Clearing Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle
δc = (pi*f*Pi)/(2*H)*(tc)^2+δo
This formula uses 1 Constants, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
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.
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.
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 Time - (Measured in Second) - Clearing Time is the time taken by the rotor to move to the critical clearing 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
Frequency: 56 Hertz --> 56 Hertz No Conversion Required
Input Power: 200 Watt --> 200 Watt No Conversion Required
Constant of Inertia: 39 Kilogram Square Meter --> 39 Kilogram Square Meter No Conversion Required
Clearing Time: 0.37 Second --> 0.37 Second No Conversion Required
Initial Power Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δc = (pi*f*Pi)/(2*H)*(tc)^2+δo --> (pi*56*200)/(2*39)*(0.37)^2+0.1745329251994
Evaluating ... ...
δc = 61.9301891289963
STEP 3: Convert Result to Output's Unit
61.9301891289963 Radian --> No Conversion Required
FINAL ANSWER
61.9301891289963 61.93019 Radian <-- Clearing Angle
(Calculation completed in 00.021 seconds)

Credits

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Created by Dipanjona Mallick
Heritage Insitute of technology (HITK), Kolkata
Dipanjona Mallick has created this Calculator and 25+ more calculators!
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Verified by Aman Dhussawat
GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY (GTBIT), NEW DELHI
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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

Clearing Angle Formula

​LaTeX ​Go
Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle
δc = (pi*f*Pi)/(2*H)*(tc)^2+δo

What is Clearing Angle?

In power system stability analysis, the clearing angle refers to the angle through which the rotor angle swings after a fault is cleared and before the system settles into a new stable state. The term is commonly associated with synchronous machines, which are key components in power systems.

How to Calculate Clearing Angle?

Clearing Angle calculator uses Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle to calculate the Clearing Angle, Clearing Angle is defined as the angle through which the rotor angle swings after a fault is cleared and before the system settles into a new stable state. Clearing Angle is denoted by δc symbol.

How to calculate Clearing Angle using this online calculator? To use this online calculator for Clearing Angle, enter Frequency (f), Input Power (Pi), Constant of Inertia (H), Clearing Time (tc) & Initial Power Angle o) and hit the calculate button. Here is how the Clearing Angle calculation can be explained with given input values -> 61.93019 = (pi*56*200)/(2*39)*(0.37)^2+0.1745329251994.

FAQ

What is Clearing Angle?
Clearing Angle is defined as the angle through which the rotor angle swings after a fault is cleared and before the system settles into a new stable state and is represented as δc = (pi*f*Pi)/(2*H)*(tc)^2+δo or Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle. 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, Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating, Clearing Time is the time taken by the rotor to move to the critical clearing angle & Initial Power Angle is the angle between a generator's internal voltage and its terminal voltage.
How to calculate Clearing Angle?
Clearing Angle is defined as the angle through which the rotor angle swings after a fault is cleared and before the system settles into a new stable state is calculated using Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle. To calculate Clearing Angle, you need Frequency (f), Input Power (Pi), Constant of Inertia (H), Clearing Time (tc) & Initial Power Angle o). With our tool, you need to enter the respective value for Frequency, Input Power, Constant of Inertia, Clearing Time & 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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