Modeling, performance analysis and economic feasibility of a mirror-augmented photovoltaic system

Energy Conversion and Management 80 (2014) 276–286

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Modeling, performance analysis and economic feasibility of a mirror-augmented photovoltaic system B. Fortunato, M. Torresi ⇑, A. Deramo Dipartimento di Meccanica, Matematica e Management (DMMM), Politecnico di Bari, via Re David 200, 70125 Bari, Italy

a r t i c l e

i n f o

Article history: Received 24 July 2013 Accepted 31 December 2013 Available online 14 February 2014 Keywords: Mirror Augmented Photovoltaic Reflective surfaces Sky-view factor Life-Cycle Cost Exergy analysis

a b s t r a c t In the last years, solar photovoltaic (PV) systems have had great impetus with research and demonstration projects, both in Italy and other European countries. The main problems with solar PV are the cost of solar electricity, which is still higher compared with other renewables (such as wind or biomass), due to the cost of semi-conductors, and the low conversion efficiency. However, PV panel prices are rapidly decreasing benefiting from favorable economies of scale. For instance, according to the Energy Information Administration (EIA) the US average levelized costs for plants entering service in the 2018 should be 144.3$/MW h for solar PV, whereas 111.0$/MW h for biomass and 86.6$/MW h for wind (Levelized Cost of New Generation Resources in the Annual Energy Outlook, 2013). In order to increase the electric yield of PV modules (which can be even doubled with respect to constant tilt configurations), without significantly increasing the system costs, it was decided to consider the addition of inclined mirrors at both sides of the PV modules, so as to deflect more solar rays towards them, as in Mirror-Augmented Photovoltaic (MAPV) systems. The system preserves its constructive simplicity with commercial flat PV modules even though dual axis tracker must be implemented, since MAPV systems harness mainly the direct radiation. The performance analysis of MAPV systems starts from the calculation of the global irradiation on the surface of the PV module which is a sum of the direct sunlight on it and the irradiation reflected by the mirrors. A mathematical model of a MAPV system is presented, which takes into account not only the increase of direct (or beam) radiation, due to the mirrors, but also the reduction of both the diffuse and reflected radiations due to the shadowing effect of the flat mirrors. In particular, under an isotropic sky assumption, a simplified analytical expression, applicable in the case of MAPV systems, for the sky-view factor has been developed. The deterioration in the performance of the PV system as a result of the increasing cell temperature with radiation augmentation due to mirrors has been also evaluated. Moreover, in order to provide a more realistic view of the process, the energy analysis is accompanied by the exergy analysis. Finally, in order to analyse the economics of MAPV systems, Net Present Value, Discounted Payback Period, Internal Rate of Return and Life-Cycle Costs, have been considered and compared with both a constant tilt building-integrated photovoltaic (BIPV) system and a system with a dual axis tracker. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction The renewable energy sources, together with flexible and intelligent infrastructures and energy efficiency measures, will represent an increasing share of European Union’s (EU) energy with regard to electricity, heating (responsible for almost half of the EU’s total energy demand), cooling and transportation, helping to reduce European dependence on conventional energy sources. In the 2030, at least a 30% share of renewable energy sources is ex⇑ Corresponding author. Tel.: +39 080 5963577; fax: +39 080 5963411. E-mail addresses: [email protected] (B. Fortunato), (M. Torresi), [email protected] (A. Deramo). http://dx.doi.org/10.1016/j.enconman.2013.12.074 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.

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pected in the energy mix of the European Union. Furthermore, it must be considered the effect of the interaction of this ambitious target with other potential goals in the context of climate and energy policy, such as greenhouse gases (GHG) emission reduction, as well as it must be assessed the impact of EU’s industry on competitiveness, including industries related to renewable energy sources. Therefore, renewables do not only contribute to address the problem of climate change and enhance energy independence but also offer great additional environmental benefits in terms of pollutant emission reduction, waste production and water usage, as well as in terms of risk reduction associated with other forms of energy production.

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The 2012 has been a favorable year for green electricity production in Italy (the gross energy production from renewables has been estimated in 92.46 TW h by GSE, the state-owned company which promotes and supports renewable energy sources in Italy) and the 2013 is going to be even better since, this year, the generation of electricity from renewable sources could probably overcome the emblematic threshold of 100 TW h. Actually, if hydropower contribution will respect forecasts, in the 2013, renewables will be able to meet 31% of the Italian electricity needs (including imports), reaching 35% of national production, despite the crisis. In the 2012, the electricity demand in Italy decreased by 2.8% compared to the 2011, dropping down to a total of 325.2 TW h, compared with 334.6 TW h in the previous year, as indicated by the Terna report. At regional level, the electricity consumptions fell by 2.5%, 3.1% and 6.1% in the North, in the Center and in the South, respectively. The 2012 is the third lowest in terms of electricity consumption in the last ten years. The only energy sources that have seen an increase in their production are photovoltaic and wind. Photovoltaic, with 18.3 TW h produced in the 2012, increased by 71.8% compared to the 2011. In order to evaluate the growth rate of solar energy in Italy, it is sufficient to consider that in the 2010 the photovoltaic energy production was only 1.9 TW h and 0.7 TW h in the 2009, which means that in four years, the increase has been 2600%. The wind, with 13.1 TW h produced in the 2012, recorded an increase in production of 34.2% compared to the 2011. The two sources together, with 31.4 TW h, actually covered 9.6% of the national electricity demand. On the other hand, hydroelectric and geothermal energy productions decreased; with 43.3 TW h (8.2% compared to the 2011) and 5.2 TW h (1.4%) produced, they have guaranteed 13.3% and the 1.7% of the demand, respectively. Overall, in the 2012 renewables have covered 24.6% of the national electricity demand. Furthermore, the thermal power generation from fossil fuels fell down, from 218:5 TW h in the 2011 to 204:8 TW h in the 2012 (6.3%), thus covering 62.2% of the demand. Electricity imports decreased too by 5.8% compared to the 2011 covering, with 43 TW h, the remaining 13.2% of the national electricity demand. Naturally, the growth in electricity generation from renewables is not a peculiarity of the Italian market but is a more general trend in the industrialized world. With nearly 270 billion dollars globally invested in this sector, the 2012 proved to be worse than the 2011 (which had exceeded 300 billion dollars) but still very favorable in the context of a global economic slowdown. From data of the 2012 [2], it emerges a widening of the market beyond the borders of the major industrialized countries such as the United States, Germany, Spain and Italy, which had lead the renewable energy sector till now. Chinese investment in clean energy sources grew by 20% in the 2012, hitting a record of 65.3 billion dollars, whereas in the United States investments have not gone beyond 35.58 billion dollars (37%). Among the new emerging markets, South Africa has reached 5.46 billion dollars of investments but investments expanded also in Australia, Morocco, Ukraine, Mexico, Kenya, Brazil, Ethiopia, Chile and South Korea: in all these countries projects have been developed, which have exceeded 250 million dollars in the 2012. In order to further increase the electricity production from renewable sources, governments need to promote research for efficient technical solutions of renewable power generation. In the field of solar photovoltaic, the main problem is that this kind of renewable energy is still more expensive compared to other forms, such as wind or biomass, due to the high cost of semi-conductors, even though the costs of PV panels are rapidly decreasing benefiting from favorable economies of scale, and their relative low conversion efficiencies (between 10% and 20%). For instance, according to the Energy Information Administration (EIA) the US average levelized costs (2011 $/MW h) for plants entering service

