A space vector pulse width modulation (SVPWM) algorithm is an important part of the permanent magnet synchronous machine (PMSM) drive to achieve direct current (DC) to alternating current (AC) conversion. The execution of the conventional SVPWM algorithm is a complex process which will limit the sampling frequency of the high-speed PMSM drive. Low sampling frequency will cause high current total harmonic distortion (THD) and eddy current loss. To increase the sampling frequency, this paper proposes a novel simplified SVPWM algorithm. The proposed SVPWM algorithm turns the vector composition problem of the conventional SVPWM algorithm into an optimization problem of the dwell time of the basic vector. The proposed SVPWM algorithm has an optimal vector dwell time (OVDT). The dwell time of the basic vector can be directly calculated by solving the optimization problem. The proposed SVPWM algorithm does not need sector identification compared to the conventional algorithm. The experiments of the proposed SVPWM algorithm are performed in a high-speed PMSM drive of a flywheel energy storage system (FESS). Compared to the conventional SVPWM algorithm, the execution time of the proposed SVPWM algorithm is reduced by 38%. By using the proposed SVPWM algorithm, the sampling frequency can be increased from 33 kHz to 40 kHz. With the higher sampling frequency, the current THD is reduced by 25.6%. The effectiveness of the proposed simplified SVPWM algorithm is verified experimentally.