1. Introduction

Concentrator photovoltaics (CPV) employ refractive or reflective optics to concentrate sunlight onto solar cells. This allows for a decrease in active solar cell area by a factor that is related to the degree of optical concentration.

Well understood benefits of CPV include:

A recent comparison of a CPV system versus a non-CPV system [3] is indicative of the challenges CPV faces. In this work, even a modest 25x concentration factor CPV system which is effective over the summer months when direct sun is available falls short of a fixed non-CPV alternative during less ideal weather conditions. The significant added costs of tracking are then hard to justify. Another detailed 2 year study of a CPV system [4] also does not provide convincing evidence to justify the added cost and complexity of CPV. More extensive analysis comparing system performance over 8 year time spans has also been published [5,6].

Tracking is widely used in non-CPV solar farm installations in order to increase collection efficiency. Very basic one-axis horizontal tracking is capable of achieving over 20% improvement in non-CPV energy yield [7]. The gain in performance arises due to improved sunlight collection and is not related to a concentration effect. The cost of simple horizontal one-axis tracking is significantly lower than two axis tracking required for medium or high concentration CPV.

Very innovative hybrid CPV systems have been proposed. A lensed multi-junction CPV solar cell array combined with additional low-cost solar cells surrounding the multi-junction cells can capture diffuse solar radiation while providing the benefits of high efficiency CPV [8–11]. Significant costs are associated with this type of hybrid system, however, and dual axis tracking is essential. Another issue with multi-junction CPV solar cells is current matching. Maintaining current matching over a wide range of concentration intensities and operating temperatures is challenging [12] and this challenge would be compounded in hybrid systems.

A comprehensive range of optical designs [13] have been proposed and tested for CPV. Optics designs, however, are not able to overcome the need for two axis tracking as well as hybrid approaches to capturing diffuse sunlight, both of which add significant cost to medium and high concentration CPV systems.

A recent analysis of the challenges faced by CPV in the context of price drops in non-CPV silicon systems [14] suggests that extreme performance levels would be required for CPV to regain competitiveness including a 50% cell efficiency at modest cost. Current multi-junction PV technology is not able to satisfy these requirements cost effectively.

In silicon-based CPV, interdigitated back contact high performance silicon solar cells primarily intended for concentrator applications were developed [15–20]. Both contact polarities were located on the back surface. An efficiency in a silicon-based concentrator cell of 27.5% [16] was achieved, although the promise of this record efficiency remains largely inaccessible in practical installations due to challenges with CPV in general, as described above. Work to further improve silicon CPV has not been a priority in the past few decades.

In this paper we propose and describe Adaptive Contact CPV (ACCPV) which represents a new approach to CPV. ACCPV will be shown to have the potential to increase system efficiency compared to non-CPV systems without the need for tracking provided that system losses can be managed. It also works in diffuse lighting conditions, and cooling may be achieved using thermally conductive heat spreaders that do not extend beyond the cell area. It is applicable to single junction or multi-junction solar cells. It does not, however, decrease the area of solar cells for a given capacity as in CPV.

The intention of this paper is to describe a scheme in which well-understood CPV improvements in efficiency could play a role in specific premium applications where tracking systems are unsuitable. Reliability issues in mechanical tracking systems are eliminated, and operation in diffuse lighting conditions is enabled.

2. Approach and theory of operation

In a traditional mechanical tracking CPV system, the goal is to illuminate the entire cell area with concentrated sunlight and to maintain this condition by mechanically adapting to the moving sun position. In contrast, the ACCPV approach eliminates the mechanical tracking requirement and instead selectively connects only those portions of the cell area that receive concentrated sunlight. Mechanical tracking CPV has the advantage of cell area reduction compared to non-CPV systems. ACCPV does not reduce cell area but it does eliminate mechanical tracking and it has the ability to function in both direct and diffuse sunlight conditions. Both CPV and ACCPV benefit from an increase in cell efficiency due to sunlight concentration.

