power transmission lines

Short Line Parameters Calculations Positive and Zero Sequence Impedance

EDSA MICRO CORPORATION 16870 West Bernardo Drive, Suite 330

San Diego, CA 92127 U.S.A.

Copyright 2008

All Rights Reserved

Version 1.30.00 October 2008

EDSA MICRO CORPORATION

WARRANTY INFORMATION

There is no warranty, implied or otherwise, on EDSA software. EDSA software is licensed to you as is. This program license provides a ninety (90) day limited warranty on the diskette that contains the program. This, the EDSA Users Guide, is not meant to alter the warranty situation described above. That is, the content of this document is not intended to, and does not, constitute a warranty of any sort, including warranty of merchantability or fitness for any particular purpose on your EDSA software package. EDSA Micro Corporation reserves the right to revise and make changes to this User's Guide and to the EDSA software without obligation to notify any person of, or provide any person with, such revision or change. EDSA programs come with verification and validation of methodology of calculation based on EDSA Micro Corporation's inhouse software development standards. EDSA performs longhand calculation and checks the programs results against published samples. However, we do not guarantee, or warranty, any program outputs, results, or conclusions reached from data generated by any programs which are all sold "as is". Since the meaning of QA/QC and the verification and validation of a program methodology are domains of vast interpretation, users are encouraged to perform their own inhouse verification and validation based on their own inhouse quality assurance, quality control policies and standards. Such operations - performed at the user's expense - will meet the user's specific needs. EDSA Micro Corporation does not accept, or acknowledge, purchase instructions based on a buyer's QA/QC and/or a buyer's verification and validation standards. Therefore, purchase orders instructions are considered to be uniquely based on EDSA's own QA/QC verification and validation standards and test systems. TRADEMARK EDSA is a trademark of EDSA Micro Corporation. COPYRIGHT Copyright 1989 - 2008 by EDSA Micro Corporation. Please accept and respect the fact that EDSA Micro Corporation has enabled you to make an authorized disk as a backup to prevent losing the contents that might occur to your original disk drive. DO NOT sell, lend, lease, give, rent or otherwise distribute EDSA programs / User's Guides to anyone without prior written permission from EDSA Micro Corporation. All Rights Reserved. No part of this publication may be reproduced without prior written consent from EDSA Micro Corporation.

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Table of Contents 1. Foreword............................................................................................................................................ 1 2. Purpose ............................................................................................................................................. 1 3. Capabilities ........................................................................................................................................ 1 4. Option 1. Aerial (Overhead) Lines ..................................................................................................... 2 5. Option 2. Three-Conductor Cables ................................................................................................... 3 6. Option 3. Three-Single Conductor Cables ........................................................................................ 3 7. Option 4. Three-Single Concentric Neutral Cables, Neutrals Solidly Grounded............................... 3 8. Three-phase Short Line Consisting of a Three-conductor Cable:..................................................... 3 8.1 Cable Configuration:............................................................................................................. 3 8.2 Parameters Identification:..................................................................................................... 4 8.3 Positive-sequence Impedance (R1, X1):.............................................................................. 4 8.4 Zero-sequence Impedance (RO, XO): ................................................................................. 4 8.4.1 Sheath return only: ............................................................................................................... 5 8.4.2 Grounded sheath-earth return: ............................................................................................. 5 8.5 Reference: ............................................................................................................................ 6 9. Three-phase Single Circuit Short Aerial (Overhead) Line With Neutral Wire: .................................. 6 9.1 General Configuration: ......................................................................................................... 6 9.2 Parameters Identification:..................................................................................................... 6 9.3 Positive-sequence Impedance (R1, X1):.............................................................................. 7 9.4 Zero-sequence Impedance (R0, X0): ................................................................................... 7 9.4.1 Earth return only: .................................................................................................................. 8 9.4.2 Neutral return only: ............................................................................................................... 9 9.4.3 Grounded neutral-earth return:............................................................................................. 9

9.5 Reference: ............................................................................................................................ 9 10. Three-phase Single Circuit Short Line Consisting of Three-single Conductor Cables: .................. 10 10.1 General Configuration: ....................................................................................................... 10 10.2 Parameters Identification:................................................................................................... 10 10.3 Positive-sequence Impedance (R1, X1):............................................................................ 11 10.3.1 With sheaths open.............................................................................................................. 11

10.3.2 With sheaths short-circuited (Bonded together):................................................................ 11 10.4 Zero-sequence Impedance (RO, XO): ............................................................................... 11

10.4.1 Earth return only:................................................................................................ 12 10.4.2 Sheaths (bonded together) return only: ............................................................. 13 10.4.3 Grounded Sheath-earth return: .......................................................................... 13

10.5 Reference ........................................................................................................................... 13 11. Mr. G.C. McDonalds Contribution................................................................................................... 14 12. Computation of Zero-sequence Impedance Following the Formulas of Westinghouse

Transmission and Distribution Reference Book: ........................................................................... 16 13. Verification and Validation: .............................................................................................................. 20 14. Computation of Positive and Zero-sequence Impedances (R & X) for Three-phase

Configuration Consisting of Three-single Concentric Neutral Cables ........................................... 22 15. Positive and Zero-sequence Impedance Calculation...................................................................... 25 16. Positive and Zero Sequence Impedance Calculation ..................................................................... 28 17. Nomenclature for Equations ............................................................................................................ 32 18. References ...................................................................................................................................... 34 19. Standalone Short Line Parameters Tutorial .................................................................................... 35 20. Network-Based Short Line Parameters Calculations ...................................................................... 46

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List of Figures Figure 1 .........................................................................................................................................................3 Figure 2 .........................................................................................................................................................5 Figure 3 .........................................................................................................................................................6 Figure 4 .........................................................................................................................................................8 Figure 5 .......................................................................................................................................................10 Figure 6 .......................................................................................................................................................12 Figure 7 .......................................................................................................................................................16 Figure 8 .......................................................................................................................................................21 Figure 9 .......................................................................................................................................................21 Figure 10 .....................................................................................................................................................21 Figure 11 .....................................................................................................................................................21 Figure 12 .....................................................................................................................................................21 Figure 13 .....................................................................................................................................................22 Figure 14 .....................................................................................................................................................25 Figure 15 .....................................................................................................................................................28 Figure 16 Tutorial Case Study (File: shtln.mzp) .........................................................................................35 Figure 17 Short Line Under Study .............................................................................................................46 Note: You can view this manual using your CD as an Adobe Acrobat PDF file. The file name is:

Short Line Parameters Short_Line_Parameters.pdf You will find the Test/Job files used in this tutorial at the following location:

C:\DesignBase\Samples\ShortLine = Short Line Parameters

Test Files: SAMPLE-RELAY-IMP, SAMPLE-RELAY-QUAD, SAMPLE-RELAY-QUAD-V&V

Copyright 2008 All Rights Reserved

Short Line Parameters

1. Foreword This program was developed in the assumption that the user is a Professional Engineer and,

therefore, familiar with the concepts under consideration. 2. Purpose To provide an easy, usable method of producing both Positive and Zero Sequence Impedance values for short aerial (overhead) lines, three-conductor cables, three-single conductor cables, and three-single concentric neutral cables. 3. Capabilities The program will provide Positive Sequence, Zero Sequence or both Positive - and Zero Impedance

values for: 1. Three-Phase, Single Circuit, Short Aerial (Overhead) Lines With Neutral Wire Return Path options: a. Earth return only; b. Neutral return only; c. Ground Neutral return. Neutral options: a. 1 Neutral Conductor; b. 2 Neutral Conductors. 2. Three-Phase Short Line Consisting of Three-Conductor Cables Return Path options: a. Sheath return only; b. Grounded Sheath-Earth return. 3. Three-Phase Single Circuit Short Line consisting of three-single conductor cables. Return Path options: a. Earth return only; b. Sheath return only;

