Krustabas
Electrical
- Nov 5, 2008
- 22
There are different ways to estimate current imbalance. The most recent and easiest to manage is given in [1, 2, and 3]. Earlier approach from [4, 5] can also be mentioned.
All these methodologies employ simple reactance formulas (ohms per 1000 feet at 60Hz):
Xii = 0.023*(K’+ln(1/rc)) (1)
Xij = 0.023*ln(1/Dij) (2)
It is often mentioned that the earliest technique is given in Buller’s paper [6] and reprinted in [7]. Unfortunately I don’t have neither [6] (can’t find anywhere) nor [7] (too expensive).
In [8] and [9] I have found the following F. Buller’s reactance formula (see Formula.png):
Xi=0.023*{K’+A+Sigma(from k=2 to n)[ln(Dik/Di(k-1))*Sigma(from j=1 to k-1)(Ij/Ii)] (3)
I am trying to understand how to apply (3) to get the current sharing among cables. The problem is that (3) contains both the unknown reactance and the unknown currents. In [9] it is said that: “…To derive the actual current sharing in a group of cables you must first calculate the current sharing based on cable impedances derived from an initial balanced current basis, then repeat the same process with the currents thus obtained…”. I guess I can calculate all the necessary reactances using IA = 1 pu, IB = a^2, IC = a but I can’t figure out how that can help me to get further (to obtain the actual unbalanced currents).
[1] IEC 60287-1-3. Electric cables - Calculation of the current rating - Part 1-3: Current rating equations (100 % load factor) and calculation of losses - Current sharing between parallel single-core cables and calculation of circulating current losses, 2002.
[2] G. Anders, “Rating of Electric Power Cables: Ampacity Computations for Transmission, Distribution, and Industrial Applications,” 1st Edition, 1997. ISBN-13: 978-0070017917.
[3] PES-ICC C35D reports ( 2011-2012.
[4] EPRI Power Plant Electrical Reference Series, Volume 4, Wire and Cable, 1987. ISBN-13: 978-0803350038.
[5] K.A. Petty, “Calculation of current division in parallel single-conductor power cables for generating station applications”, Power Delivery, IEEE Transactions on Vol. 6, Issue 2, pp. 479 - 487, Apr 1991
[6] Buller, F. H., “A Technique for Calculating Inductance, Reactance, Impedance, and Sheath Voltages of Single-Conductor Cable in Duct Banks,” General Electric Review, Vol. 52, pp. 40 - 44, March 1949.
[7] Underground Systems reference Book. Washington, D.C.: Edison Electric Institute, 1957.
[8] Adamson, Colin, “Loci of reactances of multiple-conductor circuits in the complex plane,” Proceedings of the Institution of Electrical Engineers, Vol. 114, Issue 9, September 1967.
[9] Alex Y. Wu, “Single-Conductor Cables in Parallel,” IEEE Transactions on Industry Applications, Vol. IA-20, Issue 2, March 1984.
All these methodologies employ simple reactance formulas (ohms per 1000 feet at 60Hz):
Xii = 0.023*(K’+ln(1/rc)) (1)
Xij = 0.023*ln(1/Dij) (2)
It is often mentioned that the earliest technique is given in Buller’s paper [6] and reprinted in [7]. Unfortunately I don’t have neither [6] (can’t find anywhere) nor [7] (too expensive).
In [8] and [9] I have found the following F. Buller’s reactance formula (see Formula.png):
Xi=0.023*{K’+A+Sigma(from k=2 to n)[ln(Dik/Di(k-1))*Sigma(from j=1 to k-1)(Ij/Ii)] (3)
I am trying to understand how to apply (3) to get the current sharing among cables. The problem is that (3) contains both the unknown reactance and the unknown currents. In [9] it is said that: “…To derive the actual current sharing in a group of cables you must first calculate the current sharing based on cable impedances derived from an initial balanced current basis, then repeat the same process with the currents thus obtained…”. I guess I can calculate all the necessary reactances using IA = 1 pu, IB = a^2, IC = a but I can’t figure out how that can help me to get further (to obtain the actual unbalanced currents).
[1] IEC 60287-1-3. Electric cables - Calculation of the current rating - Part 1-3: Current rating equations (100 % load factor) and calculation of losses - Current sharing between parallel single-core cables and calculation of circulating current losses, 2002.
[2] G. Anders, “Rating of Electric Power Cables: Ampacity Computations for Transmission, Distribution, and Industrial Applications,” 1st Edition, 1997. ISBN-13: 978-0070017917.
[3] PES-ICC C35D reports ( 2011-2012.
[4] EPRI Power Plant Electrical Reference Series, Volume 4, Wire and Cable, 1987. ISBN-13: 978-0803350038.
[5] K.A. Petty, “Calculation of current division in parallel single-conductor power cables for generating station applications”, Power Delivery, IEEE Transactions on Vol. 6, Issue 2, pp. 479 - 487, Apr 1991
[6] Buller, F. H., “A Technique for Calculating Inductance, Reactance, Impedance, and Sheath Voltages of Single-Conductor Cable in Duct Banks,” General Electric Review, Vol. 52, pp. 40 - 44, March 1949.
[7] Underground Systems reference Book. Washington, D.C.: Edison Electric Institute, 1957.
[8] Adamson, Colin, “Loci of reactances of multiple-conductor circuits in the complex plane,” Proceedings of the Institution of Electrical Engineers, Vol. 114, Issue 9, September 1967.
[9] Alex Y. Wu, “Single-Conductor Cables in Parallel,” IEEE Transactions on Industry Applications, Vol. IA-20, Issue 2, March 1984.