Lesson 5: Concentrating Photovoltaics

Overview

Concentrating photovoltaic systems use lenses or mirrors to concentrate sunlight onto high-efficiency solar cells. Light concentration increases the flux of photons to the surface, which increases the photovoltaic current dramatically and opens ways to raise the conversion efficiency. There are predictions that concentrating photovoltaics (CPV) will be the next big trend in solar technology, although the price of electricity delivered by CPV systems is still too high to be commercially competitive. In this lesson, we will study the principles of concentrating photovoltaic systems and see how the concentration affects different parameters of solar cells. Also, we will review materials used for manufacturing concentrating photovoltaics. Finally, in this lesson, we will turn to the examples of recently commissioned CPV plants, some of them reaching the scale of multi-megawatt power generating facilities.

Learning Objectives

By the end of this lesson, you should be able to:

understand and explain the principle of concentrating photovoltaics (CPV);
analyze the effect of light concentration on PV cell performance;
discuss examples of CPV applications on utility scale.

Readings

Cotal H. et al., III-V multijunction solar cells for concentrating photovoltaics, [1] Energy Environ. Sci., 2009, 2, 174–192

Montgomery, J., CPV Outlook: Demand Doubling, Costs Halved by 2017 [2], Renewable Energy World, Dec 12, 2013.

Wesoff, E., Biggest CPV Plant in US Now on the Grid at Alamosa [3], GreentechSolar, May 15, 2012.

5.1. What are concentrating photovoltaics?

One of the ways to increase the output from the photovoltaic systems is to supply concentrated light onto the PV cells. This can be done by using optical light collectors, such as lenses or mirrors. The PV systems that use concentrated light are called concentrating photovoltaics (CPV). The CPV collect light from a larger area and concentrate it to a smaller area solar cell. This is illustrated in Figure 5.1.

The CPV collect light from a larger area and concentrate it to a smaller area solar cell. See image caption for more details.

Figure 5.1. This is one of the common types of concentrator cells based on Fresnel lens, which takes the parallel beam of sunlight and directs it to a small area. For an effective use of the Fresnel CPV system, two-axis sun tracking is needed to ensure that the rays are perpendicular to the lens.

Credit: Mark Fedkin

Lower efficiency CPV technologies may employ silicon, CdTe, and CIGS (copper indium gallium selenide) cells, but the highest efficiencies can be achieved with multi-junction cells. Field efficiencies for these multi-junction cells are in the 30% range, and laboratory tests have achieved upwards of 40% efficiency (Kurtz, 2011).

The CPV can only use direct beam radiation and cannot use diffuse radiation (diffused from clouds and atmosphere). Therefore, these systems are suited best for areas with high direct normal irradiance. For proper light concentration, sun tracking is needed for achieving high cell performance. Tracking is especially critical for high concentration systems. In general, the CPV can be classified into low-concentration, medium-concentration, and high-concentration.

Table 5.1. Different classes of CPV systems and their requirements [Source: Green Rhino Energy, 2014]
	Low-concentration	Medium-concentration	High-concentration
Concentration ratio	2-10	10-100	100-400 (and above)
PV materials	Silicon	Silicon, CdTe, etc.	Multijunction cells
Cooling	not required	Passive cooling	Active cooling
Tracking	not required	1-axis tracking	2-axis tracking

The high concentration of sunlight achieved with multijunction cells requires more sophisticated cooling and tracking systems, which can potentially result in higher energy costs.

CPV technology is expected to grow and to expand on market. The cost effectiveness of CPV technology is related to the fact that much smaller sized solar cells are used to convert the concentrated light, which means that much less expensive PV semiconductor material is used. Also, the optics added to the system are made from glass and are usually less expensive than the cells themselves.

SPhotovoltaic power system on the roof of the St. Petersburg Academic University - Nanotechnology Centre of RAS.ee caption for image description.

Figure 5.2. Photovoltaic power system on the roof of the St. Petersburg Academic University - Nanotechnology Centre of RAS. In the center, there is a typical design of the Fresnel CPV system represented by a module of multiple cells, with a separate Fresnel lens placed on top of each single cell. On the right side of the image, a regular PV silicon cell module is shown.

