A complex time-dependent solar water pumping system is analysed in this paper. Several existing models (e.g. for the PV cell, the battery and the assembly electric motor-centrifugal pump) are used. New models are proposed for PV array and water storage tank operation. The system has two main operating modes, which depend on the level of the incident solar global irradiance. The mathematical model consists of systems of eight or five ordinary differential equations, as a function of the operating mode. Using a water storage tank improves the stability of PV pumping system operation. The mechanical power stored in the water tank is rather constant during the year. The fraction of collected solar energy that is stored in the water's gravitational energy is higher during the winter months, during the cloudy days and around sunrise and sunset. It is smaller during the summer months, during the clear sky days and in the middle of the day. The fraction of the power supplied by the battery that is stored in the gravitational energy of water is almost constant during the year. (C) 2002 Elsevier Science Ltd. All rights reserved.