Optimum design for a static LCPV concentrator

using nanocomposite high refractive index material

Maria Chiara Ubaldi, Aida Righetti, Giorgio Grasso

Fondazione CIFE P.zza L. da Vinci, 32, 20133 Milano, Italy

mariachiara.ubaldi@fondazionecife.it

Abstract-In this work we introduce novel criteria for

optimizing the design of a Modified Prism-Coupled-Compound

Parabola trackless stationary photovoltaic concentrator. In order

to take full advantage of a high refractive index secondary optics,

to increase the effective solar concentration at fixed aspect ratio,

the secondary optics is here constituted by a hybrid

nanocomposite dielectric material, based on titania-anatase

nanoparticles. By modelling the impact of Rayleigh scattering on

the concentrator performance, it is shown that the radius of the

nanoparticles must not exceed 3nm, to limit optical loss and

therefore optimize the effective optical concentration.

Keywords- Low-CPV; stationary photo voltaic concentration

module; Prism Coupled Compound Parabola; hybrid

nanocomposites; Rayleigh scattering.

I. INTRODUCTION

Concentrated PhotoVoltaic (CPV) modules coupled to highly efficient semiconductor-based solar cells are the way for the economic competitiveness of the latter, thanks to the reduction in solar cell active surface, with respect to illuminated area. As the geometric concentration gain G increases, a reduction in the solar light angular acceptance correspondingly occurs [1], and tracking of the position of the sun becomes necessary to guarantee adequate performance. However, at low G values -typically 2 < G < 5- trackless stationary planar Low Concentration PhotoVoltaic (LCPV) modules can be conceived. LCPV are particularly appealing, since they can be made equivalent in shape, weight and size to standard panels and represent the ideal optical partners for the economical sustainability of high-efficiency Silicon solar cells [2]. In literature several technological solutions have been proposed; they include among others low-gain compound parabolic concentrators (CPCs) [3,4] and Prism Coupled Compound Parabola (PCCP), where the primary parabolic reflector is optically coupled to a secondary optics made of a dielectric prism [5].

For trackless LCPV to be competitive with standard modules, the key approach is to minimize their cost, while maximizing the performance of concentrating optics in terms of yearly averaged collected energy. Recently, a novel modified version of the PCCP has been introduced [2,6], called MPCCP (Modified Prism Coupled Compound Parabola), specifically designed to boost LCPV economic

Project "Tecnologie e materiali per I 'utilizzo efficiente dell 'energia solare", Collaboration Framework be/ween National Research Council of Italy (CNR) and Regione Lombardia 1610712012, Decr. Reg. n. 3667 -29/04/2013

SoIGAin.- Competitive stationary low concentrating solar module of novel design, FP7 Project n. 315663 (1" October 2012,24 months).

Erminio Greco, Silvia Maria Pietralunga lstituto di Fotonica e Nanotecnologie, Consiglio Nazionale

delle Ricerche CNR-IFN P.zza L. da Vinci, 32 20133 Milano, Italy

silvia.pietralunga@ifn.cm.it

competitiveness. In fact, the MPCCP is an example of LCPV which cuts down the Levelized Cost of Energy (LCOE) by maximizing a performance parameter named Effective Optical Performance Ratio (Pro,eJJJ, that rates the yearly averaged efficiency of light collection at a certain geographical location [2].

The MPCCP features a low aspect ratio and highly uniform distribution of the optical intensity at the cell, by exploiting a prismatic secondary optics which concentrates sunlight by refraction and total internal reflection. The use of a high refractive index dielectric material for the secondary optics allows to increase the effective optical concentration at the solar cell and to increase the geometrical gain G of the concentrator without affecting the panel aspect ratio and optical performance [1,2].

In order to obtain cost-effective high refractive index dielectrics, one promising approach is the synthesis of hybrid nanocomposites based on metal oxide nanoparticles dispersed into polymeric transparent matrix [7]. However hybrid nanocomposites are characterized by a high degree of Rayleigh scattering [8].

The aim of the present work is to introduce the criteria for the optimization of the design of a MPCCP concentrator, when using hybrid nanocomposite dielectric for the secondary optics and accounting for the impact of the Rayleigh scattering on the concentrator performance.