In ACCPV, the portions of the cell area that receive concentrated sunlight are selectively connected to the load while the portions of the cell area that receive little or no sunlight are not connected.

An example of the ACCPV concept using simple refractive optics is illustrated in Fig. 1b) and is compared to an example of CPV illustrated in Fig. 1a). It is clear that ACCPV does not benefit from the reduction in solar cell area enjoyed by CPV. Instead, the strategy in ACCPV is to increase cell efficiency due to optical concentration resulting in an increase in the open circuit voltage and the corresponding increase in the Shockley-Quessar limit compared to non-CPV.

 

Fig. 1. a) CPV makes use of optical focussing, small solar cells and a tracking system. b) ACCPV also makes use of optical focussing but does not require tracking. A single solar cell having adaptive contacts is shown. Since the total solar power reaching the solar cell has not increased, a heat spreader equal in size to cell area is sufficient to prevent the illuminated regions of the solar cell from excessive temperature increases.

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It is clear from Fig. 1b) that some portions of the solar cell are highly illuminated while other portions are not illuminated. Although small areas of the cell are subject to concentrated sunlight, the average solar power reaching the cell is similar to that for a non-concentrating cell in the same solar conditions. For this reason a thermally conductive heat spreader is able to prevent local heating effects and maintain junction temperatures that are similar to non-CPV solar cells.

An illustrative example of ACCPV implementation is shown in Fig. 2. Here a set of switches allows portions of the rear contact of a solar cell to be either connected or disconnected from the load. The lens array shown in Fig. 1 is incorporated with the cell. Depending on the position of the sun, only those switches belonging to cell areas receiving substantial sunlight and capable of supplying power to the load are closed and switches belonging to cell areas receiving little or no sunlight and liable to dissipate power are open. In Fig. 2a), switches S₁, S₃, S₅, S₇ and S₉ are closed and switches S₂, S₄, S₆, and S₈ are open. As the sun moves through the course of the day, the status of the switches adapts to the illumination condition. In Fig. 2b) switches S₂, S₄, S₆, and S₈ are turned on while switches S₁, S₃, S₅, S₇ and S₉ are turned off. In the case of diffuse sunlight in which the solar cell becomes uniformly illuminated, all the switches would be closed for maximum power generation.

 

Fig. 2. Basic ACCPV system showing segmented rear electrode connected to individual switches. a) and b) Switches are set such that only those portions of the solar cell producing power are connected and portions of the solar cell that dissipate power are not connected. c) Smaller cell segments allow more refined selection of the connected versus disconnected cell areas. The result is a pixelated solar cell. A conceptual rendering of cell segments or “pixels” illuminated by one lens at one instant in time is shown. Cell segments inside the circle would be connected and those outside the circle would be disconnected.

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3. Modelling

A derivation based on a standard textbook p-n junction solar cell model [2] in conjunction with Kirchoff’s laws clearly presents the effect of connecting a dark solar cell in parallel with an illuminated cell. See Appendix. A solar cell of area ${A_1}$ is illuminated with a given sunlight flux density and thereby produces an open circuit voltage ${V_{\textrm{OC}}}$. If the solar cell of area ${A_1}$ that is illuminated is connected in parallel with an identical but un-illuminated solar cell of area ${A_2}$ then a decrease in ${V_{\textrm{OC}}}$ of $\Delta {V_{\textrm{OC}}}$ will occur where

 

Fig. 3. Plot of $\Delta {V_{\textrm{OC}}}$ as a function of the ratio of dark cell area ${A_2}$ to illuminated cell area ${A_1}$ for a parallel connection.

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4. Experimental validation

The applicability of the theory to two types of commercially available silicon solar cells was tested. These cells were employed to experimentally measure $\Delta {V_{\textrm{OC}}}$ as well as the improvement in solar cell performance expressed by Eq. 6. Firstly, a pair of 5 inch single crystal silicon solar cells from Sunpower was used to obtain the results according to Table 1 as shown in Fig. 4. These Sunpower cells have no electrode on the front face and instead employ interdigitated electrodes on the back face. They were chosen since their design was originally inspired by CPV applications although they are now used in non-CPV systems. High minority carrier recombination times are achieved for this type of cell, although increased carrier diffusion lengths are required due to the layout of the back face electrodes.

