Reactance of Transposed vs Un-Transposed Line

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I think you have your answer by now but just so you know, it does indeed affect the impedance balance of the long line transmission system and more so on lower voltages like 69kV than 138 kV. Actual experience in the Poconos' in PA. Long 69 kV line supplying winter peak loads, ski lodge tripping out motors dur to unbalanced supply voltages. Metering at local step down transformers supplied by the same lines showed current balance on each phase for six different substation transformers (typically 69 kV to 12 kV with 25 to 50 MVA capacity) with 20 amps of each phase supplying the area where the ski lodge was located. Voltages on the Wye side of the transformers gave a measured unbalance of between phase conductors on the 12 kV side typically as A-Phase 130 to 131 volts, B-Phase 124 to 127 volts and C-Phase 119 to 121 volts. Measurements were coordinated and taken by calibrated instruments. At the same time, we took 69 kV measurements on a Phase to ground basis using a set of calibrated PTs and found 210.8 Volts A- Phase to ground, 196.4 Volts B-Phase to ground and 184.1 Volts C-Phase to ground measured using a 350 to 1 ratio PT.

The problem was no transpositions for a double circuit line that reached just over 81 miles. Capacitive coupling to ground and inductive coupling between phases created enough of an imbalance in voltage that we were burning up a few motors. Next low peak period we transposed the line in three locations which solved the problems but it was interesting to note we had a greater imbalance in phase currents after the correction for voltage imbalance but the voltages were within 1 to 2 volts of each other on the 12 kV side.
 
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