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Clearing Time Formula

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

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

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

Clearing Time Example

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

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

Here is how the Clearing Time equation looks like.

0.3699 = \sqrt{\frac{2 \cdot 39 \cdot (61.9 - 10)}{3.1416 \cdot 56 \cdot 200}}

0.3699s = \sqrt{\frac{2 \cdot 39kg·m² \cdot (61.9rad - 10°)}{3.1416 \cdot 56Hz \cdot 200W}}

0.3699 = \sqrt{\frac{2 \cdot 39 \cdot (61.9 - 10)}{3.1416 \cdot 56 \cdot 200}}

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Clearing Time Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

t c = \sqrt{\frac{2 \cdot 39kg·m² \cdot (61.9rad - 10°)}{π \cdot 56Hz \cdot 200W}}

Next Step Substitute values of Constants

∴

t c = \sqrt{\frac{2 \cdot 39kg·m² \cdot (61.9rad - 10°)}{3.1416 \cdot 56Hz \cdot 200W}}

Next Step Convert Units

∴

t c = \sqrt{\frac{2 \cdot 39kg·m² \cdot (61.9rad - 0.1745rad)}{3.1416 \cdot 56Hz \cdot 200W}}

Next Step Prepare to Evaluate

∴

t c = \sqrt{\frac{2 \cdot 39 \cdot (61.9 - 0.1745)}{3.1416 \cdot 56 \cdot 200}}

Next Step Evaluate

∴

t c = 0.369909552064908s

LAST Step Rounding Answer

∴

t c = 0.3699s

Clearing Time Formula Elements

Variables

Constants

Functions

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

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 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

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

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Time?

Clearing Time evaluator uses Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power)) to evaluate the Clearing Time, The Clearing Time formula is defined as the Critical Clearing Time, that is defined as the time in which the rotor moves to the critical angle time. Clearing time refers to the time it takes for a protective relay or a protective system to detect a fault or disturbance in the power system, isolate the faulty section, and disconnect it from the rest of the system. Clearing Time is denoted by t_c symbol.

How to evaluate Clearing Time using this online evaluator? To use this online evaluator for Clearing Time, enter Constant of Inertia (H), Clearing Angle (δ_c), Initial Power Angle (δ_o), Frequency (f) & Input Power (P_i) and hit the calculate button.

FAQs on Clearing Time

What is the formula to find Clearing Time?

The formula of Clearing Time is expressed as Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power)). Here is an example- 0.367203 = sqrt((2*39*(61.9-0.1745329251994))/(pi*56*200)).

How to calculate Clearing Time?

With Constant of Inertia (H), Clearing Angle (δ_c), Initial Power Angle (δ_o), Frequency (f) & Input Power (P_i) we can find Clearing Time using the formula - Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Clearing Time be negative?

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

Which unit is used to measure Clearing Time?

Clearing Time is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Clearing Time can be measured.

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Clearing Time Formula

Clearing Time Example

Clearing Time Solution

Clearing Time Formula Elements

Other formulas in Power System Stability category

How to Evaluate Clearing Time?

FAQs on Clearing Time

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