A new PV module performance model based on separation of diffuse and direct light

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 113 (2015) 212–220 www.elsevier.com/locate/solener

A new PV module performance model based on separation of diffuse and direct light Blaz Kirn ⇑, Kristijan Brecl, Marko Topic University of Ljubljana, Faculty of Electrical Engineering, Trzaska cesta 25, 1000 Ljubljana, Slovenia Received 6 November 2014; received in revised form 15 December 2014; accepted 22 December 2014

Communicated by: Associate Editor Jan Kleissl

Abstract To increase the energy yield of installed solar photovoltaic (PV) systems, proper operation of all components should be ensured. One way to detect any misbehavior is to estimate the electric power of a PV system using data from meteorological stations or an in-situ integrated weather station to calculate the electric power of a PV system using a PV module performance mathematical model. By comparing the calculated and the actual electric power, the performance of a PV system can be determined. Such a PV system monitoring greatly depends on accuracy of measured weather parameters and precision of a PV module performance model used. Simple heuristic models are easy to implement but lack accuracy in particular under lower irradiances, higher share of diffuse light or higher solar incident angles. To improve accuracy, we developed a new PV module performance model with splitting diffuse and direct light including solar incident angle. As a consequence, the new model requires additional measurement of diffuse irradiance, but simplicity is maintained using simple equations with low number of fitting coefficients that were extracted for a typical multi-crystalline (mc-Si) and thin film copper indium gallium selenide (CIGS) PV module, based on outdoor monitoring data in Ljubljana, Slovenia. The new model was compared to two other heuristic models and a decrease of root mean square error (RMSE) in eight snowless month period (during October 2013 to September 2014) was observed, on average by 1%. Much larger improvement with the new model is obtained at lower irradiances: RMSE at irradiances of 200 W/m2 in June 2014 was three times lower compared to the other two models. The new PV module performance model with separated diffuse and direct irradiance component assures higher accuracy of prediction and thus higher reliability of PV system fault detection applications. Ó 2015 Elsevier Ltd. All rights reserved.

Keywords: PV system; Fault detection; PV performance model; Irradiance components; Solar incident angle

1. Introduction Due to a rapid increase in number of installed PV systems worldwide, a demand for monitoring energy yield performance, detecting failures and evaluating degradation of PV systems is growing primarily to assure higher economical sustainability. Complexity of monitoring systems depends on the size of the PV system, from simple ones ⇑ Corresponding author. Tel.: +386 14768848.

E-mail address: [email protected] (B. Kirn). http://dx.doi.org/10.1016/j.solener.2014.12.029 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.

for PV systems up to 50 kW to advanced professional monitoring systems which are also used in the certified labs. The advanced ones usually integrate prediction software for output power using a PV module performance model that depends on available input data (irradiance in a plane of array, air and PV module operating temperatures, wind speed and direction, etc.) and calculate the expected power of a PV module, string or whole system. In this way a comparison between calculated and measured power is used to determine possible failures of a PV string or system. In past years, a number of PV module performance models have

B. Kirn et al. / Solar Energy 113 (2015) 212–220

2. Heuristic models Heuristic models (Ding et al., 2012; Marion, 2008) generally assume a constant temperature coefficient of the electric power at maximum power point (c), while the maximum power at STC temperature of 25 °C (Pmodel) is a fitting function of irradiance in a plane of array (Gpoa), where TSTC = 25 °C, Tmodule is module/cell temperature and Pmpp is maximum power of a PV module, as shown in Eq. (1). P mpp ðGpoa ; T module Þ ¼ P model ðGpoa Þ  ½1 þ c  ðT module  T STC Þ

To improve accuracy at lower irradiances, the number of fitting coefficients should be increased. Advanced PV performance model, proposed by Huld et al. (2010), for example uses 6 coefficients. In this study we have focused on heuristic models which follow the form shown in Eq. (1) and have chosen two among them for comparison, a bilinear model (Pmodel-bl) with two linear segments for lower and higher irradiances separately, using three coefficients (Eq. (3)) and a nonlinear model (Pmodel-nl) with three coefficients (Eq. (4)), proposed by Ding et al. (2012). ( k bl1  Gpoa ; if Gpoa 6 200 W=m2 P model-bl ðGpoa Þ ¼ k bl2  Gpoa þ k bl3 ; if Gpoa > 200 W=m2 ð3Þ P model-nl ðGpoa Þ ¼ k nl1  Gpoa þ k nl2  G2poa þ k nll  Gpoa  ln

