Long-term validated simulation of a building integrated photovoltaic system

Solar Energy 78 (2005) 163–176 www.elsevier.com/locate/solener

Long-term validated simulation of a building integrated photovoltaic system J.D. Mondol a

a,*

, Y.G. Yohanis a, M. Smyth a, B. Norton

b

School of Built Environment, University of Ulster, Newtownabbey, Northern Ireland BT370QB, UK b Dublin Institute of Technology, Aungier Street, Dublin, Ireland Received 22 August 2003; accepted 16 April 2004 Available online 3 August 2004 Communicated by: Associate Editor Arturo Morales-Acevedo

Abstract Electrical and thermal simulations of a building integrated photovoltaic system were undertaken with a transient system simulation program using real field input weather data. Predicted results were compared with actual measured data. A site dependent global-diffuse correlation is proposed. The best-tilted surface radiation model for estimating insolation on the inclined surface was selected by statistical tests. To predict the module temperature, a linear correlation equation is developed which relates the temperature difference between module and ambient to insolation. Different combinations of tilted surface radiation model, global-diffuse correlation model and predicted module temperature were used to carry out the simulation and corresponding simulated results compared with the measured data to determine the best combination which gave the least error. Results show that modification of global-diffuse correlation and module temperature prediction improved the overall accuracy of the simulation model. The monthly error between measured and predicted PV output was lied below 16%. Over the period of simulation, the monthly average error between measured and predicted PV output was estimated to be 6.79% whereas, the monthly average error between measured and predicted inverter output was 4.74%. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Building integrated photovoltaics; TRNSYS; Simulation; Inverter

1. Introduction Building integrated photovoltaic (BIPV) system components include PV panels, power conversion systems and battery storage. BIPV electrical solar savings fraction depends on the availability of and unshaded access * Corresponding author. Tel.: +44 2890 368037; fax: +44 2890 368239. E-mail address: [email protected] (J.D. Mondol).

to solar radiation, prevailing ambient temperature, given building surface geometry, PV and inverter characteristics and connection and matching to the load (Sidrachde-Cardona and Lo´pez, 1999). Non-linear PV system simulation models allow analysis of the effect of varying different design parameter on long-term system performance (Duffie and Beckman, 1991). Bates et al. (1998) summarised the relative merits and demerits of many simulation tools available currently for PV system design and performance prediction.

0038-092X/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2004.04.021

164

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

Nomenclature Cd Ci G G0,h Gd,h Gg,h Gg,m GNOCT Gt,m Idc k0 k1 k2 kT Md Mi N Pinv Pinv,n

monthly average daily measured PV output (MJ) ith calculated value incident insolation on the PV plane (W m
2) hourly extraterrestrial radiation (MJ m
2) hourly diffuse component of global horizontal insolation (MJ m
2) hourly global horizontal insolation (MJ m
2) measured global horizontal insolation (Wm
2) insolation at NOCT (W m
2) measured global insolation on the PV plane (W m
2) dc current (A) inverter self-consumption losses coefficient for inverter losses proportional to input power coefficient for inverter losses proportional to square of input power hourly clearness index monthly average daily predicted PV output (MJ) ith measured value number of observations inverter output (MJ) normalised inverter output ac power

The applicability of such tools to different PV applications has been summarised by Sick and Erge (1996). The modelling techniques employed, applicability, usefulness and experimental validation of PV system simulation tools has been reported extensively (Menicucci and Fernandez, 1984; Menicucci, 1986; King et al., 1996; Walker et al., 2003; Mermoud, 1995; Ropp et al., 1997; Schilla et al., 1997; Atmaram and Khattar, 1982; Park et al., 2001; Bishop, 1988). The different simulation tools considered include PVFORM (Menicucci and Fernandez, 1988), PV F-Chart (Klein and Beckman, 1983), SOLCEL-II (Hoover, 1980), PVSIM (King et al., 1996), PVSYST (Mermoud et al., 1998), ENERGY-10 (Balcomb, 1997), PVNETSIM (Schilla et al., 1997), PVNet (Bishop, 1988) and TRNSYS (Klein et al., 2000). New simulation tools continue to be developed to study the performance of PV system. Travers et al. (1998) proposed a simulation tool to compare different BIPV system components, at different orientations, over a range of geographical locations. This model was designed to use direct, diffuse and ambient temperature data obtained from a specific site. The model included a non-isotropic radiation model, considering transmission and refractive index of module encapsulation, system thermal analysis and cost analysis under different tariff condition. Snow et al. (1999) developed a tech-

Pinv,rated rated capacity of inverter at input dc power (kW) Ppv PV output (MJ) Ppv,n normalised inverter input direct current power Ta ambient temperature (°C) Ta,NOCT ambient temperature at NOCT (°C) Tc PV surface temperature (°C) Tc,NOCT module temperature at NOCT (°C) Vdc dc voltage (V) a solar altitude angle (degree) sa transmittance–absorptance product gc conversion efficiency of PV module (%) ginv inverter efficiency (%)
d error (%)

Abbreviations BIPV building integrated photovoltaic MPE mean percentage error NMBE normalised mean bias error NOTC nominal operating cell temperature NRMSE normalised root mean square error STC standard test conditions TRNSYS transient simulation program

nique for simulating BIPV opportunities in urban environments based on a model for predicting energy performance, emissions and alternative energy options for cities. A geographic information system and a BIPV simulation were coupled to simulate different BIPV technologies and systems under site-specific parameters. Gow and Manning (1999) developed a circuit-based simulation model especially applicable for those PV cells, which follow a double-exponential model for determination of current. Most methods available for predicting the long-term performance of a solar photovoltaic system are based on simplified mathematical models representing different PV system components (Sukamongkol et al., 2002; Hove, 2000; Evans, 1981; Siegel et al., 1981; Ingersoll, 1985). Meyer and van Dyk (2000) predicted PV output based on regression analysis using daily irradiation and maximum daily ambient temperature data. In this work the electrical and thermal performance of a building integrated photovoltaic (BIPV) system was simulated using TRNSYS (Klein et al., 2000), a transient simulation program. Simulated results are compared with 21 months measured data. The objective of the present work is modification and development of new component models within TRNSYS and their validation with measured data.

