- The high temperature superconducting (HTS) self-limiting transformer (SLT) is a combination of a transformer and a fault current limiter in one unit. SLT is supposed to supply an HTS cable. This device may have two or more copper and/or superconducting windings and one or more YBCO cylinder(s) placed on a separate limb to operate when short circuit currents occur. We designed and built a small-size self-limiting transformer with copper primary and secondary windings and one YBCO cylinder. Experimental investigations of the quench process under a selected design scenario of current limitation are made. Analytical and numerical calculations are performed to simulate the self limiting quench performance of YBCO cylinders and the operation of the device. The simulations incorporate the HTS cable model. The results are used to inform the realization of the self-limiting transformer pre-prototype. Results of the quench model solution are evaluated in relation to the experimental results. The acceptable agreement between the experiments and theoretical modeling helps to construct the basis for the design of a 50 kVA to 100 kVA self limiting transformer device.