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Wind farm power control is key to reliable large-scale wind integration. The design of a sophisticated wind farm controller, however, is challenging partly because there is a lack of models that appropriately simplify the complex overall dynamics of a large number of wind turbine control systems (WTCSs). In this paper, using system identification approaches, we develop a simple approximate model that attempts to mimic the active and reactive power dynamics of two generic WTCS models under normal operating conditions: an analytical model described by nonlinear differential equations, and an empirical one by input-output measurement data. The approximate model contains two parts-one for active power and one for reactive-each of which is a third-order system that would have been linear if not for a static nonlinearity. For each generic model, we also provide an identification scheme that sequentially determines the approximate model parameters. Finally, we show via simulation that, despite its structural simplicity, the approximate model is accurate and versatile, capable of closely imitating several different analytical and empirical WTCS models from the literature and from real data. The results suggest that the approximate model may be used to facilitate research on wind farm power control.