By applying the equivalent circuit based transformer protection theory to single-phase two-winding transformer models， the theory's capability of distinguishing inrush currents from internal faults is analyzed. Considering that the computation of protection characteristic quantities is affected by measurement errors of current transformers and that the sensitivity of protection characteristic quantities to faults is influenced by transformers' operating status， the selection of protection criterion is studied. Analysis shows that external currents can decrease the sensitivity of characteristic quantities to internal faults， which leads to significant computational errors. As a result， an improved criterion with restraint logic is proposed to improve the reliability of protection operations， and the setting method is also provided. The tests with experimental data show that the improved criterion has good performance on sensitivity and security.