Question 9.20: PVs for the Cabin in Salt Lake City. The cabin from Example ......
PVs for the Cabin in Salt Lake City. The cabin from Example 9.18 needs 3000 Wh/day of ac delivered from an 85%-efficient inverter. For a 24-V system voltage, a 90% Coulomb efficiency, and 10% de-rating (de-rating factor = 0.90), size a PV array using Kyocera KC120 modules.
From Table 9.3, the Kyocera KC120 is a 120-W module with its maximum power point at a current of 7.1 A and a voltage of 16.9 V. From Example 9.18, the worst solar month is December, with 3.1 peak hours of sunlight at a tilt of L + 15. Using (9.35), one string of modules will therefore deliver in December about
\text{Ah to load} \ = \ I_{R} \ \times \ \text{Peak sun hours} \ \times \ \text{Coulomb efficiency} \ \times \ \text{De-rating factor} (9.35)
\text{Ah to inverter} \ = \ 7.1 \ A \ \times \ 3.1 \ {h}/{day} \ \times \ 0.90 \ \times \ 0.90 \ = \ 17.83 \ {Ah}/{day} \ \text{per string}For an 85% efficient inverter to deliver 3000 Wh/day of 120 V ac, it needs a 24-V dc input of
\text{Inverter dc input} \ = \ \frac{3000 \ {Wh}/{day}}{0.85 \ \times \ 24 \ V} \ = \ 147 \ {Ah}/{day} \ @ \ 24 \ VSince these modules have a rated voltage of 16.9 V, they are nominally “12-V modules.” Therefore two modules are needed in series to provide a single 24-V string.
The number of parallel strings of modules needed is
\text{Number of parallel strings} \ = \ \frac{147 \ {Ah}/{day}}{17.83 \ {Ah}/{\text{day-string}}} \ = \ 8.25 \ \text{strings}Suppose that we undersize it slightly and use eight parallel strings with two modules per string, for a total of 16 modules.
Including the 0.90 de-rating factor, the PVs will deliver
The batteries with 0.90 Coulomb efficiency will deliver
\text{Battery output} \ = \ 158 \ {Ah}/{day} \ \times \ 0.90 \ = \ 142 \ {Ah}/{day} \ @ \ 24 \ VdcThe 85% efficient inverter will deliver
\text{Inverter output} \ = \ 142 \ {Ah}/{day} \ \times \ 24 \ V \ \times \ 0.85 \ = \ 2900 \ {Wh}/{day} \ @ \ 120 \ VacSo, the design is just a bit shy of its goal of 3000 Wh/day ac. The system diagram for this cabin, including some of the energy flows for December, is shown in Fig. 9.51.
| TABLE 9.3 Annual Energy Production in Various Cities per kW (dc, STC) of Installed PV Capacity^a | ||||||
| Location | South Facing, L-15 Fixed | 1-Axis, Polar Mount | Ratio 1-axis/ Fixed | |||
| Average High Temp. (◦C) | Insolation (kWh/m²-d) | Annual kWh/kW | Insolation (kWh/m²-d) | Annual kWh/kW | ||
| Seattle, WA | 15.3 | 3.8 | 1006 | 4.7 | 1247 | 1.24 |
| New York, NY | 16.8 | 4.5 | 1195 | 5.6 | 1479 | 1.24 |
| Madison, WI | 13.2 | 4.5 | 1202 | 5.7 | 1519 | 1.26 |
| Boston, MA | 15.0 | 4.5 | 1209 | 5.7 | 1529 | 1.26 |
| Atlanta, GA | 21.8 | 5.0 | 1294 | 6.4 | 1639 | 1.27 |
| Honolulu, HI | 29.1 | 5.5 | 1373 | 7.4 | 1834 | 1.34 |
| Boulder, CO | 17.9 | 5.3 | 1404 | 7.2 | 1885 | 1.34 |
| Los Angeles, CA | 21.3 | 5.5 | 1420 | 7.0 | 1808 | 1.27 |
| El Paso, TX | 25.3 | 6.3 | 1583 | 8.6 | 2159 | 1.36 |
| Albuquerque, NM | 21.2 | 6.3 | 1618 | 8.5 | 2199 | 1.36 |
| ^aAssumed inverter efficiency 90%, mismatching loss 3%, dirt loss 4% | ||||||
