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Safety Against Overvoltages      209


                                  latter case, the lightning impulsive current is drained to earth, directly
                                  or via the structures that are struck. The consequent release of a large
                                  amount of energy (i.e., many hundreds of megajoules) is harmful to
                                  persons as well as destructive for equipment.
                                     The cloud-to-earth lighting is initiated by the presence of charges,
                                  usually negative, in the lower part of the cloud. The buildup of charges
                                  maycausetheresultingelectricfieldtoexceedthedielectricstrengthof
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                                  the air. The breakdown of the air and an initial discharge then occur.
                                  The discharge creates a highly conductive channel the charges can
                                  use to descend toward ground as if it were a conductor. The channel
                                  stops at the point where the dielectric strength of the air equals the
                                  electric field caused by the charges. Further charges, though, traveling
                                  from the cloud reinforce the field, perturbing the equilibrium and
                                  allowing new discharges. Thus, new conductive channels occur in a
                                  “zig-zag” fashion toward the earth. Such “stepped” discharge is due
                                  to the nonuniformity of the air, caused by the punctual variation of its
                                  parameters, such as density, humidity, etc.
                                     The charge from the cloud progressing toward the earth induces
                                  an equal amount of charge, but of opposite sign. The electric field
                                  increases and an upward-directed discharge from the soil, or a struc-
                                  ture, takes place causing an “attachment” between the upward- and
                                  downward-directed channels. This “return stroke” causes the circu-
                                  lation of the high-intensity (i.e., hundreds of thousands of amperes)
                                  impulsive lightning current to ground. Such a current is characterized
                                  by a rapid rise to the peak (i.e., within a few microseconds), a rela-
                                  tively slow decay as well as a high-frequency content (i.e., order of
                                  hundreds of kilohertzs).

                                  12.3.1 Characterization of Earthing Systems Under
                                          Impulse Conditions
                                  The grounding system used to safely drain to earth the fault currents
                                  at the power frequency is also employed to dissipate to ground the
                                  lightning current. Earthing electrodes, in fact, may be connected, by
                                  means of down-conductors, to lightning protection systems (LPS),
                                  such as masts, installed on the roof of buildings being protected.
                                     Grounding systems through which high-frequency currents cir-
                                  culate, though, do not behave in the same fashion as examined in the
                                  previous chapters for fault currents at the network frequency. Earth
                                  electrodes, in fact, cannot be assumed to be purely resistive in the
                                  presence of pulse currents, as the inductance of their metal parts can-
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                                  not be neglected. Thus, the earth electrode must be modeled as an
                                  ohmic-inductive pi circuit, and we will use the term earth impedance
                                  instead of earth resistance.
                                     To clarify the concept, let us consider, as an earth electrode, a
                                  buried horizontal wire (Fig. 12.10).
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