This paper presents a comprehensive model of the Back-to-Back (BtB) HVDC system based on the three-level Neutral-Point Diode Clamped (NPC) converter. Based on the developed model, a systematic design procedure for i) the ac-side controllers, ii) the voltage balancer of the dc-side capacitors, and iii) the net dc-bus voltage controller, are presented. The model is developed based on the generalized state-space averaging method and the principle of power balance. The developed model precisely describes the system dynamics if the ac grids are strongly or moderately stiff, and offers acceptable precision otherwise. The averaged nature of the model inherently renders itself for analysis in the SIMULINK/MATLAB environment, and thus provides a computationally efficient tool for the design and the performance evaluation of the control. The accuracy of the developed model and the controls are validated by comparing the results from MATLAB/SIMULINK with those obtained from the exact switching model of the system, based on digital time-domain simulation studies, using the PSCAD/EMTDC software package.