The large-scale penetration of intermittent sources brings serious stability problems to power systems with multiple energy complementary characteristics. The regulation performance of pumped storage plant (PSP) in suppressing frequency fluctuations induced by intermittent energy sources is essential to a multi-energy system. This paper aims to design an optimal control strategy for the pump-turbine governing system (PTGS) for a faster and smoother regulation process. To precisely describe the complicated hydraulic-mechanical transients in PTGS, a novel complete state-space model (CSSM) is proposed based on the electrical analogy method. The mathematical expressions of the subsystems in PSP are developed, and the simulation algorithm are detailed. The accuracy of the proposed model under various conditions is revealed by comparison with the method of characteristics (MOC) and measured data. Furthermore, the temporal-spatial constraint of CSSM when dealing with pipe segmentation is discussed. Subsequently, a linear quadratic regulator with anti-disturbance optimal tracking (LQR-ADOT) capability is designed based on the proposed nonlinear model. The integral of rotation speed deviation and the augmented state vector are employed to eliminate the steady-state error caused by the disturbance term and solve the trajectory tracking problem, respectively. Comparative experiments of LQR-ADOT with proportional-integral-differential (PID), fractional order PID (FOPID) and model predictive control (MPC) reveal that the proposed controller can effectively attenuate rotational speed oscillation and improve overall performance under various conditions. Notably, in frequency regulation, the settling time is decreased from 28.83 s to 16.82 s and the overshoot is reduced from 9.45% to 0.31% compared to traditional PID. • A novel state-space model of the PTGS, addressing pipelines and pump-turbine nonlinearities, is proposed. • A LQR with anti-disturbance and optimal target-tracking capability is designed. • The regulation quality of PTGS is analyzed comparatively in different scenarios. • The accuracy of the CSSM is validated by comparison with measured data and the MOC. • The computation complexity and efficiency of the CSSM is discussed. [ABSTRACT FROM AUTHOR]