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))
δcc = acos(cos(δmax)+((Pi)/(Pmax))*(δmax-δo))
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
δcc = acos(cos(δmax)+((Pi)/(Pmax))*(δmaxo)) --> acos(cos(1.0471975511964)+((200)/(1000))*(1.0471975511964-0.1745329251994))
Evaluating ... ...
δcc = 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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Power System Stability Calculators

Inertia Constant of Machine
​ LaTeX ​ Go Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency)
Speed of Synchronous Machine
​ LaTeX ​ Go Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine
Kinetic Energy of Rotor
​ LaTeX ​ Go Kinetic Energy of Rotor = (1/2)*Rotor Moment of Inertia*Synchronous Speed^2*10^-6
Rotor Acceleration
​ LaTeX ​ Go Accelerating Power = Input Power-Electromagnetic Power

Critical Clearing Angle under Power System Stability Formula

​LaTeX ​Go
Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle))
δcc = acos(cos(δmax)+((Pi)/(Pmax))*(δmax-δo))

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 δcc 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 max), Input Power (Pi), Maximum Power (Pmax) & Initial Power Angle 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 δcc = acos(cos(δmax)+((Pi)/(Pmax))*(δmaxo)) 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 max), Input Power (Pi), Maximum Power (Pmax) & Initial Power Angle 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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