277

in the 2018 has been estimated to be 144:3 =MW h for solar PV, whereas 86:6 =MW h for wind, 111:0 =MW h for biomass and 149:2 =MW h for hydro [1]. As shown before, in Italy the PV systems have been largely diffused in the last years due to very remunerative government incentives. However, the economic crisis could determine a reduction of these incentives compromising this virtuous positive trend. In order to preserve the appeal for this kind of investment, all the technical solutions trying to increase the PV efficiency are really expected. Some solutions have already been introduced, as for example: hybrid collectors [3–12]; tracking systems, in order to follow the sun trajectory; concentrating PV, which requires smaller PV surfaces in order to obtain the same amount of electric energy of a conventional PV system [13–27]. Current status and future prospects of solar photovoltaic are well summarized in [28]. During the years, many designs of concentrating collectors have been proposed. Concentrators can be reflectors or refractors. Their concentration ratios can vary over several orders of magnitude from low values in the order of unity to high values of the order of 105 [29]. However, medium and high PV concentration systems (respectively with 20–500 and over 500 concentration levels) need expensive multijunction PV cells and parabolic optical systems or Fresnel lens systems for the concentration [30]. Furthermore, when the concentration ratios increase, PV receivers need to be cooled otherwise their temperature becomes too high with a detriment in their performance and durability. Another problem to deal with is concentrating collectors, except the ones characterized by a very low concentration ratio, need to be oriented to track the sun so that beam radiation will be directed onto the absorbing surface [29]. These considerations can explain why there is the interest toward low-concentration PV systems with concentration ratios lower than 20. For instance, Cotana et al. [30] have proposed and built an experimental innovative PV low-concentration system made of a set of flat mirrors which, appropriately oriented, simulate the surface of a parabolic concentrator, allowing a double simplification with respect to the parabolic concentrators both in the manufacturing phase and the working phase of the facility. An electronic system for tracking management rotates the mirrors around the rotational axis, in such a way that the solar radiation is always concentrated on the PV receiver panel (made of common PV cells of monocrystalline silicon) during the sun daily movement. Using ASHRAE clear-sky irradiation model, Cotana et al. [30] have evaluated that, thanks to the their concentrating system, the annual energy which hits their PV panel is 4195kW h=m2 . In this work, in order to further reduce the average cost of solar energy, especially in regions where the global radiation is not particularly high, a simpler low-concentration technology is investigated. Flat mirrors are placed at both sides of commercial PV modules, as in Mirror Augmented Photovoltaic (MAPV) systems. The use of flat mirrors has been chosen in order to limit the system complexity. For instance, since the maximum achievable concentration ratio ranges only from 1.5 to 2.5, no cooling system is required. Analogous configurations have already been proposed by other authors. For instance, Solanki et al. [31] showed that, with their PV system with V-trough concentrators (made of simple metal sheets), they can double the captured solar radiation, allowing a 33:5% reduction in the area of monocrystalline silicon solar cells needed to obtain the same electric energy yield of non-augmented system. Moreover, in their experiment (performed at the Energy Area Laboratory, Agricultural Engineering Department, Federal University of Viosa, city of Viosa, Minas Gerais State, Brazil), Sant’Anna et al. [32] showed that their PV system, with V-trough concentrators (made of specular anodized aluminum mirrors) kept at a constant tilt angle equal to the local Latitude, was able to give an electric energy yield around 30% larger than the one obtained with the same PV modules without concentrators. Lin et al. [33], in their non-

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tracked MAPV system, used a high performance, low-cost solar mirror made of acrylic. Over a time-limited period of study their MAPV system produced 26.2% more power than an equivalent non-augmented panel. In the present work, coupling the MAPV system with a dual axis tracking device, in order to constantly maintain the surface of the module normal to sunlight, and optimizing the mirror width with respect to its inclination, it is shown that, in the most economic configuration, the yearly irradiance on the PV modules can be doubled. The performance analysis of the MAPV system starts from the calculation of the global irradiation on the surface of the PV module which is a sum of the direct sunlight and the irradiation reflected by the mirrors. A mathematical model of the MAPV system is presented, which takes into account not only the increase of direct (or beam) radiation, due to the mirrors, but also the reduction of both the diffuse and reflected radiations, due to the mirror shadowing. For this purpose, a modified sky-view factor has been proposed. In addition to these considerations, the variation in the performance of the PV system as a result of the cell temperature has been taken into account. Moreover, in order to obtain a deeper insight into the effects of the mirror augmentation technique on the PV performance, an exergy analysis is carried out. Finally, in order to analyze the economics of the MAPV system, Net Present Value, Discounted Payback Period, Internal Rate of Return and Life-Cycle Costs are considered and compared with both a 3 kW constant tilt building-integrated photovoltaic (BIPV) system and a 2 kW PV system with a dual axis tracking system. 2. Evaluation of global radiation In order to calculate the monthly average daily global radiation on a sloped surface with a tilt angle b; Hb , it is common to start from the available data on a horizontal surface (typically, daily global and diffuse radiation on a horizontal surface, Hh and Hhd respectively). From these two values, the computation of the direct (or beam) radiation on a horizontal surface, Hhb , is straightforward:

