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Single-phase auto-reclosing (AR) scheme is widely employed in extra high voltage (EHV) transmission networks to quench transient faults without completely removing the faulted transmission line (TL). Long EHV TLs are commonly equipped with shunt reactors to reduce the Ferranti effect overvoltages. It is common practice to disconnect these reactors under the heavy load periods during the year. Considering this point, the AR technique should be able to work properly not only when the TL shunt reactors are in service, but also when they are disconnected. This paper puts forward a novel adaptive single-phase AR approach for shunt compensated TLs based on the general mathematical model of faulted phase voltage waveform after the line isolation, which is obtained by analytical analysis conducted on the TL's equivalent circuit. The effect of capacitor voltage transformer (CVT) on the voltage measurement is taken into account using a proper model for the CVT. Performing some data processing on the faulted phase measured voltage, useful features are extracted which are used by the support vector machine classifier to reliably detect the arc extinction instant. The proposed approach performance is evaluated by extensive simulation studies, accounting for different TL compensation schemes, transposition configurations, and arc conditions. [ABSTRACT FROM AUTHOR]