Performance optimization of dense-array concentrator photovoltaic ...

Performance optimization of dense-array concentrator photovoltaic system considering effects of circumsolar radiation and slope error Chee-Woon Wong,1 Kok-Keong Chong1,2,* and Ming-Hui Tan1 1

Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Malaysia 2 [email protected] * [email protected]

Abstract: This paper presents an approach to optimize the electrical performance of dense-array concentrator photovoltaic system comprised of non-imaging dish concentrator by considering the circumsolar radiation and slope error effects. Based on the simulated flux distribution, a systematic methodology to optimize the layout configuration of solar cells interconnection circuit in dense array concentrator photovoltaic module has been proposed by minimizing the current mismatch caused by nonuniformity of concentrated sunlight. An optimized layout of interconnection solar cells circuit with minimum electrical power loss of 6.5% can be achieved by minimizing the effects of both circumsolar radiation and slope error. ©2015 Optical Society of America OCIS codes: (080.4295) Nonimaging optical systems; (080.2740) Geometric optical design; (220.1770) Concentrators.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

R. R. King, A. Boca, W. Hong, D. Law, G. Kinsey, C. Fetzer, M. Haddad, K. Edmondson, H. Yoon, P. Pien, and N. Karam, “High-efficiency multijunction photovoltaics for low-cost solar electricity,” in Proceeding of 21st Annual Meeting of the IEEE Lasers & Electro-Optics Society (IEEE, 2008), pp. 2–3. V. Andreev, V. Grilikhes, V. Rumyantsev, N. Timoshina, and M. Shvarts, “Effect of nonuniform light intensity distribution on temperature coefficients of concentrators solar cells,” in Proceeding of 3rd World Conference on Photovoltaic Energy Conversion (IEEE, 2003), pp. 881–884. K. Nishioka, T. Takamoto, T. Agui, M. Kaneiwa, Y. Uraoka, and T. Fuyuki, “Evaluation of InGaP/InGaAs/Ge triple-junction solar cell and optimization of solar cell’s structure focusing on series resistance for highffficiency concentrator photovoltaic systems,” Sol. Energy Mater. Sol. Cells 90(9), 1308–1321 (2006). P. J. Verlinden, A. Lewandowski, C. Bingham, G. S. Kinsey, R. A. Sherif, and J. B. Lasich, “Performance and reliability of multijunction III-V modules for concentrator dish and central receiver applications,” in Proceeding of the IEEE 4th World Conference on Photovoltaic Energy Conversion (IEEE, 2006), pp. 592–597. F. Reis, C. Guerreiro, F. Batista, T. Pimentel, M. Pravettoni, J. Wemans, G. Sorasio, and M. C. Brito, “Modeling the effects of inhomogeneous irradiation and temperature profile on CPV solar cell behavior,” IEEE Journal of Photovoltaics 5(1), 112–122 (2015). T. Cooper, M. Pravettoni, M. Cadruvi, G. Ambrosetti, and A. Steinfeld, “The effect of irradiance mismatch on a semi-dense array of triple-junction concentrator cells,” Sol. Energy Mater. Sol. Cells 116, 238–251 (2013). D. R. Mills and G. L. Morrison, “Compact linear fresnel reflector solar thermal powerplants,” Sol. Energy 68(3), 263–283 (2000). K. Ryu, J. G. Rhee, K. M. Park, and J. Kim, “Concept and design of modular fresnel lenses for concentration solar PV system,” Sol. Energy 80(12), 1580–1587 (2006). K. K. Chong, F. L. Siaw, C. W. Wong, and G. S. Wong, “Design and construction of non-imaging planar concentrator for concentrator photovoltaic system,” Renew. Energy 34(5), 1364–1370 (2009). K. K. Chong, C. W. Wong, F. L. Siaw, and T. K. Yew, “Optical characterization of non-imaging planar concentrator for the application in concentrator photovoltaic system,” J. Sol. Energy Eng. 132(1), 011011 (2010). M.-H. Tan, K.-K. Chong, and C.-W. Wong, “Optical characterization of nonimaging dish concentrator for the application of dense-array concentrator photovoltaic system,” Appl. Opt. 53(3), 475–486 (2014). K.-K. Chong, C.-W. Wong, T.-K. Yew, and M.-H. Tan, “Solar concentrator assembly,” U.S. Patent Application 13/901,519 (filed on May 23, 2013, pending). K.-K. Chong, C.-W. Wong, T.-K. Yew, and M.-H. Tan, “Solar concentrator assembly,” Malaysian Patent No. PI 2012002439 (filed on May 31, 2012, pending).

