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Clearing Angle Formula

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Clearing Angle is defined as the maximum change in the load angle curve before clearing fault without loss of synchronism. Check FAQs

δ c = \frac{π \cdot f \cdot P i}{2 \cdot H} \cdot {(t c)}^{2} + δ o

δ_c - Clearing Angle?f - Frequency?P_i - Input Power?H - Constant of Inertia?t_c - Clearing Time?δ_o - Initial Power Angle?π - Archimedes' constant?

Clearing Angle Example

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With units

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Here is how the Clearing Angle equation looks like with Values.

Here is how the Clearing Angle equation looks like with Units.

Here is how the Clearing Angle equation looks like.

61.9302 = \frac{3.1416 \cdot 56 \cdot 200}{2 \cdot 39} \cdot {(0.37)}^{2} + 10

61.9302rad = \frac{3.1416 \cdot 56Hz \cdot 200W}{2 \cdot 39kg·m²} \cdot {(0.37s)}^{2} + 10°

61.9302 = \frac{3.1416 \cdot 56 \cdot 200}{2 \cdot 39} \cdot {(0.37)}^{2} + 10

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Clearing Angle Solution

Follow our step by step solution on how to calculate Clearing Angle?

FIRST Step Consider the formula

δ c = \frac{π \cdot f \cdot P i}{2 \cdot H} \cdot {(t c)}^{2} + δ o

Next Step Substitute values of Variables

∴

δ c = \frac{π \cdot 56Hz \cdot 200W}{2 \cdot 39kg·m²} \cdot {(0.37s)}^{2} + 10°

Next Step Substitute values of Constants

∴

δ c = \frac{3.1416 \cdot 56Hz \cdot 200W}{2 \cdot 39kg·m²} \cdot {(0.37s)}^{2} + 10°

Next Step Convert Units

∴

δ c = \frac{3.1416 \cdot 56Hz \cdot 200W}{2 \cdot 39kg·m²} \cdot {(0.37s)}^{2} + 0.1745rad

Next Step Prepare to Evaluate

∴

δ c = \frac{3.1416 \cdot 56 \cdot 200}{2 \cdot 39} \cdot {(0.37)}^{2} + 0.1745

Next Step Evaluate

∴

δ c = 61.9301891289963rad

LAST Step Rounding Answer

∴

δ c = 61.9302rad

Clearing Angle Formula Elements

Variables

Constants

Clearing Angle

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

Symbol: δ_c

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Clearing Angle

Frequency

Frequency is defined as the number of times a repeating event occurs per unit of time.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Frequency

Input Power

Input Power is defined as the power that is supplied to a synchronous machine during operation.

Symbol: P_i

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Input Power

Constant of Inertia

Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating.

Symbol: H

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Constant of Inertia

Clearing Time

Clearing Time is the time taken by the rotor to move to the critical clearing angle.

Symbol: t_c

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Clearing Time

Initial Power Angle

Initial Power Angle is the angle between a generator's internal voltage and its terminal voltage.

Symbol: δ_o

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Initial Power Angle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Power System Stability category

Go Kinetic Energy of Rotor

KE = (\frac{1}{2}) \cdot J \cdot {ω s}^{2} \cdot 10^{- 6}

Go Speed of Synchronous Machine

ω es = (\frac{P}{2}) \cdot ω r

Go Inertia Constant of Machine

M = \frac{G \cdot H}{180 \cdot fs}

Go Rotor Acceleration

P a = P i - P ep

How to Evaluate Clearing Angle?

Clearing Angle evaluator uses Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle to evaluate 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 evaluate Clearing Angle using this online evaluator? To use this online evaluator 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.

FAQs on Clearing Angle

What is the formula to find Clearing Angle?

The formula of Clearing Angle is expressed as Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle. Here is an example- 61.93019 = (pi*56*200)/(2*39)*(0.37)^2+0.1745329251994.

How to calculate Clearing Angle?

With Frequency (f), Input Power (P_i), Constant of Inertia (H), Clearing Time (t_c) & Initial Power Angle (δ_o) we can find Clearing Angle using the formula - Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle. This formula also uses Archimedes' constant .

Can the Clearing Angle be negative?

No, the Clearing Angle, measured in Angle cannot be negative.

Which unit is used to measure Clearing Angle?

Clearing Angle is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Clearing Angle can be measured.

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Clearing Angle Formula

Clearing Angle Example

Clearing Angle Solution

Clearing Angle Formula Elements

Other formulas in Power System Stability category

How to Evaluate Clearing Angle?

FAQs on Clearing Angle

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