Hhb ¼ Hh  Hhd

ð1Þ

In the present work, in order to compute Hb , the widely used method of Liu and Jordan [34], as extended by Klein [35], has been applied:

    1 þ cos b Hb ¼ Rb Hhb direct þ Hd 2 diffusiv e   1  cos b þ q Hh 2 reflected

as a function of the corresponding direct, diffuse and reflected contributions:

Hn ¼ Hnb þ Hnd þ Hnr

ð4Þ

2.1. Direct component on a plane constantly normal to the solar rays (Hnb ) Since the relationship indicated in the UNI 8477-1 [36] tends to overestimate the real data measured by the actinometry net of ENEA (the Italian National Agency for New Technologies, Energy and Sustainable Economic Development), named TER-SOLTERM [37], the calculation of the direct component has been performed according to ENEA’s own empirical relationship. In fact, exploiting the data detected over the years, ENEA has identified a statistically valid experimental relationship, which correlates the monthly average daily beam radiation on a constantly normal plane to the solar rays, Hnb , to the corresponding extraterrestrial value, H0n :

Hnb ¼ K nb H0n

ð5Þ

where

H0n ¼

86; 400 rGsc 2p

Z

xs

 86; 400 dx ¼ rGsc xs

x s

p

ð6Þ

Gsc ¼ 1367 W=m2 is the solar constant, r is the monthly average value of r, which accounts for the daily variation of the earth-sun distance and xs is the monthly average sunset hour angle. According to the ENEA indications [37]:

K nb ¼ 0:0696K T þ 0:8114K 2T

ð7Þ

where

KT ¼

Hh H0h

ð8Þ

In Eq. (8) the monthly average daily extraterrestrial radiation on a horizontal plane, H0h , is calculated in the following way:

H0h ¼

86; 400

p

  r Gsc cos u cos d sin xs þ xs sin u sin d

ð9Þ

whilst the radiation on the ground, Hh , is taken from available ENEA’s data (ENEA TER-SOLTERM database). Fig. 1 shows the reliability of the experimental relationship identified by ENEA

ð2Þ

with Hh and Hd being the monthly average daily global and diffuse radiations on a horizontal surface, respectively, q being the diffuse reflectance of the surroundings for the total solar radiation, and Rb being the ratio of the monthly average daily beam radiation on the tilted surface, Hbb , to that on a horizontal surface, Hhb , for the month. Overbar indicates monthly average value. Rb can be estimated by assuming its value equal to that obtained outside the atmosphere [29], i.e., under extraterrestrial conditions:

Rb ¼

Hbb H0b ffi Hhb H0h

ð3Þ

As suggested by the Italian Organization for Standardization in the standard UNI 8477-1 [36], the monthly average values are not actually evaluated but approximated by the corresponding values taken in a specific representative day of the same month. In the case of implementing a dual axis solar tracking system, capable of maintaining the PV modules constantly orthogonal to the solar rays (variable tilt angle, b, and surface azimuth angle, c), the following calculation procedure can been adopted, in order to compute the monthly average daily radiation on the PV module

Fig. 1. Calculation of the transmission coefficient of the direct radiation on the ground, K bn , as a function of the global transmission coefficient, K T , on the ground: analytical interpolating law (in red) and experimental measurements (in green) of the units of the Casaccia-Rome (ENEA TER-SOLTERM) station. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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comparing the theoretical data with the actual measurements of the control unit of the Casaccia-Rome station. 2.2. Diffuse component on a plane constantly normal to the solar rays (Hnd ) According to the approximated expression by Liu and Jordan [34], the monthly average daily diffuse radiation incident on a sloped surface, with constant tilt angle b (the azimuth angle of the surface, c, is irrelevant since the diffuse radiation is supposed, with good approximation, to be isotropic), can be trivially considered equal to:

Hbd ¼

1 þ cos b Hhd 2

ð10Þ

However, in case of normal surface, since the angle b is variable, it would be necessary to average in time but, according to the ENEA [37], it is possible to introduce an equivalent tilt angle, beff , which can be evaluated according to Eq. (11):

xs þ 2 xs ðcos xs Þ2  3 cos xs sin xs cos beff ¼ cos u cos d 2 ðsin xs  xs cos xs Þ

ð11Þ

and then to use the following relationship:

Hnd ¼

1 þ cos beff Hhd 2

ð12Þ

The value of the monthly average daily diffuse radiation on a horizontal plane, Hhd , can be either extracted from a reference database or, in the absence of direct climate data, can be estimated as:

Hhd ¼ K Hh

ð13Þ

where the monthly average diffuse fraction of daily radiation, K, according to the indications of the ENEA [37], is:

  K ¼ 1  1:165 0:0695 þ 0:8114K T

ð14Þ

Other expressions, such as those of Liu and Jordan [38], Page [39], Iqbal [40], or the one introduced in the UNI 8477-1, can also be used.

