Wind power is unsteady due to the stochastic nature of wind. Pumped storage is a reliable technology for hydropower storage and generation. This paper aims to regulate wind power with a pumped storage facility by designing a mathematical model of a stand-alone wind-driven pumped storage. The available wind continuously pumps water to a high-elevation upper reservoir, while electricity is generated per demand. A case study was developed in eastern Sudan, and results show that wind energy can be regulated using pumped storage. The scheme had a 71% roundtrip efficiency, with a monthly energy yield of 23 GWh sufficient to support the whole population of the Red Sea State in Sudan. This result indicates the good potential of a wind-driven pumped storage system to deliver continuous electricity using intermittent wind. Such a scheme will benefit the developing countries in Africa, where the requirements of this system are easily found.

A theoretical formulation of the operation of wind pumps is proposed, including the starting and stopping behaviour. The paper defines a wind pump form of Froude number as the basic dimensionless parameter of the system. The influence of the turbine's power levels at low tip-speed ratios on the system performance is studied. The study is based on theoretical analysis and confirmed by experimental findings on the behaviour of constant-torque machines.

A study on the optimal matching of centrifugal pumps and large-scale wind turbines is reported. The study includes mathematical modelling of the performance of high-capacity centrifugal pumps when matched with efficient high-speed low-solidity wind turbines. The dependence of the performance of wind pumps on the dimensionless parameter v/√(gh), termed the wind pump’s Froude number, was fully analysed. Similar to earlier reported results on wind-powered piston pumps, analysis is showing that the wind pump’s Froude number is the dominant independent dimensionless parameter that fully defines the system’s performance. Operation with continuous variable transmission was analysed and shown to optimize the wind pump’s performance, particularly at medium and low wind speeds. The optimum relation between the required gearbox transmission ratio and Froude number of a wind-powered centrifugal pump was analytically established for three different pumps. In addition to continuous variable transmission operation, the analysis helps in optimally sizing constant transmission ratio systems.

The basic variables relevant to wind generation systems were formulated in this study as to relate the operational torque coefficient to the power output and wind velocity. A dimensionless number connecting wind velocity, power output, generator speed, turbine size and air density was identified and shown to be the pivotal independent parameter of the wind-generator operation. An optimization criterion based on this mathematical formulation was developed. It relates the gearbox's speed-ratio to the newly defined wind generator number. This led, in turn, to the introduction of a variable speed-ratio gearbox that has a constant speed output and a variable turbine shaft-speed to be controlled in such a way as to match continuously and optimally the operation condition. Making use of a reported experimental study of a variable pitch-angle turbine driving an induction generator, a demonstration of the design procedure was presented. The model was shown to accurately predict the experimentally produced results. The demonstration proceeded to predict the optimum performance for the reported system.

This paper presents a simplified dimensionless model for predicting the electrical performance of photovoltaic (PV) modules under varying irradiance and temperature conditions. Unlike conventional equivalent-circuit models that require detailed parameter extraction, the proposed approach employs dimensional analysis to establish direct relationships between key PVoperating points and normalized environmental variables, without assuming a predefined physical model. The model is validated using experimental datasets from Sandia National Laboratories, covering a wide range of irradiance (100–1100 W/m²) and module temperatures (15°C–75°C). Model accuracy is evaluated using normalized root mean square error (nRMSE). The results demonstrate strong predictive capability, with average nRMSE values below 2.5% for maximum power point voltage and current, below 1% for maximum power, and low errors for open-circuit voltage and short-circuit current. The proposed model provides a computationally efficient and accurate alternative to conventional PV models. Moreover, the dimensionless framework offers strong potential for predicting the performance of complex multiphysics energy systems, where conventional equivalent-circuit-based approaches are often difficult to apply or fail to achieve satisfactory accuracy.