This information is part of the Modelica Standard Library maintained by the Modelica Association.

Simplified trajectory of an impulse (like the current of lightnings) as one of two choices:

• double-exponential function y = amplitude/eta*(exp(-time/tau1) - exp(-time/tau2))
• so-called Heidler function y = amplitude/eta*(time/tau1)m/(1 + (time/tau1)m)*exp(-time/tau2)

The parameters of the trajectory are defined by:

• The amplitude of the trajectory
• Rise time T1
• Decay time to half value T2
• For the Heidler function, integer exponent m = 5..10 is recommended.

Explanations

According to Fig. 1, a straight line between 0.1 and 0.9 of the amplitude is drawn. The virtual start of the trajectory is defined by the intersection of this straight line and the abscissa. The rise time T1 is defined as the time span between the virtual start of the trajectory and the point in time when the straight line reaches the amplitude. The decay time to half value T2 is defined as the time span between the virtual start and the point in time when the output falls below 0.5 of the amplitude.

Note: Due to numerical reasons, for the double-exponential function T1 < 0.2*T2 is required.

Fig. 1: Parameters of the lightning current

Note

For a standard trajectory with amplitude = 100 kA, T1 = 10 µs, T2 = 350 µs the integral of the output reaches the required charge Q = 50 C nearly perfect.

References

• Fridolin Heidler and Klaus Stimper, Blitz und Blitzschutz. VDE 2009, ISBN 978-3-8007-2974-6.
• Fridolin Heidler, Blitzstromparameter nach IEC 62305 - Hintergrund, Erfahrung und Ausblick. Elektronik & Automation (etz) (1) 2009, pp. 57-64.
• DIN EN 62305-1 (VDE 0185-305-1):2011-10 Blitzschutz - Teil 1: Allgemeine Grundsätze.
• Michael Rock, Prüfgeneratoren zur Simulation von Blitzimpulsströmen im Labor und ihre Wechselwirkung mit den Prüfobjekten. Habilitation, Universität Ilmenau 2012, ISBN 978-3-86360-032-7.