Kinetic Energy of Rotor Calculator

✖Rotor Moment of Inertia is the rotational inertia that depends on the mass distribution and shape of the motor.ⓘ Rotor Moment of Inertia [J]			+10% -10%
✖Synchronous Speed is defined as the speed that depends on the stability of the generator or motor to maintain synchronization of the grid.ⓘ Synchronous Speed [ω_s]			+10% -10%

✖Kinetic Energy of Rotor is defined as the energy that is proportional to the moment of inertia and the square of the synchronous speed of the rotor.ⓘ Kinetic Energy of Rotor [KE]

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Formula

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Kinetic Energy of Rotor

Formula

`"KE" = (1/2)*"J"*"ω"_{"s"}^2*10^-6`

Example

`"0.000192J"=(1/2)*"6.0kg·m²"*("8.0m/s")^2*10^-6`

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Kinetic Energy of Rotor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Kinetic Energy of Rotor = (1/2)*Rotor Moment of Inertia*Synchronous Speed^2*10^-6
KE = (1/2)*J*ω_s^2*10^-6
This formula uses 3 Variables

Variables Used

Kinetic Energy of Rotor - (Measured in Joule) - Kinetic Energy of Rotor is defined as the energy that is proportional to the moment of inertia and the square of the synchronous speed of the rotor.
Rotor Moment of Inertia - (Measured in Kilogram Square Meter) - Rotor Moment of Inertia is the rotational inertia that depends on the mass distribution and shape of the motor.
Synchronous Speed - (Measured in Meter per Second) - Synchronous Speed is defined as the speed that depends on the stability of the generator or motor to maintain synchronization of the grid.

STEP 1: Convert Input(s) to Base Unit

Rotor Moment of Inertia: 6 Kilogram Square Meter --> 6 Kilogram Square Meter No Conversion Required
Synchronous Speed: 8 Meter per Second --> 8 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

KE = (1/2)*J*ω_s^2*10^-6 --> (1/2)*6*8^2*10^-6

Evaluating ... ...

KE = 0.000192

STEP 3: Convert Result to Output's Unit

0.000192 Joule --> No Conversion Required

FINAL ANSWER

0.000192 Joule <-- Kinetic Energy of Rotor

(Calculation completed in 00.004 seconds)

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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

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< 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

Kinetic Energy of Rotor Formula

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

What is the kinetic energy of rotor and how the unit convention is used?

Kinetic energy of rotor in power system stability is the key parameter that is related with the rotational mass of the power system. This kinetic energy represents the energy stored in the synchronous generator that is used to generate stability of the system. The unit is J but when the value is counted in MJ multiply the formula with 10^-6MJ.

How to Calculate Kinetic Energy of Rotor?

Kinetic Energy of Rotor calculator uses Kinetic Energy of Rotor = (1/2)*Rotor Moment of Inertia*Synchronous Speed^2*10^-6 to calculate the Kinetic Energy of Rotor, The Kinetic Energy of Rotor in power system stability is defined as the energy that is proportional to the half of moment of inertia of the rotor and square of the synchronous speed. Kinetic Energy of Rotor is denoted by KE symbol.

How to calculate Kinetic Energy of Rotor using this online calculator? To use this online calculator for Kinetic Energy of Rotor, enter Rotor Moment of Inertia (J) & Synchronous Speed (ω_s) and hit the calculate button. Here is how the Kinetic Energy of Rotor calculation can be explained with given input values -> 0.000192 = (1/2)*6*8^2*10^-6.

FAQ

What is Kinetic Energy of Rotor?

The Kinetic Energy of Rotor in power system stability is defined as the energy that is proportional to the half of moment of inertia of the rotor and square of the synchronous speed and is represented as KE = (1/2)*J*ω_s^2*10^-6 or Kinetic Energy of Rotor = (1/2)*Rotor Moment of Inertia*Synchronous Speed^2*10^-6. Rotor Moment of Inertia is the rotational inertia that depends on the mass distribution and shape of the motor & Synchronous Speed is defined as the speed that depends on the stability of the generator or motor to maintain synchronization of the grid.

How to calculate Kinetic Energy of Rotor?

The Kinetic Energy of Rotor in power system stability is defined as the energy that is proportional to the half of moment of inertia of the rotor and square of the synchronous speed is calculated using Kinetic Energy of Rotor = (1/2)*Rotor Moment of Inertia*Synchronous Speed^2*10^-6. To calculate Kinetic Energy of Rotor, you need Rotor Moment of Inertia (J) & Synchronous Speed (ω_s). With our tool, you need to enter the respective value for Rotor Moment of Inertia & Synchronous Speed 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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