Proceedings of of the the 2009 ASMEASME 2009 3rd 3rd International International Conference Conference on of Energy Proceedings EnergySustainability Sustainability ES2009 ES2009 July 19-23, 2009, San Francisco, California, July 19-23, 2009, San Francisco, CaliforniaUSA USA
ES2009-90132 ES2009-90132 SIMULATION OF UTILITY-SCALE CENTRAL RECEIVER SYSTEM POWER PLANTS Michael J. Wagner National Renewable Energy Laboratory 1617 Cole Blvd Golden, CO 80401 United States of America
[email protected]
Sanford A. Klein University of Wisconsin – Madison 1343 Engineering Research Building 1500 Engineering Drive Madison, WI 53706 United States of America
Douglas T. Reindl University of Wisconsin – Madison 843 Extension Building 432 North Lake Street Madison, WI 53706 United States of America
ABSTRACT
INTRODUCTION The purpose of the research presented in this paper is to develop a versatile fundamentals-based model for the power tower CSP technology. This task is undertaken by breaking the plant model concept into a set of sub-models for each individual subsystem in the plant – the tower receiver, heliostat field, power cycle, and thermal storage subsystems. These individual component models work together to predict the behavior of the plant as a whole, and are used for longterm plant simulations in the TRNSYS (Klein, et al., 2004) transient simulation environment. TRNSYS allows component models to be interconnected and evaluated simultaneously. This arrangement is ideal for complex thermal systems like the power tower, since weather data, the Rankine cycle, receiver, heliostat field, and storage models can be produced independently, verified, and connected to form a single large system in TRNSYS.
The operation of solar energy systems is necessarily transient. Over the lifetime of a concentrating solar power plant, the system operates at design conditions only occasionally, with the bulk of operation occurring under part-load conditions depending on solar resource availability. Credible economic analyses of solar-electric systems requires versatile models capable of predicting system performance at both design and off-design conditions. This paper introduces new and adapted simulation tools for power tower systems including models for the heliostat field, central receiver, and the power cycle. The design process for solar power tower systems differs from that for other concentrating solar power (CSP) technologies such as the parabolic trough or parabolic dish systems that are nearly modular in their design. The design of an optimum power tower system requires a determination of the heliostat field layout and receiver geometry that results in the greatest long-term energy collection per unit cost. Research presented in this paper makes use of the DELSOL3 code (Kistler, 1986) which provides this capability. An interface program called PTGEN was developed to simplify the combined use of DELSOL3 and TRNSYS. The final product integrates the optimization tool with the detailed component models to provide a comprehensive modeling tool set for the power tower technology.
In addition to modeling the behavior of existing plants, a goal of this research is to provide a tool that is able to determine an optimal plant design in a specified location given inputs such as desired electric power, reflector size, receiver size, and receiver configuration, among others. Thus, both an optimization tool and a long-term performance assessment tool were developed. Several existing simulation tools were employed in this research including the DELSOL3 code (Kistler, 1986) for power tower plant layout and the TRNSYS transient simulation environment. The DELSOL3 program is used to specify the design of the system for a specified electrical power output. TRNSYS is used to simulate the short-term performance of the system in response to varying weather
Keywords: Power tower, concentrating solar power, CSP, DELSOL3, PTGEN, optimization, detailed modeling, TRNSYS, Fortran, part-load, solar power, solar electric, SAM, Solar Advisor Model
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conditions. The PTGEN interface program was developed to simplify the use of DELSOL3 and to facilitate the use of its output by TRNSYS. This is discussed in more detail in the following section. A detailed description of PTGEN and the TRNSYS power tower component models is provided in Wagner (2008).
rely on actual hourly measurements and so it may not realistically represent the transients seen in actual weather data. Other drawbacks exist and are discussed further in Wagner (2008). The second mode that DELSOL3 can operate in is an optimization tool that takes a set of user inputs and iteratively identifies a system design capable of yielding the highest financial returns, accounting for capital and other costs against the projected electricity production. The focus of the optimization tool is the geometric relationship between the heliostat field and the central receiver. The tower height and receiver sizes are iteratively evaluated to determine the lowest cost based on a desired electricity output from the power cycle. The receiver surface is assumed to have convective and radiative losses that share a first-order relationship with the overall surface area. Detailed receiver loss calculations, as implemented in the TRNSYS power tower model developed in the current research, are not done in DELSOL3.
