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This paper presents a reformulation for the automatic generation control (AGC) in a decomposed convex relaxation algorithm. It finds an optimal solution to the AC optimal power flow (ACOPF) problem that is secure against a large set of contingencies. The original ACOPF problem which represents the system without contingency constraints, is convexified by applying the second-order cone relaxation method. The contingencies are filtered to distinguish those that will be treated with preventive actions from those that will be left for corrective actions. The selected contingencies for preventive action are included in the set of security constraints. Benders decomposition is employed to decompose the convexified Security-Constrained ACOPF problem into a master problem and several security check sub-problems. Sub-problems are evaluated in a parallel computing process with enhanced computational efficiency. AGC within each sub-problem is modeled by a set of proposed valid constraints, so the procured solution is the physical response of each generation unit during a contingency. Benders optimality cuts are generated for the sub-problems having mismatches and the cuts are passed to the master problem to encounter the security-constraints. The accuracy of the relaxation results is verified using the presented tightness measure. The effectiveness of the presented valid AGC constraints and scalability of the proposed algorithm is demonstrated in several case studies.