Mechanical Power Developed by Synchronous Motor Calculator

✖Back EMF is a voltage that is generated in a motor or generator due to the motion of the armature or rotor. It is called "back" EMF as its polarity opposes the voltage applied.ⓘ Back EMF [E_b]			+10% -10%
✖Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.ⓘ Voltage [V]			+10% -10%
✖The synchronous impedance (Z_S ) is an imaginary impedance employed to account for the voltage effects in the armature circuit of the alternator.ⓘ Synchronous Impedance [Z_S]			+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%
✖Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.ⓘ Load Angle [α]			+10% -10%

✖Mechanical Power power is the product of a force on an object and the object's velocity or the product of torque on a shaft and the shaft's angular velocity.ⓘ Mechanical Power Developed by Synchronous Motor [P_m]

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Formula

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Mechanical Power Developed by Synchronous Motor

Formula

`"P"_{"m"} = (("E"_{"b"}*"V")/"Z"_{"S"})*cos("Φ"_{"s"}-"α")-("E"_{"b"}^2/"Z"_{"S"})*cos("Φ"_{"s"})`

Example

`"587.7329W"=(("180V"*"240V")/"17.75Ω")*cos("30°"-"57°")-(("180V")^2/"17.75Ω")*cos("30°")`

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Mechanical Power Developed by Synchronous Motor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference)
P_m = ((E_b*V)/Z_S)*cos(Φ_s-α)-(E_b^2/Z_S)*cos(Φ_s)
This formula uses 1 Functions, 6 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)

Variables Used

Mechanical Power - (Measured in Watt) - Mechanical Power power is the product of a force on an object and the object's velocity or the product of torque on a shaft and the shaft's angular velocity.
Back EMF - (Measured in Volt) - Back EMF is a voltage that is generated in a motor or generator due to the motion of the armature or rotor. It is called "back" EMF as its polarity opposes the voltage applied.
Voltage - (Measured in Volt) - Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.
Synchronous Impedance - (Measured in Ohm) - The synchronous impedance (Z_S ) is an imaginary impedance employed to account for the voltage effects in the armature circuit of the alternator.
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.
Load Angle - (Measured in Radian) - Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.

STEP 1: Convert Input(s) to Base Unit

Back EMF: 180 Volt --> 180 Volt No Conversion Required
Voltage: 240 Volt --> 240 Volt No Conversion Required
Synchronous Impedance: 17.75 Ohm --> 17.75 Ohm No Conversion Required
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Load Angle: 57 Degree --> 0.994837673636581 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_m = ((E_b*V)/Z_S)*cos(Φ_s-α)-(E_b^2/Z_S)*cos(Φ_s) --> ((180*240)/17.75)*cos(0.5235987755982-0.994837673636581)-(180^2/17.75)*cos(0.5235987755982)

Evaluating ... ...

P_m = 587.73288801822

STEP 3: Convert Result to Output's Unit

587.73288801822 Watt --> No Conversion Required

FINAL ANSWER

587.73288801822 ≈ 587.7329 Watt <-- Mechanical Power

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Machine » AC Machines » Synchronous Motor » Power » Mechanical Power Developed by Synchronous Motor

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Created by Aman Dhussawat

GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY (GTBIT), NEW DELHI

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Verified by Parminder Singh

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

Mechanical Power Developed by Synchronous Motor Formula

What is the power developed by a motor?

In an electric motor, the mechanical power is defined as the speed times the torque. Mechanical power is typically defined as kilowatts (kW) or horsepower (hp) with one watt equaling one joule per second or one Newton-Meter per second.

How to Calculate Mechanical Power Developed by Synchronous Motor?

Mechanical Power Developed by Synchronous Motor calculator uses Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference) to calculate the Mechanical Power, The Mechanical Power Developed by Synchronous Motor formula is defined as the expression for net power developed by the synchronous motor by which Mechanical power developed. Mechanical Power is denoted by P_m symbol.

How to calculate Mechanical Power Developed by Synchronous Motor using this online calculator? To use this online calculator for Mechanical Power Developed by Synchronous Motor, enter Back EMF (E_b), Voltage (V), Synchronous Impedance (Z_S), Phase Difference (Φ_s) & Load Angle (α) and hit the calculate button. Here is how the Mechanical Power Developed by Synchronous Motor calculation can be explained with given input values -> 587.7329 = ((180*240)/17.75)*cos(0.5235987755982-0.994837673636581)-(180^2/17.75)*cos(0.5235987755982).

FAQ

What is Mechanical Power Developed by Synchronous Motor?

The Mechanical Power Developed by Synchronous Motor formula is defined as the expression for net power developed by the synchronous motor by which Mechanical power developed and is represented as P_m = ((E_b*V)/Z_S)*cos(Φ_s-α)-(E_b^2/Z_S)*cos(Φ_s) or Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference). Back EMF is a voltage that is generated in a motor or generator due to the motion of the armature or rotor. It is called "back" EMF as its polarity opposes the voltage applied, Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines, The synchronous impedance (Z_S ) is an imaginary impedance employed to account for the voltage effects in the armature circuit of the alternator, Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor & Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.

How to calculate Mechanical Power Developed by Synchronous Motor?

The Mechanical Power Developed by Synchronous Motor formula is defined as the expression for net power developed by the synchronous motor by which Mechanical power developed is calculated using Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference). To calculate Mechanical Power Developed by Synchronous Motor, you need Back EMF (E_b), Voltage (V), Synchronous Impedance (Z_S), Phase Difference (Φ_s) & Load Angle (α). With our tool, you need to enter the respective value for Back EMF, Voltage, Synchronous Impedance, Phase Difference & Load Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mechanical Power?

In this formula, Mechanical Power uses Back EMF, Voltage, Synchronous Impedance, Phase Difference & Load Angle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)
Mechanical Power = Input Power-Armature Current^2*Armature Resistance
Mechanical Power = Gross Torque*Synchronous Speed

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