Lossless Power Delivered in Synchronous Machine Calculator

✖Maximum Power is the amount of power that is associated with the electrical power angle.ⓘ Maximum Power [P_max]			+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%

✖Lossless Power Delivered by Synchronous Machine is the power that is converted from electrical to mechanical power without any electrical loss.ⓘ Lossless Power Delivered in Synchronous Machine [P_l]

⎘ Copy

👎

Formula

✖

Lossless Power Delivered in Synchronous Machine

Formula

`"P"_{"l"} = "P"_{"max"}*sin("δ")`

Example

`"707.1068W"="1000W"*sin("45°")`

Calculator

LaTeX

Reset

👍

Download Power System Stability Formulas PDF PDF Image

Lossless Power Delivered in Synchronous Machine Solution

STEP 0: Pre-Calculation Summary

Formula Used

Lossless Power Delivered = Maximum Power*sin(Electrical Power Angle)
P_l = P_max*sin(δ)
This formula uses 1 Functions, 3 Variables

Functions Used

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., sin(Angle)

Variables Used

Lossless Power Delivered - (Measured in Watt) - Lossless Power Delivered by Synchronous Machine is the power that is converted from electrical to mechanical power without any electrical loss.
Maximum Power - (Measured in Watt) - Maximum Power is the amount of power that is associated with the electrical power angle.
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

Maximum Power: 1000 Watt --> 1000 Watt No Conversion Required
Electrical Power Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_l = P_max*sin(δ) --> 1000*sin(0.785398163397301)

Evaluating ... ...

P_l = 707.106781186443

STEP 3: Convert Result to Output's Unit

707.106781186443 Watt --> No Conversion Required

FINAL ANSWER

707.106781186443 ≈ 707.1068 Watt <-- Lossless Power Delivered

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Electrical » Power System » Power System Stability » Lossless Power Delivered in Synchronous Machine

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

Lossless Power Delivered in Synchronous Machine Formula

Lossless Power Delivered = Maximum Power*sin(Electrical Power Angle)
P_l = P_max*sin(δ)

What is Lossless Power in Synchronous Machine?

In the Lossless Synchronous Machine the power delivered from electrical to mechanical unit depends on the sign convention of the electrical power angle.

How to Calculate Lossless Power Delivered in Synchronous Machine?

Lossless Power Delivered in Synchronous Machine calculator uses Lossless Power Delivered = Maximum Power*sin(Electrical Power Angle) to calculate the Lossless Power Delivered, Lossless Power Delivered in Synchronous Machine is defined as the product of maximum power and the sine of electrical power angle. Losses in a power system can occur due to factors such as resistance in transmission lines, transformers, and other components, as well as reactive power losses. Lossless Power Delivered is denoted by P_l symbol.

How to calculate Lossless Power Delivered in Synchronous Machine using this online calculator? To use this online calculator for Lossless Power Delivered in Synchronous Machine, enter Maximum Power (P_max) & Electrical Power Angle (δ) and hit the calculate button. Here is how the Lossless Power Delivered in Synchronous Machine calculation can be explained with given input values -> 707.1068 = 1000*sin(0.785398163397301).

FAQ

What is Lossless Power Delivered in Synchronous Machine?

Lossless Power Delivered in Synchronous Machine is defined as the product of maximum power and the sine of electrical power angle. Losses in a power system can occur due to factors such as resistance in transmission lines, transformers, and other components, as well as reactive power losses and is represented as P_l = P_max*sin(δ) or Lossless Power Delivered = Maximum Power*sin(Electrical Power Angle). Maximum Power is the amount of power that is associated with the 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.

How to calculate Lossless Power Delivered in Synchronous Machine?

Lossless Power Delivered in Synchronous Machine is defined as the product of maximum power and the sine of electrical power angle. Losses in a power system can occur due to factors such as resistance in transmission lines, transformers, and other components, as well as reactive power losses is calculated using Lossless Power Delivered = Maximum Power*sin(Electrical Power Angle). To calculate Lossless Power Delivered in Synchronous Machine, you need Maximum Power (P_max) & Electrical Power Angle (δ). With our tool, you need to enter the respective value for Maximum Power & Electrical Power Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search