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Critical Clearing Time under Power System Stability Formula

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

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

t_cc - Critical Clearing Time?H - Constant of Inertia?δ_cc - Critical Clearing Angle?δ_o - Initial Power Angle?f - Frequency?P_max - Maximum Power?π - Archimedes' constant?

Critical Clearing Time under Power System Stability Example

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Here is how the Critical Clearing Time under Power System Stability equation looks like with Values.

Here is how the Critical Clearing Time under Power System Stability equation looks like with Units.

Here is how the Critical Clearing Time under Power System Stability equation looks like.

0.017 = \sqrt{\frac{2 \cdot 39 \cdot (47.5 - 10)}{3.1416 \cdot 56 \cdot 1000}}

0.017s = \sqrt{\frac{2 \cdot 39kg·m² \cdot (47.5° - 10°)}{3.1416 \cdot 56Hz \cdot 1000W}}

0.017 = \sqrt{\frac{2 \cdot 39 \cdot (47.5 - 10)}{3.1416 \cdot 56 \cdot 1000}}

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Critical Clearing Time under Power System Stability Solution

Follow our step by step solution on how to calculate Critical Clearing Time under Power System Stability?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

t cc = \sqrt{\frac{2 \cdot 39kg·m² \cdot (47.5° - 10°)}{π \cdot 56Hz \cdot 1000W}}

Next Step Substitute values of Constants

∴

t cc = \sqrt{\frac{2 \cdot 39kg·m² \cdot (47.5° - 10°)}{3.1416 \cdot 56Hz \cdot 1000W}}

Next Step Convert Units

∴

t cc = \sqrt{\frac{2 \cdot 39kg·m² \cdot (0.829rad - 0.1745rad)}{3.1416 \cdot 56Hz \cdot 1000W}}

Next Step Prepare to Evaluate

∴

t cc = \sqrt{\frac{2 \cdot 39 \cdot (0.829 - 0.1745)}{3.1416 \cdot 56 \cdot 1000}}

Next Step Evaluate

∴

t cc = 0.0170346285967296s

LAST Step Rounding Answer

∴

t cc = 0.017s

Critical Clearing Time under Power System Stability Formula Elements

Variables

Constants

Functions

Critical Clearing Time

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

Symbol: t_cc

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Critical 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

Critical Clearing Angle

Critical Clearing Angle is defined as the maximum angle by which the rotor angle of a synchronous machine can swing after a disturbance.

Symbol: δ_cc

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Critical 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

Maximum Power

Maximum Power is the amount of power that is associated with the electrical power angle.

Symbol: P_max

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Maximum 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 Critical Clearing Time under Power System Stability?

Critical Clearing Time under Power System Stability evaluator uses Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power)) to evaluate the Critical Clearing Time, Critical Clearing Time under Power System Stability is defined as the maximum time delay that can be allowed to clear the fault without loss of synchronism. Critical Clearing Time represents the maximum time that a disturbance can persist without causing the system to lose stability. Critical Clearing Time is denoted by t_cc symbol.

How to evaluate Critical Clearing Time under Power System Stability using this online evaluator? To use this online evaluator for Critical Clearing Time under Power System Stability, enter Constant of Inertia (H), Critical Clearing Angle (δ_cc), Initial Power Angle (δ_o), Frequency (f) & Maximum Power (P_max) and hit the calculate button.

FAQs on Critical Clearing Time under Power System Stability

What is the formula to find Critical Clearing Time under Power System Stability?

The formula of Critical Clearing Time under Power System Stability is expressed as Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power)). Here is an example- 0.017035 = sqrt((2*39*(0.829031394697151-0.1745329251994))/(pi*56*1000)).

How to calculate Critical Clearing Time under Power System Stability?

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

Can the Critical Clearing Time under Power System Stability be negative?

No, the Critical Clearing Time under Power System Stability, measured in Time cannot be negative.

Which unit is used to measure Critical Clearing Time under Power System Stability?

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

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Critical Clearing Time under Power System Stability Formula

Critical Clearing Time under Power System Stability Example

Critical Clearing Time under Power System Stability Solution

Critical Clearing Time under Power System Stability Formula Elements

Other formulas in Power System Stability category

How to Evaluate Critical Clearing Time under Power System Stability?

FAQs on Critical Clearing Time under Power System Stability

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