Credit: Brücke-Osteuropa - via Wikimedia Commons [4]

Table 5.2. Advantages and disadvantages of the CPV systems
Advantages	Disadvantages
Less PV material, hence less cost	With concentrated sunlight, formation of hot spots is possible
Increased efficiency	Tracking systems increase complexity
Higher productivity throughout the day due to tracking	CPV can properly function only under direct beam radiation

CPV systems can produce significantly increased temperature on the surface of the PV material, so the energy should be distributed evenly over the cell area to avoid local overheating (hot spots), which can damage the material. Also, the thermodynamic efficiency of the photovoltaic conversion is less at elevated temperatures, so some kind of cooling may be beneficial. Active or passive cooling can be used. For the CPV cells with low and medium concentration ratios, active cooling is not necessary, since the temperatures reached are moderate. The high-concentration cells require high-capacity heat sinks to avoid thermal destruction of the materials.

5.2. Light concentration effect on PV performance and efficiency

Let us find out how the concentration of light affects the I-V characteristics of a solar cell. We remember from Lesson 4 that the generation current of a solar cell (I_L) is a function of number of photons (N) hitting the photovoltaic surface:

I_{L} = q N A

(5.1)

where q is the electron charge, and A is the surface area of the cell. When light is concentrated, the number of photons increases according to the optical concentration ratio, so does the cell current. So, for the short circuit current of a solar cell (I_sc), we can write:

$I_{s c} (concentrated light) = C_{o p t} I_{s c} (incident light, 1 Sun)$

(5.2)

where C_opt is the optical concentration ratio (its definition was covered in Lesson 3). For convenience, we can denote cell performance parameters at concentrated light with an asterisk:

$I_{s c}^{*} = C_{o p t} I_{s c}$

(5.3)

This equation essentially shows how much the cell short circuit current will change when the available light is concentrated C_opt times. Then, we can substitute this equation to the I-V characteristic equation, which describes the cell performance over ranges of voltage and current:

V_{o c}^{*} = \frac{k T}{q} \ln (\frac{C_{o p t} I_{s c}}{I_{o}} + 1)

(5.4)

where V_oc* is the open circuit voltage (at concentrated light), k is the Boltzmann constant, T is the absolute temperature, and I_o is the dark saturation current. Now, we are going to modify this equation because we want to find how the open circuit voltage at concentrated light would be related to the open circuit voltage at ambient light. We know that the short circuit current is the highest current a solar cell can show, while the dark current is a very low number, so the quotient in the parenthesis should be much greater than 1, and therefore, a simplified form of Equation (5.4) should be true:

V_{o c}^{*} \approx \frac{k T}{q} \ln (\frac{C_{o p t} I_{s c}}{I_{o}})

(5.5)

Next, this equation can be modified by extending the natural log as follows:

V_{o c}^{*} = \frac{k T}{q} {lnC}_{o p t} + \frac{k T}{q} \ln (\frac{I_{s c}}{I_{o}})

(5.6)

The second term here is equal to V_oc - the open circuit voltage without concentration, so we can write finally:

V_{o c}^{*} = V_{o c} + \frac{k T}{q} {lnC}_{o p t}

(5.7)

From Equation (5.7), it is obvious that there is logarithmic dependence between the cell open circuit voltage and the light concentration ratio. For example, if $C_{o p t} = 10$ , the $(k T / q) \ln C_{o p t}$ term would be equal to 60 milivolts at 25^oC - this is by how much the cell voltage will increase with tenfold light concentration. In case of higher concentration, for example, C_opt = 1000, the voltage increase would be expected to be closer to 178 mV at 25 °C, which is relatively modest compared to current increase.

