Sizing a Solar Power System for a Remote Seismic Station
A remote seismic station on a ridge in Fukushima Prefecture must run continuously at 15 W for a seismometer and telemetry. The station has one 12 V, 100 Ah lead-acid battery with a usable depth of discharge of 50%, and one 100 W solar panel. Winter average insolation is 2.5 kWh/m²/day, panel/system losses are 30%, and the station must ride through 5 consecutive cloudy days without sun. The panel is rated at 1000 W/m². The installer proposes adding a second identical battery but keeping the single panel. The school's maintenance team must decide whether that is sufficient, and what the minimum practical panel and battery sizes should be. They also want to avoid a design that only works in an average winter, not in a cloudy week.
1. Calculate the daily energy demand, the daily energy delivered by one panel in average winter conditions, and the usable battery energy. Is the installer's proposal adequate?
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Daily demand is 15 W × 24 h = 360 Wh/day. Winter insolation of 2.5 kWh/m²/day corresponds to 2.5 peak-sun hours at 1000 W/m². One 100 W panel therefore delivers 100 W × 2.5 h = 250 Wh/day before losses, and 250 × 0.70 = 175 Wh/day after 30% losses. That is 185 Wh/day short of the load. One 100 Ah battery stores 100 Ah × 12 V = 1,200 Wh; at 50% usable depth of discharge, only 600 Wh is available. Adding a second identical battery gives 1,200 Wh usable, which is 1,200/360 = 3.33 days, not 5 days. The installer's proposal is not adequate: the panel cannot even replace daily use in average winter, and two batteries still cannot cover the required cloudy spell.
2. The team can buy one 250 W panel and one 300 Ah battery. Check both the cloudy-week autonomy and the recharge after a sunny day. What hidden assumptions could make the design fail?
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The 300 Ah battery has 300 × 12 = 3,600 Wh nominal and 1,800 Wh usable at 50% depth of discharge. Five days need 5 × 360 = 1,800 Wh, so the battery just meets the five-day requirement with no margin. The 250 W panel gives 250 × 2.5 × 0.70 = 437.5 Wh/day, a surplus of only 77.5 Wh/day over the 360 Wh load. After a five-day cloudy spell the battery would be essentially empty, and one average sunny day adds only 437.5 Wh; full recharge would take about 1,800/77.5 ≈ 23 average winter days. That is too slow and leaves the station vulnerable to the next cloud sequence. Hidden assumptions include cold-temperature capacity loss, battery aging, snow or dirt on the panel, non-optimal tilt, actual load duty cycle, and inverter or heater loads. A more robust design would use a larger panel and battery, for example roughly 400 W of panel and 400 Ah of battery, plus a low-voltage disconnect and temperature-compensated charging.