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c. Grounded Sheath-Earth return. Sheath options: a. Open Circuit; b. Short Circuit (Bonded). 4. Three-single concentric neutral cables with the neutral solidly grounded. 4. Option 1. Aerial (Overhead) Lines Three-Phase, Single-Circuit, Short Aerial (Overhead) Lines with Neutral Wire; After selecting the Aerial (Overhead) Lines option from Line Type Options, input information with

regard to the screen instructions. When entering "Systems" information the user can press the "F2" function key for pick list to select: Units used: a. Standard. Results are in ohms/1000 feet, and will be stored in the Standard EDSA Feeder

Data File. b. Metric. Results are converted to ohms/1000 meters, and will be stored in the Metric EDSA

Feeder Data File. c. Frequency. in Hz, defaults to EDSA configuration setting. If data for the feeder already exist in the EDSA Feeder Data File, then a warning screen will present

the following: OVERWRITE EDSA FEEDER DATA WARNING SCREEN To Overwrite Existing Data: N. Do NOT overwrite existing EDSA Feeder Data (default). Y. Overwrite existing EDSA Feeder Data.

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5. Option 2. Three-Conductor Cables Three-Phase, Three-Conductor Cable. After selecting the Three-Conductor option from the Line Type Options, input the required items

according to the screen instructions. Sheath's resistivity is in ohms/cubic centimeters at the temperature under consideration. 6. Option 3. Three-Single Conductor Cables Three-Phase, Three-Single Conductor Cables. After selecting the Three-Single-Conductors option from the Line Type Options, input the required

information according to the screen instructions. 7. Option 4. Three-Single Concentric Neutral Cables, Neutrals Solidly Grounded After selecting the Three-Single Concentric Neutrals option from the Line Type Options, input the

required information based on the screen instructions. 8. Three-phase Short Line Consisting of a Three-conductor Cable: 8.1 Cable Configuration:

Figure 1

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8.2 Parameters Identification:

Rp = Effective a.c. resistance of a conductor of the cable (with sheath open) at the temperature and frequency under consideration, in ohms per 1000 feet.

(GMR)p = G.M.R. of a conductor of the cable at the frequency under

consideration, in feet. (RAD)i = Inner radius of sheath in feet. (RAD)o = Outer radius of sheath in feet. sh = Resistivity of sheath in ohms per cubic centimeter, at the sheath

temperature under consideration. (GMD)p = Mutual distance between two-phase conductors in feet. F = Frequency (c/s) under consideration. = Earth resistivity in ohms per cubic meter. Rsh = Resistance of sheath in ohms per 1000 feet.

8.3 Positive-sequence Impedance (R1, X1):

R1 = Rp ohms per phase per 1000 feet. X1 = 0.000882(F) log10 [(GMD) p/(GMR) p] ohms per phase per 1000

feet. 8.4 Zero-sequence Impedance (RO, XO):

De = 2160 F

feet.

(GMR) pg = (GMR ) (GMD)p p

23 (1)

(GMD) sep = [(RAD) i+(RAD) o]/2

Rsh = 10.443238 sh/[(RAD) 2o-(RAD) 2i] ohms per 1000 feet. (2)

NOTE: Skin effect of sheath is assumed to be negligible.

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The equivalent circuit for zero-sequence impedance calculation for three-conductor cables in terms of actual impedance in ohms per 1000 feet is shown below:

Figure 2

NOTE: To obtain per phase values, actual impedance is to be multiplied by 3.

where Rco = Rp/3, Rso = Rsh, Reo = 0.00030113(F) ohms per 1000 feet. Xco = 0.000882(F)log10[(GMD)sep/(GMR)pg] ohms per 1000 feet. Xeo = 0.000882(F)log10[De/(GMD)sep] ohms per 1000 feet.

8.4.1 Sheath return only:

RO = 3(Rco+Rso) ohms per phase per 1000 feet. XO = 3(Xco) ohms per phase per 1000 feet.

8.4.2 Grounded sheath-earth return:

Gso = 1/Rso, Seo = R2eo+X2eo, Geo = Reo/Seo, Beo = -Xeo/Seo, Gse = Gso+Geo, Bse = Beo, Sse = G2se+B2se, Rse = Gse/Sse, Xse = -Bse/Sse, RO = 3(Rco+Rse) ohms per phase per 1000 feet. XO = 3(Xco+Xse) ohms per phase per 1000 feet.

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8.5 Reference:

Wagner, C.F. and Evans, R.D., "Symmetrical Components", First edition, pp. 136-157, pp. 163-169, McGraw-Hill.

9. Three-phase Single Circuit Short Aerial (Overhead) Line With Neutral Wire: 9.1 General Configuration:

Figure 3 Conductor identification: a, b, c are the phase conductors; 1, 2 are the neutral wires. 9.2 Parameters Identification:

Rp = Effective a.c. resistance of a phase conductor at the frequency and temperature under consideration, per 1000 feet.

(GMR)p = G.M.R. of a phase conductor at the frequency under

consideration. Dpp1, Dpp2, Dpp3 = Three mutual distances among the phase conductors. Rn = Effective a.c. resistance of a neutral wire at the frequency

and temperature under consideration, per 1000 feet.

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(GMR)n = G.M.R. of a neutral wire at the frequency under consideration.

NNW = Number of neutral wires, up to a maximum of two. Dpn1, Dpn2,..., Dpnj = Mutual distances from each phase conductor to each

neutral wire where j = 3(NNW). Dnn = Distance between the two neutral wires (if NNW = 2). F = Frequency in c/s. = Earth resistivity in ohms per cubic meter.

NOTE: All G.M.R.'s and distances are in feet and the resistances are in ohms.

It is assumed that the three-phase line is properly transposed or the effect of asymmetrical spacing is negligible. The neutral wires (if two) are assumed to be symmetrically located with respect to the line.

9.3 Positive-sequence Impedance (R1, X1):

(GMD)p = (D ) (D ) (D )pp1 pp2 pp33 (3)

R1 = Rp ohms per phase per 1000 feet. X1 = 0.000882(F) log10 [(GMD) p/(GMR) p] ohms per phase per

1000 feet. 9.4 Zero-sequence Impedance (R0, X0):

(GMR)pg = (GMR ) (GMD)p p23 (4)

De = 2160F

feet. (5)

(GMR)ng = (GMR)n, if NNW = 1. (6) (GMR)ng = (GMR )(D )n nn if NNW = 2. (7) (GMD)sep = (D )(D ) . . . (D ) , j = 3(NNW)pn1 pn2 pnjj (8)

The equivalent circuit for the calculation of zero-sequence impedance for the configuration shown before in terms of actual impedance in ohms per 1000 feet is:

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Figure 4

where

Rco = Rp/3 Rno = Rn/NNW Reo = 0.00030113 (F) ohms Xco = (F1)(F)log10[(GMD)sep/(GMR)pg] ohms Xno = (F1)(F)log10[(GMD)sep/(GMR)ng] ohms Xeo = (F1)(F)log10[De/(GMD)sep] ohms (Xco + Xeo) = (F1)(F)log10[De/(GMR)pg] ohms

with F1 = 0.000882

NOTE: To obtain per phase impedance, actual impedance is to be multiplied by 3.

9.4.1 Earth return only:

RO = 3(Rco+Reo) ohms per phase per 1000 feet. XO = 3(Xco+Xeo) = 3(F1)(F)log10[De/(GMR)pg] ohms per phase

per 1000 feet.