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A841

14. K. K. Chong, S. L. Lau, T. K. Yew, and P. C. L. Tan, “Design and development in optics of concentrator photovoltaic system,” Renew. Sustain. Energy Rev. 19, 598–612 (2013). 15. G. Johnston, “On the analysis of surface error distributions on concentrated solar collectors,” J. Sol. Energy Eng. 117(4), 294–296 (1995). 16. G. Johnston and M. Shortis, “Photogrammetry: an available surface characterization tool for solar concentrators, Part II: Assessment of surfaces,” J. Sol. Energy Eng. 119(4), 286–291 (1997). 17. K. Pottler, E. Lupfert, G. H. Johnston, and M. R. Shortis, “Photogrammetry: a powerful tool for geometric analysis of solar concentrators and their components,” J. Sol. Energy Eng. 127(1), 94–101 (2005). 18. T. Marz, C. Prahl, S. Ulmer, S. Wilbert, and C. Weber, “Validation of two optical measurement methods for the qualification of the shape accuracy of mirror panels for concentrating solar systems,” J. Sol. Energy Eng. 133(3), 031022 (2011). 19. D. Buie, A. G. Monger, and C. J. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003). 20. D. Buie, C. J. Dey, and S. Bosi, “The effective size of the solar cone for solar concentrating systems,” Sol. Energy 74(5), 417–427 (2003). 21. J. E. Noring, D. F. Grether, and A. J. Hunt, “Circumsolar radiation data: the Lawrence Berkeley Laboratory reduced data base” In: National Renewable Energy Laboratory. NREL/TP-262–4429. (1991). http://rredc.nrel.gov/solar/pubs/circumsolar/title.html 22. K. K. Chong and C. W. Wong, “General formula for on-axis sun-tracking system and its application in improving tracking accuracy of solar collector,” Sol. Energy 83(3), 298–305 (2009). 23. Y. Liu, J. M. Dai, X. G. Sun, and T. H. Yu, “Factors influencing flux distribution on focal region of parabolic concentrators,” in Proceeding of International Symposium on Instrumentation Science and Technology (IOP Science, 2006), pp. 59–63. 24. http://www.spectrolab.com/DataSheets/PV/CPV/C3MJ_Dense_Array.pdf 25. F. L. Siaw and K. K. Chong, “Temperature effects on the performance of dense-array concentrator photovoltaic system,” in Proceedings of the IEEE Conference on Sustainable Utilization and Development in Engineering and Technology (IEEE, 2012), pp. 140–144. 26. K. K. Chong and F. L. Siaw, “Electrical characterization of dense array concentrator photovoltaic system,” in Proceedings of the 27th European Photovoltaic Solar Energy Conference (EU PVSEC, 2012), pp. 224–227. 27. F.-L. Siaw, K.-K. Chong, and C.-W. Wong, “A comprehensive study of dense-array concentrator photovoltaic system using non-imaging planar concentrator,” Renew. Energy 62, 542–555 (2014). 28. A. Vossier, D. Chemisana, G. Flamant, and A. Dollet, “Very high fluxes for concentrating photovoltaics: considerations from simple experiments and modeling,” Renew. Energy 38(1), 31–39 (2012). 29. R. R. King, D. Bhusari, A. Boca, D. Larrabee, X.-Q. Liu, W. Hong, C. M. Fetzer, D. C. Law, and N. H. Karam, “Band gap-voltage offset and energy production in next-generation multijunction solar cells,” in Proceedings of the 25th European Photovoltaic Solar Energy Conference (EU PVSEC, 2011), pp. 797–812.

1. Introduction Multi-junction solar cells are capable of attaining electrical conversion efficiency more than 40% by having three or more materials that are sensitive to different spectral range of the solar spectrum [1]. In fact, the performance of the multi-junction solar cells has major discrepancy between the provided testing conditions and the real operating conditions. For example, the given cell characterizations are measured under AM1.5D, uniform illumination with high solar concentration ratio and operating temperature of 25°C. It is a strenuous task to achieve these conditions in the real operation of concentrator photovoltaic (CPV) module onsite that is equipped with multi-junction solar cells. In the real operating conditions, several factors are restraining the electrical performance of solar cells, particularly the non-uniform illumination that causes current mismatch in the dense-array concentrator photovoltaic (DACPV) module that consists of bypass diodes and multi-junction solar cells that are connected in series and parallel. When non-uniform illumination is focused on the module, there will be a significant drop in efficiency as compared with the module that is operated under uniform illumination [2–4]. Reis et al. introduced a distributed diode model for solar cells to predict the behavior of solar cells that are integrated in CPV systems. The modeling showed that there is a power loss when solar cells operate under conditions of inhomogeneous distribution of temperature and illumination [5]. Furthermore, Cooper et al. has experimentally validated a model with a linear semi-dense array of five series-connected triple-junction concentrator cells [6]. Under the worst-case conditions of non-uniform illumination on the array, the efficiency of the array drops to 28.5% as compared to 39% for the case of perfect uniformity. For the sake of achieving high electrical conversion efficiency, solar concentrators that are made of relatively inexpensive optics, such as mirrors or lenses, have been developed to focus

