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In the field of electrical insulation, polymers are progressively replacing formerly used materials. When such an insulator is subjected to a voltage gradient, an internal space charge and a polarization develop, eventually reducing the apparent electrical strength of the material. We have applied the pressure wave propagation (PWP) method to the study of HV insulators, such as low density polyethylene (LDPE) used for HV cables. The spatial charge distribution is successively measured in samples subjected to various processes. The influence of additives in the development of a space charge under electric stress is directly shown. We have also observed that the nature of the electrode-iinsulator interface strongly affects the charge distribution throughout the insulator, and that charge injection from these interfaces occurs at much lower applied voltage gradients than previously assumed. The evolution in time of the charge distribution in samples submitted to voltage gradients, at 20 and 700C, is studied. These results show that an equilibrium is reached, from which the life expectancy of materials and cables can be evaluated.