With the increasing penetration of renewable energy resources, power systems face new challenges in balancing power supply and demand and maintaining the nominal frequency. This paper studies load control to handle these challenges. In particular, a fully distributed automatic load control (ALC) algorithm, which only needs local measurement and local communication, is proposed. We prove that the load control algorithm globally converges to an optimal operating point which minimizes the total disutility of users, restores the nominal frequency and the scheduled tie-line power flows, and respects the load capacity limits and the thermal constraints of transmission lines. It is further shown that the asymptotic convergence still holds even when inaccurate system parameters are used in the control algorithm. In addition, the global exponential convergence of the reduced ALC algorithm without considering the capacity limits is proved and leveraged to study the dynamical tracking performance and robustness of the algorithm. Lastly, the effectiveness, optimality, and robustness of the proposed algorithm are demonstrated via numerical simulations.