Rooftop Solar Capacity Above the Sanctioned Load
An industrial consumer has a sanctioned load of 150 kW and a contract demand of 160 kVA, fed at 11 kV through a dedicated 250 kVA distribution transformer. The roof can physically hold 180 kWp. The consumer has a quotation for 180 kWp of 540 Wp modules and a 150 kW three-phase string inverter. Local net-metering rules cap the AC capacity of the solar system at the consumer's sanctioned load, and the distribution company will not approve a larger inverter; the consumer asks whether to install the extra 30 kWp anyway on the same 150 kW inverter or to stay at 150 kWp. Module data: Voc 49.6 V, Vmp 41.8 V, Voc temperature coefficient −0.27%/°C, Vmp coefficient −0.35%/°C. Inverter data: maximum DC input 1100 V, MPPT window 200–850 V, three MPPTs. Site extremes: minimum ambient 3 °C, maximum cell temperature 65 °C. Specific yield is about 1450 kWh/kWp per year and the tariff is ₹7.20/kWh.
1. Determine the maximum admissible AC capacity and recommend the DC array size and configuration, quantifying the trade-off between extra generation and clipping.
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The AC capacity is capped at 150 kW because the sanctioned load is 150 kW and the discom will not approve a larger inverter. That cap is regulatory, not technical - the 250 kVA transformer could physically carry 150 kW of backfeed.
Option A: 150 kWp DC on a 150 kW inverter, DC:AC = 1.0. Annual generation ≈ 150 × 1450 = 217,500 kWh, worth about ₹15.66 lakh.
Option B: 180 kWp DC on the same 150 kW inverter, DC:AC = 1.2. Annual DC-side potential = 180 × 1450 = 261,000 kWh, but generation above 150 kW is clipped. At this ratio in Haryana's irradiance, clipping is typically 1.5–2%, so delivered energy ≈ 261,000 × 0.98 ≈ 255,800 kWh, about ₹18.4 lakh.
The extra 30 kWp therefore earns roughly ₹2.7 lakh a year, which comfortably beats its module, structure and cabling cost over the system life, and the inverter is already paid for. Clipping is not waste in this design: the lost energy is small compared with the gain from the extra array, and the inverter runs closer to its efficient loading band for more hours.
Configuration: 180,000/540 = 333 modules, so 16 strings of 20 modules = 320 modules = 172.8 kWp, DC:AC = 1.15, split across the three MPPTs. If the consumer wants the full 180 kWp, use 18 strings of 20 (360 modules).
2. Check the string design against the site temperature extremes. How many modules may be connected in series, and does the string stay inside the MPPT window at high cell temperature?
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Cold-condition open-circuit voltage, at 3 °C (22 °C below the 25 °C reference):
Voc(3 °C) = 49.6 × [1 + 0.0027 × 22] = 49.6 × 1.0594 = 52.55 V per module.
For 20 modules: 20 × 52.55 = 1051 V, which is below the 1100 V maximum DC input, with a 49 V margin - acceptable. For 21 modules: 21 × 52.55 = 1103 V, which exceeds 1100 V - not permissible, and the margin at 20 is already thin enough that a colder-than-design morning (−1 °C is possible in Haryana) would push 20 modules to about 1065 V. Keep 20 and confirm the inverter's absolute maximum, not just its nominal, is 1100 V.
Hot-condition MPP voltage at 65 °C (40 °C rise): Vmp(65 °C) = 41.8 × [1 − 0.0035 × 40] = 41.8 × 0.86 = 35.95 V per module. For 20 modules: 20 × 35.95 = 719 V - inside the 200–850 V MPPT window, with 131 V of headroom to the upper limit.
So 20 modules per string is the correct answer on both ends: it respects the cold Voc limit and stays inside the MPPT window at maximum cell temperature. A 22-module string would look attractive on paper for cable losses but would be destroyed on the first cold morning.
3. The consumer blames the discom's 150 kW cap on 'voltage rise on the 11 kV feeder'. Assess that claim quantitatively and state what the real technical constraints and protection requirements are.
Read the worked answer
Voltage rise check. At 11 kV the export current at 150 kW, unity power factor, is 150,000/(√3 × 11,000) = 7.87 A. If the feeder impedance from the PCC to the substation is about 0.45 + j0.65 Ω per phase, the per-phase rise is approximately I × R = 7.87 × 0.45 = 3.5 V, i.e. about 0.06% of 6350 V phase voltage. Even with reactive export the rise stays under 0.2%. Voltage rise is not the constraint at this capacity and voltage level - the consumer's claim is wrong.
Real constraints:
- The net-metering cap of 150 kW AC, tied to the sanctioned load, which is a regulatory limit and is the actual reason for refusal.
- Transformer loading: the 250 kVA unit already carries 160 kVA of demand; a 150 kW backfeed must be checked against reverse-flow loading and against the transformer's tap position, which was set for forward drop.
- Reverse power flow through the LT ACB and metering: the existing protection may be directional or non-directional; confirm the ACB and the net meter are rated for bi-directional flow.
Protection requirements: the inverter must have certified anti-islanding that disconnects within the specified time on loss of mains, a visible lockable isolator at the PCC, and a separate generation meter. Document the settings and get the discom's approval before energising, because an unapproved parallel connection is a licence violation regardless of how small the voltage rise is.