Voltage Drop Calculator

[mivey]

I was hoping to work on the MV VD equations from a weeks back today,

I was looking for that thread as I had some equation corrections and results to post.

Must have gotten locked and/or deleted. If so, then what a bunch of wasted effort. Would be a refresher on why I should avoid posting anything that takes much more than minimal effort.

I do come here to relax and enjoy a little distraction so I guess it is just better to keep away from anything too technical here and leave that to classes or different sites.

 

[mbrooke]

I was looking for that thread as I had some equation corrections and results to post.

Must have gotten locked and/or deleted. If so, then what a bunch of wasted effort. Would be a refresher on why I should avoid posting anything that takes much more than minimal effort.

I do come here to relax and enjoy a little distraction so I guess it is just better to keep away from anything too technical here and leave that to classes or different sites.

You did nothing wrong. And IMO I don't think anything was wasted I learned a TON and saved most of your solutions to a folder on my hard drive. That and I was following your GMR discussion as well.

I think what got the thread closed down was that at one point it just deteriorated into a lot of back and forth off-topic banter (myself included) rather than staying on track with the technical discussion at hand. You might not have been present when that happened.


But in any case I too need a little distraction, so I do look forward to your posts and immensely appreciate the effort behind them.



FWIW Here is the matrix you posted for a medium voltage overhead distribution circuit.

“All loads phase-phase connected. 90% power factor- 556.5 conductor ACSR- 300amps- 33,000 volts.

If possible a comparison to 556.6 ACC spacercable- same PF, pole height, voltage and current as I know that will yield better voltage regulation.”





“See the following but keep in mind these are simplified calculations. They are OK for learning concepts but I would not use them for distribution line design as there is a lot more to be considered.

Let's start with a transposed and balanced line simplification:”

For Transposed, balanced lines we know:



L = circuit length in miles

D_ij = Distance from i conductor to j conductor (ft)

D_eq = 3√(Dab * Dbc * Dca)

r = resistance of i conductor (Ω/mi)

GMR = Geometric mean radius of conductor (ft)

Z = r + j 0.1213416789 * ln(D_eq / GMR) _Ω/mi

Vsource_L-G = source voltage line to ground

I = load amps

ΔV_L-G = L * Z * I = voltage drop
VLoad_L-G = VSource_L-G - ΔV_L-G = Load voltage




Case 1: 90% power factor- 556.5 Hendrix- 300amps- 33,000 volts, L=3 miles, 30°C, D_AB = 0.958333, D_BC = 0.958333, D_AC = 0.958333, R = 0.1713014, GMR = 0.0261980



We find:


D_eq = 0.958333 ft

Z = 0.1713014 + j 0.436375 (or 0.468794 <68.57°) _Ω/mi

Vsource_L-G = 19,052.5589+ j 0 (or 19,052.5589 <0.00°) volts

I = 270+ j -130.7670 (or 300 <-25.84°) amps

ΔV_L-G = 309.9445+ j 286.2621 (or 421.9142 <42.73°) = 2.21%

VLoad_L-G = 18,742.6144+ j -286.2621 (or 18,744.8004 <-0.88°)



Case 2: 90% power factor- 556.5 ACSR on crossarms - 300amps- 33,000 volts, L=3 miles, 30°C, D_AB = 3.96162, D_BC = 3.96162, D_AC = 7.33333, r = 0.1717333, GMR = 0.0314


We find:


D_eq = 4.864249 ft

Z = 0.1717333 + j 0.611354 (or 0.635017 <74.31°) _Ω/mi


Vsource_L-G = 19,052.5589+ j 0 (or 19,052.5589 <0.00°) volts



I = 270+ j -130.7670 (or 300 <-25.84°) amps

ΔV_L-G = L * Z * I = 378.9389+ j 427.8259 (or 571.5152 <48.47°) = 3.00%



VLoad_L-G = VSource_L-G - ΔV_L-G = 18,673.6200+ j -427.8259 (or 18,678.5203 <-1.31°)

