Techno-Economic Analysis of a Solar Tower Power Plant with an Open Air Brayton Cycle and a Combined Cycle - A Simplified Calculation Method

Figure 1 provides a schematic representation of a concentrating solar tower power plant with an open air Brayton cycle. The air drawn from the atmosphere is compressed by a three stage inter-refrigerated compressor, preheated in the regenerator and sent into the receiver placed on top of the solar tower, from which it exits at high temperature. Afterwards, it is sent to the gas turbine connected to the electric generator, and before being discharged to the atmosphere, the air passes through the regenerator. A cooling tower is used to refrigerate the water used in the cooling circuit.

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Figure 1. Schematic representation of a solar tower power plant with an open air Brayton cycle

Figure 2 shows a concentrating solar tower plant with a combined cycle. It consists of a topping Brayton cycle, a heat recovery boiler and a bottoming Rankine cycle. The compressor sends the air directly into the receiver. The air at high temperatures drives the gas turbine. Afterwards, it is sent to a heat recovery steam generator, where superheated steam is produced and used to drive the steam turbine.

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Figure 2. Schematic representation of a solar tower power plant with a Brayton-Rankine combined cycle

In both systems, a constant turbine inlet temperature (TIT) equal to 1000℃ is considered, while the flow rate varies depending on the direct normal radiation (DNI). When the flow rate reaches a threshold value, it is kept constant as the DNI decreases. In order to not degrade excessively the isentropic efficiency of the compressor, the minimum air flow rate should not be lower than 60% of its nominal design value. This determines a reduction of the turbine inlet temperature, up to a minimum value of 600℃, for which the plant can still produce electricity.

The operation of the components of the two systems was simulated by the THERMOFLEX code [32], starting from the design conditions, summarized in Table 1 and Table 5 and then evaluating their performances in off-design conditions, by varying the inlet temperature of the air and the opening of the Inlet Guide Vanes (IGV) of the compressor, so as to vary the air flow rate.

Based on the results obtained, some correlations have been developed for the key variables, such as the air temperature at the compressor exit in the combined cycle plant (or at the regenerator exit in the Brayton cycle) and the thermodynamic efficiency of the gas and steam turbines in the combined cycle (or of the gas turbine in the Brayton cycle).

At low solar irradiance, the plants are operated at constant flow rate, the correlations developed concerned the thermal power transferred to the fluid in the receiver, the air temperature at the inlet of the turbine, and the thermodynamic efficiency of the turbines.

All these correlations, along with a simulation model of the heliostat field and the tower receiver, were implemented in a Matlab calculation algorithm, called TERSOLTO (thermodynamic solar tower) in the B and CC versions, respectively valid for the Brayton cycle and the combined cycle.

Through TERSOLTO, starting from the values of direct solar irradiance, air temperature and humidity, the hourly values of the electrical power generated by the plants, the average hourly and annual values of the efficiency and the electricity produced in a year can be calculated.

In the following paragraphs the models and correlations used are described in detail.

2.1 Calculation model of the Brayton Cycle

Table 1 provides the main input data for the Brayton cycle: the rated electrical power, the atmospheric air temperature, the DNI design value, the inlet temperature to the gas turbine, the pressure ratio of the compressor and the turbine.

Once defined the type of system and characteristics of the various components, the THERMOFLEX code considers the receiver as a generic heat generator, and allows to calculate the nominal air flow rate. Hence, it is possible to obtain the desired net electrical power, the thermal power supplied from the receiver to the fluid, the gross and net electrical power supplied from the gas turbine, the net thermodynamic efficiency of the cycle and many other variables of interest.

By means of the THERMOFLEX code, after determining the above mentioned variables in design conditions, calculations in off-design conditions were performed, considering: three different values of the atmospheric air temperature of 0℃, 25℃ and 50℃; three opening values of the IGV, of 100%, 80% and 60%; and maintaining the turbine inlet temperature constant at 1000℃.

Table 1. Design data of Air Brayton Solar Tower Power Plant located in Almeria

Table 2. Influence of IGV aperture and of inlet air temperature on the performance of the Brayton cycle plant

The results are summarized in Table 2. The values of air flow rate, air temperature at the regenerator exit, the heat transferred from the receiver to the fluid, the net efficiency of the power block and the net electrical power plant production, are provided for different outside air temperatures and IGV.

