Voltage Drop and Nonlinear Loads

Voltage Drop and Nonlinear Loads (First Approach)

It’s well known that in a balanced 3-phase 4-wire circuit, the current in the neutral wire is zero (this is because the neutral current is the vectorial sum of the phase currents, i.e: the sum of three vectors equal in magnitude whose angle between each vector is 120 degrees. The result is zero).

Since no current is present in the neutral wire, the circuit length to be taken into consideration for voltage drop (VD) calculations is the one way length between the source and the load.

Consider now the same balanced circuit, but where the major portion of the load consists of nonlinear loads (assume third-harmonics which is a particular case of nonlinear loads). Under this condition, the phase currents consist of the fundamental current superimposed with the third-harmonic current, whose magnitude is approximately 1/3 of the fundamental. The current in the neutral wire will be the sum of six vectors: the three vectors of the fundamental currents (whose sum, as stated above, is zero), and the three corresponding to the third-harmonic currents, which add algebraically, since they are in phase (3 x 120 degrees = 360 degrees, i.e.: 0 degrees, i.e.: in phase). Therefore, the current in the neutral wire will be approximately 3 x 1/3 = 1, i.e. the same magnitude as the phase current. Logically, the neutral wire size will be the same as the phase wire size.

What will be the VD under this condition? Since the current in the neutral wire has approximately the same value as the phase current and both phase and neutral sizes are equal, it is apparent that the VD under this condition (balanced loads where the major portion of the load consists of third-harmonic currents) is twice the VD of the first condition (balanced loads with no nonlinear loads present).

Let’s now consider the same balanced circuit, but where the major portion of the load consists of nonlinear loads (assume third-harmonics plus other harmonics or, other than third harmonics). Under this condition, the phase currents consists of the fundamental current superimposed with the various harmonics currents components, and the neutral wire current can reach a maximum theoretical value of 1.73 times the value of the phase current. The industry has adopted the practice to double the neutral (remember however that the minimum size permitted by the Code for paralleling phase or neutral conductors is 1/0).

And what will be the VD under this condition? On the one hand, the neutral current is 1.73 times the phase current (let’s approximate to 2 times). On the other hand, since the neutral was doubled, its impedance is half compared to the phase. This leads that the VD in the neutral wire has the same value as it is in the phase wire. So we can conclude that a practical way to calculate the VD under this condition (balanced loads where the major portion of the load consists of nonlinear currents) is to double the VD of the first condition (balanced loads with no nonlinear loads present).

From the above considerations we can conclude that in general, a practical way to calculate the VD of a balanced circuit where the major portion of the load consists of nonlinear loads is to calculate the VD of the same circuit without nonlinear loads and double this value.

Of course, the above considerations are basically intuitive. Let’s now do a detailed evaluation with a group of feeders taken as an example and compare the results.

Voltage Drop and Nonlinear Loads (Detailed Evaluation)

First of all we begin by differentiating two types of nonlinear loads:

For the purpose of simplicity, two types of nonlinear loads will be examined: nonlinear loads that may contain the fundamental current (60Hz) and, let’s say, the full spectrum of its harmonics (which we will call nonlinear) and, loads that contain the fundamental

current and its third-harmonic (which will be called as third-harmonic).

To get a comprehensive assessment of the results, the feeder loads range from 16A to 350A. Two calculations will be performed for each load.

The first group, for nonlinear loads (feeders ID suffix is “_N”. The second group for third-harmonic loads (feeders ID suffix is “_H”. The first group includes also the industry practice relative to the neutral sizing for nonlinear loads. Also, though not evaluated here in detail, the Excel spreadsheet show the results of the feeders under analysis where no nonlinear loads are present (feeders ID w/o suffix).

Except for the industry practice results, all of the calculations were performed according to the applicable NEC 2005 requirements.