Fig. 2. Schematic cross-section of the mirror augmented PV module; it is possible to recognize the intercepting surface of the PV module (in gray), the mirrors (in black) and the orthogonal solar rays (in yellow). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

greater than 45 , otherwise the reflected beam radiation will not reach the PV module. In order to let the solar ray incident on point C be reflected exactly on point B, the following condition must be satisfied (see Fig. 2):

 p s ¼ lm sin am ¼ ðl þ aÞ tan 2am  2  p ¼ ðl þ lm cos am Þ tan 2am  2

ð16Þ

which gives, for am > 0:

lm ¼

 cos 2am l cos am

ð17Þ

This means that, increasing the inclination of the mirrors, am , with respect to the PV module, the mirror width, lm , could be increased more and more rapidly, without wasting any mirror reflected radiation, tending asymptotically to infinity when am ¼ 90 as shown in Fig. 3. Therefore for am close to 45 the gain in collected radiation would be minimal, whereas for very large angles the width of mirrors would become unacceptably high due to the increase of weights, dimensions and costs of the system.

2.3. Reflected component on a plane constantly normal to the solar rays (Hnr )

4. Global radiation modeling for MAPV

In a similar way to what have been done for the diffuse radiation contribution, the monthly average daily reflected radiation on a plane constantly normal to the solar rays, can be derived from the equivalent expression adopted for fixed surfaces, introducing the effective value of the tilt angle, beff :

Similarly to what has been done in the calculation of the radiation incident on a surface constantly normal to the solar rays, without any reflecting system, direct, Hmb , diffuse, Hmd , and reflected, Hmr , monthly average daily radiations are separately analyzed, highlighting differences and peculiarities.

Hnr ¼ q

1  cos beff Hh 2

ð15Þ

with q taken equal to 0.2 in the present work. 3. Description of the MAPV system In order to increase the radiation incident on the PV module, in the present work, two mirrors (symmetrically placed at both sides of the module) are introduced, which reflect the beam radiation on the PV module (see Fig. 2). Under the hypothesis of a perfectly operating dual-axis solar tracking system, solar rays can be kept constantly perpendicular with respect to the PV module, hence the mirror width, lm , can be trivially optimized (assuming valid the relationship of geometrical optics relative to the angle of reflection: hinc ¼ hrefl ) in order to maximize the collectable beam radiation. First of all the inclination of the mirrors, am , must be

Fig. 3. Graphic of the relationship between the width of the module absorber and the width of the reflective surfaces as a function of the angle of inclination of the latter on the horizontal.

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4.1. Direct (Hmb ) component for the MAPV system kept constantly normal to the solar rays Limited to the direct component of the radiant energy, an effective increase of the intercepting surface is obtained due to each mirror which is actually equal to the projection of each mirror, a, on the plane of the PV module, i.e.:

a ¼ lm cos am ¼ l cos 2am

ð18Þ

and the additional fictitious theoretical area per unit length for the MAPV system is given by: 0

ltheor ¼ 2a ¼ 2 l cos 2am

ð19Þ

Considering a mirror reflection efficiency, gr , (defined as the ratio of reflected, Hrefl , and the incident, Hinc , radiations), the total direct radiation, compared to the simple PV module having width l, will thus be increased by a factor: 0

l þ gr ltheor nb ¼ ¼ 1  2 gr cos 2am l

ð20Þ

hence,

Hmb ¼ nb Hnb

been done by Liu and Jordan [34], (as shown by Rakovec and Zakšek [41]) the sky-view factor is not actually the solid angle under which the PV module sees the skydome in between the two mirrors but actually the comparison of two projections onto the horizontal plane: i.e. the projection of the visible portion of the skydome onto the horizontal plane and the projection of the entire hemisphere on the same plane. Under these simplifying conditions, it is possible to graphically identify the view factors of both the diffuse and reflected radiation, for a tilted mirror augmented PV module, as shown in Figs. 5 and 6 respectively. According to the proposed model:

Z ðpam Þ Z pb 2 1 cos h2 dh sin d 2 pr ðp2am Þ 0    2am  sin 2am 1 þ cos b ¼ 1 2 p

Rmd ffi

ð22Þ

while for adjustable surfaces, still using the value of beff , the relationship takes the form

Rmd ffi

   2am  sin 2am 1 þ cos beff 1 p 2

ð23Þ

ð21Þ

In Fig. 4, for a reflection efficiency gr ¼ 0:95, the percentage increase, nb  1, of the direct radiation due to the optimal mirroraugmented system is shown. nb  1 (equal to 2 gr cos 2am ) varies from 0%, for a mirror inclination angle am ¼ 45 (reflective surfaces of null width means that they are not present) up to a maximum of 200 gr % for an angle of inclination of am ¼ 90 (mirror surfaces of infinite width). 4.2. Diffuse (Hmd ) and reflected (Hmr ) components for the MAPV system kept constantly normal to the solar rays

from which the diffuse radiation can be obtained as:

   1 þ cos beff 2am  sin 2am Hmd ¼ Rmd Hhd ¼ 1  K Hh p 2

ð24Þ

Similarly, the fraction of the surface (or the solid angle) useful for collecting the reflected radiation can be approximated as follows:

Rmr ffi

   2am  sin 2am 1  cos beff 1 p 2

ð25Þ

from which the reflected radiation cones out to be: Concerning the diffuse radiation (in the hypothesis of isotropic sky), the presence of the mirrors causes a reduction of the portion of the skydome viewed by the PV module, to an extent proportional to the angle of inclination, am . In a similar way also the capacity of receiving the reflected radiation is reduced. In the present work, it has been assumed no contribution of mirror reflection for both diffuse and reflected radiation. In order to assess the shadowing effect of the mirrors, an approximate model, that incorporates and adapts the sky-view factors at the base of the formula by Liu and Jordan [34], has been set up. The PV module width has been neglected in comparison to its length. Furthermore, the semiplanes inclined of am , which extend the mirrors toward the skydome have been substituted by two cones with the same inclination am , for computation simplicity (see Figs. 5 and 6). Finally, similarly to what has

   2am  sin 2am 1  cos beff Hmr ¼ q 1  Hh p 2

ð26Þ

5. Evaluation of the PV system performance 5.1. Monthly average daily irradiation and total yearly irradiation The monthly average daily irradiation and the total yearly irradiation (365 days) on a single PV module have been calculated for the MAPV system, according to the previously indicated methodology and referring to the city of Bari, for angles of inclination of the mirrors, am , equal to 50 ; 60 and 70 , respectively, in comparison to a horizontal PV module (Hh ), a building-integrated photovoltaic (BIPV) module characterized by a fixed tilt angle, b ¼ 30 (Hb ) and perfectly faced south, and a PV module on a dual-axis tracking system (Hn ) (see Table 1 and Fig. 7). In order to perform the calculation, the following values have been taken into account:  Latitude u ¼ 41:13 .  Ground diffuse reflectance q ¼ 0:2.  Mirror reflection efficiency gr ¼ 0:95.

