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This paper presents a procedure for mathematical modelling of ring electric power systems for simulation of both transient and steady-state conditions. The idea of this procedure has been based on nodal voltages technique and on differentiation of Kirchhoff's current law (KCL) applied to each non-reference node of the system, the result of which a system of algebraic equations for nodal voltages has been obtained. Currents flowing through the electric power system components have been determined by solving their respective differential equations. The overall number of the algebraic and differential equations has been decreased by one third by transforming the three-phase coordinate system into Cartesian coordinate system, where the use of the latter does not ignore the DC component during transient conditions, but restricts the model's implementation for symmetrical modes of operation only. A numerical example for a four-bus ring electric power system with graphical results has been computed and illustrated.