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A842

solar irradiance with reasonably uniform distribution on the multi-junction solar cells ranging from hundreds to thousands of solar concentration ratios. In the past, some researchers have paid a lot of effort to design various types of solar concentrators for producing uniform solar illumination on the solar cells [7–13]. In Fresnel lens system, an additional secondary optical element such as flux homogenizer is added to produce uniform illumination [14]. This approach is capable of cutting down the expensive solar cell area by increasing the solar concentration ratio and the light intensity. However, there are some other factors causing the inhomogeneous illumination distributed on the solar cells, such as tracking error, misalignment of concentrator and the condition of refractive lens or reflecting mirrors. In reflection-based solar concentrators, reflected rays could deviate from the specular reflection direction and eventually not hitting on the receiver mainly caused by circumsolar radiation and mirror surface slope error. This small angular deviation of sunrays may bring a significant effect to the electrical performance of CPV system. In real system, mirror surface slope error is unavoidable due to cost and technical restraints during the manufacturing process. Typically, this error is assumed random and is reported in standard deviation units. According to the literatures, it has been verified that the slope error of mirror surface in typical solar concentrators ranges from 2 to 4 mrad [15–18]. Buie et al. showed that the amount of energy in the circumsolar region is important because sunshape plays an important role in determining the overall flux distribution and overestimated of output power may occur if all the power is assumed to fall within the extent of the solar disc only [19,20]. The seriousness of circumsolar radiation effect is rated in term of the circumsolar ratio (CSR). Noring et al. demonstrated that the CSR values typically vary in the range from zero to 0.3 [21]. The objective of the present study is to develop a systematic approach in optimizing the electrical performance of DACPV system by considering the effects of both circumsolar radiation and slope error. The numerical modeling has been carried out to analyze the solar flux distribution on the receiver. With the simulated flux distribution, the receiver size can be optimized by minimizing the spillage loss of the DACPV system. In addition, this paper also introduces an optimizing method for the electrical interconnection of solar cells in DACPV module configuration to achieve the maximum output power for different values circumsolar radiation and mirror surface slope error. As a case study, we applied this systematic approach to design and develop an optimized dense-array module incorporated with non-imaging dish concentrator (NIDC). Experimental validation of the model is under developing for fieldtesting on the optimal configuration of DACPV module with the NIDC prototype. 2. Non-imaging dish concentrator (NIDC) prototype Figure 1 shows the NIDC prototype located in Universiti Tunku Abdul Rahman (UTAR), Kuala Lumpur campus (3.22° North, 101.73° East). This prototype is capable of producing much more uniform spatial irradiance for the application of DACPV system. Instead of using a single piece of parabolic dish, the NIDC consisting of multi-faceted mirrors acts as the optical aperture to collect and to focus the incident sunlight at the common receiver that is placed at a focal distance of 210 cm. The prototype consists of 96 facet mirrors to be arranged into ten rows and ten columns on the mechanical structure. Four mirrors in the central region of concentrator are omitted due to the shading by the receiver. Flat facet mirrors with a dimension of 20 cm × 20 cm are selected to form a total reflective area of 3.84 m2. In order to avoid shadowing and blocking among adjacent mirrors, the facet mirrors are gradually lifted from central to peripheral regions of the dish concentrator as shown in Fig. 2. The detailed design of NIDC has been patented and described in our previous publications [11–13]. The prototype is operated on the most common two-axis sun-tracking system, which is azimuthelevation tracking system [22]. The design of the aforementioned NIDC prototype has been incorporated into the DACPV system and the following study mainly focuses on this optical design specification for optimizing the circuit layout of solar cells interconnection.

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A843

Fig. 1. The prototype of non-imaging dish concentrator (NIDC).

