Analysis of inhomogeneous local distribution of potential induced degradation at a rooftop photovoltaic installation
2017; Institution of Engineering and Technology; Volume: 11; Issue: 10 Linguagem: Inglês
10.1049/iet-rpg.2017.0105
ISSN1752-1424
AutoresClaudia Buerhop‐Lutz, Tobias Pickel, Tirth Patel, Frank W. Fecher, Cornelia Zetzmann, Christian Camus, Jens Hauch, Christoph J. Brabec,
Tópico(s)Solar Radiation and Photovoltaics
ResumoIET Renewable Power GenerationVolume 11, Issue 10 p. 1253-1260 Special Issue: Performance Assessment and Condition Monitoring of Photovoltaic Systems for Improved Energy YieldFree Access Analysis of inhomogeneous local distribution of potential induced degradation at a rooftop photovoltaic installation Claudia Buerhop, Corresponding Author Claudia Buerhop claudia.buerhop-lutz@zae-bayern.de Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorTobias Pickel, Tobias Pickel Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorTirth Patel, Tirth Patel Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorFrank W. Fecher, Frank W. Fecher Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorCornelia Zetzmann, Cornelia Zetzmann Rauschert GmbH, Bahnhofstraße 1, 96332 Pressig, GermanySearch for more papers by this authorChristian Camus, Christian Camus Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorJens Hauch, Jens Hauch Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorChristoph J. Brabec, Christoph J. Brabec Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, Germany Institute Materials for Electronics and Energy Technology (i-MEET), Friedrich-Alexander University Erlangen-Nürnberg (FAU), Martensstraße 7, 91058 Erlangen, GermanySearch for more papers by this author Claudia Buerhop, Corresponding Author Claudia Buerhop claudia.buerhop-lutz@zae-bayern.de Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorTobias Pickel, Tobias Pickel Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorTirth Patel, Tirth Patel Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorFrank W. Fecher, Frank W. Fecher Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorCornelia Zetzmann, Cornelia Zetzmann Rauschert GmbH, Bahnhofstraße 1, 96332 Pressig, GermanySearch for more papers by this authorChristian Camus, Christian Camus Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorJens Hauch, Jens Hauch Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, GermanySearch for more papers by this authorChristoph J. Brabec, Christoph J. Brabec Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern), Immerwahrstraße 2, 91058 Erlangen, Germany Institute Materials for Electronics and Energy Technology (i-MEET), Friedrich-Alexander University Erlangen-Nürnberg (FAU), Martensstraße 7, 91058 Erlangen, GermanySearch for more papers by this author First published: 24 August 2017 https://doi.org/10.1049/iet-rpg.2017.0105Citations: 9AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Potential induced degradation (PID) of photovoltaic (PV) modules is one of the frequently observed failures in PV installations nowadays. This study investigates the inhomogeneous and complex PID generation on rooftop installations on industrial buildings as well as its impact on the module performance. The PID development is exemplarily presented for a 314kWp PV-plant installed in the Atlantic coastal climate. Due to the complex plant geometry and resulting irradiation situation the existence of PID could not be identified based on the annual yield data. By Infrared imaging PID was clearly identified. Evaluating historic monitoring data, the impact of PID on the string and plant performance could be quantified. A linear correlation between the defect ratio and the performance rate as well as the degradation loss rate could be formulated. 1 Introduction Potential induced degradation (PID) of photovoltaic (PV) modules is a failure mode that has become more prevalent during the last years. In an article from 2016 it is supposed by interviews with operators of many big PV plants that 19% of the PV plants suffer from PID or PID suspicion [1]. This number represents an enormous economic loss for the plant operators and financial investors. PID is a PV-failure mode that causes significant power reduction. Electrically, it can be described as a reduction of the shunt resistance of the affected cells. Laboratory investigations reveal that high negative electric potential differences between the cell and the grounded module frame (due to long module strings), high humidity and high temperature are the dominant root-causes for PID and its progression [2-5]. By this, ion transport from the glass into the cell is one proposed reason for PID [6]. The PID development is also discussed for some outdoor experiments [7-10]. The functionality of PV plants is usually controlled and inspected with the monitoring data retrieved from the inverter or by using imaging techniques such as infrared (IR)-thermography or electroluminescence imaging (EL) [11]. Whereas the monitoring data is collected continuously, but only on module string resolution, the imaging techniques take a lot more time to image the whole PV plant and evaluate the images on module level. Therefore, the imaging techniques have a much lower time resolution, but they help to localise the defective module and classify the defect type due to its spatial resolution down to cell level. However, the analysis of PV plants by imaging techniques is mainly of qualitative nature and algorithms to predict the power reduction from the images are still under research. Only simple correlations could be used if module substrings or whole modules are short- or open-circuited [12]. This is the reason why for a quantitative power reduction and degradation rate of PV plants I–V measurements or the monitoring data are commonly used [11, 13-16]. Typical analysis values include energy yield and performance ratio, with the latter more accurate as it includes the real irradiance [17]. In the case of PID, the correlation between thermography in field and module power reduction has been successfully shown [18-20]. Whereas Kaden et al. generated a reference curve correlating the temperature difference and power loss of the solar cells from experimental data, Buerhop et al. simply assumed no power generation for suspicious warmer cells. Both approaches led to good results. However, the question arises how good a prediction on the performance ratio and the degradation rate of a real PVplant by taking just a single IR-thermography inspection could actually be. Therefore, for this paper, we investigated a 314kWp PV plant on an industrial rooftop in Portugal that revealed severe PID damage. Evaluation of the monitoring data of this PV plant was challenging due to partial shading of the modules by various roof installations (chimneys and other roof outlets) resulting in inhomogeneous irradiated modules within the module string by frequently alternating roof orientation and complexly connected strings (cf. Fig. 1). The annual energy yield for the last 3 years of operation was fluctuating and gave no indication for accelerated degradation of the PV plant. Nonetheless, we were able to show how the monitoring data of a real and complex PV installation can be evaluated so that degradation is detected even at this stage. Fig. 1Open in figure viewerPowerPoint Image of the roof installation on a factory-varying installation angles, roof outlets, different orientation to the sun, soiling (visible on the module rows in the background of the picture), changes of shading situations due to various roof installations The use of aerial infrared (aIR) inspection has been used previously to identify PID-degraded modules [20-23]. In our case it is interesting that the degraded module strings are not distributed homogeneously over the PV plant, but are clustered. The reason for this clustering seems to be caused by different 'micro-climates' (in terms of local operating conditions) on the roof. Besides monitoring data of the maximum power point (MPP) at string level and IR imaging, electroluminescence (EL) imaging, current–voltage (I–V) measurements (on module and module string level) and weather data complemented our investigations. 2 PV plant specification 2.1 PV plant A 314 kWp PV plant installed in 2013 and located in Trajouce, Portugal (latitude: 38.73966; longitude: −9.34070) in the Atlantic coastal climate close to the ocean was examined. It consists of 1280 polycrystalline PV modules, each with a nominal power of 245 W. From 15 to 24 modules are electrically connected in series. At STC the Voc equals 37.1 V and Vmpp equals 30.3 V. For a string with 15–20 modules this yields a string voltage Voc,string between 556.5 and 890.4 V and at MPP a voltage Vmpp,string between 454.5 and 727.2 V, respectively. There are 60 strings and 15 inverters. Most inverters control four strings, three parallel strings and one separate string. The first IR inspection with detection of PID was carried out after 2.25 years of operation. To address particular strings in specific inverters, the following nomenclature is used: I1 S2, which refers to string 2 of inverter 1. The PV modules of the installation are distributed over the roofs of several buildings, which exhibit differently inclined roof areas, various further roof installations, chimneys, and different outlets according to the respective fabrication process in the building (cf. Fig. 1). At several positions, marked in Fig. 2, outlets are shown which