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This paper deals with load control in a multiple-residence setup. The utility company adopts a cost function representing the cost of providing energy to end-users. Each residential end-user has a base load, two types of adjustable loads, and possibly a storage device. The first load type must consume a specified amount of energy over the scheduling horizon, but the consumption can be adjusted across different slots. The second type does not entail a total energy requirement, but operation away from a user-specified level results in user dissatisfaction. The research issue amounts to minimizing the electricity provider cost plus the total user dissatisfaction, subject to the individual constraints of the loads. The problem can be solved by a distributed subgradient method. The utility company and the end-users exchange information through the Advanced Metering Infrastructure (AMI)-a two-way communication network-in order to converge to the optimal amount of electricity production and the optimal power consumption schedule. The algorithm finds near-optimal schedules even when AMI messages are lost, which can happen in the presence of malfunctions or noise in the communications network. The algorithm amounts to a subgradient iteration with outdated Lagrange multipliers, for which convergence results of wide scope are established.
Gatsis et al. (Tue,) studied this question.