The electricity sector worldwide is facing considerable pressure arising out of climate change issues, depletion of fossil fuels and geo-political issues around the location of remaining fossil fuel reserves. Electricity systems are also facing technical issues of bi-directional power flows, increasing long-distance power flows and a growing contribution from fluctuating generation sources. There is a concern that these systems are vulnerable. Investigation of vulnerability has focussed on shocks to the system associated with weather risks, equipment failure, supply (fuel) failure and price shocks, and analysis has been primarily based on financial measures such as the value of lost load. As the UK electricity system makes the transition to a low carbon future, it is unclear what this new future will look like. Transition pathways research using a multi-level perspective has identified a general picture of the drivers in future systems architecture. In such futures, vulnerability becomes multi-dimensional, and security becomes a more complex issue than that of supply of fossil fuels. These issues are not specific to the UK. Electricity systems across the globe face the same issues of multi-dimensional vulnerability and complexity of security. Research into the transition to a low carbon electricity system has, to date, been primarily focussed on the national scale in the UK. The aim of this work is a critical analysis into the use of the resilience concept for electricity systems, applied in particular to the distribution network in a case study urban area in the north east of England. The case study shall examine the low carbon scenarios for the UK, what this means in particular for domestic buildings for the case study area, and the nature of the stress on the electricity distribution system which may result from the expected growth in electrical load.