Common data to each of the feeders:

208Y/120V system
Three-phase, four-wire
Balanced
Terminals rated at 75^oC
Continuous load
OCPD: Fixed-trip inverse-time breaker
OCPD not listed for operation at 100%
Ambient temperature: 30^oC
Neutral counts as a current-carrying conductor
Neutral current

= 1.73 x Phase Current (max. theoretical for nonlinear load)

= phase current for third-harmonic currents

Phase and Neutral adjustment factor = 80% (bundling factor)
PF = 90%
Length: 100 ft
Max. VD: 5%
Conductor type: CU-THHN (from 12AWG to 750 kcmil)
Raceway type: EMT
Equipment grounding conductor to be considered
No harmonic filter is considered

Step-by-step calculations will be shown only for 16A, 40A, 160A and 250A feeders. For the rest of the feeders the results (based on a computer program) are displayed in the corresponding Excel spreadsheet.

1. Nonlinear loads

NEC calculation

Feeder F16_N (16A)

1.1.1.1 Phase size:

OCPD = 1.25 x 16A = 20A
Phase size BAAF (Before Any Adjustment Factor): 12AWG

(6.53 kcmil); (Based on terminations rated at 75^oC)

Phase ampacity at 90^oC after adjustment factor = 0.8 x 30A = 24A

Since 24A > 20A (OCPD), 12AWG is OK (before VD)

Resulting phase VD (after applying appropriate formula) = 2.44%

1.1.1.2 Neutral size:

Neutral current = 1.73 x 16A = 27.7A
Neutral size BAAF: 10AWG

(10.38 kcmil); (Based on terminations rated at 75^oC)

Neutral ampacity at 90^oC after adjustment factor = 0.8 x 40A = 32A

Since 32A > 27.7A (neutral current), 10AWG is OK (before VD)

Resulting neutral VD (after applying appropriate formula) = 2.55%

1.1.1.3 Resulting VD: 5% (OK)

1.1.1.4 Equipment grounding conductor based on OCPD 20A = 12AWG

(Since neutral kcmil > gnd. wire kcmil (6.53), no change is required in neutral size)

1.1.1.5 EMT size for (3-12AWG) + (1-10AWG) + (1-12AWG): 1/2 ´´

Feeder F40_N (40A)

1.1.2.1 Phase size:

OCPD = 1.25 x 40A = 50A
Phase size BAAF (Before Any Adjustment Factor): 8AWG

(16.51 kcmil); (Based on terminations rated at 75^oC)

Phase ampacity at 90^oC after adjustment factor = 0.8 x 55A = 44A

The next std. OCPD acceptable is 45A, however since the current OCPD is 50A, it does not protect the 8AWG, therefore its size is increased to 6AWG (26.24 kcmil)

Resulting phase VD (after applying appropriate formula) = 1.56%

1.1.2.2 Neutral size:

Neutral current = 1.73 x 40A = 69.2A
Neutral size BAAF: 4AWG

(41.74 kcmil); (Based on terminations rated at 75^oC)

Neutral ampacity at 90^oC after adjustment factor = 0.8 x 95A = 76A

Since 76A > 69.2A (neutral current), 4AWG is OK (before VD)

Resulting neutral VD (after applying appropriate formula) = 1.76%

1.1.2.3 Resulting VD: 3.3% (OK)

1.1.2.4 Equipment grounding conductor based on OCPD 50A = 10AWG

(Since neutral kcmil > gnd. wire kcmil (10.38), no change is required in neutral size. However, as the phase size was increased from 16.51 kcmil to 26.24 kcmil, the gnd. wire kcmil must be increased in the same proportion, resulting that the gnd. kcmil = 26.24/16.51) x 10.38 kcmil = 16.50 kcmil, whose equivalent next std. size is 8AWG (16.51 kcmil). Again, since neutral kcmil > gnd. wire kcmil no change is required in neutral size)

1.1.2.5 EMT size for (3-6AWG) + (1-4AWG) + (1-8AWG): 1 ´´

Feeder F160_N (160A)

1.1.3.1 Phase size:

OCPD = 1.25 x 160A = 200A
Phase size BAAF: 3/0AWG

(167.8 kcmil); (Based on terminations rated at 75^oC)

Phase ampacity at 90^oC after adjustment factor = 0.8 x 225A = 180A

On the one hand, 180A > 160A. On the other hand, since 180A < 800A, NEC considers the next higher std. OCP, (i.e: 200A) as adequate to protect the phase conductor.