A general introduction on MPCCPs and related design is given in section 2. Section 3 is devoted to the description of the kind of nanocomposite material to be used, based on the dispersion of suitably functionalized titania nanoparticles into a polymeric organic matrix. The approach to the optimized design is detailed in section 4, and related results are discussed.

II. THE ST A TIONAR Y MPCCP CON CENTRA TOR

The MPCCP is a stationary solar concentrator, featuring a reduced aspect ratio at given G and uniform light intensity distribution at the solar cell [6]. The MPCCP maximizes the performance parameter P ro,effi which quantifies the yearly averaged solar light collection efficiency. Pro,el! is defined as

the ratio between the solar power collected at the cell and the power impinging onto the input aperture of the panel, both yearly averaged over the evolution in the position of the sun at one specifically geographical site [2,6]. Namely, Pro.ejJ is obtained by averaging the efficiency parameter named Optical Performance Ratio (Pro), which summarizes the loss introduced by the concentrating optics. In case of stationary LCPV, Pro evolves in time because of the excursion in the relative orientation of the concentrating optics with respect to the sun. The actual optical concentration C, i.e. the ratio between the optical intensity at the cell and the optical intensity at the system input, can be expressed by the following:

C = G x Pro (1)

In a generic scheme for concentrating optics, G is defined as the geometrical ratio between the area of the input aperture of the concentrator, Ai and the area of the solar cell, Ac (G=A;lAc). It is known that the maximum attainable concentration Cmax is related to the maximum acceptance angle of the concentrating optics, 8max by the following relation [1]:

_ nq/ Cmax - sinq ( ) max (2)

where n is the refractive index of the dielectric material surrounding the solar cell and q (q=I,2) is the number of dimensions along which concentration occurs. From (2) it is clear that Cmax can be improved just by increasing the refractive index of the dielectric material, at same values of emax. In case of trackless LCPV, the chosen value for emax has to accomodate the typical yearly angular excursion of solar position, i.e.: oO<leNSI<25° and oO<leEWI<60°, respectively for concentration in the North-South or East-West direction. The upper limit set on Cmax also states that, as C < Cmax is always verified, the actual optical concentration cannot be indefinitely increased just by acting on G, since the optical efficiency Pro would decrease accordingly (1), as Cm•x is set by (2).

The MPCCP design is an evolution of the PCCP concentrator proposed by I.R. Edmonds in 1986 [5]. The PCCP is an ideal concentrator, since it reaches the theoretical Cmax limit expressed by (2), but only in case the concentrator is axially aligned to the incident sunlight in the EW direction. Moreover, it can be demonstrated that it does not optimize Pro,el] in case of skew incidence. By acting on the curvature profiles of the parabolic mirrors and on the shape of the dielectric prism, a MPCCP (Modified Prism Coupled Compound Parabola) design was developed in order to allow a better collection of incident sunlight at skew eEW and eNS angles, so as to maximize sunlight collection over the year, without sun tracking. Details of the design rules can be found in [6]. The MPCCP is a 2D concentrator, that concentrates light in the NS plane and works with its longitudinal axis aligned in the EW direction, along which no concentration occurs; therefore in calculating Cmax, q = 1 applies in (2).

III. HYBRID NANOCOMPOSITE HIGH-INDEX DIELECTRIC

One approach to cost-effective high refractive index dielectric materials is the synthesis of hybrid organic-inorganic

nanocomposites, built up from the dispersion of metal oxide nanopartic1es inside suitable polymeric matrices. For photovoltaic applications, nanoparticles must jointly exhibit high refractive index and low absorption in the UV spectral region. For such application, Ti02 anatase nanoparticles can be good candidates, as they can be synthetized in very small size and are absorptive only below ).,=370nm [9]. The presence of Ti02 nanopartic1es inside the polymer matrix, unavoidably induces scattering events caused by the refractive index variation inside the material. In particular, Rayleigh scattering is the dominant mechanism when the size of the nanoparticles is much smaller than the wavelength of light. The Rayleigh scattering cross section of a nanoparticle inside a polymer host is given by:

where nnano and nhosl are the refractive indices of the nanopartic1e and polymer host, respectively, and rnano is the nanopartic1e radius.

