Smart grids are characterized by the availability of distributed energy resources (DER), including power switching interfaces (PSI) to connect to the grid. This creates a new scenario for the management of power grids, because DER increase the power capability and flexibility of the network at the expense of a higher complexity of control. If properly driven, however, PSI can improve power quality and distribution efficiency. On the contrary, every control misbehavior can cause voltage instability and/or circulation of useless currents, with the risk to affect network operation. Moreover, especially in case of islanded operation, smart grids can suffer from voltage distortion, asymmetry, and frequency variations, which may affect control accuracy and stability. In such a context, a cooperative control approach of PSI and any other electronic power processors (EPP) acting in the grid is needed, to ensure proper network operation even under severely disturbed conditions. This paper shows that the Conservative Power Theory (CPT) provides a viable background for the development of an optimum control technique of distributed EPP.