Purpose. To propose a method for determining the additional losses in the stator windings of electrical machines, in which the current frequency is significantly higher than the mains frequency. Methodology. The numerical methods for solving differential equations of mathematical physics are applied for the study. The Finite Element Method is used for algebraization of partial derivatives; an implicit method of backward differentiation formula is used for algebraization of time derivatives while the Newton-Raphson method is applied for solving nonlinear algebraic equations. Findings. A mathematical model, which allows counting the total losses caused by skin effect in the slot of the stator winding of a high-speed electrical machine, was created. The model takes into account: its own slot leakage flux, the main magnetic flux, a saturation of the magnetic core, various slot forms and the method of electrical connection of conductor strands in the slot. The mathematical formulation and the boundary condition of this problem are offered. The results of mathematical experiments of defining additional and total losses in the windings located in the half-closed and open slots for high-speed generator with permanent magnet excitation of 200 kW, 50 000 rpm, are presented. The cause-and-effect relationships are analyzed. Findings can help while designing such machines. Originality. The problem of calculating losses is formulated as a 2-dimensional boundary problem of electrodynamics, which allows us to take into account an interference of the above factors. Practical value. The necessity for accurate determination of the losses in the phase windings of high-speed machines occurs not only when designing the windings, but also while assessing the thermal condition of such machines.

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