THE PTGEN MODELING TOOL Plant Layout and optimization with DELSOL3 Although DELSOL3 was selected for use in this research, several existing codes were considered, including codes for plant optimization/layout and codes that provide detailed optical analysis capability for the heliostat field. These models include the University of Houston code for heliostat field layout (Lipps and Vant Hull, 1977), HFLCAL (Kiera and Schiel, 1989) for heliostat field layouts, MIRVAL (Leary and Hankins, 1979) for comparison of heliostat field layouts, SolTRACE (Wendelin, 1989) for optical analysis, and DELSOL3 (Kistler, 1986) for Central Receiver System (CRS) plant layout.
The major strength of the DELSOL3 code is its versatility to handle many different system constraints and inputs while providing the required output to define the configuration of the plant. In some cases, limitations can compromise the versatility of these options. However, the code is remarkably versatile, option-inclusive, and well-documented and it provides an excellent foundation upon which to build more advanced models. In the process of integrating the DELSOL3 code, several modifications were made to update obsolete code and improve run speed.
The current publicly available standard for calculating CRS system performance is the SOLERGY code (Stoddard, et al., 1987). Because the ultimate goal for the research presented in this paper is integration in TRNSYS and NREL’s Solar Advisor Model (Gilman, et al., 2008), it was determined that new component models with improved flexibility should be developed. Validation of SOLERGY was performed with operating data from Solar I (Alpert and Kolb, 1988), and future work is anticipated to verify the research presented here with SOLERGY. Because one specific purpose of the DELSOL3 code is to generate an optimized plant design for a central receiver system, it was considered the best match for incorporation with TRNSYS in this project. DELSOL3 is capable of generating a specific receiver geometry that is matched to a heliostat field layout. It provides useful output for long-term simulations, such as an array of net heliostat field efficiency as a function of solar position and flux distribution on the receiver surface as a function of solar position. Other advantages of using DELSOL3 include the extensive documentation that accompanies the program, and the fact that the code is written in Fortran, allowing for easy integration with other Fortran-based programs, including TRNSYS. The following section presents a brief overview of DELSOL3 and discusses some of its main features.
Implementation of DELSOL3 with PTGEN The Power Tower Generator program (PTGEN) consists of a graphical user interface and background code to assist the user in generating the required input for long-term TRNSYS simulation of the power tower system. PTGEN uses the DELSOL3 Fortran code in its entirety, as well as several other Fortran programs and subroutines that were written for input file construction, output file formatting, and output data abridgment. To obtain a complete set of input data for longterm TRNSYS simulation, multiple runs of the DELSOL3 code are required with a unique input file for each run. Instead of forcing the user to modify the original text input files for DELSOL3 before each run, the PTGEN program automates the process based on some simplified input criteria. The result is a much simpler, more time-efficient process that still takes advantage of the strengths of DELSOL3 and TRNSYS.
DELSOL3 operates in two modes. The first mode calculates the performance of an existing system. The system could be one previously generated by DELSOL3 or one specified by the user based on other external models. Although DELSOL3 is able to calculate the system performance for a requested day and time, it has several major drawbacks that have led to the implementation of detailed simulation capability in TRNSYS. For example, the receiver model in DELSOL3 assumes a fixed heat loss that is proportional to the receiver area instead of a more fundamental-based model that utilizes temperature differences for heat loss estimates. The fixed heat loss per unit area is not appropriate for some receiver designs. Additionally, the weather model used in DELSOL3 does not
PTGEN operates by taking user input from its graphic user interface and processing it into a formatted efficiency array for TRNSYS input. The code then calls DELSOL3 multiple times in three distinct capacities. The first call takes advantage of DELSOL3’s ability to optimize a solar power tower plant based on user input set-points. The second and third calls are for performance calculations that use the plant sizing information produced during the optimization run. One particularly powerful feature of DELSOL3 is its capability to output an array containing the flux distribution provided by the heliostat field and incident on the tower receiver surface. The “receiver flux” performance run needs to be called many times because the flux changes depending on the solar
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position. DELSOL3 is limited to outputting a single instantaneous flux map during each run for a specified day and time.
This plot reveals unequal spacing between the selected data points, which reduces the accuracy at which the flux map data can be approximated at a specified solar position. Points tend to closely neighbor each other near the fringes of the plot area due to the decreased rate of change of the solar position during times near the solstices. To overcome this limitation, equal spacing was enforced between the solar declination angles instead of between the days of the year. 0
Zenith Angle (Degrees)
Vertical Position (Normalized)
The generated flux map is based on aiming techniques that account for maximum flux levels based on the receiver material capabilities, heliostat field layout, and receiver geometry. The uneven flux distribution around the circumference of the receiver contributes to varying heat transfer losses at the surface, so the magnitude of these losses is an important consideration in the receiver model. Figure 1 shows an example of the flux distribution incident on the receiver surface (in units of kW/m2) at a given instant in time. The flux values are mapped as a function of normalized vertical height on the vertical axis (0 corresponds to the bottom of the receiver and 1 corresponds to the top) and circumferential position on the horizontal axis (180° represents the north facing portion of the receiver). 1 95 170 245 320 395 470 545 620 695 770
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 30
60
10 20 30 40 50 60 70 80 90 45
90
135
180
225
270
315
Azimuth Angle (Degrees) Figure 2: Solar position represented by equally spaced days throughout the half-year (180°=South, 35°N, 116°W).