Fig. 4. Increase percentage of reflected radiation for a surface provided with symmetrical appendages with reflective efficiency of reflection of 0.95 as a function of the angle of inclination.

When the PV module is installed on a dual axis tracking system the yearly irradiation is 27.2% higher than the yearly irradiation on the constantly tilted PV module. However, adding the mirrors at both side of the module, the yearly irradiation on the PV module grows significantly together with the mirror inclination. When am is equal to 70 the yearly irradiation increases of the 145.7% (see Fig. 7).

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Fig. 5. Graphical representation of the view factor of the diffuse radiation due to the tilt angle, b, and the inclination of the mirrors, am , for a general location of the module.

Fig. 6. Graphical representation of the view factor of the reflected radiation due to the tilt angle, b, and the inclination of the mirrors, am , for a general location of the module.

Table 1 Monthly average daily irradiance – (⁄) data by ENEA/TER-SOLTERM. BARI Hh ðÞ Hb ðÞ Hn Hn ðam ¼ 50 Þ Hn ðam ¼ 60 Þ Hn ðam ¼ 70 Þ

Units 2

(MJ/m ) (MJ/m2) (MJ/m2) (MJ/m2) (MJ/m2) (MJ/m2)

January

February

March

April

May

June

July

August

September

October

November

December

Year

Variation (%)

6.70 10.32 12.42 15.01 20.68 25.15

9.30 12.51 14.79 17.53 23.82 28.72

14.30 17.12 20.77 24.60 33.41 40.27

18.30 19.18 24.08 28.06 37.66 45.07

21.90 21.01 27.80 32.35 43.38 51.88

24.10 22.21 30.52 35.75 48.18 57.79

23.90 22.42 30.59 36.01 48.71 58.57

20.90 21.14 27.47 32.38 43.82 52.70

16.30 18.55 22.91 27.12 36.82 44.38

11.70 15.47 18.68 22.43 30.77 37.31

7.50 11.22 13.48 16.26 22.38 27.19

6.10 9.88 12.02 14.64 20.28 24.74

5517 6124 7787 9207 12,491 15,046

9.9

5.2. Energy produced by the PV module In this work, a commercial high efficiency PV module has been considered characterized by the following parameters:     

Nominal power under Standard Test Condition PSTC ¼ 210 Wp . Module efficiency gmodule ¼ 16:7%. Cell efficiency gcell ¼ 18:9%. Nominal Operating Cell Temperature NOCT ¼ 46  C. Power temperature coefficient C t ¼ 0:336%=K.

In order to carry out the evaluation of the energy produced by each PV module, it is worth recalling that PV modules are rated under nominal operating conditions (i.e. at T ref ¼ 25  C and

27.2 50.4 104.0 145.7

G0 ¼ 1 kW=m2 ) but actually working conditions registered in the field rarely correspond to their nominal values. In order to take into account the performance variation of the PV module with the change in cell temperature, which is a function of both irradiance and outdoor temperature, the monthly average daily energy production has been computed as follows:

E ¼ P STC tL

G g G0 T

ð27Þ

where t L is the day-light period of time (on a monthly average basis):

tL ¼

2xs 86; 400 2p

ð28Þ

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instance, in the case of the MAPV system with mirrors inclined at 70 , even though the yearly irradiation is 145.7% higher, the electricity production increases of only 133.3%. 5.3. MAPV system evaluation based on exergy analysis In order to gain further insight in the MAPV system performance, an exergy analysis of the different PV systems under investigation has been carried out. The exergy content of a system represents the maximum amount of work, which can be obtained from it when, starting from the current status, the system reaches equilibrium with respect to the surrounding environment. Hence, when the system and surroundings are in equilibrium, the exergy becomes zero. Unlike energy, exergy is not a conservative quantity and during any process (except during reversible ones) it is consumed due to irreversibilities. The exergy consumption is proportional to the generated entropy during the process. Hence, exergy is a measure of the quality of energy [43]. For a steady-state process, the overall exergy balance of a solar PV system can be written as follows:

Fig. 7. Monthly average daily irradiance.

Exin ¼ Exout þ Irr

G is the daily irradiance (on a monthly average basis):

G¼

H tL

ð29Þ

where Exin ; Exout are the exergies entering and exiting the system, respectively, and Irr are the irreversibilities of the system or the exergy losses. From the previous expression, immediately comes the concept of exergy efficiency:

ð30Þ

gex ¼

and gT is the cell temperature correction coefficient:

gT ¼ ð1 þ C t ÞðT c T ref Þ

In this work, the cell temperature, T c , has been calculated as follows:

T c ¼ T ae þ ðNOCT  20 CÞ

G 800 W=m2

ð31Þ

where T ae is the daily outdoor temperature. T ae has been considered as the daily average outdoor temperature during the daylight hours, T a , (from UNI 10349 prosp. VI [42]), increased by 10%:

T ae ¼ 1:1T a

ð33Þ

ð32Þ

Results are summarized in Table 2. When considering the electricity production, its behavior is similar to the one of the irradiation, however due to the higher cell temperature registered in the case of the MAPV systems, the percentage of performance increase is lower. For

Exout Exin

ð34Þ

Following Sudhakar and Srivastava [44], the inlet exergy of a PV system, Exin , includes only the exergy associated to the solar radiation, which can be evaluated, according to Petela [45,46], as follows:

" Exin ¼ AG 1 

   4 # 4 Ta 1 Ta þ 3 T sun 3 T sun

ð35Þ

where T sun ¼ 5780 K is the sun temperature. Concerning the exergy output, Exout , two are the main contributions under steady states conditions, i.e. thermal, Exth , and electrical, Exel , exergies. The electrical exergy is the output electrical power, V m Im , of the PV system [47]. The thermal exergy is the power ideally available when the thermal power dissipated by the PV system is converted with the Carnot efficiency

Fig. 8. Net positive values.