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

165

2. Data recorded

3. System modelling

The particular BIPV system considered comprised a PV array and an inverter unit with maximum power point tracker. The PV array was roof mounted facing due south at an inclination 45° and was located in Ballymena, Northern Ireland at latitude 55° N and longitude 6° W. The array consisted of 119 single crystalline modules (Anon, 2000), each rated at 110 WP at STC with total rated capacity 13 kWp. Seven module strings were each connected in parallel. Each module string consisted of 17 modules in series. A 13 kW rated inverter converted PV generated direct current into an alternating current. The output power was fed into the buildingÕs 415 V alternating current three-phase electrical distribution network. Two pyranometers each measured the horizontal global insolation and in-plane insolation, respectively. Ambient and PV surface temperatures were measured by T-type thermocouples. The pyranometers and thermocouples were connected to a data logger, which was set to sample every one-minute interval, and averaged over half hour periods. Electrical data from the PV was recorded by monitoring software every second and averaged over 15 min intervals, stored in a computer memory and averaged on an hourly basis. Fig. 1 shows the pyranometers, data logger and PV panels on the building roof. Global insolation on the horizontal surface (Gg,m), global insolation on the inclined surface (Gt,m), ambient temperature (Ta), the surface temperature of the module (Tc), PV dc current (Idc), PV dc voltage (Vdc), PV dc output (Ppv) and inverter ac output (Pinv) data were processed on hourly basis. A schematic diagram of the BIPV monitoring set up is shown in Fig. 2. Insolation, temperature and voltage measurements were subject to errors of ±20 W m
2, ±1 °C and ±1.5 V, respectively.

Simulation provides a practical means of optimising solar energy system design (Fiksel et al., 1995). Accuracy of the performance of any model depends on the validity of the algorithm and the accuracy and appropriateness of the system specifications input data used. Simulations of the BIPV system were carried out using TRNSYS (Klein et al., 2000). An advantage of using TRNSYS was that component programs can be modified and new components may be added as required (Klein et al., 2000). The components of TRNSYS, written as FORTRAN subroutines, are referred to as ÔtypesÕ, each of which represents a specific system part or process. Each type is composed of distinct parameters, inputs and outputs. The following standard TRNSYS components were used for this simulation study; (i) ÔData ReaderÕ which reads specified data from the input data file; (ii) ÔRadiation ProcessorÕ which calculates total, diffuse and beam component of in-plane insolation from the total horizontal insolation; (iii) ÔPhotovoltaic ArrayÕ which models PV output from the I–V characteristics of PV cell; and (iv) an inverter component which predicts alternating current output from the inverter. ÔData ReaderÕ reads weather data from the input data file. The input weather data file contained hourly values of the global horizontal insolation and ambient temperature collected from the site. The ÔRadiation ProcessorÕ subroutine within TRNSYS was used to compute total insolation on a tilted surface from hourly measured global horizontal insolation data. Array output is obtained from the component ÔPhotovoltaic ArrayÕ (TRNSYS

Fig. 1. Roof mounted PV panels and pyranometers at ECOS Environmental Centre in Ballymena, Northern Ireland, UK.

166

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

Fig. 2. Schematic diagram of the BIPV electrical monitoring.

Type 94). This component gives electrical output of the PV system by employing I–V characteristic curves. A new component model was added into TRNSYS to model inverter alternating current output and predicted results were compared with the measured data on monthly basis. 3.1. Comparison of global-diffuse correlation models The electrical output of a PV unit depends upon the incident insolation on the PV surface. Overall system performance predictions are sensitive to the accuracy of the computation of the total, beam and diffuse components of insolation on the inclined PV surface from the hourly measured horizontal global insolation data. A global-diffuse correlation was developed using global and diffuse insolation data obtained at the nearby Aldergrove meteorological station (latitude 54.6° N) to

one or beam radiation exceeding the extraterrestrial beam radiation were omitted. Diffuse and global insolation ratio was found to be related to clearness index by: 8 > 0:98 for k T 6 0:20 Gd;h < ¼ 0:5836 þ 3:6259k T
10:171k 2T þ 6:338k 3T ð1Þ Gg;h > : for k T > 0:20 where kT is the hourly clearness index defined as the ratio of hourly global horizontal radiation (Gg,h) to the extraterrestrial radiation (G0,h) (Waide and Norton, 2003) and Gd,h is the hourly diffuse component of the horizontal insolation. The performance of the correlation in Eq. (1) was assessed via comparing with two other global-diffuse models; the Reindl et al. model (Reindl et al., 1990) which is used in TRNSYS ÔRadiation processorÕ component given as (Klein et al., 2000):

8 > 1:020
0:254k T þ 0:0123 sin a for 0 6 k T 6 0:3 and Gd;h =Gg;h 6 1:0 Gd;h < ¼ 1:400
1:749k T þ 0:177 sin a for 0:3 < k T 6 0:78 and 0:1 6 Gd;h =Gg;h 6 0:97 Gg;h > : 0:486k T
0:182 sin a for 0:78 6 k T and Gd;h =Gg;h P 0:1

calculate the beam and diffuse components of the horizontal insolation. The validity of any empirically derived correlation depends upon the accuracy and quantity of the data used for developing the model. Therefore hours with missing values of global and diffuse solar radiation were not considered, and diffuse fraction greater than

ð2Þ

and the Muneer–Saluja model (Muneer and Saluja, 1986) given by 8 > 0:98 for k T 6 0:20 Gd;h < ¼ 0:687 þ 2:819k T
8:182k 2T þ 4:972k 3T ð3Þ Gg;h > : for k T > 0:20