 

Fig. 4. I-V Characteristics of a pair of Sunpower solar cells connected according to Table 1.

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Table 1. Configurations of two nominally identical silicon solar cells.

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Each of two nominally identical solar cells was separately illuminated with a dedicated white LED lamp array light source that supplied uniform illumination over the face of the cell equivalent in effective intensity to approximately 0.1 suns. The I-V characteristics of each cell were measured and plotted. Also, the I-V characteristics were re-plotted after connecting the illuminated cell in parallel with the dark cell as shown in Appendix Fig. 1. Current and voltage values are measured to within ${\pm} 1\%$.

Note that the voltage and available power are higher when the solar cells are disconnected. The value of $\Delta {V_{\textrm{OC}}}$ averaged between the two graphs in Fig. 4 is 0.0245 V.

The experiment was repeated using a pair of very typical back-surface-field, nominally identical solar cells obtained from China SunEnergy in place of the Sunpower cells. The results from the China SunEnergy cells are shown in Fig. 5.

 

Fig. 5. I-V Characteristics of a pair of China SunEnergy solar cells connected according to Table 1.

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The average value of $\Delta {V_{\textrm{OC}}}$ obtained from the two graphs of Fig. 5 is 0.0175 V which is close to the calculated value of $\Delta {V_{\textrm{OC}}} = 0.018\textrm{V}$ as derived in the Appendix. One possible explanation for the higher measured values of $\Delta {V_{\textrm{OC}}}$ in the Sunpower cells compared to theory is carrier recombination in the depletion regions of the dark cells. Depletion region recombination will lead to increased dark current and is normally discussed in terms of an ideality factor between 1 and 2 which is neglected in the diode model we have used [2].

Based on the plots of Fig. 4 and Fig. 5, approximately 4% of the increase in available power output at an optimum operating point is obtained when the dark cell is disconnected. Although this 4% power increase seems modest, it is based on an illuminated cell and a dark cell of equal areas. If a dark cell having a much larger area than the illuminated cell was tested then substantially larger increases in available open circuit voltage, and hence power, would result from disconnecting the dark cell as shown in Fig. 3.

The modelling we have reviewed is applicable to p-n junction solar cells other than silicon devices, and the energy gap of the semiconductor is not a parameter in the model.

5. Implementation strategies

Implementation of the switching scheme could be achieved using field effect transistors that have low channel on-resistance. A low resistance is critical to avoid solar cell power loss. Other methods of implementation include mechanical switches or relays. It is clear, however, that smaller rear electrode segments and hence a larger number of switches than shown in Fig. 2c) would be advantageous and would allow for a more ideal adaptive response to the sun’s position and therefore a higher realizable system efficiency. For example, in place of each switch shown in Fig. 2a) or Fig. 2b), it would be much more ideal if many more switches and associated cell electrode segments were constructed as illustrated in Fig. 2c). In this way, solar concentration factors of 10 to 100 or even higher could be well managed and only the electrode segments being substantially illuminated and supplying power, rather than draining power, would be connected while the remaining electrode segments would be disconnected. The solar cell then becomes essentially pixelated.

A portion of a p-n junction PV cell with two rear electrodes and two switches is shown in Fig. 6. Lateral current leakage due to minority electron diffusion current as well as majority hole drift current could flow within the p-region in Fig. 6 between adjacent cell segments associated with adjacent rear electrode segments. As the density of rear electrode contacts increases these leakage effects become more serious. Appropriate electrically insulating barriers can resolve this issue.

 

Fig. 6. Cross section of a single junction n⁺p solar cell showing crosstalk between segments $N$ and $N + 1$ due to minority and majority currents in the p-region. The concept of a narrow electrically insulating barrier along the dotted line is also shown.

