String sizing and yield claim for a 9 kWp rooftop PV plant
A 9 kWp rooftop array is proposed for a garment unit in Coimbatore: 20 modules of 450 Wp each (Voc 49.5 V, Vmp 41.2 V, Impp 10.93 A, beta_Voc = −0.27 %/°C, beta_Vmp = −0.40 %/°C, gamma_Pmp = −0.35 %/°C, NOCT 45 °C), wired as two strings of ten into a string inverter rated 8 kW AC with an MPPT window of 200–800 V and a 1000 V DC maximum. The site record low is −5 °C; on a 45 °C ambient day the measured cell temperature is 68 °C. Plane-of-array irradiation is 1,780 kWh/m² per year and an independent estimate puts the performance ratio at 0.78, covering soiling, temperature, mismatch, wiring and inverter losses. The owner's annual consumption is 12,000 kWh at a flat retail tariff of ₹7.40/kWh, of which he estimates 45% falls in the 09:00–17:00 window; export is credited at an avoided-cost rate of ₹3.20/kWh, not at retail. The EPC contractor calls a DC/AC ratio of 1.125 'optimal' and promises a near-zero bill.
1. Check the two-strings-of-ten configuration against the inverter voltage window at both temperature extremes, and state how many modules a single string could carry before a limit is breached.
Read the worked answer
Cold end. Voc(−5 °C) = 49.5 × [1 + (−0.0027)(−5 − 25)] = 49.5 × 1.081 = 53.5 V per module, so a ten-module string reaches 535 V. That is below the 1000 V DC maximum and below the 800 V MPPT ceiling. Passes.
Hot end. Vmp(68 °C) = 41.2 × [1 + (−0.0040)(68 − 25)] = 41.2 × 0.828 = 34.1 V, so the string sits at 341 V at noon in summer, i.e. 141 V above the 200 V MPPT floor. Passes.
Maximum string length. The binding constraint is the 1000 V cold-condition limit: 1000/53.5 = 18.7, so 18 modules (963 V) is the maximum; 19 modules would give 1017 V and destroy the inverter. Reconciling with the window: at 18 modules the hot Vmp is 18 × 34.1 = 614 V, still inside 200–800 V, so the voltage window does not limit the design - the 8 kW AC rating does, via the DC/AC ratio.
2. Estimate the annual AC energy and specific yield, and judge whether a DC/AC ratio of 1.125 will cause material clipping.
Read the worked answer
Annual AC energy = 9 kWp × 1,780 kWh/m² × 0.78 = 12,496 kWh, i.e. a specific yield of 1,388 kWh/kWp. That is a credible figure for Tamil Nadu and needs no correction.
Clipping check: instantaneous DC power is set by irradiance and cell temperature, not by the kWp label. At 68 °C cell temperature, Pmp = 9.0 × [1 + (−0.0035)(68 − 25)] = 9.0 × 0.850 = 7.65 kW, which is below the 8 kW AC ceiling, so on hot afternoons there is no clipping at all. Clipping appears only on cool, clear days: at a 45 °C cell, Pmp = 9.0 × 0.930 = 8.37 kW, so roughly 0.4 kW is spilled for a couple of hours. Integrated over the year this is a fraction of a percent of yield.
The contractor's 1.125 is therefore defensible, but for a reason he has not stated: the site's high cell temperatures, not an inherent optimum. A 7.5 kW inverter would clip noticeably; an oversized 10 kW inverter would waste capital.
3. Assess the 'near-zero bill' promise using the consumption split and the ₹3.20/kWh export rate.
Read the worked answer
Bill without PV = 12,000 × 7.40 = ₹88,800/yr.
Daytime load in the PV window = 0.45 × 12,000 = 5,400 kWh. Even with perfect instantaneous matching the array cannot self-consume more than this, so at best 5,400 kWh is offset at the full retail rate. The surplus, 12,496 − 5,400 = 7,096 kWh (57% of generation), is exported and earns only ₹3.20/kWh.
Savings = 5,400 × 7.40 + 7,096 × 3.20 = 39,960 + 22,707 = ₹62,667/yr, or about 71% of the bill. Exporting more than half the generation at an avoided-cost rate is the structural weakness of the design, not the array size.
Judgement: the 'near-zero bill' claim requires full net metering at retail, which is not what the tariff offers. Either shift daytime load (chiller, compressor, dryer) into the 09:00–17:00 window, or accept that roughly 30% of the bill remains; the payback should be computed on ₹62,667, not ₹88,800.