We have carried out an extended Huckel calculation to rationalize the role of $CuO_3$ chains and the size effect of the charged model clusters for the following charged model culsters : ${{Cu_6}{O_{21}}^{28-},;{{Cu_6}{O_{22}}^{30-};,{{Cu_9}{O_{30}}^{39-};,{{Cu_9}{O_{32}}^{43-};,{{Cu_{12}{O_{38}}^{48-};,{{Cu_{15}{O_{50}}^{65-};,{{Cu_{18}{O_{54}}^{66-};,{{Cu_{18}{O_{55}}^{68-};,{{Cu_{24}{O_{70}}^{84-};and;{{Cu_{27}{O_{78}}^{93-}$ for high-$T_c$ superconductor $YBa_2Cu_3O_7$: ${{Cu_6}{O_{18}}^{22-};,{{Cu_9}{O_{26}}^{31-}};,{{Cu_{12}{O_{32}}^{36-};,{{Cu_{15}{O_{42}}^{49-};,{{Cu_{18}{O_{46}}^{50-};,{{Cu_{24}{O_{60}}^{64-};and;{{Cu_{27}{O_{66}}^{69-}$ for insulator $YBa_2Cu_3O_6$. The results show that the electronic structures and properties of the charged model clusters relating to high-$T_c$ superconductor are very sensitive to the size change of the clusters with various environmental effects, wherease those of the charged model clusters for insulator $YBa_2Cu_3O_6$ are monotonous to the size change. The $CuO_3$ chains along the b-direction may yield cooperative electronic coupling with the $CuO_2$ layers in determining both conducting and superconducting properties of $YBa_2Cu_3O_{7-x}$ system.