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In the classical electricity grid power demand is nearly instantaneously matched by power supply. In this paradigm, the changes in power demand in a low voltage distribution grid are essentially nothing but a disturbance that is compensated for by control at the generators. The disadvantage of this methodology is that it necessarily leads to a transmission and distribution network that must cater for peak demand. So-called smart meters and smart grid technologies provide an opportunity to change this paradigm by using demand side energy storage to moderate instantaneous power demand so as to facilitate the supply-demand match within network limitations. A receding horizon model predictive control method can be used to implement this idea. In this paradigm demand is matched with supply, such that the required customer energy needs are met but power demand is moderated, while ensuring that power flow in the grid is maintained within the safe operating region, and in particular peak demand is limited. This enables a much higher utilisation of the available grid infrastructure, as it reduces the peak-to-base demand ratio as compared to the classical control methodology of power supply following power demand. This paper investigates this approach for matching energy demand to generation in the last mile of the power grid while maintaining all network constraints through a number of case studies involving the charging of electric vehicles in a typical suburban low voltage distribution network in Melbourne, Australia. [ABSTRACT FROM AUTHOR]