This paper proposes a novel frequency aware robust economic dispatch (FARED) approach to exploit the synergistic capability of accommodating uncertain loads and renewable generation by accounting for both the frequency regulation effect and optimal participation mechanism of secondary regulation reserves for conventional units in response to uncertainties in the robust optimization counterpart of security constrained economic dispatch. The FARED is formulated as a robust optimization problem. In this formulation the allowable frequency deviation and the possible load or renewable generation curtailments are expressed in terms of variable uncertainty sets. The variables in the formulation are described as interval variables and treated in affine form. In order to improve the computational tractability, the dominant constraints which can be the candidates of tight transmission constraints are determined by complementarity constraints. Then the robust optimization problem is simplified to a bilinear programming problem based on duality theory. Finally, the effectiveness and efficiency of the proposed method are illustrated based on several study cases.