The appropriate array of sample days was calculated using the relationship shown in Eq.(1). This equation is derived based on the sinusoidal nature of the solar declination angle, with a period beginning and ending on the solar solstice days of the year.
90 120 150 180 210 240 270 300 330 360
Circumferential Position (deg) 2
Figure 1: Flux on the external cylindrical receiver [kW/m ] at a solar azimuth of 276° and a solar zenith of 68°. On the horizontal axis, 180° represents the north-facing portion of the cylinder
(1)
It is impractical and time-consuming to create a flux map for every single time step that TRNSYS will use during yearly simulations on hourly or shorter time steps. It is computationally much more efficient to use a finite number of flux maps at specified positions, each of which serve as a representative flux map for the small range of solar positions immediately surrounding the calculated position.
In this relationship, the number 355 represents the day of the year on which the winter solstice occurs, the number 172 represents the day of the year on which the summer solstice occurs, nday is the number of days that will be included in the selection which was chosen to be 8, as shown below, and the array is calculated for i between 1 and nday. The floor function rounds the argument down to the nearest integer. The adjusted plot of the selection of 96 solar positions for flux map calculation is shown as Figure 3.
The first challenge in determining the best way to implement the flux maps is to identify how many flux maps are needed to allow the flux on the receiver to be estimated at any time of the year. One might expect that flux maps could be produced for each hour of the day for a certain number of days that are equally spaced throughout the year. Since the tilt of the earth’s axis with respect to the sun provides a declination angle that is a sinusoidal function, evaluation of the flux maps is only needed for one half of the year. Thus, the equally spaced distribution for only the six months between the winter solstice and the summer solstice were considered and weather effects were removed. Figure 2 shows the result of plotting the solar position (described by the zenith and azimuth angles) at equally spaced days throughout the half-year for the sunlight hours of the day.
The TRNSYS central receiver model is developed such that any given solar position is translated to the most closely neighboring solar position shown in Figure 3. The corresponding calculated flux map is selected for the given solar position. To verify that the resolution of 96 flux maps (96 total daylight hours over 8 days) is sufficient in characterizing the flux on the receiver over the course of the year, a sensitivity study was undertaken that adjusted the number of flux maps, and then ran a yearly simulation with typical meteorological year (TMY2) weather data. The flux incident on the receiver at each hour was integrated over the year and the yearly total incident flux was compared in units of kW-hr/m2 based on the number of flux maps in use. Note
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that the number of flux maps is determined by calculating the total number of daylight hours over the days of the year under consideration.
heliostat, the total mirror surface area of the field, the tower height and receiver geometry. The second portion contains output read directly from DELSOL3 calculations indicating the projected plant characteristics based on a cursory analysis done within DELSOL3. For more information on how these values are determined, refer to Kistler (1986). Also included is a capital cost breakdown that provides estimates for initial capital costs associated with construction of the plant. Table 2 provides a listing and description of each item included in the capital cost breakdown. Finally, a project cost in terms of dollars per kilowatt electric is provided.
0
Zenith Angle (Degrees)
10 20 30 40 50
Table 2: A summary of items provided by the DELSOL3 cost breakdown for projected power tower capital costs (Kistler, 1986).
60 70 80 90 45
Label LAND 90
135
180
225
270
315
Azimuth Angle (Degrees) Figure 3: Solar positions used for the flux maps spaced equally by declination angle (35°N, 116°W).
HEL WIRE
The results from this sensitivity study show that using hourly flux maps generated with 8 properly chosen days is adequate to estimate the flux distribution at any time of the year. Table 1 shows a summary of the study results using different number of days, where the change from the reference case of 96 flux maps is indicated. By using fewer flux maps, and by allowing the program to simply choose the nearest flux map neighbor for calculations instead of determining the map at each solar position, TRNSYS simulations run much more quickly.
