The inverse problem of recovering the potential transformer primary signal waveform using secondary signal waveform and information about the secondary load is solved here via two inverse neural network models. The first model uses two recurrent neural networks trained in an off-line mode. The second model is designed with the use a Dynamic Evolving Neural-Fuzzy Interface System (DENFIS) and suited for on-line application and integration into existing protection algorithms as a parallel module. It has the ability of learning and adjusting its structure in an on-line mode to reflect changes in the environment. The model is suited for real time applications and improvement of protection relay operation. The two models perform better than any existing and published models so far and are useful not only for the reconstruction of the primary signal, but for predicting the signal waveform for some time steps ahead and thus for estimating the drifts in the incoming signals and events.