Power Flow of Series Capacitor of Compensated Line Calculator

✖Sending End Voltage is defined as the voltage at the source or sending end of a transmission line in an electrical power system.ⓘ Sending End Voltage [V_s]			+10% -10%
✖Receiving End Voltage in Compensated Line is defined as the voltage magnitude and phase at the point where the electrical power is delivered to the load or consumer.ⓘ Receiving End Voltage in Compensated Line [V_R]			+10% -10%
✖Natural Impedance in Line is defined as the intrinsic impedance of the line when it is not loaded or terminated by external devices. It is also known as the characteristic impedance of the line.ⓘ Natural Impedance in Line [Z_n]			+10% -10%
✖Electrical Length of Line is defined as the effective length of a transmission line as seen by the device.ⓘ Electrical Length of Line [θ]			+10% -10%
✖Series Reactance in Capacitor is defined as the impedance that the capacitor introduces when connected in series with a transmission line or a circuit.ⓘ Series Reactance in Capacitor [X_c]			+10% -10%
✖Operating Angle in Compensated Line is the angle between the sending end voltage and receiving end voltage.ⓘ Operating Angle in Compensated Line [δ]			+10% -10%

✖Power Flow in Compensated Line is defined as the direction and magnitude of active and reactive power along the line.ⓘ Power Flow of Series Capacitor of Compensated Line [P]

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Formula

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Power Flow of Series Capacitor of Compensated Line

Formula

`"P" = ("V"_{"s"}*"V"_{"R"})/(2*"Z"_{"n"}*sin("θ"/2)-"X"_{"c"})*sin("δ")`

Example

`"1685.486W"=("54V"*"27V")/(2*"6Ω"*sin("20°"/2)-"1.32Ω")*sin("62°")`

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Power Flow of Series Capacitor of Compensated Line Solution

STEP 0: Pre-Calculation Summary

Formula Used

Power Flow in Compensated Line = (Sending End Voltage*Receiving End Voltage in Compensated Line)/(2*Natural Impedance in Line*sin(Electrical Length of Line/2)-Series Reactance in Capacitor)*sin(Operating Angle in Compensated Line)
P = (V_s*V_R)/(2*Z_n*sin(θ/2)-X_c)*sin(δ)
This formula uses 1 Functions, 7 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

Power Flow in Compensated Line - (Measured in Watt) - Power Flow in Compensated Line is defined as the direction and magnitude of active and reactive power along the line.
Sending End Voltage - (Measured in Volt) - Sending End Voltage is defined as the voltage at the source or sending end of a transmission line in an electrical power system.
Receiving End Voltage in Compensated Line - (Measured in Volt) - Receiving End Voltage in Compensated Line is defined as the voltage magnitude and phase at the point where the electrical power is delivered to the load or consumer.
Natural Impedance in Line - (Measured in Ohm) - Natural Impedance in Line is defined as the intrinsic impedance of the line when it is not loaded or terminated by external devices. It is also known as the characteristic impedance of the line.
Electrical Length of Line - (Measured in Radian) - Electrical Length of Line is defined as the effective length of a transmission line as seen by the device.
Series Reactance in Capacitor - (Measured in Ohm) - Series Reactance in Capacitor is defined as the impedance that the capacitor introduces when connected in series with a transmission line or a circuit.
Operating Angle in Compensated Line - (Measured in Radian) - Operating Angle in Compensated Line is the angle between the sending end voltage and receiving end voltage.

STEP 1: Convert Input(s) to Base Unit

Sending End Voltage: 54 Volt --> 54 Volt No Conversion Required
Receiving End Voltage in Compensated Line: 27 Volt --> 27 Volt No Conversion Required
Natural Impedance in Line: 6 Ohm --> 6 Ohm No Conversion Required
Electrical Length of Line: 20 Degree --> 0.3490658503988 Radian (Check conversion here)
Series Reactance in Capacitor: 1.32 Ohm --> 1.32 Ohm No Conversion Required
Operating Angle in Compensated Line: 62 Degree --> 1.08210413623628 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = (V_s*V_R)/(2*Z_n*sin(θ/2)-X_c)*sin(δ) --> (54*27)/(2*6*sin(0.3490658503988/2)-1.32)*sin(1.08210413623628)

Evaluating ... ...

