Analysis of formulas to calculate the AC resistance of different conductors' configurations

Abstract Skin and proximity effects in single- or multi-conductor systems can notoriously affect the AC resistance in conductors intended for electrical power transmission and distribution systems and for electronic devices. This increase of the AC resistance raises power loss and limits the conductors’ current-carrying capacity, being an important design parameter. There are some internationally recognized exact and approximated formulas to calculate the AC resistance of conductors, whose accuracy and applicability is evaluated in this paper. However, since these formulas can be applied under a wide range of configurations and operating conditions, it is necessary to evaluate the applicability of these models. This is done by comparing the results that they provide with experimental data and finite element method (FEM) simulation results. The results provided show that FEM results are very accurate and more general than those provided by the formulas, since FEM models can be applied to a wide range of conductors’ configurations and electrical frequencies.

[1]  A. E. Kennelly,et al.  Experimental researches on skin effect in conductors , 1915, Proceedings of the American Institute of Electrical Engineers.

[2]  E. W. Davis,et al.  Skin effect in large stranded conductors at low frequencies , 1921, Journal of the American Institute of Electrical Engineers.

[3]  A.E. Kennelly,et al.  Skin-Effect Resistance Measurements of Conductors, at Radio-Frequencies up to 100,000 Cycles per Second , 1916, Proceedings of the Institute of Radio Engineers.

[4]  Rafael Murillo,et al.  Procedure to accelerate calculations of additional losses in transformer foil windings , 2013 .

[5]  Jordi-Roger Riba Ruiz,et al.  Improved design of an extra-high-voltage expansion substation connector through magnetic field analysis , 2014, Simul. Model. Pract. Theory.

[6]  W. T. Weeks,et al.  Resistive and inductive skin effect in rectangular conductors , 1979 .

[7]  Juanjuan Wang,et al.  Calculation of AC Resistance for Stranded Single-Core Power Cable Conductors , 2014, IEEE Transactions on Magnetics.

[8]  Vincent T. Morgan.  The Current Distribution, Resistance and Internal Inductance of Linear Power System Conductors—A Review of Explicit Equations , 2013, IEEE Transactions on Power Delivery.

[9]  M. Kazimierczuk,et al.  Comparison of various methods for calculating the AC resistance of inductors , 2002 .

[10]  Alberto Reatti,et al.  Solid and Litz-wire winding non-linear resistance comparison , 2000, Proceedings of the 43rd IEEE Midwest Symposium on Circuits and Systems (Cat.No.CH37144).

[11]  A.A.P. Silva,et al.  Applicability and limitations of ampacity models for HTLS conductors , 2012 .

[12]  Jordi-Roger Riba.  Calculation of the ac to dc resistance ratio of conductive nonmagnetic straight conductors by applying FEM simulations , 2015 .

[13]  Vedran Boras,et al.  Accuracy of approximate formulas for internal impedance of tubular cylindrical conductors for large parameters , 2011 .

[14]  Unnur Stella Gudmundsdottir,et al.  Proximity effect in fast transient simulations of an underground transmission cable , 2014 .

[15]  Ronald F. Boisvert,et al.  NIST Handbook of Mathematical Functions , 2010 .

[16]  Glenn S. Smith.  A simple derivation for the skin effect in a round wire , 2014 .

[17]  Ignacio Lope,et al.  AC Power Losses Model for Planar Windings With Rectangular Cross-Sectional Conductors , 2014, IEEE Transactions on Power Electronics.

[18]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[19]  Jonas Larsson,et al.  Electromagnetics from a quasistatic perspective , 2007 .

[20]  Jordi-Roger Riba Ruiz,et al.  Redesign process of a 765 kVRMS AC substation connector by means of 3D-FEM simulations , 2014, Simul. Model. Pract. Theory.

[21]  A.H.M. Arnold.  The alternating-current resistance of parallel conductors of circular cross-section , 1935 .

[22]  Trevor M. Benson,et al.  A simple formula for calculating the frequency‐dependent resistance of a round wire , 1998 .

[23]  S. Haefner,et al.  Alternating-Current Resistance of Rectangular Conductors , 1937, Proceedings of the Institute of Radio Engineers.

[24]  Charles R. Sullivan,et al.  An improved calculation of proximity-effect loss in high-frequency windings of round conductors , 2003, IEEE 34th Annual Conference on Power Electronics Specialist, 2003. PESC '03..

[25]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.