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In this study, a relay with hysteresis-based control technique is analysed for a three-phase three-level neutral point clamped (NPC) ac-dc converter. The converter draws sinusoidal current with unity power factor from the supply grid and keeps total dc-link voltage constant. The hysteresis-based current control has good dynamic response but suffers from variable switching frequency. The switching frequency characterisation of hysteresis current control based on time domain approach is more complicated for the multilevel converters. Therefore there is a need to address the characterisation based on frequency domain approach. Here, describing function method and Tsypkin's method are proposed for the switching frequency characterisation of the relay with hysteresis-based system. The proposed methods determine the maximum switching frequency and amplitude of the current tracking error and permit the calculation of maximum switching frequency in simple algebraic equations. The closed-loop control scheme of the relay with hysteresis-based current control is implemented for a three-phase three-level NPC ac-dc converter system. The performance of the proposed frequency domain characterisation has been studied using MATLAB/Simulink, and a laboratory model is developed for experimental verification.