The management of demand-side resources is increasingly becoming an important issue in face of higher shares of renewable generation and the evolution to smart homes and grids. In a smart home an Automated Home Energy Management System (AHEMS) endowed with adequate algorithms should allow for an integrated optimization of the available energy resources (grid, loads, local generation and storage) in face of time-differentiated tariffs. This paper defines a novel and comprehensive smart home modeling that includes several relevant categories of energy resources as well as a set of practical comfort specifications that the user may freely decide upon. An AHEMS capable of computing compromise solutions by balancing the minimization of total cost (energy and power) and dissatisfaction caused to the users (e.g., by rescheduling load operation) is studied under this novel smart home modeling. Emphasis is given to the study of different power cost scenarios and how they affect the solutions found by the AHEMS. Two types of power cost scenarios are studied: contracted power with known fixed costs and limits on the power requested from the grid, and variable power charges according to the peak power requested from the grid. A detailed analysis of the physical characteristics of the solutions is also provided. Overall, the results show that the variable power charges scenarios surpass the contracted power scenarios in terms of cost and dissatisfaction. Besides incurring in lower power costs, the variable power charges scenarios also obtain lower energy costs. The variable power charges scenarios also provide the users with a greater flexibility over the energy resources, while removing the risk of energy supply interruptions that is present in the contracted power scenarios. In terms of grid management, the results show that the variable power charges scenarios do not present any particular risk of incurring in very high peaks of power requests. In terms of energy policy considerations and given the transition to smart homes and grids, these results suggest that contracted power scenarios may be phased out and safely replaced by variable power charges scenarios with the deployment of AHEMS. Furthermore, the feasibility of deploying the AHEMS under study in a low-cost embedded system is also assessed. The results show that this AHEMS can compute interesting and diverse solutions for practical implementation in less than 90 s.