Then, no phase size increase is necessary and 3/0AWG is OK (before VD)

Resulting phase VD (after applying appropriate formula) = 1.25%

1.1.3.2 Neutral size:

Neutral current = 1.73 x 160A = 277A

Since this is a nonlinear load, the 70% demand factor above 200A is not

applicable in this case.

Neutral size BAAF: 300 kcmil (Based on terminations rated at 75^oC)
Neutral ampacity at 90^oC after adjustment factor = 0.8 x 320A = 256A

Since 256A < 277A (neutral current), the neutral size was increased to 350 kcmil.

Resulting neutral VD (after applying appropriate formula) = 1.31%

1.1.3.3 Resulting VD: 2.6% (OK)

1.1.3.4 Equipment grounding conductor based on OCPD 200A = 6AWG (26.24 kcmil)

(Since neutral kcmil > gnd. wire kcmil (26.24), no change is required in neutral size)

1.1.3.5 EMT size for (3-3/0AWG) + (1-350 kcmil) + (1-6AWG): 2-1/2 ´´

1.1.4 Feeder F250_N (250A)

1.1.4.1 Phase size:

OCPD = 1.25 x 250A = 312.5A; next higher std.: 350A
Phase size BAAF: 400kcmil (Based on terminations rated at 75^oC)
Phase ampacity at 90^oC after adjustment factor = 0.8 x 380A = 304A

On the one hand, 304A > 250A. On the other hand, since 304A < 800A, NEC considers the next higher std. OCP, (i.e: 350A) as adequate to protect the phase conductor.

Then, no phase size increase is necessary and 400 kcmil is OK (before VD)

Resulting phase VD (after applying appropriate formula) = 1.10%

1.1.4.2 Neutral size:

Neutral current = 1.73 x 250A = 432.5A

Since this is a nonlinear load, the 70% demand factor above 200A is not

applicable in this case.

Neutral size BAAF: 700 kcmil (Based on terminations rated at 75^oC)
Neutral ampacity at 90^oC after adjustment factor = 0.8 x 520A = 416A

Since 416A < 432.5A (neutral current), the neutral size was increased to 750 kcmil, whose ampacity at 90^oC is 0.8 x 535A = 428A which still is less than the neutral current of 432.5A. Then, the next size should be used but, it is not available because we set a maximum size of 750 kcmil. Hence, the solution is to use two neutrals in parallel, each sized for a (neutral) current of 432.5A / 2 = 216.3A. Now we start over again the calculation for this figure.

(Each) neutral size BAAF: 4/0AWG
(Each) neutral ampacity at 90^oC after adjustment factor = 0.8 x 260A = 208A (Note that the adjustment factor for five current-carrying conductors is still 80%).

Since 208A is < 216.3A (neutral current in each of the two paralleled neutral conductors), the neutral size was increased to the next size, i.e. 250 kcmil, whose ampacity at 90^oC is 0.8 x 290A = 232A. On the one hand, 232A > 216.3A. On the other hand, the total neutral ampacity is 2 x 232A = 464A, which is > 350A (OCPD). Therefore, each neutral size is 250 kcmil (before VD).

