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# Voltage drop calculation methods with examples explained in details

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## Voltage drop considerations

The first consideration for voltage drop is that under the steady-state conditions of normal load, the voltage at the utilization equipment must be adequate.

Fine-print notes in the NEC recommend sizing feeders and branch circuits so that the maximum voltage drop in either does not exceed 3%, with the total voltage drop for feeders and branch circuits not to exceed 5%, for efficiency of operation.

In addition to steady-state conditions, voltage drop under transient conditions, with sudden high-current, short-time loads, must be considered.

The most common loads of this type are motor inrush currents during starting. These loads cause a voltage dip on the system as a result of the voltage drop in conductors, transformers and generators under the high current. This voltage dip can have numerous adverse effects on equipment in the system, and equipment and conductors must be designed and sized to minimize these problems.

In many cases, reduced-voltage starting of motors to reduce inrush current will be necessary.

### Voltage drop formulas

Let’s see two most common methods for calculation of voltage drop – approximate and exact methods:

#### 1. Approximate method

Voltage drop EVD = IR cosθ + IX sinθ where abbreviations are same as below “Exact Method”.

#### 2. Exact method #1

If sending end voltage and load PF are known. where:

• EVD – Voltage drop, line-to-neutral, volts
• Es – Source voltage, line-to-neutral, volts
• I – Line (Load) current, amperes
• R – Circuit (branch, feeder) resistance, ohms
• X – Circuit (branch, feeder) reactance, ohms
• cosθ – Power factor of load, decimal
• sinθ – Reactive factor of load, decimal

If the receiving end voltage, load current and power factor (PF) are known. ER is the receiving end voltage.

#### 2. Exact Method #2

If receiving or sending mVA and its power factor are known at a known sending or receiving voltage. or where:

• ER – Receiving line-line voltage in kV
• ES – Sending line-line voltage in kV
• MVAR – Receiving three-phase mVA
• MVAS – Sending three-phase mVA
• Z – Impedance between and receiving ends
• γ – The angle of impedance Z
• R – Receiving end PF
• S – Sending end PF, positive when lagging

### Voltage drop tables

Tables for calculating voltage drop for copper and aluminum conductors, in either magnetic (steel) or nonmagnetic (aluminum or non-metallic) conduit, are shown below. These tables give voltage drop per ampere per 100 ft (30 m) of circuit length.

The circuit length is from the beginning point to the end point of the circuit regardless of the number of conductors.

Tables are based on the following conditions:

#### Condition #1

Three or four single conductors in a conduit, random lay. For three-conductor cable, actual voltage drop will be approximately the same for small conductor sizes and high power factors. Actual voltage drop will be from 10 to 15% lower for larger conductor sizes and lower power factors.

#### Condition #2

Voltage drops are phase-to-phase, for three-phase, three-wire or three-phase, four-wire 60 Hz circuits. For other circuits, multiply voltage drop given in the tables by the following correction factors:

Correction factors table:

 Three-phase, four-wire, phase-to-neutral × 0.577 Single-phase, two-wire × 1.155 Single-phase, three-wire, phase-to-phase × 1.155 Single-phase, three-wire, phase-to-neutral × 0.577

#### Condition #3

Voltage drops are for a conductor temperature of 75 °C. They may be used for conductor temperatures between 60 °C and 90 °C with reasonable accuracy (within ±5%). However, correction factors in Table 1 can be applied if desired. The values in the table are in percent of total voltage drop.

• For conductor temperature of 60 °C – SUBTRACT the percentage from Table 1.
• For conductor temperature of 90 °C – ADD the percentage from Table 1.

### Calculations

To calculate voltage drop:

1. Multiply current in amperes by the length of the circuit in feet to get ampere-feet. Circuit length is the distance from the point of origin to the load end of the circuit.
2. Divide by 100.
3. Multiply by proper voltage drop value in tables. Result is voltage drop.

#### Example #1

A 460 V, 100 hp motor, running at 80% PF, draws 124 A full-load current. It is fed by three 2/0 copper conductors in steel conduit. The feeder length is 150 ft (46 m).

What is the voltage drop in the feeder? What is the percentage voltage drop?
• 124 A × 150ft (46m) = 18,600 A-ft
• Divided by 100 = 186
• Table: 2/0 copper, magnetic conduit,
80% PF = 0.0187
186 x 0.0187 = 3.48 V drop
3.48/460 x 100 = 0.76% drop

Conclusion: 0.76% voltage drop is very acceptable. (See NEC Article 215, which suggests that a voltage drop of 3% or less on a feeder is acceptable.)

To select minimum conductor size:

1. Determine maximum desired i voltage drop, in volts.
2. Divide voltage drop by ii (amperes x circuit feet).
3. Multiply by 100.
4. Find nearest lower voltage drop value in tables, in correct column for type of conductor, conduit and power factor. Read conductor size for that value.
5. Where this results in an oversized cable, verify cable lug sizes for molded case circuit breakers and fusible 4 switches. Where lug size available is exceeded, go to next higher rating.

