1. Introduction
2.Synchronous machines
3.Armature reaction
4.Steady state theory
5.Salient pole rotor
6.Transient analysis
7. Asymmetry
8.Machine reactances
9.Negative sequence reactance
10. Zero sequence reactance
11. Direct and quadrature axis values
12. Effect of saturation on machine reactances
13. Transformers
14. Transformer positive sequence equivalent circuits
15. Transformer zero sequence equivalent circuits
16. Auto-transformers
17. Transformer impedances
18. Overhead lines and cables
19. Calculation of series impedance
20. Calculation of shunt impedance
21. Overhead line circuits with or without earth wires
22. OHL equivalent circuits
23. Cable circuits
24. Overhead line and cable data
25. References
Introduction
Knowledge of the behaviour of the principal electrical system plant items under normal and fault conditions is a prerequisite
for the proper application of protection. This chapter summarises basic synchronous machine, transformer and transmission line theory and gives equivalent circuits and parameters so that a fault study can be successfully completed before the selection and application of the protection systems
described in later chapters. Only what might be referred to as ‘traditional’ synchronous machine theory is covered, as
that is all that calculations for fault level studies generally require. Readers interested in more advanced models of synchronous machines are referred to the numerous papers on the subject, of which [Ref A4.1: Physical significance of sub-subtransient quantities in dynamic behaviour of synchronous machines] is a good starting point.
Power system plant may be divided into two broad groups
- static and rotating.
The modelling of static plant for fault level calculations provides few difficulties, as plant parameters generally do not change during the period of interest following fault inception. The problem in modelling rotating plant is that the parameters change depending on the response to a change in power system conditions.
Synchronous machines
There are two main types of synchronous machine: cylindrical rotor and salient pole. In general, the former is confined to 2 and 4 pole turbine generators, while salient pole types are built with 4 poles upwards and include most classes of duty.
Both classes of machine are similar in so far that each has a stator carrying a three-phase winding distributed over its inner periphery. Within the stator bore is carried the rotor which is magnetised by a winding carrying d.c. current.
The essential difference between the two classes of machine lies in the rotor construction. The cylindrical rotor type has a uniformly cylindrical rotor that carries its excitation winding distributed over a number of slots around its periphery. This construction is unsuited to multi-polar machines but it is very sound mechanically. Hence it is particularly well adapted for the highest speed electrical machines and is universally employed for 2 pole units, plus some 4 pole units.
The salient pole type has poles that are physically separate, each carrying a concentrated excitation winding. This type of construction is in many ways complementary to that of the cylindrical rotor and is employed in machines having 4 poles or more. Except in special cases its use is exclusive in machines having more than 6 poles. Figure A4.1 illustrates a typical large cylindrical rotor generator installed in a power plant.
Two and four pole generators are most often used in applications where steam or gas turbines are used as the driver. This is because the steam turbine tends to be suited to high rotational speeds. Four pole steam turbine generators are most often found in nuclear power stations as the relative wetness of the steam makes the high rotational speed of a two-pole design unsuitable. Most generators with gas turbine drivers are four pole machines to obtain enhanced mechanical strength in the rotor, since a gearbox is often used to couple the power turbine to the generator, the choice of synchronous
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