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Critical Clearing Angle under Power System Stability Formula

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

δ cc = a \cos (\cos (δ max) + (\frac{P i}{P max}) \cdot (δ max - δ o))

δ_cc - Critical Clearing Angle?δ_max - Maximum Clearing Angle?P_i - Input Power?P_max - Maximum Power?δ_o - Initial Power Angle?

Critical Clearing Angle under Power System Stability Example

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

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

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

47.5821 = a \cos (\cos (60) + (\frac{200}{1000}) \cdot (60 - 10))

47.5821° = a \cos (\cos (60°) + (\frac{200W}{1000W}) \cdot (60° - 10°))

47.5821 = a \cos (\cos (60) + (\frac{200}{1000}) \cdot (60 - 10))

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Critical Clearing Angle under Power System Stability Solution

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

FIRST Step Consider the formula

δ cc = a \cos (\cos (δ max) + (\frac{P i}{P max}) \cdot (δ max - δ o))

Next Step Substitute values of Variables

∴

δ cc = a \cos (\cos (60°) + (\frac{200W}{1000W}) \cdot (60° - 10°))

Next Step Convert Units

∴

δ cc = a \cos (\cos (1.0472rad) + (\frac{200W}{1000W}) \cdot (1.0472rad - 0.1745rad))

Next Step Prepare to Evaluate

∴

δ cc = a \cos (\cos (1.0472) + (\frac{200}{1000}) \cdot (1.0472 - 0.1745))

Next Step Evaluate

∴

δ cc = 0.830464490459074rad

Next Step Convert to Output's Unit

∴

δ cc = 47.5821103387963°

LAST Step Rounding Answer

∴

δ cc = 47.5821°

Critical Clearing Angle under Power System Stability Formula Elements

Variables

Functions

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

Maximum Clearing Angle

Maximum Clearing Angle is defined as the maximum change in the load curve of any synchronous generator.

Symbol: δ_max

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Maximum Clearing Angle

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

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

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(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 Angle under Power System Stability?

Critical Clearing Angle under Power System Stability evaluator uses Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle)) to evaluate the Critical Clearing Angle, The Critical Clearing Angle under Power System Stability formula is defined as the maximum change in the load angle curve before clearing the fault without loss of synchronism. Critical Clearing Angle is denoted by δ_cc symbol.

How to evaluate Critical Clearing Angle under Power System Stability using this online evaluator? To use this online evaluator for Critical Clearing Angle under Power System Stability, enter Maximum Clearing Angle (δ_max), Input Power (P_i), Maximum Power (P_max) & Initial Power Angle (δ_o) and hit the calculate button.

FAQs on Critical Clearing Angle under Power System Stability

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

The formula of Critical Clearing Angle under Power System Stability is expressed as Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle)). Here is an example- 2726.254 = acos(cos(1.0471975511964)+((200)/(1000))*(1.0471975511964-0.1745329251994)).

How to calculate Critical Clearing Angle under Power System Stability?

With Maximum Clearing Angle (δ_max), Input Power (P_i), Maximum Power (P_max) & Initial Power Angle (δ_o) we can find Critical Clearing Angle under Power System Stability using the formula - Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle)). This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

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

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

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

Critical Clearing Angle under Power System Stability is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Critical Clearing Angle under Power System Stability can be measured.

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Critical Clearing Angle under Power System Stability Formula

Critical Clearing Angle under Power System Stability Example

Critical Clearing Angle under Power System Stability Solution

Critical Clearing Angle under Power System Stability Formula Elements

Other formulas in Power System Stability category

How to Evaluate Critical Clearing Angle under Power System Stability?

FAQs on Critical Clearing Angle under Power System Stability

Variable Name