Using the values shown in Table 2, by means of the DataFit program developed by Oakdale Engineering [33], correlations for the air temperature at the regenerator exit $T_{o r}$ and of the net efficiency of the gas turbine $\eta_{g t}$, as functions of a parameter x were developed; x is defined as the ratio between the air mass flow rate in the actual conditions and the nominal mass flow rate.

for $T_{A}=0^{\circ} \mathrm{C}$,

$T_{o r}=a+b \cdot x^{3}+c / x$

with $a=459.561 ; \mathrm{b}=-12.78871 ;$ $\mathrm{c}=43.25952$     (1)

$\eta_{g t}=a+b \cdot x+c x^{0.5}$

with $a=-0.49634 ; \mathrm{b}=-0.85800 ; \mathrm{c}=1.76964$     (2)

for $T_{A}=25^{\circ} \mathrm{C}$,

$T_{o r}=a+b \cdot x^{3}+c / x^{1.5}$

with a $a=486.42211 ; \mathrm{b}=-17.80170 ; \mathrm{c}=22.19127$     (3)

$\eta_{g t}=a+b \cdot x+c x^{0.5}$

with $a=-0.550466 ; \mathrm{b}=-0.895711 ; \mathrm{c}=1.85013$     (4)

for $T_{A}=50^{\circ} \mathrm{C}$,

$T_{o r}=a+b \cdot x^{3}+c / x$

with $\mathrm{a}=462.57941 ; \mathrm{b}=-13.297368 ; \mathrm{c}=43.1433$     (5)

$\eta_{g t}=a+b \cdot x+c \cdot x^{0.5}$

with $\mathrm{a}=-0.61494 ; \mathrm{b}=-0.94732 ; \mathrm{c}=1.94717$     (6)

The proposed correlations have a correlation coefficient of 99.99% and a maximum error of less than 0.5%.

They have been implemented in the TERSOLTO-B algorithm. Knowing the meteorological data of the selected location (outside air temperature, relative humidity, DNI, etc.), the algorithm allows to determine, at any time, the flow rate value (m), which ensures an outlet temperature of the receiver of 1000℃, with an iterative method using the heat balance equation between the solar thermal power supplied by the field of heliostats and the heat received by the fluid in the receiver.

The heat balance equation is:

$\operatorname{SM} \mathrm{A}_{e}$ DNI $\eta_{\text {opt}}-P_{\text {loss}}=\mathrm{m}\left(\mathrm{H}\left(\mathrm{T}_{o R}\right)-\mathrm{H}\left(T_{\text {or}}\right)\right)$     (7)

where, SM is the solar multiple, $\mathrm{A}_{e}$ is the total area of the heliostats, $\eta_{o p t}$ [34] is the optical efficiency of the heliostats field, taking into account the reflection coefficient of the mirrors, the transmissivity of the atmosphere, the cosine, shadowing, blocking, and spillage effects of the individual heliostats and the absorption coefficient of the receiver, $P_{\text {loss}}$ is the sum of the radiative and the convection losses of the receiver, m is the fluid flow rate, $\mathrm{H}\left(\mathrm{T}_{o R}\right)$ is the enthalpy of the fluid at the outlet of the receiver and $\mathrm{H}\left(T_{o r}\right)$ is the enthalpy of the fluid at the outlet of the regenerator.

The radiative loss $P_{\text {loss}}$ was evaluated by the equation:

$P_{r a d}=A_{R} \varepsilon_{R} \sigma\left(T_{R}^{4}-T_{A}^{4}\right)$     (8)

where, $A_{R}$ is the area of the receiver, $\varepsilon_{R}$ is the emissivity of the receiver, $\sigma$ is the Stephan-Boltzmann constant, $T_{R}$ is the temperature of the receiver and $T_{A}$ is the temperature of atmospheric air. For simplicity, it is assumed that the temperature of the receiver is uniform and equal to the turbine inlet temperature.

The convective loss is instead calculated using the equation:

$P_{\text {conv}}=h A_{R}\left(T_{R}-T_{A}\right)$     (9)

where, h is the convective heat transfer coefficient between the receiver and the outside air. Normally, for high temperatures of the receiver, the convective loss is negligible compared to the radiative one.

