The development and a more sophisticated structure of electric power systems, the transition towards deregulation and competition between the participants of the electric energy market cause the necessity of a complex steady state analysis, the evaluation of the electric power system stability, with its parameters being changed. The paper addresses the steady state analysis based on algebraic methods. Regular (trivial) and non-regular (additional) equilibrium points for the electric power system conservative model are determined. Changing regular and non-regular equilibrium points in a heavily loaded electric power system is studied