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B. Fortunato et al. / Energy Conversion and Management 80 (2014) 276–286 Table 2 Day-light period of time, t L , cell temperature, T c , electricity production of a single module, E, and percentage of increment with respect to one BIPV module, DE. BARI

Units

January

February

March

April

May

June

July

August

September

October

November

December

Year

tL T c ðbÞ T c ðnÞ T c;am ¼50 T c;am ¼60 T c;am ¼70

(s) (°C) (°C) (°C) (°C) (°C)

33,841 19.4 21.4 23.9 29.3 33.6

37,637 20.9 22.9 25.3 30.7 34.9

42,186 25.4 28.2 31.2 37.9 43.2

47,196 28.8 32.2 34.9 41.6 46.7

51,498 33.1 37.3 40.2 47.2 52.5

53,690 38.0 43.0 46.2 53.7 59.5

52,695 41.0 46.0 49.4 57.2 63.3

48,989 41.0 45.2 48.4 56.0 61.9

44,130 37.9 41.1 44.2 51.3 56.9

39,123 32.5 35.2 38.3 45.3 50.7

34,844 25.9 28.0 30.6 36.3 40.8

32,730 21.0 23.2 25.8 31.4 35.8

518,558

Eb En Ea¼50 Ea¼60 Ea¼70

(kW h) (kW h) (kW h) (kW h) (kW h)

0.61 0.73 0.88 1.19 1.43

0.74 0.87 1.02 1.36 1.62

0.99 1.20 1.41 1.87 2.21

1.09 1.37 1.58 2.08 2.44

1.18 1.56 1.79 2.35 2.76

1.22 1.68 1.94 2.55 3.00

1.22 1.66 1.94 2.55 3.00

1.15 1.50 1.75 2.30 2.72

1.03 1.27 1.48 1.97 2.33

0.87 1.05 1.25 1.68 2.00

0.65 0.78 0.93 1.26 1.50

0.58 0.71 0.85 1.16 1.39

345 438 512 680 804

DEn DEam ¼50 DEam ¼60 DEam ¼70

(%) (%) (%) (%)

20.3 44.2 95.1 133.8

18.2 39.0 85.4 120.4

21.3 42.3 88.8 123.6

25.6 45.0 90.3 123.8

32.3 52.5 99.8 134.6

37.4 59.2 109.2 146.1

36.4 58.8 109.2 146.5

29.9 51.5 99.8 135.6

23.5 44.7 91.8 126.8

20.8 43.5 92.3 129.0

20.1 43.7 94.0 132.2

21.7 46.9 99.8 140.0

27.0 48.7 97.2 133.3

 Ta Exel ¼ Q_ 1  Tc

ð36Þ

where

Q_ ¼ AU ðT c  T a Þ

ð37Þ

The overall heat loss coefficient, U, can be evaluated taking into account both convection and radiation losses

U ¼ hconv þ hrad

ð38Þ

with

hconv ¼ 2:8 þ 3V w

ð39Þ

according to Boyle [48], and

   hrad ¼ r T sky þ T c T 2sky þ T 2c

ð40Þ

According to Watmuff et al. [49], the effective temperature of the sky, T sky , is 6 degree lower than ambient temperature

T sky ¼ T a  6

ð41Þ

In order to evaluate the convection losses, the wind speed, V w , is necessary. Since no data where available, the wind speed as been supposed to be equal to 0.5 m/s. Together with, the exergy efficiency, gex , the energy efficiency, g, of the system can be defined as follows:

g¼

V m Im AG

Fig. 9. Comparison of energy and exergy efficiencies for the PV systems under investigation.

temperature and its thermal losses, the exergy efficiency increases too. However in a PV system, this amount of useful exergy is actually lost, taking no advantage of the high exergy content of the sunlight. This is the reason why, in order to minimize the waste of energy captured from the sun, hybrid solar collectors could be effectively substituted to regular PV modules in a new generation of MAPV system. 6. Economic feasibility

ð42Þ

It is worth saying that the global radiation, G, in the definition of both efficiencies, is the actual global radiation incident on the PV modules, which means that in the MAPV systems, the mirror augmented radiation is debitely taken into account. In Fig. 9 a comparison among the different PV systems has been carried out. It must be pointed out that, in this work, all the quantities are estimated as monthly averaged daily values. From Fig. 9, it is possible to see that, in terms of energy efficiency, the increase of the mirror augmentation effect determines a slightly detriment of the efficiency. This is due to the worsening of the PV module performance when the module temperature increases. This means that, merely on the basis of the first law of thermodynamics, the mirror augmentation technique is not favorable. However the reason for the application of this technique stands on the increase of electric energy yield per actual unit area of the PV module hence reducing the number of PV modules in order to obtain the same amount of energy. Since the definition of the exergy efficiency is based on the potential use of the system thermal losses, it is evident that increasing the global radiation captured by each module, hence increasing its

The case of a residential energy supply, amounting to 4200 kW h per year and located in the city of Bari, has been considered. In this case a small MAPV system of 2 kW (actually composed by 10 PV modules characterized by a peak power equal to 210 Wp ) mounted on a dual axis tracking system has been taken into account and compared with both a 3 kW BIPV system (actually composed by 14 PV modules characterized by a peak power equal to 210 Wp ) characterized by a constant tilt (b ¼ 30 ) faced south and a 2 kW (i.e. 10 PV modules) dual axis tracking PV system. In order to analyze the economics of the systems under comparison (which is performed in terms of Net Present Value, Discounted Payback Period, Internal Rate of Return and Life-Cycle Costs), several parameters must be taken into account: performance, interconnection agreement type, operation and maintenance (O&M), financial incentives, electricity costs, initial equipment and installation costs. It is worth to mention that the results of this analysis can significantly vary depending on the site, hence on local solar radiation. In order to perform the Life Cycle Cost (LCC) analysis, a useful system life period of 25 years has been considered. In all the cases under investigation, PV systems are supposed to be not

