A three-machine equivalent system frequency response model and its closed-form solution

The frequency response (FR) of the large-scale power system shows significant frequency spatial distribution characteristics (FSDC), still using uniform frequency models may cause large errors in the FR solution, and the FSDC should be preserved in the modeling. In this paper, a three-machine equivalent system frequency response (TM-SFR) model is proposed to preserve the FSDC by the parameter equivalent aggregation method, including load, network, and generator. The TM-SFR model is further simplified into a solvable forced vibration equation by loop-opening and approximation, and its closed-form solution (CFS) is obtained by the modal superposition method, to analytically solve the FR following a major disturbance. Case studies are introduced to verify the performance of the TM-SFR model and its CFS over the WSCC 9-bus system, the New England 39-bus system, and the IEEE 118-bus system. The results prove that the proposed model can preserve the intermachine frequency oscillation caused by the FSDC in various scenarios, and improve the FR solution accuracy at high solution speed, which can provide a more reliable basis for frequency stability emergency control.