Maximum Steady State Power Transfer 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%

✖Maximum Steady State Power Transfer is the maximum amount of electrical power that can be transferred through the transmission network without causing the system to lose stability.ⓘ Maximum Steady State Power Transfer [P_e,max]

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Formula

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Maximum Steady State Power Transfer

Formula

`"P"_{"e,max"} = ("modulus"("E"_{"g"})*"modulus"("V"))/"X"_{"s"}`

Example

`"30.87719V"=("modulus"("160V")*"modulus"("11V"))/"57Ω"`

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Maximum Steady State Power Transfer Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Steady State Power Transfer = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance
P_e,max = (modulus(E_g)*modulus(V))/X_s
This formula uses 1 Functions, 4 Variables

Functions Used

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

Variables Used

Maximum Steady State Power Transfer - (Measured in Volt) - Maximum Steady State Power Transfer is the maximum amount of electrical power that can be transferred through the transmission network without causing the system to lose stability.
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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_e,max = (modulus(E_g)*modulus(V))/X_s --> (modulus(160)*modulus(11))/57

Evaluating ... ...

P_e,max = 30.8771929824561

STEP 3: Convert Result to Output's Unit

30.8771929824561 Volt --> No Conversion Required

FINAL ANSWER

30.8771929824561 ≈ 30.87719 Volt <-- Maximum Steady State Power Transfer

(Calculation completed in 00.020 seconds)

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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Verified by Aman Dhussawat

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

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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

Maximum Steady State Power Transfer Formula

Maximum Steady State Power Transfer = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance
P_e,max = (modulus(E_g)*modulus(V))/X_s

What is Maximum Power Transfer in Steady State?

In Steady State the maximum power transfer is defined as the maximum power transfer capability under stable operating conditions without reaching a loss of synchronism or instability. It represents the upper bound on the power that can be transmitted through the network while maintaining stable and synchronized operation of the generators. In power system steady state stability is defined as ability of the power system to maintain synchronous operation under normal and steady-state operating conditions.

How to Calculate Maximum Steady State Power Transfer?

Maximum Steady State Power Transfer calculator uses Maximum Steady State Power Transfer = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance to calculate the Maximum Steady State Power Transfer, The Maximum Steady State Power Transfer formula is defined as the maximum power transfer capability under stable operating conditions without reaching a loss of synchronism or instability. Maximum Steady State Power Transfer is denoted by P_e,max symbol.

How to calculate Maximum Steady State Power Transfer using this online calculator? To use this online calculator for Maximum Steady State Power Transfer, enter EMF of Generator (E_g), Voltage of Infinite Bus (V) & Synchronous Reactance (X_s) and hit the calculate button. Here is how the Maximum Steady State Power Transfer calculation can be explained with given input values -> 30.87719 = (modulus(160)*modulus(11))/57.

FAQ

What is Maximum Steady State Power Transfer?

The Maximum Steady State Power Transfer formula is defined as the maximum power transfer capability under stable operating conditions without reaching a loss of synchronism or instability and is represented as P_e,max = (modulus(E_g)*modulus(V))/X_s or Maximum Steady State Power Transfer = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance. 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.

How to calculate Maximum Steady State Power Transfer?

The Maximum Steady State Power Transfer formula is defined as the maximum power transfer capability under stable operating conditions without reaching a loss of synchronism or instability is calculated using Maximum Steady State Power Transfer = (modulus(EMF of Generator)*modulus(Voltage of Infinite Bus))/Synchronous Reactance. To calculate Maximum Steady State Power Transfer, you need EMF of Generator (E_g), Voltage of Infinite Bus (V) & Synchronous Reactance (X_s). With our tool, you need to enter the respective value for EMF of Generator, Voltage of Infinite Bus & 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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