###### Abstract  
Wind turbine generating systems (WTGSs), which are conventionally connected to high voltage transmission networks, have frequently been employed as distributed generation units in today's distribution networks. In practice, the distribution networks always have unbalanced bus voltages and line currents due to uneven distribution of single or double phase loads over three phases and asymmetry of the lines, etc. Accordingly, in this study, for the load flow analysis of the distribution networks, Conventional Fixed speed Induction Generator (CFIG) based WTGS, one of the most widely used WTGS types, is modelled under unbalanced voltage conditions. The Developed model has active and reactive power expressions in terms of induction machine impedance parameters, terminal voltages and input power. The validity of the Developed model is confirmed with the experimental results obtained in a test system. The results of the slip calculation based phase-domain model (SCP Model), which was previously proposed in the literature for CFIG based WTGSs under unbalanced voltages, are also given for the comparison. Finally, the Developed model and the SCP model are implemented in the load flow analysis of the IEEE 34 bus test system with the CFIG based WTGSs and unbalanced loads. Thus, it is clearly pointed out that the results of the load flow analysis implemented with both models are very close to each other, and the Developed model is computationally more efficient than the SCP model. wind energy; induction generators; unbalanced conditions; distribution systems; power flow +
Footnote †: journal: Applied  
announced by the General Directorate of Renewable Energy of the Republic of Turkey, at least 30% of the energy needs are intended to be derived from renewable energy sources by 2023 [3]. Wind energy, an important renewable energy source, is a resource where countries can benefit from the advantages of their geographical location. Wind energy is converted into electrical energy by the wind turbine generator systems (WTGSs) [4]. WTGSs are generally formed with a propeller and a generator. When compared to synchronous generators, being smaller in size and having lower operation costs, asynchronous generators are widely preferred in small sized WTGSs. WTGSs can be classified under two main headings that are conventional fixed speed WTGSs and variable speed WTGSs [5]. Variable speed WTGSs have high installation and operating costs since they include high-tech power electronic components and control circuits. As a result of this, instead of variable speed induction generators, CFSIGs are preferred and are generally connected to low or medium voltage distribution networks directly. Large-scale wind farms are typically connected to the high-voltage transmission system; however, small and medium-scale distributed generation units based on wind energy are placed in the distribution systems. Generally, distribution systems are structured and operated radially; thus, it is expected to be supplied from a single source. With the increasing usage of WTGSs, multiple feeding points are emerging on the distribution system. This can cause power flow in both directions (towards source or load), unlike the conventional system operation [6]. For example, in a case where the distribution network is dominated by wind energy resources, this distribution network can behave as an active network and can give feedback to the high voltage bus. As a distributed generation system, not only WTGSs, but also other renewable or non-renewable generation systems have an impact on the conventional distribution network's voltage profile and energy losses [6; 7]. It should be acknowledged that these kinds of operations can cause a number of technical difficulties and operational issues [8]. In practice, the distribution networks always have unbalanced bus voltages and line currents due to single or double phase loads, unsymmetrical line impedances, single or two phase spurs, etc. [9].