Spatio-temporal analysis of PV diffusion patterns: an integrated neural networks and agent-based model

Ali Alderete Peralta, Cranfield University

Photovoltaic (PV) panels offer significant potentials for contributing to the UK’s energy policy goals relating to decarbonisation of the energy system, security of supply and affordability. The substantive drop in the cost of panels since 2007, coupled with the introduction of the Feed-in Tariff (FiT) Scheme in 2010, has resulted in a rapid increase in installation of PV panels in the UK from 16.1MW in 2010 January to 12.4GW by 2017 December. Yet, spatial and temporal diffusion of PVs show significant differences across the UK.

By creating reverse flows on the networks, especially at low voltage distribution networks, domestic PVs present a key challenge for network operators to manage the grid such that there is enough capacity and voltage headroom available to accommodate these flows. That’s why understanding spatio-temporal diffusion of PVs can provide valuable insights to both network operators and policy makers with a view to predict and shape their future deployment.

To date, different approaches have been used for analysing PV diffusion process, including (i) spatial regression, (ii) agent-based modelling (ABM) and (iii) epidemic models. These approaches present different strengths and weaknesses.

The spatial regression and epidemic models characterise the adoption process at a geographical scale (i.e. an aggregated level) to analyse the impact of independent variables on the PV diffusion at different scales from neighbourhood, city level up to national level. ABMs on the other hand focus on the individual decision-making process, taking into account other individuals’ choices in the agent’s network and their interactions so as to capture emerging social dynamics.

While spatial regression and epidemic models overlook the temporal dimension of the diffusion process, ABMs have limited capacity in representing large populations and characterising temporal aspects explicitly. Moreover, many ABMs are driven by rational choice theory arguing that agents have access to perfect information to undertake complex calculations to evaluate gain in their utility. The aim of this work to address these limitations by developing a novel agent-based model where agents are defined as geographical areas (rather than as individuals as commonly done). The agents’ decision-making process is defined by artificial neural networks (ANN) so that we can analyse the spatial-temporal diffusion of PVs by taking into account both peer effects and underlying spatial regularity of diffusion patterns as informed by spatial econometrics literatures. Drawing from computer and complexity sciences, geographical information systems and energy economics, and using socioeconomic data at Post Code level, the model has the following novel aspects:

• The ANN‘s ability to improve agent’s decision-making process by taking into account socioeconomic time series data
• The ABM’s ability of characterise the social dynamics at large scale using spatially explicit data sets
• The ANN’s capability to capture the evolution of the system using explicit time-horizon

The initial prototype model is developed for the City of Birmingham focusing on the PV adoption process. Our initial auto-regressive model predicts future diffusion patterns at post-code level on a monthly basis. Both limited availability of time series data and spatial influence of other agents’ estimations on a given agent’s estimation lead to accumulation of errors spatio-temporally. Emerging results using socio-economic variables highlight the importance of income, electricity consumption and the household size. We also detect strong spatial dependency in the diffusion patterns.

Overall this work will produce novel insights into potential adoption patterns that may help distribution network operators to develop better strategies to accommodate higher loads which will, in turn, help keeping the energy affordable for consumers. The model can be used further to analyse the impacts of alternative policies to influence PV adoption, such as the development of local economic incentives.