Resulting neutral VD (after applying appropriate formula) = 1.28%

1.1.4.3 Resulting VD: 2.4% (OK)

1.1.4.4 Equipment grounding conductor based on OCPD 350A = 3AWG (52.62 kcmil)

(Since neutral kcmil > gnd. wire kcmil (52.62), no change is required in neutral size)

1.1.4.5 EMT size for (3-400 kcmil) + (2-250 kcmil) + (1-3AWG): 3 ´´

2. Third-Harmonic loads

NEC calculation

Feeder F16_H (16A)

2.1.1.1 Phase size:

OCPD = 1.25 x 16A = 20A
Phase size BAAF (Before Any Adjustment Factor): 12AWG

(6.53 kcmil); (Based on terminations rated at 75^oC)

Phase ampacity at 90^oC after adjustment factor = 0.8 x 30A = 24A

Since 24A > 20A (OCPD), 12AWG is OK (before VD)

Resulting phase VD (after applying appropriate formula) = 2.44%

2.1.1.2 Neutral size:

Neutral current = 16A
Neutral size BAAF: 14AWG
Neutral ampacity at 90^oC after adjustment factor = 0.8 x 25A = 20A

Since 20A > 16A (neutral current), 14AWG would be OK, however,

the minimum size being considered is 12AWG

Resulting neutral VD (after applying appropriate formula) = 4.9%

2.1.1.3 Resulting VD: 4.9% (OK)

2.1.1.4 Equipment grounding conductor based on OCPD 20A = 12AWG

(Since neutral kcmil = gnd. wire kcmil (6.53), no change is required in neutral size)

2.1.1.5 EMT size for (3-12AWG) + (1-12AWG) + (1-12AWG): 1/2 ´´

2.1.2 Feeder F40_HH (40A)

2.1.2.1 Phase size:

OCPD = 1.25 x 40A = 50A
Phase size BAAF (Before Any Adjustment Factor): 8AWG

(16.51 kcmil); (Based on terminations rated at 75^oC)

Phase ampacity at 90^oC after adjustment factor = 0.8 x 55A = 44A

The next std. OCPD acceptable is 45A, however since the current OCPD is 50A, it does not protect the 8AWG, therefore its size is increased to 6AWG (26.24 kcmil)

Resulting phase VD (after applying appropriate formula) = 1.56%

2.1.2.2 Neutral size:

Neutral current = 40A
Neutral size BAAF: 8AWG

(16.51 kcmil); (Based on terminations rated at 75^oC)

Neutral ampacity at 90^oC after adjustment factor = 0.8 x 55A = 44A

Since 44A > 40A (neutral current), 8AWG is OK (before VD)

Resulting neutral VD (after applying appropriate formula) = 2.43%

2.1.2.3 Resulting VD: 4.0% (OK)

2.1.2.4 Equipment grounding conductor based on OCPD 50A = 10AWG

(Since neutral kcmil > gnd. wire kcmil (10.38), no change is required in neutral size. However, as the phase size was increased from 16.51 kcmil to 26.24 kcmil, the gnd. wire kcmil must be increased in the same proportion, resulting that the gnd. kcmil = 26.24/16.51) x 10.38 kcmil = 16.50 kcmil, whose equivalent next std. size is 8AWG (16.51 kcmil). Again, since neutral kcmil = gnd. wire kcmil no change is required in neutral size)

2.1.2.5 EMT size for (3-6AWG) + (1-8AWG) + (1-8AWG): ¾ ´´

2.1.3 Feeder F160_H_H (160A)

2.1.3.1 Phase size:

OCPD = 1.25 x 160A = 200A
Phase size BAAF: 3/0AWG

(167.8 kcmil); (Based on terminations rated at 75^oC)

Phase ampacity at 90^oC after adjustment factor = 0.8 x 225A = 180A

On the one hand, 180A > 160A. On the other hand, since 180A < 800A, NEC considers the next higher std. OCP, (i.e: 200A) as adequate to protect the phase conductor.

