Sizing an off-grid solar system for a Karnali health post
A health post in a remote Karnali village has no grid connection. Its solar array has four panels rated 335 Wp each, a 48 V, 200 Ah lead-acid battery bank, and a 3 kVA inverter with 90% efficiency. The measured daily loads are: a vaccine refrigerator rated 80 W with a 50% compressor duty cycle running all day; lights and a fan totalling 120 W for 6 hours; an oxygen concentrator drawing 320 W for 5 hours; and a centrifuge drawing 200 W for 1 hour. The site receives 4.5 peak sun hours per day and the whole system has a derating factor of 0.75. The battery must never be taken below 20% state of charge, and the inverter's surge capability is twice its continuous rating for a few seconds. A visiting dentist wants to add a 1.5 kW air compressor running about 2 hours per day.
1. Compute the daily AC energy demand, the DC energy drawn from the battery, the daily PV yield, and the no-sun autonomy of the battery.
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AC energy per day.
- Refrigerator: 80 W × 24 h × 0.50 = 960 Wh
- Lights and fan: 120 W × 6 h = 720 Wh
- Concentrator: 320 W × 5 h = 1,600 Wh
- Centrifuge: 200 W × 1 h = 200 Wh
- Total = 3,480 Wh ≈ 3.48 kWh/day
DC energy from the battery. Divide by inverter efficiency: 3,480 ÷ 0.90 = 3,867 Wh ≈ 3.87 kWh/day.
PV yield. 4 × 335 Wp = 1,340 Wp; 1,340 × 4.5 h × 0.75 = 4,523 Wh ≈ 4.52 kWh/day. This exceeds the 3.87 kWh demand by about 0.65 kWh (17%), a thin but positive margin.
Battery autonomy. Nominal storage = 48 V × 200 Ah = 9,600 Wh. Usable at 80% depth of discharge = 9,600 × 0.80 = 7,680 Wh. Autonomy = 7,680 ÷ 3,867 = about 2.0 days with no sun at all.
So on a normal sunny day the system balances, but the surplus is small enough that a run of cloudy days will begin drawing the battery down within a day.
2. Can the dentist's compressor be added to this system? Support your answer with numbers.
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Energy. The compressor adds 1,500 W × 2 h = 3,000 Wh AC, or 3,000 ÷ 0.90 = 3,333 Wh DC. New DC demand = 3,867 + 3,333 = 7,200 Wh/day against a PV yield of 4,523 Wh - a shortfall of about 2,680 Wh every sunny day. The battery's entire usable capacity is 7,680 Wh, so it would be emptied within roughly one day and would never recover. The array would need about 2,680 ÷ (335 × 4.5 × 0.75 ÷ 1,000 = 1.13 kWh per panel) ≈ 2.4, i.e. three additional panels, plus a larger battery bank.
Power. The compressor's starting surge is 1.5 kW × 3 = 4.5 kW. The inverter is rated 3 kVA continuous with a 2× surge (about 6 kVA for seconds), so the surge itself may be survivable, but running the compressor alongside the concentrator gives a continuous load of 1.5 + 0.32 kW plus base loads, approaching the inverter limit.
Judgement. Refuse the addition as proposed. Either schedule the compressor on alternate days with the concentrator switched off, or fund an array and inverter upgrade before accepting the dental service.
3. A three-day period of heavy cloud is forecast. What is the maximum daily AC energy the post can use, and how would you ration the oxygen concentrator?
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Available energy. With no useful PV input for three days, the whole usable bank is 7,680 Wh DC. Per day that is 7,680 ÷ 3 = 2,560 Wh DC, or 2,560 × 0.90 = 2,304 Wh AC per day - about two-thirds of the normal 3,480 Wh.
What must be protected. The vaccine refrigerator is non-negotiable: 960 Wh. The oxygen concentrator at 320 W full output would need 1,600 Wh for 5 hours, which with the refrigerator already totals 2,560 Wh - 256 Wh over the allowance before any lighting is considered.
Rationing. Light for essential examinations only, perhaps 40 W × 4 h = 160 Wh. That leaves 2,304 − 960 − 160 = 1,184 Wh for the concentrator, i.e. about 3.7 hours at 320 W. The clinical decision is therefore to run the concentrator in scheduled blocks, reserve it for hypoxic patients rather than routine use, and arrange a cylinder backup for the third day.
System insight. A load-shedding plan written in advance, with a defined priority order (vaccine cold chain > oxygen > lights > centrifuge), is the difference between a cold-chain failure and a manageable three days.