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

The global-diffuse correlation in Eq. (3) was also derived using Aldergrove meteorological data. Three statistical parameters are used for the comparison of model performance. These parameters are normalised mean bias error (NMBE), normalised root mean square error (NRMSE) and mean percentage error (MPE). NMBE is defined by: N  P 1 ðC
M Þ i i N i¼1 N  NMBE ¼ ð4Þ P 1 M i N i¼1

NRMSE is defined by:  N 12 P 2 1 ðC
M Þ i i N i¼1 N  NRMSE ¼ P 1 Mi N

ð5Þ

i¼1

and MPE is defined by: 1 MPE ¼ N

N X ðC i
M i Þ Mi i¼1

! ð6Þ

In Eqs. (4)–(6), N is the total number of observations and Ci and Mi are, respectively, the ith calculated and measured values. NMBE, NRMSE and MPE are expressed as percentages. Positive and negative values of NMBE represent overestimated and underestimated calculated values, with a small value of NMBE being desirable (Oliveria et al., 2002). NRMSE provided information on the short-term performance of a model allowing a term-by-term comparison of the actual deviation between the estimated value and the measured value. MPE gives the size of the discrepancy in the measurement and accounts for the systematic component of the normalised difference for individual observations. Large errors in the data increase NRMSE significantly. Deviations between measurements and predictions were much larger than the error associated with the measurements themselves. Experimental error is thus not considered in the calculation of NMSE, NRMSE and MPE. Results show that (see Table 1) the correlation given in Eq. (1) gives the best-predicted results compared to the other two models. The results for the Muneer–Saluja model (Muneer and Saluja, 1986) are comparable with Eq. (1). This is expected as both correlation models have

167

been derived using data collected from the same location. The Reindl et al. (1990) model gives the largest NMBE and MPE value. A negative NMBE value for the use of Eq. (1) indicates slightly underestimated predicted results. These results indicate that inclusion of the correlation given in Eq. (1) into TRNSYS improves overall simulation accuracy for the particular climatic conditions of this specific BIPV installation. 3.2. Comparison of tilted surface radiation models Four tilted surface radiation models are available in TRNSYS to calculate the total insolation on an inclined surface: an isotropic sky model (Liu and Jordan, 1963) and three anisotropic sky models (Hay and Davies, 1980; Reindl et al., 1990; Perez et al., 1986). The total in-plane insolation is computed by adding diffuse, beam and ground reflection components on the tilted surface. The ground reflection coefficient is assumed to be constant and equal to 0.2 (Liu and Jordan, 1963). This value has been shown to provide reliable results in the most comprehensive study to-date of ground reflected radiation (Ineichen et al., 1990). In order to determine the best-tilted surface radiation model, a statistical analysis was performed using measured and calculated in-plane insolation data. Statistical parameters are evaluated employing Eqs. (4)–(6) for each individual model. Six thousand eight hundred and fifty eight hourly data points were used. A summary of the results obtained is given in Table 2. Table 2 shows that NMBE is lowest for the Hay and Davies (1980) model, with 1.4%. The lowest MPE is obtained for isotropic sky model. The negative value of NMBE for the isotropic sky model indicates slightly underestimation of the calculated value. The anisotropic models gave overestimated values. In terms of NRMSE, the performance of each model is comparable, though NRMSE for the isotropic model is slightly higher than the Perez et al. (1986) model. The performances of Hay and Davies (1980) and Reindl et al. (1990) model are similar. Statistical parameters were also computed from daily measured and calculated total in-plane insolation data to show the performance of the model on daily basis. Six hundred and twenty daily data points are used. The results are given in Table 3. The lowest NMBE was obtained for the Hay and Davies (1980) model whereas the isotropic sky model provided the lowest

Table 1 Statistical parameters for global-diffuse correlation models Relationship

NMBE

NRMSE

MPE

Eq. (2) (Reindl et al., 1990) Eq. (3) (Muneer and Saluja, 1986) Eq. (1) (this work)


12.71 2.26
1.86

27.44 28.29 28.29


15.07 3.04 0.22

168

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

Table 2 Statistical parameters calculated from hourly measured and predicted in-plane insolation for four tilted surface radiation models

mostly under overcast conditions (Mondol et al., 2002), under which an isotropic sky model gives the least error.

Model

Sky

NMBE

NRMSE

3.3. Calculation of module temperature of PV

Liu and Jordan

Isotropic


2.87

24.05

7.05

Hay and Davies Reindl et al. Perez et al.

Anisotropic

1.40 2.33 3.42

25.06 25.20 23.90

10.22 11.28 8.61

MPE

Table 3 Statistical parameters calculated from daily measured and predicted in-plane insolation for four tilted surface radiation models Model

Sky

NMBE

NRMSE

MPE

Liu and Jordan

Isotropic


2.63

11.76

4.57

Hay and Davies Reindl et al. Perez et al.

Anisotropic

1.71 2.64 3.61

9.96 10.20 9.20

10.02 10.97 11.66

MPE. The lowest NRMSE was found to be 9.2% for Perez et al. (1986) model. In Fig. 3 trend lines are drawn for the percentage error between measured and calculated in-plane insolation with respect to the daily measured in-plane insolation for each tilted surface radiation model. It can be observed that calculated daily in-plane insolation is higher than the measured data for overcast days for all models. Compared to the anisotropic models, the performance of the isotropic sky model is obviously better for overcast conditions. The isotropic model provides slightly underestimated results for clear days. The operation of this particular BIPV system is

The electrical performance of a BIPV system depends on module operating temperature. The module temperature is affected by insolation, ambient temperature, wind speed and also the type of PV installation (Davis et al., 2001). In the standard TRNSYS component model, NOCT is used to predict module temperature (Klein et al., 2000). The module temperature at any time step is a function of irradiance and ambient temperature given by  G g Tc ¼ Ta þ ð7Þ ðT c;NOCT
T a;NOCT Þ 1
c GNOCT sa where Tc and Ta are the module temperature and ambient temperature, respectively at any time step, G is the incident insolation on the PV plane, GNOCT is the insolation at NOCT, Tc,NOCT and Ta,NOCT are the module and ambient temperature at NOCT, respectively. gc is the conversion efficiency of the module and sa is the transmittance–absorptance product of the module. In this study, Tc,NOCT, Ta,NOCT and GNOCT were considered as 40 °C, 20 °C and 800 W m
2, respectively. A correlation equation was developed to predict module temperature, using measured module temperature, ambient temperature and incident insolation data collected in the months of June, July and August 2002. The average of the front and back surface module temperature was considered as the module temperature. The correlation equation obtained is: T c ¼ T a þ 0:031G

ð8Þ

80 70 60

Percentage Error (%)

50 40 Reindl et al. 30

Hay and Davies

20

Liu and Jordan

10

Perez et al.

