Pump model: General requirements

The pump model should match the following characteristics:

Input/Output variables

The model should describe the dynamic evolution of the output variable - usually the flowrate - as a function of the pertinent input variables, which are basically the head and voltage input, for any conditions within the admitted operating values. Indeed, when a given voltage is applied to the pump, this will run at an operating point characterised by a flowrate yield, as well as by a current drawn from the source. Therefore current is also a function of the Voltage and Head inputs.

Functions

The general model will give all the relationships between these 4 variables, i.e. calculate any variable from the 3 other ones. Therefore it will include the determination of the Current/Voltage characteristic of the pump, which is necessary to the calculation of the operating point when coupling the pump directly to the PV array.

Without I/V information: needs a Power converter

In many cases the motor is specified for use at a nominal voltage, and detailed I/V behaviour is not available. The Flowrate is then given as a function of Head and input electrical Power. These only 3 variables are in principle sufficient for characterizing the operating point, when the power input is fed through some power-conditioning unit, which will provide an adequate (unknown) voltage, and eventually frequency, to the pump motor.

That is, a power converter is always required when the Current/Voltage are not specified.

Starting current

Besides these 4 operating variables, most positive displacement pumps also require special starting conditions, i.e. a starting peak current for overcoming the torque due to the friction forces when stopped.

Applicability to any technology

The model should cover any motor-pump's technology, available on the market for use in PV systems: centrifugal pumps, positive displacement pumps (including piston, membrane or diaphragm, progressive cavity, rotating displacer, etc.). These pumps can be driven by diverse AC or DC motor technologies.

The model will also apply to other standard pumps (not specifically designed for solar applications), with AC induction motors, driven by frequency converters (inverters).

Ideally, the parameters necessary for achieving the modelling should be available from the manufacturer data sheets, in order that any user of the program can input its own pump model characteristics. In practice, manufacturers usually give performances for only a limited set of actual operating conditions. Details about the motor or pump technology and related fundamental parameter are usually not available.

Therefore, the model will apply to the motor-pump group as a whole, without reference to intermediate values like torque or speed, which are highly technology-dependent and rely to unavailable specific technical parameters.

Model basis

The model will be a phenomenological one, based on the specification of some Operating points (FlowR, Head, Current, Voltage, Power) from which the operating properties will be interpolated or extended for any conditions.