“Now we move on to the simplified calc for the unbalanced case and keeping in mind we get much better accuracy with a more detailed model and set of equations, a more complete matrix solution, and an iterative loop calculation:”



For the untransposed, unbalanced case we can make a simplified calc at the sacrifice of some accuracy by recognizing:



ƒ = frequency (Hz): use 60
R_G = ground rod resistance (Ω): use 25

n = # ground rods per mile: use 4

ρ = soil resistivity (Ω*m): use 250
L = circuit length in miles

D_ij = Distance from i conductor to j conductor (ft)

R_i = resistance of i conductor (Ω/mi)
GMR_i = Geometric mean radius of i conductor (ft)

I_G+N = -(I_A + I_B + I_C)

Z_iN = 0.0954 + j 0.2794*LOG10(2160√(ρ/ƒ)/D_iN)
Z_ii = R_i + 0.0954 + j 0.2794*LOG10(2160√(ρ/ƒ)/GMR_i)

Z_ij = 0.0954 + j 0.2794*LOG10(2160√(ρ/ƒ)/D_ij)

Z_NN = R_N + 0.0954 + j 0.2794*LOG10(2160√(ρ/ƒ)/GMR_N)

θ = √(Z_NN / R_G/n)

μ = 1 - [ (Z_AN - Z_NN) / Z_AN ]2 * TANH(θ*L) / (θ*L)

I_N = Z_AN / Z_NN * [ (Z_NN - μZ_AN) / (Z_NN - Z_AN)] * I_G+N
I_G = I_G+N - I_N

ΔV_AG = L * ( Z_AA * I_A + Z_AB * I_B + Z_AC * I_C + Z_AN * I_N )

ΔV_BG = L * ( Z_BA * I_A + Z_BB * I_B + Z_BC * I_C + Z_BN * I_N )
ΔV_CG = L * ( Z_CA * I_A + Z_CB * I_B + Z_CC * I_C + Z_CN * I_N )

ΔV_NG = L * ( Z_NA * I_A + Z_NB * I_B + Z_NC * I_C + Z_NN * I_N )

ΔV_iN = ΔV_iG - ΔV_NG
VLoad_iN = VSource_iN - ΔV_iN

VLoad_iG = VSource_iG - ΔV_iG

Z_i = ΔV_iN / I_i
Z_i/mile = Z_i / L

We add these givens:


for case 1 (4/0 Neutral):

D_AN = 1
D_BN = 1.707665
D_CN = 1
R_A = 0.1713014

R_B = 0.1713014

R_C = 0.1713014
R_N = 0.449160
GMR_A = 0.0261980

GMR_B = 0.0261980

GMR_C = 0.0261980
GMR_N = 0.0158



and for case 2 (4/0 Neutral):
D_AN = 4.58333
D_BN = 4.25
D_CN = 4.58333
R_A = 0.1717333
R_B = 0.1717333
R_C = 0.1717333
R_N = 0.477
GMR_A = 0.0314
GMR_B = 0.0314
GMR_C = 0.0314
GMR_N = 0.00814




We also need:
VSource_A = 19,052.5589+ j 0.0000 (or 19,052.5589 <0.00°) volts
VSource_B = -9,526.2794+ j -16,500.0000 (or 19,052.5589 <-120.00°) volts
VSource_C = -9,526.2794+ j 16,500.0000 (or 19,052.5589 <120.00°) volts
I_A = 270.0000+ j -130.7670 (or 300.0000 <-25.84°) amps
I_B = -248.2475+ j -168.4434 (or 300.0000 <-145.84°) amps
I_C = -21.7525+ j 299.2103 (or 300.0000 <94.16°) amps



For untransposed with unbalanced loads (I leave it to the reader to make their own calcs):

Case 1:
ΔV_AG = 2.22%
ΔV_BG = 2.22%

ΔV_CG = 2.48%



ΔV_AN = 2.19%

ΔV_BN = 2.50%

ΔV_CN = 2.24%


Case 2:
ΔV_AG = 3.15%

ΔV_BG = 2.89%



ΔV_CG = 3.02%



ΔV_AN = 3.16%
ΔV_BN = 2.85%

ΔV_CN = 3.05%

 

[mivey]

The equation correction made a barely noticeable but slight change in results. I just typed in the individual phase to neutral formula for an intermediate step rather than an equivalent phase to neutral formula during the grounding compensation calc. It was:

...

