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Mathematical equivalent for CO-9 Curves

Mathematical equivalent for CO-9 Curves

Mathematical equivalent for CO-9 Curves

(OP)
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

RE: Mathematical equivalent for CO-9 Curves

The following equation can be used:

 t(M) = (A/(MP-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

 

RE: Mathematical equivalent for CO-9 Curves

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

         T=5,46780D/(M2.04690-1) + 0.10814D + 0.0280

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

RE: Mathematical equivalent for CO-9 Curves

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.

RE: Mathematical equivalent for CO-9 Curves

(OP)
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


RE: Mathematical equivalent for CO-9 Curves

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:

[i]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/scot229.NSF/VerityDisplay/7042F1D45630FCA185256EAC0053E7D4/$File/IB41-101u%20%20%20%20%20%20CO.pdf


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