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#127856 - 01/30/02 06:21 PM Skin Effect
Elzappr Offline
Member

Registered: 12/20/01
Posts: 273
Loc: Oregon
Anyone have a formula for calculating skin effect? Or, at least some salient parameters for determining the conductor skin effect?
Also, in a short circuit or bolted ground fault situation, can one assume a "frequency for the purposes of calculation"? Since there is a very steep rise time to current level during a fault, would an assumed 1 MHz be adequate to theoretically figure transient effects?

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#127857 - 01/30/02 07:06 PM Re: Skin Effect
Chris Rudolph Offline
Member

Registered: 05/01/01
Posts: 160
Loc: Winter Park,Fl USA
The fomula is:
skin depth in cm =5033 times the square root of conductor resistivity in ohms per cubic centimeter divided by the product of frequency in Hertz and permeability of the conducting material.
For copper at 20deg C the formula reduces to :
skin depth of copper in cm =6.62 divided by the square root of frequency in Hertz.
The frequency components of a short duration fault or bolt is hard to predict.The shorter the time the higher the frequency component.
Chris

PS For 1Mhz and copper the skin depth is 0.0026 inches.

[This message has been edited by Chris Rudolph (edited 01-30-2002).]

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#127858 - 02/02/02 06:39 PM Re: Skin Effect
Elzappr Offline
Member

Registered: 12/20/01
Posts: 273
Loc: Oregon
Thanks Chris. Can you tell me where you got the info? I used to have some info about that, but its misplaced. Your answer seems similar to the info I used to have.

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#127859 - 02/03/02 10:35 AM Re: Skin Effect
Chris Rudolph Offline
Member

Registered: 05/01/01
Posts: 160
Loc: Winter Park,Fl USA
The formula came from Electronic and Radio Engineering Handbook by Frederick E.Terman.It is a book that I had when I was in college,many years ago.
Chris

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#127860 - 02/06/02 08:33 PM Re: Skin Effect
Scott35 Offline

Broom Pusher and
Member

Registered: 10/19/00
Posts: 2724
Loc: Anaheim, CA. USA
Let me pull out and dust off the Electrical Engineer's Handbook tonight for the skin effect calcs [both Copper and Aluminum materials, and the various shapes and types of conductors - such as tubular circular, tubular square, complete circular, etc.].

The Hz for the faults would be at the fundamental Hz - maybe including any relavent Harmonics if they could contribute to the fault significantly.
The wavelengths / Hz will remain, however the peaks will rise drammatically.

The fault may impose harmonics [or something like sidebands], but the fault calcs would be made at the fundamental Hz.

I'll double check on this while getting the skin effect data.

Scott SET
_________________________
Scott " 35 " Thompson
Just Say NO To Green Eggs And Ham!

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#127861 - 02/11/02 10:32 AM Re: Skin Effect
Scott35 Offline

Broom Pusher and
Member

Registered: 10/19/00
Posts: 2724
Loc: Anaheim, CA. USA
Elzapper,

After looking through my Electrical Engineering Handbook, I regret to say that giving you any more information regarding skin effect calcs than what Chris has submitted would be almost impossible.

The topic is spread across 5 sections of my Handbook, each formula requires a variable value which is obtained from either a database, graph or table. Also, writing the formulas out as text only becomes kind of confusing!

Here are a few basic calcs - which are for Skin Effect Ratios on a Linear Cylindrical Conductor to Sinusoidal AC of a given Frequency.

First is for Effective Resistance [R']:

R' = KR (Ohms)

R = True Resistance with continuous current,
K = Value determined from a Table, in terms of x. The value of x is given by:

x = 2*pi*a* sq rt 2*f*u/p
[a = radius of conductor in Cm's, f = Frequency in CPS, u = magnetic permeability of conductor - assumed to be constant, p = resistivity in abohm-centimeters (abohm = 10^-9 ohm)].

For practical calcs, the x value can be expressed as:

x = 0.063598* sq rt f*u/R
where R = DC resistance at operating temp.

If L' is the effective Inductance:

L' = L1 + K'*L2
[L1 = External portion of Inductance, L2 = Internal portion (due to mag. field within the conductor), and K' is found in the table on some page in another section!!]

The total effective Inductance per unit ength of conductor is:

L' = 2*l*n* d/a + K'* u/2

[a = radius of conductor, d is separation of conductors, l and n are derived from some other formula in some other section!].

Best suggestion is to take a trip to your local Library and reference an EE Handbook for this data. If you can afford to buy a Handbook, that would be a nice investment [if you plan to do advanced calcs in the future - otherwise it's just an expensive paper weight!].

The calcs are really simple once you have all the data and formulas, plus the tables and charts / graphs. This stuff is close to impossible to type out and the tables would take me hours to type in a message post!

Per the Hz of faults, the figures of Intensity are plotted at the Fundamental Hz of the system, and with durations from multiple cycles [1 to 100 cycles] for longer Time-Current curves per Intensity, to fractions of a cycle [1/8 to 1/2 cycle] for shorter Time-Current curves per Intensity.
These peak values are figured with the Fundamental Hz as the plotted reference and time reference.

Scott SET.
_________________________
Scott " 35 " Thompson
Just Say NO To Green Eggs And Ham!

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