Synchronous Power of Power Angle Curve Calculator

✖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.ⓘ EMF of Generator [E_g]			+10% -10%
✖Voltage of Infinite Bus is defined as the constant voltage maintained by this idealized power source under all conditions.ⓘ Voltage of Infinite Bus [V]			+10% -10%
✖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.ⓘ Synchronous Reactance [X_s]			+10% -10%
✖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.ⓘ Electrical Power Angle [δ]			+10% -10%

✖Synchronous Power is defined as the electrical power output of a synchronous generator is influenced by the power angle.ⓘ Synchronous Power of Power Angle Curve [P_syn]

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Formula

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Synchronous Power of Power Angle Curve

Formula

`"P"_{"syn"} = ("modulus"("E"_{"g"})*"modulus"("V"))/"X"_{"s"}*cos("δ")`

Example

`"21.83347W"=("modulus"("160V")*"modulus"("11V"))/"57Ω"*cos("45°")`

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Synchronous Power of Power Angle Curve Solution

STEP 0: Pre-Calculation Summary

Formula Used

Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle)
P_syn = (modulus(E_g)*modulus(V))/X_s*cos(δ)
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
modulus - Modulus of a number is the remainder when that number is divided by another number., modulus

Variables Used

Synchronous Power - (Measured in Watt) - Synchronous Power is defined as the electrical power output of a synchronous generator is influenced by the power angle.
EMF of Generator - (Measured in Volt) - 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.
Voltage of Infinite Bus - (Measured in Volt) - Voltage of Infinite Bus is defined as the constant voltage maintained by this idealized power source under all conditions.
Synchronous Reactance - (Measured in Ohm) - 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.
Electrical Power Angle - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

EMF of Generator: 160 Volt --> 160 Volt No Conversion Required
Voltage of Infinite Bus: 11 Volt --> 11 Volt No Conversion Required
Synchronous Reactance: 57 Ohm --> 57 Ohm No Conversion Required
Electrical Power Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_syn = (modulus(E_g)*modulus(V))/X_s*cos(δ) --> (modulus(160)*modulus(11))/57*cos(0.785398163397301)

Evaluating ... ...

P_syn = 21.8334725419036

STEP 3: Convert Result to Output's Unit

21.8334725419036 Watt --> No Conversion Required

FINAL ANSWER

21.8334725419036 ≈ 21.83347 Watt <-- Synchronous Power

(Calculation completed in 00.004 seconds)

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Credits

Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

Dipanjona Mallick has created this Calculator and 50+ more calculators!

Verified by Aman Dhussawat

GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY (GTBIT), NEW DELHI

Aman Dhussawat has verified this Calculator and 100+ more calculators!

< 20 Power System Stability Calculators

Active Power by Infinite Bus

Go Active Power of Infinite Bus = (Voltage of Infinite Bus)^2/sqrt((Resistance)^2+(Synchronous Reactance)^2)-(Voltage of Infinite Bus)^2/((Resistance)^2+(Synchronous Reactance)^2)

Critical Clearing Angle under Power System Stability

Go Critical Clearing Angle = acos(cos(Maximum Clearing Angle)+((Input Power)/(Maximum Power))*(Maximum Clearing Angle-Initial Power Angle))

Critical Clearing Time under Power System Stability

Go Critical Clearing Time = sqrt((2*Constant of Inertia*(Critical Clearing Angle-Initial Power Angle))/(pi*Frequency*Maximum Power))

Synchronous Power of Power Angle Curve

Go Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle)

Real Power of Generator under Power Angle Curve

Go Real Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*sin(Electrical Power Angle)

Clearing Time

Go Clearing Time = sqrt((2*Constant of Inertia*(Clearing Angle-Initial Power Angle))/(pi*Frequency*Input Power))

Clearing Angle

Go Clearing Angle = (pi*Frequency*Input Power)/(2*Constant of Inertia)*(Clearing Time)^2+Initial Power Angle

Maximum Steady State Power Transfer

Go Maximum Steady State Power Transfer = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance

Output Power of Generator under Power System Stability

Go Output Power of Generator = (EMF of Generator*Terminal Voltage*sin(Power Angle))/Magnetic Reluctance

Time Constant in Power System Stability

Go Time Constant = (2*Constant of Inertia)/(pi*Damping Frequency of Oscillation*Damping Coefficient)

Moment of Inertia of Machine under Power System Stability

Go Moment of Inertia = Rotor Moment of Inertia*(2/Number of Machine Poles)^2*Rotor Speed of Synchronous Machine*10^-6

Inertia Constant of Machine

Go Inertia Constant of Machine = (Three Phase MVA Rating of Machine*Constant of Inertia)/(180*Synchronous Frequency)

Angular Displacement of Machine under Power System Stability

Go Angular Displacement of Machine = Angular Displacement of Rotor-Synchronous Speed*Time of Angular Displacement

Damped Frequency of Oscillation in Power System Stability

Go Damping Frequency of Oscillation = Natural Frequency of Oscillation*sqrt(1-(Oscillation Constant)^2)

Lossless Power Delivered in Synchronous Machine

Go Lossless Power Delivered = Maximum Power*sin(Electrical Power Angle)

Speed of Synchronous Machine

Go Speed of Synchronous Machine = (Number of Machine Poles/2)*Rotor Speed of Synchronous Machine

Kinetic Energy of Rotor

Go Kinetic Energy of Rotor = (1/2)*Rotor Moment of Inertia*Synchronous Speed^2*10^-6

Accelerating Torque of Generator under Power System Stability

Go Accelerating Torque = Mechanical Torque-Electrical Torque

Rotor Acceleration

Go Accelerating Power = Input Power-Electromagnetic Power

Complex Power of Generator under Power Angle Curve

Go Complex Power = Phasor Voltage*Phasor Current

Synchronous Power of Power Angle Curve Formula

Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle)
P_syn = (modulus(E_g)*modulus(V))/X_s*cos(δ)

What is Synchronous Power?

The electrical power output of a synchronous generator is influenced by the power angle. The power angle curve shows how changes in the power angle affect the generator's ability to deliver active power to the grid. The power angle must be within certain limits for the generator to remain in synchronism with the power system.

How to Calculate Synchronous Power of Power Angle Curve?

Synchronous Power of Power Angle Curve calculator uses Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle) to calculate 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 calculate Synchronous Power of Power Angle Curve using this online calculator? To use this online calculator 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. Here is how the Synchronous Power of Power Angle Curve calculation can be explained with given input values -> 21.83347 = (modulus(160)*modulus(11))/57*cos(0.785398163397301).

FAQ

What is Synchronous Power of Power Angle Curve?

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 and is represented as P_syn = (modulus(E_g)*modulus(V))/X_s*cos(δ) or Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle). 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, Voltage of Infinite Bus is defined as the constant voltage maintained by this idealized power source under all conditions, 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 & 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.

How to calculate Synchronous Power of Power Angle Curve?

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 is calculated using Synchronous Power = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance*cos(Electrical Power Angle). To calculate Synchronous Power of Power Angle Curve, you need EMF of Generator (E_g), Voltage of Infinite Bus (V), Synchronous Reactance (X_s) & Electrical Power Angle (δ). With our tool, you need to enter the respective value for EMF of Generator, Voltage of Infinite Bus, Synchronous Reactance & Electrical Power Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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