INTRODUCTION

For this example, we will demonstrate the Cylindrical receiver functionality of FluxTracer that can be used to optimize the dimensions (optimal combination of height and diameter) of a cylindrical receiver of a surround heliostat field. This functionality will be applied at the ASTRI heliostat field. The resulting receiver size will be compared to the receiver implemented in the actual plant.

COMPUTING WORKFLOW

As mentioned in the introduction, for testing the cylinder analysis functionality, the Australian Solar Thermal Research Initiative (ASTRI) heliostat field is chosen as a test case, since available information exists about its design it's main technical specifications [1]. The ASTRI tower reference plant is a typical two tank molten salt solar tower plant with a gross capacity of 111 MWe, a net capacity of 100 MWe and a four hours of thermal storage which is located in Alice Springs (lat: -23.8 deg, long: 133.88 deg, elevation: 547 m). This heliostat field, shown in Figure 1, is of a surround type, and it is composed of 6177 mirrors of 37.21m2 (6.1m x 6.1m) each, thus constituting a total reflecting area of 222'846m2. Initially, the reference power plant of ASTRI was designed for 100 MWe of net capacity and had a receiver of 15 m in diameter and 18.67 m in height. Later on, a 25 MWe was designed based on the initial one, by reducing the dimension linearly by 2 times, which is not considered as an optimal solution. In the later case, the receiver had a diameter of 7.5 m and a height of 9.335 m. For this example, this reference 25 MWe ASTRI field is taken under investigation.

Note: Please request all the relevant files mentioned in this tutorial from [email protected]

Figure 1. Top view of the ASTRI heliostat field colored by annual optical efficiency

Figure 2 illustrates the overall workflow that we will follow. For this example, the computing workflow contains the following steps:

• Annual simulation points calculation using SunPath
• Ray-tracing on the calculated sun positions using Tonatiuh
• FluxTracer simulation based on the ray-tracing data using the Cylindrical analysis functionality
• Post-processing of the FluxTracer results using Paraview

Figure 2. Simulation workflow

The following sections describe all the steps in detail.

ANNUAL SIMULATION POINTS CALCULATION (SUNPATH)

Prior to the ray tracing calculations, for minimizing the number of ray-tracing simulations needed for estimating the annual performance of the plant, an interpolation and integration technique over the sun path is employed, calculating annual weighted average points that will be used for the ray tracing simulations. To calculate a set of representative annual simulation points, SunPath is used for the specific location of Alice Spring where the ASTRI heliostat field is located. In total, 50 simulation points representative of the annual performance of the plant are used for this test case.

For the present example, the computation grid adopted for the ASTRI annual simulations in the current study is shown in Figure 3 and corresponds to an angular resolution of 15.6 degrees, thus 50 simulation points are considered. The bubble size in Figure 3 corresponds to the weight used, while the coloring represents the declination angle.

Figure 3. Schematic of annual sun path adopted for the ASTRI simulations

MONTE CARLO RAY TRACING RUNS (TONATIUH)

For generating the rays required for the cylinder analysis functionality, the entire heliostat field of ASTRI was simulated in Tonatiuh with each heliostat aiming at the focal point. The Tonatiuh scene however, did not include any receiver at the focal point, and instead, a virtual surface (plane) was present above the focal point. Within Tonatiuh, the different segments that define a ray can be identified based on their interceptions with the surfaces of the solar concentrating system. For this case, the ray segments that are saved for post-processing are those that are reflected by the heliostat field and reach a "virtual" plane that is placed at an appropriate distance over the focal point. Virtual here means that the plane's optical properties are treated so as to allow the rays to pass freely from the light source surface (i.e. the sun) to the heliostat field without changing any of their characteristics, but the reflected rays form the heliostat to the virtual plane are stopped on the latter. The absence of a receiver in the ray-tracing simulations and the addition of the virtual plane, allows obtaining rays from Tonatiuh which are independent of the receiver size and dimensions. Of course, all the heliostats are set to aim at the focal point of the heliostat field, usually located along the vertical center axis of the receiver.

