Session: 05-07 CSP System Analysis, Controls, and Standards

Paper Number: 111479

111479 - Layout and Optimization of a Novel Two-Stage Heliostat Field 

A novel two-stage heliostat design consists of a tracking stage and a concentrating stage. The tracking stage mirrors share a common angle and a common set of drives that move the mirrors together based on the sun position, while the concentrating stage mirrors are stationary, and each has a unique angle in order to direct the rays towards the receiver. The proposed design combines the advantages of both larger-area conventional heliostats with fewer drives and small-area heliostats with lower support costs in order to lower cost. Due to its very different heliostat geometry, the radial-stagger field layout that is common for a conventional heliostat might not be the most optimal for a two-stage heliostat design. Therefore, the optimal field layout with a two-stage heliostat design is determined in this paper. 

The basic tool used for this work is a ray tracing model, SolTrace, coupled to a genetic optimization algorithm in order to minimize field cost while maintaining a specified design day power. Field parameters, such as the length between adjacent mirrors in a unit (i.e., a set of mirrors attached to one drive set) and the length between opposite mirrors in a unit are optimized by the genetic algorithm. The fitness value for a specific design is based on the cost-per-thermal-power delivered from the receiver. The optimization algorithm generates an initial population of field designs, each with their own randomly generated set of variable values. For each candidate design, a field layout is selected that considers the annual energy production from a large sample of possible heliostats.

Optical characterization of this system requires ray tracing, and evaluation must be made at a relatively large sample of times throughout the year. Therefore, a relatively small number of rays must be used to evaluate each design, and the performance of each heliostat is subject to nontrivial uncertainty. The selection of heliostats to include in each layout thus relies on a curve-fitting method that seeks to reduce the impact of random uncertainty. This method smooths out this annual performance uncertainty by fitting all heliostat units along one spatial dimension with a second-order polynomial which is then used in place of computed heliostat productivity. Next, the algorithm iterates through annual energy cutoff values to determine which units are kept. At each x-position, the annual energy values for the different y-positions are inspected. There are three possible outcomes from this inspection: (i) all the heliostat energy values are above the cutoff, (ii) all the energy values are below the cutoff, or (iii) the energy values are above and below the cutoff. If all values are above the cutoff, every unit is kept for that x-position; if all values are below the cutoff, no units are kept. If values fall above and below the cutoff, the polynomial fit data is referenced to determine which units to keep. The design-day power of the kept units is summed to calculate the total design-day power. The algorithm iterates through different annual energy cutoff values until the error between desired and actual design-day power is minimized. The results of this process are presented and its efficacy is discussed.

 It is expected that the highest efficiency design will favor large concentrating mirrors and will also tend to separate adjacent mirrors and units as much as possible. However, the cost model will prefer smaller concentrating mirrors and will also want to bring the mirrors and units close together. The optimal design generated from the genetic algorithm balances these two effects to produce a low-cost field, with a total field efficiency of around 60 to 65%.

Presenting Author: Sammie Lundin University of Wisconsin-Madison

Presenting Author Biography: Sammie Lundin is a first-year mechanical engineering graduate student at the University of Wisconsin-Madison. She earned her bachelor's degree in mechanical engineering in the spring of 2022 at the University of Wisconsin-Madison. Sammie is advised by Michael Wagner and Gregory Nellis.