Voltage drop - chapter 9 tables & effective Z

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shespuzzling

Member
Location
new york
Hi,

I'm struggling to understand why the effective Z of conductors, which is used to calculate voltage drop, changes with respect to the power factor. For a given current I, I don't understand why the wire resistance could possibly be affected by the PF.

Furthermore, I tried calculating the effective Z at 0.85 PF via the formula given in the footnotes (Z=Rcos(theta)+Xsin(theta)) and am not coming up with the same values as listed in the code! It doesn't appear to be a rounding change or anything.

Any help would be appreciated!
 

Smart $

Esteemed Member
Location
Ohio
Hi,

I'm struggling to understand why the effective Z of conductors, which is used to calculate voltage drop, changes with respect to the power factor. For a given current I, I don't understand why the wire resistance could possibly be affected by the PF.
When dealing with AC, it's about impedance (Z=RCL), not just resistance (R).

Furthermore, I tried calculating the effective Z at 0.85 PF via the formula given in the footnotes (Z=Rcos(theta)+Xsin(theta)) and am not coming up with the same values as listed in the code! It doesn't appear to be a rounding change or anything.
Did you convert the power factor to it's equivalent angle θ?

arccos(pf) = θ

Why not just use the formula given:
Ze = R × PF + XL sin[arccos(PF)]
 

shespuzzling

Member
Location
new york
When dealing with AC, it's about impedance (Z=RCL), not just resistance (R).

You're right I meant impedance. I just don't see why power factor could effect the impedance of a cable of you're dealing with the same current, voltage, etc.

Did you convert the power factor to it's equivalent angle θ?

arccos(pf) = θ

Why not just use the formula given:
Ze = R × PF + XL sin[arccos(PF)]

yep that's exactly what I used and I get different values from the NEC for the same PF.
 

Smart $

Esteemed Member
Location
Ohio
You're right I meant impedance. I just don't see why power factor could effect the impedance of a cable of you're dealing with the same current, voltage, etc.
Well how does power factor affect the impedance of an inductive load, say a motor for example. Measure the resistance of the windings and try to figure the current the motor draws from that resistance value alone.

yep that's exactly what I used and I get different values from the NEC for the same PF.
Hard to figure out where the problem is if you don't show your work.
 

shespuzzling

Member
Location
new york
Well how does power factor affect the impedance of an inductive load, say a motor for example. Measure the resistance of the windings and try to figure the current the motor draws from that resistance value alone.

Hmm, not sure what you mean. My problem is that for a given current I, voltage V and wire size, the voltage drop will change if the power factor of the circuit (even if you hold the current constant). A conductor sees a sinusoidal current. Whether that current is in phase with the voltage, leading or lagging shouldn't make a difference to the impedance of the wire, but apparently it does. That's what I'm trying to understand. Maybe the better question is why does a wire have a reactance, and why does that value change with the PF of the load?

Hard to figure out where the problem is if you don't show your work.

Here's one example, i set up a spreadsheet and did all of the wire sizes and the effective Z was inconsistent with the NEC values.

#12 AWG copper, PVC conduit, 085 PF

arccos(.85)=31.7883
sin(31.7883)=0.527

Z=6.6*.85+.177*.527=5.7 (NEC value is 5.6)

I know it's only off by a tenth and maybe it's not anything to worry about but it just seems odd
 

Smart $

Esteemed Member
Location
Ohio
Hmm, not sure what you mean. My problem is that for a given current I, voltage V and wire size, the voltage drop will change if the power factor of the circuit (even if you hold the current constant). A conductor sees a sinusoidal current. Whether that current is in phase with the voltage, leading or lagging shouldn't make a difference to the impedance of the wire, but apparently it does. That's what I'm trying to understand. Maybe the better question is why does a wire have a reactance, and why does that value change with the PF of the load?
Let's see if this makes sense and jogs the noggin'...

