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Detecting High Impedance Faults (HIFs) in Distribution Systems (DSs) still requires effective solutions. HIFs can cause damage, such as shock hazards and bushfires. However, conventional protection cannot identify HIFs due to their low fault current, and most existing solutions neglect the multiple operating scenarios of the DSs. Thus, this paper proposes a new self-adaptive approach for HIF detection, considering the conductor fall period in a system with distributed generation, a condition usually overlooked in existing studies. The algorithm is based only on the fundamental component and third harmonic extracted from the neutral current using the Stockwell Transform. The approach was thoroughly evaluated, considering several scenarios, such as changes in the system loading, background noise, events that can cause false detection, and variations in the distributed generator power output. The tests considered HIFs signals from real field measurements and generated by a simulation model. The results showed that the algorithm is promising, with high detection rates for all the evaluated scenarios, which included over 400,000 HIF and 6,000 non-HIF cases. Additionally, a comparison proved the superiority of the proposed approach over existing methodologies.