Dynamic model of a complex system including PV cells, electric battery, electrical motor and water pump

The time dependent operation of several components of a PV pumping system (i.e. the PV cell, the PV array, the battery and the assembly electric motor—centrifugal pump) is modelled in this paper. 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 seven or four ordinary differential equations, respectively, according to the operating mode. A computer simulation code is developed. Clear days with high incident solar irradiance and high cell temperature Tcell are characterised by lower PV efficiency, while the cell efficiency is larger on cloudy days, when the temperature Tcell is smaller. The sun-to-user efficiency is larger during the winter months. The battery acts as a buffer, as the main part of the electricity supplied by the PV array is used to drive the motor. The value of the PV cell series resistance Rs causes the battery to operate under two different regimes: when Rs is larger, the battery is over-discharged once or twice each month in the cold season. In case Rs is small, the battery is over-charged once per month in the warm season. The electric power used to drive the motor is rather constant during the year.