Abstract-Multiple sets of solutions for the selective harmonic elimination pulse-width modulation method for inverter control exist. These sets present an independent solution to the same problem but further investigation reveals that certain sets may offer an improved overall harmonic performance. In this paper, a minimization method is discussed as a way to obtain these multiple sets of switching angles. A simple distortion harmonic factor that takes into account the first two most significant harmonics present in the generated waveform is considered in order to evaluate the performance of each set. The bipolar waveform is thoroughly analyzed and two cases are considered; single-phase patterns which eliminate all odd harmonics and three-phase counterparts which eliminate only the nontriplen odd harmonics from the line-to-neutral pattern but such harmonics are naturally eliminated from the line-to-line waveform. Experimental results support the theoretical considerations reported in the paper. Index Terms-Selective harmonic elimination pulse-width modulation (SHEPWM).

Finite-element analysis can be used to determine the magnetization characteristics in terms of curves of flux-linkage against current or rotor position. The "frozen permeabilities" technique is presented as a method of apportioning flux-linkage contributions to the phase currents and permanent magnets, and for inductance calculations. Results from a split-phase interior permanent magnet motor are presented and compared with experimental data. Drawbacks to the method are discussed.

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The flux-magnetomotive force (flux-MMF) diagram, or "energy conversion loop," is a powerful tool for computing the parameters of saturated interior permanent-magnet brushless motors, especially when the assumptions underlying classical dq theory are not valid, as is often the case in modern practice. Efficient finite-element computation of the flux-MMF diagram is possible when the motor current is known a priori, but in high-speed operation the current regulator can lose control of the current waveform and the computation becomes "voltage-driven" rather than "current-driven." This paper describes an efficient method for estimating the motor performance-average torque, inductances-by solving the voltage-driven problem. It presents experimental validation for a two-pole brushless interior permanent-magnet motor. The paper also discusses the general conditions under which this method is appropriate, and compares the method with alternative approaches. . It is well known that when the magnets are embedded inside the rotor iron, as in the "interior permanent-magnet motor" (IPM), calculations based on classical theory can be unreliable, mainly because of the variation of parameters due to saturation. IndexFor example in such machines can vary by at least 700% between no-load and full-load, while cross saturation influences the -axis parameters in a complex manner [1]- [7], [9]. The difficulties are increased by the use of fractional-slot windings with small numbers of slots/pole (even less than 1), non-circular laminations, and other departures from the ideal machine, so that neither the EMF waveform nor the variation of inductance with rotor position is sinusoidal. , and although they allow for cross-saturation effects they restrict themselves to steady-state operation and ignore the effect of rotor position on the -axis parameters.As long as the current waveform is known a priori, these problems can be overcome in an efficient computation in which the finite-element method is used to determine one cycle of the flux-linkage waveform, which is then plotted against the current waveform to establish a "loop" whose area gives the average electromagnetic torque. This loop diagram is known as the "flux-MMF diagram" or "i-psi loop" or "energy conversion loop" [9]. Bearing in mind that finite-element formulations are fundamentally always "current-driven," the computation is efficient because of the foreknowledge of the current waveform, so that a series of current values can be used as inputs to the finite-element process. This method does not necessarily rely on theory. At higher speeds it is normal for the current-regulator to lose control of the current waveform, and ultimately at the highest speeds the drive may operate in six-step mode. In this case, the applied voltage waveform is known but the current waveform is not. Similarly, if the machine is generating into a rectifier, the applied voltage at the machine terminals is known or calculable, whereas the current waveform is unknown.The accuracy of the finite-element m...

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Abstract-This paper presents a detailed quasi-steady-state approach to different torque components (average and pulsating) for a single-phase capacitor-run permanent-magnet (PM) motor. By employing average electromagnetic torque, and the expected envelope of the pulsating torque, an accurate prediction of starting torque components behavior is made. The quasi-steady-state analysis of the asynchronous performance of the single-phase capacitor-start capacitor-run PM motor is realized through a combination of symmetrical components and -axes theory. The developed approach is valid for any -phase ac motor-induction, synchronous reluctance, or synchronous PM.

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