Then, no phase size increase is necessary and 3/0AWG is OK (before VD)

Resulting phase VD (after applying appropriate formula) = 1.25%

2.1.3.2 Neutral size:

Neutral current = 160A
Neutral size BAAF: 2/0AWG (Based on terminations rated at 75^oC)
Neutral ampacity at 90^oC after adjustment factor = 0.8 x 195A = 156A

Since 156A < 160A (neutral current), the neutral size was increased to 3/0AWG.

Resulting neutral VD (after applying appropriate formula) = 1.25%

2.1.3.3 Resulting VD: 2.5% (OK)

2.1.3.4 Equipment grounding conductor based on OCPD 200A = 6AWG (26.24 kcmil)

(Since neutral kcmil > gnd. wire kcmil (26.24), no change is required in neutral size)

2.1.3.5 EMT size for (3-3/0AWG) + (1-3/0AWG) + (1-6AWG): 2 ´´

2.1.4 Feeder F250_HH (250A)

2.1.4.1 Phase size:

OCPD = 1.25 x 250A = 312.5A; next higher std.: 350A
Phase size BAAF: 400kcmil (Based on terminations rated at 75^oC)
Phase ampacity at 90^oC after adjustment factor = 0.8 x 380A = 304A

On the one hand, 304A > 250A. On the other hand, since 304A < 800A, NEC considers the next higher std. OCP, (i.e: 350A) as adequate to protect the phase conductor.

Then, no phase size increase is necessary and 400 kcmil is OK (before VD)

Resulting phase VD (after applying appropriate formula) = 1.10%

2.1.4.2 Neutral size:

Neutral current = 250A

Since this is a nonlinear load, the 70% demand factor above 200A is not

applicable in this case.

Neutral size BAAF: 250 kcmil (Based on terminations rated at 75^oC)
Neutral ampacity at 90^oC after adjustment factor = 0.8 x 290A = 232A

Since 232A < 250A (neutral current), the neutral size was increased to 300 kcmil, whose ampacity at 90^oC is 0.8 x 320A = 256A which is > 250A. Then, no further increase in neutral size is necessary and 300 kcmil is OK.

Resulting neutral VD (after applying appropriate formula) = 1.3%

2.1.4.3 Resulting VD: 2.4% (OK)

2.1.4.4 Equipment grounding conductor based on OCPD 350A = 3AWG (52.62 kcmil)

(Since neutral kcmil > gnd. wire kcmil (52.62), no change is required in neutral size)

2.1.4.5 EMT size for (3-400 kcmil) + (1-300 kcmil) + (1-3AWG): 2-1/2 ´´

CONCLUSIONS:

In general, both for third harmonic and nonlinear loads, VD is approximately equal in the phase and in the neutral conductor for a given feeder.
In general, VD is approximately constant independently of the load (assuming the same feeder length).
Both for feeders w/o nonlinear loads or feeders whose third-harmonic currents are appreciable, it would seem at first glance that for circuits like the ones evaluated here (three-phase, four-wire, balanced), the neutral conductor size will be the same as the phase conductor size. However, as it has been demonstrated, this is not always true. The reason is that the phase conductor size is dependent (among other factors) on the OCPD value, while the neutral conductor depends (among other factors) on the neutral current.

The above conclusions are general.

Click on the following to view:

Jacob Mendelovici, P.E.

Mike Holt’s Comment: I sent the above to my “Electrical Engineer” buddy Mr. Eric Stromberg for his thoughts and they are as follows:

The voltage drop paper and calculations look good. Mr. Medelovici did an admirable job. The paper is clear. The thought process is discernible. The calculations pretty much are in line with some similar calculations I did a few years ago.

A few thoughts:

He states that 1/0 is the minimum for paralleling conductors. 310.4 exception No. 4 allows 2 AWG and larger to be paralleled under engineering supervision.

As with most calculations of this type, the results are conservative, or worst case. It looks like the intended result here is to say that, worst case, the neutral should be doubled, the voltage drop should be considered to be in both directions. This is a reasonable result when the loads are mostly non-linear, as described.

Best Regards,

Eric Stromberg, P.E.