0 -10 -20 -30 0

3

5 8 10 13 15 18 20 23 25 Measured Daily Total In-plane Insolation (MJm-2)

28

30

Fig. 3. Trend lines for four tilted surface radiation model correlating the percentage error between measured and calculated daily in-plane insolation to daily measured in-plane insolation.

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

169

lower than measured. It is clear from the corresponding cases shown in Fig. 5 that module temperature prediction is improved by use of Eq. (8).

This correlation equation is similar to the regression equation derived using data from the BIPV system installed on the Northumberland Building, UK (Wilshaw et al., 1996). Eq. (8) was utilised in TRNSYS to calculate the module operating temperature. Fig. 4 illustrates the temperature difference between measured module and ambient temperature and between predicted module temperature and measured ambient temperature as a function of in-plane insolation. Fig. 4 shows that predicted module temperature elevation predicted using the NOCT relationship in Eq. (7) are much

3.4. Modelling PV output The TRNSYS standard ÔPhotovoltaic ArrayÕ (Klein et al., 2000) component models the electrical output of a PV generator. The main inputs to this submodel are total, beam and diffuse insolation on the inclined PV surface calculated by a ÔRadiation ProcessorÕ component

50 Measured difference between PV and ambient temperature

40 Temperature Difference (K)

Predicted difference between PV and ambient temperature using Equation 8 for PV temperature

30

20

10 Predicetd difference between PV and ambient temperature using Equation 7 for PV temperature

0

-10 100

200

300

400

500

600

700

800

900

1000

1100

Measured In-plane Insolation (Wm-2)

Fig. 4. Measured difference between PV module and ambient temperature and two predicted differences between PV module and ambient temperature as functions of measured in-plane insolation.

70 Equation 7

Predicted Module Temperature (˚C)

Perfect agreement

Equation 8

60

Equation 8 Equation 7

50

40

30

20

10

0 0

10

20 30 40 50 Measured Module Temperature (˚C)

60

70

Fig. 5. Comparison of measured and predicted PV module temperature employing NOCT equation given in Eq. (7) and the correlation in Eq. (8).

170

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

using ambient temperature measured at the site, the PV array slope, beam insolation angle of incidence at the PV surface and PV specification parameters. An equivalent circuit is used to model crystalline PV modules (Klein et al., 2000) whose parameters are module photocurrent at reference conditions (IL,ref); diode reverse saturation current at reference conditions (I0,ref); empirical PV curve-fitting factor and module series resistance (Rs). An ÔIncident angle modifierÕ calculates the reflection losses from the PV surface from the transmittance– absorptance product (sa) and beam and diffuse radiation components of the in-plane insolation (Klein et al., 2000). This particular BIPV system employed a maximum power point tracking device, so the electrical PV output was estimated at the maximum power point. Table 4 shows the parameters used in the model. The electrical output of the PV was simulated using different combinations of global-diffuse correlations and tilted surface radiation models. The effect of the module temperature on the predicted PV output was also studied. NMBE and NRMSE were computed for each combination from predicted and measured daily PV output data. Reindl et al. global-diffuse correlation (Eq. (2)) and Eq. (1) were used to calculate horizontal beam and diffuse components insolation. Models by Liu and Jordan (1963), Hay and Davies (1980), Reindl et al. (1990) and Perez et al. (1986) were employed to calculate the insolation incident on the inclined PV surface. Eqs. (7) and (8) were used to calculate the module tem-

perature. Table 6 shows the statistical results obtained for each tilted surface radiation model corresponding to the four cases in Table 5. The isotropic sky model when employed with the combination in Case 4 gives the lowest value of NMBE and NRMSE. For each Case, the least deviation between measured and predicted result is obtained when the isotropic sky model is used for in-plane insolation calculation. The comparison of NMBE values for each tilted surface radiation model shows that the NMBE values for the isotropic sky model are 89%, 107% and 120% lower than the Hay and Davies (1980), Reindl et al. (1990) and Perez et al. (1986) model, respectively for Case 4. Positive values of NMBE indicate overestimated predicted results. The difference in NRMSE are 14%, 19.5% and 20%, respectively. It can be seen from Table 6 that the errors reduces considerably for Case 4, the combination of global-diffuse correlation given by Eq. (1) and module temperature given by Eq. (8). Case 1 whose simulation predictions are without modifications to TRNSYS types gave least accuracy. Modification of the calculation of module operating temperature has a major effect on predicted electrical PV output. This can be shown from comparison of statistical parameters evaluated before and after the introduction of Eq. (8) into the model. The NMBE and NRMSE for the combinations in Case 4 are reduced by 34% and 7%, respectively, compared to Case 3. The statistical analysis shows that the PV electrical output is predicted

Table 4 PV specification parameters (Anon, 2000) Parameter

Value

Short circuit current at STC (Isc) Open circuit voltage at STC (Voc) Rated current at reference conditions (Imp) Rated voltage at reference conditions (Vmp) Temperature coefficient of short circuit current (lIsc,ref) Temperature coefficient of open circuit voltage (lVoc,ref) Number of cells connected in series in module Number of modules in parallel in the array Number of modules in series in the array Individual module area (A) Transmittance–absorptance product at normal incidence Semiconductor bandgap