Gpoa GSTC ð4Þ

Both models will be tested and compared to a newly developed model to evaluate its gain in accuracy with separating solar irradiance into diffuse and direct irradiances. 2.1. Heuristic models at lower irradiances As mentioned before, accuracy of heuristic models decreases at lower irradiances, which occur not only in early mornings and late afternoons but also middays at cloudy conditions. Under these conditions, the share of diffuse irradiance is higher and thus the solar spectrum is different compared to clear sky conditions. Crystalline PV modules can render up to 3% spectral losses under clear sky conditions, however, under cloudy conditions spectral influence is positive with up to 4% gain in efficiency (Martı´n and Ruiz, 1999). Also, solar incident angle is relatively higher at lower irradiance conditions in the mornings and evenings thus angular losses can increase significantly. Furthermore, angular losses also influence on behavior of a 300 measured values Pmodel-nl (Equation 4)

250

P mpp@Tstc [W]

been developed. Generally, performance models can be divided into two groups, analytical and heuristic ones. Analytical models (De Soto et al., 2006; Marion, 2002; Marion et al., 2004; King et al., 2004; Tsuno et al., 2009) usually deal with the entire I–V curve and require characterization of PV modules by measuring their I–V curve under different steady-state conditions, normally over many matrix-based combinations of PV module temperature and irradiance. On the other hand, heuristic models are based on outdoor measurement and present maximum output power as a fitting function of PV module’s operating conditions, such as temperature and solar irradiance (Marion et al., 2004). Many comparisons of heuristic modules have been already performed (Ding et al., 2012; Friesen et al., 2009; Dittmann et al., 2010), showing that increase in complexity of a power model fitting function does not necessarily bring significant improvement in accuracy. Accuracy is limited especially at lower irradiance levels when the ratio of diffuse to total irradiance is higher and the sun position is lower thus direct light hits PV modules at higher incident angles. In this paper, the possibilities to increase accuracy of heuristic PV performance models by separating irradiance in a plane of array into diffuse and direct irradiances will be shown. In this manner, proposed heuristic model is separated into diffuse light and direct light power model with additional compensation for solar incident angle losses of PV module. Newly developed model is evaluated for multi-crystalline silicon (mc-Si) and thin film copper indium gallium selenide (CIGS) PV modules, showing the particularities of the technologies in PV module performance model. It should be noted, that increased accuracy was achieved for irradiances even up to 500 W/m2, so instead of widely used margin of 200 W/m2 (Luque and Hegedus, 2011), irradiances up to 500 W/m2 are referred as lower irradiances in this paper.

213

200

Coefficients (Equation 4): k nl1 = 0.269 m2

150

k nll = 0.036 m2

k nl2 = -4.28E-5 m4W -1

100 Pmax@STC = 225.7 W

ð1Þ 50

Various models suggest different fitting functions for Pmodel(Gpoa), which can be classified by the number of fitting coefficients. Simplest models suggest linear relationship between Pmodel and Gpoa (Marion, 2008). P model ðGpoa Þ ¼

P STC Gpoa GSTC

ð2Þ

0

0

200

400

600

800

1000

1200

Gpoa [W] Fig. 1. mc-Si PV module maximum power (normalized to 25 °C) versus irradiance in the plane of array, measured in June 2014 in Ljubljana, with the nonlinear 3 coefficient PV performance model Pmodel-nl (Eq. (4)).

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PV module under diffuse irradiance, since it arrives at a PV module surface at all angles from 0° to 90°. The effect of these loss mechanisms is shown in Fig. 1, where a plot of PV module electric power translated to 25 °C (Pmpp@Tstc) versus Gpoa of a mc-Si PV module is shown for June 2014. The PV module was measured at the outdoor PV monitoring site in Ljubljana, Slovenia (Kurnik et al., 2008). The non-linear 3 coefficient PV performance model Pmodel-nl (Eq. (4)) is also plotted to indicate power scattering at lower irradiances (up to 500 W/m2). Even if regression function achieves good average matching, there is still high instantaneous error present at lower irradiances. A decrease in accuracy at lower irradiances is generally ignored by most heuristic models since it is assumed that the dominant contribution to the energy yield of PV modules is represented by higher irradiance conditions. Considering higher instant errors are present at lower irradiances even up to 500 W/m2 (Fig. 1), this may not be the case on all locations. We will make a case study for Ljubljana, Central Europe (N46°30 800 E14°300 2000 ). Fig. 2 shows histogram of total diffuse and direct irradiation in a horizontal plane (Hh-tot) measured at the rooftop of the Faculty of Electrical Engineering, University of Ljubljana in 2013. Lower irradiances (below 500 W/m2) with relatively higher share of diffuse irradiance contributed 42.3% of the global solar irradiation (1189 kWh/m2) in 2013. Considering a relatively large contribution of lower irradiances to the total horizontal irradiation, accuracy at lower irradiances should be improved especially if the purpose of a PV performance model is a PV system’s fault detection where instantaneous errors can cause false alarms or misdetection of faults. Therefore, we developed a new PV module performance model with consideration of diffuse and direct light including solar incident angle to improve the accuracy and fault detection reliability at lower irradiances also. It is based on the data obtained from our outdoor PV monitoring site. On the monitoring 60 Diffuse irradiation Direct irradiation

