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.