Three-phase resistance measurements
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Three-Phase Resistance Measurements L. W. M A T S C . C. BASU G. R. HORGHER MEMBER AIEE STUDENT MEMBER AIEE ASSOCIATE AIEE L ARGE DISCREPANCIES between the measured 1 values of resistance of three identical conductors with 3-phase current have been reported by observers. 1 It has been the practice to take the average of the values of resistance measured on the three conductors as being the true value of a-c resistance of each. This procedure is valid if the resistances of three conductors are actually equal. Unsymmetrical spacing of the three conductors produces unbalanced inductive reactances which in turn produce errors in the measured conductor resistance. These errors can be eliminated by making measurements, first with 3- phase current of one-phase sequence and then with 3- phase current of the opposite phase sequence. The average value of the resistances measured on any one conductor with the two phase sequences is the true value of a-c resistance. Figure 1 shows a diagram of the measuring circuit which is very similar to that described by Summers. 2 This circuit is an a-c potentiometer. The voltage drop across a stand- ard resistor, shunted by a voltage divider, in the secondary of a current transformer plus the voltage in the secondary of a mutual inductance is made equal to the drop between the potential points on the conductor. The conductors on which these measurements were made are three copper tubes each 30 feet in length with an inner diameter of 0.375 inch and an outer diameter of 0.540 inch. Two potential leads were connected on the outside of each conductor at points 15 feet apart and brought away at right angles to a distance of about 18 feet, then closed to form a rectangular loop. The leads were twisted from this loop to the measuring circuit. In order to minimize the effect of stray fields, two measurements with opposite polarities were made on each conductor for both phase sequences. With a conductor spacing of approximately 2 inches, 2y 4 inches, and 2 3 / 4 inches, the resistance of ^4-phase con- ductor measured with positive sequence current was 1.55 milliohms and with negative sequence current 1.30 milli- ohms giving an average of 1.425 milliohms. The d-c resist- ance of the same conductor, measured with a Kelvin bridge, was 1.406 ohm. With positive- and negative-phase se- quence currents the measured resistances on i?-phase con- ductor were 1.08 and 1.28 milliohms respectively, giving an average value of 1.18 milliohms. The d-c resistance of B- phase conductor was 1.152 milliohms. The corresponding a-c values for C-phase conductor were 1.08 and 1.14 giving an average of 1.11 milliohms compared with a d-c value of 1.087 milliohms. Measurements were repeated for differ- ent conductor spacings, and the average values of the indi- vidual conductor resistance obtained with opposite phase Digest of paper 50-75, "Three-Phase Measurements of Resistance," recommended by the AIEE Committee on Instruments and Measurements and approved by the AIEE Technical Program Committee for presentation at the AIEE Winter General Meeting, New York, . Y., January 30-February 3, 1950. Scheduled for publication in AIEE Transactions, volume 69, 1950. L. W. Matsch is with the Department of Electrical Engineering, Illinois Institute of Technology, Chicago, 111., and N. C. Basu is a graduate student at the Institute. G. R. Horcher is with the University of Kansas, Lawrence, Kans. Figure 1. Circuit diagram for 3-phase measurements of resistance and reactance sequences were substantially the same as those obtained originally. Inductive-reactance measurements were also made, computed from the setting of the mutual inductance , as shown in Figure 1. It can be shown that using only positive-sequence current, the error in the measured value of resistance on 4-phase conductor (conductor number 1) is — 0.866 (^¥#i 2 — Xd n ) where Xd\ 2 is the separation component of reactance be- tween A- and i?-phase conductors and Xd n is the sepa- ration component of reactance between C- and 4-phase con- ductors. 3 The apparent a-c resistance was computed by adding this term to the d-c resistance. Table I shows a comparison between computed values and measured values of resistance with positive sequence current only. Table I. Computed Apparent Conductor Resistance for Positive Sequence Current Phase 0.866(Xdn-Xdn) Resistance, Computed milliohms Measured A —0.118 1.53 1.55 +0.081 1.07 1.08 . c 1.12 1.08 Three-phase measurement of resistance followed by one with currents of opposite phase sequence will yield data from which the true value of a-c resistance for each indi- vidual conductor can be obtained. REFERENCES 1. Problems in the Measurement of A-G Resistance and Reactance of Large Con- ductors, . H. Salter. AIEE Transactions, volume 68, 1948, pages 1390-6. 2. Effective Resistance and Inductance of 3-Gonductor Shipboard Power Cables, Samuel D. Summers. AIEE Transactions, volume 68, 1948, pages 1345-50. 3. The Transmission of Electric Power, Volume I (book), W. A. Lewis. Edwards Brothers, Inc., Ann Arbor, Mich., 1948. MAY 1950 Matsch, Basu, Horcher—Three-Phase Resistance Measurements 443
Transcript of Three-phase resistance measurements
Three-Phase Resistance Measurements L. W. M A T S C Η Ν. C. B A S U G. R. H O R G H E R
M E M B E R A I E E S T U D E N T M E M B E R A I E E A S S O C I A T E A I E E
LA R G E DISCREPANCIES between the measured 1 values of resistance of three identical conductors with
3-phase current have been reported by observers. 1 I t has been the practice to take the average of the values of resistance measured on the three conductors as being the t rue value of a-c resistance of each. This procedure is valid if the resistances of three conductors are actually equal.
