0000000000122282
AUTHOR
Georgi Hristov Yordanov
Relative efficiency revealed: Equations for k<inf>1</inf>&#x2013;k<inf>6</inf> of the PVGIS model
The European PV Geographical Information System (PVGIS) describes module performance in terms of the relative efficiency with respect to Standard Testing Conditions (STC). The efficiency's dependence on irradiance and operating temperature is modeled with a bi-quadratic polynomial with respect to the relative temperature and the logarithm of relative irradiance. In earlier works, the present author derived relations between two model coefficients describing the irradiance dependence at 25°C, k 1 and k 2 , and I–V curve model parameters such as the series resistance RS and the ideality factor n. There was good agreement between the theoretical and fitted values of k 1 , but the fitted values…
Stability of the performance of thin film modules during one year of operation
At the University of Agder in Grimstad, Southern Norway, a test bench for photovoltaic modules is in operation since December 2010. Currently, various c-Si as well as aSi, CIS and HIT modules are under investigation. This project is part of the Norwegian contribution to IEA PVPS Task13. The paper focuses on the stability of the modules' MPP-performance in the course of one year. For this purpose, data on the DC response are logged together with irradiance and module temperature at one-minute intervals. Data analysis is performed in monthly blocks. The modeling involves two steps. First, the short-circuit current is expressed as function of irradiance and module temperature. Then, the MPP po…
Ideality factor behavior between the maximum power point and open circuit
The local ideality factor analysis of dark and light I-V curves has been used in the past to study various performance degradation effects in solar cells. Trapping, edge recombination and injection-level-dependent recombination are expressed as “lumps, humps and bumps” in the plots of the local ideality factor over cell voltage (m-V plots). Earlier applications of this differential technique did not correct the plots for the series resistance effect. Thus, the bumps at the higher voltages introduced by some mechanisms were more difficult to quantify. A possible solution is to analyze ISC-VOC curves, but their measurement is not always possible. We present a formula for calculation of the RS…
PV modules with variable ideality factors
The classical single-exponential I–V curve model for crystalline-Si PV devices assumes a constant ideality factor. The model is widely applied in e.g. modeling the power output of PV systems at different irradiances and temperatures, and also in calculating the Equivalent Cell Temperature (ECT) from the open-circuit voltage. The present paper presents results from several crystalline-Si (c-Si) module types suggesting that the ideality factor may change with irradiance. The possible implications of such variability are discussed, in particular the need for a new ECT calculation procedure as well as for revision of some PV performance models.
Series resistance determination and further characterization of c-Si PV modules
Abstract This paper presents a new algorithm for determination of the series resistance of crystalline-Si PV modules from individual illuminated I–V curves. The ideality factor and the reverse saturation current are then extracted in the classic way. The approach is applied to in-situ measured data from modules based on two types of mc-Si feedstock. The results indicate that the method yields physically meaningful parameters. An improved definition of local ideality factor is suggested, resulting in m-V plots unaffected by the series resistance. In addition, m-I plots are introduced for the first time. The novel differential techniques reveal an unexpected rise of the ideality factor at ope…
100-millisecond Resolution for Accurate Overirradiance Measurements
Cloud enhancement of sunlight results in peak irradiance well exceeding extraterrestrial levels, even at high latitudes. Values above 1.8 kW/m2 are possible in the equatorial regions. Recently, we detected bursts over 1.5 kW/m2 in Northern Europe at latitude close to 60°N. Overirradiance events (intensities much higher than 1 sun) can last tens of minutes, as well as less than 1 s. They may have caused series arcing in photovoltaic modules, leading to fires and loss of property. The accurate measurement of short bursts requires sensors with response times on the order of milliseconds. The long response times of thermopile pyranometers smooth out important details of very short-lived peaks a…
Optimal temporal resolution for detailed studies of cloud-enhanced sunlight (Overirradiance)
Enhancement of sunlight by clouds can lead to irradiance peaks much exceeding the extraterrestrial levels - close to 2 suns near the Equator and at least 1.5 suns at latitudes of about 60°. Some extreme overirradiance events can last many minutes, but durations in the order of 1 second are also possible. The present paper reports the shortest bursts recorded in Southern Norway in the years 2012 and 2013. Our records of 10-millisecond resolution from 2012 show that the optimal instantaneous irradiance sampling interval is less than 0.15 s at the present test site, while the optimal averaging time is less than 0.13 s. We propose simple equations for deriving these times in an arbitrary geogra…
