#### LESSONS OF EASTER ISLAND

March 17th, 2016

G. 1 INTRODUCTION

Aspects of insolation data manipulation are discussed in preparation for designing a stand-alone, directly-coupled PV powered water pumping system. This is followed by an analysis and discussion of typical PV module characteristics and output and the relevance for water pumping system design. An example system design is provided, including discussion of each part of the procedure.

H. 2 INSOLATION DATA MANIPULATION

Determine the maximum (solar noon) daily light intensity (I) incident on the array (at inclination angle P for each of the design months, for both sunny days (Is) and typical cloudy days (Ic). Refer to Chapter 1 for further details about insolation data and note that various computer programs are available to help with such calculations (Silvestre, 2003). For our purpose here we use an approximation that discriminates between ‘sunny’ and ‘cloudy’ days (see Chapter 1, Section 1.8.3.2). Using Eqn.

(1.19) from Chapter 1 (Hu & White, 1983), in conjunction with Fig. H.1, we get, for sunny days

Isi = 1.353 x 0.7Ам°’т x1.10 x sin (a + p) (H.1)

where the units are kW/m2, a is the noon-time altitude of the sun for month i, given by Eqn. (1.22), ft is the angle of inclination of the array on which Isi is incident, AM is the air mass (1/sina) and the factor 1.10 allows for the inclusion of the diffuse component for a cloudless day.

Similarly, for typical cloudy days, the maximum light intensity Ici for month i is estimated from

0.678

Ici = 1.353 x 0.7AM x 0.20 (H.2)

where the factor 0.20 represents the assumed diffuse light intensity, which is assumed to be independent of b.

1. From the values for Isi and Ici for each month i, use Fig. H.2 to estimate the light intensity incident on the array at inclination angle ft throughout each day for sunny and cloudy days, respectively. This facilitates the calculation of the kWh/m2/day for both sunny and cloudy days by using appropriate values for the ‘time’ axis, as given by N in Fig. H.2.

2. Determine the percentage of sunny days given by Fig. H.2 with I equated to Isi for each month. This can be found from Eqn. (H.3), which gives the average daily global radiation (G) falling on the array at inclination ft for each month (i) in the design period as the sum of the sunny-day and cloudy – day components of insolation

Gt = Xt x 6.76 x Ni x Isi + Y x 6.76 x N x Iri(H.3)

where X and Yi represent the fraction of sunny and cloudy days, respectively.

For a directly-coupled system, we make the assumption that no pumping takes place during cloudy weather because of poor sub-system performance in the presence of greatly reduced operating currents. We therefore use the sunny weather component of the global radiation in Eqn. (H.3) (X x N x 6.76 x Is) as being the useful global insolation (Ru) incident on the solar panels.

This is equivalent to saying that on a sunny day, with peak intensity Is, we have E hours of sunshine at the light intensity of Isa. To determine the corresponding monthly number of such hours for month i (Emi) we use

Emi= XiMiEi (H.6)

and if needed, the overall annual total of such hours (Ey) is given by

Ey =X Emi(H.7)

i

Note, however, that two hours of operation at ISJ2 intensity is not equivalent to one hour of operation at Isa intensity, owing to poorer part-load performance of centrifugal pumps and non-optimal matching of the load to the solar panel current-voltage characteristics. Therefore, for the first iteration, assume the above number of equivalent daylight hours is for only

0. 80 x Isa kW/m2 and accordingly design for maximum system efficiency at this light intensity. This will build a necessary degree of conservatism into the design, and will also greatly increase the daily system efficiency, when allowing for the reduced light intensities for large parts of each day (Fig.

G. 2).

4. For a system with adequate water storage, the design can be done so as to provide the correct annual amount of pumped water. For systems with limited or no water storage, the water demand and water pumped throughout the whole design period need to be matched. In either case, we determine a volume V that must be pumped each sunny day (which will be an absolute or an average value depending on storage capabilities). This volume V is to be pumped in E hours using solar panels that will provide the necessary power at a light intensity of 0.80 x Isa,

For a design without storage, any imbalance between Ei and Vi values throughout the year should be minimised by optimising the tilt angle. Varying the tilt angle will change Ei values for different months relative to each other. Ideally, we want Et values proportional to V’ values for the design months.

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