3 Phase Input Power of Synchronous Motor Calculator

✖The Load Voltage is defined as the voltage between two terminals of load.ⓘ Load Voltage [V_L]			+10% -10%
✖Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.ⓘ Load Current [I_L]			+10% -10%
✖Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.ⓘ Phase Difference [Φ_s]			+10% -10%

✖Three Phase Input Power is defined as the three phase power supplied an synchronous motor.ⓘ 3 Phase Input Power of Synchronous Motor [P_in(3Φ)]

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Formula

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3 Phase Input Power of Synchronous Motor

Formula

`"P"_{"in(3Φ)"} = sqrt(3)*"V"_{"L"}*"I"_{"L"}*cos("Φ"_{"s"})`

Example

`"1584W"=sqrt(3)*"192V"*"5.5A"*cos("30°")`

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3 Phase Input Power of Synchronous Motor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference)
P_in(3Φ) = sqrt(3)*V_L*I_L*cos(Φ_s)
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., sqrt(Number)

Variables Used

Three Phase Input Power - (Measured in Watt) - Three Phase Input Power is defined as the three phase power supplied an synchronous motor.
Load Voltage - (Measured in Volt) - The Load Voltage is defined as the voltage between two terminals of load.
Load Current - (Measured in Ampere) - Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.
Phase Difference - (Measured in Radian) - Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

STEP 1: Convert Input(s) to Base Unit

Load Voltage: 192 Volt --> 192 Volt No Conversion Required
Load Current: 5.5 Ampere --> 5.5 Ampere No Conversion Required
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_in(3Φ) = sqrt(3)*V_L*I_L*cos(Φ_s) --> sqrt(3)*192*5.5*cos(0.5235987755982)

Evaluating ... ...

P_in(3Φ) = 1584

STEP 3: Convert Result to Output's Unit

1584 Watt --> No Conversion Required

FINAL ANSWER

1584 Watt <-- Three Phase Input Power

(Calculation completed in 00.004 seconds)

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Created by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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Chandigarh University (CU), Punjab

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< 8 Power Calculators

Mechanical Power Developed by Synchronous Motor

Go Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference)

3 Phase Input Power of Synchronous Motor

Go Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference)

Mechanical Power of Synchronous Motor

Go Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)

3 Phase Mechanical Power of Synchronous Motor

Go Three Phase Mechanical Power = Three Phase Input Power-3*Armature Current^2*Armature Resistance

Input Power of Synchronous Motor

Go Input Power = Armature Current*Voltage*cos(Phase Difference)

Mechanical Power of Synchronous Motor given Input Power

Go Mechanical Power = Input Power-Armature Current^2*Armature Resistance

Output Power for Synchronous Motor

Go Output Power = Armature Current^2*Armature Resistance

Mechanical Power of Synchronous Motor given Gross Torque

Go Mechanical Power = Gross Torque*Synchronous Speed

< 25 Synchronous Motor Circuit Calculators

Load Current of Synchronous Motor given 3 Phase Mechanical Power

Go Load Current = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*cos(Phase Difference))

Power Factor of Synchronous Motor given 3 Phase Mechanical Power

Go Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)

Distribution Factor in Synchronous Motor

Go Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2))

Load Current of Synchronous Motor using 3 Phase Input Power

Go Load Current = Three Phase Input Power/(sqrt(3)*Load Voltage*cos(Phase Difference))

3 Phase Input Power of Synchronous Motor

Go Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference)

Mechanical Power of Synchronous Motor

Go Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)

Armature Current of Synchronous Motor given 3 Phase Mechanical Power

Go Armature Current = sqrt((Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Resistance))

Armature Current of Synchronous Motor given Mechanical Power

Go Armature Current = sqrt((Input Power-Mechanical Power)/Armature Resistance)

Power Factor of Synchronous Motor using 3 Phase Input Power

Go Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current)

Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power

Go Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2)

3 Phase Mechanical Power of Synchronous Motor

Go Three Phase Mechanical Power = Three Phase Input Power-3*Armature Current^2*Armature Resistance

Phase Angle between Voltage and Armature Current given Input Power

Go Phase Difference = acos(Input Power/(Voltage*Armature Current))

Armature Current of Synchronous Motor given Input Power

Go Armature Current = Input Power/(cos(Phase Difference)*Voltage)

Input Power of Synchronous Motor

Go Input Power = Armature Current*Voltage*cos(Phase Difference)

Armature Resistance of Synchronous Motor given Input Power

Go Armature Resistance = (Input Power-Mechanical Power)/(Armature Current^2)

Magnetic Flux of Synchronous Motor given Back EMF

Go Magnetic Flux = Back EMF/(Armature Winding Constant*Synchronous Speed)

Armature Winding Constant of Synchronous Motor

Go Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed)

Mechanical Power of Synchronous Motor given Input Power

Go Mechanical Power = Input Power-Armature Current^2*Armature Resistance

Power Factor of Synchronous Motor given Input Power

Go Power Factor = Input Power/(Voltage*Armature Current)

Angular Slot Pitch in Synchronous Motor

Go Angular Slot Pitch = (Number of Poles*180)/(Number of Slots*2)

Output Power for Synchronous Motor

Go Output Power = Armature Current^2*Armature Resistance

Number of Poles given Synchronous Speed in Synchronous Motor

Go Number of Poles = (Frequency*120)/Synchronous Speed

Synchronous Speed of Synchronous Motor

Go Synchronous Speed = (120*Frequency)/Number of Poles

Synchronous Speed of Synchronous Motor given Mechanical Power

Go Synchronous Speed = Mechanical Power/Gross Torque

Mechanical Power of Synchronous Motor given Gross Torque

Go Mechanical Power = Gross Torque*Synchronous Speed

3 Phase Input Power of Synchronous Motor Formula

Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference)
P_in(3Φ) = sqrt(3)*V_L*I_L*cos(Φ_s)

What are the characteristics of a synchronous motor?

Synchronous motors operate at a constant speed determined by the frequency of the power supply and the number of poles in the motor. They have a high power factor, precise speed control, require DC excitation for the rotor, and offer high efficiency and starting torque, making them suitable for heavy loads.

How to Calculate 3 Phase Input Power of Synchronous Motor?

3 Phase Input Power of Synchronous Motor calculator uses Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference) to calculate 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 calculate 3 Phase Input Power of Synchronous Motor using this online calculator? To use this online calculator 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. Here is how the 3 Phase Input Power of Synchronous Motor calculation can be explained with given input values -> 1584 = sqrt(3)*192*5.5*cos(0.5235987755982).

FAQ

What is 3 Phase Input Power of Synchronous Motor?

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 and is represented as P_in(3Φ) = sqrt(3)*V_L*I_L*cos(Φ_s) or Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference). The Load Voltage is defined as the voltage between two terminals of load, Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it & Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

How to calculate 3 Phase Input Power of Synchronous Motor?

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 is calculated using Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference). To calculate 3 Phase Input Power of Synchronous Motor, you need Load Voltage (V_L), Load Current (I_L) & Phase Difference (Φ_s). With our tool, you need to enter the respective value for Load Voltage, Load Current & Phase Difference and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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