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9.4.2 Neutral return only:

RO = 3(Rco+Rno) ohms per phase per 1000 feet. XO = 3(Xco+Xno) ohms per phase per 1000 feet.

9.4.3 Grounded neutral-earth return:

ZO = 3[Zco+(Parallel combination of Zno and Zeo)] Sno = R2no+X2no; Gno = Rno/Sno; Bno = -Xno/Sno; Seo = R2eo+X2eo Geo = Reo/Seo; Beo = -Xeo/Seo; Gone = Gno+Geo; Bone = Bno+Beo; Sone = G2one+B2one; Rone = Gone/Sone; Xone = -Bone/Sone

RO = 3(Rco+Rone) ohms per phase per 1000 feet. XO = 3(Xco+Xone) ohms per phase per 1000 feet.

9.5 Reference:

Wagner, C.F. and Evans, R.D., "Symmetrical Components", First edition, pp. 136-157, pp. 163-169, McGraw-Hill.

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10. Three-phase Single Circuit Short Line Consisting of Three-single Conductor Cables:

10.1 General Configuration:

Figure 5

10.2 Parameters Identification:

Rp = Effective a.c. resistance of a conductor of a cable (with its sheath open) at the temperature and frequency under consideration, in ohms per 1000 feet.

(GMR)p = G.M.R. of a conductor of a cable at the frequency under

consideration, in feet. (RAD)i = Inner radius of the sheath, in feet. (RAD)o = Outer radius of the sheath, in feet. sh = Resistivity of sheath in ohms per cubic centimeter at the sheath

temperature under consideration. Dpp1, Dpp2, Dpp3 = Mutual distances among the three-phase conductors, in feet. F = Frequency in c/s. = Earth resistivity in ohms per cubic meter.

NOTE: It is assumed that three-phases are properly transposed or the effect of

asymmetrical spacing is negligible.

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10.3 Positive-sequence Impedance (R1, X1): 10.3.1 With sheaths open

(GMD)p = (D ) (D ) (D )pp1 pp2 pp33 (9)

R1 = Rp ohms per phase per 1000 feet. X1 = 0.000882(F)log10[(GMD)p/(GMR)p] ohms per phase per 1000 feet.

10.3.2 With sheaths short-circuited (Bonded together): Rsh = Resistance of a sheath in ohms per 1000 feet. Rsh = 10.443238 sh/[(RAD)2o- (RAD)2i] ohms per 1000 feet. (10)

NOTE: Skin effect on sheath is assumed to be negligible.

Xm = Mutual reactance between conductors and sheaths per phase per 1000 feet.

Xm = 0.000882(F)log10[(2)(GMD)p/[(RAD)o+(RAD)i]] ohms per phase per

1000 feet.

G.M.R. of sheath = [(RAD)o + (RAD)i]/2 R1 = Rp+[(Xm)2(Rsh)/[(Xm)2+(Rsh)2]] ohms per phase per 1000 feet. X1 = 0.000882 (F)log10[(GMD)p/(GMR)p] - [(Xm)3/[(Xm)2+(Rsh)2]] ohms

per phase per 1000 feet 10.4 Zero-sequence Impedance (RO, XO):

De = 2160 f feet.

(GMR) pg = pp23 sh

o (GMR ) (GMD) ; (GMR ) = (RAD) + (RAD)

2i (11)

Separation of a sheath from its conductor = [(RAD)o+(RAD)i]/2 = (SEP)shc

(GMD)sep = (SEP) (GMD)shc p

23 (12)

(GMR)pg = GMR of the phase conductors as a group

(GMR)sh = GMR of sheath

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Equivalent circuit for zero-sequence impedance calculation for the cable configuration

shown before in terms of actual impedance per 1000 feet, in ohms:

Figure 6

where

Rco = Rp/3; Rso = Rsh/3; Reo = 0.00030113(F) ohms per 1000 feet. Xco = 0.000882(F)log10[(GMD)sep/(GMR)pg] ohms per 1000 feet. Xeo = 0.000882(F)log10[De/(GMD)sep] ohms per 1000 feet. Xco+Xeo = 0.000882(F)log10[De/(GMR)pg] ohms per 1000 feet. (13)

NOTE: To obtain per phase impedance, actual impedance is to be multiplied by 3. 10.4.1 Earth return only:

RO = 3(Rco+Reo) ohms per phase per 1000 feet.

XO = 3(Xco+Xeo) = 3(0.000882)(F)log10[De/(GMR)pg] ohms per phase per 1000 feet.

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10.4.2 Sheaths (bonded together) return only:

RO = 3(Rco+Rso) ohms per phase per 1000 feet. XO = 3(Xco) ohms per phase per 1000 feet.

10.4.3 Grounded Sheath-earth return:

Gso = 1/Rso; Seo = R2eo+X2eo; Geo = Reo/Seo; Beo = -Xeo/Seo; Gse = Gso+Geo; Bse = Beo; Sse = G2se+B2se; Rse = Gse/Sse; Xse = -Bse/Sse. RO = 3(Rco+Rse) ohms per phase per 1000 feet. XO = 3(Xco+Xse) ohms per phase per 1000 feet.

10.5 Reference:

Wagner, C.F. and Evans, R.D., "Symmetrical Components", First edition, pp. 198-214, McGraw-Hill.

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11. Mr. G.C. McDonalds Contribution

EDSA Micro Corporation gratefully acknowledges the following work contributed by Mr. Glen Craig McDonald, P. Eng., Distribution Planning Engineer for the City of Saskatoon, Saskatchewan, Canada. 2/0 ACSR QUAIL 72 KV Positive- and Zero-Sequence Impedance of 72KV Line. (Refer to attached sketch of tangent structure.) 1. Spacing between phases is - 132 inches - 134 inches - 89 inches GMD - 116.3 inches-->9.69 ft 2. Spacing between phases and shield is: -180 inches - 93 inches -166 inches 3. Assume a 55-foot-pole set seven feet into the ground. height of the lowest conductor would be: 55 ft. - 7 ft. - 14.8 ft. = 33 ft.

X1e 12.3060

log10 (2)(33) = 0.373 (28) 4. The phase conductors are 2/0 ACSR Quail. From the Aluminum Electrical Conductor Handbook

(#81-71410 page 4-27, Library of Congress). resistance r at ra--> 75C - 0.9299 ohms/mile - 0.1759 / 1000 ft. reactance Xa - 0.599 shunt cap - 0.1182 mega. ohm/mile - 60 hz. 1 ft. spacing GMR - 0.0072

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5. Ground cable (shield) is #2 Copperweld (Turan Gnen, "Electrical Power Distribution System

Engineering", McGraw-Hill, Table A7, page 656, ISBN 0-07-023707-7, Library of Congress). GMR - 0.00763 rg - at 25C - 0.882 ohm/mile 167.045/1000 ft. rg - at 50C - 0.979 ohm/mile induct Xg - 0.592 ohm/mile Shunt capacitor Xg - 0.1241 mega ohm/mile

Xe(g) = 12.30

60log10(2)(48') = 0.4064 mega ohm/mile (29)

6. Calculate +Z sequence (phase conductors only) Xd = 0.2799 log10 (GMD) (30) = 0.2794 log10 (9.69 ft.) in ohms/mile = 0.2756 Xd = ra + j(Xa = Xd) (31) Z+ve = 0.929 + j(0.599 + 0.2756) (32) = (0.929 + j0.8746) ohm/mile = (0.1759 + j0.1656) ohm/1000 ft. 7. Capacitive effect + ve sequence (phase conductors) X1 = X1a + X1d = 0.1182 + 0.06831 log10 (9.69 ft.) (33) = 0.1182 + 0.06737 X1 = X1a + X1d = 0.1856 mega ohm/mile (34)

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Figure 7 12. Computation of Zero-sequence Impedance Following the Formulas of

Westinghouse Transmission and Distribution Reference Book: GROUNDED NEUTRAL-EARTH RETURN PATH: For one ground-wire case: Zo(a) = ra + re + j(Xe + Xa - 2Xd) per mile per phase (35) where

Xd = 16

( 0.2794 f60

log10 dij )

dij being all possible six distances between phase conductors.

