Recently, more frequency and voltage stability issues have been caused by the uncertain load demand and intermittent renewable energy generation in smart grids. This has put significant pressure on turbine governor action. One potential solution is load participation in primary control. In this study, we investigate a general class of local load control (LLC) to provide grid frequency and voltage support while minimizing the pre-defined disutility to utilities and clients. Our approach relies only on local frequency and voltage measurements. We prove that the network dynamics under optimality conditions solve the dual problem of the disutility function adaptively, providing a principled way to guide forward engineering in local load control design. Simulation-based comparative study of choosing different types of disutility functions is conducted on response performance concerning frequency/voltage nadir and steady-state error. Moreover, the effectiveness and rationality of the proposed approach are verified in MATLAB/SIMULINK under various scenarios, including load variations, renewable power output fluctuations, and different penetrations of renewable energy.