Problem $1$ Three single$-$phase transformers are connected in delta$-$grounded wye serving an unbalanced load. The ratings of the three transformers are as follows: $$ Phase AB: $100$ kVA, $12,470-120$ V$,=1\mathrm{.}3+1\mathrm{.}7\%$ Phase BC: $50$ kVA, $12,470-120$ V$,=1\mathrm{.}1+1\mathrm{.}4\%$ Phase CA: same as Phase B$-$C transformer The unbalanced loads are: $$ Phase a: $40$ kVA, $0\mathrm{.}8$ lagging power factor at $$ Phase b: $85$ kVA, $0\mathrm{.}95$ lagging power factor at $$ Phase c: $50$ kVA, $0\mathrm{.}8$ lagging power factor at a$.$ Determine the forward and backward sweep matrices for this connection. b$.$ Computer the load currents. c$.$ Compute the primary line$-$to$-$neutral voltages. d$.$ Compute the primary line$-$to$-$line voltages. e$.$ Compute the primary currents. f$.$ Compute the currents in the delta primary windings. g$.$ Compute the transformer bank power loss.