This paper proposes a new model reduction algorithm for power systems based on an extension of balanced truncation. The algorithm is applicable to power systems which are divided into a study area which requires a high-fidelity model and an external area, making up most of the power system, which is to be reduced. The division of the power system can be made arbitrarily and does not rely on the identification of coherent generators. The proposed algorithm yields a reduced order system with a full nonlinear description of the study area and a reduced linear model of the external area.