2B.1 Basic theoretical equations for transient dimensioning
2B.1.1 Short-circuit
The following equations refer to a C-O duty cycle. C-O-C-O duty cycles are treated in 2B.1.3
The general expression for the instantaneous value of a short-circuit current may be defined.
For simplification purposes the fault inception angle and system impedance angle can be summed up to one single angle which makes the calculation easier to understand from the mathematical point of view.
The angles and both describe the possibility of varying the fault inception angle and therefore can be applied alternatively as suitable but according to their definition.
A possibly reduced range of fault inception angle can be used to define a reduced asymmetry which may lead to a reduced factor in some special cases.
NOTE The possibility of restricting the current inception angle is not covered in this standard, but will be discussed in the Technical Report IEC 61869-100.
2B.1.2 Transient dimensioning factor
The transient dimensioning factor is the final parameter for the core dimensioning and is given on the rating plate. It can be calculated from different functions of the transient factor as given in the equations below and as shown in Figure 2B.3.
In some cases, the protection system may require a value which is not constant and depends on various parameters of the short-circuit current. Therefore the transient dimensioning factor can also be obtained from relay stability type tests and given by the manufacturer of the protection system.
The transient factor given in this section is derived from the differential equation of the equivalent circuit with a constant inductivity of the current transformer core, with an ohmic burden and without consideration of remanence. In this annex, the solutions of the differential equation are given either as curve diagrams or as simplified formulas.
NOTE The differential equation and the exact solution is given in the Technical Report IEC 61869-100 TR.
The secondary linked flux depend likewise on time and, in the end, on the time to accuracy limit required by the protection system. By calculating with the linear inductivity, the solution is only valid up to the first saturation of the current transformer.
