Active consumer: problem of joint optimization of energy consumption and local generation

As a part of managing behavior of an active consumer of electric power in prospective smart grids it is necessary to create a mathematical model that meets his or her economic interests. Existing models either do not take into account all relevant aspects or turn out to be too complicated for the purposes of multi-agent modeling. Mathematical model of an active consumer and its use for investigating the problem of consumption and local generation regimes optimization is proposed. The conditions when the consumer's problem has a pretty simple and efficient solution are derived. The proposed approach is illustrated by optimizing the operating modes of equipment for a single household.