The scattering cross section CCOI is related to the mean scattering length MSL by:

MSL = _1_ (4) NCscat

where N is the concentration of the scattering center, I.e. nanoparticles per unit volume. From (3) it could seem that the lower is the nanoparticle radius, the more effective is the reduction of Rayleigh scattering, but it must paid attention not to get too close to Bohr radius of the material itself (nearly 2nm for Ti02) [10]; in that regime quantic effects start rising, furtherly reducing the overall refractive index of the nanocomposite. On the other side, it's not possible to increase N indefinitely, as beyond a certain limit, depending on particle shape and functionalization, the nanoparticles tend to aggregate inside the matrix causing Mie scattering phenomena. The nanocomposite refractive index (Lorentz-Lorenz equation) depends on the loading volumetric fraction, which is related to concentration and size of nanopartic1es. If concentration increases the mean free path shortens, therefore boosting Rayleigh scattering. In this work we have used the well-known approximation of Lorentz-Lorenz formula, in order simplify software optimization :

where /nano is the nanoparticle volumetric fraction. The Rayleigh effect is particularly critical for the present application, where the nanocomposite material is in bulk form. Usually literature refers to nanocomposite thin films, with thickness up to some microns: within this range the influence of scattering is negligible. In order to realize bulk 3D shapes (a prismatic element in this paper), the general procedure to be applied is depicted in Fig. 1:

Ti02dispersioninMMA � plus inl.!iru.9! Polymerization

Fig. I Formation of bulk TIO,-doped polymethil-methacrilate matrix: dispersion of functionalized nanoparticles in monomer is followed by initiator addition and then polymerized via thermal curing.

For the implementation of optical components with typical size of some millimeters, we must accept a compromise between the abovementioned parameters to achieve a maximum refractive index compatible with scattering mmlllllzation: such index also optimizes, for a given geometrical gain and radius, the value of Pro,ej]'

IV. NANOCOMPOSITE-BASED MPCCP DESIGN

The optical performances and the geometrical parameters of the MPCCP design have been evaluated and optimized using a commercially available 3D ray tracing software (ZEMAX). The simulations have been performed using the non-sequential mode, i.e. by assuming that there is no pre-defined path for any ray, which accordingly may be reflected, refracted, scattered, split into child rays, etc .. A schematic view of the MPCCP cross-section in the NS plane is shown in Fig. 2. The dielectric prism of refractive index n is placed between two compound parabolic mirrors with reflectivity Rm. A photovoltaic cell of width w is placed below the prism at the exit aperture of the concentrator and optically coupled to it..

The main geometrical parameters of the concentrator have been optimized in order to maximize Pro,ejJ for the LCPV stationary module. The optimization has been carried out by considering an optical extended source to simulate the typical yearly average angular distribution of sun light radiation (0° < leNSI < 25° and 0° < leEWI < 60°). The simulation steps, including optimization variables and the geometric constraints in the design, are summarized in the flow chart in Fig. 3. The simulations take into account the losses due to the reflection coefficient Rm of parabolic mirrors, the Fresnel reflection coefficient at prism-air interface Rp, and the optical absorption within the prism. In particular, the effect of the losses due to the Rayleigh scattering has been considered in greater details, by evaluating the effect of the radius of the nanoparticles, r nano, on the optical efficiency Pro,ejJof the concentrator.

The Rayleigh scattering intensity is modeled by considering the Mean Scattering Length parameter (MSL), as defined in (4). The fraction of scattered rays can be determined from the integrated scattering probability for rays, with a travel distance x within the volume, given by:

x P(x) = 1 - e-MSL (6).

Since the MSL varies with wavelength according to the equation:

the fraction of scattered rays will depend also on the solar spectrum. In the simulations, standard AMl.5G values have been used.

Fig. 2 MPCCP cross-section showing the path of sunlight rays with different incidence angles, inpinging on the prismatic secondary optics. In this case G=4.

Parametric analysis has been carried out taking into account three G values (G=3-7-5) for the LCPV and different dimensions of the nanoparticles radius (rnano=2 nm -7- 5nm).

