A detailed deduction of the mathematical procedure is not given within the context of this book, but only the final equations are quoted. 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 capaci tive 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.

In this chapter, an outline of different types of short-circuits in three-phase a.c. systems is provided such as three-phase short-circuit,double-phase short-circuit without earth/ground connection, double-phase short-circuit with earth/ground connection and line-to-earth (line-to-ground) short-circuit. The method for calculating short-circuit current in a.c. three-phase high-voltage system is also provided.

IEC 60781 presents an application guide for the calculation of short-circuit currents in low-voltage radial systems. The short-circuits are treated as far-from-generator short-circuits. This assumption is valid in the future as well, even with an increasing number of distributed generation units in low-voltage systems.

Several factors for the calculation of short-circuit (s.-c.) currents have been introduced in previous sections, the origin of which will be explained within this section. · Voltage factor c_max and c_min for different voltage levels as per Table 4.1. · Correction factor using the %/MVA or the p.u.-system as mentioned in Chapter 2. · Impedance correction factors for synchronous machines, power station units and transformers as per Tables 3.2, 3.3, 3.5 and 3.6. · Factors for the calculation of different parameters of the short-circuit current based on the initial short-circuit current as per Chapter 4. The factors are necessary as the method of the equivalent voltage source at the short-circuit location is used for the calculation of short-circuit currents which is based on some simplifications such as neglecting the load current prior to fault, assuming the tap-changer of transformers in middle-position, calculating the impedance of equipment based on the name-plate data or on data for rated operating conditions and neglecting voltage control gear for generators and transformers. The main task of short-circuit analysis is to determine the maximal short-circuit current which is one of the main criteria for the rating of equipment in electrical power systems. It is obvious that the parameters of the short-circuit current as calculated with the equivalent voltage source at the short-circuit location will differ from those currents, which may be measured during short-circuit tests or may be calculated with transient network analysing programmes. In order to obtain results on the safe side without uneconomic safety margin the correction factors will be applied. Detailed deductions of the various correction factors are given in IEC 60909-1:1991-10.

Calculation methods for the thermal and electromagnetic effects of short-circuit currents are dealt with IEC 61660-2, which is applicable to short-circuit currents in d.c. auxiliary installations in power plants and substations and IEC 60865-1, related to three-phase a.c. systems.

Interference between overhead lines, communication circuits and pipelines is caused by asymmetrical currents, which may be due to short-circuits, asymmetrical operation or asymmetrical design of equipment, especially asymmetrical outline of overhead line towers with respect to pipelines and communication circuits. This interference is based on inductive, ohmic and capacitive coupling between the short-circuit path (e.g., overhead line) and the circuit affected by interference (e.g., pipeline). Normal operating currents, respectively voltages, cause magnetic as well as electric fields which are asymmetrical in the vicinity of overhead lines which may cause interference problems in the long-time range.