Starting with a brief review on the existing methods of impedance emulation, this paper addresses a general and systematic approach to programmable and reconfigurable emulation of power impedances. The proposed approach not only enables the impedance value to be programed, but also allows the characteristics (i.e., type) of the impedance to be reconfigured instantly during the operation. Based on the proposed control method, emulation of at least six types of emulated power impedances (EPI) can be easily attained. In particular, it is theoretically and practically demonstrated that the impedance characteristic can be emulated through a combination of different functions. The systematic derivation of these functions is explained. New techniques that compensate the circuit power losses are introduced. This general approach has been practically verified in several EPI. Both steady-state and dynamic performance of these EPI confirm the programmability and reconfigurability. It is envisaged that the proposed method can be applied to a range of functions, such as power filtering, energy storage, and even power conversion based on direct impedance control.