Multilayer modeling of adoption dynamics in energy demand management

Abstract

Due to the emerging of new technologies, the whole electricity system is undergoing transformations on a scale and pace never observed before. In particular, the decentralisation of energy resources and the smart grid have changed the rules of the game and have forced utility services to rethink their relationships with customers. The so-called demand response (DR) seeks to adjust the demand for power instead of adjusting the supply. However, DR business models rely on customer participation and might only be effective if large numbers of customers in close geographic vicinity, e.g. connected to the same transformer, opt in. Here, we introduce a model for the dynamics of service adoption, in which the behaviour of a customer is influenced by its social contacts, in addition of also depending on the specific spatial configuration of other customers in close proximity within the power grid service area. In particular, we use a multiplex network with two layers coupled together, the social layer among customers and the power-grid layer connecting the households. While the adoption process, modelled as an epidemic spreading, runs on the social layer, the node-and timedependent recovery rate of the nodes depends on the states of their neighbours on the power-grid layer, so that the dynamics tends to preserve clusters of infected individuals by making an infected node surrounded by nodes in the same state less keen to recover. Numerical simulations of the model on synthetic and real-world networks show that strong local influence of the costumers actions leads to a discontinuous transition where either no or all nodes in the network are infected, depending on the infection rate and the social pressure to adopt. We find that clusters of local early adopters act as points of high local pressure, helping maintaining adopters, and facilitating an eventual adoption of all nodes. This suggests direct marketing strategies on how to efficiently establish and maintain new technologies such as DR schemes.The electricity system is in the midst of large transformations, and new business models have emerged quickly to facilitate new modes of operation of the electricity supply. The so-called demand response seeks to coordinate demand from a large number of users, through incentives which are usually economic such as variable pricing tariffs. Here, we propose a simple mathematical framework to model consumer behaviours under demand response. Our model considers at the same time social influence and customer benefits to opt into and stay within new control schemes. In our model information about the existence of a contract propagates through the links of a social network, while the geographic proximity of clusters of adopters influences the likelihood of participation by decreasing the likelihood of opting out. The results of our work can help to take informed decision in energy demand management.

Social contagion on higher-order structures

“…While temporally resolved data can help understand whether cliques in an aggregated network actually correspond to group meetings or not, as discussed in For instance, the authors of [31] study the case in which 𝜆 3 < 0, i.e., an individual is less likely to adopt a trend if this trend is popular in the group, and call this ingredient the "hipster effect"; this effect also can lead to a region of bi-stability in the phase diagram [31]. Note that heterogeneous recovery rates [42,43] and "complex recovery" rates depending on the state of the surrounding individuals have also been considered in the literature [44].…”

On the Dual Nature of Adoption Processes in Complex Networks

“…Recently, it has been shown that differences between the recovery rates of the nodes, that is, considering heterogeneous distributions of parameters instead of constant, can also dramatically change the epidemiological dynamics [55][56][57]. In addition, models of complex recovery, in which the social influence mechanism acts on the recovery rule rather than on the infection one, showed that this change of perspective might lead to explosive adoption dynamics [58]. This behavior is especially pronounced in spatial systems, whose effects on the contagion dynamics have also been the focus of several studies [59][60][61][62].…”

On the dual nature of adoption processes in complex networks

“…Recently, it has been shown that differences between the recovery rates of the nodes, i.e., considering heterogeneous distributions of parameters instead of constant, can also dramatically change the epidemiological dynamics [55][56][57]. In addition, models of complex recovery, in which the social influence mechanism acts on the recovery rule rather than on the infection one, showed that this change of perspective might lead to explosive adoption dynamics [58]. This behavior is especially pronounced in spatial systems, whose effects on the contagion dynamics have also been the focus of several studies [59][60][61][62].…”