Clearing Angle Calculator

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

✖Clearing Angle is defined as the maximum change in the load angle curve before clearing fault without loss of synchronism.ⓘ Clearing Angle [δ_c]

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Formula

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Clearing Angle

Formula

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

Example

`"61.93019rad"=(pi*"56Hz"*"200W")/(2*"39kg·m²")*("0.37s")^2+"10°"`

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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
δ_c = (pi*f*P_i)/(2*H)*(t_c)^2+δ_o
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

δ_c = (pi*f*P_i)/(2*H)*(t_c)^2+δ_o --> (pi*56*200)/(2*39)*(0.37)^2+0.1745329251994

Evaluating ... ...

δ_c = 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 00.004 seconds)

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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Verified by Aman Dhussawat

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

Clearing Angle Formula

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

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 δ_c symbol.

How to calculate Clearing Angle using this online calculator? To use this online calculator for Clearing Angle, enter Frequency (f), Input Power (P_i), Constant of Inertia (H), Clearing Time (t_c) & Initial Power Angle (δ_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 δ_c = (pi*f*P_i)/(2*H)*(t_c)^2+δ_o 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 (P_i), Constant of Inertia (H), Clearing Time (t_c) & Initial Power Angle (δ_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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