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The lightning impulse duty for 400 kV underground power cables using ATP is investigated and the recommended design level based on a probabilistic analysis is reassessed. A comprehensive study of the transient overvoltages experienced by cables within the UK National Grid's transmission system has been performed. The paper investigates the effects of transient overvoltages due to lightning. To determine the peak voltages that a cable would experience, direct lightning strikes and backflashovers onto the overhead-line phase conductor were simulated both near a cable termination and at air-insulated substation (AIS) and gas-insulated substation (GIS) zones. A second paper will present the investigation into transient overvoltages due to switching, faults and other temporary overvoltages (TOV). A probabilistic approach to argue for a reduction of the basic insulation level (BIL) for 400 kV cables to a value of 1050 kVp is used.