## 2 Conceptual Model for Coordinated Automatic Generation Control in a Multimachine Smart System
### Economic and Technical Considerations  
A key feature of this model is its ability to balance economic and technical objectives simultaneously. The model coordinates these objectives to ensure that the power system operates optimally, with neither economic efficiency nor technical performance being compromised. This conceptual model, which is shown in Figure 1, represents a holistic approach to power system management, integrating both economic and technical considerations into a single, adaptable framework that can respond to the dynamic demands of a multimachine smart system. According to the conceptual model which is shown in Figure 1, the proposed framework for AGC integrates NLMPC with data-driven methods to address dynamic challenges in multimachine power systems. The process begins with system monitoring and data  
Figure 1: Proposed conceptual framework for an NLMPC-based approach to automatic generation control. acquisition, where real-time measurements of critical variables such as voltage, frequency, rotor speed, turbine temperature, and generator outputs are collected through sensors. Historical and real-time data are logged to support further analysis, and disturbances, including sudden frequency or voltage deviations and line outages, are promptly identified. The next stage involves dynamic modeling and system identification. A dynamic state-space model is developed to capture the physical and electrical dynamics of the system, including equations governing rotor angle, speed deviations, turbine dynamics, and governor mechanisms. To enhance the model's accuracy, data-driven methods are employed to estimate unmodeled dynamics and disturbances. These methods predict nonlinear and time-varying behaviors that are not captured by first-principles models. Using this integrated dynamic and data-driven model, the NLMPC framework enters the prediction phase, where it estimates the system's future behavior over a defined prediction horizon. A multi-objective cost function is formulated to optimize key objectives, including minimizing generation costs, frequency and voltage deviations, and emissions penalties. During this stage, the dynamic constraints of the system, such as governor saturation, generation rate constraints (GRC), and turbine thermal limits, are incorporated into the optimization problem. Real-time optimization follows, where the NLMPC solves the optimization problem to determine the optimal control actions that balance system stability requirements with cost minimization. The framework employs a hierarchical control structure consisting of three levels. At the primary level, real-time regulation of power flow and frequency is managed. The secondary level focuses on technical parameters such as oscillation damping, voltage regulation, and loss minimization. The tertiary level adapts generation schedules to balance technical and economic objectives over the long term. Control actions derived from the optimization are then implemented in real time. Optimized control signals, such as valve positions and excitation voltages, are sent to the respective components, including turbines and governors, for immediate execution. A feedback mechanism ensures continuous monitoring and adjustment of control actions in response to real-time system data, maintaining system stability and performance. A key innovation in the proposed framework is the error correction stage, where discrepancies between predicted and actual system behavior are identified. Data-driven models are periodically retrained using updated operational data to improve prediction accuracy. This adaptive capability allows the controller to dynamically respond to unmodeled disturbances and changes in system conditions, ensuring robust operation. The final stage focuses on performance evaluation and adaptation. Simulation results validate the effectiveness of the framework in minimizing deviations and optimizing operational costs under various scenarios.