Eigencalculation is a challenging task in large-scale power systems with high power electronics penetration for at least two reasons. First, the well-known inter-area modes are no longer the only coupling modes as such couplings may involve also power converters. Next, it is difficult to find all coupling modes without a priori knowledge about the system. In this paper we propose a new method to overcome these difficulties. It is fully analytic, i.e., does not need operator manipulations like dynamic simulations, and exhaustive in the sense that makes a full scan of the system for coupling modes. As a consequence, the real modes can also be fully identified. The approach involves concepts from matrix computation and dynamic systems analysis which hold in large-scale and need no hypothesis (like the one about large inertia generators usually associated to inter-area modes) or knowledge about the structure of the power system. Validations on several models are presented, including realistic large-scale model (more than 1000 generators/dynamic devices) of the European power system.