In this article, we explain the voltage drop calculation, one of the most crucial calculations in electrical engineering. Here, we outline the formula used to determine voltage drop, which is based on factors like operating voltage, wire gauge, conductor material, load distance, current (amperage), etc.
We also include several exercises for calculating voltage drop.
We recommend using an Excel file available on Hotmart for conducting various calculations. This file allows for easy voltage drop calculations, as explained below.
Voltage drop calculation refers to the reduction in voltage from the power source to the load. In other words, the voltage at the source will not be the same as the voltage that reaches the load.
This reduction occurs due to natural power losses, such as cable heating and other factors. The greater the distance between the source and the load, the more significant the voltage drop. Similarly, with lower voltages, the voltage drop becomes more noticeable. High-voltage transmission lines typically operate above 33,000 volts to minimize voltage drop.
A mobile app also performs voltage drop calculations, along with other useful low-voltage electrical construction calculations. This app is available on both iOS and Android and is highly recommended as it adheres to NOM standards.
Voltage drop calculations are essential to prevent equipment failures since lower voltages cause higher currents, as per Ohm’s Law. Increased current can lead to equipment failure or conductor overloading.
Therefore, it is recommended to calculate the conductor size based on voltage drop requirements.
Voltage Drop Formula
The formula for calculating single-phase voltage drop is as follows:
The formula for calculating three-phase voltage drop is as follows:
Where:
- ppp: Conductor material resistivity.
- III: Current in amperes (A).
- LLL: Distance to load in meters (m).
- SSS: Conductor cross-sectional area (mm²).
- VVV: System voltage or initial voltage in volts (V).
- EEE: Voltage drop in volts (V).
- %E\%E%E: Voltage drop percentage (%).
Resistivity of copper: 0.0172 (ohm-mm²/m). Resistivity of aluminum: 0.0282.
Note: Using the above equations, it is also possible to calculate the required conductor size based on voltage drop, which we’ll explain in another tutorial.
Voltage Drop Calculation Examples
Example 1
We have a single-phase system operating at 240 V. It supplies a load consuming 50 A, located 100 meters away, using a 4 AWG copper conductor (21.2 mm²).
Problem: Calculate the single-phase voltage drop.Using an application:
(The image will open in a new screen for better details)
Manual Calculation: For aluminum resistivity, we use 0.0172.
By plugging in the values, we can determine the voltage drop for this feeder.
Result: Voltage drop is 8.11 V and 3.38%.
Example 2
A 10 kW load with a 0.91 power factor is fed by a 2 AWG aluminum conductor (33.6 mm²). The load is 1 kilometer from the substation, which is a three-phase system operating at 440 V.
Problem: Calculate the voltage drop and the final voltage at the load.
For aluminum resistivity, we use 0.0282.
First, calculate the load current using the following electrical power formula:
I=14.42 A
Next, substitute the values into the equation:
The percentage:
Voltage Drop: E=20.96 V
Percentage Drop: %E=4.76%
Final Voltage: 440 V – 20.96 V = 419.04 V.
Example 3
An agricultural irrigation well uses a pump with a 100 HP three-phase motor, rated at 440 V and 124 A. The motor will be fed by a 2/0 AWG copper conductor (67.43 mm²).
Problem: If the maximum allowable voltage drop is 3%, what is the maximum allowable distance between the substation and the pump?
Using copper resistivity of 0.0172:
First, calculate the voltage drop in volts for a 3% drop.
Then calculate the allowable distance based on a 3% voltage drop.
Result: Maximum allowable distance is 240.95 m.
The pump can be located up to 240 meters from the substation connection point.
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