Fig. 2. Schematic diagram to show how all the mirrors are gradually lifted from central to peripheral regions of the non-imaging dish concentrator to prevent shadowing and blocking among adjacent mirrors.

3. Optical analysis 3.1. Numerical simulation using ray-tracing method Referring to Fig. 3, Cartesian coordinate system is applied for representing the main coordinate system (x, y, z) attached to the dish concentrator and the sub-coordinate system (x′, y′, z′) attached to the i, j-mirror, where i and j refer to the mirror location at i-th row and j-th column of the dish concentrator respectively. The origins of main coordinate system and subcoordinate system are located at the center of the concentrator, O (0, 0, 0), and the center of i,

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A844

j-mirror, (HCx, HCy, HCz)ij, respectively. The incident angle (θ) of the sunray, relative to i, jmirror, and the tilted angles of i, j-mirror about x′-axis (γ) and y′-axis (σ) can be derived in terms of (HCx, HCy, HCz)ij and the focal length of the dish concentrator, f as shown in our previous publications [9–11]. An initial coordinate of the reflective point on the i,j-mirror is designated as (Hx, Hy, Hz)ijkl, where k and l represent the position of the reflective point at k-th row and l-th column of the facet mirror respectively. A new coordinate (H′x, H′y, H′z)ijkl was formed when each individual mirror has to be aligned with its corresponding tilted angles (γ and σ) for superposing all the mirror images at the common receiver. According to the previous work, the final coordinate (H′x, H′y, H′z)ijkl can be obtained in the matrix form via the coordinate transformations from the initial coordinate (Hx, Hy, Hz)ijkl [9–11].

Fig. 3. Cartesian coordinate system is used to represent the main coordinate system (x, y, z) attached to the plane of the dish concentrator and the sub-coordinate system (x′, y′, z′) is defined attached to the i, j-mirror.

In practice, mirror surface is not perfect due to the slope error as depicted in Fig. 4. The deviation from the perfect surface normal of the ideal mirror shape has caused distortion in the reflected image. The imperfect surface normal of the mirror can be determined by the following angles [23]:

θr =

( −2δ ) ln (1 − r )

ϕ = 2π rϕ

2

θ

0 ≤ rθ ≤ 1

(1)

0 ≤ rϕ ≤ 1

(2)

where rθ and rφ are the random numbers, δ is the standard deviation of slope error.

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A845

Fig. 4. Schematic diagram to show how a mirror surface with slope error can cause the reflected ray to be deviated from the specular reflection direction.

Similar to the case of the reflective point, the initial unit vector normal, Nˆ = zˆ , also undergoes four rotational coordinate transformations to form the new unit vector normal when the facet mirror is tilted and the slope error is considered. Therefore, the new unit vector normal can be derived as

[ N ′]ijkl = [γ ]ij [σ ]ij [ϕ ]ijkl [θ r ]ijkl [ N ]ijkl 0  N x′  1 N′  0 cos γ  y =   N z′  0 sin γ    0  1  ijkl 0 cos ϕ  sin ϕ   0   0

0 − sin γ cos γ 0

− sin ϕ cos ϕ 0 0

0  cos σ 0   0 × 0   sin σ   1  ij  0

0 − sin σ 1 0 0 cos σ 0 0

0 0 0 1   0 0 0 cos θ r ×  0 sin θ r 1 0   0 1  ijkl  0 0

0 − sin θ r cos θ r 0

0 0  × 0  1  ij

(3)

0  Nx   N  0 × y  Nz  0    1  ijkl  1  ijkl

According to Snell-Descartes law, the incident ray, (Ix, Iy, Iz) and the normal vector of the mirror are required to obtain the reflected ray. As a result, the unit vector of the principal reflected ray can be obtained as  2 I N ' + I y N y' + I z N z' ) N x' − I x   Rx   ( x x   R  = 2 I N ' + I N ' + I N ' N ' − I  ( ) y x x y y z z y y      Rz   ' ' ' '  + + − I N I N I N N I 2 ( ) x x y y z z z z  

(4)

where Ix = 0, Iy = 0, Iz = 1 by considering the incident ray exactly normal relative to the dish concentrator plane. For each principal reflected ray, Rˆ , from the i-th, j-th, k-th, l-th reflective point, P subrays are generated within the solar cone, which subtend to the effective half angle of 43.6 mrad [19,20], and each sub-ray is denoted as Rˆ m = Rmx xˆ + Rmy yˆ + Rmz zˆ , where m = 1, 2, 3,…P. By solving the line equation of the sub-ray and the surface equation of the receiver plane, the coordinate of the intersection point on the receiver can be calculated as

