We consider a scenario where price-responsive energy consumers are allowed to optimize their individual utilities via mechanisms of load-shifting in a distribution network subject to capacity constraints. The uncoordinated selfish behavior of the consumers would lead, in general, to requests that could not be served by the distribution network because of such constraints. Thus, a centralized or hierarchically coordination mechanism is required. We derive algorithms and methods to determine in real-time the largest set of consumers' decisions that are compatible with the physical constraints of the network and capable of avoiding congestion phenomena in the future. These methods are shown to be applicable to the design of coordination mechanisms with the aim of providing a large number of degrees of freedom to the users while guaranteeing the integrity of the system.