Question 9.22: Sizing an Array for a 150-ft Well in Santa Maria, California......

From the solar radiation tables given in Appendix E, the worst month is December, with an insolation of 4.9 kwh/m²-day. From (9.60)

Q\left(gpm\right) \ = \ \frac{\text{Daily demand} \ \left({gal}/{day}\right)}{\text{Insolation}\left({h}/{day \ @ \ 1-\text{sun}}\right) \ \times \ 60 \ {min}/{h}} (9.60)

From Fig. 9.60, at 4.1 gpm the total dynamic head is about 170 ft and the pump efficiency is about 34%. From (9.59), the estimated pump input power is

P_{in} \ \left(W\right) \ \text{to pump} \ = \ \frac{\text{Power to fluid}}{\text{Pump efficiency}} \ = \ \frac{0.1885 \ \times \ H\left(ft\right) \ \times \ Q\left(gpm\right)}{\eta_{p}} (9.59)

From Fig. 9.60, at 4.1 gpm and 170 ft of head, the pump voltage is a little under 45 V, which means that at 15 V per module, three modules in series should be sufficient.

Using (9.62), we can decide upon the number of parallel strings of modules

\# \ \text{strings} \ = \ \frac{\text{Pump input power} \ P_{in}\left(W\right)}{\# \ \text{mods in series} \ \times \ 15 \ {V}/{mod} \ \times \ I_{R}\left(A\right) \ \times \ \text{de-rating}} (9.62)

so choose two parallel strings.

From (9.63), estimated delivery in January with two strings of three modules would be

A system diagram is shown in Fig. 9.61.