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For the purposes of on-line security calculations a method for deriving steady-state network equivalents is presented which is based on a radial tree-shaped structure. This is not able to give a perfect replica of the original network, but the accuracy of the representation of different network regions is controllable. The impedances and the structure of the radial equivalent are found by a search procedure directed at minimizing an error function on the transfer impedances to be matched by the equivalent. Injections are treated in terms of the REI-network. Results for practical power systems are given, which show the feasibility of this reduction method with security calculations.