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Frequency dependent impedance of stranded conductors using the subdivision method

University of British Columbia

Accurate determination of frequency dependent resistance of stranded conductors in transmission lines has not been thoroughly investigated for a wide frequency range of DCto 10 MHz. The main objective of this thesis project has been to write a computer program that calculates the resistance and inductance of stranded conductors in the indicated frequency range. The fundamental idea in the implemented technique is to subdivide the cross section of each strand with circular and straight line segments forming circular and elemental shape subconductors (or elements). Then, assuming uniform current density within each area, resistance, self inductance, and mutual inductances for all subconductors are calculated. The resistances and inductances are placed into a complex impedance matrix which is then reduced through mathematical manipulations to obtain a single complex number that represents the equivalent resistance and inductance of the whole conductor. The advantage of this method is that it automatically considers the skin effect and proximity effect of all of the subconductors in the conductor. Elemental shape subdivisions are more efficient than circular or rectangular shape subdivisions. In addition, the positioning of the elements within each strand is optimized for accuracy and CPU time. The electromagnetic transients program EMTP requires the values of the line parameters in the frequency range of DC to 10 MHz, and it uses the "TUBE" approximation to calculate them. As shown in this thesis, the TUBE approximation does not provide accurate results for resistance of stranded conductors above 5 kHz. The proposed program needs an IBM compatible (80386 or above) personal computer and runs with minimum user intervention. The results obtained in this research with the Subdivision method suggest that the log(R) versus log (frequency) graph can be approximated by a straight line in its high frequency range. Slopes of graphs for conductors with different number of strands have been calculated, and an exponential formula for resistance calculations above 5 kHz is devel-oped. The resistance value at 5 kHz is found by the TUBE formula, and then using the appropriate slope, the resistance of the stranded conductor is estimated at higher frequencies.

Thesis/Dissertation

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2008-10-10

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http://hdl.handle.net/2429/2548

Electrical and Computer Engineering

University of British Columbia

UBCV

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