  The Western Electricity Coordinating Council (WECC) composite load model is a
newly developed load model that has drawn great interest from the industry. To
analyze its dynamic characteristics with both mathematical and engineering
rigor, a detailed mathematical model is needed. Although WECC composite load
model is available in commercial software as a module and its detailed block
diagrams can be found in several public reports, there is no complete
mathematical representation of the full model in literature. This paper
addresses a challenging problem of deriving detailed mathematical
representation of WECC composite load model from its block diagrams. In
particular, for the first time, we have derived the mathematical representation
of the new DER_A model. The developed mathematical model is verified using both
Matlab and PSS/E to show its effectiveness in representing WECC composite load
model. The derived mathematical representation serves as an important
foundation for parameter identification, order reduction and other dynamic
analysis.