...
Z_NN = R_N + 0.0954 + j 0.2794*LOG10(2160√(ρ/ƒ)/GMR_N)
θ = √(Z_NN / R_G/n)
μ = 1 - [ (Z_AN - Z_NN) / Z_AN ]2 * TANH(θ*L) */ (θ*L)
I_N = Z_AN / Z_NN * [ (Z_NN - μZ_AN) / (Z_NN - Z_AN)] * I_G+N
...

should have been:

...
Z_NN = R_N + 0.0954 + j 0.2794*LOG10(2160√(ρ/ƒ)/GMR_N)
D_eqN = 3√(D_AN * D_BN * D_CN)
Z_PN = R_P + 0.0954 + j 0.2794*LOG10(2160√(ρ/ƒ)/D_eqN)
θ = √(Z_NN / R_G/n)
μ = 1 - [ (Z_PN - Z_NN) / Z_PN ]2 * TANH(θ*L) */ (θ*L)
I_N = Z_PN / Z_NN * [ (Z_NN - μZ_PN) / (Z_NN - Z_PN)] * I_G+N
...

 

[mbrooke]

Noted

 

[ramsy]

..FWIW Here is the matrix you posted for a medium voltage overhead distribution circuit.

Now lets see you crunch those numbers, much less tell us what the symbols mean?

 

[MyCleveland]

Infinity.....feedback ?

ramsy......Posts 30 & 39
I will try and incorporate temp soon.

Ingenieur..Post 34
"All are approximations of sorts"....and I am back to Z effective.
Would anyone model nominal -5 or 10% utility variation ?
Calc would be out of bounds before starting.

Attached a sketch of Z values, looking for an explanation of why using Zeff from NEC table 9 is advised.
Using the load PF to adjust the actual line values simply forces the line to have the same phase angle....sketch.

 

[Ingenieur]

MyCleveland
please run it at pf 0.75 and 1.00

 

[MyCleveland]

MyCleveland
please run it at pf 0.75 and 1.00

Attached...

 

[Ingenieur]

Attached...

less than 0.3 v delta 0.75 to 1.00 pf
so the 0.85 the NEC uses seems like a good compromise

using NEC eff Z vs your 0.88 pf
300/1000 x 1.1 x 36 = 11.9 vac vs 13
your Z 0.36
eff Z from table ~ 300/1000 x 1.1 = 0.33

I assume the 300 is to/from, not one way

wonder why your Z is ~9% higher?

 

[kingpb]

3Ø
208V
1600 amps
Copper
Installed in EMT
Max VD=3%
Parallel sets=4
Conductors=600 Kcmil
Max one way distance?

Max distance is 167'. This number was derived using ETAP and the parameters above.

 

[ramsy]

Attached a sketch of Z values, looking for an explanation of why using Zeff from NEC table 9 is advised. Using the load PF to adjust the actual line values simply forces the line to have the same phase angle....sketch.

NEC table-9 has assumptions that limits its use to: 600-Volt Cables, 3-Phase, 60 Hz, 75°C (167°F) — Three Single Conductors in Conduit

0-600 volt cables & conduits fit my spreadsheet, which can select other table conditions (310.17, Tray, Bus), but not with higher voltages in Distribution, or Transmission.

 

[ramsy]

Max distance is 167'. This number was derived using ETAP and the parameters above.

ETAP is a black box, which won't estimate conductor temperature, and my NEC tables adjustments would need a 50% Power Factor to match @ 167 feet.

 

[MyCleveland]

ETAP is a black box, which won't estimate conductor temperature, and my NEC tables adjustments would need a 50% Power Factor to match @ 167 feet.

This is what I have been trying to pin down...using the NEC Zeff does not seem to work well.

Going back to "kingpb" post, if I use my modified calc method I get 178' at PF=1. So I would not dismiss this answer as a "Black Box" without digging further.

