Solar Inverter Oversizing: DC/AC Ratio and Clipping Loss

The year contains 365 × 24 one-hour midpoint samples in local solar time. The samples are processed month by month, retaining every hour. Solar declination uses the Cooper approximation; the sun vector is projected onto the selected fixed plane(s). Haurwitz clear-sky horizontal irradiance is $G_{cs}=1098\cos z\exp(-0.059/\cos z)$ W/m², zero below the horizon. The user cloud multiplier scales it. A user-selected constant diffuse fraction separates horizontal irradiance into beam and diffuse; isotropic sky and 0.2 ground albedo transpose it to each plane. These weather and transposition choices are a simplified scenario, not the complete PVWatts irradiance model.

Module conversion: NREL PVWatts Version 5 Manual (attached s3, file page 12, printed p. 9), equation 8: $P_{dc}=P_{STC}(G/1000)[1+\gamma(T_c-25)]$. Here a derived steady-state approximation $T_c=T_a+\Delta T_{800}G/800$ replaces the PVWatts Fuentes thermal model. Other system losses are applied once, separately from the inverter (s3 file pages 13–14).

Current and AC limits: derive per-tracker operating current from the temperature-adjusted module DC power divided by $N_{MPPT}V_{MPP}$. Cap this current at the usable MPPT rating, then multiply accepted current by the same fixed voltage and apply other DC losses. Thus each tracker obeys $P_{dc,accepted}\leq V_{MPP}I_{MPPT}(1-L_{dc})$, including cold conditions. The entered fixed voltage must lie inside the hot/cold string MPP bounds, themselves within the inverter window and below cold open-circuit voltage. This is a constant-MPP-voltage approximation, not an IV-curve solution. PVsyst's inverter-operating-limits reference (attached s8) describes the simultaneous power, voltage and current boundaries; this tool does not model migration along an IV curve. PVWatts part-load efficiency follows equation 10 (s3 file page 14): $\eta=(\eta_{nom}/0.9637)(-0.0162\zeta-0.0059/\zeta+0.9858)$, $P_{dc0}=P_{ac0}/\eta_{nom}$. Clamp negative low-load output to zero and AC output to its nameplate. For the counterfactual potential above rating, hold efficiency at its nominal value; the fitted part-load curve is not extrapolated to arbitrary overload.

Energy accounting is sequential: potential AC → MPPT current loss → AC clipping loss → export curtailment → delivered AC to the local load and grid. The schematic and moving cursor show this delivered power. Annual and monthly available AC before export curtailment remain separate counterfactual quantities for the loss accounting. Both inverter loss percentages use potential AC before either inverter limit as the denominator; export loss is excluded. Export allowance is applied after local load, so accepted PV is $\min(P_{ac},P_{load}+P_{grid})$ when enabled. Sum hourly powers × 1 h for annual energy. The daily curve uses 15-minute samples for illustration only.

Compare both arrays on the same inverter, orientations, temperatures and loads. Annual incremental value is added self-consumed kWh × entered self-use value plus added exported kWh × entered export value. Simple payback divides incremental installed cost by positive annual incremental value. The sweep covers sizes up to the smallest entered DC-power/per-MPPT-Isc/total-Isc ceiling, with the entered string voltages held fixed.

Three attached, quote-verified pvlib numeric cases validate the DC and inverter submodels. An independent cold-weather limiting case uses the published power/current/voltage relationship to require exactly 2 × 350 V × 5 A = 3.50 kW when sufficient DC power is available. These cases do not independently validate the synthetic annual resource.

The independent-review export-boundary case requires 0.5 kW local demand + 3.68 kW permitted export = 4.18 kW delivered AC at the default solar noon, despite 5 kW available before curtailment.

• Generic illustrative equipment inputs, not a preselected certified inverter/module combination. Both baseline and proposed arrays share the same string voltage and are balanced equally across identical active MPPTs. Additional capacity represents parallel panel area; select feasible integer strings separately.
• Equator-facing azimuth is south in the northern hemisphere and north in the southern hemisphere. East–west means exactly 50% east and 50% west, equal tilt and separate MPPT groups; an even number of active trackers is required.
• Uniform cloud transmission, uniform diffuse fraction, constant daytime ambient temperature and simple steady-state cell heating. No hourly weather feed, wind, altitude, horizon, refraction, inter-row shading, bifacial gain, snow dynamics or cloud enhancement.
• Lumped DC system losses are uniform and exclude inverter and export losses. Operating current is inferred from irradiance- and temperature-adjusted PVWatts module power at the entered constant MPP voltage. The power temperature coefficient is applied before current limiting; detailed IV-curve changes and operating-voltage shifts are not modeled.
• Design Isc = inferred STC Imp × datasheet Isc/Imp × the user correction factor. This is a screening check; confirm actual module Isc, parallel string counts, temperature corrections, total current limits and the manufacturer's rating definitions.
• Constant coincident local load; no battery, storage charging or time-of-use tariff. AC rating is active power after any required power-factor/temperature derating. No night standby consumption.
• Cost and energy-value defaults are arbitrary examples dated 2026-10-28, in one user-chosen currency. No jurisdiction-specific tariff, incentive or regulatory sizing rule is applied. The default 1.25 Isc correction is illustrative, not a compliance prescription.

For fixed arrays at latitudes −65° to +65°, within all entered manufacturer limits, as an educational and preliminary sizing comparison. Results are conditional on synthetic irradiance and temperature assumptions; do not use the annual number as a warranted yield or a bankable financial forecast. Hourly midpoints can miss short high-power events and underestimate real clipping.

Hard-limit violations hold back result cards. Neither AC clipping nor export limiting protects against excessive DC nameplate, open-circuit voltage or short-circuit current. Enter hot/cold string voltages computed for the actual modules and site; startup voltage, detailed IV behavior, asymmetric trackers, string fuses and wiring are not designed here. Check against equipment documentation, the standard in force and applicable grid rules. Installation work belongs to a qualified person.