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• Transformerless SqZSI with common-ground and minimum leakage current features is an attractive and cost-effective option as a PV microinverter. • SqZSI injects second harmonic and DC components under certain conditions, which is undesirable in terms of published power-quality standards. • The experimental study on power quality improvement of this family of inverters (SqZSI) is currently limited. • Closed-loop compensation methods based on well-known linear control techniques e.g. PI & PR controllers can mitigate extensively the power quality issues. The transformerless single-phase semi-quasi-Z-source inverter (SqZSI) provides several advantages over classical PWM converters. Reduced or eliminated leakage current, high power density, and low cost are important features making this topology an attractive choice for PV micro-inverter applications. Two drawbacks of this topology are DC and second harmonic injection in the output AC port, which in some cases prevent the fulfillment of standard requirements. To alleviate this power quality issue, four novel harmonic mitigation algorithms based on PI and PR controllers are proposed, analyzed, and experimentally verified with the 90 W SqZSI in this paper. Moreover, a modified modulation reference waveform strategy is introduced. Consequently, the converter performance, in terms of total harmonic distortion (THD V) is achieved at about 1.27% under full power load. Also, in this paper, the non-ideal state-space model of the SqZSI with the effect of the equivalent series resistance of inductors is developed and the generation origin of DC and second harmonic component is analyzed based on the obtained model. The achieved results confirms the significant THD reduction by more than 75%, the DC component suppression, the second harmonic mitigation, and the power quality improvement. [ABSTRACT FROM AUTHOR]