In this paper, a mathematical model and the structure of variable speed pump storage unit (VSPSU) are proposed. Transient processes of VSPSU main parameters are analyzed. The influence of transients on the operating conditions of electrical power system is discussed. The system of non-linear differential equations given in matrix form and representing the VSPSU mathematical model is solved by digital integration. Electrodynamic transients of VSPSU generator and pump operation are simulated by imitation of the active and reactive power variation in the electrical power system. Marginal hydroelectric parameters of the pump storage unit are evaluated. Excitation control algorithms are based on the functional structures of voltage and current controllers represented by compensation units consisting of proportional integrating and integrating-differentiating filters.