International Journal of Smart Grid Belkaid et al., Vol.2, No.4, December, 2018 Abstract— With the development of power electronics, directly driven permanent magnet synchronous generators (PMSGs) have attracted increasing interest from wind turbine (WT) producers because of their benefits over other variable speed WTs. PMSGs have a big number of poles and competitive costs. In this article simplified model and real modeling of a small power wind conversion system are offered. The system consists on a horizontal axis WT, PMSG, diodes rectifier, and a low voltage lead-acid battery. The models implemented in the Matlab-Simulink software can reflect the real physical phenomena. A longer calculation time is required when adopting the detailed model compared to the simplified model. The results of the simulation demonstrate that the suggested simplified model has enough precision to analyze the dynamics of the WT system. Index Terms—modeling, wind turbine, PMSG, simplified model. I. INTRODUCTION Global energy consumption has augmented dramatically these last years, because of the huge industrialization, which tends to increase more and more. The risks of fossil fuel depletion and their effects on weather change once again underline the importance of using renewable energy [1]. Among these, we meet the wind energy that has experienced strong growth and has become competitive through the developing of the wind turbine manufacturing, and the advances in semiconductor technology, as well as novel methodologies of turbine control at variable speeds. Nevertheless, several problems encountered, related on the one hand to the complication of wind energy conversion schemes; that is, the need for the gearbox between the turbine and the generator, and the instability of the wind speed on the other hand [2-4]. The use of well-designed wind structures, such as the high-pole PMSG, makes variable-speed wind turbine conversion systems more attractive than fixed-speed wind turbine systems because of the possibility of optimal power for diverse wind speeds, and reduced mechanical stress by eliminating the gear box, which enhances the reliability of the system, and reduced maintenance costs. [2,5]. Electrical systems in wind energy conversion can be subdivided into several main groups. Fixed speed systems use inductive generators connected directly to the network. Variable speed electrical systems use asynchronous machines, synchronous machines or unconventional machines. These are complicated and are all equipped with electronic converters. The chains of conversion of small power (some 100 W) and those of large power (more than 40 kW) are then very different. Either in isolated sites of small power or in systems connected to the network (also in small power), an intermediate DC bus is used before transforming the energy into alternating current. In the case of very small powers, the energy is directly consumed in direct current. The continuous bus has the advantage of more easily interconnecting various production systems (wind, photovoltaic, diesel, fuel cell, etc.) and electrochemical batteries that can be directly buffered on such buses. Such systems are called hybrid. The use of wind energy for the production of electrical energy is booming. The category of small wind turbines from 1 to 100 kW mainly owes its development generally in hybrid wind- photovoltaic or wind-diesel applications. Small power conversion chains are mainly for isolated sites. They are based on the use of a permanent magnet synchronous machine, which flows directly through a diode rectifier into a generally low voltage electrochemical accumulator (12 to 48 V). This configuration allows direct drive without speed multiplier and still connected directly to a diode rectifier. It has a reduced cost and fewer losses [6]. The ultimate goal is to contribute to the study of a hybrid wind and photovoltaic conversion chain with an electrochemical accumulator. In this paper, after a theoretical description of the characteristics of wind turbines, we propose a mathematical modeling of the wind energy system. The model is validated by numerical simulation via Matlab/Simulink software. The rest of the document is intended as follows; the second part gives the description of the studied system; followed by characteristics of the wind turbine in the third part; simplified model and real modeling of the global wind conversion system are offered respectively in part 4 and 5; the sixth part analyzes and comments on the results of the simulation. Finally, in the seventh part, conclusions and perspectives are proposed. Modeling of a Permanent Magnet Synchronous Generator in a Power Wind Generation System with an Electrochemical Energy Storage Abdelhakim BELKAID a,b , Ilhami COLAK c,* , Korhan KAYISLI c , Ramazan BAYINDIR d, belkaid08@yahoo.fr; ilhcol@gmail.com; korhankayisli@gmail.com; bayindir@gazi.edu.tr a Department of Electromechanics, University of BordjBouArreridj, El-Anasser 34030, BordjBouArreridj, Algeria b Automatic Laboratory of Setif (LAS), University of Setif 1, El Maabouda, Street of Bejaia, 19000 Setif, Algeria c Engineering and Architecture Faculty of Nisantasi University, Istanbul, Turkey d Department of Electrical & Electronics Engineering, Gazi University, Faculty of Technology, 06500, Turkey