Xa = .2794 f

60 log10

1( GMR )a

(36)

re = .00477f

16


Xe = 32

x (0.2794) x f60

log10 4.665 x 106 f

(37)

= .006985f log10 4.665 x 106 f

At 25C, ra = .929 /mile Xe = 2.8879 Xa = .5987 re = .2862 Xd = .27566 Zo(a) = 1.2152 + j2.93528 (38) Zo(g) = 3rg + re + j(Xe + 3Xg) (39) where:

Xg = .2794 f

60log10

1( GMR )a

(40)

At 25C, rg = .882 /mile Xg = .59162 Zo(g) = 2.9322 + j4.66276 (41) = 5.5081 57.84 Zo(ag) = re + j(Xe - 3Xd) (42) where

Xd = 13

[Xag1 + Xbg1 + Ccg1] (43)

with Xag1 = .004657f log10 dag1, etc. Xd = .29862

17


Zo(ag) = .2862 + j1.99204 (44) = 2.0125 81.82

Zo = Z0 ( a ) - ZZ0

2(ag)

0(g) (45)

= 1.2152 + j2.93528 -

= 1.2152 + j2.93528 - .73531 105.8 = 1.2152 + j2.93528 + .20021 - j.70752 = 1.41541 + j2.22776 /mile = 0.2687 + j0.42192 per 1000 ft. which match almost exactly the computer results. As per equation (40) of Westinghouse Transmission and Distribution Reference Book, for n = 1

Zo(ag) = .00477f + j0.01397f 10e

ag1 bg1 cg13log D

(d d d ) (46)

= .00477f + j0.01397f 10 e 10 ag1 bg1 cg13log D - j0.01397 f log d d d

but

De = 2160 f

Zo(ag) = .00477f + j0.01397f log10 2160 f - j0.01397f(1/3)log10 (dag1 dbg1 dcg1) (47)

= .00477f + j0.01397f log10 [4.6656 x 106 (f

)] - j0.01397f/3 x 3 x 13

log10 (dag1dbg1dcg1)

= j3[ 13

x .004657f log10 (dag1 dbg1 dcg1)]

Zo(ag) = .00477f + j0.006895f log10 ( 4.6656 x 106 f

) - j3[_( Xag1 Xbg1 + Xcg1 )] (48)

18


where Xag1 = .004657f log10 dag1 etc. (49) Zo(ag) = re + j( Xe - 3Xd ) (50) where re = 0.00477f

Xe = 0.006985f log10 ( 4.6656 x 106 f

) (51)

Xd = 13

[ Xag1 + Xbg1 + Xcg1 ] (52)

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13. Verification and Validation: EDSA Micro Corp. - (c) Copyright 2008 Job File Name : 2TRANS.MZP Date : Positive and Zero Sequence Calculation Time : Job Title : QA/QC JOBFILES Project Number : Units (US, Metric) : US Standard Frequency : 60 From Node : To Node : Feeder Name : EE1 Line Type : 1 - Overhead Lines Earth Resistance (ohm-ft) : 100.000 Phase Conductor Resistance (ohms/1000ft) : 0.1800000 G.M.R. of Phase Conductor (ft) : 0.0072000 Distance between Phase Conductors (ft) Conductors 1-2 : 11.0000000 Conductors 2-3 : 7.4200000 Conductors 3-1 : 11.1700000 Calculation Method : 3 - Both Zero and Positive Sequence Return Type : 3 - Ground Neutral-Earth Number of Neutral Conductors : 1 Neutral Conductor Resistance (ohms/1000ft) : 0.1670450 G.M.R. of Neutral Conductor (ft) : 0.0076300 Distance from Phase Conductor to 1st Neutral (ft) Phase 1 to Neutral : 13.8300000 Phase 2 to Neutral : 7.7500000 Phase 3 to Neutral : 15.0000000 OUTPUT RESULTS ---> Zero Sequence Resistance (R0) : 0.26416 (Ohms/Phase/1000ft) Reactance (X0) : 0.40391 (Ohms/Phase/1000ft) Positive Sequence Resistance (R1) : 0.18000 (Ohms/Phase/1000ft) Reactance (X1) : 0.16560 (Ohms/Phase/1000ft)


Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

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14. Computation of Positive and Zero-sequence Impedances (R & X) for Three-

phase Configuration Consisting of Three-single Concentric Neutral Cables WITH THE NEUTRALS SOLIDLY GROUNDED: EDSA Micro Corporation gratefully acknowledges the contributions of Mr. Glen C. McDonald and

Ms. Jun Sun, P. Engs. for the City of Saskatoon, Sask., Canada, and of Dr. A. Miah, Associate Professor at the South Carolina State University, Orangeburg, South Carolina, U.S.A.

The following figure shows the three-phase configuration consisting of three identical single

concentric neutral cables.

Figure 13

The equations which have been used for the computation of Positive and Zero-sequence

impedances are shown in the following pages. The different variables of the equations are identified below:

GMRa = Geometric mean radius of a phase conductor, in ft.; GMRn = Geometric mean radius of a single neutral strand, in ft.;

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Ra,Rn = Effective A.C. resistance of a phase conductor and a neutral strand respectively in ohms/1000 ft. at the temperature and frequency under consideration;

f = Frequency in c/s(Hz) under consideration; = Earth resistivity in ohm-meter; Sab = GMD of the three-phase conductors = (dab x dbc x dca)1/3, in ft.;

D = Diameter of the circle defined by the neutral strand centers of one concentric neutral cable, in ft.;

N = Number of neutral strands wrapped around the insulation of one concentric neutral

cable; Kn = Spacing factor = 1N-1N NOTE: For the Metric System of Units, proper conversion factors have been used in the program. The equations are:

Zaa-g = [ ]r 4.788 10 2 f j2 f 4.681 10 6.096 10 log 1GMR fa 5 4 5 e a+ + +

(53)

Zab-g = [ ]4.788 10 2 f j2 f 4.681 10 6.096 10 log 1S f5 4 5 e ab + +

(54)

Znn-g3 = [ 3 N + 4.788 10 2 f + j2 f 4.681 10 + 6.096 10-5 -4 -5rn

e eab

23log

f+ log 1

S.

+ +

6 096 10 5 1

3Nlog 1

GMR( N 1) log 1

K D2

en

en

(55)

23


Zan-g3 = [ ] 4.788 10 2 f + j2 f-5

4.681 10 + 6.096 10 log 1

D2

S

f

-4 -5e

ab23

(56)

Znn-p = rN

j2 f 6.096 10 N 1N

log 2K D

1N

log 1GMR

log 1S

n 5e

Ne

ne

ab+ +

(57)

Zan-p = j2 f 6.096 10 log2D

log 1S

5e e

ab

(58)

Z13 = Z ZZZaa g ab g

2an p

nn p

ohms per 1000 ft. (59)

Z03 = Z 2Z3ZZaa g ab g

2an g3

nn g3

+

ohms per 1000 ft. (60)

24


15. Positive and Zero-sequence Impedance Calculation CONCENTRIC NEUTRAL CABLE:

EXAMPLE 1 INPUT DATA: Cable description: C-500-14.4-C-31

Figure 14

PHASE CONDUCTOR DATA: Phase Conductor Resistance (ra) (ac 60Hz at 90C): 0.0275 ohms/1000 ft. Diameter of Conductor Dc: 0.7890 inches Strands: 36 Constant based on strands Kg: 0.7678

