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Synchronous Power of Power Angle Curve Formula

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Synchronous Power is defined as the electrical power output of a synchronous generator is influenced by the power angle. Check FAQs

P syn = \frac{mod \underset{̲}{u} s (E g) \cdot mod \underset{̲}{u} s (V)}{X s} \cdot \cos (δ)

P_syn - Synchronous Power?E_g - EMF of Generator?V - Voltage of Infinite Bus?X_s - Synchronous Reactance?δ - Electrical Power Angle?

Synchronous Power of Power Angle Curve Example

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Here is how the Synchronous Power of Power Angle Curve equation looks like with Values.

Here is how the Synchronous Power of Power Angle Curve equation looks like with Units.

Here is how the Synchronous Power of Power Angle Curve equation looks like.

21.8335 = \frac{mod \underset{̲}{u} s (160) \cdot mod \underset{̲}{u} s (11)}{57} \cdot \cos (45)

21.8335W = \frac{mod \underset{̲}{u} s (160V) \cdot mod \underset{̲}{u} s (11V)}{57Ω} \cdot \cos (45°)

21.8335 = \frac{mod \underset{̲}{u} s (160) \cdot mod \underset{̲}{u} s (11)}{57} \cdot \cos (45)

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Synchronous Power of Power Angle Curve Solution

Follow our step by step solution on how to calculate Synchronous Power of Power Angle Curve?

FIRST Step Consider the formula

P syn = \frac{mod \underset{̲}{u} s (E g) \cdot mod \underset{̲}{u} s (V)}{X s} \cdot \cos (δ)

Next Step Substitute values of Variables

∴

P syn = \frac{mod \underset{̲}{u} s (160V) \cdot mod \underset{̲}{u} s (11V)}{57Ω} \cdot \cos (45°)

Next Step Convert Units

∴

P syn = \frac{mod \underset{̲}{u} s (160V) \cdot mod \underset{̲}{u} s (11V)}{57Ω} \cdot \cos (0.7854rad)

Next Step Prepare to Evaluate

∴

P syn = \frac{mod \underset{̲}{u} s (160) \cdot mod \underset{̲}{u} s (11)}{57} \cdot \cos (0.7854)

Next Step Evaluate

∴

P syn = 21.8334725419036W

LAST Step Rounding Answer

∴

P syn = 21.8335W

Synchronous Power of Power Angle Curve Formula Elements

Variables

Functions

Synchronous Power

Synchronous Power is defined as the electrical power output of a synchronous generator is influenced by the power angle.

Symbol: P_syn

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Synchronous Power

EMF of Generator

EMF of Generator is defined as the energy per unit electric charge that is imparted by an energy source, such as an electric generator or a battery.

Symbol: E_g

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find EMF of Generator

Voltage of Infinite Bus

Voltage of Infinite Bus is defined as the constant voltage maintained by this idealized power source under all conditions.

Symbol: V

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Voltage of Infinite Bus

Synchronous Reactance

Synchronous Reactance is defined as the internal reactance of the synchronous machine and is critical for understanding the machine's performance, especially in the context of power systems.

Symbol: X_s

Measurement: Electric ResistanceUnit: Ω

Note: Value should be greater than 0.

Formulas to find Synchronous Reactance

Electrical Power Angle

Electrical Power Angle is the angular displacement between the rotor and stator position in the magnetic field of a synchronous machine, also known as the Load Angle used in power angle curve.

Symbol: δ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Electrical 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)

modulus

Modulus of a number is the remainder when that number is divided by another number.

Syntax: modulus

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 Synchronous Power of Power Angle Curve?

Synchronous Power of Power Angle Curve evaluator uses Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle) to evaluate the Synchronous Power, The Synchronous Power of Power Angle Curve formula is defined as the electrical power output of a synchronous generator is influenced by the power angle. Synchronous Power is denoted by P_syn symbol.

How to evaluate Synchronous Power of Power Angle Curve using this online evaluator? To use this online evaluator for Synchronous Power of Power Angle Curve, enter EMF of Generator (E_g), Voltage of Infinite Bus (V), Synchronous Reactance (X_s) & Electrical Power Angle (δ) and hit the calculate button.

FAQs on Synchronous Power of Power Angle Curve

What is the formula to find Synchronous Power of Power Angle Curve?

The formula of Synchronous Power of Power Angle Curve is expressed as Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle). Here is an example- 21.83347 = (modulus(160)*modulus(11))/57*cos(0.785398163397301).

How to calculate Synchronous Power of Power Angle Curve?

With EMF of Generator (E_g), Voltage of Infinite Bus (V), Synchronous Reactance (X_s) & Electrical Power Angle (δ) we can find Synchronous Power of Power Angle Curve using the formula - Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle). This formula also uses Cosine, "Modulus Function" function(s).

Can the Synchronous Power of Power Angle Curve be negative?

No, the Synchronous Power of Power Angle Curve, measured in Power cannot be negative.

Which unit is used to measure Synchronous Power of Power Angle Curve?

Synchronous Power of Power Angle Curve is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Synchronous Power of Power Angle Curve can be measured.

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Synchronous Power of Power Angle Curve Formula

Synchronous Power of Power Angle Curve Example

Synchronous Power of Power Angle Curve Solution

Synchronous Power of Power Angle Curve Formula Elements

Other formulas in Power System Stability category

How to Evaluate Synchronous Power of Power Angle Curve?

FAQs on Synchronous Power of Power Angle Curve

Variable Name