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In this paper, we present an extension for an analytical method of calculating the required amplitudes and phase angles of the injected harmonic currents, to generate a determined torque ripple for synchronous machines. With the consideration of reluctance torque in the system equations, this method is valid not only for synchronous machines with surface magnets, but also for those with interior magnets. First, we describe the machine equations as a function of the phase current and the back electromotive force. We then introduce an analytical way to calculate the reluctance torque. After combining the equations, we establish a linear system of equations. The solution of the equation system yields the amplitudes and phase angles of the harmonic currents to be injected. Finally, we validate the equations for calculating the reluctance Torque and the method to generate the determined torque ripple with several finite element method simulations. This allowed us to generate the desired torque fluctuations even for synchronous machines with interior magnets.

An Analytical Method for Generating Determined Torque Ripple in Synchronous Machine with Interior Magnets by Harmonic Current Injection