Comparison of Modelled and Measured Tilted Solar Irradiance for Photovoltaic Applications

Abstract

This work assesses the performance of five transposition models that estimate the global and diffuse solar irradiance on tilted planes based on the global horizontal irradiance. The modelled tilted irradiance values are compared to measured one-minute values from pyranometers and silicon sensors tilted at different angles at Hannover (Germany) and NREL (Golden, CO, USA). It can be recognized that the deviations of the model of Liu and Jordan, Klucher and Perez from the measurements increases as the tilt angle increases and as the sensors are oriented away from the south direction, where they receive lower direct radiation than south-oriented surfaces. Accordingly, the vertical E, W and N planes show the highest deviation. Best results are found by the models from Hay and Davies and Reindl, when horizontal pyranometer measurements and a constant albedo value of 0.2 are used. The relative root mean squared difference (rRMSD) of the anisotropic models does not exceed 11% for south orientation and low inclination angles (β = 10-60 • ), but reaches up to 28.9% at vertical planes. For sunny locations such as Golden, the Perez model provides the best estimates of global tilted irradiance for south-facing surfaces. The relative mean absolute difference (rMAD) of the Perez model at NREL ranges from 4.2% for 40 • tilt to 8.7% for 90 • tilt angle, when horizontal pyranometer measurements and a measured albedo value are used; the use of measured albedo values instead of a constant value of 0.2 leads to a reduction of the deviation to 3.9% and 6.0%, respectively. The use of higher albedo values leads to a significant increase of rMAD. We also investigated the uncertainty resulting from using horizontal pyranometer measurements, in combination with constant albedo values, to estimate the incident irradiance on tilted photovoltaic (PV) modules. We found that these uncertainties are small or negligible.

A Comprehensive Approach for Modelling Horizontal Diffuse Radiation, Direct Normal Irradiance and Total Tilted Solar Radiation Based on Global Radiation under Danish Climate Conditions

“…The isotropic sky model under-predicts total radiation on a tilted surface and is not recommended for general use. The HD and Reindl models were recommended in the mentioned references [25,26]. The HD model has also been selected to predict total tilted solar radiation in Greece [45].…”

“…Mubarak et al [25] compared five empirical models for PV applications. The authors concluded that the models of Hay and Davies and Reindl are recommended to estimate tilted irradiance for south-facing modules in regions with mainly cloudy conditions and when albedo measurements are not available.…”

Prediction of Solar Irradiance Based on Artificial Neural Networks

“…A pyranometer is used to measure the irradiance of the sun [3]. It can be installed on a surface to measure the global irradiance received from the hemisphere, as shown in Figure 1 [4][5][6]. It is used to measure global (diffuse and beam) irradiance on a horizontal plane [3,6].…”

“…It can be installed on a surface to measure the global irradiance received from the hemisphere, as shown in Figure 1 [4][5][6]. It is used to measure global (diffuse and beam) irradiance on a horizontal plane [3,6]. However, pyranometers have several disadvantages: (1) the price can be between $300 (with low accuracy) and $1800 (with high accuracy), (2) the sensitivity can vary with time, (3) exposure of irradiance with long time and high temperature (>50 °C) can reduce the accuracy of the device, and (4) the pyranometer needs to be calibrated daily and whenever there is a significant variation in weather conditions [3].…”

Response to Referee #1

“…In our field sites LAI ranged from 0.0-2.1 and was <1 in most sites. In another study, Inge (1968) reported that silicon pyranometers overestimated plant, sand, water, and rock albedo by ∼0.03, and suggested caution should be taken for measuring snow albedo as the overestimation can be as high as 0.09. Stroeve et al (2005) found that silicon pyranometers can overestimate albedo by 0.04-0.09.…”