This paper aims to study the stability of low water head grid-connected primary frequency governing condition (PFGC) of pumped-storage unit (PSU). Firstly, a nonlinear mathematical model of the pumped-storage unit governing system (PSUGS) considering the nonlinear characteristics of water head loss and fifth-order synchronous generator is proposed, and the nonlinear state equation in power control mode is derived. On this basis, the PFGC bifurcation characteristics of the governing system coupled with the first-order and third-order synchronous generator models are explored, and the action mechanism of the excitation characteristics in the nonlinear PSUGS model is proposed in this paper on the nonlinear dynamic response of the system is revealed. Furthermore, the transient characteristics of the nonlinear PSUGS considering the fifth-order synchronous generator model under different water head conditions are studied, the multi-scale oscillation characteristics and stability of the PSUGS under low water head PFGC are analyzed, and the influence laws of hydraulic factors, mechanical factors and electrical factors on the stability of the nonlinear PSUGS are revealed. The results show that under the PFGC, the nonlinear PSUGS meets the supercritical Hopf bifurcation. The high frequency wavelet is excited by the generator excitation system in the PFGC oscillation of the governing system. At the same time, the low-frequency wavelet in the PFGC transient oscillation is mainly caused by the power grid stability and maps with the water hammer effect in the dynamic process. The results of this paper provide a theoretical basis for the stability analysis and optimal governing of low water head PFGC of PSU.