There are 3 steps in order to design a medium voltage cable:
1) short-circuit current withstand
2) ampacity [allowable current-carrying capacity]
3) Voltage drop [mainly if a large induction motor will start D.O.L or Wye- Delta].
1) Usually for 13.8 kV the average rms short-circuit current will be 30 kA and the protection clearance time could be -close 0.1 sec and reserve 0.5 sec. For 30 kA and 0.5 sec fault clearance time, copper conductor, XLPE insulation [250 dgr.C short-time temperature limit] 300 kcmil [150 sqr.mm] will be suitable.
2) Ampacity could be stated from NEC art. 310. Let's say the cable will run in earth at 90 RHO -thermal resistance 20 dgr.C. Transformer rated current will be 1000/13.8/sqrt(3)=41.84 A.
According to Table 450.3(A) Maximum Rating or Setting of Overcurrent Protection for Transformers for less than 6% transformer rated impedance overcurrent protection required is 600% transformer rated [6*41.84=251 A].
Art.240.4 Protection of Conductors: overcurrent protection shall not be more than feeder ampacity[for less than 800 A could be a little more in certain conditions]
According to NEC Art.310 Table 310.60(C)(83) Conductors Cabled Within an Overall Covering (Three-Conductor Cable), Directly Buried in Earth. For Detail 5[one cable] 5001-35000 V 250 kcmil copper conductor 90oC insulation rated ampacity is 380 A.