A simplified numerical model of a small-scale (25 - 100 kWe) parabolic concentrating solar power (CSP) plant is presented that can be utilized during the planning stages for a CSP plant, utilizing only simplified information that would be available at the preliminary stages of a project. This is important because existing models currently used for planning purposes, such as the System Advisor Model (SAM) from the National Renewable Energy Laboratory (NREL), do not cover small-scale CSP plants. The model can be used to predict real-time performance, or it can be used with TMY data to estimate annual performance. The model was validated using performance data from an operating small-scale CSP power plant, which is a unique contribution of this work. The results showed that the model correlated well with actual operating measurements for all seasons of the year, and provided a useful tool for planning of future small-scale CSP plants.
The accurate prediction of any power plant’s operation and performance is crucial in order to determine the feasibility of a potential project. Resolving issues due to site selection, such as effect of the local irradiance, incidence angle modifiers (IAM), array configuration, and soiling, or the degradation of concentrating mirror reflectance as a result of dust accumulation [
The model determined the temperature, thermodynamic properties, and the generated power of the START Lab using locally generated inputs of ambient temperature, humidity, and DNI. Once the simulation model was constructed, model validation was conducted comparing model outputs to experimentally measured outputs. A comparison between measured data and simulated data is presented below.
Due to the nature of solar power production, larger solar power plants on a commercial scale are generally more economically feasible, and most previous modeling research emphasizes the detailed modeling of large scale power plants for optimum feasibility. Regarding similar power plant configurations to the one constructed at UL Lafayette, various models emphasizing the thermodynamic potential of ORC working fluids and configurations have been presented [
Existing models have been geared toward differing target scales (commercial or central generating vs. distributed), and they have employed a variety of approaches (commercial software vs. open source, physics-based vs. empirical, incorporating energy storage or financial analysis models). Steady-state and transient models have been developed based on the Engineering Equation Solver (EES) software, Aspen Plus process simulator, Modelica, Automation studio, System Advisor Model (SAM), among others. Due to the detailed modeling approach they employ, over 50 input parameters might be required for these types of models [
Small-scale solar power plant system models recently have described solar organic Rankine cycles, parabolic through collectors, thermal storage, and alternatives to turbines such as scroll expanders [
This work describes and validates analytic modeling of the energy flows in a parabolic trough solar thermal power plant with a Rankine cycle heat engine. The relationships presented here are straightforward to implement and evaluate, relating the heat transfer within the solar collectors to the power cycle and the efficiencies of the various components.
The comparison of simulations against experimental performance currently has considerable limitations. Published experimental measurements of any meaningful extent for such solar thermal power plants are exceptionally limited [
In can be seen that for a unique system such as the pilot scale ORC CSP plant at UL Lafayette a modeling strategy which requires only limited known quantities to be employed while design considerations such as site location, collector area, collector type, solar multiple, heat engine (steam, ORC, Brayton, etc.) would prove useful. In this work, a simplified model for an ORC CSP plant is presented using very limited and only necessary parameters, which is suitable for the early stages of the design process. Also, Simulink is employed as the modeling tool [
The numerical model was constructed utilizing the integration of three fluid loops via counter-flow heat exchanger: the solar collector field, which contains the water and 15% wt. ethylene glycol mixture heat transfer fluid (HTF), the power block, which consists of an organic Rankine cycle containing the R245fa working fluid (WF), and a cooling loop, which consists of a condensing cooling tower containing cooling water.
1) WF evaporator/boiler outlet to turbine inlet
2) WF turbine outlet to condenser inlet
3) WF condenser outlet to pump inlet
4) WF pump outlet to boiler inlet
5) HTF pump to west solar collector inlet
6) HTF west collector outlet to east collector inlet
7) HTF east collector outlet to ORC boiler inlet
8) HTF boiler exit to HTF pump
9) Cooling water - cooling tower outlet to WF condenser inlet
10) Cooling water - WF condenser outlet to cooling tower inlet
The START Lab solar loop utilizes Gossamer Space Frames parabolic Large Aperture Troughs (LATs) to transfer heat captured from the sun to the HTF (
has a high-absorptivity coating with vacuum in the annular space to minimize convection losses. The HCE geometry and material properties (absorptivity, reflectivity, etc.) were utilized as inputs to the model, as published by the manufacturer.
