Flat Plate Collector (Surrogate)

from watertap_contrib.reflo.solar_models import FlatPlateSurrogate

This Flat Plate Collector (FPC) unit model is a surrogate model that inherits its base model structure from the Solar Energy Base Class. The unit model is trained using data generated by the Solar Water Heating model from PySAM which is is a Python package for the National Renewable Energy Laboratory’s System Advisor Model (SAM). Like the corollary in SAM, the FPC model is assumed to include both the solar field and the thermal energy storage system.

Model Structure

Outputs from the surrogate model are used to estimate the performance and the cost of the FPC system. The degrees of freedom depends on the number of surrogate input variables set by the user in the model configuration. The model can have between 1 and 3 degrees of freedom, depending on the configuration. By default, the surrogate model includes the following input variables:

Variable	Variable Name	Symbol	Units	Description
System capacity	`system_capacity`	\(P_{th}\)	\(\text{MW}\)	Maximum thermal power output of the system
Hours of storage	`hours_storage`	\(t_{storage}\)	\(\text{hr}\)	Number of hours of thermal storage
Target hot temperature	`temperature_hot`	\(T_{hot}\)	\(\text{°C}\)	Hot target outlet temperature

System capacity is a required input surrogate variable. The others are optional. Users can choose to use a fixed value for the hours of storage or target hot temperature when generating data using PySAM.

The following parameters are required outputs of the surrogate model:

Variable	Variable Name	Symbol	Units	Description
Heat annual	`heat_annual`	\(H_{annual}\)	\(\text{kWh}\)	Annual thermal energy produced by the system
Electricity annual	`electricity_annual`	\(E_{annual}\)	\(\text{kWh}\)	Annual electricity demand of the system

Additional parameters included on the FPC model block are:

Parameter	Parameter Name	Symbol	Default Value	Units	Description
Water specific heat	`specific_heat_water`	\(c_p\)	4.181	\(\text{kJ/kg/K}\)	Specific heat of water
Water density	`dens_water`	\(\rho\)	1000	\(\text{kg/m}^3\)	Density of water
Cold temperature	`temperature_cold`	\(T_{cold}\)	25	\(\text{K}\)	Temperature of the cold influent stream
Temperature difference factor	`factor_delta_T`	\(\Delta T\)	0.03	\(\text{K}\)	Temperature between the influent stream and ambient temperature
Collector area	`collector_area_per`	\(A_{collector}\)	2.98	\(\text{m}^2\)	Area of each collector
FRta	`FR_ta`	\(FR_{ta}\)	0.689	\(\text{kW/m}^2\)	Product of collector heat removal factor (FR), cover transmittance (t), and shortwave absorptivity of absorber (a); optical gain a in Hottel-Whillier-Bliss equation
FRUL	`FR_UL`	\(FR_{UL}\)	3.85	\(\text{kW/m}^2\text{/K}\)	Product of collector heat removal factor (FR) and overall heat loss coeff. of collector (UL); thermal loss coeff b in Hottel-Whillier-Bliss equation

The total collector area is calculated as follows:

\[A_{total} = \frac{P_{th}}{(FR_{ta} - FR_{UL} \times \Delta T)}\]

And the total number of flate plate collectors required is:

\[N_{collectors} = A_{total} / A_{collector}\]

The thermal storage volume is calculated with:

\[V_{storage} = \frac{h_{storage} \times P_{th}}{\rho \times c_p \times(T_{hot} - T_{cold})}\]

Generating Data

The data for the surrogate model can be generated using the generate_fpc_data function in run_pysam_flat_plate.py in the REFLO package. This script uses the Swh model from PySAM to generate the data. Running this script will use the default weather file and configuration file included in the REFLO package, but users should update these files for their specific location and application. Weather files can be downloaded from the National Solar Radiation Database and configuration .json files can be created using SAM.

