Inertia Constant of Machine Calculator

✖Three Phase MVA Rating of Machine is also known as base MVA of a machine that is a crucial parameter to provide the per unit parameter in a synchronous generator.ⓘ Three Phase MVA Rating of Machine [G]			+10% -10%
✖Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating.ⓘ Constant of Inertia [H]			+10% -10%
✖Synchronous Frequency is defined as the frequency in which the synchronous machine operates in steady-state conditions.ⓘ Synchronous Frequency [fs]			+10% -10%

✖Inertia Constant of machine is the ratio of the product of three-phase MVA rating of the machine and the inertia constant in MJ/MVA to the product of 180 and the frequency.ⓘ Inertia Constant of Machine [M]

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Formula

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Inertia Constant of Machine

Formula

`"M" = ("G"*"H")/(180*"fs")`

Example

`"0.059091"=("15"*"39kg·m²")/(180*"55Hz")`

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Inertia Constant of Machine Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency)
M = (G*H)/(180*fs)
This formula uses 4 Variables

Variables Used

Inertia Constant of Machine - Inertia Constant of machine is the ratio of the product of three-phase MVA rating of the machine and the inertia constant in MJ/MVA to the product of 180 and the frequency.
Three Phase MVA Rating of Machine - Three Phase MVA Rating of Machine is also known as base MVA of a machine that is a crucial parameter to provide the per unit parameter in a synchronous generator.
Constant of Inertia - (Measured in Kilogram Square Meter) - Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating.
Synchronous Frequency - (Measured in Hertz) - Synchronous Frequency is defined as the frequency in which the synchronous machine operates in steady-state conditions.

STEP 1: Convert Input(s) to Base Unit

Three Phase MVA Rating of Machine: 15 --> No Conversion Required
Constant of Inertia: 39 Kilogram Square Meter --> 39 Kilogram Square Meter No Conversion Required
Synchronous Frequency: 55 Hertz --> 55 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = (G*H)/(180*fs) --> (15*39)/(180*55)

Evaluating ... ...

M = 0.0590909090909091

STEP 3: Convert Result to Output's Unit

0.0590909090909091 --> No Conversion Required

FINAL ANSWER

0.0590909090909091 ≈ 0.059091 <-- Inertia Constant of Machine

(Calculation completed in 00.020 seconds)

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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

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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))

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

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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)

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

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

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

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

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Go Accelerating Torque = Mechanical Torque-Electrical Torque

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Inertia Constant of Machine Formula

Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency)
M = (G*H)/(180*fs)

What is Inertia Constant of Machine?

In some of the machines like synchronous machines the inertia constant is the key parameter to analyze the ability of the machine to store kinetic energy in the rotor. This stored kinetic energy plays an important role in providing stability of the system.

How to Calculate Inertia Constant of Machine?

Inertia Constant of Machine calculator uses Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency) to calculate the Inertia Constant of Machine, Inertia Constant of Machine is the ratio of Inertia Constant of machine is the ratio of the product of three-phase MVA rating of the machine and the inertia constant in MJ/MVA to the product of 180 and the synchronous frequency. Inertia Constant of Machine is denoted by M symbol.

How to calculate Inertia Constant of Machine using this online calculator? To use this online calculator for Inertia Constant of Machine, enter Three Phase MVA Rating of Machine (G), Constant of Inertia (H) & Synchronous Frequency (fs) and hit the calculate button. Here is how the Inertia Constant of Machine calculation can be explained with given input values -> 0.059091 = (15*39)/(180*55).

FAQ

What is Inertia Constant of Machine?

Inertia Constant of Machine is the ratio of Inertia Constant of machine is the ratio of the product of three-phase MVA rating of the machine and the inertia constant in MJ/MVA to the product of 180 and the synchronous frequency and is represented as M = (G*H)/(180*fs) or Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency). Three Phase MVA Rating of Machine is also known as base MVA of a machine that is a crucial parameter to provide the per unit parameter in a synchronous generator, Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating & Synchronous Frequency is defined as the frequency in which the synchronous machine operates in steady-state conditions.

How to calculate Inertia Constant of Machine?

Inertia Constant of Machine is the ratio of Inertia Constant of machine is the ratio of the product of three-phase MVA rating of the machine and the inertia constant in MJ/MVA to the product of 180 and the synchronous frequency is calculated using Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency). To calculate Inertia Constant of Machine, you need Three Phase MVA Rating of Machine (G), Constant of Inertia (H) & Synchronous Frequency (fs). With our tool, you need to enter the respective value for Three Phase MVA Rating of Machine, Constant of Inertia & Synchronous Frequency 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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