Active Power by Infinite Bus Calculator

✖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%
✖Resistance of infinite bus is a parameter used in mathematical models to account for voltage drops and losses in the transmission network.ⓘ Resistance [R]			+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%

✖Active Power of Infinite Bus is considered to be idealized and remains constant regardless of the amount of power injected or withdrawn from the bus.ⓘ Active Power by Infinite Bus [P_inf]

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Formula

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Active Power by Infinite Bus

Formula

`"P"_{"inf"} = ("V")^2/sqrt(("R")^2+("X"_{"s"})^2)-("V")^2/(("R")^2+("X"_{"s"})^2)`

Example

`"2.084176W"=("11V")^2/sqrt(("2.1Ω")^2+("57Ω")^2)-("11V")^2/(("2.1Ω")^2+("57Ω")^2)`

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Active Power by Infinite Bus Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
P_inf = (V)^2/sqrt((R)^2+(X_s)^2)-(V)^2/((R)^2+(X_s)^2)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Active Power of Infinite Bus - (Measured in Watt) - Active Power of Infinite Bus is considered to be idealized and remains constant regardless of the amount of power injected or withdrawn from the bus.
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.
Resistance - (Measured in Ohm) - Resistance of infinite bus is a parameter used in mathematical models to account for voltage drops and losses in the transmission network.
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.

STEP 1: Convert Input(s) to Base Unit

Voltage of Infinite Bus: 11 Volt --> 11 Volt No Conversion Required
Resistance: 2.1 Ohm --> 2.1 Ohm No Conversion Required
Synchronous Reactance: 57 Ohm --> 57 Ohm No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_inf = (V)^2/sqrt((R)^2+(X_s)^2)-(V)^2/((R)^2+(X_s)^2) --> (11)^2/sqrt((2.1)^2+(57)^2)-(11)^2/((2.1)^2+(57)^2)

Evaluating ... ...

P_inf = 2.08417604980442

STEP 3: Convert Result to Output's Unit

2.08417604980442 Watt --> No Conversion Required

FINAL ANSWER

2.08417604980442 ≈ 2.084176 Watt <-- Active Power of Infinite Bus

(Calculation completed in 00.004 seconds)

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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< 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

Active Power by Infinite Bus Formula

What is Active Power by Infinite Bus?

Active Power of an Infinite Bus does not change with variations in load or generation elsewhere in the power system. The active power of the infinite bus is considered to be idealized and remains constant regardless of the amount of power injected or withdrawn from the bus. The infinite bus is often used as a reference or a source/sink of power that maintains a stable voltage.

How to Calculate Active Power by Infinite Bus?

Active Power by Infinite Bus calculator uses 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) to calculate the Active Power of Infinite Bus, The Active Power by Infinite Bus formula is defined as constant amount of power injected or withdrawn from an infinite bus. This active power is produced when more mechanical power is produced by the turbine of the generator. This is used to define the ratio of square of the voltage and square of the sum of the resistances and reactance. Active Power of Infinite Bus is denoted by P_inf symbol.

How to calculate Active Power by Infinite Bus using this online calculator? To use this online calculator for Active Power by Infinite Bus, enter Voltage of Infinite Bus (V), Resistance (R) & Synchronous Reactance (X_s) and hit the calculate button. Here is how the Active Power by Infinite Bus calculation can be explained with given input values -> 2.084305 = (11)^2/sqrt((2.1)^2+(57)^2)-(11)^2/((2.1)^2+(57)^2).

FAQ

What is Active Power by Infinite Bus?

The Active Power by Infinite Bus formula is defined as constant amount of power injected or withdrawn from an infinite bus. This active power is produced when more mechanical power is produced by the turbine of the generator. This is used to define the ratio of square of the voltage and square of the sum of the resistances and reactance and is represented as P_inf = (V)^2/sqrt((R)^2+(X_s)^2)-(V)^2/((R)^2+(X_s)^2) or 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). Voltage of Infinite Bus is defined as the constant voltage maintained by this idealized power source under all conditions, Resistance of infinite bus is a parameter used in mathematical models to account for voltage drops and losses in the transmission network & 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.

How to calculate Active Power by Infinite Bus?

The Active Power by Infinite Bus formula is defined as constant amount of power injected or withdrawn from an infinite bus. This active power is produced when more mechanical power is produced by the turbine of the generator. This is used to define the ratio of square of the voltage and square of the sum of the resistances and reactance is calculated using 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). To calculate Active Power by Infinite Bus, you need Voltage of Infinite Bus (V), Resistance (R) & Synchronous Reactance (X_s). With our tool, you need to enter the respective value for Voltage of Infinite Bus, Resistance & Synchronous Reactance 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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