Frequency Response Model and Its Closed-Form Solution of Two-Machine Equivalent Power System

For the purpose of considering the spatial-temporal characteristics (STC) of large-scale interconnected power system in the modeling, calculation, and analysis of dynamic frequency response (FR), this paper establishes a two-machine equivalent frequency response (TEFR) model and gets its closed-form solution (CFS), which can be used to analytically analysis and fast calculation. In the modeling, the network structure is idealized through simplified matrix of DC power flow and the system is reduced to a typical two-degree-of-freedom vibration system with viscous damping and excitation forces through breaking closed-loop and variable approximation. After that, modal analysis method is managed to obtain TEFR-CFS which represent the dynamic FR of TEFR model as the superposition of system FR and frequency oscillation. And the influence of parameters on frequency oscillation, such as electrical distance, inertial distribution, initial disturbance power distribution coefficient, etc., are analyzed. Furthermore, the analytical expressions of the key characteristics of dynamic FR, such as the initial decline slope, the nadir and the arrival time of nadir, etc., are derived. Numerical simulation proves that STC has significant influence on FR and can be described by TEFR model, TEFR-CFS and the expressions of its key characteristics with accuracy and efficiency.