50

site, each PV module I–V curve together with weather data is measured every 10 min (Kurnik et al., 2008). Gpoa is measured using Kipp&Zonnen CMP6 thermopile pyranometer. Also, global horizontal (Gh-tot) and diffuse horizontal (Gh-dif) irradiances are measured using CMP21 pyranometers, with one pyranometer equipped with shadow ring for measuring Gh-dif. Since PV modules at the monitoring site are facing south with inclination of 30°, diffuse irradiance has to be recalculated from the measured values on a horizontal plane. In our study, model proposed by Tian et al. (2001) was used to calculate diffuse irradiance in a plane of array. Tian model is a two-part geometry based linear equation (Eq. (5)) consisting of sky and ground view factor defined by tilt angle b in degrees (Fig. 3). Ground view factor is multiplied with ground albedo (agr), for which we assumed the value of 0.2 which is the actual albedo, but also generally used if ground albedo is unknown (Luque and Hegedus, 2011).     b b Gpoa-dif ¼ Gh-dif  1   þ a ; b < 90 gr 180 180 ð5Þ 3. Direct-diffuse power rating model The Direct-Diffuse Power Rating model (DDPR) splits the Gpoa into diffuse (Gpoa-dif) and direct (Gpoa-dir) irradiance and consists of three separate equations. First one (Pmodel-dif) describes relationship between electric power output and Gpoa-dif and the second one (Pmodel-dir) between electric power output and Gpoa-dir, including the solar incident angle (hs). Third equation, similar to other heuristic models, compensates the sum of electric power from both diffuse and direct light power equations for the Tmodule. The process of calibrating the coefficients of DDPR model consists of four steps, which will be explained in this section on a case study of a mc-Si PV module with rated power of 240 W. The module was measured at outdoor monitoring site (Kurnik et al., 2008) for more than a year, and obtained data in a period of one month (June 2014) was used to calibrate DDPR model coefficients.

40 42.3 %

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2

Gh-tot [W/m ] Fig. 2. Histogram of global irradiation distributed by global irradiance in Ljubljana, Slovenia in 2013.

Fig. 3. Sky and ground view geometry of Tian model.

B. Kirn et al. / Solar Energy 113 (2015) 212–220

3.1. Temperature dependence of Pmpp Temperature dependence of Pmpp is modeled similarly to other heuristic models with linear function using the relative temperature coefficient c. This coefficient can be obtained from PV module technical specifications or by indoor/outdoor measurement of Pmpp and Tmodule under 1 sun irradiance (1000 W/m2). In our study, outdoor measurements were used, with data filtered by Gpoa being between 950 and 1050 W/m2. The measured maximum electric power was linearly translated to 1000 W/m2 (GSTC) and plotted versus the Tmodule, which was measured at the backsheet. Since the temperature of solar cells inside the module under sunlight is higher than the temperature at the backsheet of the module, King et al. (2004) suggest to increase measured value by 2–3 °C for open rack mounted modules. Following the results from the module’s temperature measurement techniques study (Jankovec and Topicˇ, 2013) we used a different approach in our experiment. A temperature sensor at the back of the module was covered with small piece of extruded polystyrene (XPS) thermal insulation material with lateral diameter of 1 cm to prevent cooling of the sensor and represent the actual cell temperature inside the module. If the PV module operating temperature measurement is not available, it can also be calculated from weather conditions using a PV module thermodynamical model (Kurnik et al., 2011). Linear regression of normalized electric power (Pmpp@Gstc) versus Tmodule is used to determine the relative temperature coefficient c. The calculation of c is presented in Fig. 4. 3.2. Diffuse light power rating model To evaluate the impact of diffuse irradiance on Pmpp one should filter measured data by the ratio of diffuse to total irradiance in a plane of array (Gdif/Gtot) being equal or close to 1, which assumes that most of the generated power