3.45 A 43.5 V 3.15 A 35.0 V 0.0004 A/K
0.034 V/K 72 7 17 0.87 m2 0.9 1.2 eV

Table 5 Four combinations of global-diffuse correlation and module temperature prediction equations evaluated Global-diffuse correlation

Module temperature prediction Eq. (7) (Klein et al., 2000) Eq. (8) (this work)

Eq. (2) (Reindl et al., 1990)

Eq. (1) (this work)

Case 1 Case 2

Case 3 Case 4

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

171

Table 6 Statistical parameters calculated from daily measured and predicted PV output for four cases corresponding to four tilted surface radiation models Case

Statistical parameter (%)

Isotropic sky

Anisotropic sky

Liu and Jordan

Hay and Davies

Reindl et al.

Perez et al.

1

NMBE NRMSE

13.45 18.06

23.80 23.07

19.78 23.91

20.68 24.62

2

NMBE NRMSE

11.21 16.23

16.31 20.57

17.27 21.31

18.13 21.94

3

NMBE NRMSE

8.06 15.57

13.68 18.66

14.80 19.61

15.61 19.86

4

NMBE NRMSE

6.01 14.53

11.38 16.54

12.46 17.35

13.23 17.43

for the modified model than the standard TRNSYS model particularly at lower insolation. A comparison of measured and predicted PV output was carried out on monthly basis from the monthly average daily data. The predicted values were obtained from the four cases defined previously. The error between measured and predicted result is given by   Cd
M d ed ¼  100% ð9Þ Md

for this particular installation with least error using a combination of the global-diffuse correlations given by Eq. (1), an isotropic sky model and the modified module operating temperature given by Eq. (8). Fig. 6 illustrates the correlation between daily measured and predicted PV output using the combination in Cases 1 and 4. The isotropic sky model was used for calculating in-plane insolation. Fig. 6 shows that the predicted PV output for Case 4 combination gave better agreement to the measured results compared to the Case 1 combination, particularly upper region of the curve when measured PV output is large. Fig. 7 presents the percentage deviation between predicted and measured data with respect to the in-plane insolation before and after the modification and shows that the error is less

where Cd and Md are the predicted and measured monthly average daily PV output. Table 7 shows the predicted and measured monthly daily average electrical PV output and corresponding error for the four cases. The isotropic sky model was

350 Case 1 Case 4

Predicted Daily Total PV Output (MJ)

300

250

200 Case 1

150

100 Case 4

50

0 0

50

100

150

200

250

300

350

Measured Daily Total PV Output (MJ)

Fig. 6. Comparison of measured and predicted daily PV electrical output for Cases 1 and 4. Isotropic sky model is used to calculate the in-plane insolation.

172

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176 100 90 80

Percentage Error (%)

70 60

Case 1

50 40 Case 4

30 20 10 0 -10 -20 -30 0.0

2.5

5.0

7.5

10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0

Measured Daily Total In-plane Insolation (MJm-2)

Fig. 7. Percentage error between measured and predicted PV electrical output before and after modifications of global-diffuse correlation model and module temperature model.

Table 7 Monthly average daily measured and predicted PV output and corresponding difference between measured and predicted results for four cases (Cases 1–4) Year

Month

Measured PV output (MJ)

Predicted PV output (MJ) Case 1

Case 2

Case 3

Case 4

Case 1

Case 2

Case 3

Case 4

2001

Apr May Jun Jul Aug Sep Oct Nov Dec

95.8 170.6 133.6 130.3 123.1 91.8 61.6 26.6 47.9

112.3 182.2 147.2 140.4 136.4 101.2 73.8 37.8 56.5

110.2 177.8 144.7 137.5 133.6 99.4 72.7 37.4 55.4

108.4 180.0 146.2 139.3 132.5 95.0 66.2 31.0 45.4

106.2 175.7 143.6 136.8 130.0 93.6 65.2 31.0 44.6

17.37 6.87 10.40 7.61 10.90 9.98 19.90 42.62 17.87

15.04 4.26 8.38 5.44 8.64 8.16 17.83 40.98 15.93

13.23 5.62 9.56 6.92 7.86 3.46 7.53 16.95 5.76

11.11 3.08 7.59 4.82 5.76 1.87 5.83 15.82 7.08

2002

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

29.5 52.9 123.1 125.3 149.4 118.1 100.1 114.5 120.2 62.3 47.9 33.5

39.6 68.0 135.4 137.9 163.4 131.4 110.9 133.6 139.0 74.5 57.2 40.0

38.9 66.6 132.1 135.0 159.8 128.9 109.1 130.7 135.7 73.4 56.2 39.2

32.4 58.3 129.6 134.3 161.6 131.4 110.5 129.2 129.6 65.2 53.6 33.1

31.7 57.2 126.4 131.4 158.4 129.2 108.7 126.7 126.4 64.1 52.9 32.8

33.58 28.66 10.03 10.16 9.30 11.29 11.09 16.61 15.86 20.09 19.64 19.31

31.45 26.31 7.43 7.76 6.89 9.31 9.27 14.26 13.02 17.98 17.49 17.33

9.18 10.23 5.17 7.18 8.20 11.39 10.77 12.92 7.86 4.67 12.38 0.39

7.72 8.48 2.75 4.92 5.88 9.45 8.98 10.73 5.39 3.05 10.37 1.84

93.2

105.7

103.5

100.6

98.7

16.63

14.44

8.44

6.79

Average

used for calculating the in-plane insolation. Results indicate that error reduces significantly for each month when Eq. (1) is used as the global-diffuse correlation and Eq. (8) is used as the module temperature. To show the effect of global-diffuse correlation on predicted PV