Parameters chosen for the numerical model were selected based on the START lab.
Organic fluids are characterized by their low boiling temperature and positive
SYMBOL | DESCRIPTION | VALUE | units |
---|---|---|---|
C P , H T F | Specific heat, heat transfer fluid | 4.186 | J/(g・˚C) |
C P , W F | Specific heat, working fluid | 1.330 | J/(g・˚C) |
DNImin | Minimum radiation for system start-up | 350 | W/m2 |
Lat | Latitude | 30˚13'27''N | |
D 5 | Outside diameter of HCE glass envelope | 0.125 | m |
ε 5 | Emissivity of outer surface of glass envelope | 0.093 | |
α A B S | Absorptivity of HCE selective coating | 0.955 | |
η E N V | Effective optical efficiency of HCE envelope | 0.67 | |
α E N V | Absorptivity of HCE glass envelope | 0.20 | |
A | Reflective area of one SCA | 525 | m2 |
L | Length of one HCE receiver section | 6 | m |
T 5 , S T | Glass envelope outer surface initial temperature | 96.3 | C |
K 56 | Thermal conductance of air at T5-6 | 0.6969 | W/(m・K) |
α 56 | Thermal diffusivity of air at T5-6 | 0.00002207 | m2/s |
ν 56 , S T | Kinematic viscosity of air at T5-6 | 0.000001568 | m2/s |
T 5 | Initial HTF temperature entering solar panel | 28 | ˚C |
T 4 | Initial WF temperature entering boiler | 18 | ˚C |
T 9 | Initial cooling water temperature entering condenser | 23.11 | ˚C |
η B | Thermal efficiency of boiler | 0.85 | |
η t u r b | Thermal efficiency of turbine/expander | 0.75 | |
η c o n d | Thermal efficiency of condenser | 0.60 | |
η p u m p | Isentropic efficiency of pump | 0.60 | |
η g e n | Electric efficiency of generator | 0.91 | |
η C T | Thermal efficiency of cooling tower | 0.75 | |
m ˙ | Mass flow rate of condensing loop | 12.6 | kg/s |
m ˙ | Mass flow rate of HTF | 6.14 | kg/s |
m ˙ | Initial mass flow rate of WF | 0.859 | kg/s |
P l o w | Low pressure point of WF | 0.142 | MPa |
P h i g h | High pressure point of WF | 0.716 | MPa |
σ | Stefan-Boltzmann constant | 5.67037 × 10−08 | W/(m2・K4) |
saturated vapor slope on a T-s diagram, illustrated in
There were several simplifying assumptions employed in order to keep the model as simple as possible (limiting number of process parameters needed), while still providing results with limited uncertainty so that usefulness is maximized. The simplifying assumptions are tabulated in
Many of the assumptions (2, 3, 4, 5, 10) could be made due to the minimal effect on calculated system performance needed at the initial stages of design;
while for others (1, 8, 9, 10) more specificity regarding a certain configuration would be required and the model could be easily extended to handle the addition if required. The remaining assumptions (6, 7, 11) are functions of investment in maintenance of a plant that will come after operation begins.
Regarding boiler/evaporator performance, the value of the heat transferred, Qin, in the boiler was determined from the HTF inlet temperature (T7), flowrate, and an assumed boiler efficiency (a model parameter), effectively a boiler pinch point, where the pinch-point temperature is defined as the minimum temperature difference occurring in the heat exchanger. This occurs at the WF liquid saturation point in most cycles. The WF is assumed to be saturated liquid leaving the evaporator. The temperature of the WF exiting the condenser is assumed
Description | Model affected | |
---|---|---|
1 | Pre-heating, recuperation, cascading neglected | ORC Loop |
2 | Constant fluid flowrates | Solar loop, Cooling loop |
3 | Constant fluid specific heats over temperature range | Solar loop, ORC loop, Cooling loop |
4 | Collector tracking error neglected | Solar loop |
5 | Wind speed neglected | Solar loop |
6 | Soiling neglected (perfect mirror specularity) | Solar loop |
7 | All mirrors, reflectors and HCE tubes assumed unbroken and in good working order | Solar loop |
8 | Incident Angle Modifiers neglected | Solar loop |
9 | Balance of plant piping perfectly insulated | Solar loop, Cooling loop |
10 | Thermal inertia neglected | Solar loop, ORC loop, Cooling loop |
11 | Power plant availability due to maintenance neglected | System |
equivalent to the cooling water leaving the condenser (and confirmed through observation (
The HTF temperature at the boiler outlet was then determined from the constant mass flow rates of 6.14 kg/s and 1.849 kg/s (parameters) the heat exchanger efficiency, η B , and temperature rise in the evaporator, T 8 .