is a consequence of diffuse light. However, to address possible measurement uncertainty, measured data were filtered by (Gdif/Gtot) being larger than 0.95. Pmpp of filtered data was translated to 25 °C by using the measured relative temperature power coefficient c. The relationship between temperature compensated maximum power (Pmpp-dif@Tstc) and Gpoa-dif is described in diffuse light power model. If PV modules do not suffer any shunting problem (and exhibit normal FF values) then the simplest, i.e. linear, relationship with one fitting coefficient (kdif) can be applied (Eq. (6)). P model-dif ðGpoa-dif Þ ¼ k dif  Gpoa-dif

3.3. Direct light power rating model To determine the impact of direct sunlight on Pmpp not only the fundamental Gpoa-dir but also the solar incident angle needs to be considered. The latter adds some complexity to the calculations of advanced heuristic models. In our case, we calculated a yearly lookup table of solar incident angles in 10 min interval for geographical location and orientation of our outdoor monitoring site using Sun– Earth geometrical equations (Eicker, 2003) to simplify our further calculations. The importance of considering the incident angle of direct light is indicated by nonlinearity at lower Gpoa-dir (Fig. 6). A relative transmittance factor F(hs), which describes the solar incident angle dependence (Martin and Ruiz, 2001), turned out to improve the agreement and was added to DDPR model (Eq. (7)). F ðhs Þ ¼ 1 

100

measured values power temperature compensation model

P mpp-dif@Tstc [W]

P mpp@Gstc [W]

eð

cos hs ar

Þ  eða1r Þ

ð7Þ

1  e ð a r Þ 1

120

240

220

200

160 30

ð6Þ

Filtered outdoor measured data of the tested mc-Si module for diffuse light power model are shown in Fig. 5, together with the linear regression line.

260

180

215

Relative temperature coefficient of maximal power (Equation 1): = -0.37 %/°C

40

50

measured values Pmodel-dif (Equation 6)

80 60 40 Coefficient (Equation 6): 2 k dif = 0.228 m

20

60

70

80

Tmodule [°C] Fig. 4. mc-Si PV module maximum power measurements during June 2014 normalized to GSTC = 1000 W/m2 versus module operating temperature with linear regression function.

0 0

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400

500

600

2

Gpoa-dif [W/m ]

Fig. 5. mc-Si PV module measured diffuse light maximum electrical power versus diffuse irradiance in the plane of array with linear regression function of diffuse light power model Pmodel-dif (Eq. (6)).

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B. Kirn et al. / Solar Energy 113 (2015) 212–220 250

1.4 measured values Pdir-irr (Equation 8)

P mpp-dir@Tstc [W]

200

Angular loss factor (Equation 7): ar = 0.196

1.2

Pmodel-dir (Equation 9)

1.0

Coefficients (Equation 8): k dir1 = 0.238 m2

150

0.8

k dir2 = -1.46E-5 m4 W-1

0.6

100

0.4 50 measured values

0.2 0 0

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800

1000

0.0 0

20

40

60

80

Gpoa-dir [W/m2]

Fig. 6. Measurements of mc-Si PV module direct light power normalized to 25 °C versus irradiance in the plane of array with Pdir-irr and final direct light power model Pmodel-dir.

The proposed equation uses only one coefficient, i.e. angular loss factor (ar), which maintains simplicity of DDPR model. Lower angular loss factor means lower angular losses and thus higher ability of a PV module to capture light from higher incident angles, which is determined by the performance of an antireflective coating, texture of the front surface of PV module and also the amount of soiling on the surface (Luque and Hegedus, 2011). A slight downward trend of Pmpp-dir@Tstc at higher irradiances can also be observed, which can be explained by increased series resistance losses in the PV module. To compensate also nonlinearity at higher irradiances, 2nd degree polynomial function without the constant term was used as a fitting function of direct light induced power (Pdir-irr). The resulted Eq. (8) has similar form compared to the threecoefficient model (Eq. (4)). The only difference is the absence of non-linear logarithmic factor, since the nonlinearities at lower irradiances are addressed by Eqs. (6) and (7) in DDPR model.   P dir-irr ðGpoa-dir Þ ¼ k dir1  Gpoa-dir þ k dir2  G2poa-dir ð8Þ The final direct light power equation of DDPR model is a product of Eqs. (7) and (8): h i P model-dir ðGpoa-dir ; hs Þ ¼ k dir1  Gpoa-dir þ k dir2  G2poa-dir " # cos hs 1 e ð  a r Þ  e ð a r Þ  1 ð9Þ 1 1  e ð a r Þ Direct light power model consists of two input parameters (Gpoa-dir and hs) and three coefficients (kdir1, kdir2 and ar). To extract these coefficients, Pmodel-dir was calculated from measured data by reducing measured Pmpp by Pmodel-dif (for which coefficients were already obtained) and further translating to 25 °C (using measured coefficient c). Coefficients were obtained by least squared error fitting of Eq. (9) on calculated Pmodel-dir. To improve coefficient

