Separating temperature from irradiance in outdoor photovoltaic cooling trials: a paired-differential assessment of heat sink and water spray cooling

Abstract Outdoor photovoltaic cooling trials without an irradiance sensor often quantify the benefit by regressing module power on module temperature, a fit exposed to omitted-variable bias because irradiance drives both. This paper formalises a paired-differential estimator that contrasts each treated module with a simultaneously sampled untreated reference, and states when the common irradiance term cancels: a shared irradiance history, no module-specific shading, soiling or water film, synchronous sampling and an untreated reference. An analytical bound converts residual irradiance mismatch into bias on the open-circuit voltage coefficient. A proposed plausibility screen tests logged short-circuit current and open-circuit voltage of uninstrumented records against a clear-sky plane-of-array envelope. Both tools were applied to a seven-day campaign in Bandung, Indonesia, with four 30 W modules under no cooling, heat sinks, water spray and both (70 hourly records). The modules were canopy-shaded at every sampled hour and not cleaned, and the electrical values were hand-recorded, some entries not independently verifiable. The record fell outside the clear-sky envelope. Short-circuit current reached 3.39 times the clear-sky expectation, and the open-circuit voltage lacked the expected irradiance dependence (−0.002 ± 0.030 V per unit ln G against 0.97 to 1.25 V expected). The electrical results, including a voltage coefficient of −88.2 mV/°C and power gains below 1% reconstructed from V_oc and I_sc at a constant fill factor, are presented as an illustration of the estimator. Thermocouple temperature differences are indicative: −1.45, −1.08 and −2.12 °C for heat sink, spray and combined treatment. With theoretical pump runtime and nameplate power, the sign of the spray energy balance is not determined.