GMRa = D K

2c g : 0.3028971 inches Geometric Mean Radius of the Phase Conductor (61)

GMD : 7.559526 inches GMD = ( AB x BC x CA ) = ( 6 x 6 x 12)3 3 (62) NEUTRAL CONDUCTOR DATA: Neutral Conductor Resistance (rn') (AC 60Hz at 75C): 1.9342638 ohms/1000 ft. Adjustment for the Lay Length of neutral wires:

rn = rn' x 15

15 (assuming Lay Length = 15 x Lay Diameter) (63)

= 2.339375 Number of wires N: 26 Neutral wire GMRn: 0.031464 inches Geometric Mean Radius of a single neutral strand. DO (outside diameter of the neutral): 1.475 inches Di (inside diameter of the neutral): 1.330 inches

25


EDSA Micro Corp. - (c) Copyright 2008 Job File Name : 4NEUTRAL.MZP Date : Positive and Zero Sequence Calculation Time : Job Title : QA/QC JOBFILES Project Number : Units (US, Metric) : Metric Standard Frequency : 60 From Node : To Node : Feeder Name : TEST4 Line Type : 4 - Three-Single Concentric Neutrals Earth Resistance (ohm-m) : 10.000 Phase Conductor Resistance (ohms/1000m) : 0.0275000 G.M.R. of Phase Conductor (m) : 0.0252414 Distance between Phase Conductors (m) Conductors A-B : 0.5000000 Conductors B-C : 0.5000000 Conductors C-A : 1.0000000 Calculation Method : 3 - Both Zero and Positive Sequence Return Type : 3 - Ground Neutral-Earth Single Neutral Strand AC Resistance (ohms/m) : 2.3393750 G.M.R. of Single Neutral Strand (m) : 0.0026220 Diameter of Neutral Centers (m) : 0.1168750 Number of Neutral Strands : 26 OUTPUT RESULTS ---> Zero Sequence Resistance (R0) : 0.11665 (Ohms/Phase/1000m) Reactance (X0) : 0.06793 (Ohms/Phase/1000m) Positive Sequence Resistance (R1) : 0.09966 (Ohms/Phase/1000m)

26


Reactance (X1) : 0.09915 (Ohms/Phase/1000m) CALCULATION: EARTH RESISTIVITY :100 ohms - meter CALCULATION

Spacing factor Kn = 1

N - 1N

= 1.1391973 (64) All GMR, GMD and D are in inches.

Zaa-g = [ ] r + 4.788 x10 x 2 f + 2 f 4.681x10 + 6.096 x 10 1n 12 x / fGMR

-5 -4 -5

aa

(65)

= 0.0455503 + j 0.2668939 ohms/1000 ft.

Zab-g = [ ] 4.788 x 10 x 2 f + j2 f 4.681x10 + 6.096 x10 1n 12 x / fGMD-5 -4 -5

(66)

= 0.0180503 + j 0.1929589 ohms/1000 ft.

Znn-g 3 = [ r3 + 4.788 x10 x 2 f + j2 f 4.681x10 + 6.096 x10 1n / fnN -5 -4 -5 (67)

+6.096x10-51n 1

(GMD )+ 6.096 x10 x

13 N

1n 12GMR

(N- )1n 4 x 12K x (D + D )23

-5

n n o+

1 i

= 0.0480423 + j0.2111278 ohms/1000 ft.

Zan-g 3 = [ ]4.788 x10 x 2 f + j2 f 4.681x10 + 6.096 x10 1n 12 x f4

x (GMD)3

-5 -4 -5

D + D0 i 2

(68)

= 0.0180503 + j0.2111732 ohms/1000 ft.

Znn-p = n -5n i n

rN

+ j2 f 6.096 10 N-1N

1n 4 x 12K (D + D )

+ 1N

1n 12GMR

-1n 12GMD

0 (69)

27


= 0.0899760 + j0.0545066 ohms/1000 ft.

Zan-p = j2 f x 6.096 x 10 1n 4 x 12

(D + D ) - 1n 12

GMD-5

i

0

(70)

= j0.0546428 ohms/1000 ft.

Z13 = aa-g ab-gan-p2

nn-pZ - Z -

ZZ

= 0.0617760 + j0.0592289 ohms/ 1000 ft. (71)

Z03 = aa-g ab-gan-g 32

nn-g 3Z + 2 Z -

3ZZ

= 0.1147475 + j0.0313168 ohms/ 1000 ft.

(72)

16. Positive and Zero Sequence Impedance Calculation CONCENTRIC NEUTRAL CABLE: EXAMPLE 2 INPUT DATA: Cable Description: C-250-4.16-C-30 Phase Conductor Data: Figure 15 Phase Conductor Resistance (ra) (AC 60Hz at 90C): 0.0542 ohms/1000 ft. Diameter of Conductor Dc: 0.5580 inches Strands: 37 Constant based on strands Kg: 0.7678

GMRa = c gD x K

2 : 0.2142162 inches

(73)

GMD: 1.17 inches GMD = ( AB x BC x CA ) = ( 1.17 x 1.17 x 1.17 )3 3 (74) NEUTRAL CONDUCTOR DATA: Neutral conductor resistance (rn') (AC 60Hz at 75C): 3.06855 ohms/1000 ft. Adjustment for the Lay Length of neutral wires:

nr x 15 +

15 (assuming Lay Length = 15 Diameter) = 3.7112364 ohms/1000 ft. (75)

28


Number of wires N: 24 Neutral Wire GMRn: 0.024961 inches Do (outside diameter of the neutral): 0.9950 inches Di (inside diameter of the neutral): 0.8900 inches CALCULATION: EARTH RESISTIVITY :100 ohms - meter CALCULATION

Spacing factor Kn = 1

N-1N

= 1.1481779 (76) All GMR, GMD and D are in inches.

Zaa-g = [ ]a -5 -4 -5a

r + 4.788 x10 x 2 f + 2 f 4.681x10 + 6.096 x10 1n 12 x

GMR

f

(77)

= 0.0722503 + j0.2748549 ohms/ft.

Zab-g = [ ]4.788 x10 2 f + j2 f 4.681x10 + 6.096 x10 1n 12 x GMD-5 -4 -5 f

(78)

= 0.0180503 + j 0.2358377 ohms/ft.

Znn-g 3 = nN

-5 -4 -5r3

+ 4.788 x10 x 2 f + j2 f 4.681x10 + 6.096 x10 1n

f (79)

+6.096 x10 1n1

(GMD )+ 6.096 x10 x

13N

1n 12GMR

+ (N-1)1n 4 x 12K x (D + D )

-523

-5

n n 0

i

= 0.0695952 + j0.2427273 ohms/1000 ft.

29


Zan-g 3 = [ ]4.788 x10 x 2 f + j2 f 4.681x10 + 6.096 x10 1n 12 x f4

x (GMD 2)3

-5 -4 -5

D + iD0

(80)

= 0.0180503 + j0.2428039 ohms/1000 ft.

Znn-p = n -5n i n

rN

+ 2 f x 6.096 x10N - 1

N1n 4 x 12

K x (D + D )+ 1

N1n 12

GMR-1n 12

GMDj

0

= 0.1546346 + j0.0206688 ohms/1000 ft. (81)

Zan-p = j2 fx 6.096 x10 1n4 x 12

(D + D ) - 1n

12GMD

-5

O i

(82)

= j0.0208986 ohms/1000 ft.

