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The effect of discontinuities in a transmission line on lightning-induced voltages is studied using a new field-to-line coupling model. For a shielding wire with an isolated grounding, it is shown that the mitigation of the induced voltages is due to the actuation of the localized grounding, when it is illuminated. It protects the line at its location and behind it, reducing the induced voltages by an amount that depends on the grounding resistance and the geometry of the conductors of the line, and also protects some points in front of it, but only within a certain ldquoeffective distancerdquo that is dependent on the rise time of the induced voltages. For a periodically grounded shielding wire, it is shown that the reflection, at the grounding points, of the voltage reduction waves produced by the other groundings, produce oscillating induced overvoltages that are mainly confined in the line span in front of the strike. The effectiveness of the shielding wire can be enhanced if the insulation of the shielding wire is utilized as a protective gap. It is also shown that the effect of the ground resistivity is very important but is very different depending on the permittivity of the ground.