Cellular polymeric materials may show interesting quasi-piezoelectric properties, upon charging under specific conditions of electrical field, temperature, pressure and environment. Electrical charging is the trigger of electret properties. It has been proved that the occurrence of electrical avalanches in the cavities which are present in a material is associated with the appearance of electret behavior, but the precise nature of the phenomena involved in this transformation is still under investigation. This paper provides a contribution to the study of these materials focusing on the relation between the appearance of electret properties and the presence of charge injection and partial discharge phenomena. For this purpose, space charge, partial discharges and low-frequency polarization measurements were carried out on polypropylene (PP) cellular materials, at different fields and temperatures. The existence of a threshold field for the start up of electret behavior that is larger than the threshold for space charge injection and partial discharge inception was observed. Steady charge is accumulated in the material, thus generating electret behavior, only if partial discharge repetition rate becomes sufficiently high and space charge is injected from electrodes. Space charge measurements were performed through the pulsed electroacoustic technique, in spite of significant attenuation of acoustic waves due to the cellular nature of the materials. Partial discharge measurements were carried out by an advanced system recording each discharge pulse, thus allowing observation of single and multiple pulses, besides achieving statistics of discharge pulse amplitude and phase. By such approach, space charge and partial discharge measurements proved to constitute a valuable tool to investigate the phenomena leading to piezoelectric behavior and, also, to infer electret time stability and optimize charging methodologies.