Starting from the initial value of x=1 (valid in design conditions), at the considered hour, for the outside air temperature value an initial value of the outlet temperature from the regenerator is calculated by interpolation, using Eqns. (1), (3) and (5). Considering the quality of moist air, the enthalpies $\mathrm{H}\left(\mathrm{T}_{o R}\right)$ and $\mathrm{H}\left(\mathrm{T}_{o r}\right)$ are calculated and, by Eq. (7), an initial value for the air flow rate and the parameter x are obtained. This procedure is repeated until x reaches convergence and for the final value of x the gas turbine efficiency and the electrical power delivered by the plant are determined.

When the thermal power transmitted from the receiver to the Power Block is larger than 136 MW, 10% higher than the nominal design value, part of the heliostats is supposed to defocus, so as not to exceed this maximum power value. Hence, the maximum value of the dimensionless parameter x is 1.1.

When the x value is lower than 0.6 (60% of the nominal flow rate), for low values of DNI, it is assumed, as already stated, that the flow rate is kept constant, and the plant operates with a variable TIT up to a minimum value of 600℃.

To evaluate the TIT under these conditions, further calculations have been carried out by the THERMOFLEX code, maintaining the fluid flow rate constant and varying the TIT between 1000℃ and 600℃. From the data obtained, the following correlations for the TIT (Q) and the gas turbine efficiency $\eta_{g t}$ (TIT) have been determined:

for $T_{A}=0^{\circ} \mathrm{C}$,

$T I T=a+b \cdot Q^{0.5}+c / Q$

with $\mathrm{a}=317.763 ; \mathrm{b}=82.5716 ; \mathrm{c}=203.540$     (10)

$\eta_{g t}=a+b \cdot T I T^{0.5}+c / T I T^{2}$

with $a=0.63151 ; \mathrm{b}=-2.70358 \cdot 10^{-3} ;$ $\mathrm{c}=-187992.161$     (11)

for $T_{A}=25^{\circ} \mathrm{C}$,

$T I T=a+b \cdot Q^{0.5}+c / Q$

with $a=318,95934 ; \mathrm{b}=82.03883 ; \mathrm{c}=198.48652$     (12)

$\begin{aligned} \eta_{g t} &=a \cdot T I T^{3}+b \cdot T I T^{2}+c \cdot T I T+d \\ \text { with } \mathrm{a} &=3.7425 \cdot 10^{-9} ; \mathrm{b}=-1.0478 \cdot 10^{-5} \\ & \mathrm{c}=1.0245 \cdot 10^{-2} ; \mathrm{d}=-3.1633 \end{aligned}$     (13)

for $T_{A}=50^{\circ} \mathrm{C}$,

$T I T=a+\mathrm{b} \cdot Q^{0.5}+c / Q$

with $a=317.92342 ; \mathrm{b}=82.0407 ; \mathrm{c}=$$209.2899 ;$     (14)

$\eta_{g t}=a+b \cdot T I T^{0.5}+c / T I T^{2}$

with $a=0.458811 ; \mathrm{b}=3.118367 \cdot 10^{-11}$; $\mathrm{c}=209.2899$     (15)

In the above equations Q is the thermal power transferred to the fluid in the receiver.

All correlations have a correlation coefficient of 99.99% and a maximum error of less than 0.5%.

The calculation of the total area of the heliostats $A_{e}$, of the height of the tower, of the size of the receiver, of the average optical efficiency of the heliostats $\eta_{\text {opt}}$, see Eq. (7), has been carried out by the DELSOL-3 code [35], assuming a configuration of the Surround-field type and an outer cylindrical receiver, using an optimization procedure of the field-receiver system performance. For the value of SM = 1, in the design conditions, summarized in Table 1, the following values were obtained: an area of the heliostats field of 302,499 $m^{2}$, a tower height of 102.5 m, a 6.615 m receiver diameter and a receiver height of 8.818 m.

The values of the optical efficiency, calculated by DELSOL-3 code for SM 1.2, as a function of the zenith and azimuth angle of the sun, are given in Table 3.

Table 3. Optical efficiency of the solar field of the Brayton Cycle Plant for SM=1.2

The optical performance of the heliostats can be evaluated at any time of the day and month for interpolation. This calculation is made by the TERSOLTO program.