Test of the European Joint Research Centre performance model for c-Si PV modules
The performance of ten c-Si PV modules is studied at different levels of illumination and module temperatures and is modeled in terms of relative efficiency with respect to Standard Testing Conditions (STC). A recently proposed model is tested in Nordic conditions for generic mono- and mc-Si devices with screen-printed cells as well as for some high-efficiency cell designs. Two of the modules are field aged. Averaged model coefficients are derived and compared to values found in the literature. Irradiance and module temperatures measured in 2011 are then used to estimate the expected annual energy yields. The measured yields equal the predicted ones within 1.6% (mean bias error −1.0%) which…
Development of a test station for accurate in situ I-V curve measurements of photovoltaic modules in Southern Norway
The development of an outdoor test station for accurate in situ I-V curve measurements of photovoltaic (PV) modules is described. The modules are installed in an open-rack configuration at the University of Agder in Southern Norway. Seven new and three aged PV modules of different type and make are being tested, including mono-and multicrystalline silicon from differing manufacturing routes, triple-junction amorphous silicon, and CIS. Data acquisition is controlled with a multichannel electronic load system and LabVIEW software, recording high-resolution I-V curves at one-minute intervals. Between I-V curve sweeps, each module is operated at the maximum power point. Characteristic electrica…
On the Variability of the Temperature Coefficients of mc-Si Solar Cells with Irradiance
Abstract The temperature sensitivity of silicon solar cells is in general assumed to be constant with irradiance in PV forecasting models, although it has been demonstrated experimentally that this is not true. In this study a theoretical model is established that describes the variation of the temperature coefficients of a silicon solar cell as a function of the irradiance. It is shown that the temperature sensitivity of the solar cell efficiency is decreasing with the irradiance and that the main reason for this behavior comes from the increase of the open-circuit voltage with light intensity. Moreover, a dependency of the cell's ideality factor on the irradiance has to be assumed to rece…
1.6 suns at 58&#x00B0;20&#x2032;N - the solar resource in Southern Norway
We measured an extreme overirradiance event of 1.6 suns at latitude 58°20′N during a solar resource assessment in southern Norway. The burst occurred when the sun showed in a narrow gap between broken, optically thin altocumulus clouds. The enhancement was most intense within 3° around the solar disk. The annual solar irradiation in the plane of an optimally tilted PV array peaked at 1.30 MWh/m2 in the year 2013, and measured 1.20 MWh/m2 in the previous two years. These values exclude irradiance below 0.05 suns but include reflections from the sea surface and terrain which have not been quantified. The long-term average predicted by the Photovoltaic Geographical Information System (PVGIS) i…
A study of extreme overirradiance events for solar energy applications using NASA’s I3RC Monte Carlo radiative transfer model
Abstract Near the Equator, some cloud types can boost the terrestrial solar irradiance to above 1.8 kW/m2. Even at high latitude close to 60°N, we have measured bursts up to 1.6 kW/m2, almost at sea level. For comparison, the extraterrestrial irradiance peaks at about 1.4 kW/m2 in early January. The global upper limit for extreme overirradiance is still unknown. The enhancement is strongest within about 3° from the unobstructed solar disk. We use the NASA’s I3RC Monte Carlo model to simulate the radiative transfer of solar photons in a cloudy atmosphere. The geometry includes an overhead sun and an infinite plane parallel water cloud with a ‘circular’ gap of the same angular diameter as tha…
Modeling and parameter identification of crystalline silicon photovoltaic devices
This paper tests the standard single-exponential model of the electrical characteristics of crystalline-Si photovoltaic devices, focusing on the (apparent) shunt current. Measured characteristics of illuminated polycrystalline-Si photovoltaic modules are modeled, and the apparent shunt current is analyzed. It is shown that an Ohmic-like behavior only takes place at voltages well below the maximum-power point. At higher voltages, the apparent shunt current quickly drops to negligible values. Modeling a crystalline-Si PV device with a fixed shunt resistance may therefore lead to underestimation of the maximum power exceeding 10% at certain irradiance levels.
