This contribution wants to show some recent applications of neural networks in the field of power electronics, with particular emphasis on the sensorless control of AC drives and examines improvements that can be attained when using linear neural networks. At first it presents some theoretical aspects of linear neural networks, particularly the TLS EXIN neuron. Then it describes some original applications in electrical drives and power quality as follows: 1) least square and neural identification of electrical machines 2) neural sensorless control of AC drives 3)neural enhanced single-phase DG system with APF capability Simulation and experimental results are provided to validate the theories.