cause shading, soiling or may lead to increased temperatures in their vicinity. There are air outlet temperatures above 50°C or higher depending on the production process in the factory. Fig. 2Open in figure viewerPowerPoint Aerial picture of the roof installation of the investigated PV plant on an industrial building. Positions of outlets emitting heat or dust are marked by the numbers 1–6. A, B, C, and D define distinct local roof areas with differing ground conditions and positions within the PV-plant. Predominately module type 'A' is present which has been originally installed. One module string has been replaced by module type 'B' for unknown reasons. The colour code indicates the defect ratio of the strings. The defect ratio is the basis for the ranking of the strings. (Imagery © 2017 Google, Map data © 2017 Google) Studying the influence of the roof location, the roof is sectioned in four main areas A, B, C, and D and some subareas due to ambient conditions and wind exposure. The ranking is based on the defect ratio k defined by (1) in Section 3.2. The locations of these areas are marked in Fig. 2. Areas A1 and A2 address porch roofs near A, which are more exposed to the wind. Area B2 is a porch roof close to B, whereas B1 is in the centre between factory installations, walls and crossovers. These subsections are created because in these areas differing conditions for heat transfer (A1, A2, B2 more exposed to the wind) and exceptionally high heat emission due to a spray dryer 1 (area B1) are present. A further peculiarity is that many strings connect modules which are located at differently inclined roof sections. This is typical for the installation in area A. 2.2 Weather The installation is located close to the Atlantic Ocean in a maritime climate. Meteorological data from the closest weather station (the Lisbon Metro area) are presented in Figs. 3 and 4 for the time period of interest [24, 25]. Typical weather conditions at this site are moderate temperatures in summer and winter of 4–33°C, constant humidity of 60–90%. Wind is always present due to the short distance to the coast. The average wind speed is 15 km/h, but high wind (7 Beaufort) with a maximum wind speed of 52 km/h is also common, as shown in Fig. 3. Therefore, moderate amounts of airborne sea water mist are common for this area. The annual solar irradiance is ∼1850 kWh/m2, as shown in Fig. 4. Fig. 3Open in figure viewerPowerPoint Weather data, wind speed, air temperature and humidity evaluated monthly for the Lisbon Metro area from 2013 to 2016 [24, 25] Fig. 4Open in figure viewerPowerPoint Solar irradiance monthly averaged over 30 years 1971–2000 for Lisbon Metro Area, Portugal [25] The meteorological data, solar irradiance and ambient temperature as well as the module temperature obtained from the monitoring system are plotted in Fig. 5. The seasonality of the data is distinctive. In winter irradiance E and air temperature Tair are rather low, minimum values are E = 50–150 Wh/m2 and Tair = 3–10°C, respectively. The daily irradiance reaches 400 Wh/m2 during summer. While the average temperatures of Tair and Tmod are very similar, the maximum module temperature is higher than the maximum air temperature, Tair,max = 35.6°C, Tmod,max = 47.3°C. The fairly small temperature difference between Tmod and Tair can be explained by large convective heat transfer due to steady and rather strong blowing wind at this location near the coast. Fig. 5Open in figure viewerPowerPoint Weather conditions, daily irradiance and averaged air and module temperature for the operation period of 3 years 3 Experimental procedure 3.1 Data collection For the investigation, monitoring data from a Sunny Webbox with Sensorbox (SMA Solar Technology AG, Germany) are available. The temporal resolution of the data is 5 min. Weather data (solar irradiance, air temperature, module temperature) in Trajouce and electric plant information have been recorded since February 2014. There are data for the strings, the inverters and the PV plant. The data with the best resolution are collected from the string data (string current, string voltage and string power). Inverter data are often not helpful because the strings of one inverter are spread all over the PV plant and behave totally differently due to the different locations, i.e. irradiation and local temperature. There is one weather station with one reference cell for the entire PV installation located at an unshaded position in area C (Fig. 2). The weather and electric data are post-processed to characterise every day by averaged day values as well as maximum or minimum values. Both solar irradiance and string power are integrated over the whole day for every string. This is done for all 1020 days of historic