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3 Phase Input Power of Synchronous Motor Formula

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Three Phase Input Power is defined as the three phase power supplied an synchronous motor. Check FAQs

P in(3Φ) = \sqrt{3} \cdot V L \cdot I L \cdot \cos (Φ s)

P_in(3Φ) - Three Phase Input Power?V_L - Load Voltage?I_L - Load Current?Φ_s - Phase Difference?

3 Phase Input Power of Synchronous Motor Example

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Here is how the 3 Phase Input Power of Synchronous Motor equation looks like with Values.

Here is how the 3 Phase Input Power of Synchronous Motor equation looks like with Units.

Here is how the 3 Phase Input Power of Synchronous Motor equation looks like.

1584 = \sqrt{3} \cdot 192 \cdot 5.5 \cdot \cos (30)

1584W = \sqrt{3} \cdot 192V \cdot 5.5A \cdot \cos (30°)

1584 = \sqrt{3} \cdot 192 \cdot 5.5 \cdot \cos (30)

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3 Phase Input Power of Synchronous Motor Solution

Follow our step by step solution on how to calculate 3 Phase Input Power of Synchronous Motor?

FIRST Step Consider the formula

P in(3Φ) = \sqrt{3} \cdot V L \cdot I L \cdot \cos (Φ s)

Next Step Substitute values of Variables

∴

P in(3Φ) = \sqrt{3} \cdot 192V \cdot 5.5A \cdot \cos (30°)

Next Step Convert Units

∴

P in(3Φ) = \sqrt{3} \cdot 192V \cdot 5.5A \cdot \cos (0.5236rad)

Next Step Prepare to Evaluate

∴

P in(3Φ) = \sqrt{3} \cdot 192 \cdot 5.5 \cdot \cos (0.5236)

LAST Step Evaluate

∴

P in(3Φ) = 1584W

3 Phase Input Power of Synchronous Motor Formula Elements

Variables

Functions

Three Phase Input Power

Three Phase Input Power is defined as the three phase power supplied an synchronous motor.

Symbol: P_in(3Φ)

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Three Phase Input Power

Load Voltage

The Load Voltage is defined as the voltage between two terminals of load.

Symbol: V_L

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Load Voltage

Load Current

Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.

Symbol: I_L

Measurement: Electric CurrentUnit: A

Note: Value should be greater than 0.

Formulas to find Load Current

Phase Difference

Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

Symbol: Φ_s

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Phase Difference

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Power category

Go Armature Current of Synchronous Motor given 3 Phase Mechanical Power

I a = \sqrt{\frac{P in(3Φ) - P me(3Φ)}{3 \cdot R a}}

Go Armature Current of Synchronous Motor given Input Power

I a = \frac{P in}{\cos (Φ s) \cdot V}

Go Armature Current of Synchronous Motor given Mechanical Power

I a = \sqrt{\frac{P in - P m}{R a}}

Go Load Current of Synchronous Motor given 3 Phase Mechanical Power

I L = \frac{P me(3Φ) + 3 \cdot {I a}^{2} \cdot R a}{\sqrt{3} \cdot V L \cdot \cos (Φ s)}

How to Evaluate 3 Phase Input Power of Synchronous Motor?

3 Phase Input Power of Synchronous Motor evaluator uses Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference) to evaluate the Three Phase Input Power, The 3 Phase Input Power of Synchronous Motor formula is defined as the power which is given to the synchronous motor by a 3-phase supply. Three Phase Input Power is denoted by P_in(3Φ) symbol.

How to evaluate 3 Phase Input Power of Synchronous Motor using this online evaluator? To use this online evaluator for 3 Phase Input Power of Synchronous Motor, enter Load Voltage (V_L), Load Current (I_L) & Phase Difference (Φ_s) and hit the calculate button.

FAQs on 3 Phase Input Power of Synchronous Motor

What is the formula to find 3 Phase Input Power of Synchronous Motor?

The formula of 3 Phase Input Power of Synchronous Motor is expressed as Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference). Here is an example- 1584 = sqrt(3)*192*5.5*cos(0.5235987755982).

How to calculate 3 Phase Input Power of Synchronous Motor?

With Load Voltage (V_L), Load Current (I_L) & Phase Difference (Φ_s) we can find 3 Phase Input Power of Synchronous Motor using the formula - Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

Can the 3 Phase Input Power of Synchronous Motor be negative?

Yes, the 3 Phase Input Power of Synchronous Motor, measured in Power can be negative.

Which unit is used to measure 3 Phase Input Power of Synchronous Motor?

3 Phase Input Power of Synchronous Motor is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which 3 Phase Input Power of Synchronous Motor can be measured.

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