Figures 3-5 show, the time trends of DNI, of optical efficiency of the heliostats field and of net electrical power, for a solar multiple of 1.2, for a clear day in June and an intermediate day in December.

Table 4 shows the annual electricity supplied from the plant, the annual thermal energy supplied to the fluid, the average annual efficiency of field-receiver system, the average efficiency of the power block, the global efficiency of the plant and the load factor CF (percentage of equivalent hours of working at nominal power compared to the total number of hours available in a year), as a function of solar multiple SM.

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Figure 3. DNI as a function of time for a clear day in June and an intermediate day in December in Almeria

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Figure 4. Heliostat optical efficiency as a function of the time in the Brayton Cycle

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Figure 5. Electrical Power as a function of time in the Brayton Cycle plant

Table 4. Annual data of Brayton Cycle Plant

2.2 Calculation Model of the combined cycle

Like for the open air Brayton cycle, a similar analysis has been performed for the solar tower power plant with a combined cycle. Table 5 summarizes the design data.

Table 6 provides the values of the air flow rate $(\mathrm{m}),$ of the air temperature at compressor outlet, of the thermal power(Q), of the gas turbine $\left(\eta_{g t}\right)$ and steam turbine efficiencies $\left(\eta_{s t}\right),$ of the net efficiency of the power block $\left(\eta_{P B}\right)$ and of the net electrical power output from the plant, for different outside air temperature and IGV.

By means of the THERMOFLEX code, the following correlations for the exit temperature from the compressor $T_{\text {oc }}$ for the gas turbine efficiency $\eta_{g t}$ and the steam turbine efficiency $\eta_{s t}$ have been developed, considering a variable air flow rate:

for $T_{A}=0^{\circ} \mathrm{C}$,

$T_{o c}=a+\mathrm{b} \cdot x^{3}$

with $\mathrm{a}=246.5919 ; \mathrm{b}=90.25454 ;$     (16)

$\eta_{g t}=a+b / x^{2}$

with $\mathrm{a}=0.308604 ; \mathrm{b}=-3.373074 \cdot 10^{-2}$     (17)

$\eta_{s t}=a+b / x$

with $\mathrm{a}=0.103356 ; \mathrm{b}=-6.824015 \cdot 10^{-2} ;$     (18)

for $T_{A}=25^{\circ} \mathrm{C}$,

$T_{o c}=a \cdot b^{x}$

with $\mathrm{a}=204.3563 ; \mathrm{b}=1.85103 ;$     (19)

$\eta_{g t}=a+b / x^{2}$

with $\mathrm{a}=0.300301 ; \mathrm{b}=-3.125406 \cdot 10^{-2};$     (20)

$\eta_{s t}=a \cdot x^{b}$

with $\mathrm{a}=0.182133 ; \mathrm{b}=-0.414489 ;$     (21)

Table 5. Design data of the Solar Tower Power Plant with Combined Cycle located in Almeria

Table 6. Influence of IGV aperture and of inlet air temperature on the performance of the CC plant

for $T_{A}=50^{\circ} \mathrm{C}$,

$T_{o c}=a \cdot b^{x}$

with a $=255.1888 ; \mathrm{b}=1.60495$     (22)

$\eta_{g t}=a+b / x$

with $\mathrm{a}=0.38281 ; \mathrm{b}=-0.112634$     (23)

$\begin{array}{c}\eta_{s t}=a \cdot b^{x} \\ \text { with } \mathrm{a}=0.347898 ; \mathrm{b}=-0.545025\end{array}$     (24)

For a constant flow rate operation and variable TIT the following correlations were obtained:

for $T_{A}=0^{\circ} C$,

$T I T=a \cdot Q^{3}+\cdot Q^{2}+c \cdot Q+d$

with $a=5.898722 \cdot 10^{-5} ; \mathrm{b}=-2.019249 \cdot 10^{-2}$

$\mathrm{c}=10.918839 ; \mathrm{d}=190.248464$     (25)

$\eta_{g t}=a+b \cdot T I T^{0.5}+c / T I T^{1.5}$

with $a=0.326549 ; \mathrm{b}=-1.445094 \cdot 10^{-7} ;$

$\mathrm{c}=-3228.2688 ;$     (26)

