can write this without simlarity This study addresses the per unit calculation and steady$-$state analysis of a $500$ MVA, $20$ kV$,50$ Hz synchronous generator with specified inductances and resistances for stator and field windings. The inductances LdL$\_$dLd$,$ LqL$\_$qLq$,$ LadL$\_\{$ad$\}$Lad$,$ and LaqL$\_\{$aq$\}$Laq$$ were calculated, followed by determining base values for stator and rotor quantities using machine ratings. The per unit values of key electrical parameters were derived. Additionally, damper windings' per unit values were integrated, and the internal angle $\backslash$delta and other electrical variables were computed under rated conditions. The dq$0$ transform of three$-$phase currents was also explored, with analytical and SIMULINK$-$based validation of idi$\_$did$$ and iqi$\_$qiq$$ under different axis alignments, revealing the effects of axis orientation on current components. This comprehensive analysis facilitates a deeper understanding of synchronous generator behavior under steady$-$state and transient conditions.