Operation behaviour of power transmission lines

Derive the telegrapher’s equations by considering a differential line element.

How are harmonic, position-dependent voltage, and current phasors obtained from the telegrapher’s equations?

What is the general solution of the wave equation in this case? In particular, explain the characteristic impedance and the complex propagation constant.

How is the complete solution of the wave equation for harmonic, position-dependent voltage, and current phasors obtained from the boundary conditions?

Give a general expression for a standing wave and explain the relationships between the propagation constant, propagation velocity, and wavelength.

What are the characteristic impedance and the surge impedance loading? What is their significance for wave propagation, and how can they be interpreted physically?

What properties do the characteristic impedance, propagation constant, and surge impedance loading (SIL) have for a lossless line, and what form do the voltage and current distributions along the line take in this case?

What constitutes the reactive power balance of a transmission line, and which measures can be applied to compensate it?

Sketch the relationship between transmitted active power and reactive power of a line, and describe the different regions of the characteristic curve.

What is meant by under-SIL, over-SIL, and SIL operation of a line? How do overhead lines differ from cable lines in this respect?

Sketch the voltage profile along a long transmission line under super-natural, sub-natural, and natural operation conditions.

What is the Ferranti effect? How can it be calculated, and how can it be mitigated?

Using the power-voltage curve, describe the relationship between the receiving-end voltage and the transmitted active power. What are the implications for power transmission over a line?

State an expression for the active power transmission of an electrically short, lossless transmission line and specify the theoretical and practical operating ranges.

How can the parameters of a Π equivalent circuit of a transmission line be derived from the solutions of the line equations? Which simplifications are commonly used in practice?

Identify the most frequently used transmission line equivalent circuits for different voltage levels and line lengths.

How can the transmitted power be determined if the ABCD matrix of the line and the voltages at the beginning and end are known?

If the apparent power and voltage at the receiving end are given, how can the longitudinal and transverse voltage drops along the line be calculated? Within the HV range, how are changes in voltage magnitude and transmission angle related to transmitted active and reactive power?

Sketch the phasor diagram of a line modelled by a Π equivalent circuit when the voltage and power at the receiving end are known.

Sketch the phasor diagram of a line modelled by a Π equivalent circuit for operation at surge impedance loading, under no-load conditions, and under short-circuit conditions.

On which factors does the thermal load capacity of an overhead line depend, and how can it be calculated in principle? Give typical values for the thermal limiting current density of overhead lines and cables.

Explain the limits of transmission capacity of a line using a diagram of transmitted power versus line length.

What functions do compensation systems fulfil in power system operation? Name and briefly describe the most important types.

Describe the operating principle and typical application range of compensation using shunt capacitors.

Describe the operating principle and typical application range of compensation using shunt reactors.

Describe the operating principle and typical application range of compensation using series capacitors.

How is the degree of compensation defined for shunt and series compensation?

Apart from passive reactances, which other options are available for providing and/or controlling reactive power?