In sensorless control for synchronous machines at low speed and standstill, the position estimation can be sensitive to the choice of the carrier frequency of the injection method. Moreover, electromagnetic saturation or temperature variation in the machine might also affect the estimation error. In order to better describe the high-frequency (HF) behaviour of the machine, the effective HF inductances and resistances are presented in this paper. Then, the analytical expression for the carrier frequency dependent error is explained using the calculated HF-equivalent model and is proposed to be integrated into the sensorless control scheme when a rotating HF voltage injection is employed. Numerical simulations highlight the frequency dependent error and prove the satisfactory operation of the compensation.