Unsymmetrical spacing of the three conductors produces unbalanced inductive reactances which in turn produce errors in the measured conductor resistance. These errors can be eliminated by making measurements, first with 3-phase current of one-phase sequence and then with 3-phase current of the opposite phase sequence. The average value of the resistances measured on any one conductor with the two phase sequences is the true value of a-c resistance.
Figure 1 shows a diagram of the measuring circuit which is very similar to that described by Summers. 2 This circuit is an a-c potentiometer. The voltage drop across a standard resistor, shunted by a voltage divider, in the secondary of a current transformer plus the voltage in the secondary of a mutual inductance is made equal to the drop between the potential points on the conductor. The conductors on which these measurements were made are three copper tubes each 30 feet in length with an inner diameter of 0.375 inch and an outer diameter of 0.540 inch. Two potential leads were connected on the outside of each conductor at points 15 feet apart and brought away at right angles to a distance of about 18 feet, then closed to form a rectangular loop. T h e leads were twisted from this loop to the measuring circuit. In order to minimize the effect of stray fields, two measurements with opposite polarities were made on each conductor for both phase sequences.
With a conductor spacing of approximately 2 inches, 2 y 4 inches, and 2 3 / 4 inches, the resistance of ^4-phase conductor measured with positive sequence current was 1.55 milliohms and with negative sequence current 1.30 milli-ohms giving an average of 1.425 milliohms. The d-c resistance of the same conductor, measured with a Kelvin bridge, was 1.406 ohm. With positive- and negative-phase sequence currents the measured resistances on i?-phase conductor were 1.08 and 1.28 milliohms respectively, giving an average value of 1.18 milliohms. The d-c resistance of B-phase conductor was 1.152 milliohms. The corresponding a-c values for C-phase conductor were 1.08 and 1.14 giving an average of 1.11 milliohms compared with a d-c value of 1.087 milliohms. Measurements were repeated for different conductor spacings, and the average values of the individual conductor resistance obtained with opposite phase
Digest of paper 50-75, "Three-Phase Measurements of Resistance," recommended by the AIEE Committee on Instruments and Measurements and approved by the AIEE Technical Program Committee for presentation at the AIEE Winter General Meeting, New York, Ν. Y., January 30-February 3, 1950. Scheduled for publication in AIEE Transactions, volume 69, 1950.
L. W. Matsch is with the Department of Electrical Engineering, Illinois Institute of Technology, Chicago, 111., and N. C. Basu is a graduate student at the Institute. G. R. Horcher is with the University of Kansas, Lawrence, Kans.
F i g u r e 1. Circuit d iagram for 3 -phase m e a s u r e m e n t s of res i s tance a n d reactance
sequences were substantially the same as those obtained originally. Inductive-reactance measurements were also made, computed from the setting of the mutual inductance Μ, as shown in Figure 1.
It can be shown that using only positive-sequence current, the error in the measured value of resistance on 4-phase conductor (conductor number 1) is — 0.866 ( ^ ¥ # i 2 — Xdn) where Xd\2 is the separation component of reactance between A- and i?-phase conductors and Xdn is the separation component of reactance between C- and 4-phase conductors. 3 T h e apparent a-c resistance was computed by adding this term to the d-c resistance. Table I shows a comparison between computed values and measured values of resistance with positive sequence current only.
T a b l e I. C o m p u t e d A p p a r e n t Conductor Res i s tance for Pos i t ive S e q u e n c e Current
Phase 0.866(Xdn-Xdn) Resistance,
Computed milliohms
Measured
A —0.118 1.53 1.55 Β + 0 . 0 8 1 1.07 1.08 . c 1.12 1.08
Three-phase measurement of resistance followed by one with currents of opposite phase sequence will yield data from which the true value of a-c resistance for each individual conductor can be obtained.
R E F E R E N C E S 1. Problems in the Measurement of A-G Resistance and Reactance of Large Conductors, Ε. H. Salter. AIEE Transactions, volume 68, 1948, pages 1390-6.
2. Effective Resistance and Inductance of 3-Gonductor Shipboard Power Cables, Samuel D. Summers. AIEE Transactions, volume 68, 1948, pages 1345-50.
3. The Transmission of Electric Power, Volume I (book), W. A. Lewis. Edwards Brothers, Inc., Ann Arbor, Mich., 1948.
M A Y 1950 Matsch, Basu, Horcher—Three-Phase Resistance Measurements 443
