Due to the increasing importance of power system simulation for dynamic studies, this paper is dedicated to the derivation of highly accurate mathematical models for synchronous generator (SG) and excitation system (EXS) of a grid-connected hydroelectric distributed generation unit. Considering the substantial parameters in the proposed model, a two-stage system identification procedure on the ground of the load rejection (LR) tests and a particle swarm algorithm (PSO) is also recommended in the paper to determine parameters precisely. It is worth mentioning that a fast load angle measurement method is proposed in the paper to record the load angle and compute direct (d) and quadrature (q) axis components of the stator voltage and current. These values are used in the estimation procedure of SG parameters. Finally, the proposed model and parameter estimation method is adapted to an 11 MW hydroelectric unit, and the experimental results are discussed.