TOW
REC PIPE
PUMP
Table 1: Sensitivity Study results for determining the best number of flux maps. Number of Days
Hourly Frequency
4 8 10 12 8 16 16
Once/hour Once/hour Once/hour Once/hour Twice/hour Once/hour Twice/hour
Total No. of Flux Maps 48 96 120 144 184 190 368
Average Change [%] 0.123 0.024 0.033 0.007 0.038 0.047
STOR
Maximum Node Change [%] 0.525 0.491 0.365 0.016 0.402 0.391
EPGS HTXC HG FIXED
Description Cost of the unimproved land area required for the plant, increased by 30% to account for roads and other additional surrounding land required, and increased by a fixed amount to account for improvements to the core land area of the plant. Cost for the heliostats, including wiring and installation Additional costs for wiring, if not included in heliostat costs. Costs associated with the tower structure. The cost scales with tower height. Towers taller than 120m are assumed to be concrete, while shorter towers are assumed to be steel. Cost of the receiver. The cost scales with square footage of surface area. Costs for piping from the power cycle/storage to the receiver, designed for molten salt in proportion to tower height and flow rate. Costs for pumps to move molten salt through storage, power cycle, and to receiver. Scale with flow rate and tower height. Costs for thermal storage, including tank costs. If size reaches limit of 12,300 m3, two equal volume tanks are used. Cost for the electric generating sub-system including the generator and turbine plant. Cost of the heat exchangers, scaled with thermal power of the plant. Assumed common field costs (buildings and roads, controls, etc.). Some costs scale with plant size.
The second output file contains the heliostat field net efficiency as a function of solar position (note that PTGEN produces an additional file that also contains this information, but it is laid out in a more easily viewed 2-D matrix). This array contains values, which indicate the overall heliostat field efficiency as solar azimuth and zenith angles vary. Total field efficiency is defined in Eq.(2), as the total radiation incident on the receiver divided by the total radiation incident on the heliostat field mirrors for a given solar position.
PTGEN Program Output PTGEN produces three output files. The first is a general plant summary file, called “plant_summary.txt”. This file contains information read from DELSOL3 output. Important information contained in this file includes receiver geometry, heliostat field and heliostat information, and projected plant construction costs per kilowatt. It should be noted that the default DELSOL3 settings provide economic outputs in terms of 1984 dollars. These values can be adjusted by manually setting the economic parameters in the optimization input file.
(2)
The first portion of the summary.txt file provides information about the physical characteristics of the system, including the number of heliostats in the optimized system, the size of each
In this equation, is the total average flux incident on the receiver surface, is the area of the receiver surface, is the beam-normal solar radiation, is the area of
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one heliostat, and field.
places the heliostats in their stow position in the case that the wind velocity exceeds the cutoff value. The component also includes a defocus control that can be used to partially defocus the field if the power block and/or storage cannot accommodate the thermal power provided by the receiver.
is the total number of heliostats in the
Figure 4 shows this field efficiency for an 11 MWe external receiver at 35°N, 116°W. Since the heliostat field is more heavily distributed on the north side of the tower, efficiency values are higher when the solar position is in the southern sky relative to the tower. Optical losses also dominate when the sun is low in the sky, and this behavior is reflected at zenith angles closer to 90°. This information is provided as an input to the heliostat field component in TRNSYS.
Additional parasitic losses associated with heliostat tracking and startup/shutdown should be accounted for, but they are peripheral to the core behavior of the field. The field efficiency is determined by interpolating a two-dimensional array containing the efficiency values over a range of solar azimuth and zenith angle positions. The number of solar azimuth and zenith angles used to create this array must be provided. The receiver flux distribution is not implemented using the heliostat field component model; instead it is applied directly using the receiver model since the receiver component makes use of the flux distribution information. Table 3 summarizes the fixed-value inputs (parameters), variablevalue inputs (inputs), and the outputs for the heliostat field component (Type 221). Depending on the resolution of the weather file used in the simulation, these arguments can be passed on an hourly or sub-hourly basis.
Solar Zenith (Degrees)
0 0.17 0.22 0.27 0.32 0.37 0.42 0.47 0.52 0.57 0.62 0.67 0.72
15 30 45 60 75 90 0
30
60
90 120 150 180 210 240 270 300 330
Table 3: A summary of the parameters, inputs, and outputs for Type 221, the heliostat field component Parameters Unit no of input file No of zenith angle data points No of azimuth angle data points Number of heliostats Startup energy of unit Power to track 1 unit Max allowed wind-speed Inputs Wind speed Defocus factor Solar zenith angle solar azimuth angle Outputs Parasitic tracking power concentrator field efficiency
Solar Azimuth (Degrees, 180=North)
Figure 4: A field net efficiency map as a function of solar position.
