EME 810
Solar Resource Assessment and Economics

6.3 Engineering Tools to Maximize Solar Utility


Reading Assignment

  • J.R. Brownson, Solar Energy Conversion Systems (SECS), Chapter 6: "A Comment on Optimal Tilt" (small section at the end of the chapter) and see Figure 6.16.

Optional Reading

  • M. Lave and J. Kleissl. (2011) Optimum fixed orientations and benefits of tracking for capturing solar radiation in the continental United States. Renewable Energy, 36:1145–1152.
  • C. B. Christensen and G. M. Barker (2001) Effects of tilt and azimuth on annual incident solar radiation for United States locations. In Proceedings of Solar Forum 2001: Solar Energy: The Power to Choose, April 21-25 2001
  • T. Huld, M. Šúri, T. Cebecauer, E. D. Dunlop (2008) Comparison of electricity yield from fixed and sun-tracking PV systems in Europe. European Commission, Joint Research CentreInstitute for Energy, Renewable Energies Unit, via E. Fermi 2749, TP 450, I-21027 Ispra (VA), Italy (poster, PDF)
  • Greentech Media Article: Solar Balance-of-System: To Track or Not to Track, Part I (Nov. 2012)

Engineering Approaches to Increase Solar Utility

Locale is the space or an address in time and place within which the client occupies and demands energy resources. Recall that our clients are on the demand side of solar goods and services, and as such they seek maximal utility when making decisions.

The goal of solar design is to:

  1. Maximize the solar utility
  2. for the client or group of stakeholders
  3. in a given locale.

We have already learned that the solar resource can be affected by the locale of the site. The solar resource is determined by the locale, as the climate regime affects the seasonal and daily irradiation patterns and frequencies of intermittence. The character or quality of the solar resource will in turn constrain the design team's options for technological solutions that compete with conventional fuel-based technologies.

According to our review of SECS Chapter 6: given that goal for solar project design, we have three main engineering approaches that we can leverage to affect the solar utility for a client in a given locale:

  1. Reduce the cosine projection effect on an aperture/receiver. These are the extreme angles of incidence (also called low glancing angles);
  2. Reduce the angle of incidence ( θ ) on an aperture/receiver; and
  3. Reduce losses from shading on an aperture/receiver.

These are the three main engineering parameters linked to the locale that will constrain your design options (you can look back to the Angular Solar Symbols guide to refresh your memory). They all affect system performance, without necessarily directly influencing the cost of the system (in the beginning). Let's review how they affect system performance.

Reduce the cosine projection effect

Image 1 show the inverse square law effect on the Sun-Earth view factor. Image 2 show the cosine projection effect reduction of view factor.
Figure 6.1 The top image shows the effect of inverse square law on the Sun-Earth view factor
( F SunEarth ). The bottom image shows the cosine projection effect as it affects the Sun-Earth view factor (the inverse cosine of the zenith angle reduces the intensity of the Sun's irradiance).
Credit: Jeffrey R. S. Brownson © Penn State University is licensed under CC BY-NC-SA 4.0

How does the tilt and azimuth each affect the design in SECS, and how does regionality affect the design decisions in solar energy?

We have seen in our reading of Lave and Kleissl that an annual optimum for tilt and azimuth can be selected, while Christensen and Barker demonstrate that annual optimum is not really "peaky," and fixed-tilt systems can be oriented across a broad range of directions in a given locale without dropping solar gains by more than 10-20%. If we were to adjust the tilt for a seasonal optimum, we would select a lower tilt for the summer season and a higher tilt for the winter season. Effectively, we are working to correct for the cosine projection effect of our particular latitude and climate regime (one climate regime per season, recall the "fingerprints").

On broad scales, sites near the equator will have different design constraints than sites near the Arctic Circle, due to the cosine projection effect driving our solar resource across latitudes and the seasons. In this context, the project locale serves as an effective system constraint. The amount of sunlight available on a daily basis and on a seasonal basis differs with locale. Using and implementing the same system design for a client in State College, Pennsylvania ( ϕ=+ 40.86 ° , λ= 77.83 ° ) and another in Lagos, Nigeria ( ϕ=+ 6.45 ° , λ=+ 3.39 ° ), for example, will yield totally different results and lead to unsatisfied clients.

You see two images of a cartoon Sun, drawn from Ch 4 of the SECS text. The top image shows the effect of inverse square law on the Sun-Earth view factor ( F SunEarth ). The distance of 150 million km reduces the intensity of the Sun from 6.33× 10 7 W/ m 2 to 1361 W/ m 2 |( G s c ). This effect is fairly uniform year-round. The bottom image shows the cosine projection effect as it affects the Sun-Earth view factor. Here, the inverse cosine of the zenith angle ( θ z ) reduces the intensity of the Sun's irradiance. Hence, the farther away your client is located from the Equator, the more the designer will need to make collector orientation adjustments to compensate for the losses from the cosine projection effect.

Note also that the tilt of the Earth's axis will drive one to consider summer or winter optimized orientations (away from the Equator).

Reduce the angle of incidence

How does tracking affect the design decisions in solar energy?

Well, a fixed axis SECS is often oriented toward the equator at a tilt ( β ) somewhat less than the local latitude (do not fall for the latitude = tilt rule of thumb), per our readings from Christensen and Barker, and Lave and Kleissl. When we track the Sun, then more beam is collected (the angle of incidence tends to be consistently lower than for a fixed tilt). By looking at the poster from Huld et al. (2008), we see that a single-axis tracking system, with an axis inclined at an optimum angle towards South, should offer 12-50% improvement over a fixed axis tilted at the optimum, where a 2-axis tracker will offer a very similar solar gain of 13-55%.

So, a tracking system will minimize the angle of incidence ( θ ), but there will be a cost in terms of land requirements. Why? Because of shading. There will also be a cost in terms of the balance of systems (e.g., the non-SECS trackers). This is why we could read "Solar Balance-of-Systems: To Track or Not to Track, Part I" for more information.

But the reality of solar development (whether on a rooftop or on a field) is that the systems are often "area constrained." We can make certain tradeoffs in systems choices to deliver a better unit cost to the client, but we may not get all the land that we desire to accomplish an optimal tracking system. As such, we must work with the stakeholders to find the highest solar utility solution given the available area.

Reduce losses from shading

Finally, a large group of our SECSs rely on access to the shortwave light from the Sun. If we shade a collector, then we reduce or remove that working energy that we wish to convert to heat or electricity. We performed the shading analysis in Lesson 2 using orthographic and spherical projections specifically to be able to avoid shading of our array over the course of an entire year.

Of course, if we were to design a system to avoid the Sun's rays, that would be different. We have seen examples of solar design for Parasoleil frameworks (shading systems) in the beginning of the textbook (e.g., southern awnings).