08-10-2012, 02:50 PM
Short-circuit Currents
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Introduction
Objectives
This book deals with the calculation of short-circuit currents in two- and three-phase
a.c. systems as well as in d.c. systems, installed as auxiliary installations in power
plants and substations. It is not the objective of this book to repeat definitions and
rules of norms and standards, but to explain the procedure for calculating short-circuit
currents and their effects on installations and equipment. In some cases repetition
of equations, tables and diagrams from norms and standards however are deemed
necessary for easy understanding. It should be emphasised in this respect that the
presentation within this book is mainly concentrated on installations and equipment
in high voltage systems, i.e., voltage levels up to 500 kV. Special considerations have
to be taken in the case of long transmission lines and in power systems with nominal
voltages above 500 kV. The calculation of short-circuit currents and of their effects
are based on the procedures and rules defined in the IEC documents 61660, 60909,
60865 and 60781 as outlined in Table 1.1.
Importance of short-circuit currents
Electrical power systems have to be planned, projected, constructed, commissioned
and operated in such a way to enable a safe, reliable and economic supply of the
load. The knowledge of the loading of the equipment at the time of commissioning
and as foreseeable in the future is necessary for the design and determination
of the rating of the individual equipment and of the power system as a whole.
Faults, i.e., short-circuits in the power system cannot be avoided despite careful
planning and design, good maintenance and thorough operation of the system. This
implies influences from outside the system, such as short-circuits following lightning
strokes into phase-conductors of overhead lines and damages of cables due to
earth construction works as well as internal faults, e.g., due to ageing of insulation materials. Short-circuit currents therefore have an important influence on the design
and operation of equipment and power systems.
Maximal and minimal short-circuit currents
Depending on the task of engineering studies, the maximal or minimal short-circuit
current has to be calculated. The maximal short-circuit current is the main design
criteria for the rating of equipment to withstand the effects of short-circuit currents,
i.e., thermal and electromagnetic effects. The minimal short-circuit current is needed
for the design of protection systems and the minimal setting of protection relays.
The short-circuit current itself depends on various parameters, such as voltage level,
actual operating voltage, impedance of the system between any generation unit and
the short-circuit location, impedance at the short-circuit location itself, the number
of generation units in the system, the temperature of the equipment influencing the
resistances and other parameters. The determination of the maximal and the minimal
short-circuit current therefore is not as simple as might be seen at this stage [36]. It
requires detailed knowledge of the system operation, i.e., which cables, overheadlines,
transformers, generators, machines and reactors are in operation and which are
switched-off. The assessment of the results of any calculation of short-circuit currents
must take into account these restrictions in order to ensure that the results are on the
safe side, i.e., that the safety margin of the calculated maximal short-circuit current is
large enough without resulting in an uneconomic high rating of the equipment. The
same applies to the minimal short-circuit current for which the safety margin must
be assessed in such a way as to distinguish between the highest operating current and
any short-circuit current, which has to be switched-off.
Norms and standards
Technical standards are harmonised on international basis. The international
organisation to coordinate the works and strategies is the ISO(International Standards
Organisation), whereas IEC (International Electrotechnical Commission) is responsible
for the electrotechnical standardisation. The national standard organisations
such as CENELEC in Europe, BSI in the United Kingdom, DKE in Germany, ANSI
in the United States, JSI in Japan as well as national electrotechnical organisations
such as IEE, VDE, IEEE, JES etc. are working in the working groups of IEC to
include their sight and knowledge on technical items in the international standards
and documents. On national basis, standards are adopted to the widest extent to
the internationally agreed standards and documents. In some cases additions to the
international standards are included in the national standards, however their status is
‘for information only’.
Theoretical background
General
A detailed deduction of the mathematical procedure is not given within the context
of this book, but only the final equations are quoted. For further reading, reference is
made to [1], [13]. In general, equipment in power systems is represented by equivalent
circuits, which are designed for the individual tasks of power system analysis. For the
calculation of no-load current and the no-load reactive power of a transformer, the
no-load equivalent circuit is sufficient. Regarding the calculation of short-circuits,
voltage drops and load characteristic a different equivalent circuit is required. The
individual components of the equivalent circuits are resistance, inductive and capacitive
reactance (reactor and capacitor), voltage source and ideal transformer. Voltage
and currents of the individual components and of the equivalent circuit are linked by
Ohm’s law.
System of symmetrical components
Transformation matrix
The relationships between voltages and currents of a three-phase system can be represented
by a matrix equation, e.g., with the aid of the impedance or admittance matrix.
The equivalent circuits created by electrical equipment, such as lines, cables, transformers
and machines, in this case have couplings in the three-phase system which
are of an inductive, capacitive and galvanic type. This can be explained by using
any short element of an overhead line in accordance with Figure 2.4 as an example,
see also [1], [7].