With the development of wind turbine technology, more wind turbines operate in the partial load region, where one of the main objectives is to maximize captured wind energy. This paper presents the development of an optimal control framework to maximize wind energy capture for wind turbines with limited rotor speed ranges. Numerical optimal control (NOC) techniques were applied to search for the achievable maximum power coefficient, thus maximum wind energy capture. Augmentations of these optimal techniques significantly reduced the computational cost. Simulation results show that, in comparison with the traditional torque feedback and conventional optimal control algorithms, the proposed augmented optimal control algorithm increases the harvested energy while minimizing the computational expense for speed-constrained wind turbines during partial load operation.