Security of supply to customers is a major concern for electricity distribution network operators. This research concentrates in particular on the UK distribution system, and on sub-transmission and extra high voltage networks within that system. It seeks first to understand the principal causes of network risk and consequent loss of supply to customers as a result of faults at these voltage levels. It then develops a suite of methodologies to evaluate that risk, in terms of expected annual cost to the network operator, under a range of different scenarios and for both simple and complex network topologies. The scenarios considered include asset ageing, network automation and increasing utilisation as a consequence of electric vehicles and heat pumps. The methodologies also evaluate possible mitigation options, including active network management, and capital expenditure for both asset replacement and network reinforcement. A composite methodology is also developed, to consider combinations of scenarios and combinations of mitigation strategies. The thesis concludes by considering issues likely to affect the extent and possible increase of network risk over the period 2010-2030.