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It is clear from Fig. 6 that thin film solar cells are more readily amenable to implementation for ACCPV since it is more challenging to pattern and form insulating barriers between segments of thicker bulk substrates such as wafer-type crystalline silicon cells than it is for thin film cells.

A FET switch array connected to the rear of a solar panel requires solar detection and control hardware that constitute the system by which instantaneous solar conditions are monitored, and by which appropriate segments are activated. For example, a camera in conjunction with a processor could determine the settings of the switches for maximum solar power on a real time basis.

The optimal dimension of the electrode segments or pixels depends on a number of factors. More, smaller pixels will allow for optimal adaptivity to regions where sunlight is concentrated as illustrated in Fig. 2c). However leakage currents and cost could favour fewer pixels. For example, if the red circle diameter in Fig. 2c) is 1 cm then the pixels shown would be under 1 mm in dimension. Optimal pixel dimensions would tend to decrease as concentration factor increases.

One interesting approach to achieve ACCPV at potentially low cost is to use a photoconductive layer behind the solar cell as shown in Fig. 7.

 

Fig. 7. Cross section of typical n⁺p solar cell showing a photoconductive layer behind the solar cell. Infrared sunlight that is not absorbed by the solar cell is used to generate electron-hole pairs in this photoconductive layer in order to control carrier flow to the rear electrode in a spatially selective manner.

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Sunlight contains infrared radiation extending from approximately 1100 nm to 2500 nm that is not fully absorbed in typical solar cells and that is available at the back of such cells. This part of the solar spectrum could therefore be used to detect solar intensity and directly control current flow between the rear electrode and the collection layer (p-type region in the case of Fig. 6) in the p-n junction of the solar cell. Photoconductors may possess long carrier lifetimes which greatly exceed the carrier transit time through the photoconductive layer thickness thereby enabling gain. Gains of ${10^4}$ are common for photoconductors [23]. Materials absorbing in this infrared range include PbS, PbSe, PbTe, InSb and InAs among others.

Challenges with the use of photoconductors include these key aspects:

 

Fig. 8. ACCPV as applied to multijunction solar cell. In this example three cells are shown. As in Fig. 7, lateral barriers are needed to prevent unwanted lateral current flow. Tunnel junctions exist between stacked cells.

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A 15% increase in the Shockley-Queisser efficiency limit for single junction silicon solar cells at 100 suns concentration and a 22% increase for single junction GaAs solar cells at 100 suns concentration have been predicted [21]. However, the highest reported single crystal silicon CPV efficiency is 27.6% versus the highest single crystal silicon non-CPV efficiency of 26.1% [22]. These efficiency improvements fall well short of modelling predictions due to factors including series resistance losses and other effects [23]. Experimental results for single junction GaAs cells also show small gains in CPV efficiency. As a result, triple-junction and other multi-junction cells currently might be good candidates for ACCPV.

Triple junction cells have achieved experimental efficiencies of 44.4% (CPV) versus 37.9% (non-CPV) [22]. CPV therefore provides a relative 17% improvement which includes series resistance and Auger considerations but not optical losses. Therefore optical losses in an ACCPV system must be less than 17% to yield a net advantage. Optical losses of 9% in lensed concentrators have been achieved [24]. This could lead to a potential net gain of 8% in triple junction efficiency which translates into an actual efficiency gain of over 3% from 37.9% to almost 41%. Actual efficiency gain would depend strongly on pixelation losses.

In addition to pixelation losses, more detailed analysis of lensed optics under a mix of lighting conditions including diffuse lighting will be required to more precisely calculate overall net performance. Sunlight reflection losses are angle dependent, and the concentration factor of direct sunlight also varies with angle and on details of lens design.

6. Conclusions

ACCPV has been presented and justified both mathematically and experimentally as a concept for efficiency improvement in photovoltaics. In triple junction cells, efficiency gain is projected to enable approximately 41% conversion, neglecting switching losses. Gains in single junction solar cell efficiency are also possible but series resistance losses may limit net efficiency gains. Cost of such a system might be high, but diffuse lighting performance would be enabled unlike in CPV systems.

