###### Abstract
There are balanced power flow models for directly network connected CFIGs in the literature. [10; 11]. The use of these models for unbalanced distribution system power flow analysis may lead to erroneous results [12]. Therefore, a symmetrical component based model of induction generators is introduced in the study of [PERSON] et al. [12] and [PERSON] et al. [13]. The accurate estimation of the rotor slip value is difficult and requires computationally expensive iterative methods. In addition to this, the need for a solution for complex phase currents/voltages brings extra computational complexity for power flow analysis. Therefore, in most of the unbalanced power flow analyses in the literature, asynchronous generators are modeled as balanced and fixed Active (P)-Reactive (Q) Power sources by ignoring the effect of the imbalance (Constant P, Q Model) [14; 15; 16]. In some studies, this simplified model has been updated by the calculation of the reactive power demand from the grid. For this purpose, the reactive power demanded from the grid brought into a function of positive sequence voltage (\(V_{sp}\)) and machine impedance parameters, and, thereby, this updated model has been applied to power flow analysis (Constant P, Q(\(V_{sp}\)) Model) [14; 15; 16]. Preliminary results of this paper were presented in a conference [17]. In addition to preliminary results, this study includes load flow analysis and experimental validation of the model. In this paper, for the load flow analysis of the distribution networks, CFIG based WTGSs are modelled under unbalanced voltage conditions. The Developed model has active and reactive power expressions in terms of induction machine impedance parameters, input power and terminal voltages. In the Developed model, magnitude of the positive- sequence rotor side voltage is expressed via bi-quadratic equation, which is generally used to calculate node voltages in the load flow analysis [10; 11; 14; 18; 19]. In the study of [PERSON] and [PERSON] [18], a slightly modified model of the [PERSON] et al. study [10] is given and the advantages of the bi-quadratic equation based models are highlighted. In addition, such models have an iterative algorithm to find the positive- and negative-sequence rotor side powers, the sum of which is equal to the wind power. Unlike the slip calculation based models, the Developedmodel does not require prior knowledge on the angles of sequence voltages and currents, thus it can be implemented with a lesser number of operations. To verify the Developed model for WTGSs, a laboratory testing was carried out. An induction generator coupled with a controllable induction motor was used. Finally, both the Developed Model and the SCP Model [12] are applied by the authors to phase domain power flow analysis in a 34 bus radial distribution test system published by IEEE [20], and the results were analyzed comparatively. In addition, the complexity analysis of these two models are compared in terms of required mathematical operations. The three-phase load flow analysis of models was performed via Matlab 2012a [21] by using open source software OpenDSS (Open Distribution System Simulator) [22] program libraries. The library files of models (DLLs (Dynamic Link Library)) were created in Delphi\({}^{\text{\textregistered}}\)XE5.