#### Example #2

A three-phase, four-wire lighting feeder on a 208 V circuit is 250 ft (76.2 m) long. The load is 175 A at 90% PF. It is desired to use aluminum 7 conductors in aluminum conduit.

What size conductor is required to limit the voltage drop to 2% phase-to-phase?
• VD = 2/100 × 208  = 4.16 V
• 4.16 / (175 × 250) = 0.0000951
• 0.0000951 × 100= 0.00951
• In table, under aluminum conductors, nonmagnetic conduit, 90% PF, the nearest lower value is 0.0091. Conductor required is 12 500 kcmil.
(Size 4/0 THW would have adequate ampacity, but the voltage drop would be excessive.)

Table 2 – Voltage Drop—Volts per Ampere per 100 Feet (30 m); Three-Phase, Phase-to-Phase Table 2 – Voltage drop – Volts per ampere per 100 Feet (30 m); Three-phase, phase-to-phase

Reference // Power Distribution Systems by EATON

Get access to premium HV/MV/LV technical articles, electrical engineering guides, research studies and much more! It helps you to shape up your technical skills in your everyday life as an electrical engineer. ### Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.

1. Mark Monlinong
Sep 15, 2020

Hi,

How do you compute the voltage drop of a feeder installed in cable tray? Considering also the ambient temperature. I want to reduce cost by proper selection of cable size and number of set considering the voltage drop of main feeder cable.

2. zahir
Jul 18, 2020

i wont voltage drop 70sqmm 3 cor HV cable.( 600m lenght)..

voltage start from stepup transformer 11,000kv.
600m end is my other resort.

3. Dionisio Urbina Jr
Apr 02, 2020

In a previous example:
124 x 154ft ÷ 100 = 186 x 0.0187 = 3.48drop

I need to clarify that in a 3-phase system you have to multiply it by 1.732

Vd = 1.732 x Amp x Length x R / 100f

4. Mohamed Gaber
Sep 24, 2019

Dear Edvard Csanyi;
Kindly advise me if the Demand factor should be used for the calculation of Voltage drop or not? Kindly submit the formula if the demand factor should be used.

5. Sep 09, 2019

NO Response!!!!!!!!!!!!!!!!!!!!!!!!

6. Aug 29, 2019

Is there any change in voltage drop calculation if the cable is armoured and if so let us know the correction to be applied

7. Aug 24, 2019

pls send sample computation for volatage drop and short circuit using per unit method

8. RAJKUMAR
Aug 13, 2019

I Want Voltage Drop Calculation For Single Phase System (Solar). Please share

9. Abiodun Sobayo
Mar 24, 2019

Nice to know this. Bit can we get a link to download all these calculations for better understanding and to teach others.

10. Tariq
Mar 24, 2019

Dear Edvard:
Please Show The Mathematical Derive Of The Equation Of Exact Method #1 (And How Sending End Voltage (Vs) Appears In Voltage Drop Formula .

Best Regards ,

11. Jan 01, 2019

Hi everybody,
In fact I have a confussion for which power factor I use in determining voltage drop of main cable (30m length) which supplies two motors (1st one 50HP , o.85 p.f, with 100m cable) and (2nd one 100HP , o.75 p.f,with 300m cable) .

• kamal
Aug 14, 2019

1- APPLY SUPERPOSITION THEOREM
2- APPLY PHASOR SUMMATION MOY ALGEBRAIC SUMMATION
3- THE MAIN SUPPLY WILL HAVE A DIFFERENT P.F. FROM BOTH

12. Chirantan Gupta
Nov 27, 2018

I saw the comments above and I guess what Gerald is referring to is the K factor method which is popularly followed by NEC. However, NEC also supports the IEEE 141-1993 formula. Refer to bottom of Table 9 Note 2 of NEC which clearly says: Multiplying current by effective impedance gives good approximation for line to neutral voltage drop. Thus, the approximate formula (Sqrt(3)*I*(Rcosphi+Xsinphi) can be followed. For all practical purposes, I have used this formula for last 25 years. The exact formula can also be used, and there is a vectorial method to get the solution.

13. Eng. Abdolgabar Ahmed Mahmood
Oct 25, 2018

Dear Engineers,
GERALD NEWTON AND TOMMY RICE.
Please tell me your methods of voltage drop calculations I will be grateful for you to let me know the best way of calculation because I am new in this field.
best regards
Eng. Abdolgabar Ahmed

14. Gerald Newton
Mar 08, 2017

Your voltage drop calculation article is off the wall. Sorry, but this is not how it is done. Furthermore, the State of Washington specifically states in a news letter how the inspectors want the calculation done. I have been in this business for over 40 years and have never, ever seen anything like your method. I suggest you do some research on how practical engineers and electricians do voltage drop calculations.

• tommy rice
Apr 01, 2017

could you e-mail me and tell me how Washington state wants their calculations done. I use a different method for voltage drop calculations than edvard csanyi