Possible implementations of ACCPV have been outlined and discussed. Challenges that need to be considered and overcome for ACCPV to become practical include the achievement of very low series and switch resistances, barriers to limit electrical cross-talk between illuminated and dark solar cell material, and low loss concentrator optics. A potentially low cost implementation using infrared photoconductivity in place of transistor switches has been proposed. Further study of optical concentrators over a range of lighting conditions is required.

ACCPV has potential relevance in applications where mechanical tracking is not feasible. Single or multi-junction ACCPV could be viewed as a “premium” CPV approach that eliminates moving parts and is both highly reliable and compact, and hence optimized for specialty applications while enabling effective operation in both diffuse and non-diffuse lighting conditions. In principle, multi-junction ACCPV could lead to the highest achievable power output in a non-tracking solar cell system.

Appendix

Consider a single solar cell illuminated uniformly with light flux $\Phi $ (photons/s). The current-voltage equation describing a single p-n junction solar cell is

(1)$$I = {I_0}\left( {\exp \frac{{qV}}{{kT}} - 1} \right) - {I_{\textrm{SC}}}$$

where short circuit current ${I_{\textrm{SC}}} = q\gamma \Phi $. Here, $\gamma $ is the fraction of light flux photons producing electron-hole pairs that may be collected by the solar cell. Open circuit voltage ${V_{\textrm{OC}}}$ is given by

$${V_{\textrm{OC}}} = \frac{{kT}}{q}\ln \left( {\frac{{{I_{\textrm{SC}}}}}{{{I_0}}} + 1} \right)$$

where ${I_0}$ is the product of reverse saturation current density ${J_0}$ and cell area A We can therefore write

(2)$${V_{\textrm{OC}}} = \frac{{kT}}{q}\ln \left( {\frac{{q\gamma \Phi }}{{{J_0}{A_{\textrm{total}}}}} + 1} \right)$$

for the single cell of area ${A_{\textrm{total}}}$.

To extend this model to a situation in which portions of the solar cell are illuminated while other portions of the cell are not illuminated, we will now consider an illuminated solar cell connected in parallel with a dark solar cell such that the total area of the two cells is ${A_{\textrm{total}}}$.

A first, illuminated p-n junction solar cell of junction area ${A_1}$ is connected in parallel to a second, dark solar cell of junction area ${A_2}$ as shown in Fig. 9 such that ${A_1} + {A_2} = {A_{\textrm{total}}}$ The current-voltage diagram indicating the operating points of the two cells is also shown. We will assume a light flux $\Phi $ (photons/s) illuminating cell 1.

 

Fig. 9. One illuminated cell and one dark cell are connected in parallel. In the absence of a load, voltage ${V_{\textrm{OC}}}$ will be produced when their currents are equal in magnitude and opposite in direction.

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In the case of the un-loaded parallel cells of Fig. 2, Kirchhoff’s current law requires that the current I flowing through cell 1 and cell 2 is the same in magnitude, but opposite in direction. Using Eq. 1 for each cell and applying Kirchhoff’s law,

$${J_0}{A_1}\left( {\exp \frac{{q{V_{\textrm{OC}}}}}{{kT}} - 1} \right) - q\gamma \Phi ={-} {J_0}{A_2}\left( {\exp \frac{{q{V_{\textrm{OC}}}}}{{kT}} - 1} \right)$$

where voltage ${V_{\textrm{OC}}}$ is shown in Fig. 9. Now,

$${J_0}({{A_1} + {A_2}} )\left( {\exp \frac{{q{V_{\textrm{OC}}}}}{{kT}} - 1} \right) = q\gamma \Phi $$

and re-arranging, we obtain

(3)$${V_{\textrm{OC}}} = \frac{{kT}}{q}\ln \left( {\frac{{q\gamma \phi }}{{{J_0}({{A_1} + {A_2}} )}} + 1} \right) = \frac{{kT}}{q}\ln \left( {\frac{{q\gamma \phi }}{{{J_0}{A_{\textrm{total}}}}} + 1} \right)$$

which is identical to Eq. 2. For this reason, the overall $I - V$ relationship describing the parallel-connected illuminated cell/dark cell pair is represented by Eq. 1 where ${I_{\textrm{SC}}} = q\gamma \Phi$, except that $\Phi$ is now the light flux arriving exclusively at the illuminated cell. We have neither gained nor lost overall performance in a cell pair having a given light flux concentrated on the illuminated cell as compared to having a single solar cell uniformly illuminated by the same light flux.

