Mathematical equivalent for CO-9 Curves 1

[MarkAthay]

I'm trying to set up relay coordination curves on a spredsheet to assist me in establishing some relay settings. I know it sounds like a lot of work, but it's the best I have right now without spending $15K on the right software.

I've got the calculations for Schweitzer relays, which we have a bunch of, and the hard numbers on fuses, but I don't have a mathematical representation for a CO-9 relay. Anybody have it or know where I could find it?

Mark in Utah

 

[busbar]

Possibly IEEE Standard C37.112-1996 Inverse-Time Characteristic Equations for Overcurrent Relays described at

http://standards.ieee.org/reading/ieee/std_public/description/relaying/C37.112-1996_desc.html

 

[jghrist]

The following equation can be used:

t(M) = (A/(M^P-C) + B)·(14·n - 5)/9

where M is the multiple of pickup
n is the time dial
A, B, C, and P are constants

Using the Mathcad minerr function, I have determined the best fit for the constants to be:

A = 2.073 B = 0.060 C = 1.299 P = 1.813

with a correlation coefficient of 99.96%

Coefficients for a CO-8 are:

A = 2.187 B = 0.094 C = 1.266 P = 1.540

 

[cuky2000]

The published equation for the Very Inverse Time overcurrent relay Westinghouse (ABB)CO-9 is as follow:

T=5,46780D/(M^2.04690-1) + 0.10814D + 0.0280

_{Where:
D = Time Dial
M= Multiple of pickup (pu)
T= Trip Time.}

 

[jghrist]

cuky2000,

Where was the equation published? Using your equation with M=5 and D=3, I get a time of 0.984 sec (assuming that your comma in 5,46780 should actually be a decimal point).

I get 0.742 sec with my equation.

ABB CO-9 current time curve #418266 shows a time between 0.7 and 0.8 sec.

 

[MarkAthay]

These two equations give dramatically different results.

For example:

TD=2, and various pickup multiples, I get:

P/U 1st curve 2nd curve
2.48 1.52 sec. 2.27 sec.
5.24 0.43 sec. 0.63 sec.
9.05 0.25 sec. 0.37 sec.

I haven't compared this to the published curves, but something's not adding up. Any ideas?

Mark in Utah

 

[cuky2000]

The equation presented is the emulation of the Basler overcurrent relay with the electromechanical relay ABB CO-9. To make a comparison below is a set of equivalent time dialer values:

_{Time Dialer Equivalence
ABB CO-9: 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
BASLER: .3, .7, 1.4, 2.1, 3.0, 3.9, 4.8, 5.7, 6.7,7.8, 8.7, 9.6}

The enclose spreadsheet could help to made easier the calculation

http://www.basler.com/php/download2.php

COMMENT:
For direct calculation of the time pickup, use the second sheet (TCC Curve & Calcs) and type the value of time dialer D=2.1. The result could be observed in the last column of the calculated table shown in (green).

For the proposed example of the ABB relay with D=3, replace in the above table by the Basler equivalent value corresponding to 2.1. The result will be as follow:

_{Mult. IEEE Std
M C37-112
(PU) Jrist Basler
1.20 92.150 25.638
1.30 27.730 16.406
1.40 15.986 11.840
1.50 11.080 9.134
1.75 6.087 5.611
2.00 4.095 3.921
2.30 2.887 2.806
2.70 2.039 1.985
3.00 1.660 1.610
3.40 1.326 1.276
4.00 1.018 0.969
4.40 0.884 0.836
5.00 0.742 0.697
6.00 0.595 0.556
7.00 0.507 0.473
8.00 0.449 0.420
9.00 0.409 0.384
10.00 0.380 0.359
12.00 0.342 0.327
14.00 0.319 0.307
17.00 0.297 0.290
20.00 0.284 0.280
22.00 0.278 0.276
26.00 0.270 0.270
30.00 0.265 0.266}

COMMENTS:

The two equations are equivalent in the range published by the manufacturer

1- For D=3 and M>2 the two equation provide similar values.

2- Even though the equations diverge for D=3 and M<2 this divergence may not be important since the manufacturer do not publish values for M<2

For CO-9 performance curve, see page 13 in the enclose site:

http://library.abb.com/GLOBAL/SCOT/...185256EAC0053E7D4/$File/IB41-101u CO.pdf