Power consumption due to transmissions in base stations (BSs) has been a major contributor to communication-related CO₂ emissions. A power optimization model is developed in this study with respect to radio resource allocation and activation in a multiple Component Carrier (CC) environment. We formulate and solve the power-minimization problem of the BS transceivers for multiple-CC networks with carrier aggregation, while maintaining the overall system and respective users' utilities above minimum levels. The optimized power consumption based on this model can be viewed as a lower bound of that of other algorithms employed in practice. A suboptimal scheme with low computation complexity is proposed. Numerical results show that the power consumption of our scheme is much better than that of the conventional one in which all CCs are always active, if both schemes maintain the same required utilities.