Error (%)

output, consider results for the Cases 2 and 4 for which the predicted module temperatures were the same but different global-diffuse correlations were used. A significant improvement of simulation prediction accuracy was observed during the winter months (November, Decem-

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

ber, January and February) when Eq. (1) was used as the global-diffuse correlation model. The diffuse radiation component predominantly determined PV electrical output because during this period the PV system operated mostly under overcast conditions. Modification of the global-diffuse correlation reduced the monthly percentage error between the measured and predicted results within the range of 55–70% during this period. In the summer, the model performance was improved by 15– 30% using Eq. (1). The effect of the accuracy of temperature prediction on the predicted results can be observed by comparing the percentage error obtained for Cases 3 and 4. These two cases use the same global-diffuse correlation model but different predicted module temperature models were used. The use of Eq. (8) to determine the module temperature improved the model performance in summer when higher module temperatures prevailed and their effect on the PV output was thus significant. In the month of May 2001, use of Eq. (8) reduced the percentage error between measured and predicted PV output by about 45% less than the error incurred using Eq. (7). For the other summer months model performance improved within the range of 15–30% depending on the incident insolation intensity. For Case 4, the monthly error lies between 1.8% and 16%. Over the simulation period the average monthly error before and after the modification is 16.63% and 6.79%, respectively. Therefore the overall modification of the simulation model contributed a 59% reduction of the error between measured and predicted PV electrical output. 3.5. Modelling inverter output The standard TRNSYS component ÔRegulator/InverterÕ assumes that the efficiency of the inverter is constant. In reality, inverter efficiency is a function of actual power, self-consumption losses and load dependent

173

losses (Jantsch et al., 1992). A new component model was developed for use in TRNSYS to predict inverter output. The normalised inverter output is expressed as second-order polynomial (Peippo and Lund, 1994); P inv;n ¼ k 0 þ k 1 P pv;n þ k 2 P 2pv;n

ð10Þ

where P pv;n ¼

P pv P inv;rated

ð11Þ

P inv P inv;rated

ð12Þ

and P inv;n ¼

where Ppv,n and Pinv,n are the normalised inverter input and output power, respectively. Ppv and Pinv are PV dc input and ac output from the inverter at any instant of time respectively and Pinv,rated is the rated inverter input capacity. k0 is the normalised self-consumption loss; k1 is the linear efficiency coefficient and k2 is the coefficient for losses proportional to input power squared (Peippo and Lund, 1994). Inverter efficiency (ginv) is defined as: ginv ¼

P inv;n P pv;n

ð13Þ

The rated capacity of the inverter in the particular installation considered was 13 kW. From correlations relating inverter efficiency to the fraction of input load to the inverterÕs rated capacity, the coefficients k0, k1 and k2 were found to be
0.015, 0.98 and
0.09, respectively. In order to validate the inverter component model, actual hourly measured PV dc power was used as input to the component. The corresponding predicted inverter output was compared with actual measured data. The predicted and measured inverter efficiency as a function of normalised dc-input power is shown in Fig. 8. Fig. 8 indicates that at low input power level the inverter

100 90 Inverter Efficiency (%)

80 70 60 50 40 30 20 Measured Predicetd

10 0 0.00

0.10

0.20 0.30 0.40 0.50 0.60 0.70 Normalised dc-Input Power [PPV/Pinv,n]

0.80

0.90

1.00

Fig. 8. Measured and predicted inverter efficiency as a function of normalised dc-input power i.e., ratio of inverter input dc power to the nominal input capacity.

174

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

monthly average daily measured and predicted inverter output when modified simulated PV output calculated using Eqs. (10)–(12) was used as input to the inverter model. The corresponding percentage error between measured and simulated monthly average daily ac output from the inverter is also shown in Fig. 8. The magnitude of the error varies from 2% to 12%. Table 8

efficiency is zero, which is due to self-consumption losses in the inverter. The inverter can only start its operation when input power to the inverter unit reaches above its threshold level. For a large capacity inverter this threshold energy level is also large, requiring a larger energy input to commence operation. Therefore the loss is also higher for low input conditions. Fig. 9 illustrates

15 Measured Predicted Percentage Error

160

10

140 120

5

100 0 80 -5

60 40

Percentage Error (%)

Average Daily Inverter Output (MJ)

180

-10

20 -15

0 01 01 01 1 01 01 01 01 01 02 02 02 02 02 02 2 02 02 02 02 02 r- ay- n- ul-0 g- p- ct- v- ec- n- b- ar- r- ay- n- ul-0 g- p- ct- v- ecAp M Ju J Au Se O No D Ja Fe M Ap M Ju J Au Se O No D

Month

Fig. 9. Monthly daily average measured and predicted inverter output and corresponding percentage error.

Table 8 Monthly average daily measured and predicted inverter output and corresponding difference between measured and predicted results for four cases (Cases 1–4) Year

Month

Measured inverter output (MJ)

