The design of reliable controllers for wind energy conversion systems (WECSs) requires a dynamic model and accurate parameters of the wind generator. In this paper, a dynamic model and the parameter measurement and control of a direct-drive variable-speed WECS with a permanent magnet synchronous generator (PMSG) are presented. An experimental method is developed for measuring the key parameters of the PMSG. The measured parameters are used in the design of the controllers. The generator-side converter is controlled using a vector control scheme that maximizes the power extraction under varying wind speeds. A model predictive controller (MPC) is designed for the grid-side voltage source converter (VSC) to regulate the active and reactive power flows to the power grid by controlling the d- and q-axis currents in the synchronous reference frame. The MPC predicts the future values of the control variables and takes control actions based on the minimum value of the cost functions. To comply with the grid code requirement, a modified design approach for an LCL filter is presented and incorporated into the system. The design process is simple and incorporates significant filter parameters while avoiding iterative calculations. The comparative analysis of the designed filter with conventional L, LC, and iterative LCL filters demonstrates the effectiveness of the modified design approach. The proposed wind energy system with MPC and LCL filter is simulated in MATLAB/Simulink and experimentally implemented in the laboratory using the dSpace digital signal processor (DSP) system. The simulation and experimental results validate the efficacy of the designed controllers using the measured parameters and show dynamic and steady-state performance under varying wind speeds.