Fig. 7. Measurements of mc-Si PV module relative transmittance and F(hs).

of determination, measured data was also filtered by Gdif/ Gtot being lower than 0.6 (chosen empirically, may differ under different climatic conditions) in order to include high solar incident angle conditions and filter out cloudy conditions with small share of direct light. Direct light power model with the extracted coefficients is shown in Figs. 6 and 7. In Fig. 6, relationship between Pmpp-dir@Tstc and Gpoa-dir is shown, together with Pdir-irr (Eq. (8)) and final Pmodel-dir including angular loss compensation (Eq. (9)). Negative deviation of measured values can be observed at lower irradiances where solar incident angles are higher. To compensate angular losses, Pdir-irr is multiplied by relative transmittance and thus final Pmodel-dir model achieves good agreement with measured values. The measured relative transmittance (ratio of measured values and Pdir-irr), and F(hs), which present angular losses (Eq. (7)), are shown in Fig. 7. The resulting values of diffuse and direct light power models are summed and translated to PV module operating temperature using Eq. (10), which describes a newly developed DDPR model: P mpp-DDPR ðGpoa-dif ; Gpoa-dir ; hs ; T module Þ  ¼ P model-dif ðGpoa-dif Þ þ P model-dir ðGpoa-dir ; hs Þ  ½1 þ c  ðT module  T STC Þ

ð10Þ

3.4. Diffuse light Power Rating model for CIGS modules To evaluate the possibility to also use the newly developed DDPR model on thin film (TF) PV modules we used a CIGS PV module, which was also measured at our outdoor monitoring site beside the tested mc-Si module in June 2014. Procedures used to extract model coefficients were the same as at the mc-Si PV module, however, DDPR model needed small modification in diffuse light power model to achieve the desired accuracy. As it turned out, relationship between Pmpp-dif@Tstc and Gpoa-dif have a

B. Kirn et al. / Solar Energy 113 (2015) 212–220

conditions and underwent some ageing which led to decrease of rated power from specified 57 W to measured 47.8 W (June 2014). Additional comparison of modules with different thin film technologies and operational time is needed to assess the impact of technology and degradation level to relationship of diffuse irradiance and electric power of PV modules.

25 Linear diffuse light power model coefficient (Equation 6): k dif1 = 0.041 m2 CIGS diffuse light power model coefficients (Equation 11): k dif1 = 0.051 m2

Pmpp-dif@Tstc [W]

20

217

k dif-ll = 0.007 m2

15

10

4. Validation of DDPR model measured values Pmodel-dif (Equation 4) Pmodel-dif-CIGS (Equation 11)

5

DDPR model was validated for two PV modules being in operation for several years, one mc-Si with rated power of 240 W and efficiency 14.6% (actual measured power at STC in June 2014 was 225.7 W) and one thin film CIGS module with rated power of 57 W and efficiency 6.5% (actual measured power at STC in June 2014 was 47.8 W). Both modules are facing south with inclination of 30° and are located at our outdoor PV monitoring site in Ljubljana, Slovenia. DDPR model coefficients were extracted for both modules using previously described procedure with outdoor data measured in June 2014. Further the DDPR model was compared to the two basic heuristic models introduced earlier, the bilinear and nonlinear 3 coefficient one. Both models use Tmodule and Gpoa as input parameters and consist of two parts, temperature compensation and power vs irradiance equation. Coefficients of all PV module performance models for the tested mc-Si and CIGS modules are shown in Table 1. All three models were compared on a daily and monthly basis. For demonstration of a daily accuracy, a sunny day (9 June 2014) was chosen. Since all models are reasonably accurate at higher irradiances and the largest deviations are expected at lower irradiances, a detailed view of evening hours is presented in Fig. 9. Solar incident angle in the plane of array reaches 90° at around 19:15 on the observed day. Afterwards, when only diffuse irradiance is present,

