Rooftop Solar for a Hostel: Sizing, Payback and a Vendor Claim
A campus sustainability committee is evaluating a rooftop photovoltaic system for a men's hostel. The flat roof measures 12 m × 8 m; a 1 m clear walkway is required along every edge for maintenance and fire access, and the remaining area can be fully covered with panels. Each panel occupies 1.65 m² and is rated 400 W at standard test conditions. Average daily insolation on the horizontal roof is 5.2 kWh/m² per day, and the committee applies a performance ratio of 0.75 to cover temperature, soiling, inverter and wiring losses. The hostel consumes 60 kWh per day and pays ₹7.50 per kWh. Installed cost is quoted at ₹45,000 per kW of panel capacity, with no battery. A vendor separately offers a battery-backed version at ₹18,000 per kWh of storage and claims that the rooftop array alone will supply 120% of the hostel's demand. The hostel's demand peaks between 18:00 and 23:00, when the array produces nothing.
1. Determine how many panels fit, the array's daily energy yield, and what fraction of the hostel load that covers.
Read the worked answer
Usable roof after the 1 m walkway on all four sides: (12 − 2) × (8 − 2) = 10 × 6 = 60 m².
Panel count: 60/1.65 = 36.4, so 36 panels (the walkway and inter-row gaps leave no room for a 37th). Installed DC capacity = 36 × 400 W = 14.4 kW.
Daily yield: E = capacity × peak-sun hours × performance ratio = 14.4 × 5.2 × 0.75 ≈ 56 kWh/day.
Cross-check by area: 60 m² × 5.2 kWh/m² × (400/1650 = 0.242 module efficiency) × 0.75 ≈ 56.7 kWh/day. The two routes agree, which is a useful sanity check that the panel rating and the roof area are mutually consistent.
Coverage: 56/60 ≈ 94% of the hostel's average daily demand. The system is close to net-zero on a daily-energy basis but does not reach it, and it has no capability at all to shift generation into the 18:00–23:00 peak.
2. Compute the simple payback period and state which assumptions would push the real figure upward.
Read the worked answer
Capital cost = 14.4 kW × ₹45,000/kW = ₹6,48,000.
Annual savings = 56 kWh/day × ₹7.50/kWh × 365 = ₹420/day × 365 ≈ ₹1,53,300 per year.
Simple payback = 6,48,000/1,53,300 ≈ 4.2 years.
This is the optimistic bound. It assumes every generated kWh is consumed on site and credited at the full retail tariff, which requires either a net-metering arrangement or daytime loads that happen to match generation. Real-world upward pressure comes from: module degradation (~0.5–0.7% per year, a few percent over the payback window), inverter replacement around year 10–12, cleaning and insurance, and any export tariff below ₹7.50. A realistic payback is closer to 5–6 years. Even so, well inside a 25-year module life, the investment is sound on energy grounds.
3. Assess the vendor's 120% claim and judge whether adding battery storage changes the recommendation.
Read the worked answer
The claim fails on area before it fails on anything else. 120% of 60 kWh is 72 kWh/day. Required capacity = 72/(5.2 × 0.75) = 18.5 kW, i.e. 46 panels of 400 W, occupying 46 × 1.65 ≈ 76 m². The roof offers 60 m², so the claim exceeds the physical limit by about 27%. A vendor reaching 120% is probably quoting DC nameplate against a peak-sun-hour number without a performance ratio, or assuming a tilted, tracked array.
Battery verdict: to shift the evening peak, roughly 24 kWh of usable storage is needed. At 80% depth of discharge that is 30 kWh nominal, costing 30 × ₹18,000 = ₹5.4 lakh - an 83% increase on the ₹6.48 lakh array, before round-trip losses of about 10–15%. Payback stretches past 8 years and beyond typical battery warranty. Judgment: install the array now, keep it grid-tied under net metering, and defer storage until tariffs, export rules or battery prices change - the array alone already delivers the cheapest kWh on the table.