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A846

 Rmx   R ( f − H z′ ) + H x′  mz  Tx     R my T  = ′ ′ (5)  y   R ( f − Hz ) + Hy   Tz   mz   f     In addition to mirror slope error, circumsolar radiation also contributes to the distortion of the flux distribution on the receiver. Circumsolar radiation is also considered in the optical analysis of the dish concentrator, where the solar rays that strikes on the mirror surface and the receiver are treated as cone rays. In order to study the influence of circumsolar radiation to the flux distribution, the magnitude of sunshape model has to be determined as follow [19,20]:  cos(0.326θ i )  φ (θi ) =  cos(0.308θi )  eκ θi γ 

0 ≤ θ i ≤ θ sun

(6)

θ sun ≤ θi ≤ 43.6

where κ = 0.9 ln(13.5χ)χ-0.3, γ = 2.2 ln(0.52χ)χ-0.43 − 0.1, χ is the circumsolar ratio (CRS), θi is the radial displacement about the solar vector, θsun is the solar disc half angle of 4.65 mrad, i = 1, 2, 3, … P with P is the total number of rays within the solar cone. The pattern of solar flux distribution on the receiver plane can be plotted according to the computed intersection point (Tx, Ty). In order to achieve a smooth simulated result of illumination distribution at the receiver plane, each facet mirror of dimension 20 cm × 20 cm is sub-divided into 201 × 201 reflective points and the sub-rays within a cone has a resolution of 101 rays per aperture diameter. In addition, a matrix of 401 rows and 401 columns of pixels represent the receiver area of 40.0 cm × 40.0 cm and hence the solar concentration ratio (number of suns) on each pixel can be calculated as follow:    area of reflective point (cm 2 ) cos θ   × φ (θ i ) × P C =  2 n =1  area of receiver pixel (cm ) φ (θi )    i =1   N

(7)

where area of reflective point = (20/201)2, area of receiver pixel = (40/401)2, N is the total count of sub-rays hitting on the corresponding pixel on the receiver plane. 3.2. Optical characterization of NIDC In this paper, an optical characterization of the prototype of NIDC has been carried out using the aforementioned ray-tracing method by changing of the values of CSR in the range from 0 to 0.4, and, δ in the range from 0 to 4 mrad. Figure 5 shows the simulated results of solar flux distribution of NIDC in 2-D and 3-D mesh plots with a value of zero in both CSR and δ. Without considering circumsolar radiation and mirror surface slope error, the dish concentrator is capable of producing 338 cm2 of uniform illumination area, which is consisted of a flat top area in the central region of flux distribution where the solar concentration ratio is nearly constant, with maximum solar concentration ratio of 88 suns at the receiver. The solar flux distribution pattern with the highest solar concentration ratio of 88 suns for different values of CSR and δ were simulated and plotted as shown in Fig. 6. From the simulated results, the uniform illumination area reduces as the values of CSR and δ increase. By increasing the slope error, the uniform illumination region narrows while the base region of flux distribution broadens. This phenomenon is insignificant in the case of increasing the effect of circumsolar radiation as compared to that of slope error. To quantify the influence of

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A847

circumsolar radiation and slope error effects towards the quality of solar flux distribution at the receiver, optical characterization of the NIDC have been performed for different values of CSR and δ, including uniformity of solar illumination, spillage loss, the optimization of receiver size and the optimization of DACPV module configuration.

Fig. 5. The simulated results of solar flux distribution produced by non-imaging dish concentrator in 2-D and 3-D mesh plots with CSR = 0 and δ = 0.

Spillage loss (or percentage of solar irradiance falling beyond the boundary of the receiver) and solar concentration ratio at the edge of receiver were simulated by adopting different sizes of square receiver. Figure 7 illustrates the spillage loss (with marker) and its corresponding lowest solar concentration ratio at receiver edge (without marker) versus the receiver size (square in shape) from 10 cm to 30 cm for five different values of δ, i.e. 0 mrad, 1 mrad, 2 mrad, 3 mrad and 4 mrad, were plotted in the case of CSR = 0. According to the results, the increment of the slope error from 0 mrad to 4 mrad can cause the uniform illumination area decreasing from 338 cm2 to 144 cm2. The optimized receiver size to capture a reasonably uniform solar flux distribution with less than 5% variation of flux distribution (difference between the highest and the lowest solar concentration ratio within the receiver in percentage) and its corresponding spillage loss is summarized as the following. The optimized receiver size (spillage loss) for the cases of the slope error at 0 mrad, 1 mrad, 2 mrad, 3 mrad and 4 mrad are 18.8 cm (17.6%), 18.4 cm (21.2%), 17.2 cm (31.2%), 15.8 cm (42.0%) and 14.2 cm (53.2%) respectively. The higher the slope error the smaller the optimized receiver size will be. Figure 8 shows the spillage loss (with marker) and its corresponding lowest solar concentration ratio at receiver edge (without marker) versus the receiver size (square in

