The analysis by TSDC of a large variety of cables subjected to long annealing times, has resulted in spectra that sometimes show an oscillation of the current peak observed at 99°C. This process has been observed in some cables only and it is scarcely reproducible. We present an explanation of this behavior based on the formation of charge packets and some other assumptions: charge injection occurs mainly from the negative electrode, and chemical components that act as trapping centers are diffused continously from the semiconducting layers into the bulk during annealing. When the field is applied the negative electrode injects charge that get trapped in these centers, so that a virtual electrode is formed. The electric field created by this layer results in a decrease of the field in the gap between the injecting and virtual electrodes, preventing new charge injection. On the other hand, during polarization the virtual electrode shifts through the insulation bulk towards the opposite electrode. This layer that acts as a virtual electrode becomes neutral by means of recombination when it reaches the opposite electrode, so that the electric field in the region between the electrodes recovers its initial value and the whole process happens again cyclically. This model can explain the observed TSDC oscillating spectra of annealed samples. It can also explain why the oscillations can not be observed in most cases.