To estimate the concentration effect on maximum power output, we will use the equation (which was introduced in Lesson 4):

P_{m a x}^{*} = V_{o c}^{*} \times I_{s c}^{*} \times F F

(5.8)

Substituting here Equations (5.3) and (5.7) and re-arranging, we obtain:

\[P_{\max }^* = {P_{\max }}{C_{opt}}\left( {1 + \frac{{kT}}{q}\frac{{\ln {C_{opt}}}}{{{V_{oc}}}}} \right)\]

(5.9)

Self-Check Question 1

A solar cell generates maximum power of 2.3 W at regular light conditions at 25 °C. The open circuit voltage is measured at 0.55 V. Can you apply Equation (5.9) to estimate the maximum power of the solar cell if the light is concentrated 10 times (C_opt = 10)?

As you can see, the cell power can raise dramatically because of light concentration, mainly because the cell current is significantly increased.

From the maximum power equation, we can further derive the effect of concentration on cell efficiency:

η = \frac{P_{\max}}{G}

(5.10)

In this equation efficiency, (η) is expressed as the ratio of maximum cell power output to the irradiance on the cell surface. So, for concentrated light, the irradiance will be amplified to G* (which is proportional to C_opt). The maximum power output at the concentrated light, P_max, can be expressed as V_oc*I_sc*FF according to equation (4.9) in Lesson 4. Therefore, the expression for efficiency at the concentrated light can be modified as follows:

η^{*} = \frac{V_{o c}^{*} I_{s c}^{*} F F}{G^{*}} = η (1 + \frac{k T}{q} \frac{\ln C_{o p t}}{V_{o c}})

(5.11)

The algebraic transformation above is done by substituting Equations (5.3) and (5.7) into the equation (you can check). As a result, we see how "concentrated" efficiency (η*) is related to "non-concentrated" efficiency (η) through the optical concentration ratio. Try to apply this equation to find out what happens with the efficiency if you concentrate light ten times:

Self-Check Question 2

A solar cell has efficiency of conversion 15% at 25 ^oC (298 K). Open circuit voltage of the cell is 0.55 V. What efficiency ideally can we expect from it, when light is concentrated ten times (C_opt = 10)? Use equation (5.11) and type your number (in percent) below:

As you can see, the efficiency of the solar cell increases slightly in concentrated light, but this increase is not as apparent as for absolute output parameters (e.g. power). This is because in efficiency we always consider a ratio of the output to input energy. Both output and input energies increase due to concentration, so based on Eq. (5.10) the efficiency does not change much. Moreover, the efficiency of real solar cells cannot increase indefinitely because of power losses to heat. The amount of those losses is determined by the cell series resistance (R_s). The higher the series resistance, the bigger the power losses:

P_{l o s s} = I^{2} \times R_{S}

(5.12)

Because the current flowing through the cell is proportional to the light concentration ratio, the power wasted can be presented as:

P_{l o s s} ≅ C_{o p t}^{2} \times I s c^{2} \times R_{S}

(5.13)

The power loss will grow very rapidly as the concentration ratio increases because of the exponent factor. So, there is no sense to increase concentration infinitely because those efforts may not pay off in terms of useful power increase. According to some studies (Luque, 1989), there is an optimum concentration ratio for each type of cells. It is pretty much dictated by the cell series resistance and can be expressed as follows:

C_{o p t} ≅ (\frac{k T}{q}) \frac{1}{I_{s c} R_{s}}

(5.14)

Example

We are going to use Equation 5.14 to estimate the optimal concentration ratio for a solar cell of internal series resistance of 0.01 Ohm and producing short circuit current of 150 mA (at regular light).

The factor (kT/q) at 25 °C will be equal to 0.026 V, so for the optimal concentration, we can write:

$C_{o p t} = 0.026 / (0.01 O h m × 0.150 A) = 17.33$
That means that concentrating light at much greater than x17 ratios becomes unfeasible because of excessive losses.

Many solar cells designed for concentrated light in fact have special features to reduce the series resistance, but the limits of design may still be dependent on the cell material. For silicon, for example, it is hard to create cells that would be efficient at concentration ratios higher than 200 (Markvart, 2000).