This virtual plane was placed parallel to the ground and centered along the vertical axis, 20 m above the focal point, ensuring that the rays reflected from the heliostats towards the aiming point will cross the focal region of the heliostat field (Figure 4). The optical properties of the virtual surface are treated in a proper way so as to allow the incoming rays from the light source (i.e. the sun) to pass through it without changing any of the ray characteristics. The reference center for the configuration (0, 0, 0) m is placed at the center of the tower base and the aiming point coordinate is at (0, 95, 0) m. The x-axis is positive towards East, the z-axis is positive towards South, and the y-axis is positive towards the Zenith. The absence of a receiver in the ray-tracing simulations and the addition of the virtual plane, allows obtaining rays from Tonatiuh which are independent of the receiver size and dimensions. Of course, all the heliostats are set to aim at the focal point of the heliostat field, usually located along the vertical center axis of the receiver.

In the details of the simulation, the sunshape selected was the Buie sunshape with a circumsolar ratio (CSR) of 2%. The reflectivity of the heliostats was set to 1, and their slope error distribution was set to normal with a standard deviation of 1.53 mrad. For the ray tracing simulations, 300 million rays are cast over the entire heliostat field resulting in many millions of rays traversing the region of interest. The adopted number of rays to use for the simulations was obtained after performing a ray independence study. The material properties for all heliostat reflectors was set with the normal sigma slope error model in Tonatiuh.

As described before, the simulation points (i.e sun positions) required for simulating the heliostat field during a year's time, were obtained by employing a weighted sample approach over the sun path, which resulted in having to run Tonatiuh fifty times at specific sun positions and with specific values of the direct normal solar irradiance. For each position (see Figure 3), the DNI entered was not an instantaneous irradiance, measured in W/m2, but the corresponding sun position weight, measured in kWh/m2. For the simulations, the scripting plugin of Tonatiuh was employed which enabled full automatization of the annual simulation process. To see a step-by-step-guide on how to do this, please click here. Finally, the whole photon data map including all the reflection events of the LCCS system obtained from the simulations, is transferred into FluxTracer, in which the receiver design optimization space is explored to find the optimal size of the required receiver.

Figure 4. The ASTRI heliostat field scene as simulated in Tonatiuh ray tracer

FLUXTRACER SIMULATIONS

In FluxTracer, the user should provide the following information to the program:

• The interval (dMin, dMax) of diameters of the cylindrical receivers to be analyzed,
• The interval (hMin, hmax) of heights of the cylindrical receivers to be analyzed.
• The number of divisions of the interval of diamaters (dDivs) to be considered.
• The number of divisions of the interval of heights (hDivs) to be considered.
• The coordinates of the focal point of the optical system of the plant, which is usually located along the center axis of the receiver. (These coordinates should be identical to the coordinates of the focal point defined in the ray-tracing software.) These can be set-up in FluxTracer using the Cylindrical Receiver functionality as shown in Figure 5.

Figure 5: Setting-up FluxTracer

The cylindrical receiver functionality command line is shown below.

<CylindricalReceiver center="0., 95., 0." dMin="0.1" dMax="15." dDivs="100" hMin="0." hMax="15." hDivs="200" output="CylindricalReceiver.csv"/>

The coordinates of the focal point of the optical system of the plant to be provide to FluxTracer is usually located along the center axis of the receiver and are set here as the center parameter. These coordinates should be identical to the coordinates of the focal point defined in the ray-tracing software. For this example, FluxTracer will perform calculations for cylinder diameters from 0.1m to 15m and for cylinder heights ranging from 0 to 15m. For this functionality, the output file is a .csv file.

POST-PROCESSING

The post-processing for this functionality is performed using Mathematica. The mathematica notebook for direct post-processing of the .csv file can be downloaded by pressing here.

As mentioned before, as output, the program provides a table with the amount of energy captured by the bins which is then post-processed accordingly. The most straightforward way to visualize the results is by constructing 2D contour maps as shown in Figure 6, which correlate the receiver's height at the vertical axis against its diameter on the horizontal axis for a given intersection percentage, shown with black lines. The white lines lying on top of the contours correspond to constant receiver area, while the blue line corresponds to the maximal intersection percentage for the given receiver area. The receiver area shown ranges between 25 and 300m2. Note that the intersection percentage is defined by the percentage of the total number of rays that are reflected from the heliostats to the number of rays that actually intersect the receiver's surface. The first thing that can be noticed is that the intersection for a fixed diameter is a monotonic function of height, while, vice versa, the intersection for a fixed height is not a monotonic function of diameter. This is pretty much expected since a number of the rays that intersect the cap surfaces of the receiver does not contribute to the receiver valid intersection. For proper evaluation of the results the following analysis is performed in order to get receiver costing values for the actual ASTRI reference plant. The actual receiver implemented in the ASTRI reference plant had a diameter of D=7.5m and height H=9.335m, thus the absorptive area of the receiver was A=πDH=219.95m2. The cost of receiver C is directly related to its surface area A and is usually estimated as

