A unified probabilistic theory of the incidence of direct and indirect lightning strikes

The basic probabilistic properties of direct lightning strikes and field-induced effects are identified, reviewed, and combined into a unified and comprehensive setting. The probabilistic aspects of the incidence of direct and indirect lightning strikes and their effects on general power systems are modeled and analyzed on the basis of a concept of system perception. The bias of the statistical distribution of the perceived lightning current amplitudes, as stemming from impairment of the natural lightning distribution by censoring of distant and weak strikes, is formalized into a general problem setting. Here the perceptive zone, viewed as a function of the natural lightning current amplitude, is the key concept. The effective area of the perceptive zone, defined through the number of perceived flashes per year and the lightning ground flash density, is obtained as a statistical average. The implications of the general theory are further studied under special conditions regarding system geometry, functional perceptive zone strike current amplitude relationship, and natural lightning current amplitude distribution. It is demonstrated that the problem lends itself to a simple analytical study assuming point or line type geometry, power function type amplitude relationship, and log-normal amplitude distribution