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Gpoa-dif [W/m 2 ] Fig. 8. Two diffuse light power models for a CIGS thin film module.

nonlinear characteristic at lower irradiances and linear fitting function would result in higher deviation, relatively. To achieve a good agreement with experimental results, a non-linear term according to Ding et al. (2012) was added in the equation of the diffuse light power model. The modified model Pmodel-dif-CIGS (with additional coefficient kdif-ll) is described as: P model-dif -CIGS ðGpoa-dif Þ ¼ k dif 1  Gpoa-dif þ k dif -ll  Gpoa-dif  ln

Gpoa-dif GSTC

ð11Þ

The nonlinearity of Pmpp-dif@Tstc of the CIGS module is shown in Fig. 8. Nonlinear fitting function (Eq. (11)) shows a good match with measured values, while a simple linear regression that was successfully applied to the mc-Si PV performance model is not adequate to achieve targeted accuracy. It should be noted, that the CIGS module used in our experiment has been previously under outdoor

Table 1 Extracted coefficients for mc-Si and CIGS PV modules under test and RMSE of compared PV performance models, calculated in a 1 year period from October 2013 to September 2014 at irradiances above 100 W/m2. Coefficient

Unit

mc-Si PV module

CIGS PV module

c

%/°C

0.37

0.17

kbl1 kbl2 kbl3

m2 m2 W

0.209 0.230 4.22 10.4/4.5a

0.0342 0.0513 3.43 10.0/4.7a

knl1 knl2 Nonlinear 3 coefficient model knl3 RMSE of the nonlinear 3 coefficient model (%)

m2 m2 m4/W

0.269 0.0359 4.28E5 10.6/4.7a

0.060 0.014 1.21E5 10.2/4.8a

kdif1 kdif2 kdir1 kdir2 ar

m2 m2 m2 m4/W

0.228 0 0.238 1.46E5 0.196 9.7/3.6a

0.051 0.007 0.054 4.68E6 0.291 10.1/3.9a

Bilinear model RMSE of the bilinear model (%)

DDPR model

RMSE of the DDPR model (%) a

RMSE for eight months snowless conditions.

B. Kirn et al. / Solar Energy 113 (2015) 212–220 16

80

60

measured values Pmodel-bl model

14

Pmodel-nl model

12

8 Bilinear model 3 coefficient nonlinear model DDPR model Final yield

40

RMSE [%]

Tmodule

Pmpp

P mpp [W]

DDPR model

6

10 8

4

6

Y F [kWh/kW]

218

Time of day

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0 18:00:00

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0 1200

2

Gpoa [W/m ]

Time of day Fig. 9. Comparison of measured mc-Si PV module maximum power and modeled values for using three different PV module performance models.

the bilinear model shows good accuracy while the nonlinear 3 coefficient model exhibit a better fit until 19:15. Our newly developed DDPR model shows precise fit to the measured data in the evening hours. It is the only model which follows the kink of the solar irradiance after “sunset”. During morning hours, a better agreement of the bilinear model and the nonlinear one is turned around, whereas DDPR model also shows best fit during all phases of sunrise. Similar improvement of accuracy can be obtained also for partially cloudy days, when conditions are changing from cloudy (only diffuse irradiance) to sunny (diffuse and direct irradiances). For longer period comparison, root mean square error (RMSE) of Pmpp compared to measured power (Pmeasure) in June 2014 was calculated for all models at different values of Gpoa in intervals of 10 W/m2, using Eq. (12). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Pn 2 1  ðP  P Þ mpp;i measure;i i¼1 n Pn RMSEðGpoa ; 5 W=m2 Þ ¼ 1  i¼1 P measure;i n ð12Þ In the first calculation, all three tested PV module performance models were exhibiting unexpectedly higher RMSE for some measurements at higher irradiances (above 500 W/m2). This was caused by the principle of PV monitoring site operation, where maximum electric power is extracted by relatively short I–V curve measurement (approximate 200 ms) rather than longer period maximum power point average. This can cause mismatch between measured irradiance and maximum power point during rapid changes of irradiance at partially cloudy condition. To avoid the problem, measurements for validation were filtered based on dynamic changes of irradiance, which was compared to previous and next measurement and if more than 25% change was detected, it was excluded from validation. Fig. 10 shows RMSE of tested modules with filtered measurements by dynamic irradiance change criterium (<25% change). Here, few relatively larger RMSE values at higher irradiances still remain, but trends for all