Define optimization Variables: Q/" Height of the parabolic mirrors: he R.. ..

V

Curvature of the parabolic mirrors � "" Heightoftheprism:hp 1\.1_.;._

Parameters:

Geometric gain: G = (3 ... 5)

Radius nanoparticles: rl101'10 = (2 +5) Refractive index prism: nc = {l.5+ 1.9}

losses: Reflection mirrors: Rm = 95% Prism reflection: (Rfl = 1%) Prism absorption: (a=O.Ol cm·l) Rayleigh scattering neglected

Losses: Reflection mirrors: Rm = 95l'6 Prism reflection: (Rp = 1%) Prism absorption: (a=O.Ol cm·l) Rayleigh scattering

Optimization:

MaICimize P fO,�f1(Effective Optical Performance Ratio) defined as the

ratio between the solar power collected by the cell and the power impinging onto the input aperture of the panel averaged on the

position of the sun in one year.

Fig. 3 Block diagram of simulation steps for the design of the optimized MPCCP concentrator.

Figure 4 shows how the Rayleigh scattering affects the Pro,efJ, at two different G values (G=4 and G=5), as a function of the refractive index nco The starting value for nc is set at nc=nhos,=1.5. The optical performance is worsened in the presence of scattering and does not increase indefmitely with

the refractive index; in case G=4 and rnana=2.5nm an optimum value for nc can be clearly identified.

Pro_effVs"c (G, parameter) 95.0% ,-------------

90."" +------=-�-----_G=4 (No scattering)

� 85.0% ........ G;5 (No scattering)

� ;..0 1 80.0% t----_____ -""'----------; -... G=4 (Scattering r_nano =2.5 nr .: _ .... ---- ....

75.0% +-----:��------- -k- G;;5 (Scattering r_nano ;2.5 nr

70."" +--�--�--�-� 1.5 1.6 1.7 1.8 1.9 Refractive Index"c

Fig.4 Pm.,jJ, behavior at G=4 and G=5, as a function of the nc, in the absence and in the presence of Raileigh scattering.

95.0%

90.""

� 85."" :t: � I £ SO.""

75.0%

70.0%

Pro_eff Vs "c (r n3no ,Parameter)

1::;;ie::=:;::===:::::::::=---- ..... G=4 (r_nano = 2 nm) ..... G=4 (,_nana = 2.5 nm)

+--�;::---------- ... G=4 (,_nana = 3 nm)

1.5 1.6 1.7 1.8 Refractive Index"c

-+-G=4 (,_nana = 4 nm)

1.9

Fig. 5 Pm.ejJ, behavior at fixed G=4 and variable rnano, as a function of the nco

In Fig. 5, the behavior of Pro.ejf, vs. nc is shown at constant G=4, for different rnano values (2nm < rnano< 4nm). In the refractive index range taken into consideration, as r nana increases, the optical performance changes. P ro.eff, indefmitely increases with nc at rnana=2nm; it shows an optimwn condition for rnano=2.5nm and rnano=3nm and monotonically decreases in case rnano=4nm.

Therefore, due to the strong influence of the Rayleigh scattering, the increase in the value of the refractive index nc of the hybrid dielectric has to be obtained by using Ti02 nanoparticles of radius rnano ::; 3nm, not to hamper Pro,eff,. In this way, an authentic improvement in the actual optical concentration C can be reached.

V. CONCLUSIONS

In this study, we have optimized the design of a MPCCP LCPV, whose secondary optics is constituted of high refractive index hybrid organic-inorganic nanocomposite (TiOranatase nanoparticles embedded in PMMA matrix) in bulk form. In such a case, the contribution of Rayleigh scattering to optical loss has to be accounted for, for an accurate design of the concentrator.

The optical performance of the concentrator has been evaluated by means of ray-tracing simulations, including the modelling of scattering via the MSL parameter. A parametric analysis on Pro,ejJ as function of the refractive index, by varying geometrical gain and nanoparticle radius, has been carried on.

Due to the strong influence of the Rayleigh scattering, the increase in the value of the refractive index has to be achieved by using nanoparticles of radius rnano ::; 3nm, in order to obtain a real improvement in Pro,ejJ values and therefore in the effective optical concentration C.

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