Another option to backup protection of the transformer would be to use an overcurrent or distance relay. Also, you might possibly be able to use the neutral CT for ground protection, but you'll have to investigate this very carefully. The neutral current more often than not will reverse for...
This may or may not be applicable, but...
If you look at IEEE Std 80 - IEEE Guide for Safety in Substation Grounding, it gives eqns. for calculating the upper and lower ground system resistance that can be obtained from your soil resistivity model. It may be that no matter how much copper you...
