Historically, the structure of an Artificial Neural Network (ANN) has been defined through trial-and-error or excessive computation leading to reduced accuracy and increased training time, respectively. For many disciplines, especially power systems, models must both be accurate and support fast computations in order to be viable for large-scale use. These requirements often render poorly structured ANNs useless. However, using power system behavioral knowledge to create an ANN structure could provide a near best case estimate for a model that maximizes accuracy and minimizes computational run-time. This paper considers the relationship between the dominant modes of a power system and the hidden neurons (units) in an ANN. In this study, several ANNs were created with varying number of neurons. These ANNs were used to predict rotor angle response to faults at generator buses that were cleared at varying times and compared with actual responses, as obtained through simulation. The number of neurons used include the hypothesized dominant mode number and five known heuristic estimates. The resultant method is a domain-dependent algorithm to structure an ANN without relying on trial-and-error or additional unnecessary computation time for power system models.