Frequency optimisation and performance analysis of photovoltaic-battery water pumping system

Photovoltaic-battery water pumping systems (PVBWPSs) can provide fresh water and irrigation in off-grid areas. Previous research has focused on direct current (DC) voltage versus frequency to control the speed of a pump. However, the use of photovoltaic (PV) modules with batteries to create a high-performance hybrid system with fixed and variable frequencies of supply power remains challenging, particularly in an off-grid water pumping system with limited power and water supplies. Based on a conventional frequency conversion mode and power balance, this work addresses fixed and variable frequencies under changing solar irradiance conditions for a PV system and a PV system combined with a battery (PVB) mode to improve energy utilisation. According to DC power balance and centrifugal pump theories, a mathematical model of the power supply frequency in the PVBWPS is presented, as well as the loss of load probability (LLP) and pumping coefficient (C_p), through which the performance metrics are obtained. The formulated models are validated through the experimental PVBWPS, which includes 2.19 kWp PV modules, a 9.6 kWh battery bank, and a 0.75 kW centrifugal pump. The experimental results show that the root mean square error (RMSE) and maximum relevant error (RE) of the frequency are 0.14 Hz and 0.74 %, respectively. Consequently, the output performances are revealed via software simulation. The calculated results indicate that the maximum pumping volume for fixed-power-frequency operation is 48 Hz, which is 27.56 m³ on a sunny day and 17.63 m³ on a cloudy day. On a rainy day, the maximum pumping volume is 3.27 m³ at 41 Hz. Similarly, the C_p values reach maxima of 2.51 m³/kWh and 2.11 m³/kWh at 48 Hz in both sunny weather and cloudy weather, respectively, while on rainy days, the C_p peaks at 0.77 m³/kWh at 41 Hz. Moreover, every 1 Hz increase in the fixed frequency mode leads to a rise in the LLP, while the minimum change is at 46–48 Hz for cloudy and rainy days. Furthermore, the simulations revealed that for variable frequency control, the volume of water pumped in the PVB mode reached 40.19 m³, 29.36 m³, and 15.11 m³, which are increased by 4.91 %, 21.83 % and 103.09 % compared with the variable frequency PV mode, and 45.83 %, 66.53 % and 362.08 % higher than in PV fixed frequency mode, respectively. Compared with the PV mode, the system weighted efficiency of the variable-frequency PVB mode is increased by 2.06 %, 4.98 %, and 8.36 % under three weather conditions. This work provides critical theoretical guidelines for the design and operation of high-performance PVBWPs.