Time Constant in Power System Stability Calculator

✖Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating.ⓘ Constant of Inertia [H]			+10% -10%
✖Damping Frequency of Oscillation is defined as the frequency in which one oscillation occurs in a time period.ⓘ Damping Frequency of Oscillation [ω_df]			+10% -10%
✖Damping Coefficient is defined as the measure of how quickly it returns to rest as the frictional force dissipates its oscillation energy.ⓘ Damping Coefficient [D]			+10% -10%

✖Time Constant is defined as the time taken by the capacitor to be charged to about 63.2% of its full value through a resistor connected to it in series.ⓘ Time Constant in Power System Stability [T]

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Formula

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Time Constant in Power System Stability

Formula

`"T" = (2*"H")/(pi*"ω"_{"df"}*"D")`

Example

`"0.110964s"=(2*"39kg·m²")/(pi*"8.95Hz"*"25Ns/m")`

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Time Constant in Power System Stability Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Constant = (2*Constant of Inertia)/(pi*Damping Frequency of Oscillation*Damping Coefficient)
T = (2*H)/(pi*ω_df*D)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Time Constant - (Measured in Second) - Time Constant is defined as the time taken by the capacitor to be charged to about 63.2% of its full value through a resistor connected to it in series.
Constant of Inertia - (Measured in Kilogram Square Meter) - Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating.
Damping Frequency of Oscillation - (Measured in Hertz) - Damping Frequency of Oscillation is defined as the frequency in which one oscillation occurs in a time period.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is defined as the measure of how quickly it returns to rest as the frictional force dissipates its oscillation energy.

STEP 1: Convert Input(s) to Base Unit

Constant of Inertia: 39 Kilogram Square Meter --> 39 Kilogram Square Meter No Conversion Required
Damping Frequency of Oscillation: 8.95 Hertz --> 8.95 Hertz No Conversion Required
Damping Coefficient: 25 Newton Second per Meter --> 25 Newton Second per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = (2*H)/(pi*ω_df*D) --> (2*39)/(pi*8.95*25)

Evaluating ... ...

T = 0.110963893284182

STEP 3: Convert Result to Output's Unit

0.110963893284182 Second --> No Conversion Required

FINAL ANSWER

0.110963893284182 ≈ 0.110964 Second <-- Time Constant

(Calculation completed in 00.004 seconds)

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Created by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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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

Time Constant in Power System Stability Formula

Time Constant = (2*Constant of Inertia)/(pi*Damping Frequency of Oscillation*Damping Coefficient)
T = (2*H)/(pi*ω_df*D)

What is Time Constant?

Time Constant is defined as the amount of time required by any sensor to sense. This is measured in terms of frequency, Damping Coefficient and inertia constant of the system.

How to Calculate Time Constant in Power System Stability?

Time Constant in Power System Stability calculator uses Time Constant = (2*Constant of Inertia)/(pi*Damping Frequency of Oscillation*Damping Coefficient) to calculate the Time Constant, The Time Constant in Power System Stability formula is defined as time taken by the capacitor to be charged to about 63.2% of its full value through a resistor connected to it in series. Time Constant is denoted by T symbol.

How to calculate Time Constant in Power System Stability using this online calculator? To use this online calculator for Time Constant in Power System Stability, enter Constant of Inertia (H), Damping Frequency of Oscillation (ω_df) & Damping Coefficient (D) and hit the calculate button. Here is how the Time Constant in Power System Stability calculation can be explained with given input values -> 0.110964 = (2*39)/(pi*8.95*25).

FAQ

What is Time Constant in Power System Stability?

The Time Constant in Power System Stability formula is defined as time taken by the capacitor to be charged to about 63.2% of its full value through a resistor connected to it in series and is represented as T = (2*H)/(pi*ω_df*D) or Time Constant = (2*Constant of Inertia)/(pi*Damping Frequency of Oscillation*Damping Coefficient). Constant of Inertia is defined as the ratio of kinetic energy stored at the synchronous speed to the generator kVA or MVA rating, Damping Frequency of Oscillation is defined as the frequency in which one oscillation occurs in a time period & Damping Coefficient is defined as the measure of how quickly it returns to rest as the frictional force dissipates its oscillation energy.

How to calculate Time Constant in Power System Stability?

The Time Constant in Power System Stability formula is defined as time taken by the capacitor to be charged to about 63.2% of its full value through a resistor connected to it in series is calculated using Time Constant = (2*Constant of Inertia)/(pi*Damping Frequency of Oscillation*Damping Coefficient). To calculate Time Constant in Power System Stability, you need Constant of Inertia (H), Damping Frequency of Oscillation (ω_df) & Damping Coefficient (D). With our tool, you need to enter the respective value for Constant of Inertia, Damping Frequency of Oscillation & Damping Coefficient 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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