Although the sample field efficiency map in Figure 4 corresponds to a sample plant that was optimized for latitude 35° in the northern hemisphere, the map itself is independent of location. The heliostat field optical efficiency varies only with solar position. For this reason, all solar positions are shown, rather than only those that are possible for the 35°N location. For the plant in question, only the solar position needs to be provided to determine the overall field efficiency regardless of the plant’s latitudinal and longitudinal location. The third file produced by a PTGEN run contains the flux distribution on the receiver for a number of solar positions. A discussion of the theory behind this output is provided in the section above.
The Tower Receiver Model The central receiver design has traditionally been one of two possible configurations – either a fully exposed cylindrical surface, or a concave surface nested inside of a protective cavity. The exposed cylindrical surface, commonly referred to as the external receiver, consists of a number of individual receiver panels arranged in a vertical cylinder at the top of a tower. These panels are typically exposed to ambient conditions without glazing or protection. The cavity receiver, like the external receiver, is often an assembly of multiple panels. However, this configuration provides some degree of protection from the ambient conditions, as it is situated inside an open cavity which reduces radiation and convection losses.
These files provide the required data for a full TRNSYS simulation. The plant geometry generated in the PTGEN optimization run is used by the central receiver (Type 222), heliostat (Type 221), and storage (Type 4) components. These components were developed as a part of this research, and are discussed in detail in the next section. The flux distribution file is used by the central receiver component, and the heliostat field efficiency matrix is used by the heliostat field component. The following section discusses these components in more detail. TRANSIENT SIMULATION TOOLS
The solar receiver geometry to be employed in this model is based on the Solar II demonstration project, which was conducted from June 1996 to April 1999 near Barstow, CA (Pacheco, et al., 2002). The receiver at Solar II successfully demonstrated the power tower technology using an external receiver, and provides a sound conceptual basis for formulating this model.
The Heliostat Component Model The heliostat field performance is fully defined by the field efficiency map and the flux map discussed in the previous section. The heliostat component model is not required to do run-time optical analysis or any calculation beyond reading and returning the appropriate efficiency value for the field. The heliostat model also monitors the ambient wind speed and
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There are several purposes for developing a detailed receiver model. First, the goal of a detailed thermal model is to accurately predict the net thermal power absorbed by the receiver. This goal requires that both the incident absorbed flux and the thermal losses must be predicted. Second, the model must be capable of predicting the temperature distribution on the receiver surface to assure that the limits established for the receiver material and the heat transfer fluid are not exceeded. A detailed receiver model allows alternative fluid circuiting arrangements to be considered and their individual performance to be evaluated. The model calculates conditions at multiple points on the receiver, which allows more estimates of temperature distributions within the receiver to be made; thereby, these capabilities allow the user to model a receiver that is geometrically unique from previously modeled systems.
this panel, tube-to-tube conduction and radiation exchange is neglected for tubes within the same panel. Radiation between tubes on adjacent panels is assumed to have negligible effect on the receiver performance. Axial conduction is also neglected since the much larger internal convection due to salt flowing in the tubes dominates over the relatively large resistance to conduction.
The basic building block of the receiver model is a single tube of length , where is some finite portion of the overall panel length in the vertical direction. This element is subject to multiple heat transfer mechanisms, including incident radiation ( ), external convection ( ), and radiation exchange with the surroundings ( ). Radiation that is reflected from the tube surface ( ) is an additional consideration. The energy balance for each element is presented in Figure 5.
The terms in Eq.(3) can be expressed as integrals with respect to axial position, x, over the length of the element . The incident irradiative flux on each panel with one azimuthal data point and multiple vertical data points is given by:
The various heat transfer flows can be expressed in terms of a differential element of length dx, shown in Figure 5. For each differential element dx, the overall steady-state energy balance on the heat flow components leaving and entering the control volume is: (3)
(4)
(5) In Eq.(4), the value of is not known, but the integrated quantity is provided by the flux distribution shown in Figure 1 above. The number of tubes in each panel is given by . The energy that is initially reflected from the tower is represented by the term. The receiver model assumes a constant, spectrally independent, hemispherical absorptivity (α) for the tower surface. Since the tower surface is opaque, the reflectivity is . (6) Radiation emitted from the receiver to the ambient surroundings is considered through the term in Figure 5 above. A view factor from the tower to the surroundings ( ) was calculated using the EES (Klein, 2008) correlation for a cylinder that is surrounded on both sides by parallel cylinders of the same diameter, all of which lie in a single plane.
Figure 5: Energy balance on a receiver tube element.
