The current error space phasor (CESP) based hysteresis controller employed for front-end converter requires two (inner and outer) hysteresis bands for vector selection and sector detection, respectively. As a result of this, the CESP moves out of the fixed (hexagonal) inner boundary many times in one fundamental cycle (and touches outer hysteresis band) to detect appropriate sector. This distorts the supply current waveform and increases the implementation complexity. To provide effective solution to the said issue, in this article, a fractal approach with a triangularization technique is proposed and analyzed to eliminate the outer hysteresis band and lookup table for sector change detection. The novelty proposed in this article is the integration of the fractal approach to CESP-based hysteresis controller, which reduces the complexity of the implementation of CESP-based hysteresis controller for any general multilevel front-end converter. The detailed analysis of the proposed technique for sector detections is presented considering the voltage space phasor structure of three-level and five-level converters. A generalized flowchart for any multilevel converter employing CESP-based hysteresis controller with proposed sector detection technique is developed and presented. Laboratory prototype is developed for a three-level flying capacitor front-end converter with an effective capacitor voltage balancing scheme. The experimental results are presented to validate the effectiveness of the proposed current controller in terms of unity power factor and low harmonic distortion in the line current under various practical conditions.