This paper establishes a mathematical model of three-phase four-wire center-split single-turned hybrid active power filters（HAPF）in d-q-0coordinate. Based on this mathematical model，the filtering characteristics of the passive part of the single-tuned HAPF with and without neutral inductor are analyzed and discussed. According to the HAPF active part capacity analysis and the filtering characteristics of its passive part，the structure of the three-phase four-wire single-turned HAPF can be optimized and its minimum DC-link voltage expression can be deduced based on the general harmonic current contents of the loading. Therefore，the cost of the HAPF can be lowered by reducing its active part capacity. Finally，the correctness of the minimum DC-link voltage theory and the effectiveness of this optimized structure are verified by simulation.