Z13 = aa-g ab-gan-p2

nn-pZ - Z -

ZZ

= 0.0569748 + j0.0386463 ohms/1000 ft. (83)

Z03 = aa-g ab-gan-g 32

nn-g 3Z + 2 Z -

3ZZ

= 0.2002247 + j0.0482579 ohms/1000 ft. (84)

Longhand Program % Deviance Zero Sequence R0 0.2002247 0.19925 0 X0 0.482579 0.4977 0 Positive Sequence R1 0.0569748 0.05697 0 X1 0.0386463 0.03865 0 Program and longhand calculation results match 100%

30


EDSA Micro Corp. - (c) Copyright 2008 Job File Name : 5NEUTRAL.MZP Date : Positive and Zero Sequence Calculation Time : Job Title : QA/QC JOBFILES Project Number : Units (US, Metric) : US Standard Frequency : 60 From Node : To Node : Feeder Name : TEST5 Line Type : 4 - Three-Single Concentric Neutrals Earth Resistance (ohm-ft) : 100.000 Phase Conductor Resistance (ohms/1000ft) : 0.0542000 G.M.R. of Phase Conductor (ft) : 0.0178513 Distance between Phase Conductors (ft) Conductors A-B : 0.0975000 Conductors B-C : 0.0975000 Conductors C-A : 0.0975000 Calculation Method : 3 - Both Zero and Positive Sequence Return Type : 3 - Ground Neutral-Earth Single Neutral Strand AC Resistance (ohms/1000ft) : 3.7112364 G.M.R. of Single Neutral Strand (ft) : 0.0020800 Diameter of Neutral Centers (ft) : 0.0785410 Number of Neutral Strands : 24 OUTPUT RESULTS ---> Zero Sequence Resistance (R0) : 0.19925 (Ohms/Phase/1000ft) Reactance (X0) : 0.04977 (Ohms/Phase/1000ft) Positive Sequence Resistance (R1) : 0.05697 (Ohms/Phase/1000ft) Reactance (X1) : 0.03865 (Ohms/Phase/1000ft)

31


17. Nomenclature for Equations D = diameter of the circle defined by the neutral strand centers of one concentric neutral cable

(see Figure 1, page 3) in feet. Values of D can be derived from information published in cable manufacturers' catalogues.

f = frequency - Hertz GMRa, = Geometric Mean Radius of the phase conductor (subscript a) and a single neutral strand GMRn (subscript n) - in feet. GMRa is readily available from tables such as those in References 1,

3, and 5. GMRn can also be obtained from tables but, since each strand has a solid, circular cross section, it is readily calculated using GMRa = .3894dn, where dn is the diameter of a single neutral strand in feet (see Figure 1).

j = the complex operator, 1 90 KN = spacing factor which, when multiplied by D/2, gives the geometric mean spacing among the

N neutral strands of one concentric neutral cable. KN is obtained from the expression KN=(N)1/(N-1).

N = number of neutral strands wrapped around the insulation of one concentric neutral cable

(see cable manufacturers' catalogues). ra,rn = resistance of the phase conductor (subscript a) and a single neutral strand (subscript n) -

ohms/1000 feet (see cable manufacturers' catalogs). There should be a c resistance values calculated for the expected operating temperatures of the phase and neutral conductors. They should include skin effect and proximity effect, wherever these effects can be readily determined.

re = ohms/1000 ft. = earth resistivity - ohms meter. Sab = geometric mean spacing of the three-phase conductors - feet. Referring to Figure 1,

Sab=(dabdbcdca). Zaa-g, = self impedance of a phase conductor (subscript aa) and self impedance of a group of Znn-g3 paralleled neutral strands (subscript nn) with earth return - ohms/1000 feet.

32


Zab-g3, = mutual impedance between two conductors or two groups of conductors with earth return-

Zan-g3ohms/1000 feet. Subscripts a and b denote phase conductors and subscript n denotes a group of neutral conductors. In a three-phase circuit there are actually three mutual impedances among the three-phase conductors: Zab-g, Zbc-g, and Zca-g. However, in Equation (A2) the use of a geometric mean spacing Sab instead of the actual interphase spacing means that the resulting value of Zab-g is the arithmetic mean of the three actual values. In a similar sense Zan-g3 is an average of the three actual mutual impedances that exist between each of the three- phase conductors and the entire group of neutral conductors.

Zan-p = positive sequence mutual impedance between the phase conductors of the cable and their

concentric neutrals - ohms/1000 feet.* Znn-p = positive sequence self impedance of the three-phase circuit formed by the concentric

neutrals of the cables - ohms/1000 feet.* Z13, = positive and zero sequence impedance, respectively, of a three-phase concentric neutral Zo3 circuit ohms/1000 feet. * When positive sequence currents flow in the phase conductors of a three-phase concentric

neutral circuit induced currents will circulate between each phase's neutral and the earth return path. The magnitude of this current depends upon neutral resistance, interphase spacing, and the diameter of the circle of centers of concentric neutral strands. In turn, the positive sequence impedance of the circuit is modified by the magnitude of these neutral currents. Z2an-p/Zna-p is the factor which reflects the effect of neutral circulating current on the positive sequence impedance of three-phase concentric neutral cable. On an overhead open wire transmission or distribution circuit this effect is negligible. Recent studies have shown that it is not negligible for the close spacing associated with concentric neutral cable.

33


34

18. References 1. Clarke, Edith, Circuit Analysis of A-C Power Systems, Vol. I, John Wiley and Sons, New

York, 1943. 2. Clarke, Edith, Circuit Analysis of A-C Power Systems, Vol. II, John Wiley and Sons, New

York, 1943. 3. Wagner, C. F., and R. D. Evans, Symmetrical Components, McGraw-Hill Book Co., New

York, 1933. 4. Stevenson, W. D., Jr., Elements of Power System Analysis, McGraw-Hill Book Co., New

York, 1955. 5. Electrical Transmission and Distribution Reference Book, Westinghouse Electric

Corporation, Pittsburgh, Fourth Edition, 1964. 6. Smith, D. R., and J. L. Barger, "Impedance and Circulating Current Calculations for UD

Multi-Wire Concentric Neutral Circuits," IEEE Conference Record of 1971 Conference on Underground Distribution, September 27-October 1, 1971, Detroit, Michigan, pp. 130-138.

7. Edison Electric Institute and the Bell Telephone System, Engineering Reports of the Joint

Subcommittee on Development and Research, Vol. II, Report No. 14. 8. Edison Electric Institute and the Bell Telephone System, Engineering Reports of the Joint

Subcommittee on Development and Research, Vol. IV, Report No. 37. 9. "Rome Cable UD Technical Manual," Third Edition, Rome Cable Co., Rome, N.Y., 13440. 10. IEEE Power Group, Conference Record (69C1-PWR) and Conference Record

Supplement (69C1-PWR (SUP.)) for the Special Technical Conference on Underground distribution, Anaheim, California, May 12-16, 1969.

11. Ramo, S. and J. R. Whinnery, Fields and Waves in Modern Radio, 2nd edition, John Wiley

& Sons, Inc., New York, 1953.


19. Standalone Short Line Parameters Tutorial

1813

.45

13.4

5 13.45

13.45

18

10

Phase 1 Phase 2 Phase 3

Neutral 1 Neutral 2

18

Figure 16 Tutorial Case Study (File: shtln.mzp) This tutorial will illustrate the step-by-step procedure required to calculate the following short-line parameters using EDSA's "Short Line Parameters Calculation" program:

1. Zero Sequence Resistance & Reactance 2. Positive Sequence Resistance & Reactance

The tutorial is based on a 3-phase circuit equipped with two neutral return conductors. Figure 23 shows the geometrical/structural configuration of the circuit. All the dimensions shown in the figure are expressed in feet. General data for each circuit follows: Line Type: Overhead Line Earth Resistance (ohm-ft): 100.000 Ph. Cond. Res. (ohms/1000ft): 0.0445070 G.M.R. of Phase Conductor (ft): 0.0277000 Return Type: 2 Neutral Conductors

35


Distance between Phase Conductors:

Conductors 1-2: 18.00 ft. Conductors 2-3: 18.00 ft. Conductors 3-1: 36.00 ft.

