The existing second-order transfer function models (TFMs) for solar collector dynamic tests are reviewed in light of the heat transfer principles, their inherent relationship, and limitations. Then, another form of TFM in terms of the collector heat removal factor F-R is put forward in this study. And the equivalent relationships among different forms of TFMs are elucidated. Strict error analysis and the weighed least square (WLS) method are used to construct model coefficients in the TFMs due to random measurement errors of data points in dynamic tests. Accuracy levels of the three TFMs will be validated with experimental data in the companion paper (Deng et al., 2015). (C) 2015 Elsevier Ltd. All rights reserved.