We report physical architectures and mathematical models for electric-power management of multiple homes. The notion of home is a unit of small-scale electric power system close to consumers and corresponds to an entity of the physical architecture for electric-power management. The home includes own energy source, energy storage, residential load, power conversion circuits, and control systems. An entire power system consists of multiple homes that are interconnected via a distribution network and are connected to the commercial power grid. By applying a technology of grid-connected inverters for each home, we show that the mathematical model derived for the power system has a coupling structure similar to that in the multi degree-of-freedom swing equations for analysis of multi-machine power systems. Numerical simulations of the model allow us to define nominal dynamics of the power system, in which the supercritical Hopf bifurcation and associated sustained oscillations in frequency and active power are identified under a realistic setting of model parameters.