Research on dynamic analysis and optimization algorithms for large-scale power systems

Modern power systems face severe dynamic stability and operational scheduling challenges due to the rapid penetration of renewable energy sources (RES). Aiming at the problems of insufficient dynamic modeling accuracy, low efficiency of stability analysis, and the difficulty in balancing operational safety and economy under high RES integration, this study proposes an integrated theoretical and methodological framework for large-scale power system dynamic analysis and optimal scheduling. First, a sixth-order nonlinear differential equation model is established by integrating the electromechanical transients of synchronous generators, excitation regulation dynamics, load characteristics, and network power flow balance, which makes up for the deficiency of the traditional second-order swing equation in ignoring multi-subsystem coupling. Based on Taylor expansion at the equilibrium point, a linearized state-space representation is derived, and the analytical expressions of three key transient stability indices (the maximum rate of change of power angle, steady-state power angle deviation, and power angle oscillation amplitude) are obtained, which quantitatively reveal the influence of key parameters such as excitation gain and synchronous torque coefficient on system stability. Second, an improved ADMM-based distributed optimization algorithm with variable splitting and asynchronous iteration mechanisms is developed, which embeds dynamic security constraints into a multi-timescale scheduling framework. A two-layer control structure combining ADMM distributed global optimization and MPC centralized local control is constructed to solve the inefficiency of traditional centralized algorithms in large-scale system scheduling. Finally, the effectiveness of the proposed model and algorithm is verified on the IEEE 10-machine 39-bus system and extended to the 100-machine 300-bus system for scalability analysis.