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To solve problems of demand management in terms of smart energy systems (Smart grid), we need a mathematical model of active consumer decision-making. Existing models either do not consider important aspects of consumer behavior, or are too complex for use in multi-agent simulation. A mathematical model of an active consumer is proposed, based on which we formulate and solve the problem of optimization of electrical appliances and consumer equipment, as well as determine the loading conditions of self-generation, under which the consumer problem allows simple and effective solution. The proposed approach is illustrated by equipment optimization of a single household.