We report on the interpretation of the thermally stimulated depolarization current (TSDC) experiments, with partial polarization methods, on the dielectric alpha-relaxation. The results obtained on polyvinyl acetate are rationalized on the basis of the Boltzmann superposition principle in combination with a Kohlrausch-Williams-Watts (KWW) time decay of the polarization (with the beta exponent essentially temperature independent and equal to the value determined by conventional dielectric methods at T-g). From this analysis of the global TSDC spectrum we found a complex temperature dependence of the KWW relaxation time, which is Arrhenius-like at the lowest temperatures but crosses over to the Vogel-Fulcher behavior observed above T-g in the temperature range of the TSDC peak. On the basis of these results, we found the way of predicting the TSDC spectra measured after partial polarization procedures. We found that, the distribution of activation energies and compensation behavior deduced by following the standard way of analysis are associated to the assumption of an Arrhenius-like temperature dependence of the alpha-relaxation time in the temperature range explored by TSDC. Therefore we conclude that both the distribution of activation energies and compensation behavior obtained by following the standard way of analysis do not give a proper physical picture of the alpha-relaxation of glassy polymers around the glass-transition temperature. Our results also show that the partial polarization TSDC methods are not able to give insight about the actual existence or not of a distribution of relaxation times at the origin of the nonexponentiality of the alpha-relaxation of polymers.