5.3. Advanced materials for CPV

Traditional PV systems use a large amount of silicon; in contrast, CPV systems use a small amounts of high‐efficiency PV materials. A typical example of such high-efficiency cells employed in high concentration CPV systems is a multijunction cell. The term multijunction refers to the cell structure, which has multiple p-n junctions combined within a single cell. Each junction is responsible for absorbing light within a particular wavelength range. All the junction currents are then combined to one output.

Combination of multiple p-n junctions within one cell is achieved by blending several semiconductor materials in layers or in other heterostructural formations. Manufacturing those formations can be tricky, and therefore costly. However, the pay-off on the efficiency side of the technology proves to be worthy. While single junction PV cells have the maximum theoretical efficiency around 34%, multiple junction cells can achieve in ideal case the limiting efficiency of 86.8% under concentrated sunlight (Wikipedia, Multijunction PV cell).

Consider the two single junction cases below (high band gap and low band gap) (Figure 5.3.1 and 5.3.2).

Band gap of 0.75 eV. See caption and below text for details

Figure 5.3.1. Low band gap cell produces high current (because a large portion of the spectrum is involved), but low voltage (because E_g is low). As a result, the access energy is lost to heat.

Credit: adapted from National Renewable Energy Laboratory (NREL) / S.Kurtz

Band gap of 2.5 eV. See caption and below text for details

Figure 5.3.2. High band gap cell produces high voltage (because E_g is high), but low current (because few photons will participate). The light below the band gap will be lost.

Credit: adapted from National Renewable Energy Laboratory (NREL) / S.Kurtz

Figures 5.3.1 & 5.3.2 show two scenarios that illustrate the use of low band gap (top) and high band gap (bottom) materials. They both have limitations, which are responsible for low efficiency of single-junction PV cells. This is why tuning the different bandgaps to different components of light is a good idea in terms of minimizing power losses. Specific disadvantage of each scenario is stated under the plots. Combining different materials with different band gaps allows the cell to absorb a wide range of wavelengths and thereby to reach the highest efficiency.

To combine different materials in the multijunction cell, certain requirements need to be met for lattice-matching, current matching, and providing high opto-electronic performance. Regarding the first requirement of lattice-matching, one needs to make sure that the lattice constants of materials included are close. If the mismatch is significant, intercrystal defects can lead to quick degradation of electronic properties. For current matching, ordering of semiconductor layers within the multijunction cell is done in such a way that high-bandgap materials are placed on the top of the "sandwich," while the low-bandgap materials are placed on the bottom (Figure 5.4). That allows the light with low energy (greater wave lengths) to transmit to the lower layers and to be usefully absorbed. This concept is demonstrated in Figure 5.4. In this design, the suitable bandgaps need to be chosen so that the currents generated at each p-n junction are matched. If, for example, one of the junctions produces much lower current, it will be detrimental to the total current of the cell (because the layers are connected in series).

3 cells stacked. Cell 1 (Eg1), cell 2 (Eg2), then cell 3 (Eg3), Eg1 ia greater than Eg2 is greater than Eg3

Figure 5.4. The arrangement of different band gap materials within a multijunction PV cell.

Credit: NASA via Wikimedia Commons [5]

Check Your Understanding - Question 3 (Essay)

The configuration of layers shown in Figure 5.4 is logical in order to allow the maximum amount of light to be absorbed. What would happen if we accidentally put Cell 3 on top of the "sandwich"? Explain, then click for answer.

Next, we will refer to the following review on multijunction cell materials, their materials and design.

Reading Assignment

Journal Article: Cotal H. et al., III-V multijunction solar cells for concentrating photovoltaics, Energy Environ. Sci., 2009, 2, 174–192. [1]

Reading this article, note the basic principles of operation of multijunction cells and define the key parameters that are responsible for their high efficiency. The reading quiz in this lesson is largely based on this material.

Reading Quiz

Now it would be the best time to take the Reading Quiz. Go to Canvas Module 5 to complete the assignment.

