Damped Frequency of Oscillation in Power System Stability Calculator

✖Natural Frequency of Oscillation is defined as the frequency or rate that it vibrates naturally when external force is applied.ⓘ Natural Frequency of Oscillation [ω_fn]			+10% -10%
✖Oscillation Constant is defined as the constant amplitude and period where there is absence of any external force in the field of oscillation.ⓘ Oscillation Constant [ξ]			+10% -10%

✖Damping Frequency of Oscillation is defined as the frequency in which one oscillation occurs in a time period.ⓘ Damped Frequency of Oscillation in Power System Stability [ω_df]

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Damped Frequency of Oscillation in Power System Stability

Formula

`"ω"_{"df"} = "ω"_{"fn"}*sqrt(1-("ξ")^2)`

Example

`"8.954887Hz"="9Hz"*sqrt(1-("0.1")^2)`

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Damped Frequency of Oscillation in Power System Stability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Damping Frequency of Oscillation = Natural Frequency of Oscillation*sqrt(1-(Oscillation Constant)^2)
ω_df = ω_fn*sqrt(1-(ξ)^2)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Damping Frequency of Oscillation - (Measured in Hertz) - Damping Frequency of Oscillation is defined as the frequency in which one oscillation occurs in a time period.
Natural Frequency of Oscillation - (Measured in Hertz) - Natural Frequency of Oscillation is defined as the frequency or rate that it vibrates naturally when external force is applied.
Oscillation Constant - Oscillation Constant is defined as the constant amplitude and period where there is absence of any external force in the field of oscillation.

STEP 1: Convert Input(s) to Base Unit

Natural Frequency of Oscillation: 9 Hertz --> 9 Hertz No Conversion Required
Oscillation Constant: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_df = ω_fn*sqrt(1-(ξ)^2) --> 9*sqrt(1-(0.1)^2)

Evaluating ... ...

ω_df = 8.95488693395958

STEP 3: Convert Result to Output's Unit

8.95488693395958 Hertz --> No Conversion Required

FINAL ANSWER

8.95488693395958 ≈ 8.954887 Hertz <-- Damping Frequency of Oscillation

(Calculation completed in 00.020 seconds)

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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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)

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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 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

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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)

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

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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

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Complex Power of Generator under Power Angle Curve

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Damped Frequency of Oscillation in Power System Stability Formula

Damping Frequency of Oscillation = Natural Frequency of Oscillation*sqrt(1-(Oscillation Constant)^2)
ω_df = ω_fn*sqrt(1-(ξ)^2)

What is Damped Frequency of Oscillation?

The Damped Frequency of Oscillation in Power System Stability is defined as the frequency in which one oscillation occurs in a time period. The damped frequency occurs when external force is exerted to reduce the frequency in which the object starts to set in motion.

How to Calculate Damped Frequency of Oscillation in Power System Stability?

Damped Frequency of Oscillation in Power System Stability calculator uses Damping Frequency of Oscillation = Natural Frequency of Oscillation*sqrt(1-(Oscillation Constant)^2) to calculate the Damping Frequency of Oscillation, The Damped Frequency of Oscillation in Power System Stability formula is defined as the frequency in which one oscillation occurs in a time period. Damped frequency of oscillation refers to the frequency at which the oscillations in the system decay or damp out over time. Damping Frequency of Oscillation is denoted by ω_df symbol.

How to calculate Damped Frequency of Oscillation in Power System Stability using this online calculator? To use this online calculator for Damped Frequency of Oscillation in Power System Stability, enter Natural Frequency of Oscillation (ω_fn) & Oscillation Constant (ξ) and hit the calculate button. Here is how the Damped Frequency of Oscillation in Power System Stability calculation can be explained with given input values -> 8.954887 = 9*sqrt(1-(0.1)^2).

FAQ

What is Damped Frequency of Oscillation in Power System Stability?

The Damped Frequency of Oscillation in Power System Stability formula is defined as the frequency in which one oscillation occurs in a time period. Damped frequency of oscillation refers to the frequency at which the oscillations in the system decay or damp out over time and is represented as ω_df = ω_fn*sqrt(1-(ξ)^2) or Damping Frequency of Oscillation = Natural Frequency of Oscillation*sqrt(1-(Oscillation Constant)^2). Natural Frequency of Oscillation is defined as the frequency or rate that it vibrates naturally when external force is applied & Oscillation Constant is defined as the constant amplitude and period where there is absence of any external force in the field of oscillation.

How to calculate Damped Frequency of Oscillation in Power System Stability?

The Damped Frequency of Oscillation in Power System Stability formula is defined as the frequency in which one oscillation occurs in a time period. Damped frequency of oscillation refers to the frequency at which the oscillations in the system decay or damp out over time is calculated using Damping Frequency of Oscillation = Natural Frequency of Oscillation*sqrt(1-(Oscillation Constant)^2). To calculate Damped Frequency of Oscillation in Power System Stability, you need Natural Frequency of Oscillation (ω_fn) & Oscillation Constant (ξ). With our tool, you need to enter the respective value for Natural Frequency of Oscillation & Oscillation Constant 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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