Solar Power for a Rural Clinic: Is the Donation Enough?
The Island Council clinic on a rural islet has no mains electricity. A donor offers one 300 W solar panel, one 12 V 200 Ah battery, a 1 000 W inverter and a charge controller. The clinic needs three loads: a 120 W vaccine refrigerator whose compressor runs about 40% of every 24-hour period and cannot be switched off; four 5 W LED lights used 5 hours each night; and a 25 W radio used 6 hours a day. The panel receives an average of 4.5 peak sun hours per day, but the technician warns that dust, heat and cable losses cut output to about 75% of the rated figure, and that on a heavily overcast day output falls to 25% of the average. The inverter is 90% efficient. The battery must not be taken below 50% depth of discharge. The council must decide whether the donation is adequate, and if not, which single addition gives the safest service without changing the refrigerator.
1. Carry out a daily energy audit and decide whether the single 300 W panel can supply it. Show the unit reasoning.
Read the worked answer
Loads at the appliance (Wh per day).
- Refrigerator: 120 W × 0.40 × 24 h = 1 152 Wh. The 40% duty cycle is the whole point - a 120 W appliance does not draw 120 W × 24 h.
- Lights: 4 × 5 W × 5 h = 100 Wh.
- Radio: 25 W × 6 h = 150 Wh.
- Total at the load = 1 402 Wh/day.
Through the inverter. The battery must supply 1 402 ÷ 0.9 = 1 558 Wh/day, because 10% is lost as heat in the inverter.
Panel supply. Rated output = 300 W × 4.5 h = 1 350 Wh. Derated by 0.75 = 1 013 Wh/day delivered.
Verdict. 1 013 − 1 558 = −545 Wh/day; the array meets only 1 013 ÷ 1 558 = 65% of demand. The panel needed is 1 558 ÷ (4.5 × 0.75) ≈ 462 W, so a single 300 W panel is not adequate. Note that ignoring the inverter loss (using 1 402 Wh) still leaves a deficit of 389 Wh - the conclusion does not depend on that refinement.
2. Test the battery: is the 12 V 200 Ah battery adequate for a normal night, and what happens on a heavily overcast day? Show the day/night split.
Read the worked answer
Capacity. 12 V × 200 Ah = 2 400 Wh stored; at 50% depth of discharge only 1 200 Wh is usable.
Night load (about 12 h of darkness). Fridge: 120 × 0.40 × 12 = 576 Wh. Lights: 100 Wh. Radio: 0 (used by day). Total 676 Wh at the load, ÷ 0.9 = 751 Wh from the battery - comfortably inside 1 200 Wh. Sized for the night alone, the battery is adequate.
But energy must also balance over 24 h. With only 1 013 Wh arriving and 1 558 Wh leaving, the battery is drained by about 545 Wh every day and never recovers; after two days it is flat.
Overcast day. Panel output = 0.25 × 1 013 ≈ 253 Wh. Deficit to be drawn from the battery = 1 558 − 253 = 1 305 Wh, which exceeds the 1 200 Wh usable limit. The battery would be pushed past 50% depth of discharge, its life shortened, and the refrigerator would warm - a vaccine-loss risk, not just an inconvenience.
So the battery passes the night test but fails the bad-weather test, and the real failure is the daily energy balance.
3. Recommend the single addition that gives the safest service, justify it with numbers, and state one non-electrical alternative and why it also works.
Read the worked answer
Option A - a second 300 W panel. Two panels deliver 2 × 1 013 = 2 026 Wh/day against 1 558 Wh demand, a surplus of about 468 Wh/day that recharges the battery after a poor day. On an overcast day: 506 Wh supplied, deficit 1 052 Wh, still inside the 1 200 Wh usable capacity - so one bad day no longer destroys the battery. This is the single addition that fixes the daily deficit.
Option B - a bigger battery only. It would store more energy but cannot create it: the 545 Wh/day deficit remains, so the clinic would simply run out more slowly. Reject it as the sole fix.
Non-electrical alternative - cut the refrigerator load. The 545 Wh gap equals about a third of fridge consumption, so reducing the duty cycle from 40% to about 21% (thick lid insulation, shaded housing, clean condenser, fewer door openings, pre-chilled water bottles) would close the gap without a panel. This is usually cheaper than a panel and easier to maintain locally.
Recommendation: add the second panel, because it secures supply and gives cloudy-day reserve, and in the same visit train staff to insulate and shade the refrigerator - the two together give margin for heat, dust and a failed panel.