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A848

shape) from 10 cm to 30 cm for five different values of CSR, i.e. 0, 0.1, 0.2, 0.3 and 0.4, are plotted in the case of δ = 0 mrad. For the case of without slope error, the uniform illumination area decreases from 338 cm2 to 154 cm2 when the circumsolar ratio is increased from 0 to 0.4. Besides, the optimized receiver sizes (spillage loss) for the circumsolar ratios (CSR) 0, 0.1, 0.2, 0.3 and 0.4 are 18.8 cm (17.6%), 18.6 cm (19.9%), 18.2 cm (23.7%), 17.4 cm (30.4%) and 16.2 cm (39.7%) respectively. Therefore, the reduction of optimized receiver area for DACPV system is less significant as the circumsolar ratio increases up to 0.2.

Fig. 6. The simulated results to show the influence of both circumsolar ratio (CSR) and slope error (δ) to the solar flux distribution of NIDC with 96 facet mirrors and a focal distance of 210 cm.

According to the simulated results, the spillage loss for the optimized receiver size becomes very severe, as high as 58.7%, if we increase slope error to 4 mrad and CSR to 0.4 and hence the percentage of energy within uniform illumination area is less than 50%. Practically, it is not a wise idea to design the DACPV module that just only covers the uniform illumination area especially for the case of high spillage loss. Despite there is current mismatch problem for the DACPV module working under non-uniform flux distribution, the electrical performance of the DACPV module can be optimized in such a manner that the appropriateness of serial and parallel interconnection among the solar cells can compensate the inhomogeneous illumination. In order to minimize the spillage loss and oversizing of the receiver, proper selection and detailed analysis of receiver size are very important tasks. In

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A849

this study, the receiver with a dimension of 25 cm × 25 cm is chosen. According to Fig. 9, the receiver has a maximum spillage loss of 4.3% for all the values of CSR and δ.

Fig. 7. Spillage loss (with marker) and its corresponding lowest solar concentration ratio at receiver edge (without marker) versus receiver size (square in shape) for five different values of δ, i.e. 0 mrad, 1 mrad, 2 mrad, 3 mrad and 4 mrad, are plotted in the case of CSR = 0.

Fig. 8. Spillage loss (with marker) and its corresponding lowest solar concentration ratio at receiver edge (without marker) versus receiver size (square in shape) for five different values of CSR, i.e. 0, 0.1, 0.2, 0.3 and 0.4, are plotted in the case of δ = 0 mrad.

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A850

Fig. 9. The spillage loss of receiver with a dimension of 25 cm × 25 cm.

4. Electrical analysis 4.1 Methodology of optimizing configuration of DACPV module The Spectrolab CPV dense array solar cell (GaInP/GaInAs/Ge) with dimension of 1.5 cm × 1.0 cm is introduced in this study [24]. For optimizing the electrical interconnection of DACPV module to achieve maximum electrical power, we have to compute average solar concentration ratio within the area that matches with the solar cell size after the numerical simulation of solar flux distribution. Figure 10 shows the dense array of solar cells with each of them mapped with the computed average solar concentration ratio at its respective position on the receiver plane. The solar concentration ratio was determined according to the numerical simulation result of solar flux distribution in the case of both CSR and δ are zero. Increasing in both values of CSR and δ can cause solar concentration ratio of solar cells located near the central region to be spread towards solar cells located near the peripheral region of the receiver. There are total of 320 solar cells to be arranged into twenty rows and sixteen columns on the receiver plane with dimension of 25.5 cm × 24.0 cm. The arrangement of the solar cells is organized in such a way that it keeps gap spacing among the adjacent solar cells of 0.1 cm along row direction and 0.2 cm along column direction. The gap is necessary for practical consideration in the assembling process of DACPV module, i.e. solder reflow process to attach the solar cells on the direct bond copper (DBC) substrate, and ribbon bonding process to connect the solar cells in serial or parallel interconnection. From Fig. 10, the solar cells were grouped into two major regions: those rows of solar cells with higher solar concentration ratio are assigned as region A (Region A is further divided into four symmetrical quadrants), and those rows of solar cells with the lower solar concentration ratio are assigned as region B. In this study, a special modeling method using solar cell block from SimElectronics is developed in Matlab platform to analyze the electrical performance of DACPV module [25– 27]. The five-parameter model is applied to solar cell block and it is good enough to perform a reasonably accurate investigation on the performance of DACPV module. The solar cells are parameterized in terms of short-circuit current (ISC), open-circuit voltage (VOC), diode ideality factor (N), series resistance (RS) and irradiance level. According to the literatures, both short-circuit current, ISC and open-circuit voltage, VOC can be represented by the following equations [28, 29]: 1 I SC = I SC C

