Angular Displacement of Machine under Power System Stability Calculator

✖Angular Displacement of Rotor is defined as the position of the rotor of a rotating machine (such as a generator or motor) relative to a reference point.ⓘ Angular Displacement of Rotor [θ_m]			+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%
✖Time of Angular Displacement is defined as the duration taken for the rotor of a rotating machine-like generator or motor to undergo a certain change in angular position.ⓘ Time of Angular Displacement [t]			+10% -10%

✖Angular Displacement of Machine is defined as the change in the angular position of its rotating through a specified axis.ⓘ Angular Displacement of Machine under Power System Stability [δ_a]

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Angular Displacement of Machine under Power System Stability

Formula

`"δ"_{"a"} = "θ"_{"m"}-"ω"_{"s"}*"t"`

Example

`"20.2rad"="109rad"-"8.0m/s"*"11.1s"`

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Angular Displacement of Machine under Power System Stability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Displacement of Machine = Angular Displacement of Rotor-Synchronous Speed*Time of Angular Displacement
δ_a = θ_m-ω_s*t
This formula uses 4 Variables

Variables Used

Angular Displacement of Machine - (Measured in Radian) - Angular Displacement of Machine is defined as the change in the angular position of its rotating through a specified axis.
Angular Displacement of Rotor - (Measured in Radian) - Angular Displacement of Rotor is defined as the position of the rotor of a rotating machine (such as a generator or motor) relative to a reference point.
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.
Time of Angular Displacement - (Measured in Second) - Time of Angular Displacement is defined as the duration taken for the rotor of a rotating machine-like generator or motor to undergo a certain change in angular position.

STEP 1: Convert Input(s) to Base Unit

Angular Displacement of Rotor: 109 Radian --> 109 Radian No Conversion Required
Synchronous Speed: 8 Meter per Second --> 8 Meter per Second No Conversion Required
Time of Angular Displacement: 11.1 Second --> 11.1 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ_a = θ_m-ω_s*t --> 109-8*11.1

Evaluating ... ...

δ_a = 20.2

STEP 3: Convert Result to Output's Unit

20.2 Radian --> No Conversion Required

FINAL ANSWER

20.2 Radian <-- Angular Displacement of Machine

(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

Angular Displacement of Machine under Power System Stability Formula

Angular Displacement of Machine = Angular Displacement of Rotor-Synchronous Speed*Time of Angular Displacement
δ_a = θ_m-ω_s*t

What do you mean by Angular Displacement of Machine?

Angular Displacement of Machine is the measure of how far a rotating object has moved or rotated from a specific reference point. In the context of power system, it represents the difference between the rotor position and the synchronous speed. as a whole, angular displacement is fundamental for engineers working with rotating machinery, and it plays a key role in the analysis, design, and operation of various mechanical and electrical systems.

How to Calculate Angular Displacement of Machine under Power System Stability?

Angular Displacement of Machine under Power System Stability calculator uses Angular Displacement of Machine = Angular Displacement of Rotor-Synchronous Speed*Time of Angular Displacement to calculate the Angular Displacement of Machine, Angular Displacement of Machine under Power System Stability formula is defined as the change in angular position or orientation of a rotating part or component of the machine. It is a measure of how much the angle of rotation has changed from a reference point. Angular Displacement of Machine is denoted by δ_a symbol.

How to calculate Angular Displacement of Machine under Power System Stability using this online calculator? To use this online calculator for Angular Displacement of Machine under Power System Stability, enter Angular Displacement of Rotor (θ_m), Synchronous Speed (ω_s) & Time of Angular Displacement (t) and hit the calculate button. Here is how the Angular Displacement of Machine under Power System Stability calculation can be explained with given input values -> 20.2 = 109-8*11.1.

FAQ

What is Angular Displacement of Machine under Power System Stability?

Angular Displacement of Machine under Power System Stability formula is defined as the change in angular position or orientation of a rotating part or component of the machine. It is a measure of how much the angle of rotation has changed from a reference point and is represented as δ_a = θ_m-ω_s*t or Angular Displacement of Machine = Angular Displacement of Rotor-Synchronous Speed*Time of Angular Displacement. Angular Displacement of Rotor is defined as the position of the rotor of a rotating machine (such as a generator or motor) relative to a reference point, Synchronous Speed is defined as the speed that depends on the stability of the generator or motor to maintain synchronization of the grid & Time of Angular Displacement is defined as the duration taken for the rotor of a rotating machine-like generator or motor to undergo a certain change in angular position.

How to calculate Angular Displacement of Machine under Power System Stability?

Angular Displacement of Machine under Power System Stability formula is defined as the change in angular position or orientation of a rotating part or component of the machine. It is a measure of how much the angle of rotation has changed from a reference point is calculated using Angular Displacement of Machine = Angular Displacement of Rotor-Synchronous Speed*Time of Angular Displacement. To calculate Angular Displacement of Machine under Power System Stability, you need Angular Displacement of Rotor (θ_m), Synchronous Speed (ω_s) & Time of Angular Displacement (t). With our tool, you need to enter the respective value for Angular Displacement of Rotor, Synchronous Speed & Time of Angular Displacement 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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