Fig. 10. Root mean square error of three tested PV module performance models with measurements filtered by dynamic irradiance change criteria and energy yield of the tested mc-Si module during June 2014.

the models using the coefficients in Table 1 are well seen. Errors are below 2% for irradiances higher than 600 W/m2 and below 4% for irradiances higher than 400 W/m2 for all tested PV module performance models. At irradiances below 400 W/m2, the newly developed DDPR model has much lower RMSE (more than three times lower RMSE at irradiances around 200 W/m2 compared to other tested models). At irradiances below 200 W/m2, bilinear model also renders lower errors (200 W/m2 is the limit for two segment bilinear model) but still not as low as the DDPR model, while the 3 coefficient nonlinear model is performing the worst (with RMSE near 15%). In Fig. 10, histogram of PV module energy yield (YF) is also shown, with a peak at the Gpoa 985 ± 5 W/m2. Larger part of energy yield is a contribution from higher irradiances, however lower irradiances also contribute a considerable part (22.5% below 400 W/m2, where the differences in RMSE between the models become significant). Validation was performed also for the tested thin film CIGS PV module. Graph of RMSE versus Gpoa is shown in Fig. 11. Generally, errors were higher for the tested CIGS module compared to the mc-Si module. However, the trend is similar with new DDPR model showing lowest RMSE at irradiances below 400 W/m2. The models were also compared in term of seasonal performance. For mc-Si module, maximum power was calculated using all three models in one year period, from October 2013 to September 2014. For each month, RMSE of modeled power was calculated for irradiances higher than 100 W/m2 to limit the impact of higher RMSE at lower irradiances. Results are shown in Fig. 12, together with monthly energy yield of the PV module. As it was expected, errors are relatively high for winter months due to snow (November to February), which is not cleaned manually from the surface of PV modules on our monitoring site. However, for other months, all models show RMSE around 5% and below, with DDPR model performing noticeably better than the other two. For snowless

B. Kirn et al. / Solar Energy 113 (2015) 212–220 8

20 Bilinear model 3 coefficient nonlinear model DDPR model Final yield

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Y F [kWh/kW]

RMSE [%]

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Gpoa [W/m 2 ] Fig. 11. Root mean square error of three tested PV module performance models with measurements filtered by dynamic irradiance change criteria and energy yield of the tested CIGS module during June 2014.

250 Final yield bilinear model RMSE nonlinear 3 coefficient model RMSE DDPR model RMSE

RMSE [%]

40

200

30

150

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0

ry ry er er er ch April mb anua brua Mar mb t ob J Oc Nove Dece Fe

y e Ma Jun

r t y Jul ugus embe A ept S

YF [kWh/kW]

50

0

Months in 2013 and 2014 Fig. 12. Monthly RMSE for irradiances higher than 100 W/m2 for PV performance models tested on the mc-Si PV module with energy yield of the same module.

months (March to October) DDPR model in average renders 3.6% RMSE, 0.9% lower than bilinear model and 1.1% lower compared to 3 coefficient nonlinear model (Table 1). It should be noted, that RMSE is calculated for irradiance range from 100 W/m2 up and smaller errors at lower irradiances of DDPR model have limited impact on overall RMSE calculation, otherwise the difference in RMSE would be even higher. Since all models’ coefficients were extracted from June measurement data, error is lowest for that month. 5. Conclusion The developed DDPR PV module performance model which separates the diffuse and direct irradiance contribution to electric power and includes solar incident angle compensation has shown promising results in term of accuracy at lower irradiances. This is observed especially in morning and evening hours when conditions are migrating from direct irradiances at high incident angles to fully

