Electricity generation from moving currents without using dams (i.e., in-stream hydrokinetic electricity) has the potential to introduce multiple GW of renewable power to U.S. grids. This study evaluates a control system designed to regulate the generator rotor rate (rpm) to improve power production from in-stream hydrokinetic turbines. The control algorithm is evaluated using numerical models of both a rigidly mounted tidal turbine (TT) and a moored ocean current turbine (OCT) coupled to an induction electric machine model. The moored simulation utilizes an innovative approach for coupling a multiple degrees-of-freedom (DOF) nonlinear hydrodynamic/mechanical turbine model with a nonlinear electromechanical generator model. Based on the turbine torque-speed characteristic, as well as the asynchronous machine features, a proportional-integral (PI) controller is used to generate a correction term for the frequency of the three-phase sinusoidal voltages that are supplied to the asynchronous generator. The speed control of the induction generator through the supply frequency is accomplished by a simplified voltage source inverter (VSI). The simplified VSI consists of control voltage sources (CVSs), while the comparison with a real VSI using diodes and transistors, which are controlled by pulse width modulation (PWM) technique, is also presented. Simulations are used to evaluate the developed algorithms showing that rpm fluctuations are around 0.02 for a tidal turbine operating in a wave field with a 6m significant wave height and around 0.005 for a moored ocean current turbine operating in a wave field with a 2m significant wave height.