Composite load model of Western Electricity Coordinating Council (WECC) is a newly developed load model that has drawn great interest from the industry. To analyze its dynamic characteristics with both mathematical and engineering rigors, a detailed mathematical model is needed. Although composite load model of WECC 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

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... odel in literature. This paper addresses a challenging problem of deriving detailed mathematical representation of composite load model of WECC from its block diagrams. In particular, 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 composite load model of WECC. The derived mathematical representation serves as an important foundation for parameter identification, order reduction and other dynamic analysis. Index Terms--Composite load model, dynamic load modeling, mathematical model, three-phase motor, DER_A model.