In this paper, we present a new analytical method to calculate the required amplitudes and phase angles of the injected harmonic currents, to generate a determined torque ripple for synchronous machines with surface-mounted permanent magnets. First, we described the machine equations as a function of the phase current and the back electromotive force. We then introduced a new asymmetrical power system. After combining the equations, we established a linear system of equations. The solution of the equation system yielded the amplitudes and phase angles of the harmonic currents to be injected. Finally, we validated the method with several finite element method simulations. With this method, a previously defined torque ripple could be generated very accurately for synchronous machines with surface magnets.