  In smart energy communities, households of a particular geographical location
make a cooperative group to achieve the community's social welfare. Prosumers
are the users that both consume and produce energy. In this paper, we develop
stochastic and distributed algorithms to regulate the number of consumers and
the number of prosumers with heterogeneous energy sources in the smart energy
community. In the community, each prosumer has one of the heterogeneous energy
sources such as solar photovoltaic panels or wind turbines installed in their
household. The prosumers and consumers decide in a probabilistic way when to be
active. They keep their information private and do not need to share it with
other prosumers or consumers in the community. Moreover, we consider a central
server that keeps track of the total number of active prosumers and consumers
and sends feedback signals in the community at each time step; the prosumers
and consumers use these signals to calculate their probabilistic intent. We
present experimental results to check the efficacy of the algorithms. We
observe that the average number of times prosumers and consumers are active
reaches the optimal value over time, and the community asymptotically achieves
the social optimum value.