The voltage across each reactive component of a circuit is out of phase with the voltage of the source. That makes the voltage drop out of phase, too. The arithmetic sum is not equal to the vectorial parts.
:D


Here's one example, i set up a spreadsheet and did all of the wire sizes and the effective Z was inconsistent with the NEC values.

#12 AWG copper, PVC conduit, 085 PF

arccos(.85)=31.7883
sin(31.7883)=0.527

Z=6.6*.85+.177*.527=5.7 (NEC value is 5.6)

I know it's only off by a tenth and maybe it's not anything to worry about but it just seems odd
I see what you mean. Tried with Imperial values (Ohms to Neutral per 1000 Feet) for same #12 and it yields same as NEC. I don't know the source of that table or how accurate the values are. It's been in the NEC for a long time and don't recall anyone on this board challenging its validity. As for the calculation discrepancy, who knows? Maybe it was assembled back when they still used slidesticks. :p
 

GoldDigger

Moderator
Staff member
Location
Placerville, CA, USA
Occupation
Retired PV System Designer
Let's see if this makes sense and jogs the noggin'...

The voltage across each reactive component of a circuit is out of phase with the voltage of the source. That makes the voltage drop out of phase, too. The arithmetic sum is not equal to the vectorial parts.
:D



I see what you mean. Tried with Imperial values (Ohms to Neutral per 1000 Feet) for same #12 and it yields same as NEC. I don't know the source of that table or how accurate the values are. It's been in the NEC for a long time and don't recall anyone on this board challenging its validity. As for the calculation discrepancy, who knows? Maybe it was assembled back when they still used slidesticks. :p
Allow me to take a crack at this:
1. The total current through the circuit is out of phase with the source voltage whenever the overall power factor is less than one.
2. The difference in voltage between the two ends of a pure resistor (an approximation to a real wire) will be directly proportional to and in phase with the current.
3. But a valid definition of "voltage drop" is the difference in magnitude of the voltages at the two ends of the wire. That is what affects the operation of the load served by the wire.
4. The difference in the magnitude of the voltages is less than the magnitude of the difference vector, as mentioned in the previous post.
5. So, the voltage drop associated with a given wire and a given magnitude current will depend on the power factor of that current.
 

Smart $

Esteemed Member
Location
Ohio
V-drop_diagram.gif
 

shespuzzling

Member
Location
new york
Thank you both for your responses. I understand that the angle of the current will affect the voltage drop. What I'm still struggling with is the fact that in many of these voltage drop problems we're given in the NEC (I can transcribe a problem if it helps) we are told the FLA of the load and the PF of the load to use in the calcs. Those values though will change depending on the impedance of the wire so it doesn't make sense to use them to calculate voltage drop unless we are assuming that the wire impedance is so small compared to the load that the current magnitude and PF will be largely dependent on the load.

Maybe that's why we use the effective impedance calculation....do you happen to know where I can find that derived or explained?

Also can anybody confirm if my understanding is correct?
 

Smart $

Esteemed Member
Location
Ohio
...unless we are assuming that the wire impedance is so small compared to the load that the current magnitude and PF will be largely dependent on the load.
Our concern is the [worst] nominally-marginal case. Quite often a very rough approximation is all that is necessary, if that. Voltage drop in operation varies with the change in load and seldom are the loads a constant exact value.

You can calculate the total PF of the circuit if you want, but consider how much the result will deviate from the PF of just the load when the wiring method voltage drop is not more than the recommended 5%. Then take into consideration that often the power factor value we use for the load is typically not very accurate. The usual conclusion of attempting to be as accurate as possible is that it is most often... but not always... a waste of time and effort.

Maybe that's why we use the effective impedance calculation....do you happen to know where I can find that derived or explained?
The voltage drop (IZ), its resistive (IR) and reactive (IX) components are depicted vectorially in the image I posted above. As shown, we typically calculate only the "real" component of the "complex" drop.
 
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