The resolution of the flux data on the receiver surface provided by DELSOL3 is limited to an array of data points. Therefore, receiver model calculation nodes can be distributed with approximately one data point per panel in the circumferential direction and several flux points per panel in the vertical direction. Each of the parallel tube elements at vertical position x in a receiver panel are represented by the same energy balance. This assumption is also made because the neighboring tubes on the same panel share a common header where the fluid temperature enters the tubes at the same temperature. Therefore, the result of an energy balance applied to a single tube at position x on panel N can be scaled by the number of tubes in that panel. Since each tube in one of the panels is then, essentially, identical to its neighbors in
The value of the view factor adjusts the outbound radiation from the half-cylinder exposed to the surroundings to account for radiation exchange between the cylinders. Emissivity, , is given as 0.88 (Taumoefolau et al., 2004). Thus the rate of energy transfer from the panel by radiation is defined in Eq.(7).
(7)
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The heat transfer to the fluid and the associated temperature rise of the fluid across the finite length can be calculated by using these thermal resistances in series. The driving temperature difference for the heat transfer is the difference between the surface temperature and the average heat transfer fluid temperature at position x. This relationship is shown in Eq.(13).
Note that surface temperature is a function of position in the xdirection and cannot normally be evaluated in an integral without first defining its relationship with x. For this analysis, we have assumed that for each discrete element of length Δx, the surface temperature and other properties are constant. This simplification allows the evaluation of the integrals with respect to x within the element. The validity of this assumption is discussed below.
(13)
The convective losses ( ) are proportional to the temperature difference between the external surface of the receiver tube and the free stream air temperature ( ). Properties of air are evaluated at the film temperature, defined as the average of the tube surface and the ambient air temperatures. The convective losses are proportional to a mixed convection coefficient ( ). This coefficient incorporates both natural and forced convection from the receiver surface using correlations developed for the central receiver by Siebers and Kraabel (1984). (8)
The final term is the thermal energy that is added to the heat transfer fluid, and is described by the term. Since all other heat terms have been determined, the remaining unknown is the change in temperature of the heat transfer fluid across the control volume. (9)
Figure 6: Heat flow balance across the receiver tube wall
(10)
The resulting model incorporates these energy balances and relationships to model the receiver in a detailed manner. The inputs, parameters, and outputs are summarized in Table 4. Table 4: Parameters, Inputs and Outputs for the receiver model.
To determine the average surface temperature of a receiver tube, an additional energy balance is required. This balance considers the thermal resistance between the outer surface of the tube and the heat transfer fluid running through the tube. Figure 6 presents a thermal resistance network for this heat transfer problem on a cross-section view of the receiver tube. The conduction resistance and convective resistance between the inner tube wall and the heat transfer fluid are shown, and can be calculated as described in Eqs. (11) and (12). The heat flux into the control volume ( ) represents the flux entering the tube after outer surface losses have been accounted for.
Input Solar azimuth Solar zenith Outlet heat transfer fluid temperature Inlet heat transfer fluid temperature Wind velocity Ambient pressure Pump efficiency Hour of the day Dew point temperature Direct Normal Irradiation Field efficiency Dry Bulb Temperature
(11)
(12)
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Parameter Number of Panels Receiver diameter Panel Height Tower height Tube outer diameter Tube thickness Material type Coolant type Flow Pattern Plant latitude Logical Unit Output Salt flow rate Receiver thermal efficiency Pump power Convection losses Radiation losses Thermal power Heat transfer fluid outlet temperature
(15)
(16) The temperature difference that drives the steam mass flow rate in the Rankine cycle is the difference between the hot heat transfer fluid inlet temperature and the saturation temperature of the steam boiler pressure. Therefore, HTF temperatures are non-dimensionalized according to this temperature difference. For the non-dimensional cold heat transfer fluid outlet temperature, the expected value near design conditions is minus one.
(17)
The Rankine Power Cycle Model The thermal power from the central receiver system is assumed in the model to be used to drive an electric power generation cycle. The most common generation cycle for this application is the steam Rankine cycle. As with any steam Rankine power generation cycle, the central receiver power cycle can include a variety of configurations to ease implementation and boost efficiency. The following discussion summarizes the Rankine cycle model introduced by that is intended for general use with multiple cycle design configurations. Additional detail is provided by Wagner (2008).
(18)
The heat transfer fluid mass flow rate and the cooling water mass flow rate are non-dimensionalized according to their nominal rates at design conditions.
(19)
The Rankine cycle behavior under part-load conditions can be approximated with the use of a multiple non-linear regression technique based on several non-dimensionalized quantities. In this study, a representative power cycle with two open feedwater heaters, three turbine stages, pre-heat and super-heat is used to measure the response of the cycle thermal efficiency, the cycle power output, the heat transfer fluid outlet temperature, and the cooling water outlet temperature as the cycle operating conditions varied. Each input and output (with the exception of the condenser cooling water inlet temperature) is non-dimensionalized with respect to a characteristic quantity. In several cases, the scaling quantity is the design value for the power cycle, which is generally readily available to the plant modeler. In other cases, as in the heat transfer fluid temperatures, a thermodynamically significant value is chosen.
