Critical Clearing Time under Power System Stability 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%
✖Critical Clearing Angle is defined as the maximum angle by which the rotor angle of a synchronous machine can swing after a disturbance.ⓘ Critical Clearing Angle [δ_cc]			+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%
✖Maximum Power is the amount of power that is associated with the electrical power angle.ⓘ Maximum Power [P_max]			+10% -10%

✖Critical Clearing Time is the time taken by the rotor to move to the critical clearing angle.ⓘ Critical Clearing Time under Power System Stability [t_cc]

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Formula

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Critical Clearing Time under Power System Stability

Formula

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

Example

`"0.017035s"=sqrt((2*"39kg·m²"*("47.5°"-"10°"))/(pi*"56Hz"*"1000W"))`

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Critical Clearing Time under Power System Stability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power))
t_cc = sqrt((2*H*(δ_cc-δ_o))/(pi*f*P_max))
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

Critical Clearing Time - (Measured in Second) - Critical 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.
Critical Clearing Angle - (Measured in Radian) - Critical Clearing Angle is defined as the maximum angle by which the rotor angle of a synchronous machine can swing after a disturbance.
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.
Maximum Power - (Measured in Watt) - Maximum Power is the amount of power that is associated with the electrical power angle.

STEP 1: Convert Input(s) to Base Unit

Constant of Inertia: 39 Kilogram Square Meter --> 39 Kilogram Square Meter No Conversion Required
Critical Clearing Angle: 47.5 Degree --> 0.829031394697151 Radian (Check conversion here)
Initial Power Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Frequency: 56 Hertz --> 56 Hertz No Conversion Required
Maximum Power: 1000 Watt --> 1000 Watt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_cc = sqrt((2*H*(δ_cc-δ_o))/(pi*f*P_max)) --> sqrt((2*39*(0.829031394697151-0.1745329251994))/(pi*56*1000))

Evaluating ... ...

t_cc = 0.0170346285967296

STEP 3: Convert Result to Output's Unit

0.0170346285967296 Second --> No Conversion Required

FINAL ANSWER

0.0170346285967296 ≈ 0.017035 Second <-- Critical Clearing Time

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Power System Stability » Critical Clearing Time under Power System Stability

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

Dipanjona Mallick has created this Calculator and 25+ 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

Critical Clearing Time under Power System Stability Formula

Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power))
t_cc = sqrt((2*H*(δ_cc-δ_o))/(pi*f*P_max))

What is the Critical Clearing Time?

Critical clearing time is the time when the rotor would have moved to the critical clearing angle. It helps us to design the operating times of the relay and circuit breaker so that the total time taken by them should be less than the critical clearing time for stable operation of the system.

How to Calculate Critical Clearing Time under Power System Stability?

Critical Clearing Time under Power System Stability calculator uses Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power)) to calculate the Critical Clearing Time, Critical Clearing Time under Power System Stability is defined as the maximum time delay that can be allowed to clear the fault without loss of synchronism. Critical Clearing Time represents the maximum time that a disturbance can persist without causing the system to lose stability. Critical Clearing Time is denoted by t_cc symbol.

How to calculate Critical Clearing Time under Power System Stability using this online calculator? To use this online calculator for Critical Clearing Time under Power System Stability, enter Constant of Inertia (H), Critical Clearing Angle (δ_cc), Initial Power Angle (δ_o), Frequency (f) & Maximum Power (P_max) and hit the calculate button. Here is how the Critical Clearing Time under Power System Stability calculation can be explained with given input values -> 0.017035 = sqrt((2*39*(0.829031394697151-0.1745329251994))/(pi*56*1000)).

FAQ

What is Critical Clearing Time under Power System Stability?

Critical Clearing Time under Power System Stability is defined as the maximum time delay that can be allowed to clear the fault without loss of synchronism. Critical Clearing Time represents the maximum time that a disturbance can persist without causing the system to lose stability and is represented as t_cc = sqrt((2*H*(δ_cc-δ_o))/(pi*f*P_max)) or Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power)). Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating, Critical Clearing Angle is defined as the maximum angle by which the rotor angle of a synchronous machine can swing after a disturbance, 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 & Maximum Power is the amount of power that is associated with the electrical power angle.

How to calculate Critical Clearing Time under Power System Stability?

Critical Clearing Time under Power System Stability is defined as the maximum time delay that can be allowed to clear the fault without loss of synchronism. Critical Clearing Time represents the maximum time that a disturbance can persist without causing the system to lose stability is calculated using Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power)). To calculate Critical Clearing Time under Power System Stability, you need Constant of Inertia (H), Critical Clearing Angle (δ_cc), Initial Power Angle (δ_o), Frequency (f) & Maximum Power (P_max). With our tool, you need to enter the respective value for Constant of Inertia, Critical Clearing Angle, Initial Power Angle, Frequency & Maximum 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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