No. of Neutral Cond.: 2 Distance between Neutral Conductors: 18.00 ft Neutral Cond. Res. (ohms/1000ft): 0.0445070 G.M.R. of Neutral Conductor (ft): 0.0277000 Distance from Phase Conductor to 1st Neutral:

Phase 1 to Neutral: 13.45 ft. Phase 2 to Neutral: 13.45 ft. Phase 3 to Neutral: 28.80 ft.

Distance from Phase Conductor to 2nd Neutral:

Phase 1 to Neutral: 28.80 ft. Phase 2 to Neutral: 13.45 ft. Phase 3 to Neutral: 13.45 ft.

1.1 From the EDSA TECHNICAL 2004 main menu screen invoke the Short Line Parameters program as follows: > Select Analysis / Miscellaneous Analysis / Line Constants / Short Line Parameters

36


1.2 Once in the Positive and Zero Sequence Calculation program main menu, proceed to create

the new file as follows: > Select File / Select New

1.3 Once in the Enter Data screen proceed as follows: > From the Select a Page field select Job Title > In the Project Num. field type the appropriate job id. Number - Tutorial 99

> In the Feeder Name field type the appropriate label for the feeder being studied - Tutorial Feeder

37


> In the Job Title field type an appropriate description for the project > In the From Node field type the node id. from which the feeder originates - 1 > In the To Node field type the destination node id. - 2 > Return to the Select a Page field and select Line Type

1.4 As the program displays the Line Data information screen enter the data pertaining to the line as

follows: > From the Line Type picklist select 1 - Overhead Lines > From the Calculation Method field select Both (for Positive & Zero Sequence) > From the Unit Type field select US > In the Frequency (Hz) field type 60 > In the Earth Resistance (ohm-ft) field type 100 > In the Phase Conductor Resistance (ohms/1000 ft) field type 0.0445070 > In the G.M.R of Phase Conductor (ft) field type 0.0277000 (Geometric Mean Radius)

> Return to the Select a Page field and select Return Type

38


1.5 Proceed to describe the type of current return path according to the following procedure: > From the Return Type picklist select 2 - Neutral

> Notice that once Neutral is selected a new page named Neutral appears in the Select a page field. This will allow the user to enter the neutral conductor(s) information.

> Proceed to enter the Distance between Phase Conductors (ft) information as follows: > Conductor 1 - 2: 18.00 (ft) (Refer to Figure 23) > Conductor 2 - 3: 18.00 (ft) (Refer to Figure 23) > Conductor 3 - 1: 36.00 (ft) (Refer to Figure 23) > Return to the Select a Page field and select Neutral

1.6 Finally, proceed to define the neutral current return-circuit according to the following guidelines:

39


> In the Number of Neutral Conductors field select 2

40


> In the Neutral Conductor Resistance (ohms/1000 ft) field type 0.0445070 > In the G.M.R of Neutral Conductor (ft) field type 0.0277000 (Geometric Mean Radius) > In the Distance between Neutral Conductors (ft) field type 18.00 (Refer to Figure 23) > Proceed to enter the Distance form Phase Conductor to Neutrals (ft) information as follows:

1st Neutral 2nd Neutral

Phase 1 13.45 ft 28.80 ft Phase 2 13.45 ft 13.45 ft Phase 3 28.80 ft 13.45 ft

> The above distances can be calculated based on the dimensions specified in Figure 23.

> Press .

1.7 Once the data input process is concluded, proceed to save the file according to the following

procedure: > Select File / Save As > In the File Name field type "shtln.mzp" > Press

41


1.8 Once the file has been input and saved, the main menu screen space shows a summary of the

data. At this point the program is ready to run the calculations. To do so, follow this procedure: > Select Output / Calculate

> Or simply select the icon

1.9 Once the calculations are completed, the results are shown in the output screen. With the aid of

the tool bar menu, the user has the following options: Scroll up and down to read the results, Print the results, and Save the results to either a Feeder file or Text file.

42


1.10 To save the results to a feeder file, proceed as follows: > Select Output / Save to Feeder File

1.11 If the output is saved to a feeder file EDSA will acknowledge by means of the above dialog box.

Press .

43


1.12 To save the results to a text file proceed as follows: > Select Outpu / Save to Text File

1.13 Proceed to save the results into the text file according to the following procedure: > In the File Name field type "shtln.txt" > Press

44


45

1.14 Following are the results of the analysis: EDSA Micro Corp. - (c) Copyright 2008 Job File Name : SHTLN.MZP Date : Positive and Zero Sequence Calculation Time : Job Title : Tutorial Exercise for Short Line Parameter Calculations EDSA Micro Corporation January 1999 Project Number : Tutorial 99 Units (US, Metric) : US Standard Frequency : 60 From Node : 1 To Node : 2 Feeder Name : Tutorial Feeder Line Type : 1 - Overhead Lines Earth Resistance (ohm-ft) : 100.000 Phase Conductor Resistance (ohms/1000ft) : 0.0445070 G.M.R. of Phase Conductor (ft) : 0.0277000 Distance between Phase Conductors (ft) Conductors 1-2 : 18.0000000 Conductors 2-3 : 18.0000000 Conductors 3-1 : 36.0000000 Calculation Method : 3 - Both Zero and Positive Sequence Return Type : 2 - Neutral Number of Neutral Conductors : 2 Distance between Neutral Conductors (ft) : 18.0000000 Neutral Conductor Resistance (ohms/1000ft) : 0.0445070 G.M.R. of Neutral Conductor (ft) : 0.0277000 Distance from Phase Conductor to 1st Neutral (ft) Phase 1 to Neutral : 13.4500000 Phase 2 to Neutral : 13.4500000 Phase 3 to Neutral : 28.8000000 Distance from Phase Conductor to 2nd Neutral (ft) Phase 1 to Neutral : 28.8000000 Phase 2 to Neutral : 13.4500000 Phase 3 to Neutral : 13.4500000 OUTPUT RESULTS ---> Zero Sequence Resistance (R0) : 0.11127 (Ohms/Phase/1000ft) Reactance (X0) : 0.35633 (Ohms/Phase/1000ft) Positive Sequence Resistance (R1) : 0.04451 (Ohms/Phase/1000ft) Reactance (X1) : 0.15416 (Ohms/Phase/1000ft))


20. Network-Based Short Line Parameters Calculations

18

13.4

5

13.4

5 13.45

13.45

18

10

Phase 1 Phase 2 Phase 3

Neutral 1 Neutral 2

18

Figure 17 Short Line Under Study This tutorial will illustrate the step-by-step procedure required to calculate the following short-line parameters using EDSA Technical 2004 "Short Line Parameters Calculation" program: 1. Zero Sequence Resistance & Reactance 2. Positive Sequence Resistance & Reactance The tutorial is based on a 3-phase circuit equipped with two neutral return conductors. The above figure (Figure 24) shows the geometrical/structural configuration of the circuit. All the dimensions shown in the figure are expressed in feet. General data for each circuit is shown in the next page.