monitoring data. Additionally, maximum, minimum averaged air and module temperature are determined daily, as well as the maximum differences between air and module temperature. Here, the temperature of one module located in area C is measured to represent all modules installed in the PV plant. In addition to the continuous data collection, periodic IR-, EL-images, and IV-curves of the installed modules were obtained. In order to avoid damaging the modules, the measurements were carried out on-site. That means no dismounting, no transport, no handling of the modules are necessary, which introduce the potential to induce defects. The IR measurements were carried out twice, in November 2015 and June 2016. The measurement system consists of a drone equipped with an IR- and VIS-camera and various sensors for flight control. A GoPro Hero3+ as VIS-camera and an Optris PI 450 as IR-camera are used. The Optris PI 450 has a bolometer detector with 382 × 288 pixels. The effective lateral resolution ranges from 3 × 3 pixel up to 5 × 5 pixel per cell. The view angle is perpendicular to the module surface in order to avoid disturbing reflections. In addition, IV curves of all strings were measured with an IV-Curve-Tracer PVPM 1000CX with a silicon reference cell (SOZ-03) and a PT100 temperature sensor. In order to accelerate the IV measurements, thus ensuring most constant measuring conditions, the reference cell and the temperature sensor remained at the same position near to the sensors of the monitoring system. For the sake of data comparability, the measured data are extrapolated to STC conditions (25°C, 1000 W/m2, 1.5 AM). During all measurements the weather conditions were recorded with a Vantage Pro2 Plus weather station from Davis. For the punctual/individual measurements, as IR imaging and IV curves, time intervals of stable weather conditions were necessary. That means high irradiance E > 700 W/m2, constant air movement and no clouds. Predominantly, these conditions were present from 11:00 am to 4:00 pm. 3.2 Data evaluation IR imaging provides an easy method to identify PID affected cells by their slightly increased temperature [20]. Thus, manually counting the number of PID affected cells in a module as well as within a module string enables the determination of a defect ratio or PID ratio k, which describes the number of PID affected cells with an increased temperature within a string (1) with n being the number of PID-affected cells within one string and N the number of all cells within a string. With the monitoring data the electric performance of the PV plant can be determined for the historic/past operation period. The highest resolution available is on string level. This allows a space-resolved statement concerning the performance and the specific energy yield Y. Since the strings have differing number of modules, the specific string energy yield Y is suitable for comparing string performance (2) with output power P (in W) and nominal power P0 (in Wp) of the string, respectively. For comparison of different days with varying solar irradiance the performance ratio PRDC on the DC-side of the inverter is an appropriate approach. Then, temporal changes and degradations can be recognised and quantified. The performance ratio is determined as follows: (3) with irradiance E0 = 1000 W/m2 and Δt = 5 min, time-resolved monitored power output P(t) and irradiance E(t), for P ≥ 10 W and irradiance E ≥ 60 W/m2. In order to define the change of PRDC with time, the slope of the performance ratio with respect to the operation period is taken as a first approach. For a first-order approximation, a linear ageing behaviour is assumed, though it is known that actual ageing is more complex. However, for a rather short evaluation period as evaluated here, a first-order approximation is considered to be sufficient (4) with ΔPRDC the change of PRDC for time intervals Δt of integer multiples of entire years. The progress of degradation is determined as the change of PRDC in time, called PRDC loss rate . 4 Results and discussion 4.1 IR-based identification and quantification of PID For identification of PID in installed PV modules, IR imaging is a valuable tool [20]. PID-affected modules show a typical temperature pattern. The affected cells have a slightly increased temperature of 1–2 K with respect to PID-free adjacent cells. The variety of patterns of differently affected modules is shown in Fig. 6. Some modules have only a few heated cells, in other modules almost all cells suffer from PID. Fig. 6Open in figure viewerPowerPoint IR overview showing several module rows of roof area B (I1 S1, I7 S1, I9 S1, I1 S2) and dryer 6 marked in Fig. 2; homogeneous temperature distribution indicates defect-free modules