#233456 © 2015 OSA

(8)

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A851

1 VOC ≅ VOC +N

kT ln C q

(9)

1 1 where I SC and VOC are the short-circuit current and open-circuit voltage of the solar cell under one sun respectively, C is the solar concentration ratio (suns), N is the effective diode ideality factor, T is the operating temperature (Kelvin), k is the Boltzmann constant and q is the electronic charge. For this study, the solar cells are assumed to have zero value in series resistance, Rs = 0 Ω and effective diode ideality factor, N = 3. According to the Spectrolab CPV dense array solar cells datasheet, the one sun short-circuit current and open-circuit voltage under standard test condition are 20.9 mA and 2.76 V respectively [24]. Moreover, the solar cells are assumed operating at the temperature of 298 Kelvin and the irradiance level of 1000 W/m2.

Fig. 10. Schematic diagram to show the average solar concentration ratio mapped to each solar cell at its respective position on the receiver plane based on the simulated solar flux distribution with a total dimension of 25.5 cm × 24.0 cm.

Referring to Fig. 11, the flowchart illustrates the procedure of how to optimize the layout of solar cells interconnection circuit in the DACPV module. After mapping the solar concentrator ratio to each solar cell, both ISC and VOC of the solar cells are determined by using the Eqs. (8) and (9) respectively. In the region A, a basic module is defined as the maximum number of solar cells connected in parallel and located in the same row within the same quadrant. There are thirty-two basic modules that each of them connects eight solar cells in parallel are formed in the region A as shown in Fig. 10. The connection from one basic module to another basic module is in series via ribbon bonding. The short circuit current and open circuit voltage of each basic module can be determined by adding the ISC and averaging the VOC of the solar cells that are connected in parallel in a basic module respectively.

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A852

Fig. 11. Flow chart to show the algorithm on how to optimize the electrical interconnection of dense array solar cells in DACPV module.

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A853

Fig. 12. Schematic diagram to show five different optimal configurations for δ ranging from 0 to 4 mrad. Optimal configuration I, II, III, IV and V are the most optimized layout of solar cells interconnection circuits, which are designed based on the simulated flux distribution with slope error at 0, 1 mrad, 2 mrad, 3 mrad and 4 mrad respectively in the case of CSR = 0.

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A854

We set the basic module located at the innermost row of the quadrant in region A as the reference basic module. For example, reference basic module is selected in the region A1 as shown in Fig. 10. The current mismatch is computed to compare the amount of output current between the other basic modules and the reference basic module. If the amount of current mismatch is larger than 3%, the algorithm will select solar cells that are located in the outermost row of region B to connect in parallel externally with the corresponding basic modules for reducing the current mismatch to below 3%. Those solar cells in the outermost row of region B that is not utilized for compensating current mismatch will be removed in the end of optimization process. The subsequent row of solar cells after the outermost row in region B is define as special basic module in which all solar cells are connected in parallel. The current mismatch is also calculated to compare with the reference basic module. If the amount of current mismatch is larger than 3%, the underperformed solar cells in the special basic module will be removed so that the current mismatch is well to below 3%. Referring to Fig. 12, five different optimal configurations of DACPV module based on five different flux distributions have been determined using the aforementioned optimizing algorithm. Optimal configuration I, II, III, IV and V are the most optimized layout of solar cells interconnection circuits, which are designed based on the simulated flux distribution with slope error at 0, 1 mrad, 2 mrad, 3 mrad and 4 mrad respectively in the case of CSR = 0. For the optimal configuration I, the outermost row of solar cells in region B are all omitted because the current mismatch of all basic modules in region A is minimum and thus compensation of current mismatch is not required. For the special modules in this configuration, twelve solar cells are connected in parallel so that the current mismatch is less than 3% as compared to that of the reference basic module. There are eight solar cells in the inner row of region B are omitted. 4.2 Electrical performance of DACPV module After the optimization process, five optimal configurations of DACPV module have been simulated in Matlab platform to obtain the maximum output power for the values of CSR ranging from 0 to 0.4 and, δ ranging from 0 to 4 mrad. In this simulation, each basic module is modeled to be connected in parallel with bypass diode in opposite polarity to protect solar cells from reverse-bias breakdown that could cause permanent damage to the cells. When current mismatch occurs in basic module, bypass diode will be forward biased so that the current of the array can safely pass through. The bypass diode creates an alternative path for the current so that the underperforming basic module is protected. When array current passes through bypass diodes, the diodes will turn on and hold its corresponding group of cells to a small negative voltage that will limit any further drop in the total voltage of the array. Five optimal configurations are capable of producing maximum output power of 1.1 kW for the ideal case of zero values in CSR and δ. The electrical power losses of the five optimal configurations have been analyzed for different values of CSR and δ. The electrical power losses can be calculated with the equation Power loss =