η B = Q i n , R 245 Q i n , H T F (1)
T 8 = T 7 − η B m O R C c p ( T 1 A − T 1 B ) R 245 m H T F c p (2)
T 3 = T 10 (3)
The solar loop incorporated a heat transfer model to calculate the rise in temperature as water flows through the solar panels. The model was a one dimensional steady-state energy balance of the cross section of the receiver that was modified from the model developed in the same manner as the Forristall heat transfer model for parabolic trough receivers originally implemented in Engineering Equation Solver (EES) [
The model takes into account the heat gained by the absorption of solar irradiation in the steel pipe and the glass tube. It also takes into account the convection, radiation and convection heat losses of the glass envelope.
To calculate the energy gain and temperature rise of the HTF through the
solar collectors, each SCA was discretized into receiver components. The inputs were the local DNI, and ambient temperature conditions. The cosine corrected DNI was calculated from the collector incidence angle in the manner presented by Marion and Dobbs for a one-axis tracker [
T 6 = ( q 3 , S O L A B S + 2 q 5 , S O L A B S − q 56 , C O N V − q 57 , R A D ) L m ˙ S L c p 5 + T 5 (4)
T 7 = ( q 3 , S O L A B S + 2 q 5 , S O L A B S − q 56 , C O N V − q 57 , R A D ) L m ˙ S L c p , W F 6 + T 6 (5)
Here, the radiative heat flux into the glass envelop (point 5 in
q 3 , S O L A B S = q s i η A B S α A B S (6)
q 5 , S O L A B S = q s i η E N V α E N V (7)
where α A B S is the absorptivity of the HCE selective coating, η E N V is the effective optical efficiency of the HCE envelope and α E N V is the absorptivity of the HCE glass envelope, all of which are input parameters. The effective optical efficiency of the HCE selective coating, η A B S , is taken as:
η A B S = 0.97 η E N V (8)
The incident radiation per unit length, q s i , to the HCE is:
q s i = D N I ∗ A L (9)
The heat loss of the element due to convection, q 56 , C O N V , is found from [
q 56 , C O N V = h 56 D 5 π ( T 5 − T A M B ) (10)
where the convective heat transfer coefficient, h 56 , is a function of the Nusselt number, N u D 5 , and the thermal conductance of air, K 56 :
h 56 = K 56 N u D 5 D 5 (11)
N u D 5 = [ 0.6 + ( 0.387 R a D 5 1 6 ) ( 1 + ( 0.599 P r 56 ) 9 16 ) 8 27 ] 2 (12)
P r 56 = υ 56 α 56 (13)
where R a D 5 is the Rayleigh number and P r 56 is the Prandtl number,
R a D 5 = 9.81 β ( T 5 , S T − T A M B ) D 5 3 α 56 υ 56 (14)
And,
T 56 = T 5 , S T + T a m b 2 (15)
β = 1 T 5 , S T + 273 (16)
Finally, the radiative heat loss is
q 57 , R A D = σ π D 5 ε 5 ( ( T 5 + 273 ) 4 − ( T 7 + 273 ) 4 ) (17)
where T7, the effective sky temperature is estimated as:
T 7 , S T = T A M B − 8 (18)
The ORC was modeled utilizing the four basic sections of a Rankine cycle (as shown in
P 1 = P h i g h (19)
T 1 = η B Q i n m ˙ O R C c p , H T F + T 4 (20)
h 1 = h @ P 1 & T 1 (21)
s 1 = s @ P 1 & T 1 (22)
In Section 2, the vapor undergoes isentropic expansion, producing mechanical work [
P 2 = P l o w (23)
s 2 = s 1 (24)
T 2 = T @ P 2 & s 2 (25)
h 2 , i d e a l = h @ P 2 & s 2 (26)
h 2 = h 1 − η t u r b ( h 1 − h 2 , i d e a l ) (27)
W ˙ t u r b = − m ˙ ( h 2 − h 1 ) (28)
W ˙ g e n = W ˙ t u r b η g e n (29)
Section 3 is isobaric heat removal from the system by heat transfer from the low-pressure WF vapor to the cooling water in an adiabatic counter-flow heat exchanger [
P 3 = P 2 (30)
T 3 = T 10 (31)
h 3 = h @ P 3 & T 3 (32)
s 3 = s @ P 3 & T 3 (33)
v 4 = v @ P 3 & T 3 (34)
