#### LESSONS OF EASTER ISLAND

March 17th, 2016

A directly-coupled system is one where a low starting torque pump (such as a centrifugal pump) can be driven by a DC motor that receives its power directly from the solar panels. No batteries, inverters, or power conditioning circuitry are used, other than perhaps safety cut-out relays activated by level, flow or pressure sensing transducers. When the sun shines sufficiently brightly, the system operates and water is pumped either for storage or direct use.

An approach for designing directly-coupled PV-powered water pumping systems is provided in Appendix H. Important considerations are as follows:

1. The volume of water to be pumped and over what period. The volume to be pumped may vary significantly throughout the year and in fact may be entirely non-critical for some months of the year, as for some irrigation applications. This will have important implications regarding array tilt angles. For instance:

• If the demand profile throughout the year is reasonably constant (such as for a domestic water supply), a tilt angle in the vicinity of latitude + 20° will be necessary to give the most uniform insolation levels throughout the year falling on the solar panels.

• If the amount of water to be pumped is to be reasonably constant throughout the year, but with a definite bias towards summer months (such as for drinking water), a tilt angle in the vicinity of latitude + 10° will probably be desirable.

• If the annual amount of water pumped is to be maximised (such as with a large storage reservoir), a tilt angle in the range latitude to latitude – 10° should be used.

• If the water pumped during summer months is to be maximised (such as for some irrigation applications), a tilt angle in the vicinity of latitude – 20° will be preferable, to ensure the solar panels point more directly at the midday summer sun.

In general, more uniform pumping throughout the year will be provided by increasing the tilt angle.

2. The pumping head and its seasonal variations must be known and, where possible, information regarding water source replenishment rates should be obtained.

3. The inclusion and economics of water storage should be considered in conjunction with consumer needs.

4. Any available insolation data should be obtained and used in conjunction with the guidelines given in Appendix B and Chapter 1. Fig. H.1 indicates the procedure for determining the light intensity incident on the solar panels at angle P at noon.

5. Select a pump to suit starting torque requirements, the range of operating heads, any physical dimension constraints imposed by the application, and one that will pump the required volume of water when operating at its maximum efficiency point. It is essential the torque-speed characteristics of the selected pump be known, to facilitate system matching.

6. Select a motor with a torque-speed characteristic compatible with that of the pump. It is important that the motor operate near maximum efficiency when producing the necessary torque, to drive the pump at its design speed. Recall that

Vm = IaRa + КФМ (12.1)

where Vm is the motor voltage, Ia is the armature current, Ra is the resistance of the armature, K is the motor constant, Ф is the flux density and N is the speed of rotation.

In Eqn. 12.1, the voltage applied to the motor terminals (Vm) has two components—IaRa is the resistive voltage drop across the armature windings and KФN is the back emf generated, which is hence proportional to the speed of rotation N and the flux density Ф.

If we now consider a permanent magnet DC motor, then Ф remains approximately constant, independent of the voltage applied or current consumed, and Ia becomes the total motor current Im, since no current is required for field windings. Thus, we can rewrite Eqn. (12.1) as

Vm = ImRa + КФМ (12.2)

The electromagnetic torque (те) developed by such a motor is proportional to the armature current (and hence Im) and also the flux density Ф (which is a constant). This gives us

ге = К ‘ФІт (12.3)

where К’ is a constant related to the physical dimensions of the motor and the number of windings in the armature (Hambley, 2002).

When the motor drives a load (such as a water pump), the speed of the motor will continue to alter until steady state is reached; that is, when

ге = T, (12.4)

where t, is the torque required to drive the load at that particular speed.

For any commercial pump, the torque versus speed (t, versus N) characteristics should be available from the supplier. For each value of N, t, is thus obtainable and, using Eqns. (12.3) and (12.4), Im can be calculated. Subsequent use of Im and N in Eqn. (12.2) gives the corresponding value of Vm. Therefore, for each N of the pump, the motor voltage and current required from the solar panels are determined. However, the actual voltage generated by the solar panels needs to be about 2% higher than that calculated, to allow for resistive losses in the wiring.

7. Appropriate sizing of the photovoltaic system will enable overall system specifications to be met, while simultaneously maximising overall system efficiency. For this, both the voltage and current at maximum power point need to be optimised. Unfortunately, little choice exists with regard to the voltages available with standard commercial modules. They are normally designed for 12 V systems (including considerable excess voltage capacity to allow for battery charging, regulation, blocking diode etc.), and can be connected in series to increase system voltage to multiples of 12 V. This restriction can be overcome by the use of a DC-to-DC converter. In comparison, a reasonable choice in short circuit currents exists, owing to the range of solar cell sizes and technologies used by different manufacturers. An approach for optimising the photovoltaic configuration by matching the requirements of the water pumping subsystem to the output of the photovoltaics is provided in Appendix H.

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