## 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
ωes = (P/2)*ωr
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
ωes = (P/2)*ωr --> (2/2)*121
Evaluating ... ...
ωes = 121
STEP 3: Convert Result to Output's Unit
121 Meter per Second --> No Conversion Required
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
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## < 20 Power System Stability Calculators

Active Power by Infinite Bus
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
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
Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power))
Synchronous Power of Power Angle Curve
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
Real Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*sin(Electrical Power Angle)
Clearing Time
Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power))
Clearing Angle
Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle
Maximum Steady State Power Transfer = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance
Output Power of Generator under Power System Stability
Output Power of Generator = (EMF of Generator*Terminal Voltage*sin(Power Angle))/Magnetic Reluctance
Time Constant in Power System Stability
Time Constant = (2*Constant of Inertia)/(pi*Damping Frequency of Oscillation*Damping Coefficient)
Moment of Inertia of Machine under Power System Stability
Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6
Inertia Constant of Machine
Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency)
Angular Displacement of Machine under Power System Stability
Angular Displacement of Machine = Angular Displacement of Rotor-Synchronous Speed*Time of Angular Displacement
Damped Frequency of Oscillation in Power System Stability
Damping Frequency of Oscillation = Natural Frequency of Oscillation*sqrt(1-(Oscillation Constant)^2)
Lossless Power Delivered in Synchronous Machine
Lossless Power Delivered = Maximum Power*sin(Electrical Power Angle)
Speed of Synchronous Machine
Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine
Kinetic Energy of Rotor
Kinetic Energy of Rotor = (1/2)*Rotor Moment of Inertia*Synchronous Speed^2*10^-6
Accelerating Torque of Generator under Power System Stability
Accelerating Torque = Mechanical Torque-Electrical Torque
Rotor Acceleration
Accelerating Power = Input Power-Electromagnetic Power
Complex Power of Generator under Power Angle Curve
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
ωes = (P/2)*ωr

## 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 ωes 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 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 ωes = (P/2)*ωr 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 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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