. Use of Staged faults

5. Summary

6. Appendix

Appendix (for section 3.2 and 3.6-Norm Fischer)

A refresher on inductance, assume two wire solid round conductor system as shown inFig. A3.2_1. Conductor B is the return path for the current in conductor A.

Fig A3.2_1 A simple two wire single phase

Let us consider the current in conductor A only

.


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Rev 1.2

H/m

H/m

[A3.2.1]If we now consider the current in conductor B only

H/m

[A3.2.2]

But we now that the current in conductor A is 180 out of phase with the current in

conductor B , the flux linkages produced by the two currents in is in the same direction

and thus the resulting flux for the two conductors can be obtained by simply adding theindividual mmfs together.

Therefore the inductance for the two wire circuit cans be written as follows:

H/m

[A3.2.3]

Equations [3.2.1] and [3.2.2] are referred to the inductance per conductor and that ofEquation [3.2.3] the inductance per loop.

The following worked examples on how to calculate the series and shunt components for

a transmission line are taken form Paul Anderson book Analysis of Faulted Powersystems.

Series Component Calculation Examples:


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Rev 1.2

A

B

C

1 1 '

3 6 '

6 . 5 '

8 '

4 '

5 '

6 '


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Rev 1.2


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Rev 1.2


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Rev 1.2

Problem 4.34

6 . 5 '

8 '

A

B

C

1 1 '

3 6 '

4 '

5 '

6 '

1 '


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Rev 1.2


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Rev 1.2


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Rev 1.2


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Rev 1.2


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Rev 1.2

A

B

C

1 1 '

3 6 '

6 . 5 '

8 '

4 '

5 '

6 '


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Rev 1.2


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Rev 1.2


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Rev 1.2


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Rev 1.2

Shunt Component Calculation Examples (excluding the Conductance):


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Rev 1.2


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.


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Rev 1.2

Appendixs

A1

B1

C1

1 1 '

3 6 '

6 . 5 '

8 '

4 '

5 '

6 '

5 5 '

1 5 '

1 5 '

A2

B2

C2

G1

G2

G3

1 5 '1 5 '

5 0 '

d6 transmission model parameter draft1-2_9!3!2010

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