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.

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Following on a preceding paper of the same title [1], and the establishment of the dependence of the wind-pump performance on the wind-pump's Froude number, υ/√ gh, an analytical analysis of the wind-pump's design parameters is further developed in this work. The result was the formulation of the system criteria that continuously match the load with the varying wind speed and water head. This led to a design procedure that entails variation of the pump stroke, the rotational speed-ratio or the turbine's pitch angle to sustain a continuous peak performance. The stroke and speed-ratio variations are such that any of them is continuously proportional to the square of the wind-pump's Froude number. The pitch-angle variation technique requires an inverse relation between the design torque-coefficient and the square of Froude number. The suggested power maximization techniques lead to the continuous operation of the turbine at its maximum power-coefficient point, as long as the operational Froude number is above its stop limit. The arrangements have the implicit advantage of minimizing the start and stop wind speeds of the wind pump.

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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.