Pelec Pelec − max

× 100 %

(10)

where Pelec is the maximum output power for different values of CSR and δ, and Pelec-max is the maximum output power of 1.1 kW for the ideal case of zero values in CSR and δ. Figure 13 shows the electrical power losses of five optimal configurations for the values of CSR, ranging from 0 to 0.4 and δ, ranging from 0 to 4 mrad. According to the results, the optimal configuration I has the highest electrical power losses for all values of CSR and δ as compared to the others configuration. This indicates that a significant performance drop will happen to the configuration of DACPV that is designed without considering the effect of slope error. The higher the slope error the higher the power loss will be. The maximum power loss of 22.4% happens to the optimal configuration I when CSR = 0.4 and δ = 4 mrad.

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A855

Referring to Fig. 13, the optimal configuration V is the best configuration to minimize the electrical power losses caused by the increases of CSR and δ. The maximum electrical power loss of this configuration is only 6.5% at CSR = 0.4 and δ = 4 mrad. Consequently, the result shows that the optimal configuration V, which is designed based on the simulated flux distribution at the highest value of slope error, δ = 4 mrad, is capable of reducing the impacts of circumsolar radiation and slope error to the electrical performance of DACPV module.

Fig. 13. Bar chart to show the power losses in percentage for five different optimal configurations with CSR ranging from 0 to 0.4, and δ ranging from 0 to 4 mrad.

5. Conclusions A systematic approach to optimize the electrical performance of DACPV system has been developed by considering both the effects of circumsolar radiation and mirror slope error. The principle and the methodology for analyzing the optical characteristics of the NIDC have been described in details. From the simulated results, we can conclude that the circumsolar ratio and slope error can cause serious deterioration to the uniform flux distribution area and the percentage of energy within the uniform illumination area. The influence of the slope error to the flux distribution at the receiver is more significant compared to that of the

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A856

circumsolar radiation. In addition, the simulated results are very useful for the designer to optimize the size of receiver by considering the spillage losses. In addition, the methodology to optimize the layout of solar cells interconnection circuit in DACPV module has been proposed. Optimal configuration I, II, III, IV and V are the most optimized layout of solar cells interconnection circuits, which are designed based on the simulated flux distribution with slope error at 0, 1 mrad, 2 mrad, 3 mrad and 4 mrad respectively in the case of CSR = 0. The optimal configuration V is the best configuration to minimize the electrical power losses caused by the increases of CSR and δ. The maximum electrical power loss of this configuration is only 6.5% at CSR = 0.4 and δ = 4 mrad. As a conclusion, a comprehensive study has been carried out to optimize the electrical output power of DACPV system by considering the circumsolar ratio and slope error in the solar flux distribution. For the validation of the model with respect to the effects of both circumsolar radiation and slope error, DACPV module that is designed based on the optimal configuration V is under developing for an out-door testing. Acknowledgments The authors would like to express their gratitude to the Ministry of Energy, Green Technology and Water (AAIBE Trust Fund) and the Ministry of Science, Technology and Innovation (e-Science Fund with project number 03-02-11-SF0143) for their financial support. The authors would also like to thank the project advisor Ir. Dr. Philip Tan Chee Lin for his many insightful suggestions.

#233456 © 2015 OSA

Received 5 Feb 2015; revised 2 Apr 2015; accepted 17 Apr 2015; published 19 Jun 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.00A841 | OPTICS EXPRESS A857