whereas inhomogeneous chessboard like temperature distributions mark defective modules. Typical temperature patterns of PID-affected modules show cells with slightly increased temperatures, E = 900–950 W/m2, Tamb = 27°C, vwind = 2 m/s Measured IV data confirm the presence of PID, as shown for selected modules of one string in Fig. 7. The PID characteristic decrease of the fill factor and voltage, especially open-circuit voltage, is obvious. This increase of PID-affected modules towards the end (indicated by the higher module position) yields a reduction of power output at maximum power point Pmpp for STC: Pmpp(module 0) = 244 W, Pmpp(module 16) = 225 W, Pmpp(module 18) = 151 W, and Pmpp(module 20) = 118 W. Fig. 7Open in figure viewerPowerPoint IV curves of module 15, 18, and 20 of one string with 24 modules in total, image taken from [20] IR imaging allows for a quantitative analysis of the PID ratio for entire PV plants. For quantitative evaluation the number of PID modules and PID cells are counted for all strings and inverters. The statistical evaluation of the IR images reveals that 30% of the modules and 6% of all cells suffer from PID. In order to study local influences a defect ratio k for all strings is determined. k ranges from 1 up to 22%. All but one strings exhibit at least some PID-affected modules, see therefore the distribution of defect ratio of all strings shown in Fig. 8. The defect ratio varies strongly across the PV plant with the location at the roof, also compare Fig. 2. Here, the application of IR imaging for inspection and quality check is advantageous because location, spatial distribution and degree of impact are visualised easily and reliably. Fig. 8Open in figure viewerPowerPoint Defect ratio k and performance ratio PRDC averaged over the operation period for all strings with increasing order of k The defect ratio for the different areas is given in Fig. 9. Fig. 9Open in figure viewerPowerPoint Distribution of PID ratio k for the defined areas A, B, C, and D The defect ratios for the different areas clustering certain strings vary significantly; see Fig. 9 and Table 1. Strings with k > 11 and k < 2% are not frequently detected in the PV plant. Table 1 shows that the mean PID ratio k ranges from 3.7 up to 9.3% depending on the selected area. A t-test on a 5%-confidence interval confirms that areas A and D differ significantly from areas B and C. Operating conditions of the modules in areas A and D such as increased ambient temperatures due to frequently used heat emitting industrial roof installations, like kilns, promote the development of PID and result in high defect ratios. Table 1. Statistical evaluation of area A (including A1 and A2), B (including B1 and B2), C, and D presenting mean PID ratio k and its standard deviation σ Area A B C D number of strings 23 23 8 6 mean k, % 6.3 4.5 3.7 9.4 σ2 0.0015 0.0006 0.0005 0.0032 It is supposed that the presence of roof installations have a negative influence of the formation and degradation of PID. Roof installations, as chimneys, spray dryers, dryers and air conditioners, cause partial shading as well as increased temperatures in their surrounding by emitting heat radiation, hot dust and vapour. The hot kiln chimney with air temperatures above 200°C seems to force the progress and the development of PID in its direct surrounding in area A. It is concluded that the outlets (with hot air and dust from the production process) have a major impact on PID formation and lead to heterogeneous PID appearance. Thus, the PID degradation seems to be dominated by local microclimates (on the roof). 4.2 Electric performance on PV plant level The expected annual energy yield is 442.2 MWh based on the web-portal. For the investigated period of 3 years the annual energy yield varies according to the data logger data. In 2014, the energy yield was 427.74 MWh, it increased in 2015 to 449.75 MWh and dropped in 2016 to 427.05 MWh. This data give no indication for abnormal degradation, because variations due to differing solar irradiance are not considered. Therefore, the performance ratio PRDC which considers the actual solar irradiance is a well-known and suitable parameter to describe the electric performance. Fig. 8 shows the increasing defect ratio k in relation to the mean PRDC of the string. Although the PRDC data scatter a little bit the trend is visible that the PRDC decreases with increasing k. The scattering might be due to differing roof inclinations and orientations which strongly influence the yield. The available monitoring data enable the calculation of a mean PRDC averaged over all strings for each day. Historic up to date data are presented in Fig. 10 for the entire plant and three strings from different areas. Two