This paper presents a small signal modeling of a direct-driven permanent magnet synchronous generator (PMSG) based on wind turbine which is connected to the grid via back-to-back converters. The proposed small signal model includes two maximum power point tracking (MPPT) controllers: tip speed ratio (TSR) control and optimal torque control (OTC). These methods are analytically compared to illustrate MPPT and power smoothing capability. Then, to compare the MPPT and power smoothing operation of the mentioned methods, simulations are performed in MATLAB/Simulink software. From the simulation results, OTC is highly efficient in power smoothing enhancement and has clearly good performance to extract maximum power from wind; however, TSR control has definitely fast responses to wind speed variations with the expense of higher fluctuations due to its non-minimum phase characteristic. (C) 2014 Elsevier Ltd. All rights reserved.