Extreme overirradiance events in Norway: 1.6 suns measured close to 60°N
Abstract We report the most extreme overirradiance event of 1.6 kW/m 2 measured so far in Grimstad, southern Norway (latitude 58°20′), at altitude of only about 60 m a.s.l. Images of the sky conditions taken with a wide-dynamic-range camera suggest that this is not the ultimate value for our location, but that extremes as high as 1.7 kW/m 2 may be possible. The phenomenon was caused by strong forward scattering of sunlight within 3° around the solar disk in thin, broken altocumulus clouds. The normalized spectrum of sunlight during such extreme events is very similar to the normalized clear-sky spectrum measured at Air Mass 1.4 and irradiance of 1.0 kW/m 2 . We suggest that the values excee…
Equivalent cell temperature calculation for PV modules with variable ideality factors
Outdoor testing of PV modules involves monitoring their operating temperatures which have strong influence on the output power. Back-of-module sensing is associated with significant uncertainty due to temperature drop across the back encapsulation and also due to non-uniform temperature over the module's area. The international standard IEC 60904-5 defines a procedure for calculating the Equivalent Cell Temperature (ECT) of PV devices from their open-circuit voltage. This and other standards (as well as some module performance models) assume a single-exponential I-V curve model with a constant ideality factor. However, this parameter may vary with the illumination level and the operating te…
A new analytical solar cell I–V curve model
Abstract A simple mathematical equation that can represent empirical I–V curves of individual solar cells, systems of solar cells and modules has been found. The basic model is determined by four parameters: the open circuit voltage, the short circuit current and two shape parameters. With the four parameters determined, the complete current–voltage curve, the fill factor and the maximum power point are given by simple analytical functions. The model is valid both in the positive and the negative (dark condition) voltage range. Several simple examples demonstrate some of the potential of the model. Due to its mathematical simplicity, it is suggested that the model will be suitable for analy…
Extracting parameters from semi-log plots of polycrystalline silicon PV modules outdoor I&#x2013;V data: Double-exponential model revisited
This paper presents a method for extracting physically meaningful parameters from measured I–V curves of PV modules. The 7-parameter double-exponential model is applied in the modeling. The method is based on linear fitting of semi-logarithmic plots. The paper demonstrates a new technique to estimate the series resistance of a module with high accuracy from such plots. As a result, also the reverse saturation current and the quality factor of the diffusion diode can be determined. The method is applied to outdoor I–V data from a test station with three similar, but not identical, polycrystalline-Si modules. The values of the series resistances found with this method deviate somewhat from th…
Modeling and parameter identification of crystalline silicon photovoltaic devices
In this paper the physical correctness of the standard single-exponential (one-diode) model of crystalline-Si photovoltaic devices is examined. In particular, we focus on the shunt current. I-V curves of in situ illuminated polycrystalline-Si photovoltaic modules are measured, and based on these measurements, we extract the shunt current. There is a certain voltage range in which the shunt current shows an Ohmic-like behavior, but the value of the resistance varies with irradiance and the quality of illumination. In addition, the Ohmic behavior takes place at voltages well below the maximum-power point (MPP). At higher voltages, the shunt current drops to negligible values. We conclude that…
Overirradiance (Cloud Enhancement) Events at High Latitudes
Contrary to intuition, solar irradiance peaks at partially cloudy conditions. Clouds can boost sunlight by over 1.5 times, even at high latitudes. Depending on cloud velocity, the bursts last from seconds to minutes. Measuring irradiance on a tilted surface with 10-ms resolution allows for a detailed study of such events in Southern Norway, almost at sea level. All monthly maxima from April through September 2011 exceeded 1300 W/m2. The slow sensor registered an annual maximum of 1413 W/m2, while the fast sensor's range was found insufficient. A burst reaching 1528 W/m2 was registered in June 2012. Near the Equator, bursts exceeding 1800 W/m2 have been observed. These numbers are striking s…
Physically-consistent parameterization in the modeling of solar photovoltaic devices
This research tests the standard one-diode model of a crystalline-Si photovoltaic cell, focusing on the physical accuracy. In particular, the (apparent) shunt resistance and the diode ideality factor are studied. Current-voltage characteristics of illuminated crystalline-Si photovoltaic modules are analyzed, and some limits of applicability of the standard model are given. Typical values of the ideality factor for crystalline-Si devices are derived from own experimental data as well as from recently published literature. It is shown that the contribution of the apparent shunt resistance is only significant for cell voltages below about 0.45 V, and depends on irradiance. This result is consi…
Contributions to the knowledge base on PV performance: Evaluation of the operation of PV systems using different technologies installed in southern Norway
To assist in establishing an accepted knowledge base on PV-modules and systems performance using a representative range of technologies, devices have to be installed at diverse locations, covering a broad range of environmental conditions. For the example of a high latitude location, modules and systems are installed and under investigation in southern Norway (Kristiansand region) by the University of Agder in cooperation with industrial partners. This paper presents first results of the analysis of module performance. The operational behavior of the modules is used to derive a modeling scheme applicable for performance prediction. This use is demonstrated by giving the expected annual perf…
A qualitative examination of performance and energy yield of photovoltaic modules in southern Norway
Three different, commercially available photovoltaic modules have been monitored outdoors in the town of Grimstad, Norway. The present paper describes the experimental setup that was implemented, in particular details of the low-cost electronic loads. Results compare measured performance with manufacturer's data, and temperature measurements enable a comparison with performance at standard test condition temperature. Overall, the monocrystalline module performed best both regarding maximum efficiency and overall energy production, whereas the module based on triple junction amorphous silicon technology had the worst performance considering these criteria. The gross numbers of energy yield c…