A non-phthalate catalyst system for olefin polymerization, comprising: (a) a solid Ziegler-Natta catalyst composition comprising a transition metal, a Group 2 metal, and one or more halogens; and one or more internal electron donor compounds selected from the group consisting of: i) a diether compound having a formula of and ii) a succinate compound having a formula of wherein: each of R 1 and R 2 is independently H or an alkyl, cycloalkyl, aryl, or aralkyl group, each having from 1 to 18 carbon atoms; or, R 1 and R 2 together form one or more saturated or unsaturated mono- or poly- cyclic structures; each R 3 is independently an alkyl, aryl, or aralkyl group having from 1 to 18 carbon atoms, each R 4 is H or R 3; each of R 13 and R 14 is independently a C 1 to C 18 hydrocarbyl group; and wherein each of R 1, R 2, R 3, R 4, R 13, and R 14 can contain one or more heteroatoms that replace one or more carbon atoms in the hydrocarbyl group, wherein the one or more heteroatoms are selected from the group consisting of halogens, P, N, O, S, and Si; and (b) an external electron donor compound consisting of one or more compounds selected from the group consisting of: i) a triester compound having a formula of and ii) an oxo-substituted diester compound having a formula of wherein: each R is independently a C 1 -C 10 hydrocarbyl group, each R' is independently H or R, each n is independently an integer from 1 to 4, and n' is an integer from 0 to 4. (a) a solid Ziegler-Natta catalyst composition comprising a transition metal, a Group 2 metal, and one or more halogens; and one or more internal electron donor compounds selected from the group consisting of: i) a diether compound having a formula of and ii) a succinate compound having a formula of wherein: each of R 1 and R 2 is independently H or an alkyl, cycloalkyl, aryl, or aralkyl group, each having from 1 to 18 carbon atoms; or, R 1 and R 2 together form one or more saturated or unsaturated mono- or poly- cyclic structures; each R 3 is independently an alkyl, aryl, or aralkyl group having from 1 to 18 carbon atoms, each R 4 is H or R 3; each of R 13 and R 14 is independently a C 1 to C 18 hydrocarbyl group; and wherein each of R 1, R 2, R 3, R 4, R 13, and R 14 can contain one or more heteroatoms that replace one or more carbon atoms in the hydrocarbyl group, wherein the one or more heteroatoms are selected from the group consisting of halogens, P, N, O, S, and Si; and i) a diether compound having a formula of and ii) a succinate compound having a formula of wherein: each of R 1 and R 2 is independently H or an alkyl, cycloalkyl, aryl, or aralkyl group, each having from 1 to 18 carbon atoms; or, R 1 and R 2 together form one or more saturated or unsaturated mono- or poly- cyclic structures; each R 3 is independently an alkyl, aryl, or aralkyl group having from 1 to 18 carbon atoms, each R 4 is H or R 3; each of R 13 and R 14 is independently a C 1 to C 18 hydrocarbyl group; and wherein each of R 1, R 2, R 3, R 4, R 13, and R 14 can contain one or more heteroatoms that replace one or more carbon atoms in the hydrocarbyl group, wherein the one or more heteroatoms are selected from the group consisting of halogens, P, N, O, S, and Si; and each of R 1 and R 2 is independently H or an alkyl, cycloalkyl, aryl, or aralkyl group, each having from 1 to 18 carbon atoms; or, R 1 and R 2 together form one or more saturated or unsaturated mono- or poly- cyclic structures; each R 3 is independently an alkyl, aryl, or aralkyl group having from 1 to 18 carbon atoms, each R 4 is H or R 3; each of R 13 and R 14 is independently a C 1 to C 18 hydrocarbyl group; and wherein each of R 1, R 2, R 3, R 4, R 13, and R 14 can contain one or more heteroatoms that replace one or more carbon atoms in the hydrocarbyl group, wherein the one or more heteroatoms are selected from the group consisting of halogens, P, N, O, S, and Si; and (b) an external electron donor compound consisting of one or more compounds selected from the group consisting of: i) a triester compound having a formula of and ii) an oxo-substituted diester compound having a formula of wherein: each R is independently a C 1 -C 10 hydrocarbyl group, each R' is independently H or R, each n is independently an integer from 1 to 4, and n' is an integer from 0 to 4. i) a triester compound having a formula of and ii) an oxo-substituted diester compound having a formula of wherein: each R is independently a C 1 -C 10 hydrocarbyl group, each R' is independently H or R, each n is independently an integer from 1 to 4, and n' is an integer from 0 to 4. each R is independently a C 1 -C 10 hydrocarbyl group, each R' is independently H or R, each n is independently an integer from 1 to 4, and n' is an integer from 0 to 4.