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financed, hence no initial or operating costs are claimed as business expenses. Comparison of the costs related to the different PV systems under investigation are summarized in Table 3. All initial and future expenses and revenues have been quantified including initial and O&M costs. The PV systems are supposed to be installed under the Italian 5th feed-in scheme, which has come into effect on July 15, 2012. The tariffs of the 5th feed-in scheme are alternative to net metering, simplified purchase and resale arrangements and sale of electricity in the market. 6.1. Initial costs Initial costs of grid-connected PV systems are associated to: equipments, installation, interconnection fees (100 €), system design, site preparation, engineering work (0:4 €=Wp for BIPV whilst 0:6 €=Wp when considering tracking systems), design of the eventual concrete foundation in the cases where the tracking system is considered, etc. The equipment costs take into account: PV modules (1:2 €=Wp ), inverters, mounting hardware (only mounting clip, with a specific cost of 0:3 €=Wp , for BIPV plus frame, gear-drive, and controller for tracking systems, increasing the specific cost up to 0:7 €=Wp ), miscellanea (wiring, fuses, conduit, etc. equal to 0:3 €=Wp for BIPV and 0:35 €=Wp for tracking systems), PV installation labor (0:5 €=Wp ). Furthermore, when tracking systems are implemented, costs related to concrete foundation, trenching for electrical wiring from the system to the building and supporting pole need to be added (in this work considered equal to 0:8 €=Wp ). Consequently, on a peak watt (Wp ) basis, the installation costs of tracking systems are actually higher than the one in the case of stationary systems and they can grow becoming more than twice that of stationary systems. Moreover, when MAPV applications are considered, the increment of the overall surface (sum of the surfaces of both the PV module, SPV , and the mirrors, Sm ) must be taken into account when designing the tracking system and foundation, due to the increment of the mechanical stresses. For this reason, an augmentation coefficient, AC, has been introduced evaluating at 30% the effect of the increased overall surface due to the mirror surfaces:

AC ¼ 1 þ

0:3Sm SPV

ð43Þ

Finally, the mirror cost has been considered to be equal to 30 €/m2. 6.2. Operation and maintenance costs Operation and maintenance costs (under the hypothesis of having no battery backup) can be considered minimal. Maintenance tasks may include: annual visual inspection and cleaning of the PV modules; hardware checking and wiring fastening to ensure tightness every few years; integrity checks of sealants around

outdoor electrical boxes; and periodic checks of energy yield and power output. In this work, annual O&M costs have been assumed to be equal to 0.1% of the initial installed costs of the systems. However, the cost of replacing the inverters if they fail after the warranty has expired (grid-tied inverters usually have a 10 or 15 year warranty though some are now offered at 25 years) must be accounted for. Currently a 1 to 3 kW inverter can approximately cost 0:6 €=W. However, inverter prices are predicted to decrease by approximately 35% in ten years and 50% in twenty years. In this work, the replacement of the inverter is assumed to be required every ten years, hence twice in the system life cycle, and the costs for their substitutions are assumed to be consistent with these percentages of reduction. Labor costs for the substitution of the inverters are assumed to be 30% of the equipment costs. 6.3. Future estimated energy generation and savings To approximate future energy savings of each system, the degradation in performance of PV modules, due to age over their useful life, has been taken into account. According to long-term performance and reliability studies of multi-crystalline PV modules, degradation rates typically range from 0.5% to 0.7% per year. For this work, the degradation rate was assumed to be 0.5% per year. The Italian 5th feed-in scheme grants, for 20 years, an all-inclusive feed-in tariff (based on the capacity and type of plant) to the share of net electricity injected into the grid and a premium tariff to the share of net electricity consumed on site. The considered tariff is the one applicable upon the date of commissioning of the plant (which is supposed to be January 1, 2014, i.e. during the 1st semester of the 2nd year since the actuation of the Italian 5th feed-in scheme) and will be paid over a period of 20 years beginning there on. The value of the feed-in tariff remains constant throughout the support period. In this work, since battery backup is not available, the produced electricity is supposed to be consumed on site (with a premium tariff equal to 0.070 €/kW h which becomes 0:075 €=kW h for BIPV) only for a 50% share of the required electricity (with an incremental cost equal to 0:2 €=kW h), whilst the remaining share is supposed to be injected into the grid (with a feed-in tariff equal to 0.152 €/kW h which becomes 0.157 €/kW h for BIPV). In order to perform the Life Cycle Cost (LCC) analysis, a long-term average discount rate, DR, equal to 6% has been assumed in order to estimate future electric price indices. This discount rate value was chosen according to the analysis carried out by the Italian Electricity and Gas Authority (AEEG) based on the Electricity Market Authority (GME) data, which shows that, in the period from May 2004 to May 2012, the average annual increase in energy costs has been exactly equal to 6%. Actually this is a conservative choice, since over shorter periods, the values of the average annual increase have been even higher. For instance, in the period April 2004–April 2008 the average annual increase was 13.7%, whereas

Table 3 Comparison of PV system costs. COSTS

Units

BIPV 3 kWp

Tracking PV 2 kWp

MAPV @50° 2 kWp

MAPV @60 2 kWp

MAPV @70 2 kWp

Utility interconnection fee Engineering PV modules Inverter Mounting hardware Miscellanea PV installation labor Mirrors Concrete foundation/trenching/pole materials/labor Utility interconnection fee Total costs

(€) (€) (€) (€) (€) (€) (€) (€) (€) (€) (€)