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diffuse radiation after sunset and vice versa at sunrise. At those conditions, commonly used heuristic models show higher errors in contrast to DDPR model, whereas at higher irradiance conditions on sunny middays there is no noticeable difference in accuracy. The higher model accuracy at lower irradiances has a relatively small impact on energy yield calculations, since larger share of the PV module’s yearly energy output is produced at higher irradiances. However, when instant accuracy is desired, for example when performance model is used to monitor the operation of PV module(s) for detecting any possible faults, improved accuracy can have major impact in regularity of (mis)detected faults at lower irradiances. The improvement with DDPR model was achieved by considering diffuse and direct irradiance together with solar incident angle rather than only total irradiance in a plane of array. Considering this, the new model is especially applicable for locations with higher share of diffused irradiation, e.g. Central or Northern Europe. Separation of irradiance into diffuse and direct one adds two additional input parameters to the model but equations are kept simple so the DDPR model stays practically implementable. Additional parameters require additional measurement equipment for measuring diffuse irradiance. It was shown in our case that diffuse irradiance can be measured in a horizontal plane and translated to a tilted plane of array using simple Tian’s model. All calculations for DDPR model were performed in software package MS Excel, what further proves its simplicity and ease of implementation. In practical experience that was gained by developing the new PV module performance model it can be concluded that if higher accuracy of PV module instant power modeling is required, solar incident angle together with direct and diffuse irradiance component are required parameters. It was shown in the case of newly developed DDPR model that RMSE at 200 W/m2 is three times lower for the mc-Si module and two times for the thin film CIGS module compared to other heuristic models. Also, average RMSE at irradiances above 100 W/m2 in eight snowless months period is approximately 1% lower than using other compared models. Acknowledgements Authors thank Marko Jankovec and Bostjan Glazar for helpful discussion and continuous support at the PV outdoor monitoring site. The authors acknowledge the financial support from the Slovenian Research Agency (Research Programme P2-0197). B. Kirn personally acknowledges the Slovenian Research Agency for providing PhD funding. References De Soto, W., Klein, S.A., Beckman, W.A., 2006. Improvement and validation of a model for photovoltaic array performance. Sol. Energy 80 (1), 78–88. Ding, K., Ye, Z., Reindl, T., 2012. Comparison of parameterisation models for the estimation of the maximum power output of PV modules. Energy Proc. 25, 101–107.

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Dittmann, S. et al., 2010. Results of the 3rd modeling round robin within the European project “PERFORMANCE” - comparison of module energy rating methods. In: Proceedings of the 25th European Photovoltaics Solar Energy Conference, pp. 4333–4338. Eicker, U., 2003. Solar Technologies for Buildings. Wiley. Friesen, G. et al., 2009. Intercomparison of different energy prediction methods within the European project “Performance” - results of the 2nd round robin. In: Proceedings of the 24th European Photovoltaics Solar Energy Conference, pp. 3189–3197. Huld, T. et al., 2010. Mapping the performance of PV modules, effects of module type and data averaging. Sol. Energy 84 (2), 324–338. Jankovec, M., Topicˇ, M., 2013. Intercomparison of temperature sensors for outdoor monitoring of photovoltaic modules. J. Sol. Energy Eng. 135 (3), 031012. King, D.L., Boyson, W.E., Kratochvill, J.A., 2004. Photovoltaic Array Performance Model. Sandia National Laboratories. Kurnik, J. et al., 2008. Development of outdoor photovoltaic module monitoring system. Informacije MIDEM 38, 75–80. Kurnik, J. et al., 2011. Outdoor testing of PV module temperature and performance under different mounting and operational conditions. Sol. Energy Mater. Sol. Cells 95 (1), 373–376.

Luque, A., Hegedus, S. (Eds.), 2011. Handbook of Photovoltaic Science and Engineering, second ed. John Wiley & Sons, Ltd. Marion, B., 2002. A method for modeling the current–voltage curve of a PV module for outdoor conditions. Prog. Photovoltaics Res. Appl. 10 (3), 205–214. Marion, B., 2008. Comparison of predictive models for photovoltaic module performance. In: 33rd IEEE Photovolatic Specialists Conference. IEEE, pp. 1–6. Marion, B., Rummel, S., Anderberg, A., 2004. Current–voltage curve translation by bilinear interpolation. Prog. Photovoltaics Res. Appl. 12 (8), 593–607. Martı´n, N., Ruiz, J.M., 1999. A new method for the spectral characterisation of PV modules. Prog. Photovoltaics Res. Appl. 7 (4), 299–310. Martin, N., Ruiz, J.M., 2001. Calculation of the PV modules angular losses under field conditions by means of an analytical model. Sol. Energy Mater. Sol. Cells 70 (1), 25–38. Tian, Y.Q. et al., 2001. Estimating solar radiation on slopes of arbitrary aspect. Agric. For. Meteorol. 109 (1), 67–74. Tsuno, Y., Hishikawa, Y., Kurokawa, K., 2009. Modeling of the I–V curves of the PV modules using linear interpolation/extrapolation. Sol. Energy Mater. Sol. Cells 93 (6–7), 1070–1073.