In this work we analyze the resulting RGE running of couplings of additional U(1) appearing in MSSM-like models coming from orbifold compactifications of heterotic strings. We calculate the coefficients of the beta function to obtain the values of the coupling constant of the additional Z' in the unification scale MGUT and Z' breaking scale, both as a functions of MGUT. We indicate the first most frequent of these results and the total range of values. At low energies, we find in realistic models that the structure constant of Z' forces can have values from 18.732 to 95.853, which might influence future searches of Z' at colliders. We also identify models that present unification and describe the spectrum of some models.