Speed of Synchronous Machine Calculator

✖Number of Machine Poles is defined as the number of magnetic poles present on a rotor or a stator.ⓘ Number of Machine Poles [P]			+10% -10%
✖Rotor Speed of Synchronous Machine is defined as the speed actual speed at which the synchronous machine rotates.ⓘ Rotor Speed of Synchronous Machine [ω_r]			+10% -10%

✖Speed of Synchronous Machine is defined as the product of number of poles in machine and the rotor speed of the machine.ⓘ Speed of Synchronous Machine [ω_es]

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Formula

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Speed of Synchronous Machine

Formula

`"ω"_{"es"} = ("P"/2)*"ω"_{"r"}`

Example

`"121m/s"=("2"/2)*"121m/s"`

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Speed of Synchronous Machine Solution

STEP 0: Pre-Calculation Summary

Formula Used

Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine
ω_es = (P/2)*ω_r
This formula uses 3 Variables

Variables Used

Speed of Synchronous Machine - (Measured in Meter per Second) - Speed of Synchronous Machine is defined as the product of number of poles in machine and the rotor speed of the machine.
Number of Machine Poles - Number of Machine Poles is defined as the number of magnetic poles present on a rotor or a stator.
Rotor Speed of Synchronous Machine - (Measured in Meter per Second) - Rotor Speed of Synchronous Machine is defined as the speed actual speed at which the synchronous machine rotates.

STEP 1: Convert Input(s) to Base Unit

Number of Machine Poles: 2 --> No Conversion Required
Rotor Speed of Synchronous Machine: 121 Meter per Second --> 121 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_es = (P/2)*ω_r --> (2/2)*121

Evaluating ... ...

ω_es = 121

STEP 3: Convert Result to Output's Unit

121 Meter per Second --> No Conversion Required

FINAL ANSWER

121 Meter per Second <-- Speed of Synchronous Machine

(Calculation completed in 00.004 seconds)

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Credits

Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

Dipanjona Mallick has created this Calculator and 50+ more calculators!

Verified by Aman Dhussawat

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

Aman Dhussawat has verified this Calculator and 100+ more calculators!

< 20 Power System Stability Calculators

Active Power by Infinite Bus

Go Active Power of Infinite Bus = (Voltage of Infinite Bus)^2/sqrt((Resistance)^2+(Synchronous Reactance)^2)-(Voltage of Infinite Bus)^2/((Resistance)^2+(Synchronous Reactance)^2)

Critical Clearing Angle under Power System Stability

Go Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle))

Critical Clearing Time under Power System Stability

Go Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power))

Synchronous Power of Power Angle Curve

Go Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle)

Real Power of Generator under Power Angle Curve

Go Real Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*sin(Electrical Power Angle)

Clearing Time

Go Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power))

Clearing Angle

Go Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle

Maximum Steady State Power Transfer

Go Maximum Steady State Power Transfer = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance

Output Power of Generator under Power System Stability

Go Output Power of Generator = (EMF of Generator*Terminal Voltage*sin(Power Angle))/Magnetic Reluctance

Time Constant in Power System Stability

Go Time Constant = (2*Constant of Inertia)/(pi*Damping Frequency of Oscillation*Damping Coefficient)

Moment of Inertia of Machine under Power System Stability

Go Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6

Inertia Constant of Machine

Go Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency)

Angular Displacement of Machine under Power System Stability

Go Angular Displacement of Machine = Angular Displacement of Rotor-Synchronous Speed*Time of Angular Displacement

Damped Frequency of Oscillation in Power System Stability

Go Damping Frequency of Oscillation = Natural Frequency of Oscillation*sqrt(1-(Oscillation Constant)^2)

Lossless Power Delivered in Synchronous Machine

Go Lossless Power Delivered = Maximum Power*sin(Electrical Power Angle)

Speed of Synchronous Machine

Go Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine

Kinetic Energy of Rotor

Go Kinetic Energy of Rotor = (1/2)*Rotor Moment of Inertia*Synchronous Speed^2*10^-6

Accelerating Torque of Generator under Power System Stability

Go Accelerating Torque = Mechanical Torque-Electrical Torque

Rotor Acceleration

Go Accelerating Power = Input Power-Electromagnetic Power

Complex Power of Generator under Power Angle Curve

Go Complex Power = Phasor Voltage*Phasor Current

Speed of Synchronous Machine Formula

Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine
ω_es = (P/2)*ω_r

What is the Speed of Synchronous machine?

Speed of Synchronous machine is the speed of a machine under transient system of stability that plays a crucial role in the power system stability. This is mainly used to analyze protection system and sometimes measured in electrical radian, in that case the rotor speed is also taken in radians.

How to Calculate Speed of Synchronous Machine?

Speed of Synchronous Machine calculator uses Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine to calculate the Speed of Synchronous Machine, Speed of Synchronous Machine in power system stability is defined as the product of number of poles in the machine and the rotor speed of that machine. Speed of Synchronous Machine is denoted by ω_es symbol.

How to calculate Speed of Synchronous Machine using this online calculator? To use this online calculator for Speed of Synchronous Machine, enter Number of Machine Poles (P) & Rotor Speed of Synchronous Machine (ω_r) and hit the calculate button. Here is how the Speed of Synchronous Machine calculation can be explained with given input values -> 120 = (2/2)*121.

FAQ

What is Speed of Synchronous Machine?

Speed of Synchronous Machine in power system stability is defined as the product of number of poles in the machine and the rotor speed of that machine and is represented as ω_es = (P/2)*ω_r or Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine. Number of Machine Poles is defined as the number of magnetic poles present on a rotor or a stator & Rotor Speed of Synchronous Machine is defined as the speed actual speed at which the synchronous machine rotates.

How to calculate Speed of Synchronous Machine?

Speed of Synchronous Machine in power system stability is defined as the product of number of poles in the machine and the rotor speed of that machine is calculated using Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine. To calculate Speed of Synchronous Machine, you need Number of Machine Poles (P) & Rotor Speed of Synchronous Machine (ω_r). With our tool, you need to enter the respective value for Number of Machine Poles & Rotor Speed of Synchronous Machine 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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