**Abstract**

Soft starters based on thyristor voltage converters are widely used to reduce the voltage dips during start-up of high-voltage induction motors. In this way, the start of the high inertial electric drives is accompanied by overheating of the rotor winding, which causes severe thermomechanical stress for the rotor elements leading to the motor failure. The aim of this work is to obtain analytical relations for approximate estimation of the rotor winding overheating in the starting modes. In this paper, we used analytical methods based on Fredholm integral equations and numerical simulation based on the method of thermal circuits in Matlab/Simulink. Based on solution of the Fredholm equation, the analytical relations were obtained to calculate the maximum temperature of the rotor winding during starting considering of heat transfer into the environment. The calculation results obtained by these expressions were tested using an integrated model that includes all the elements of the drive from the supply net to the operating mechanism. It is shown that the adiabatic approach to estimating of the rotor winding temperature maximum during start-up at which the heat transfer to the environment is not taken into account can lead to substantial error. The analytical expressions were obtained to perform approximate allowance for the uneven distribution of rotor winding temperatures when evaluating its maximum temperature. The proposed approach allows estimation of the maximum winding temperature at start-up on the basis of the relations between the temperature of motor components and the energy that is released in them and transferred to the environment, without the solution of differential equations, which describe the time variation of temperature. The obtained results make it possible to evaluate the maximum temperature of the rotor winding at start-up modes without the involvement of the numerical modeling, for which the electric drive designer often does not have not enough information.

**Keywords**

Induction motor, rotor winding, Fredholm integral equation, thermal model, thermomechanical stress.

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