Haynes et al. (1977) derived a nonlinear differential equation to determine the spread of innovations within a social network across space and time. This model depends upon the imitators and the innovators within the social system, where the imitators respond to internal influences, whilst the innovators react to external factors. Here, this differential equation is applied to simulate the uptake of a low-carbon technology (LCT) within a real local electricity network that is situated in the UK. This network comprises of many households that are assigned to certain feeders. Firstly, travelling wave solutions of Haynes’ model are used to predict adoption times as a function of the imitation and innovation influences. Then, the grid that represents the electricity network is created so that the finite element method (FEM) can be implemented. Next, innovation diffusion is modelled with Haynes’ equation and the FEM, where varying magnitudes of the internal and external pressures are imposed. Consequently, the impact of these model parameters is investigated. Moreover, LCT adoption trajectories at fixed feeder locations are calculated, which give a macroscopic understanding of the uptake behaviour at specific network sites. Lastly, the adoption of LCTs at a household level is examined, where microscopic and macroscopic approaches are combined.
|Number of pages||13|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Early online date||31 Aug 2017|
|Publication status||Published - 15 Jan 2018|