IEEE 141 VD Calculation

[MyCleveland]

I need help in resolving Vs value....whether it is positive or negative for a given problem.

If someone understands this method and can spare the time, I would appreciate four example problems where 2 result in a positive Vs and 2 result in a negative Vs.

Not written out results... just the problem parameters that result matches Vs provided.
EX: 480V-3p load, 200', #4/0 CU wire (1 set), conduit type, 175 amp, PF = 0.9
Result Vs = xx.xx degs (positive or negative)

 

[Julius Right]

Cable 1: 480V-3p load, 200', #4/0 CU wire (1 set), 175 amp, PF = 0.9
NEC Table 9 Rac=0.062 ohm/kft. X=0.041 ohm/kft.
sinφ=0.43589
φ negative=inductive
Vs=√{[Vr+I*(R*cosφ+X*sinφ)]^2+[I*X*cosφ-I*R*sinφ]}^2
Vs=√{[277.13+175*(0.0124*0.9+0.0082*0.4359)]^2+[175*0.0082*0.9-175*0.0124*0.0082]}^2
Vs=279.7068 V
sinψ=I*(X*cosφ-R*sinφ)/Vs
sinψ=0.001236 ; arcsinφ=0.001236 rad=0.070797 degrees
φ positive=capacitive
Vs=√{[Vr+I*R*cosφ-I*X*sinφ]^2+[IR*sinφ+IX*cosφ)]^2}
Vs=278.4646; sinψ=0.008035 ; arcsin=0.008035 rad=0.460355 degrees.
Cable 2 :The same cable but cosfi=0.5 inductive [or capacitive] and length 1000'
φ negative=inductive
Vs=288.8253 V; sinφ=-0.00402 ; arcsin=-0.23047 degrees
φ positive=capacitive
Vs=276.6443V; sinφ=0.009387 arcsin=0.537834 degrees

 

[MyCleveland]

Thanks JR...didn't want to bother you, but thank you for the response.

Posting print out for Cable 1....appears I have same answer using PVC conduit values.

Not clear on your Cable 2 response.
Assumed values 480v-3p, 1 set 4/0 CU, pvc conduit, 175a load, 1000' distance

Output using 1000' length
Vs = 288.8253
V angle = - 1.1524

Output using 200' length
Vs = 279.4583
V angle = - 0.2382

 

[Julius Right]

You are right. I took the wrong length.:ashamed1:

 

[MyCleveland]

Thanks again for your help.