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The stellarator Wendelstein 7-X is a steady-state fusion experiment being built at the Greifswald Branch Institute of the Max-Planck Institut für Plasmaphysik (IPP). During an emergency discharge of the superconducting magnet system, eddy currents are generated in the steel case of the coils. Knowledge of the eddy currents distribution is important for a reliable operation of the system. We apply a method of calculating the eddy currents based on the finite-integration technique with the perfect boundary approximation technique. A description of the magnet system, principles of the applied method, the model, and sample results are presented in this paper.