This project investigates when irrational vertex operator algebras (VOAs) satisfy the strong unital property. We will focuses on two families of irrational VOAs: the orbifold Heisenberg VOA and the affine Lie algebra VOA at irrational level. Our strategy is to translate the verification of the strong unital property into a problem of solving a large system of algebraic equations derived from explicit structural data. VOAs that satisfy this property give rise to generalized Verlinde bundles, vector bundles on the moduli space of stable curves which play a central role in moduli theory and conformal field theory.