(20)
Finally, the cooling water outlet temperature is nondimensionalized according to the nominal temperature drop across the cooling water at design conditions.
(21)
The goal of using non-dimensional parameters in the regression model is to obtain a model that can be applied to any Rankine power cycle over a wide range of operating conditions. The model requires, as input, several parameters related to their specific Rankine cycle configuration, including: Rankine plant design electric power output Rankine cycle efficiency at design conditions Plant inlet and outlet heat transfer fluid temperatures at design conditions Heat transfer fluid mass flow rate
Cycle power output, cycle heat addition, and thermal efficiency can be scaled directly with their design values. The cycle heat addition is defined as the rate of heat flow from the heat transfer fluid through the heat exchangers to the steam in the Rankine cycle.
(14)
These values should be readily available to the plant designer through the power cycle manufacturer as they describe the
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system performance at its reference or design condition. The regression model will then calculate the change in the output variables (e.g., power, heat rejection, return salt temperature) with respect to the deviation of the inputs from their reference design condition values.
from design conditions. The regression process is involved and is beyond the scope of this paper; for more information refer to Wagner (2008). The total effect on each output is the sum of the effects provided by each input variable and interaction. For example, the total cycle power output is dependent on all of the highlighted variables and interactions in the first column of Table 5. If the relationships defining the HTF inlet temperature and the HTF flow rate result in a 10% decrease in the power output and none of the other input variables impact the power output, the total reduction in power would be 20% from the design value.
The regression model was constructed by correlating the nondimensionalized outputs from a detailed Rankine cycle model developed in EES. These outputs of interest include: Actual cycle electric power output Cycle thermal efficiency Heat transfer fluid outlet temperature Condenser cooling water outlet temperature Cycle heat addition rate
Wagner (2008) presents an analysis that compares the regression model to a detailed thermodynamic model in EES (Klein, 2008) over a range of heat transfer fluid mass flow rates and inlet temperatures. The models were tested for three different heat transfer fluid temperatures at along a series of heat transfer fluid mass flow rates.
These outputs define the cycle’s interaction with the surrounding components, and are a function of the conditions under which the cycle is operating. The results of this study are demonstrated with the use of the Lenth’s method t-test statistic (Wu and Hamada, 2000), where the statistical significance of each of the effects is compared to the cutoff value at the desired level of significance. A significance of 95% certainty was chosen for this experiment, corresponding to a cutoff value of 2.16 (Wu and Hamada, 2000). A higher level of certainty was not selected because in this analysis, it is better to erroneously include an effect that is not actually significant than it would be to erroneously exclude a significant effect. A test statistic that is greater than this cutoff value indicates significance for that effect, with a 5% chance that the statistic has erroneously been deemed significant. The calculated test statistics are presented in Table 5, with the significant values emphasized. Two-variable interactions are denoted with a vertical bar.
The results of this analysis show that the regression model matches well with the output of the EES model, with percentage errors in output generally limited to a few percentage points. Error is defined as shown in Eq.(22).
(22)
The magnitude of the error increases as the deviation from design conditions increases. The highest error is observed at low HTF mass flow rates and cooler HTF inlet temperatures. The Rankine cycle model was compared to limited data provided by the Solar II Rankine cycle, as presented in Pacheco (2002).
Table 5: The regression analysis test statistics are shown. Variables whose effect on the outputs are likely insignificant are shaded. A cutoff value at 95% significance was used, corresponding to 2.16.
150.6 28.76 2.670 245.0
1613 36.56 3.228 2716
54.81 119.2 8.131 501.2
108.1 263.7 17.91 42.91
64.07 4.053 29.81 109.7
3.814
2.690
8.911
0.729 33.72
0.733 389.3
1.818 59.42
0.436 2.866
0.667 4.219
41.68
16.03
0.003 7.111
0.037 8.463
0.160 2.901
0.059 3.497
1.099
1.307
2.125
5.097
0.257 1.036 7.190
Data taken at steady state from the Solar II Rankine cycle are compared to the predicted data using the regression model. Two target salt inlet temperatures were used over a range of target HTF flow rates. The results of the comparison are most clearly presented as the relationship between cycle power output and the HTF flow rate as shown in Figure 7. The results of the comparison show good agreement, with the largest error at low flow rates, as expected.
