For Artificial Neural Networks (ANN) to become more widely used in power systems and the future smart grids, ANN based algorithms must be capable of scaling up as they try to identify and control larger and larger parts of a power system. This paper goes through the process of scaling up an ANN based identifier as it is driven to identify increasingly larger portions of a power system. Distributed and centralized approaches for scaling up are taken and the pros and cons of each are presented. The New England/New York 68-bus power network is used as the test bed for the studies. It is shown that while a fully-connected (centralized) ANNs is capable of identification of the system with appropriate accuracy, the increase in the training times required to obtain an acceptable set of weights becomes prohibitive as the system size is increased.