Moment of Inertia of Machine under Power System Stability 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%
✖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%

✖Moment of Inertia is defined as the product of mass of section and the square of the distance between the reference axis and the centroid of the section.ⓘ Moment of Inertia of Machine under Power System Stability [M_i]

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Formula

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Moment of Inertia of Machine under Power System Stability

Formula

`"M"_{"i"} = "J"*(2/"P")^2*"ω"_{"r"}*10^-6`

Example

`"0.000726kg·m²"="6.0kg·m²"*(2/"2")^2*"121m/s"*10^-6`

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Moment of Inertia of Machine under Power System Stability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6
M_i = J*(2/P)^2*ω_r*10^-6
This formula uses 4 Variables

Variables Used

Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is defined as the product of mass of section and the square of the distance between the reference axis and the centroid of the section.
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.
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

Rotor Moment of Inertia: 6 Kilogram Square Meter --> 6 Kilogram Square Meter No Conversion Required
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

M_i = J*(2/P)^2*ω_r*10^-6 --> 6*(2/2)^2*121*10^-6

Evaluating ... ...

M_i = 0.000726

STEP 3: Convert Result to Output's Unit

0.000726 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

0.000726 Kilogram Square Meter <-- Moment of Inertia

(Calculation completed in 00.004 seconds)

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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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

Moment of Inertia of Machine under Power System Stability Formula

Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6
M_i = J*(2/P)^2*ω_r*10^-6

What do you mean by Moment of Inertia of Machine?

.The moment of inertia is a quantity that describes a body's resistance to angular acceleration. It's the sum of the product of each particle's mass and the square of its distance from the axis of rotation. This is basically a quantitative measure of a body's rotational inertia, which is the body's resistance to having its rotation speed about an axis changed by a turning force.

How to Calculate Moment of Inertia of Machine under Power System Stability?

Moment of Inertia of Machine under Power System Stability calculator uses Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6 to calculate the Moment of Inertia, The Moment of Inertia of Machine under Power System Stability formula helps to define the dynamics of synchronous machine in synchronous machine that basically defines the development of Swing Equation in power system stability. Moment of Inertia is denoted by M_i symbol.

How to calculate Moment of Inertia of Machine under Power System Stability using this online calculator? To use this online calculator for Moment of Inertia of Machine under Power System Stability, enter Rotor Moment of Inertia (J), Number of Machine Poles (P) & Rotor Speed of Synchronous Machine (ω_r) and hit the calculate button. Here is how the Moment of Inertia of Machine under Power System Stability calculation can be explained with given input values -> 0.00072 = 6*(2/2)^2*121*10^-6.

FAQ

What is Moment of Inertia of Machine under Power System Stability?

The Moment of Inertia of Machine under Power System Stability formula helps to define the dynamics of synchronous machine in synchronous machine that basically defines the development of Swing Equation in power system stability and is represented as M_i = J*(2/P)^2*ω_r*10^-6 or Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6. Rotor Moment of Inertia is the rotational inertia that depends on the mass distribution and shape of the motor, 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 Moment of Inertia of Machine under Power System Stability?

The Moment of Inertia of Machine under Power System Stability formula helps to define the dynamics of synchronous machine in synchronous machine that basically defines the development of Swing Equation in power system stability is calculated using Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6. To calculate Moment of Inertia of Machine under Power System Stability, you need Rotor Moment of Inertia (J), Number of Machine Poles (P) & Rotor Speed of Synchronous Machine (ω_r). With our tool, you need to enter the respective value for Rotor Moment of Inertia, 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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