Permanent-magnet synchronous machines (PMSMs) are well suited for high-speed (HS) applications due to their high efficiency, power density, and dynamic response capability. The heat extraction area decreases as the speed increases, making thermal effects more dominant at high speed. The temperature-dependent properties of permanent magnets necessitate high-detail thermal models. This paper presents a 2-D analytical model for a HS PMSM magnet. The diffusion equation is solved where three of the PM boundaries experience convection heat flow; as the case is in radial flux machines. The heat generated on the rotor surface due to eddy currents is also taken into account. The model is verified using numerical techniques and shows good correlation (within 1.5%). The model is also validated through experiments performed on a 4 kW, 30 000 r/min PMSM.

Active magnetic bearings (AMBs) have become a key technology in various industrial applications. Self-sensing AMBs provide an integrated sensorless solution for position estimation, consolidating the sensing and actuating functions into a single electromagnetic transducer. The approach aims to reduce possible hardware failure points, production costs, and system complexity. Despite these advantages, self-sensing methods must address various technical challenges to maximize the performance thereof. This paper presents the direct current measurement (DCM) approach for self-sensing AMBs, denoting the direct measurement of the current ripple component. In AMB systems, switching power amplifiers (PAs) modulate the rotor position information onto the current waveform. Demodulation self-sensing techniques then use bandpass and lowpass filters to estimate the rotor position from the voltage and current signals. However, the additional phase-shift introduced by these filters results in lower stability margins. The DCM approach utilizes a novel PA switching method that directly measures the current ripple to obtain duty-cycle invariant position estimates. Demodulation filters are largely excluded to minimize additional phase-shift in the position estimates. Basic functionality and performance of the proposed self-sensing approach are demonstrated via a transient simulation model as well as a high current (10 A) experimental system. A digital implementation of amplitude modulation self-sensing serves as a comparative estimator.