The generate_fpc_data function takes the following arguments:

Name	Keyword	Units	Description
System capacity	`system_capacities`	\(\text{MW}\)	List of range of values of interest for the trough system capacity
Hours of storage	`hours_storage`	\(\text{hr}\)	List of range of values of interest for the hours of thermal storage
Target hot temperature	`temperatures_hot`	\(\text{°C}\)	List of range of values of interest for the target hot outlet temperature
Weather file	`weather_file`	N/A	Path to the weather file
Configuration file	`config_file`	N/A	Path to the configuration file for the PySAM model
Dataset file name	`dataset_filename`	N/A	Desired name of the output dataset file

from watertap_contrib.reflo.solar_models import generate_fpc_data

data = generate_fpc_data(
    system_capacities=[10, 20, 30, 40, 50],
    hours_storages=[6, 12, 24],
    temperatures_hot=[60, 70, 80],
    weather_file="path/to/weather/file.csv",
    config_file="path/to/config/file.json",
    dataset_filename="path/to/dataset/filename.pkl",
)

Costing

The costing approach is adopted from the SAM costing for flat plate collector systems. The following parameters are constructed on the costing block for FPC costing:

Cost Component	Variable	Symbol	Value	Units	Description
Cost per area collector	`cost_per_area_collector`	\(c_{fpc}\)	600	\(\text{USD/m}^2\)	Cost per area for solar collector
Cost per volume storage	`cost_per_volume_storage`	\(c_{tes}\)	120	\(\text{USD}\text{/m}^3\)	Cost per volume for thermal storage
Contingency factor	`contingency_frac_direct_cost`	\(X_{c}\)	0.07	\(\text{dimensionless}\)	Fraction of direct costs for contingency
Indirect cost factor	`indirect_frac_direct_cost`	\(X_{i}\)	0.11	\(\text{dimensionless}\)	Fraction of direct costs for indirect costs
Fixed operating cost per system capacity	`fixed_operating_by_capacity`	\(c_{fix,op}\)	16	\(\text{USD/kW/year}\)	Fixed operating cost of flat plate plant per kW capacity

These are used the calculate the following capital and operating costs:

Cost Component	Symbol	Equation
Collector cost	\(C_{coll}\)	\(c_{fpc} \times A_{total}\)
Thermal storage cost	\(C_{tes}\)	\(c_{tes} \times V_{storage}\)
Land cost	\(C_{land}\)	\(c_{land} \times A_{land}\)
Fixed operating cost	\(C_{fix,op}\)	\(c_{fix,op} \times P_{th}\)

The direct costs include the cost of the collectors, storage, and contingency.

\[C_{direct} = (C_{coll} + C_{tes}) (1 + X_{c})\]

Indirect costs are calculated as a fraction of the direct costs and the land cost:

\[C_{indirect} = A_{land} c_{land} + C_{direct} X_{i}\]

The total capital cost of the FPC system is the sum of direct and indirect costs and sales tax:

\[C_{capital} = (C_{indirect} + C_{direct}) (1 + X_{t})\]

Note that by default, REFLO assumes no sales tax (i.e., \(X_{t} = 0\)) or land cost (i.e., \(c_{land} = 0\)).

The total operating cost is the fixed operating cost:

\[C_{operating} = C_{fix,op}\]

Energy Balance

The FPC model has both thermal and electric power flows. The steady-state thermal output of the FPC system is calculated as:

\[Q_{out} = H_{annual} / 8760\]

\(Q_{out}\) is the steady-state thermal output (in kW) at the target temperature
\(H_{annual}\) is the annual thermal energy generation (in kWh)

The parasitic power consumption of the FPC system is calculated as:

\[P_{cons} = E_{annual} / 8760\]

\(P_{cons}\) is the parasitic power consumption (in kW)
\(E_{annual}\) is the annual electric energy consumption (in kWh)

References

Blair, N.; Dobos, A.; Freeman, J.; Neises, T.; Wagner, M.; Ferguson, T.; Gilman, P.; Janzou, S. (2014).
System Advisor Model™, SAM™ 2014.1.14: General Description.
NREL/TP-6A20-61019. National Renewable Energy Laboratory. Golden, CO. Accessed May 23, 2025. www.nrel.gov/docs/fy14osti/61019.pdf .

System Advisor Model™ Version 2025.4.16 (SAM™ 2025.4.16).

National Renewable Energy Laboratory. Golden, CO. Accessed May 23, 2025. https://sam.nrel.gov