PIER M
 
Progress In Electromagnetics Research M
ISSN: 1937-8726
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 16 > pp. 171-184

ACCURACY OF APPROXIMATE FORMULAS FOR INTERNAL IMPEDANCE OF TUBULAR CYLINDRICAL CONDUCTORS FOR LARGE PARAMETERS

By D. Lovric, V. Boras, and S. Vujevic

Full Article PDF (374 KB)

Abstract:
Exact formulas for internal impedance per unit length of tubular cylindrical conductors energized by time-harmonic current involve Bessel functions. These functions are defined by infinite series, which yield unstable and often erroneous results for complex arguments of large magnitudes. Although it is well known how to evaluate Bessel functions numerically and many routines are now available to perform the actual computation, the available software routines often fail when computing equations that consist of a product and a quotient of Bessel functions under large complex or real arguments. For such cases, different approximate formulas can be used. In this paper, three types of approximate formulas for internal impedance of tubular cylindrical conductors are compared with respect to numerical stability and accuracy.

Citation:
D. Lovric, V. Boras, and S. Vujevic, "Accuracy of Approximate Formulas for Internal Impedance of Tubular Cylindrical Conductors for Large Parameters," Progress In Electromagnetics Research M, Vol. 16, 171-184, 2011.
doi:10.2528/PIERM10121503

References:
1. Stratton, J. A., Electromagnetic Theory, 532-533, IEEE Press Series on Electromagnetic Wave Theory, Wiley-IEEE Press, 2007.

2. Saraj┬Ěcev, P. and S. Vujevie, "Grounding grid analysis: Historical background and classification of methods," International Review of Electrical Engineering (IREE), Vol. 4, No. 4, 670-683, 2009.

3. Dommel, H. W., EMTP Theory Book, 2nd Ed., Microtran Power System Analysis Corporation, Vancouver, 1992.

4. Dawalibi, F. P. and R. D. Southey, "Analysis of electrical interference from power lines to gas pipelines --- Part I: Computation methods," IEEE Transactions on Power Delivery, Vol. 4, No. 3, 1840-1846, 1989.
doi:10.1109/61.32680

5. Moore, J. and R. Pizer, Moment Methods in Electromagnetics --- Techniques and Applications, John Wiley & Sons, New York, 1984.

6. Stevenson, W. D., Elements of Power System Analysis, 2nd Ed., Vol. 76, No. 93, McGraw-Hill, New York, 1962.

7. Spiegel, M. R. and J. Liu, "Mathematical Handbook of Formulas and Tables,", Schaum's Outlines Series, 150-159, McGraw-Hill, New York, 1999.

8. Jeffrey, A. and H.-H. Dai, "Handbook of Mathematical Formulas and Integrals," Elsevier, Amsterdam, 289-299, 2008.

9. Abramowitz, M. and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables," Applied Mathematical Series 55', 358-385, National Bureau of Standards, 1964.

10. Paul, C. R., "Analysis of Multiconductor Transmission Lines," John Wiley & Sons, New York, 164-167, 1994.

11. Wang, Y. J. and S. J. Liu, "A review of methods for calculation of frequency-dependent impedance of overhead power transmission lines," Proc. Natl. Sci. Counc. ROC(A), Vol. 25, No. 6, 329-338, 2001.

12. Amos, D. E., "A subroutine package for Bessel functions of a complex argument and nonnegative order,", SAND85-1018, Sandia National Laboratories, Albuquerque, NM., 1985.

13. Amos, D. E., "Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order," ACM Transactions on Mathematical Software, Vol. 12, No. 3, 265-273, 1986.
doi:10.1145/7921.214331

14. Nahman, N. S. and D. R. Holt, "Transient analysis of coaxial cables using the skin effect approximation A + Bs," IEEE Transactions on Circuit Theory, Vol. 19, No. 5, 443-{451, 1972.
doi:10.1109/TCT.1972.1083513

15. Semlyen, A. and A. Deri, "Time domain modeling of frequency dependent three phase transmission line impedance," IEEE Transactions on Power Apparatus and Systems, Vol. 104, No. 6, 1549-1555, 1985.
doi:10.1109/TPAS.1985.319171

16. Wedepohl, L. M. and D. J. Wilcox, "Transient analysis of underground power transmission systems: System-model and wave propagation characteristics," EE Proceedings on Generation, Transmission and Distribution, Vol. 20, No. 2, 253-260, 1973.

17. Vujevic , S., V. Boras, and P. Saraj┬Ěcev, "A novel algorithm for internal impedance computation of solid and tubular cylindrical conductors," International Review of Electrical Engineering (IREE), Vol. 4, No. 6, Part B, 1418-1425, 2009.

18. Mingli, W. and F. Yu, "Numerical calculations of internal impedance of solid and tubular cylindrical conductors under large parameters," IEE Proceedings --- Generation, Transmission and Distribution, Vol. 151, No. 1, 67-72, 2004.
doi:10.1049/ip-gtd:20030981

19. Knight, D. W., "Practical continuous functions and formulae for the internal impedance of cylindrical conductors,", March 2010, http://www.g3ynh.info/zdocs/comps/Zint.pdf.

20. Schelkunoff, S. A., "The electromagnetic theory of coaxial transmission lines and cylindrical shields," Bell System Technical Journal, 532-578, 1934.


© Copyright 2010 EMW Publishing. All Rights Reserved