This same analysis may be extended to argue equivalence in performance of a cell receiving a total light flux focused on a small area of the cell relative to an identical cell receiving the same total light flux uniformly over its surface.

At this point, we can make an argument for selectively contacting portions of the solar cell in Fig. 1b) in order to maximize the collection of electrical power and hence take advantage of the available increase in the Shockley-Queisser limit.

Referring to Fig. 2, if we could remove the dark cell from the circuit, we would be left with a single, illuminated cell having $I - V$ equation given by

$$I = {I_0}\left( {\exp \frac{{qV}}{{kT}} - 1} \right) - {I_{\textrm{SC}}} = {J_0}{A_1}\left( {\exp \frac{{qV}}{{kT}} - 1} \right) - q\gamma \Phi $$

The resulting short circuit current is once again $q\gamma \Phi $ however the open circuit voltage is now

(4)$${V_{\textrm{OC (single cell)}}} = \frac{{kT}}{q}\ln \left( {\frac{{q\gamma \Phi }}{{{J_0}{A_1}}} + 1} \right)$$

Since ${A_1}$ is less than ${A_{\textrm{total}}}$ it is clear that ${V_{\textrm{OC(single cell)}}}$ is larger compared to ${V_{\textrm{OC}}}$ in Eq. (3). This is the origin of the improvement in cell efficiency and the corresponding increase in the Shockley-Queisser limit due to optical concentration. The difference in the open circuit voltages obtained from Eqs. 3 and 4 is

(5)$${V_{\textrm{OC (single cell)}}} - {V_{\textrm{OC}}} = \frac{{kT}}{q}\ln \left( {\frac{{q\gamma \phi }}{{{J_0}{A_1}}} + 1} \right) - \frac{{kT}}{q}\ln \left( {\frac{{q\gamma \phi }}{{{J_0}({{A_1} + {A_2}} )}} + 1} \right)$$

We may assume that the arguments of the natural logs in Eq. 5 are much larger than unity because ${V_{\textrm{OC}}} \gg \frac{{kT}}{q}$ at room temperature. We can therefore conclude that

$${V_{\textrm{OC (single cell)}}} - {V_{\textrm{OC}}} \simeq \frac{{kT}}{q}\ln \left( {\frac{{q\gamma \phi }}{{{J_0}{A_1}}}} \right) - \frac{{kT}}{q}\ln \left( {\frac{{q\gamma \phi }}{{{J_0}({{A_1} + {A_2}} )}}} \right)$$

Upon simplification we obtain

(6)$${V_{\textrm{OC (single cell)}}} - {V_{\textrm{OC}}} \simeq \frac{{kT}}{q}\ln \left( {\frac{{{A_1} + {A_2}}}{{{A_1}}}} \right)$$

In the special case that the illuminated cell and the dark cell have the same area such that ${A_1} = {A_2}$ then the change in open circuit voltage becomes

$$\Delta {V_{\textrm{OC}}} = {V_{\textrm{OC (single cell)}}} - {V_{\textrm{OC}}} \simeq \frac{{kT}}{q}\ln 2 = 0.018\textrm{V}$$

Funding

Natural Sciences and Engineering Research Council of Canada (RGPIN-05259-2014).

Acknowledgments

The author would like to thank the Natural Sciences and Engineering Research Council of Canada for financial support, and Rafael Kleiman for useful discussions.

Disclosures

The author declares no conflicts of interest.

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