Critical Clearing Angle under Power System Stability Calculator

✖Maximum Clearing Angle is defined as the maximum change in the load curve of any synchronous generator.ⓘ Maximum Clearing Angle [δ_max]			+10% -10%
✖Input Power is defined as the power that is supplied to a synchronous machine during operation.ⓘ Input Power [P_i]			+10% -10%
✖Maximum Power is the amount of power that is associated with the electrical power angle.ⓘ Maximum Power [P_max]			+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%

✖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 under Power System Stability [δ_cc]

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Critical Clearing Angle under Power System Stability

Formula

`"δ"_{"cc"} = acos(cos("δ"_{"max"})+(("P"_{"i"})/("P"_{"max"}))*("δ"_{"max"}-"δ"_{"o"}))`

Example

`"47.58211°"=acos(cos("60°")+(("200W")/("1000W"))*("60°"-"10°"))`

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Critical Clearing Angle under Power System Stability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle))
δ_cc = acos(cos(δ_max)+((P_i)/(P_max))*(δ_max-δ_o))
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

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.
Maximum Clearing Angle - (Measured in Radian) - Maximum Clearing Angle is defined as the maximum change in the load curve of any synchronous generator.
Input Power - (Measured in Watt) - Input Power is defined as the power that is supplied to a synchronous machine during operation.
Maximum Power - (Measured in Watt) - Maximum Power is the amount of power that is associated with the electrical power angle.
Initial Power Angle - (Measured in Radian) - Initial Power Angle is the angle between a generator's internal voltage and its terminal voltage.

STEP 1: Convert Input(s) to Base Unit

Maximum Clearing Angle: 60 Degree --> 1.0471975511964 Radian (Check conversion here)
Input Power: 200 Watt --> 200 Watt No Conversion Required
Maximum Power: 1000 Watt --> 1000 Watt No Conversion Required
Initial Power Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ_cc = acos(cos(δ_max)+((P_i)/(P_max))*(δ_max-δ_o)) --> acos(cos(1.0471975511964)+((200)/(1000))*(1.0471975511964-0.1745329251994))

Evaluating ... ...

δ_cc = 0.830464490459074

STEP 3: Convert Result to Output's Unit

0.830464490459074 Radian -->47.5821103387963 Degree (Check conversion here)

FINAL ANSWER

47.5821103387963 ≈ 47.58211 Degree <-- Critical Clearing Angle

(Calculation completed in 00.004 seconds)

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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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

Critical Clearing Angle under Power System Stability Formula

Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle))
δ_cc = acos(cos(δ_max)+((P_i)/(P_max))*(δ_max-δ_o))

What is the Critical Clearing Angle?

The critical clearing angle is defined as the maximum change in the load angle curve before clearing the fault without loss of synchronism. In other words, when the fault occurs in the system the load angle curve begin to increase, and the system becomes unstable.

How to Calculate Critical Clearing Angle under Power System Stability?

Critical Clearing Angle under Power System Stability calculator uses Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle)) to calculate the Critical Clearing Angle, The Critical Clearing Angle under Power System Stability formula is defined as the maximum change in the load angle curve before clearing the fault without loss of synchronism. Critical Clearing Angle is denoted by δ_cc symbol.

How to calculate Critical Clearing Angle under Power System Stability using this online calculator? To use this online calculator for Critical Clearing Angle under Power System Stability, enter Maximum Clearing Angle (δ_max), Input Power (P_i), Maximum Power (P_max) & Initial Power Angle (δ_o) and hit the calculate button. Here is how the Critical Clearing Angle under Power System Stability calculation can be explained with given input values -> 2726.254 = acos(cos(1.0471975511964)+((200)/(1000))*(1.0471975511964-0.1745329251994)).

FAQ

What is Critical Clearing Angle under Power System Stability?

The Critical Clearing Angle under Power System Stability formula is defined as the maximum change in the load angle curve before clearing the fault without loss of synchronism and is represented as δ_cc = acos(cos(δ_max)+((P_i)/(P_max))*(δ_max-δ_o)) or Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle)). Maximum Clearing Angle is defined as the maximum change in the load curve of any synchronous generator, Input Power is defined as the power that is supplied to a synchronous machine during operation, Maximum Power is the amount of power that is associated with the electrical power angle & Initial Power Angle is the angle between a generator's internal voltage and its terminal voltage.

How to calculate Critical Clearing Angle under Power System Stability?

The Critical Clearing Angle under Power System Stability formula is defined as the maximum change in the load angle curve before clearing the fault without loss of synchronism is calculated using Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle)). To calculate Critical Clearing Angle under Power System Stability, you need Maximum Clearing Angle (δ_max), Input Power (P_i), Maximum Power (P_max) & Initial Power Angle (δ_o). With our tool, you need to enter the respective value for Maximum Clearing Angle, Input Power, Maximum Power & Initial Power Angle 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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