# Why Three-phase Voltage is 440 Volts?

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## What is Single Phase?

An electrical system with only one source of alternating voltage is called a single-phase system.Single-phase uses only two wires, or conductors: a “phase” wire and a “neutral” wire.It is between a phase and the neutral that voltage is measured.

Single Phase Voltage = 230V i.e., Phase to Neutral

Phase VoltageVPH = Line Voltage /âˆš3 = VL/âˆš3

= 400V /âˆš3 â‰ˆ 230V

## What is Three Phase?

In an electrical system, the voltage between any two of those three phases is referred to as the three-phase system.In a three-phase supply, there are three supply lines, all of which are phase-shifted by an angle of 120 degrees relative to one another.Consequently, there is a net voltage differential of 440 volts between the two phases, which corresponds to a phase angle of 120 degrees.

Three Phase Voltage = 400V

i.e.,Line to Line (or) Phase to Phase

Line Voltage VL = âˆš3 x Phase Voltage = âˆš3 xVPH

= âˆš3 x 230V = 398V â‰ˆ 400V

## Why is 440V used for Three Phase?

When consider 230V single phase voltage, they simply increase it by three for three phase addition, as seen below:

230V + 230V + 230V = 690V

However, this is inapplicable in the case of a three-phase power supply system. Because the EMF produced in three phase systems is a vector (most likely a phasor, which can be simplified by phasor diagrams) quantity with magnitude and direction. The vector difference between two 230V lines is 400V.

In this particular instance, the phasor or vector quantities that have a phase difference.

Based on the phasor diagram for a three-supply system, where each line has 230V, the vector difference is about 400V for each phase, i.e., Phase 1& Phase 2, Phase 2 & Phase 3, or Phase 3 & Phase 1.

This is because the phase angle between two phases is 120 degrees, and all three phases change direction with respect to time, and in the case of 230V, the sine wave changes direction 50 times per second due to the frequency of 50Hz.

According to the Rule of Cosine, the voltage between any two phases in a three-phase system is 400V rather than 660 or 690V. This applies only if there are three phases.

[230V2 – 2 x 230V2 x cos (120Â°)] = 398.37V â‰ˆ 400V

## Why 440V in three phases rather than 660V or 690V?

From a different perspective, if draw the sinusoidal waves of three phase power lines that are 120 degrees apart, the graph clearly reveals that circuit only have two Positive (+Ve) values at the same time and the third is Negative (-Ve). They only calculate two of the three cycles because they all change direction with regard to time. In summary, either Phase 1 & 2, Phase 2 &3, or Phase 3 & 1 are positive, whereas Phase 3, Phase 2, or Phase 1 are negative. As a result, two phases of a three-phase system contain 440V rather than 600, 660, or 690V.

## What is the purpose of 440 volts?

Using 440 volts for motors results in a reduction in motor load current, which is half the amount of current produced by 230 volts.

According to the formula,

kWloss = I2R/1000

the load current is responsible for the line losses.

## If a single-phase circuit is 230V, why is a three-phase circuit 440V and not 690V?

1. Voltage is the potential difference between the two points.

2. A single phase voltage is the voltage between two phases. While the 3-phase is a combination of any two of those three phases.

3. All three phases, i.e., the three wires in the three-phase supply, have the same maximum rms (avg.) value. In other words, if measure the voltage of any of the phases against neutral, it will be 220 or 240 volts. However, when the voltage is measured from one phase to the other, it equals 440.

4. Consider a sin wave with a maximum amplitude of 220 relative to its axis. So, whether in a positive or negative cycle, it can reach a maximum of 220 (+220 or -220).

5. In the case of three phases, the voltage might be applied between two phases rather than one phase and neutral. So, there are three phases, but the voltage between two phases can be calculated. Even though there are three phases, calculate the voltage between any two of them at the same time. And the maximum voltage that received from any two phases is when one is at the top of its positive cycle (i.e., + 220) and the other is at the bottom of its negative cycle (-220).

((+220) -(-220) =440)

And this is the highest value can beachieved by comparing any two points in any of the phases to each other.

## Difference between 415V & 440V

As an electrical engineer with 5 years of experience, I focus on transformer and circuit breaker reliability in 110/33-11kV and 33/11kV substations. I am a professional electrical engineer with experience in transformer service and maintenance. I understand electrical principles and have expertise troubleshooting, repairing, and maintaining transformers, circuit breakers, and testing them.