P = 1685.48631657275

STEP 3: Convert Result to Output's Unit

1685.48631657275 Watt --> No Conversion Required

FINAL ANSWER

1685.48631657275 ≈ 1685.486 Watt <-- Power Flow in Compensated Line

(Calculation completed in 00.020 seconds)

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Home » Engineering » Electrical » Power System » FACTS Devices » Static Synchronous Series Compensator(SSSC) » Power Flow of Series Capacitor of Compensated Line

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< 7 Static Synchronous Series Compensator(SSSC) Calculators

Power Flow of Series Capacitor of Compensated Line

Go Power Flow in Compensated Line = (Sending End Voltage*Receiving End Voltage in Compensated Line)/(2*Natural Impedance in Line*sin(Electrical Length of Line/2)-Series Reactance in Capacitor)*sin(Operating Angle in Compensated Line)

Degree of Series Compensation

Go Degree in Series Compensation = Series Reactance in Capacitor/(Natural Impedance in Line*Electrical Length of Line)

Resonance Frequency for Shunt Capacitor Compensation

Go Resonance Frequency of Shunt Capacitor = Operating System Frequency*sqrt(1/(1-Degree in Shunt Compensation))

Electrical Resonance Frequency for Series Capacitor Compensation

Go Resonance Frequency of Series Capacitor = Operating System Frequency*sqrt(1-Degree in Series Compensation)

Power Flow in SSSC

Go Power Flow in SSSC = Maximum Power in UPFC+(Series Voltage of UPFC*Shunt Current of UPFC)/4

Series Reactance of Capacitors

Go Series Reactance in Capacitor = Line Reactance*(1-Degree in Series Compensation)

Rating of SSSC

Go SSSC Rating = Maximum Current in SSSC*Maximum Inductive Reactive Voltage

Power Flow of Series Capacitor of Compensated Line Formula

What do you mean by Power Flow of Series Capacitor of Compensated Line?

Power flow in a compensated transmission line refers to the transfer of electrical power from the sending end to the receiving end of the line, accounting for the effects of compensation elements such as series or shunt devices. The goal of compensation is often to enhance the power transfer capability and control voltage profiles in the transmission line.

How to Calculate Power Flow of Series Capacitor of Compensated Line?

Power Flow of Series Capacitor of Compensated Line calculator uses Power Flow in Compensated Line = (Sending End Voltage*Receiving End Voltage in Compensated Line)/(2*Natural Impedance in Line*sin(Electrical Length of Line/2)-Series Reactance in Capacitor)*sin(Operating Angle in Compensated Line) to calculate the Power Flow in Compensated Line, Power Flow of Series Capacitor of Compensated Line is defined as the he transfer of electrical power from the sending end to the receiving end of the line. Power Flow in Compensated Line is denoted by P symbol.

How to calculate Power Flow of Series Capacitor of Compensated Line using this online calculator? To use this online calculator for Power Flow of Series Capacitor of Compensated Line, enter Sending End Voltage (V_s), Receiving End Voltage in Compensated Line (V_R), Natural Impedance in Line (Z_n), Electrical Length of Line (θ), Series Reactance in Capacitor (X_c) & Operating Angle in Compensated Line (δ) and hit the calculate button. Here is how the Power Flow of Series Capacitor of Compensated Line calculation can be explained with given input values -> 1685.486 = (54*27)/(2*6*sin(0.3490658503988/2)-1.32)*sin(1.08210413623628).

FAQ

What is Power Flow of Series Capacitor of Compensated Line?

Power Flow of Series Capacitor of Compensated Line is defined as the he transfer of electrical power from the sending end to the receiving end of the line and is represented as P = (V_s*V_R)/(2*Z_n*sin(θ/2)-X_c)*sin(δ) or Power Flow in Compensated Line = (Sending End Voltage*Receiving End Voltage in Compensated Line)/(2*Natural Impedance in Line*sin(Electrical Length of Line/2)-Series Reactance in Capacitor)*sin(Operating Angle in Compensated Line). Sending End Voltage is defined as the voltage at the source or sending end of a transmission line in an electrical power system, Receiving End Voltage in Compensated Line is defined as the voltage magnitude and phase at the point where the electrical power is delivered to the load or consumer, Natural Impedance in Line is defined as the intrinsic impedance of the line when it is not loaded or terminated by external devices. It is also known as the characteristic impedance of the line, Electrical Length of Line is defined as the effective length of a transmission line as seen by the device, Series Reactance in Capacitor is defined as the impedance that the capacitor introduces when connected in series with a transmission line or a circuit & Operating Angle in Compensated Line is the angle between the sending end voltage and receiving end voltage.

How to calculate Power Flow of Series Capacitor of Compensated Line?

Power Flow of Series Capacitor of Compensated Line is defined as the he transfer of electrical power from the sending end to the receiving end of the line is calculated using Power Flow in Compensated Line = (Sending End Voltage*Receiving End Voltage in Compensated Line)/(2*Natural Impedance in Line*sin(Electrical Length of Line/2)-Series Reactance in Capacitor)*sin(Operating Angle in Compensated Line). To calculate Power Flow of Series Capacitor of Compensated Line, you need Sending End Voltage (V_s), Receiving End Voltage in Compensated Line (V_R), Natural Impedance in Line (Z_n), Electrical Length of Line (θ), Series Reactance in Capacitor (X_c) & Operating Angle in Compensated Line (δ). With our tool, you need to enter the respective value for Sending End Voltage, Receiving End Voltage in Compensated Line, Natural Impedance in Line, Electrical Length of Line, Series Reactance in Capacitor & Operating Angle in Compensated Line 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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