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Real Power of Generator under Power Angle Curve Formula

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Real Power is defined as the actual power consumed by a circuit or the actual power delivered by a source, such as a generator. Check FAQs

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

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

Real Power of Generator under Power Angle Curve Example

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Here is how the Real Power of Generator under Power Angle Curve equation looks like with Values.

Here is how the Real Power of Generator under Power Angle Curve equation looks like with Units.

Here is how the Real Power of Generator under Power Angle Curve equation looks like.

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

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

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

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Real Power of Generator under Power Angle Curve Solution

Follow our step by step solution on how to calculate Real Power of Generator under Power Angle Curve?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

P e = 21.8334725418972W

LAST Step Rounding Answer

∴

P e = 21.8335W

Real Power of Generator under Power Angle Curve Formula Elements

Variables

Functions

Real Power

Real Power is defined as the actual power consumed by a circuit or the actual power delivered by a source, such as a generator.

Symbol: P_e

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Real 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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(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 Real Power of Generator under Power Angle Curve?

Real Power of Generator under Power Angle Curve evaluator uses Real Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*sin(Electrical Power Angle) to evaluate the Real Power, The Real Power of Generator under Power Angle Curve formula is defined as the actual electrical energy that is available for consumption by loads. It is the power that performs useful work, such as turning motors, producing light, or operating electronic devices. Real Power is denoted by P_e symbol.

How to evaluate Real Power of Generator under Power Angle Curve using this online evaluator? To use this online evaluator for Real Power of Generator under 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 Real Power of Generator under Power Angle Curve

What is the formula to find Real Power of Generator under Power Angle Curve?

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

How to calculate Real Power of Generator under 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 Real Power of Generator under Power Angle Curve using the formula - Real Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*sin(Electrical Power Angle). This formula also uses Sine (sin), Modulus (modulus) function(s).

Can the Real Power of Generator under Power Angle Curve be negative?

No, the Real Power of Generator under Power Angle Curve, measured in Power cannot be negative.

Which unit is used to measure Real Power of Generator under Power Angle Curve?

Real Power of Generator under 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 Real Power of Generator under Power Angle Curve can be measured.

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Real Power of Generator under Power Angle Curve Formula

Real Power of Generator under Power Angle Curve Example

Real Power of Generator under Power Angle Curve Solution

Real Power of Generator under Power Angle Curve Formula Elements

Other formulas in Power System Stability category

How to Evaluate Real Power of Generator under Power Angle Curve?

FAQs on Real Power of Generator under Power Angle Curve

Variable Name