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Moment of Inertia of Machine under Power System Stability Formula

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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. Check FAQs

M i = J \cdot {(\frac{2}{P})}^{2} \cdot ω r \cdot 10^{- 6}

M_i - Moment of Inertia?J - Rotor Moment of Inertia?P - Number of Machine Poles?ω_r - Rotor Speed of Synchronous Machine?

Moment of Inertia of Machine under Power System Stability Example

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Here is how the Moment of Inertia of Machine under Power System Stability equation looks like with Values.

Here is how the Moment of Inertia of Machine under Power System Stability equation looks like with Units.

Here is how the Moment of Inertia of Machine under Power System Stability equation looks like.

0.0007 = 6 \cdot {(\frac{2}{2})}^{2} \cdot 121 \cdot 10^{- 6}

0.0007kg·m² = 6kg·m² \cdot {(\frac{2}{2})}^{2} \cdot 121m/s \cdot 10^{- 6}

0.0007 = 6 \cdot {(\frac{2}{2})}^{2} \cdot 121 \cdot 10^{- 6}

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Moment of Inertia of Machine under Power System Stability Solution

Follow our step by step solution on how to calculate Moment of Inertia of Machine under Power System Stability?

FIRST Step Consider the formula

M i = J \cdot {(\frac{2}{P})}^{2} \cdot ω r \cdot 10^{- 6}

Next Step Substitute values of Variables

∴

M i = 6kg·m² \cdot {(\frac{2}{2})}^{2} \cdot 121m/s \cdot 10^{- 6}

Next Step Prepare to Evaluate

∴

M i = 6 \cdot {(\frac{2}{2})}^{2} \cdot 121 \cdot 10^{- 6}

Next Step Evaluate

∴

M i = 0.000726kg·m²

LAST Step Rounding Answer

∴

M i = 0.0007kg·m²

Moment of Inertia of Machine under Power System Stability Formula Elements

Variables

Moment of Inertia

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.

Symbol: M_i

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

Rotor Moment of Inertia

Rotor Moment of Inertia is the rotational inertia that depends on the mass distribution and shape of the motor.

Symbol: J

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Rotor Moment of Inertia

Number of Machine Poles

Number of Machine Poles is defined as the number of magnetic poles present on a rotor or a stator.

Symbol: P

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Machine Poles

Rotor Speed of Synchronous Machine

Rotor Speed of Synchronous Machine is defined as the speed actual speed at which the synchronous machine rotates.

Symbol: ω_r

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Rotor Speed of Synchronous Machine

Other formulas in Power System Stability category

Go Kinetic Energy of Rotor

KE = (\frac{1}{2}) \cdot J \cdot {ω s}^{2} \cdot 10^{- 6}

Go Speed of Synchronous Machine

ω es = (\frac{P}{2}) \cdot ω r

Go Inertia Constant of Machine

M = \frac{G \cdot H}{180 \cdot fs}

Go Rotor Acceleration

P a = P i - P ep

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

Moment of Inertia of Machine under Power System Stability evaluator uses Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6 to evaluate 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 evaluate Moment of Inertia of Machine under Power System Stability using this online evaluator? To use this online evaluator 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.

FAQs on Moment of Inertia of Machine under Power System Stability

What is the formula to find Moment of Inertia of Machine under Power System Stability?

The formula of Moment of Inertia of Machine under Power System Stability is expressed as Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6. Here is an example- 0.00072 = 6*(2/2)^2*121*10^-6.

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

With Rotor Moment of Inertia (J), Number of Machine Poles (P) & Rotor Speed of Synchronous Machine (ω_r) we can find Moment of Inertia of Machine under Power System Stability using the formula - Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6.

Can the Moment of Inertia of Machine under Power System Stability be negative?

No, the Moment of Inertia of Machine under Power System Stability, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia of Machine under Power System Stability?

Moment of Inertia of Machine under Power System Stability is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Moment of Inertia of Machine under Power System Stability can be measured.

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Moment of Inertia of Machine under Power System Stability Formula

Moment of Inertia of Machine under Power System Stability Example

Moment of Inertia of Machine under Power System Stability Solution

Moment of Inertia of Machine under Power System Stability Formula Elements

Other formulas in Power System Stability category

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

FAQs on Moment of Inertia of Machine under Power System Stability

Variable Name