In Section 4, the WF undergoes isentropic compression (addition of mechanical work) that raises the pressure of the WF to the desired working pressure of the boiler, P h i g h [
s 4 = s 3 (35)
P 4 = P h i g h (36)
v 4 = v s a t @ P 4 (37)
h 4 , i d e a l = h 3 + v 3 ( P 1 − P 2 ) (38)
h 4 = h 3 + h 4 , i d e a l − h 3 η p u m p (39)
T 4 = T @ s 4 & h 4 (40)
W ˙ p u m p = − m ˙ ( h 1 − h 4 ) (41)
The methodology used to model the process in the cooling loop is divided into two portions. The first section is the outlet of the cooling tower. In order to calculate the temperature of the cooling water exiting the cooling tower, T 9 , the wet bulb temperature, T w b and the efficiency of the cooling tower, η C T are used. The wet bulb temperature is the lower temperature limit of the outlet water from a cooling tower. To calculate the wet bulb temperature, an empirical model is employed [
T w b = T a m b ∗ a t a n ( 0.151977 ∗ H U M + 8.313659 ) + a t a n ( T a m b + H U M ) − a t a n ( H U M − 1.676331 ) + 0.00391838 ( H U M ) 3 2 ∗ a t a n ( 0.023101 ∗ H U M ) − 4.68035 (42)
T 9 = T 10 − η C T ( T 10 − T w b ) (43)
T 10 = Q o u t m ˙ C L c p w + T 9 (44)
Solar radiation measurements were taken onsite by a weather station consisting of a Kipp & Zonen SOLYS 2 Sun Tracker with CHP 1 pyreheliometer and CMP10 Pyranometers. The SOLYS 2 sun tracker provides fully automated year-round two-axis tracking of the position of the Sun with a pointing accuracy of less than 0.1 degrees. It has Baseline Surface Radiation Network (BSRN) levels of performance and reliability. Mounted on the SOLYS 2 are a CHP1 pyrheliometer which fully complies with the most current ISO and WMO performance criteria for First Class Normal Incidence pyrheliometer with a World Radiometric Reference (WRR) calibration certificate. For a first class pyrheliometer, the WMO limits maximum errors to 3% for hourly radiation totals. In the daily total an error of 2% is expected, because some response variations cancel each other out for longer integration periods. Kipp & Zonen, however anticipates maximum uncertainty of 2% for hourly totals and 1% for daily totals for the CHP 1 pyrheliometer [
The model was validated using data collected on several days throughout the years of 2015, 2016, and 2017 in order to have representation from each season affected by the local climate. The UL Lafayette START Lab is located in Crowley, Louisiana, about 20 miles west of Lafayette, with a latitude of 30˚13'27''N. The parabolic solar troughs are oriented in a north-south configuration, while tracking the sun from east to west. Measured inputs of local DNI, ambient temperature, and humidity were input into the model and the simulated results were compared to measured values of the system temperatures, thermal energy, electric power, and system efficiency. Temperatures were measured at the inlet and outlet of the collector field loop, the ORC evaporator, condenser, and turbine. A constant flow rate of 97.5 gpm, and 220 gpm were assumed for the Solar Loop and Cooling loop, respectively.
Data were generated for the thermal output of each SCA, both in terms of thermal energy (kWth) and in temperature rise (ΔT) and plotted versus the DNI over the course of a summer day and a winter day. Both experimental and modeled data were recorded in
greater deviation in the winter data is accounted for by larger radiative losses than accounted for in the model due to uninsulated piping in the balance of plant. In addition, IAMs for the site are not included which will be more pronounced in the winter season.