Predicted inverter output (MJ) Case 1

Case 2

Case 3

Case 4

Error (%) Case 1

Case 2

Case 3

Case 4

2001

Apr May Jun Jul Aug Sep Oct Nov Dec

81.7 151.3 115.7 113.5 107.8 78.7 54.3 21.9 43.3

97.3 160.7 129.1 122.6 119.6 88.3 63.9 31.3 49.4

95.4 156.8 126.7 120.1 117.1 86.7 62.8 30.9 48.5

93.7 158.8 128.2 121.8 116.2 82.7 56.9 24.9 38.8

91.9 155.0 125.8 119.3 113.9 81.4 55.9 24.6 38.2

19.09 6.18 11.59 8.08 10.91 12.08 17.67 42.86 13.99

16.69 3.62 9.49 5.86 8.62 10.16 15.56 41.03 12.05

14.71 4.91 10.73 7.33 7.73 5.08 4.68 13.78
10.38

12.50 2.41 8.69 5.18 5.60 3.39 2.93 12.50
11.72

2002

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

25.4 46.0 109.6 111.7 132.3 101.1 86.2 99.8 107.4 53.2 41.9 29.2

33.2 58.7 119.1 120.8 143.8 114.3 95.6 117.1 122.4 64.4 49.5 34.0

32.7 57.6 116.3 118.1 140.7 112.3 93.9 114.7 119.4 63.2 48.5 33.4

26.5 49.8 113.6 117.4 142.3 114.4 95.3 113.2 113.7 55.6 46.2 27.9

26.1 48.9 111.0 114.9 139.3 112.4 93.7 110.9 111.1 54.7 45.3 27.4

31.00 27.66 8.60 8.16 8.69 13.16 10.94 17.33 13.98 21.13 17.97 16.50

28.76 25.25 6.05 5.79 6.29 11.08 9.02 14.93 11.21 18.93 15.76 14.46

4.42 8.20 3.63 5.14 7.56 13.24 10.58 13.42 5.95 4.58 10.10
4.55

2.87 6.38 1.25 2.91 5.24 11.21 8.71 11.18 3.52 2.87 8.04
6.06

81.5

92.1

90.3

87.5

85.8

16.07

13.84

6.71

4.74

Average

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

175

summarises the monthly average daily measured and predicted inverter output and the corresponding error between measured and predicted results for Cases 1–4. The average monthly error is found to be 4.74% over the reported simulation period.

mates. The use of such, more narrowly applicable, models enables systems to be sized correctly. Moreover this approach needs to be employed with care as to its applicability.

4. Conclusions

References

The electrical and thermal performance of a building integrated PV system has been predicted using TRNSYS. A new component model has been developed for modelling inverter output and modifications have been made to standard TRNSYS types for global-diffuse correlation and PV module temperature. Statistical analysis has been performed with the measured and predicted data for three global-diffuse correlations and four tilted surface radiation models to determine those best for estimating the beam and diffuse components of the horizontal insolation and total, beam and diffuse components of insolation at the inclined PV surface, respectively. A sitespecific global-diffuse correlation and an isotropic sky model are shown to provide best results for the particular installation considered. A linear relationship relating the difference between module and ambient temperature to in-plane insolation derived from the measured data has been introduced into the standard TRNSYS component for to predict module temperature. Comparison of measured and predicted module temperature shows that this modification improves the estimation of module temperature when compared with the standard NOCT relationship used in the standard TRNSYS model. Measured and simulated electrical PV outputs have been compared on daily basis. The performance of the simulation model before and after modification has been tested by statistical analysis. Results show that the least error occurred when proposed global-diffuse correlation, isotropic sky model and modified module temperature are employed in TRNSYS. It has been observed from analysis of monthly simulation results that modification of the global-diffuse correlation improves simulation accuracy within the range of 55–70% particularly in winter months whereas the modification of the module temperature model influences the accuracy of the simulation results more in the summer months and improves the model performance within the range of 15–30%. The average monthly inverter output has been modelled based on the input output characteristics of the inverter. The developed model has been validated with measured data. The average monthly error between measured and predicted PV and inverter output was found to be 6.79% and 4.74%, respectively. The relationships developed can be used to predict the performance of installations with similar specification components in comparable temperate maritime cli-

Anon., 2000. Siemens Photovoltaic Module SM110/100. Siemens Solar Industries, Technical Specification. Atmaram, G.H., Khattar, M., 1982. A comparison of SOLCEL II and TRNSYS PV systems simulations with operational results of a PV residential facility. In: 16th IEEE Photovoltaic Specialists Conference, San Diego, California, 27–30 September, pp. 978–979. Balcomb, J.D., 1997. ENERGY-10: a design tool for low energy buildings. In: Building SimulationÕ97. International Building Performance Simulation, Prague, Czech Republic, 8–10 September. Bates, J.R., Standeven, M.A., Pearsall, N.M., Jones, D.L., 1998. Evaluation and validation of simulation packages for use in the design of building integrated photovoltaic systems. In: 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion, Vienna, Austria, 6– 10 July, pp. 2736–2739. Bishop, J.W., 1988. Computer simulation of the effects of electrical mismatches in photovoltaic cell interconnection circuits. Solar Cells 25, 73–89. Davis, M.W., Fanney, A.H., Dougherty, B.P., 2001. Prediction of building integrated photovoltaic cell temperatures. ASME Journal of Solar Energy Engineering 123, 200–210. Duffie, J.A., Beckman, W.A., 1991. Solar Engineering of Thermal Processes, second ed. Wiley Interscience, New York, pp. 669–671. Evans, D.L., 1981. Simplified method for predicting photovoltaic array output. Solar Energy 27 (6), 555–560. Fiksel, A., Thornton, J.W., Klein, S.A., Beckman, W.A., 1995. Developments to the TRNSYS simulation program. ASME Journal of Solar Energy Engineering 117, 123–127. Gow, J.A., Manning, C.D., 1999. Development of a photovoltaic array model for use in power-electronics simulation studies. IEE Proceedings: Electric Power Applications 146 (2), 193–200. Hay, J.E., Davies, J.A., 1980. Calculation of the solar radiation incident on an inclined surface. In: Proceedings First Canadian Solar Radiation Workshop, pp. 59–72. Hoover, E.R., 1980. SOLCEL II-an improved photovoltaic system analysis program, Sandia National Laboratories Report, SAND79-1785. Hove, T., 2000. A method for predicting long-term average performance of photovoltaic systems. Renewable Energy 21, 207–229. Ineichen, P., Guisan, O., Perez, R., 1990. Ground-reflected radiation and albedo. Solar Energy 44, 207–214. Ingersoll, J.G., 1985. Simplified prediction of annual energy generation by residential photovoltaic arrays. In: 18th IEEE Photovoltaic Specialists Conference, Las Vegas, NV, USA, 21–25 October, pp. 208–213. Jantsch, M., Schmidt, H., Schmid, J., 1992. Results of the concentrated action on power conditioning and control. In:

176

J.D. Mondol et al. / Solar Energy 78 (2005) 163–176

11th E.C. Photovoltaic Solar Energy Conference, Montreux, Switzerland, 12–16 October, pp. 1589–1593. King, D.L., Dudley, J.K., Boyson, W.E., 1996. PVSIMÓ: a simulation program for photovoltaic cells, modules, and arrays. In: 25th IEEE Photovoltaic Specialists Conference, Washington, DC, 13–17 May, pp. 1295–1297. Klein, S.A., Beckman, W.A., 1983. PV F-Chart userÕs manual, Microcomputer version 1.0, Middleton, Wisconsin. Klein et al., 2000. TRNSYS 15, A Transient Simulation Program. Solar Energy Laboratory, University of Wisconsin, Madison, Wisconsin, WI. Liu, B.Y.H., Jordan, R.C., 1963. The long term average performance of flat-plate solar-energy collectors. Solar Energy 7 (2), 53–74. Menicucci, D.F., 1986. Photovoltaic array performance simulation models. Solar Cells 18, 383–392. Menicucci, D.F., Fernandez, J.P., 1984. Verification of photovoltaic system modelling codes based on system experiment data. In: 17th IEEE Photovoltaic Specialists Conference, Kissimmee, FL, USA, 1–4 May, pp. 1335–1340. Menicucci, D.F., Fernandez, J.P., 1988. UserÕs manual for PVFORM: a photovoltaic system simulation program for stand-alone and grid-interactive applications. Sandia National Laboratories Report, SAND85-0376. Mermoud, A., 1995. Use and validation of PVSYST, a userfriendly software for PV-system design. In: 13th European Photovoltaic Solar Energy Conference, Nice, France, 23–27 October, pp. 736–739. Mermoud, A., Rocker, C., Bonvin, J., Mu¨ller, A., 1998. PVSYST 3.0 software: ergonomics and accessibility. In: 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion, Vienna, Austria, 6–10 July, pp. 2632–2635. Meyer, E.L., van Dyk, E.E., 2000. Development of energy model based on total daily irradiation and maximum ambient temperature. Renewable Energy 21, 37–47. Mondol, J.D., Yohanis, Y.G., Smyth, M., Norton, B., 2002. Monitoring building integrated photovoltaics at the ECOS Millennium Environmental Centre in Northern Ireland. In: World Renewable Energy Congress VII, Cologne, Germany, 29 June–5 July. Muneer, T., Saluja, G.S., 1986. Correlation between hourly diffuse and global solar irradiation for the UK. Building Services and Engineering Research and Technology 7, 37– 43. Oliveria, A.P., Escobedo, J.F., Machado, A.J., Soares, J., 2002. Correlation models of diffuse solar-radiation applied to the city of Sa˜o Paulo, Brazil. Applied Energy 71, 59–73. Park, M., Kim, B., Yu, I., 2001. A novel simulation method for PV power generation systems using real weather conditions. In: IEEE International Symposium on Industrial Electronics 1, Pusan, South Korea, 12–16 June, pp. 526–530.

Peippo, K., Lund, P.D., 1994. Optimal sizing of solar array and inverter in grid-connected photovoltaic systems. Solar Energy Materials and Solar Cells 32, 95–114. Perez, R.S., Arbogast, C., Seals, R., Scott, J., 1986. An anisotropic hourly diffuse radiation model for sloping surfaces: description, performance validation, site dependence evaluation. Solar Energy 39, 487–497. Reindl, D.T., Beckman, W.A., Duffie, J.A., 1990. Evaluation of hourly tilted surface radiation models. Solar Energy 45, 9– 17. Ropp, M.E., Begovic, M., Rohatgi, A., Long, R., 1997. Design consideration for large roof-integrated photovoltaic array. Progress in Photovoltaics: Research and Application 5, 55– 67. Schilla, T., Hill, R., Pearsall, N., Bucher, G., 1997. PVNetSim a versatile PV simulation software based on the design center Schematics, PSPICE and PROBE. In: 14th European Photovoltaic Solar Energy Conference, Barcelona, Spain, 30 June–4 July, pp. 1558–1561. Sick, F., Erge, T., 1996. Photovoltaics in Buildings: A Design Handbook for Architects and Engineers, first ed. James and James (Science Publishers) Ltd, p. 166. Sidrach-de-Cardona, M., Lo´pez, L.M., 1999. Performance analysis of a grid-connected photovoltaic system. Energy 24, 93–102. Siegel, M.D., Klein, S.A., Beckman, W.A., 1981. A simplified method for estimating the monthly-average performance of photovoltaic systems. Solar Energy 26, 413–418. Snow, M., Jones, P., Prasad, D.K., 1999. Photovoltaics (PV) modelling for cities: a GIS-building integrated PV (BIPV) simulation approach. In: ISES Solar World Congress 2, Jerusalem, Israel, pp. 147–155. Sukamongkol, Y., Chungpaibulpatana, S., Ongsakul, W., 2002. A simulation model for predicting the performance of a solar photovoltaic system with alternating current loads. Renewable Energy 27, 237–258. Travers, D., Watt, M., MacGill, I., Kaye, J., Kunzi, S., Spooner, T., 1998. Evaluation tool for building integrated photovoltaic systems. In: 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion, Vienna, Austria, 6–10 July, pp. 2579–2582. Waide, P.A., Norton, B., 2003. Variation of insolation transmission with glazing plane position and sky conditions. ASME Journal of Solar Energy Engineering 125, 182– 189. Walker, A., Balcomb, D., Kiss, G., Weaver, N., Becker, H.M., 2003. Analyzing two federal building-integrated photovoltaics projects using ENERGY-10 simulations. ASME Journal of Solar Energy Engineering 125, 28–33. Wilshaw, A.R., Bates, J.R., Pearsall, N.M., 1996. Photovoltaic module operating temperature effects. In: Proceedings of Eurosun 96, Freiburg, Germany, pp. 940–944.