5.4. CPV Market overview

CPV systems have been much less represented on market compared to traditional PV. In 2012, the only utility-scale CPV plant in operation was a 5 MW project in Hatch, New Mexico, (commissioned in June 2011) (Mendelsohn et al., 2012). However, the number of CPV projects launched for utility electricity production was rapidly growing. In 2012, CPV market was characterized by NREL as follows:

"The limited commercial success of CPV to date is partly due to the fact that these systems are more complex than PV systems. During 2008, as silicon prices were reaching new market highs, CPV systems appeared ready for a commercial breakthrough. Prices have since collapsed, however, and this has changed the economics of several alternative technologies, including CPV. Despite the dramatic decreases in silicon and conventional module pricing, the CPV market looks to be entering a tentative growth stage. According to NREL’s database, at least 10 utility-scale CPV projects, representing about 471 MW, are currently in development and hold long-term PPAs with utilities. San Diego Gas and Electric (SDG&E) holds the majority of these PPAs, both in terms of megawatts (410 MW, or 86% of total) and absolute numbers. One CPV project, the 30 MW Alamosa Solar Generating Project in Colorado, will be the largest CPV installation in the world when completed in 2012. Project developer Cogentrix received a DOE loan guarantee of $90.6 million in September 2011; this was the only loan guarantee awarded to a CPV project. Continued market growth for CPV will be the most important factor in keeping its costs competitive with traditional PV and with fossil fuels. Without manufacturing in the tens of megawatts per year, it is unlikely that CPV will achieve the cost reductions necessary to make it an economic technology, despite its high efficiencies" (Mendelsohn et al., 2012)..

Obviously, there is a certain degree of skepticism related to the economic viability of CPV utility-scale facilities, which currently rely on loans from government and investors. In spite of this fact, many energy analysts predicted fast growth of concentrated photovoltaics during the second decade of 21st century. The following web article talks about this trend based on some actual data.

Reading Assignment

Web Article: Montgomery, J., CPV Outlook: Demand Doubling, Costs Halved by 2017 [6], Renewable Energy World, Dec 12, 2013. Available from: Renewable Energy World

Check You Understanding Question 4 (Multiple Choice)

Check Your Understanding Question 5 (Essay)

Name some leading companies dealing with CPV installations mentioned in the article:

Check You Understanding Question 6 (Multiple Choice)

Check Your Understanding Question 7 (Essay)

Explain the Levelized Cost of Electricity (LCOE) metric.

Check You Understanding Question 8 (Multiple Choice)

Recent Updates

The above analysis and predictions were made seven years ago. Since then, PV market experienced rapid changes, and the rate and scope of those changes went beyond many predictions and proved to be disruptive to a number of current energy markets. CPV development has also been impacted. Let us take a look at a more recent NREL report that analyzed the status and promise of the CPV technology.

Reading Assignment

NREL Report: Wiesenfarth, M., Philipps, S.P., Bett, A.W., Horowitz, K., Kurtz, S., Current Status of Concentrator Photovoltaic (CPV) Technology, Version 1.3. Fraunhofer ISE / NREL, April 2017. [7]

5.5. Ongoing activities and projects in CPV

With the fast progress in research and development of concentrating photovoltaic technology, projects started to grow to implement CPV on the commercial scale. This section of the lesson introduces some examples of such implementations.

A summary of CPV projects now operating in the U.S. is given in Table 5.3 below. While CPV is less common in other world's locations, it would be worth to mention Golmud Plant [8] in China (2012-2013), with two phases adding up to 137 MW capacity and Touwsrivier CPV Project [9] in South Africa (2014), which is also one of the largest installations - 44.2 MW .

Table 5.3. U.S. CPV operating facilities based on the information from the CPV Consortium
Project	State	DNI (kWh/m² yr.)	Land area (ha)	Company operating	Capacity (MW)
Alamosa Solar Project	CO	2482	91	Arzon Solar	35.28
Arizona Western College	AZ	2628	1	PPA Partners	1.25
Craftons Hill College	CA	2263	3	Craftons Hill College	1.61
Eubank Landfill Solar Array	NM	2449	-	Suncore PV Technology	1.21
Newberry Solar 1	CA	2650	10	Soitec	1.68
Nichols Farms	CA	2263	2	Nichols Farms	1.28
Victor Valley College	CA	2592	2	Victor Valley College	1.26

The Alamosa Solar Plant is one of the biggest project commissioned in the US, and represents one of the cover stories of CPV implementation. Some more details on this case are presented below.

