Sizing an off-grid photovoltaic system for a rural clinic
A rural clinic in a region with a pronounced dry season asks for an off-grid photovoltaic system. Its daily electrical demand is 4.2 kW h, of which 1.1 kW h is a vaccine fridge that must run continuously. There is no grid connection and no backup generator. A supplier proposes 6 panels, each rated 250 W at 25 °C and 1000 W m⁻², a 48 V battery bank of 220 A h, and an inverter of 92% efficiency. Local figures: average daily irradiation in the worst month 2.1 kW h m⁻², ambient temperature in the worst month 34 °C, panel temperature coefficient −0.40% per °C above 25 °C, and other losses (dust, wiring, MPPT) totalling 12%. The battery is specified to 80% depth of discharge and the clinic wants two days of autonomy for the fridge. The supplier claims the array 'meets demand with margin'.
1. Calculate the worst-month daily a.c. energy the proposed array can deliver and evaluate the supplier's claim. State how many panels would actually be needed.
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Energy at the panels' operating temperature. 2.1 kW h m⁻² per day is equivalent to 2.1 h at the 1000 W m⁻² rating, so the array's rated output is 6 × 250 = 1500 W and the STC-condition energy is 1500 × 2.1 = 3.15 kW h.
Temperature derating: taking the cells at about the 34 °C ambient, ΔT = 9 °C, factor = 1 − 0.0040 × 9 = 0.964, giving 3.15 × 0.964 = 3.04 kW h.
Other losses (12%): 3.04 × 0.88 = 2.67 kW h of d.c. energy.
Inverter at 92%: 2.67 × 0.92 = 2.46 kW h per day of a.c. energy.
Verdict: demand is 4.2 kW h, so the shortfall is 1.74 kW h per day - the array supplies only 59% of demand. The claim of 'margin' is false; it is probably based on the nameplate 1500 W × 2.1 h = 3.15 kW h and ignores derating and the inverter.
Panels needed: each panel contributes 2.46/6 = 0.41 kW h per day, so 4.2/0.41 = 10.2 → 11 panels, giving 4.51 kW h and a 7% margin. Enlarging only the battery would not help, because the deficit is a daily energy deficit, not a storage deficit.
2. Assess the proposed battery against the stated autonomy requirement, and comment on whether the battery or the array is the limiting component.
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Battery energy. 220 A h × 48 V = 10.56 kW h nominal. At 80% depth of discharge the usable d.c. energy is 0.80 × 10.56 = 8.45 kW h; after the inverter this is 8.45 × 0.92 = 7.77 kW h of a.c. energy.
Against the fridge-only requirement. The fridge needs 1.1 kW h a.c. per day, which is 1.1/0.92 = 1.20 kW h d.c. per day. Two days of autonomy is 2.39 kW h d.c., and with the 80% DoD limit the required nominal capacity is 2.39/0.80 = 2.99 kW h, i.e. 62 A h at 48 V. The 220 A h bank is about 3.5 times larger than this requirement - it is heavily over-specified for the fridge alone. It would support the whole 4.2 kW h load for 7.77/4.2 = 1.85 days, short of two full days.
Which is limiting. The array is limiting: it fails to recharge 4.2 kW h per day in the worst month by 1.74 kW h. Enlarging the battery without enlarging the array simply delays failure - over a 90-day dry season the deficit is about 157 kW h, far more than the 7.77 kW h the bank can hold. The money would be better spent on four or five extra panels than on extra cells.
3. The clinic suggests covering the winter shortfall by letting the battery cycle more deeply. Evaluate this proposal using the numbers, and state two consequences for the system.
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Can the bank cover one winter day? Yes, numerically: the daily deficit is 1.74 kW h a.c., and one extra day of full demand (4.2 kW h) needs 4.2/0.92 = 4.57 kW h d.c., which is 43% of the 10.56 kW h nominal capacity. Discharging to about 43% DoD for one night is within the 80% limit, so the battery can bridge a single poor day.
Why it fails as a seasonal strategy. The battery is a buffer, not a source. Over a 90-day dry season the cumulative deficit is about 157 kW h a.c., roughly 20 times the usable capacity of the bank. Once the bank is empty it cannot recover, because the array output is less than the daily demand every day; the deficit compounds until the load must be shed.
Consequences: (i) the battery would sit for long periods at high DoD; lead-acid cells that are not regularly fully recharged sulphate and lose capacity, and cycle life falls steeply with depth of discharge, so the bank would need early replacement; (ii) the fridge - the critical load - would be at risk on consecutive cloudy days. The defensible options are more panels, load reduction (efficiency retrofit of lights and fridge), or a small backup generator as a seasonal top-up, not deeper cycling.