 

[kingpb]

ETAP is a black box, which won't estimate conductor temperature, and my NEC tables adjustments would need a 50% Power Factor to match @ 167 feet.

When you speak of temperature, I assume you are talking about the maximum operating temperature of the cable allowed by code; e.g. 75degC max, of which Table 8 values give the DC Resistance at 75DegC. This is a fixed value and when used in a Voltage Drop Calculation gives you the worst case, which is what is needed from a design standpoint.

Perhaps you can explain what significance you feel is necessary to "estimate conductor temperature" at any other temperature as it relates to designing for Maximum voltage drop of a circuit.

 

[ramsy]

..what significance you feel is necessary to "estimate conductor temperature"..

In a Word, NEC 110.14(C).

Lots of existing equipment under 100A, and NM cables often not listed or labeled to exceed 60°C.

Some 90°C+ cables can't be assumed compatible with 75°C equipment.

"conductor shall be selected and coordinated so as not to exceed the lowest temperature rating of any connected termination"

This adopted Law requires keeping temperature below the weakest link in the chain; a critical adjustment often missed, along with Voltage Drop, & motors.

 

[Ingenieur]

doing by hand
v = 120/0
i = 40/28.36, pf 0.88
line z = 0.3 (1.2 + 0.063j) from nec x and r values
eff z = 0.3 x 1.1 from nec table
(adjusted for pf 0.88) to 0.3 x 1.23

phasor v drop ~ 14.42
z eff v drop ~ 14.72
negligible and on the safe side

 

[Ingenieur]

mycleveland

do this
relabel your z 'load' section to z 'total'

relabel your z 'cct' to 'load' and instead of adding z load (now total) to z line SUBTRACT z line from z 'total', this will give you z 'load'

change
i = v/z(new 'total', old 'load')
this will give you i load of 40 vs 36

change pf to 0.85 and run
compare the v drop to Zeff x 40 A

 

[MyCleveland]

mycleveland

do this
relabel your z 'load' section to z 'total'

relabel your z 'cct' to 'load' and instead of adding z load (now total) to z line SUBTRACT z line from z 'total', this will give you z 'load'

change
i = v/z(new 'total', old 'load')
this will give you i load of 40 vs 36

change pf to 0.85 and run
compare the v drop to Zeff x 40 A

Why would I do that...I have tried modeling my approach to problems as I have watched your responses for a year +.
In other words...do and show the math.
The LOAD is what ever we select it to be...at a given mag and PF.
This then yields a given Z per phase.
The LINE or wire Z is a real value....at smaller loads and wire sizes this has a major effect on Icct specifically its phase angle.

While I do not have your knowledge or expertise, my take away on this Zeff is that by forcing the LINE Z to match the load Z in phase angle allows a simple V=I*Z v drop calc where the phase angles cancel each other.

 

[ramsy]

This is what I have been trying to pin down...using the NEC Zeff does not seem to work well..

Rather than working with Black Boxes, a community spreadsheet project may help settle this.

Lesser efforts get certified under open source licenses, are more accessible than ETAP, and more usable than NEC idiot tables, where bending over backwards --for cross referenced adjustment factors-- makes casualties of Motor loads, Termination Temperatures, and Voltage Drop spec. limits.

 

[Ingenieur]

Why would I do that...I have tried modeling my approach to problems as I have watched your responses for a year +.
In other words...do and show the math.
The LOAD is what ever we select it to be...at a given mag and PF.
This then yields a given Z per phase.
The LINE or wire Z is a real value....at smaller loads and wire sizes this has a major effect on Icct specifically its phase angle.

While I do not have your knowledge or expertise, my take away on this Zeff is that by forcing the LINE Z to match the load Z in phase angle allows a simple V=I*Z v drop calc where the phase angles cancel each other.

because it will only take a minute

v / z total ckt = i should = 40, not 36
that is where the difference phasor vs nec eff comes from
humor me
v/i = z total = z load + z line

you have v/i = z load = z total + z line or z total = z load - z line