IEEE 242 - Cable Overload Time-Current Curve Data Points

[kfrazie1]

I'm working on a project to determine Solid State Trip Controller S/L/I settings for Low Voltage, 480V Circuit Breakers for both feeder and branch circuits. In order to do this, I've been plotting motor thermal damage curves on the Controller Time-Current Curves to select approrpiate LTPU and delay settings. I'm currently at the point where I'm trying to plot thermal damage curves of cable in accordance with IEEE 242-2001 Reccommended Practice for Protection and Coordination of Industrial and Commerical Power Systems, Section 9.5 - Overload Protection of Cables. Within this section, IEEE utilizes the following equation to develop a table for cable overloads:

Perecent Overload Capability = Ie/In % = SQRT(((Te-To)/(Tn-To)-e^(-theta*K))/(1-e^(-theta*K))*(230+Tn)/(230+Te)*100)

where: Te = Conductor Emergency Temp
Tn = Normal Temp
To = Ambient Temp
K is a constant, dependent on cable size and installation type (See Table 9-5)
e is base for natural logs

This equation is used to develop the table in 9-6:
K = 1, Insul - THW, Tn=75C, Te=95C

Time % Overload
10s 987
100s 329
1000s 148
10000s 121
18000s 121

I can not figure out how they tabulated this data from the aforementioned equation. I believe there is an issue with my Time Constant Value "K" in the equation. I'm not sure what theta is and how to express the K Value in this equation to get the values they get in their tables.

 

[7anoter4]

There are some mistakes in your formula:
1)If it is in excel [Microsoft] it is better to put exp() instead of e^().
2)the last digits [100] have to be out of radical:
Ie/In% = SQRT(((Te-To)/(Tn-To)-exp(-Θ*K))/(1-exp(-θ*K))*(230+Tn)/(230+Te))*100

 

[7anoter4]

I almost forgot it: Q[theta] =duration of overload in hours=secs/3600

 

[kfrazie1]

1) Yes I was using exp - thank you

2) After playing around for another 2 hrs, I finally realized it was out of the radical hahah. Such a simple mistake took me 2 hrs to figure out.....

3) I did finally realize it was in hours instead of seconds. It would be nice if IEEE posted units in their variables...

THANK YOU for the quick response!!!