Clearing Time Calculator

✖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%
✖Clearing Angle is defined as the maximum change in the load angle curve before clearing fault without loss of synchronism.ⓘ Clearing Angle [δ_c]			+10% -10%
✖Initial Power Angle is the angle between a generator's internal voltage and its terminal voltage.ⓘ Initial Power Angle [δ_o]			+10% -10%
✖Frequency is defined as the number of times a repeating event occurs per unit of time.ⓘ Frequency [f]			+10% -10%
✖Input Power is defined as the power that is supplied to a synchronous machine during operation.ⓘ Input Power [P_i]			+10% -10%

✖Clearing Time is the time taken by the rotor to move to the critical clearing angle.ⓘ Clearing Time [t_c]

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Formula

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Clearing Time

Formula

`"t"_{"c"} = sqrt((2*"H"*("δ"_{"c"}-"δ"_{"o"}))/(pi*"f"*"P"_{"i"}))`

Example

`"0.36991s"=sqrt((2*"39kg·m²"*("61.9rad"-"10°"))/(pi*"56Hz"*"200W"))`

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Clearing Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power))
t_c = sqrt((2*H*(δ_c-δ_o))/(pi*f*P_i))
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Clearing Time - (Measured in Second) - Clearing Time is the time taken by the rotor to move to the critical clearing angle.
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.
Clearing Angle - (Measured in Radian) - Clearing Angle is defined as the maximum change in the load angle curve before clearing fault without loss of synchronism.
Initial Power Angle - (Measured in Radian) - Initial Power Angle is the angle between a generator's internal voltage and its terminal voltage.
Frequency - (Measured in Hertz) - Frequency is defined as the number of times a repeating event occurs per unit of time.
Input Power - (Measured in Watt) - Input Power is defined as the power that is supplied to a synchronous machine during operation.

STEP 1: Convert Input(s) to Base Unit

Constant of Inertia: 39 Kilogram Square Meter --> 39 Kilogram Square Meter No Conversion Required
Clearing Angle: 61.9 Radian --> 61.9 Radian No Conversion Required
Initial Power Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Frequency: 56 Hertz --> 56 Hertz No Conversion Required
Input Power: 200 Watt --> 200 Watt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_c = sqrt((2*H*(δ_c-δ_o))/(pi*f*P_i)) --> sqrt((2*39*(61.9-0.1745329251994))/(pi*56*200))

Evaluating ... ...

t_c = 0.369909552064908

STEP 3: Convert Result to Output's Unit

0.369909552064908 Second --> No Conversion Required

FINAL ANSWER

0.369909552064908 ≈ 0.36991 Second <-- Clearing Time

(Calculation completed in 00.004 seconds)

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Credits

Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

Dipanjona Mallick has created this Calculator and 50+ more calculators!

Verified by Aman Dhussawat

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

Aman Dhussawat has verified this Calculator and 100+ more calculators!

< 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

Clearing Time Formula

Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power))
t_c = sqrt((2*H*(δ_c-δ_o))/(pi*f*P_i))

What is Clearing Time?

Clearing Time is the Critical Clearing Time, that is defined as the time in which the rotor moves to the critical angle time. This is the maximum time a disturbance can be applied without the system losing stability.

How to Calculate Clearing Time?

Clearing Time calculator uses Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power)) to calculate the Clearing Time, The Clearing Time formula is defined as the Critical Clearing Time, that is defined as the time in which the rotor moves to the critical angle time. Clearing time refers to the time it takes for a protective relay or a protective system to detect a fault or disturbance in the power system, isolate the faulty section, and disconnect it from the rest of the system. Clearing Time is denoted by t_c symbol.

How to calculate Clearing Time using this online calculator? To use this online calculator for Clearing Time, enter Constant of Inertia (H), Clearing Angle (δ_c), Initial Power Angle (δ_o), Frequency (f) & Input Power (P_i) and hit the calculate button. Here is how the Clearing Time calculation can be explained with given input values -> 0.367203 = sqrt((2*39*(61.9-0.1745329251994))/(pi*56*200)).

FAQ

What is Clearing Time?

The Clearing Time formula is defined as the Critical Clearing Time, that is defined as the time in which the rotor moves to the critical angle time. Clearing time refers to the time it takes for a protective relay or a protective system to detect a fault or disturbance in the power system, isolate the faulty section, and disconnect it from the rest of the system and is represented as t_c = sqrt((2*H*(δ_c-δ_o))/(pi*f*P_i)) or Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power)). Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating, Clearing Angle is defined as the maximum change in the load angle curve before clearing fault without loss of synchronism, Initial Power Angle is the angle between a generator's internal voltage and its terminal voltage, Frequency is defined as the number of times a repeating event occurs per unit of time & Input Power is defined as the power that is supplied to a synchronous machine during operation.

How to calculate Clearing Time?

The Clearing Time formula is defined as the Critical Clearing Time, that is defined as the time in which the rotor moves to the critical angle time. Clearing time refers to the time it takes for a protective relay or a protective system to detect a fault or disturbance in the power system, isolate the faulty section, and disconnect it from the rest of the system is calculated using Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power)). To calculate Clearing Time, you need Constant of Inertia (H), Clearing Angle (δ_c), Initial Power Angle (δ_o), Frequency (f) & Input Power (P_i). With our tool, you need to enter the respective value for Constant of Inertia, Clearing Angle, Initial Power Angle, Frequency & Input Power 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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