Considering the automatic generation control (AGC) system as an intermediary between the economic dispatch problem and synchronous generator dynamics, this study introduces a novel formulation for the AGC system. The proposed scheduling framework is based on a stochastic $N-1$ lossy network-constrained economic dispatch problem formulated as a mixed-integer linear programming instance. Transmission losses are represented through piecewise linear expressions. After the primary frequency control finishes, the proposed scheduling methodology selects the generation units that will be activated and determines their regulation participation factors to minimize the activation and operational costs in a two-stage stochastic problem, incorporating the load-voltage dependency phenomenon, and modeling transmission power flow and power losses using linear lossy shift-factors. The proposed formulation also considers the distinctive possibility of AGC units to both increase and decrease power for addressing under-frequency events economically, offering an effective generation capability that co-optimizes energy and reserves, providing a more flexible and efficient control strategy compared to traditional AGC systems. The effectiveness of the proposed methodology is demonstrated in a 50-bus electrical system, evaluating its performance with diverse operational conditions and contingency generation events using DIgSILENT PowerFactory. Extensive computational RMS experiments are conducted to assess the frequency stability in the electrical power system.