where Cref is the cost per receiver reference area to account for receiver installation costs, including labor and equipment, Aref is the receiver area on which the receiver reference cost is based, and κ is a scaling exponent that defines the nonlinear relationship between receiver cost and receiver area based on the reference cost conditions provided. The values that are frequently used according to SAM model are Cref=104.6M$, Aref=1571m2, and κ=0.7. Therefore, the cost of the ASTRI reference plant receiver was Crec=26.4M$. The cost of the receiver contributed to 12% of the total construction cost of power plant Ctot, thus Ctot=Crec/0.12=220M$, cost which includes the erection of the heliostat field, the power block, the storage, the tower structure and so on. Thus, the total cost C0 excluding the receiver is C0=Ctot−Crec=193.6M$. Finally the optimal size i.e (surface area A) of the receiver can be selected as a minimum of a normalized price of electricity function which can be defined as

which is directly proportional to the electricity price. Here, η(A) denotes the interception as a function of the receiver area.

Figure 6. Interception of the ASTRI reference plant receiver as a function of diameter and height.

Figure 7 shows a plot of the normalized price of electricity function with regards to the receiver area, based on Equation (2). FluxTracer calculates the global minimum of this function and then finds the corresponding receiver area which for the given heliostat field is the optimum. The dashed horizontal line in the figure corresponds to the minimum of the function, and its intersection (black dot) with the first vertical line corresponds to the optimum receiver area calculated by FluxTracer (FTOpt.), i.e. 210.70m2. For comparison, the point that corresponds to the actual receiver area of the ASTRI reference field is also shown on the plot as a second black dot (ASTRI ref.) It is clear that although there is a global minimum in the function, it is very shallow, and in reality reducing the electricity price substantially is not an easy task since, if the area of receiver is in the range from 150 to 300m2, the electricity price varies only by 1%.

Figure 7: (a) Normalized price of electricity as a function of area, (b) receiver's cost as a function of its area.

In sequence, these two dots, i.e FTOpt. ans ASTRI ref., are then superimposed on the contour maps of Figures 7a and 7b. Having in mind the calculated optimum receiver area, FluxTracer positions the FTOpt. dot on the intersection point of the corresponding constant area white line and the blue line which corresponds to the maximal intersection percentage for the given receiver area. Then, from the intersection point the optimal combination of height H and diameter D is derived. In comparison with the actual ASTRI reference plant receiver size (ASTRI ref. dot), it can be seen that the calculated optimum receiver point FTOpt. differs from the actual ASTRI diameter-height combination, and it is clear that the actual receiver size implemented is slightly shifted towards a larger than required receiver geometry. In terms of cost, this corresponds to an overspend of nearly 0.8M$ as seen in Figure 7b, which shows a plot of the receiver cost as a function of the receiver area.

Figure 8: The maximal interception as a function of receiver area.

A line plot of the interception percentage as a function of the receiver area is also shown in Figure 8, along with the two points of comparison, FTOpt. and ASTRI ref. For the given heliostat field, although the actual receiver of the ASTRI reference plant achieves a slightly higher interception (96.24%) in comparison to the interception calculated by FluxTracer (95.92%), the design is not optimal in terms of minimizing the normalized price of electricity function, leading to significant overspend due to the increased surface area of receiver. Finally, Table 1 shows details of the current optimal receiver sizing analysis in conjunction with the actual values implemented in the ASTRI reference plant.

Table 1: Comparison of the actual ASTRI reference plant details to the ones calculated by FluxTracer.

REFERENCES [1] Mehdi Aghaeimeybodi (CSIRO ), Andrew Beath (CSIRO), Brian Webby, Technoeconomic analysis of Solar Tower Reference plant, ASTRI technical report.