facts are striking: first, the decreasing trend of PRDC, second, the repeated PRDC loss in winter. At the beginning of the monitoring in 2014, a PRDC (plant) = 83% was calculated. Today's PRDC (plant) is around 67%. Thus, a severe PRDC reduction occurred during the operation period. The general PRDC-loss is superimposed by a periodical PRDC-reduction during winter time, which recovers in spring. The highest PRDC is regularly measured in March. Then, high solar irradiance is present and the temperatures are still low. The string data illustrate some of the variety of PRDC due to the different installation positions. Fig. 10Open in figure viewerPowerPoint Mean daily performance ratio PRDC of PID-affected PV plant for three representative strings of area A (I3 S2), B (I11 S4), C (I13 S2) and PV-plant with trend lines indicating the PRDC decrease The PRDC reduction during the winter months is outstanding and repeats periodically. One explanation is shading of various modules and strings at certain time periods during the day. Fig. 11 illustrates the influence of shading for two strings in case of comparable summer and winter days in terms of good irradiance. The maximum irradiance reaches 1196 and 781 W/m2 at the single non-ideally oriented irradiance sensor for the differently inclined and orientated modules (seen by comparison of the maxima for irradiance and string powers). At the summer day the string powers of both, string I1 S1 and I15 S2, are almost identical besides the small curtailment at noon. In winter, it is obvious that the power output during the day differs for I1 S1 and I15 S2. The energy yield of I1 S1 is reduced in the morning and in the evening. This string suffers from shading by other modules and various surrounding roof installations. However, there are unshaded strings like I15 S2 in the south west corner, which do not show a temporal PRDC reduction in winter. Fig. 11Open in figure viewerPowerPoint Influence of temporal shading under clear sky conditions: in winter (bottom), it affects string power curves differently compared to an unshaded summer day (top), PRDC (I1 S1, May 2015) = 75%, PRDC (I15 S2, May 2015) = 73.9%, PRDC (I1 S1, December 2015) = 63.1%, PRDC (I1 S2, December 2015) = 74.3% (a) Summer day, (b) Winter day This shading during winter for various strings depending on their installation location causes the large spread of PRDC in winter. Therefore, for large PV plants, especially with differently oriented modules, more irradiance sensors would increase the lateral PRDC resolution. As a result, more reasonable and comparable PRDC values throughout the whole year would be available. With increasing number of sensors also the distribution of the module temperatures would be enhanced resulting in more precise PRDC data (when temperature-corrected). This would enhance PRDC values as a reliable quality feature. Nonetheless, the performance ratio is appropriate to verify and describe the electric performance of a complex PV installation. The data clearly reveals the temporal PRDC reduction caused by differing shading of the strings in winter. PRDC clearly shows the long-term degradation of strings and consequently the modules. Finally, it can be seen that PRDC varies for different strings. 4.3 Electric performance on module string level 4.3.1 Present performance The number of PID-affected cells within a string influences the string performance. The correlation for defect ratio k and PRDC for all strings is shown in Figs. 8 and 12. With increasing defect ratio k the determined performance ratio data decrease. Fig. 12 shows performance ratios measured in June 2016. In this diagram, the PVPM measurement gives PRs for a short measurement time at noon. Almost no shading is present at that time. All other data points represent performance ratios from the monitoring data separated with respect to different roof areas. These data represent the mean PRDC values over the whole day. Because of this the IV measurement using the PVPM yields a higher PRDC than the monitoring data. Both data sets reveal almost parallel linear relationships between the defect ratio k and PRDC. The resulting equations for the trend line are given in Fig. 12. It results in a 10–15% offset between the two data sets. Note, that the parameter of the regression line may differ with the day evaluated from the monitoring data, but the general trend remains. Fig. 12Open in figure viewerPowerPoint Performance ratio PRDC versus PID defect ratio k for all strings determined by monitoring data (2 June 2016 with daily irradiance of 307 Wh/m2 and mean ambient temperature of 25.6°C) and measurement data (7 June 2016) It is also obvious, that some strings at cer
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