Consider a PV array charging batteries for an off-the-grid, stand-alone system near Boulder, Colorado You plan to run everything in the house on 120 V ac.
a. Suppose the load is estimated to consist of the following 120 V ac appliances. Supplement load data given below with values from Table 9.10.
A 19-cu. ft. refrigerator/freezer.
A 1000-W microwave used 15 min./day. Five 20-W compact fluorescent lamps, each used 8 hrs/day.
A horizontal-axis washing machine used 3 hrs/week
A 24-V well pump that delivers 288 gal/day at 1.6 gpm of water from 100-ft depth
A 19-inch color TV used 2 hrs/day and drawing standby power the other 22 hrs/day
A satellite receiver system for the TV, used 2 hours/day and in standby mode 22 hrs.
A laptop computer used 4 hrs/day,
Six 3-W transformer units for chargers that run all day long
Find the total watt-hrs per day needed by these appliances.
b. Pick an appropriate system voltage.
c. How many amp-hours/day would the battery bank have to deliver if the loads are all ac provided by an 85% efficient inverter?
d. How many Ah/d would have to be delivered to the batteries if they have a Coulomb efficiency of 90%?
e. Suppose 5% of the PV output is lost due to dirt, etc. How many Ah/d should the PVs provide before that derating?
f. Using the worst month in Boulder with south-facing panels tilted at L + 15, how many AstroPower APex 90-W modules with DC, STC rated current 5.3 A and rated voltage 17.1 volts would be needed in series and parallel? If they cost $400 each, what is the cost of PVs?
g. What is the maximum current that you might expect in the wires connecting the array to battery system (just use the rated current)? What gage wire would you suggest using?
h. If your design goal is to provide needed electricity 95% of the time, about how many days of usable battery storage would you need?
i. If the coldest temperature the batteries might experience is -20° C, what is the maximum depth of discharge that lead-acid batteries could tolerate without freezing?
j. If a C/72 discharge rate is assumed along with -20° C and the results from (c), what should be the rated (nominal) Ah capacity of the battery bank?
k. Suppose you use Concorde PVX 1080 batteries. How many batteries in series and how many in parallel would you recommend (round up if necessary). At $160 each, how much would the batteries cost?
l. Assume a power control unit with inverter costs $1/watt and they come in 500 W increments (1 kW, 1.5 kW, 2 kW, 2.5 kW, etc). You want one big enough to cover all your appliances on at once. Pick an inverter and how much would it cost?
m. Draw the system "wiring" diagram showing series/parallel combinations of the PV modules and batteries, similar to Figure 9.51.
n. What would the total system cost be?
o. Using the annual insolation in Boulder, estimate the average Amphours/day (at the system voltage) that the PVs could deliver all year long. If all of that electricity is run through the batteries and inverter and ends up being used in the house, how many kWh/year would be delivered (i.e., in the better months you use all of the kWh not just the design load specified in (a))?
p. Paying for the system with a 15-year, 5% loan, find the first-year cost of electricity ($/kWh) for someone in the 36% marginal tax bracket if the loan interest is tax deductible.
