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A 3-phase, 50 Hz, 20 km long overhead line supplies 500 kW at 22kV,0.9 p.f. lagging. The line resistance is 5.5Ω per phase and line inductance is 10mH per phase. Calculate the Reactance of the Line, Current flowing through th transmission line, Sending end voltage, Voltage regulation and Efficiency of transmission.

Inductive Reactance
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User DaVince
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Final answer:

The inductive reactance of a transmission line is found using the formula X_L = 2πfL. The current through the line is calculated from the power equation, and sending end voltage is determined by adding the voltage drop across the line to the receiving end voltage. Voltage regulation and efficiency are calculated using standard formulas.

Step-by-step explanation:

To calculate the various parameters of a transmission line, we utilize the given data:

  • Frequency (f) = 50 Hz
  • Power (P) = 500 kW
  • Line voltage (Vl) = 22 kV
  • Power factor (pf) = 0.9 lagging
  • Line resistance (R) = 5.5 Ω per phase
  • Line inductance (L) = 10 mH per phase

Inductive Reactance

The inductive reactance (XL) of the line is calculated using the formula XL = 2πfL.

Current Through the Line

The current flowing through the transmission line (I) using the formula P = √3 * Vl * I * pf.

Sending End Voltage

To find the sending end voltage (Vs), we use the line voltage, current, resistance, and reactance to calculate the voltage drop across the line and then add it to the receiving end voltage.

Voltage Regulation

Voltage regulation is calculated as the difference between no-load and full-load voltages, divided by the full-load voltage, expressed as a percentage.

Efficiency

The efficiency of the transmission line is the ratio of the output power to the input power, generally expressed as a percentage.

User Stena
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