The collector model was then used to predict the collector thermal efficiency over a range of irradiance and HTF flowrate values (
η c o l l e c t o r = Q i n , c o l l D N I ∗ A (45)
where
Q i n , c o l l = m ˙ H T F C p Δ T (46)
The curves are presented in Figure. The efficiency drops as flow rate increases, which reduces the residence time for heat transfer. The efficiency also increases as DNI increases, due to the increase in intensity of the energy into the system.
The full data from a single summer day and a single winter data are presented in
The ORC model performance can be seen visually by plotting the HTF temperature exiting the boiler/evaporator and returning to the solar field, a measure of the heat gain into the system. The evaporator model performed well over the range of DNI values for both winter and summer days (
varying conditions (
The collector and power block models together produce system-level outputs and efficiencies. Values for the measured power, simulated power, and DNI are
plotted in
be integrated into the solar loop, this would smooth the energy input into the power block and the power block model would have a further reduction in error.
The results of the system analysis are summarized in
Based on the validated model, the annual performance of a theoretical system
could be modeled within the uncertainties found above. Typical meteorological year (TMY) data from the National Solar Radiation Database (NSRDB) was utilized as an input to the model with daily and monthly thermal outputs from the solar field and electric outputs from the power plant tabulated. The total thermal output was predicted to be 919 MWhr-thermal per annum, while the total electric output was predicted to be 48 MWhr-electric, an effective annual system efficiency. The plant was predicted to operate on 169 days based on the start-up
Model Error (% Difference) | ||||||
---|---|---|---|---|---|---|
Spring | Stnd. Dev. | Summer | Stnd. Dev. | Winter | Stnd. Dev. | |
Collector Thermal Power (kWth) | 11.65 | 5.23 | 10.46 | 37.05 | 13.8 | 25.5 |
Power Block Electric Power (kWe) | 10.3 | 5.06 | 11.46 | 3.90 | 15.34 | 4.26 |
Collector Efficiency | 8.3 | 15.34 | 9.74 | 4.63 | 13.4 | 4.7 |
System Efficiency | 7.55 | 0.67 | 9.4 | 0.42 | 13.8 | 0.73 |
criteria.
found to be 3.2% on an insolation-to-electric basis (
A numerical model of a small-scale parabolic trough organic Rankine cycle power plant has been presented with operational data for validation. A simplified model, with relatively few required parametric data for operation, can be useful in planning and optimization of small-scale plants. The addition of
validation data to the numerical model produces a quantifiable uncertainty, so that the usefulness of the model is increased. A simple Rankine cycle model generated results with relatively low uncertainties. The greatest error occurred in the solar field, where additional modeling focus should be applied, especially when storage strategies are to be considered in future work. A thermal buffer will level and smooth the input to the power block, reducing transient effects that the model generated but were not measured physically. There was greater
deviation in the seasonal winter data, accounted for by larger radiative losses than accounted for in the model in uninsulated areas of the balance of plant. IAMs for the site are not included in the model which will be more pronounced in the winter season. Negative deviation from the model is expected in both seasons due to ideal assumptions of specularity and tracking error. Transient effects and thermal inertia created significant discrepancies in the solar field data. These occurrences cannot be accurately modeled in the system model due to the fact that the model is in effectively steady state.
Overall, the model predicted the performance of the within acceptable limits for preliminary planning purposes and system optimization, yielding system errors between 10 and 15 percent. The errors can be primarily attributed to thermal inertia and transient changes in the measured data.
Future work includes the comparison of monthly and yearly experimental data to the model. Additional options will be included, such as variable flowrates in the collector field and updating to a transient model. Focus will be on the improvement of the solar loop heat transfer model without adding to complexity in required input parameters. Economic calculations will also be included for future plant planning. Case studies will be developed on the use of solar irradiance forecast for optimized operation strategies of solar thermal power plants.
This study was supported by Cleco Power, LLC. The original CSP installation was supported by Cleco Power, LLC, and the DOE through the Louisiana Department of Natural Resources and the Empower Louisiana―Renewable Energy Program, grant number RE-06.
The authors declare no conflicts of interest regarding the publication of this paper.
Raush, J.R., Ritter, K., Prilliman, M., Hebert, M., Pan, Z. and Chambers, T.L. (2018) Numerical Model and Performance Validation of a Small-Scale Concentrating Solar Thermal Power Plant in Louisiana. Journal of Power and Energy Engineering, 6, 112-140. https://doi.org/10.4236/jpee.2018.69011