Neural networks are used in a wide number of fields including signal and image processing, modeling and control and pattern recognition. Some of the most common type of neural networks is the multilayer perceptrons and the recurrent neural networks. Most of these networks consist of large number of neurons and hidden layers, which results in a longer training time. A Generalized Neuron (GN) has a compact structure and overcomes the problem of long training time. Due to its simple structure and lesser memory requirements, the GN is attractive for hardware implementations. This paper presents the online training of a GN with the Particle Swarm Optimization (PSO) algorithm. A comparative study of the GN and the MLP online trained with PSO is presented for function approximations. The GN based identification of the Static VAR Compensator (SVC) dynamics in a 12 bus FACTS benchmark power system trained online with the PSO is also presented