100 1176 3528 1764 882 882 1470 0 0 100 9802

100 1260 2520 1260 1470 735 1050 0 1680 100 10,075

100 1260 2520 1260 1708 735 1050 204 1952 100 10,790

100 1260 2520 1260 2352 735 1050 757 2688 100 12,722

100 1260 2520 1260 3445 735 1050 1694 3938 100 16,003

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in the period June 2009–June 2012 the same value was 14.5%. In between these two periods of strong growth, a significant electricity cost reduction was experienced. Again, due to the global crisis particularly significant in Italy, during the period from the end of the 2012 and the beginning of the 2013, an electricity cost reduction was observed but already at the end of the 2013 this value was growing again. 6.4. Salvage value The salvage value of the PV components at the end of the system life cycle (25 year in this work) has been neglected, in accordance to what is done with other rapidly advancing technologies which have reached the end of their warranty period, being considered obsolete. In fact, although the PV system may continue to produce energy at a reduced rate for more than 40 years, electrical codes, efficiencies and manufacturing practices will have changed over the years. Furthermore, currently, there is no existing, reliable secondary market in place that can assign a value to mass produced more than 25 year old modules and inverters. 6.5. Estimated total yearly production When comparing the total yearly electricity production of the systems under investigation (in the city of Bari), the first consideration is that using 10 PV modules (characterized by a P STC ¼ 210 Wp ) mounted on a dual axis tracking system allows one to have almost the same electricity production obtainable with 14 of the same PV modules used for a BIPV system with a tilt angle equal to 30 (4377 and 4824 kW h respectively). Furthermore, the yearly electricity production is almost doubled (actually 8041 kW h in comparison to 4824 kW h) when the 10 PV modules are used in a MAPV system with mirrors inclined at 70 . All the data are summarized in Table 4. 6.6. Economic appraisal outcome In order to perform an economic appraisal of the different PV systems under consideration, first of all the Net Positive Values (NPV) have been calculated, as shown in Table 5 and in Fig. 8. According to the model hypotheses, in the 10th and 20th years, NPV’s are significantly lower due to the cost of inverter substitutions. Furthermore, in the last 5 years (from the 21st to the 25th year) lower NPV’s are due to the end of the incentives granted by the Italian 5th feed-in tariff. From the NPV, the evaluation of the discounted payback periods (DPBP) and the Internal Rate of Return (IRR) are straightforward. Actually, for the BIPV, the standard dual axis tracking PV and the MAPV with mirrors inclined at 50°, 60° and 70°, the DPBPs are 11.78, 12.82, 12.34, 11.84 and 13.19 years, and the IRRs are 12.02%, 10.81%, 11.14%, 11.39% and 9.73%, respectively. Both the lowest DPBP and the highest IRR are for the BIPV system. The main reason is that this is the only system without any tracking system. However, at DR ¼ 4%, the DPBP for the MAPV system with mirrors inclined at 60 is almost the same (11.84 years) and the IRR only slightly lower (11.39%) due to the

Table 4 Estimated total annual electricity yields. Type of PV system

Peak power (kWp)

Yearly averaged production (kW h)

BIPV system (b ¼ 30 ) PV system with dual axis tracker MAPV system with mirrors at 50 MAPV system with mirrors at 60 MAPV system with mirrors at 70

2.940 2.100 2.100 2.100 2.100

4824 4377 5125 6795 8041

Table 5 Comparison of net present values (DR ¼ 4%). Year

BIPV (b ¼ 30 )

Tracking PV

MAPV @50

MAPV @60

MAPV@70

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

8807 978 961 946 932 920 908 897 888 168 872 865 860 855 851 848 846 844 844 299 610 622 634 647 660 9613

9172 889 877 865 855 845 837 830 823 69 812 808 805 803 801 800 800 801 802 415 610 622 634 647 659 8539

9774 997 980 964 949 936 924 912 902 145 885 878 872 866 862 859 856 854 853 464 610 622 634 647 659 9356

11,454 1238 1211 1185 1161 1138 1117 1097 1079 314 1047 1033 1020 1008 998 988 980 973 966 572 609 621 633 646 658 10,839

14,549 1416 1381 1348 1316 1287 1259 1234 1210 439 1166 1147 1129 1113 1098 1084 1071 1060 1050 653 607 620 632 644 657 10,073

higher electricity production which compensates the higher costs associated with the tracking system. When considering lower inclinations (e.g. 50 ), even though the costs associated with the tracking system decrease, having smaller mirrors, the reduction in electricity production dominates. Conversely, when considering higher inclinations (e.g. 70 ), the increase in electricity production is not able to counterbalance the growth of the costs associated with the tracking system (due to the higher mirror dimensions). Finally, in terms of Life-Cycle Costs (LCC), the BIPV, the standard dual axis tracking PV and the MAPV with mirrors inclined at 50, 60 and 70 , account for 0.102, 0.110, 0.100, 0.088 and 0.092, €/kW h, respectively.

7. Conclusions In the present work, a mathematical model of a MAPV system is presented, which accounts for both the increase of direct radiation, due to the reflecting surfaces of the mirrors, and the reduction of diffuse and reflected radiations due to the shadowing effect of the mirrors. In particular, the shadowing effect has been introduced by means of a simplified analytical expression for the skyview factor. The deterioration in the performance of the PV system as a result of the high temperature of the cell has been also taken into account. Furthermore, the effects of the mirror augmentation technique on the PV performance has been investigated by means of an exergy analysis. The results of this analysis is that, in order to minimize the waste of energy captured from the sun, hybrid solar collectors could effectively replace regular PV modules in a new generation of MAPV systems. Finally, the economic appraisal of the different PV systems has been performed. The advantage of a MAPV system is remarkable in terms of electricity production. For instance, in comparison with a dual axis tracking PV system using the same number of modules, a MAPV system with mirrors inclined at 60 gives an electricity yield 55.3% higher. In terms of DPBP and IRR, a 2 kWp MAPV system with mirrors inclined at 60 is comparable with a 3 kWp BIPV system with a tilt angle equal to 30 , however, in terms of LCC, the MAPV system performs significantly

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