Power System Analysis (EELE 4351)

Assad Abu-Jasser, PhD Electric Power Engineering The Islamic University of Gaza ajasser@iugaza.edu.ps http://site.iugaza.edu.ps/ajasser

Current and Voltage Relations on a Transmission Line Chapter 6 Current and Voltage Relations on a Transmission Line

Transmission Lines Introduction

Representation of Lines

The Short Transmission Line length  50 mi (80 km)

Example 6.1 A 300-MVA 20-kV three-phase generator has a subtransient reactance of 20%. The generator supplies a number of synchronous motors over a 64-km transmission line having transformers at both ends as shown on the one-line diagram. The motors, all rated 13.2 kV, are represented by just two equivalent motors. Rated inputs to the motors are 200 MVA and 100 MVA for M1 and M2 respectively. For both motors Xd=20%. The three-phase transformer T1 is rated 350 MVA, 230/20 kV with leakage reactance of 10%. Transformer T2 is composed of three single-phase transformers, each rated 127/13.2 kV, 100 MVA with leakage reactance of 10%. Series reactance of the transmission line is 0.5 Ω/km. Draw the reactance diagram with all reactances marked in per unit. Select the generator rating as base in the generator circuit.

Example 6.2 If the motor M1 and M2 have inputs of 120 and 60 MW, respectively, at 13.2 kV, and both operate at unity power factor, find the voltage at the terminals of the generator and the voltage regulation of the line.

The Medium Transmission Line 50 mi (80 km) length150 mi (240 km)

The Long Transmission Line 150 mi (240 km) length

The Long Transmission Line Hyperbolic Form of the Equations

Example 6.3 A single-circuit 60-Hz transmission line is 370 km (230 mi) long. The conductors are Rook with flat horizontal spacing and 7.25 m (23.8ft) between conductors. The load on the line is 125 MW at 215 kV with 100% power factor. Find the voltage, current and power at the sending-end and the voltage regulation of the line. Also, determine the wavelength and velocity of propagation of the line.

Example 6.4 A single-circuit 60-Hz transmission line is 370 km (230 mi) long. The conductors are Rook with flat horizontal spacing and 7.25 m (23.8ft) between conductors. The load on the line is 125 MW at 215 kV with 100% power factor. Find the voltage, current and power at the sending-end and the voltage regulation of the line. Also, determine the wavelength and velocity of propagation of the line. Use per-Unit Quantities.

The Equivalent Circuit of a Long Line

Example 6.5 Find the equivalent-π circuit for the transmission line described in Example 6.3 and compare it with the nominal-π circuit.

Power Flow Through Transmission Line

Reactive Power Compensation Series and Shunt Compensation

Reactive Power Compensation Series Compensation

Reactive Power Compensation Shunt Compensation

Example 6.6 Find the ABCD constants of the transmission line of Example 6.3 when uncompensated and for a series compensation of 70%.

Example 6.7 Find the voltage regulation of the line of Example 6.3 when a shunt inductor is connected at the receiving-end of the line during no-load conditions if the reactor compensates for 70% of the total shunt admittance of the line.

End Of Chapter Six