advanced search

The Basics of Conductor Resistance at High Frequencies

Mar 1, 2009 12:00 PM

Learn what factors significantly influence conductor resistance as the frequency increases

With the advent of systems at frequencies above 60 Hz, we've seen increased interest in the rating of cables in these applications. Mainframe computer systems, running at 400 Hz, certainly come to mind here.

There are several factors that significantly influence conductor resistance as the frequency increases. Let's talk about each in detail and provide a suggested method for determining conductor ampacity at 400 Hz as related to that at 60 Hz.

Key factors

In general, you would design 3-phase, 400-Hz power systems the same way as 60-Hz systems, but you must realize that the higher frequency will increase the skin and proximity effects in the conductor. This, in turn, will increase the effective conductor resistance. The increased frequency will also increase circuit reactance, which when combined with resistance, will increase voltage drop.

The higher frequency will also increase the effect of magnetic materials on cable reactance and heating. It's for this very reason you should not run 400-Hz conductors in magnetic conduit or too close to magnetic structures in a building.

The losses due to frequency are proportional to the square of the line current. So for very small currents, these losses may be negligible. For large currents, however, they can be significant.

Cables in air and nonmagnetic conduit

We'll limit our discussion here to single conductor 600V cables. For frequencies up to about 1,000 Hz, you can assume that reactance is directly proportional to frequency. You can neglect the reduction in inductance due to frequencies up to this magnitude, because it's minimal — and the purposely introduced error is negligible. For frequencies higher than 1,000 Hz, however, you should include the inductance correction. In these cases, the inductance is defined by the following equation:

L = ( [0.1404 × log₁₀ 2S/D_C] + [0.0153 × L/L_O] ) × 10^-3 Henries per 1,000 ft

Where,

L = inductance to neutral

L/L_O = correction factor from Table 1 (click here to see Table 1)

S = axial spacing between conductors (in.)

D_C = Conductor diameter (in.)

Calculating resistance ratios

From the original Neher McGrath paper titled “The Calculation of Temperature Rise and Load Capability of Cable Systems,” we know that for any cable system, the AC/DC resistance ratio of the conductor (R_AC/R_DC) is expressed by the following equation:

R_AC/R_DC = 1 + Y_C + Y_S + Y_P (Eq. 1)

Where Y_C, Y_S, and Y_P are the effects due to the conductor, sheath, and conduit, respectively. Because we're considering only nonmetallic sheaths in air or nonmetallic conduit, we have to be concerned only with Y_C in our discussion.

The Neher McGrath paper also shows that you can express Y_C as follows:

Y_C = Y_CS + Y_CP

Where Y_CS is the conductor component due to skin effect and Y_CP is the conductor component due to proximity effect.

So taking into consideration the above comments, Equation 1 becomes:

R_AC/R_DC = 1 + Y_CS + Y_CP (Eq. 2)

Both the skin and proximity effects are a function of F_(x) which for solid and concentric round conductors is given in Table 1. Thus, for Y_CS and Y_CP, we have the following equations:

Y_CS = F_(x) (Eq. 3)

Y_CP = F_(x) K² × [ (1.18/F_(X) + 0.27) + 0.312K² ] (Eq. 4)

Where,

K = D_C/S,

x = 0.0276 × √f/R_DC

f = frequency in Hz

R_DC = conductor direct current resistance at operating temperature (ohms per 1,000 ft)

D_C = conductor diameter (in.)

S = axial spacing between conductors (in.)

F_(x) = function of x from Table 1

Table 2 (click here to see Table 2)lists the AC/DC resistance ratios as calculated from Equations 3 and 4.

You can determine the ampacity of a given conductor size at 400 Hz by multiplying the 60-Hz rating by the corresponding derating factor. For the larger sizes, the deratings are on the conservative side in that they are actually based on DC ratings of the conductors. You can consider the small error, on the safe side, as negligible in view of the possible variations in insulation thicknesses, etc.

In addition, the resistance ratios provided here do not include losses in any metal sheath, armor, or conduit. Losses in a thin aluminum armor tape may be small, but those in a metal conduit could be large enough to cause trouble if currents are large.

Want to use this article? Click here for options!

© 2012 Penton Business Media, Inc.

---

Acceptable Use Policy blog comments powered by Disqus

Browse Back Issues Select an Issue EC&M Magazine | April 2012 March 2012 February 2012 January 2012 December 2011 November 2011 October 2011 September 2011 August 2011 July 2011 June 2011 May 2011 April 2011 March 2011 February 2011 January 2011 December 2010 November 2010 October 2010 September 2010 August 2010 July 2010 June 2010 May 2010 April 2010 March 2010 February 2010 January 2010 December 2009 November 2009 October 2009 September 2009 August 2009 July 2009 June 2009 May 2009 April 2009 March 2009 February 2009 January 1, 2009 December 2008 November 2008 October 1, 2008 September 2008 August 2008 July 2008 June 1, 2008 May 2008 April 2008 March 2008 February 2008 January 2008 December 2007 November 2007 October 2007 September 2007 August 2007 July 2007 June 2007 May 2007 April 2007 March 2007 February 2007 January 2007 December 2006 November 2006 October 2006 September 2006 August 2006 July 2006 June 1, 2006 May 1, 2006 April 2006 March 1, 2006 February 2006 January 2006 December 2005 November 2005 October 2005 September 2005 August 2005 July 2005 June 2005 May 2005 April 2005 March 2005 February 2005 January 2005 December 2004 November 2004 October 2004 September 2004 August 2004 July 2004 June 2004 May 2004 April 2004 March 2004 February 1, 2004 January 1, 2004 December 1, 2003 November 1, 2003 October 1, 2003 September 1, 2003 August 1, 2003 July 1, 2003 June 1, 2003 May 1, 2003 April 1, 2003 March 1, 2003 February 1, 2003 January 1, 2003 December 1, 2002 November 1, 2002 October 1, 2002 September 1, 2002 August 1, 2002 July 1, 2002 June 1, 2002 May 1, 2002 April 1, 2002 March 1, 2002 February 1, 2002 January 1, 2002 December 1, 2001 November 1, 2001 October 1, 2001 September 1, 2001 August 1, 2001 July 1, 2001 June 1, 2001 May 1, 2001 April 1, 2001 March 1, 2001 February 1, 2001 February 1, 1995 January 1, 2001 December 1, 2000 November 1, 2000 October 1, 2000 September 1, 2000 August 1, 2000 July 1, 2000 June 1, 2000 May 1, 2000 April 1, 2000 March 1, 2000 February 1, 2000 January 1, 2000 December 1, 1999 November 1, 1999 October 1, 1999 September 1, 1999 August 1, 1999 July 1, 1999 June 1, 1999 May 1, 1999 April 1, 1999 March 1, 1999 February 1, 1999 January 1, 1999 December 1, 1998 November 1, 1998 October 1, 1998 September 1, 1998 August 1, 1998 July 1, 1998 June 1, 1998 May 1, 1998 April 1, 1998 March 1, 1998 February 1, 1998 January 1, 1998 December 1, 1997 November 1, 1997 December 1, 1996 November 1, 1996 October 1, 1996 September 1, 1996 August 1, 1996 July 1, 1996 June 1, 1996 May 1, 1996 April 1, 1996 March 1, 1996 February 1, 1996 January 1, 1996 December 1, 1995 November 30, 1995 November 1, 1995 October 1, 1995 September 1, 1995 August 1, 1995 July 1, 1995 June 1, 1995 May 1, 1995 April 1, 1995 March 1, 1995

browse e-newsletters