Each of the outputs of interest is examined to determine the way that their value depends on the various significant input variables highlighted in Table 5. For those input values that have a significant impact on the output values, parametric runs were performed, varying the input over a wide range of possible values. With input and output values normalized to design conditions or some other consideration, polynomial fits were assigned to each relationship. These polynomials provide the individual effect of each input value as it deviates
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Kiera, M., Schiel, W. (1989). Measurement and Analysis of Heliostat Images. Journal of Solar Energy Engineering, Vol 111, Issue 1, pages 2-9. Kistler, B.L. (1986). A User’s Manual for DELSOL3: A Computer Code for Calculating the Optical Performance and Optimal System Design for Solar Thermal Central Receiver Plants. Sandia National Labs, Albuquerque, NM. SAND868018. Klein, S.A., et al. (2004). TRNSYS 16 – A Transient SYstem Simulation program, User manual. Solar Energy Laboratory, University of Wisconsin – Madison. Klein, S.A., Alvarado, F. (2008). Engineering Equation Solver, F-Chart Software. Madison, Wisconsin. Leary, P.L., Hankins, J.D. (1979). User’s guide for MIRVAL: a computer code for comparing designs of heliostat-receiver optics for central receiver solar power plants. Sandia National Labs, Livermore, CA. SAND-77-8280.
Figure 7: The results of a comparison between Solar II Rankine cycle data (Pacheco, 2002) and the predicted value.
CONCLUSIONS The purpose of this research was to develop a robust fundamentals-based model for the central receiver system power plant for use in long-term transient simulation. The major contributions of this research are the development of the PTGEN interface and program that makes use of the previously developed DELSOL3 code, the development and implementation of specific plant components in TRNSYS, including the heliostat field, central receiver, and Rankine power cycle. These components represent an improvement in model detail over existing public domain models for the power tower technology.
Lipps, F.W., Vant Hull, L.L. (1977). A cellwise method for the optimization of large central receiver systems. International Solar Energy Society, Annual Meeting, Orlando, Fla., June 6-10, 1977.
The PTGEN interface and supporting code provides a new avenue of use for a previously developed and validated optimization/layout code. Continuous development and improvement of the PTGEN program is anticipated in future work, and an adaptation of this model is anticipated in the National Renewable Energy Laboratory/DOE’s Solar Advisor Model (Gilman, et al., 2008).
Stoddard, M.C., Faas, S.E., Chiang, C.J., Dirks, J.A. (1987). SOLERGY – A Computer Code For Calculating the Annual Energy from Central Receiver Power Plants. Sandia National Labs, Albuquerque, NM, and Livermore, CA. SAND86-8060.
Pacheco, J.E., et al. (2002). Final Test and Evaluation from the Solar Two Project. Sandia National Labs, Albuquerque, NM. SAND2002-0120. Siebers, D.L., Kraabel, J.S. (1984). Estimating convective energy losses from solar central receivers. Sandia National Labs, Sandia, New Mexico. SAND84-8717.
Taumoefolau, T., Paitoonsurikarn, S., Hughes, G., Lovegrove, K. (2004). Experimental Investigation of Natural Convection Heat Loss From a Model Solar Concentrator Cavity Receiver. Journal of Solar Energy Engineering, Volume 126, Issue 2, 801.
ACKNOWLEDGEMENTS The authors acknowledge Nate Blair, Mark Mehos, and Chuck Kutscher at the National Renewable Energy Lab in Golden, Colorado, for their assistance in the development of this material. Additional thanks are due to Greg Kolb at Sandia National Lab in Albuquerque, New Mexico, for his guidance with the DELSOL3 and SOLERGY codes.
Wagner, M.J. (2008). Simulation and predictive performance modeling of utility-scale central receiver system power plants. Masters thesis, University of Wisconsin – Madison. Available online at http://sel.me.wisc.edu . Wendelin, T. (1989). SOLTRACE: A NEW OPTICAL MODELING TOOL FOR CONCENTRATING SOLAR OPTICS. Solar Engineering 1989, American Society of Mechanical Engineers.
REFERENCES Alpert, D.J., Kolb, G.J. (1988). Performance of the Solar One Power Plant as Simulated by the SOLERGY Computer Code. Sandia National Labs, Albuquerque, NM. SAND88-0321.
Wu, C.F.J., Hamada, M. (2000). Experiments: Planning, Analysis, and Parameter Design Optimization. WileyInterscience, New York.
Gilman, P., Blair, N., Mehos, M., Christensen, C., Janzou, S., Cameron, C. (2008). Solar Advisor Model User Guide for Version 2.0. 133 pp.; NREL Report No. TP-670-43704.
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