Alamosa Solar Project

The Alamosa solar plant is located on 225 acres of land in Colorado and supplies electricity to the grid of the Public Service Company of Colorado. At the time of commissioning, Alamosa was the largest CPV plant in the world, but was later surpassed by the newly built plants in China. The plant boasts a set of the advanced controls to ensure grid efficiency. The loan issued on the project guarantees low risk profile, while it is clear that the CPV development still needs to provide lower electricity prices in the future to be long-term competitive with regular silicon PV and fossil fuel power plants. The news releases about the Alamosa plant are linked below.

Reading Assignment

Web Article: Wesoff, E., Biggest CPV Plant in US Now on the Grid at Alamosa, GreentechSolar [10], May 15, 2012. Available from GreentechMedia.

Web Article: Wesoff, E., Korean Utility Kepco Buys 30 MW Alamosa CPV Plant for $34M [11], August 30, 2016. Available from GreentechMedia.

Alamosa demonstrates the robustness and reliability of the Amonix CPV modules (Amonix 7700). The modules are grouped by seven into CPV systems (7 modules each). Every one of those systems has a separate inverter and controls.

Check out the design of the Amonix module in the following documents:

ArzonSolar Technology Fact Sheet 1 [12]

ArzonSolar Technology Fact Sheet 2 [13]

Summary and Final Tasks

In this lesson, you learned about the special type of PV systems - concentrating photovoltaics. There are a few important features that make this technology attractive. They include:

high efficiency of light conversion (reaching 40% and above based on some laboratory tests);
small size of cells, which allows the use of less expensive PV materials;
economic land use by CPV systems.

At the same time, sophisticated design, necessary for precise tracking and cell cooling, is responsible for higher cost of CPV systems and high price of electricity compared to regular PV or non-renewable power generation systems. The activities in this lesson are oriented towards understanding some fundamental parameters of PV and CPV system analysis.

The table below summarizes all activities that are due for this lesson. Some of those have been included in the body of the lesson, and this list simply repeats them for your reference.

Lesson 5 Assignments
Type	Description/Instructions	Deadline
Reading Quiz/Reflection	This assignment presents you with a set of questions, which check your knowledge and understanding of some concepts discussed in the paper assigned for reading: Cotal H. et al., III-V multijunction solar cells for concentrating photovoltaics, Energy Environ. Sci., 2009, 2, 174.	Due date - next Wednesday
Written Assignment	Please refer to Lesson 5 Module in Canvas to find the Lesson 5 assignment activity sheet. Using concepts learned in this and previous lessons, solve all the problems, showing your work and marking the answers clearly. You can type your solutions, or you can hand-write them and scan to a PDF (just make sure that all is legible). Submit your work to Lesson 5 Dropbox.	Due date - next Wednesday
Yellowdig discussion	Join the Yellowdig community for conversation about this lesson material. Check Module 5 in Canvas for suggested topics.	The point earning period for this week runs from Saturday to next Friday

References for Lesson 5

Green Rhino Energy, Concentrating Photovoltaics [14] 2014.

Kurtz, S. (June 2011). “Opportunities and Challenges for Development of a Mature Concentrating Photovoltaic Power Industry.” Golden, CO: National Renewable Energy Laboratory.. Accessed July 2011.

Luque A., Solar cells and Optics for Photovoltaic Concentration, Adam Hilger, Bristol, 1989.

Markvart, T., Solar Electricity, 2nd Edition, John Wiley and Sons. 2000.

Mendelsohn, M., Lowder, T., and Canavan, B., Utility-Scale Concentrating Solar Power and Photovoltaics Projects: A Technology and Market Overview, NREL/TP-6A20-51137. Technical Report. 2012