Detecting inter-turn short circuits in ultra-high voltage shunt reactors is challenging due to weak fault signatures. This paper establishes an accurate three-segment fault model and derives, for the first time, explicit analytical expressions for the short-circuit phase equivalent resistance (Req) as a function of both short-circuit turn ratio (α) and transition resistance (Rk). In particular, this model reveals specific Req variation laws: monotonic decrease with α for metal faults and non-monotonic behavior for transition resistance faults. Leveraging these insights, an innovative identification method is proposed. Its core innovation is a theory-driven, flexible threshold (Rset) calculation based solely on the derived Req=f(α,Rk) function and user-defined pa-rameters (minimum detectable αmin and maximum tolerable Rk_max), thereby reducing reliance on empirical values. Simulation results validate the proposed model and method, demonstrating superior sensitivity and ac-curacy, especially for small-turn inter-turn short circuits with transition resistance, compared to conventional ze-ro-sequence methods. This provides a robust theoretical foundation for practical fault detection.