46


Overhead Line Electrical and Physical Topology Data

Line Type: Overhead Line Earth Resistance (ohm-ft): 100.000 Ph. Conductor Resistance (/1000ft): 0.0445070 G.M.R. of Phase Conductor (ft): 0.0277000 Return Type: 2 Neutral Conductors Distance between Phase Conductors: Conductors 1-2: 18.00 ft. Conductors 2-3: 18.00 ft. Conductors 3-1: 36.00 ft. No. of Neutral Conductors: 2 Distance between Neutrals: 18.00 ft Neutral Cond. Res. ( /1000ft): 0.0445070 G.M.R. of Neutral Conductor (ft): 0.0277000 Distance from Phase Conductor to 1st Neutral: Phase 1 to Neutral: 13.45 ft. Phase 2 to Neutral: 13.45 ft. Phase 3 to Neutral: 28.80 ft. Distance from Phase Conductor to 2nd Neutral: Phase 1 to Neutral: 28.80 ft. Phase 2 to Neutral: 13.45 ft. Phase 3 to Neutral: 13.45 ft.

47


48

Step 1. Open the tutorial file called SHORT_LINE.axd. We will proceed to calculate the positive and zero sequence parameters of this line according to the Electrical and Physical Topology data shown in Figure 1.

Step 2. Double click on the line called FEEDER No.1.

Step 3. Once the feeder editor appears, select Calculate Short Line Parameters.


Step 4. Select Job Title.

Step 6. Select Save As. This data is automatically

updated from the job files single line diagram.

Step 7. Assign an appropriate name for the file, and select the folder in which it is to be stored. Press OK.

Step 5. Proceed to enter all the pertinent descriptive data for the line under study, as shown in this example.

49


Step 8. Select the Line Type editor.

Step 10. Select the Return Type editor.

Step 11. Proceed to describe the return type (Neutral) and the distance between the phase conductors of the line. Proceed as indicated here.

Step 9. Proceed to describe the electrical characteristics of the line (Overhead Line) under study as well as the Units and the Calculation Method required. Proceed as indicated here.

50


51

Step 12. Select the Neutral editor.

Step 13. Proceed to select the number of neutral conductors (2) and describe their electrical characteristics. Enter the distance between each phase conductors with respect to each of the neutral conductors. Proceed as indicated here.

Step 14. Once the data entry process has been completed, select Save and then select OK.

Step 15. Once the OK button is pressed, the program returns to the feeder editor. Select the Short Circuit tab, and the sequence impedance results calculated by the program have been automatically calculated and updated as shown here.


52

Step 16. To add this feeder data to a library, select the library in which it is to be saved and then select Save to Library. In this example the feeder will be saved to the default EDSA Standard library under the Transmission Line description.

1

3

2

4

Step 17. Select the specific library to be used. In this example, select US Non-Magnetic.

Step 19. Select OK.

Step 18. Specify the Resistance and Reactance correction factors as required.


53

Step 20. To verify that the new feeder has been added to the library, select the Library pick-list from within the feeder editor screen.

Step 21. Verify that the feeder has been added to the following library US Std. Library/Feeder/3 Phase/EDSA/ Transmission Line


2.1 Editing and Existing Network-Based Study

Step 1. Open the tutorial file called SHORT_LINE.axd.

Step 2. Double click on the line called FEEDER No.1.

Step 3. Once the feeder editor appears, select Calculate Short Line Parameters.

54


Step 4. Select Open File.

Step 5. Select the file that is to be modified. At this point, the user can also select any other standalone file to be re-assigned to this feeder. In this example, select SLT.MZP and press OK.

Step 6. Once in the editor screens, select the data to be modified and re-run the analysis as shown in previous sections of this tutorial. Select Save and then select OK, in order to update the feeder data.

55


3.0 Standalone Short Line Parameters Calculation

Step 1. From the EDSA Technical 2004 main menu, select the Short Line Parameters application as shown here.

This exercise is based on the overhead line topology shown in Figure 1 of this tutorial.

Step 2. From the Short Line Parameters program main menu, proceed to create a new file by selecting File/New.

56


Step 3.

Select Job Title. Step 4. Proceed to enter all the pertinent descriptive data for the line under study, as shown in this example.

Step 5. Select Save As. This data is manually

entered and customized by the user.

Step 6. Assign an appropriate name for the file, and select the folder in which it is to be stored. Press OK.

57


Step 7. Select the Line Type editor.

Step 9. Select the Return Type editor.

Step 8. Proceed to describe the electrical characteristics of the line under study as well as the Units and the Calculation Method required. Proceed as indicated here.

Step 10. Proceed to describe the return type and the distance between the phase conductors of the line under study. Proceed as indicated here.

58


Step 11. Select the Neutral editor.

Step 12. Proceed to select the number of neutral conductors (2) and describe their electrical characteristics. Enter the distance between each phase conductors with respect to each of the neutral conductors. Proceed as indicated here.

Step 13. Once the data entry process has been completed, select Save and then select OK.

Step 14. To run the analysis, select the Running Man icon.

Step 15. The results of the calculation are shown here in red.

59


60

Step 17. To edit any section of the input data, select Edit/Edit or simply click on the Edit icon.

Step 18. Proceed to modify and re-run the analysis as required.

Step 19. Once the data entry process and the final calculations have been completed, select Save

Step 16. An alternate way to run the analysis is by selecting Output/Calculate. This will produce the same results shown in step 16.

Step 20. To create a text output report of the analysis, select Save to Text File.


Step 21. Assign a name and a folder location for the text output file as indicated here. Select OK.

Step 22. To view the output report, open the text file using the windows Notepad or any other word processor of preference.

61


62

Step 23. To save the newly created feeder file into an EDSA library, select Save to Feeder File.

Step 24. Proceed as indicated in steps 16 to 21.

Short Line Parameters CalculationsPositive and Zero Sequence ImpedanceTable of ContentsList of Figures1. Foreword2. Purpose3. Capabilities4. Option 1. Aerial (Overhead) Lines5. Option 2. Three-Conductor Cables6. Option 3. Three-Single Conductor Cables7. Option 4. Three-Single Concentric Neutral Cables, Neutrals Solidly Grounded8. Three-phase Short Line Consisting of a Three-conductor Cable: 8.1 Cable Configuration:8.2 Parameters Identification: 8.3 Positive-sequence Impedance (R1, X1): 8.4 Zero-sequence Impedance (RO, XO): 8.4.1 Sheath return only: 8.4.2 Grounded sheath-earth return:

8.5 Reference:

9. Three-phase Single Circuit Short Aerial (Overhead) Line With Neutral Wire: 9.1 General Configuration: 9.2 Parameters Identification: 9.3 Positive-sequence Impedance (R1, X1): 9.4 Zero-sequence Impedance (R0, X0): 9.4.1 Earth return only: 9.4.2 Neutral return only: 9.4.3 Grounded neutral-earth return:

9.5 Reference:

10. Three-phase Single Circuit Short Line Consisting of Three-single Conductor Cables: 10.1 General Configuration: 10.2 Parameters Identification:10.3 Positive-sequence Impedance (R1, X1): 10.3.1 With sheaths open 10.3.2 With sheaths short-circuited (Bonded together):

10.4 Zero-sequence Impedance (RO, XO): 10.4.1 Earth return only:10.4.2 Sheaths (bonded together) return only: 10.4.3 Grounded Sheath-earth return:

10.5 Reference:

11. Mr. G.C. McDonalds Contribution 12. Computation of Zero-sequence Impedance Following the Formulas of Westinghouse Transmission and Distribution Reference Book:13. Verification and Validation:14. Computation of Positive and Zero-sequence Impedances (R & X) for Three-phase Configuration Consisting of Three-single Concentric Neutral Cables15. Positive and Zero-sequence Impedance Calculation16. Positive and Zero Sequence Impedance Calculation17. Nomenclature for Equations 18. References19. Standalone Short Line Parameters Tutorial20. Network-Based Short Line Parameters Calculations2.1 Editing and Existing Network-Based Study

3.0 Standalone Short Line Parameters Calculation

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