$\eta_{s t}=a \cdot T I T^{3}+b \cdot T I T^{2}+c \cdot T I T+d$

with $a=8.33333 \cdot 10^{-11} ; b=-6.214285 \cdot 10^{-7} ;$

$c=10.918839 \cdot 10^{-3} ; d=-0.296885$     (27)

for $T_{A}=25^{\circ} \mathrm{C}$,

$T I T=a \cdot Q^{3}+b \cdot Q^{2}+c \cdot Q+d$

with $a=7.86633 \cdot 10^{-5} ; b=-2.38838 \cdot 10^{-2}$;

$c=11.733322 ; \mathrm{d}=214.908106$     (28)

$\eta_{g t}=a+b \cdot T I T+c / T I T^{1.5}$

with a $=0.323386 ; \mathrm{b}=-7.309416 \cdot 10^{-6} ;$

$\mathrm{c}=-3214.9926$     (29)

$\eta_{s t}=a+b \cdot T I T^{2}+c \cdot T I T^{0.5}$

with a $=-0.480034 ; \mathrm{b}=-1.443485 \cdot 10^{-7} ;$

$\mathrm{c}=2.629234 \cdot 10^{-2}$     (30)

for $T_{A}=50^{\circ} \mathrm{C}$,

$T I T=a+b \cdot x^{0.5}+c / x^{0.5}$

with $a=-1013.990342 ; \mathrm{b}=205.346943 ;$

$\mathrm{c}=2663.537571$     (31)

$\eta_{g t}=a+b \cdot T I T^{0.5}+c / T I T^{2}$

with a $=0.147127 ; \mathrm{b}=3.3784093 \cdot 10^{-3}$;

$\mathrm{c}=-66915.18$     (32)

$\eta_{s t}=a \cdot T I T^{2}+b \cdot T I T+c$

with $a=-0.0000003 ; \mathrm{b}=-6.99999 \cdot 10^{-4} ; \mathrm{c}=-0.149$     (33)

All above correlations have a correlation coefficient of 99.99% and a maximum error less than 0.5%.

The maximum thermal power transmitted from the receiver to the power block, in this plant, is 122 MW.

Using DELSOL-3 code, the total area of the heliostats $A_{e}$, for SM = 1, in the design conditions of Table 5, resulted to be 273,784 $m^{2}$; the height of the tower and the size of the receiver resulted equal to those of the Brayton cycle plant.

The values of the optical efficiency, calculated by DELSOL-3 code for SM = 1.2, as a function of the zenith and azimuth angle of the sun, are given in Table 7.

Table 7. Optical efficiency of the solar field of the Combined Cycle Plant for SM=1.2 as a function of sun zenith and azimuth angles

Figures 6-7 show the optical efficiency of the heliostats field and the net electrical power as functions of time for the same value of the solar multiple, for a clear day in June and an intermediate day in December.

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Figure 6. Heliostat optical efficiency as a function of time in the Combined Cycle plant

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Figure 7. Electrical power as a function of time in the Combined Cycle plant

Table 8 shows the annual electricity $\left(E_{e l}\right)$ supplied by the plant and the thermal energy (Q) supplied to the fluid, the average annual values of the field-receiver system efficiency $\left(\eta_{F R}\right),$ the efficiency of the power block $\left(\eta_{P B}\right),$ the global efficiency $\left(\eta_{P}\right)$ and the capacity factor CF as functions of the solar multiple SM.

Table 8. Annual data of CC Plant

To establish the economic convenience of the two solar plants, the calculation of the levelized cost of energy LCOE ($/kWh) was carried out, utilizing the NREL algorithm [37].

LCOE is defined as [37, 38]:

$L C O E=\frac{\text {Capital cost} \cdot \mathrm{CRF}+\text {Fixed } \text { O&M cost }}{8760 \cdot \mathrm{CF}}$$+ Variable O\&M Cost$     (34)

Being

$C R F=\frac{i(1+i)^{n}}{(1+i)^{n}-1}$     (35)

In Eq. (34) Capital Cost is the unit power cost (\$/kW) of the plant, Fixed O&M Cost represents the fixed operation and maintenance cost in a year (\$/kWy), Variable O&M Cost is the variable operation and maintenance cost (\$/kWh), CF is the capacity factor and 8760 is the number of hours in a year.

In Eq. (35) i is the discount rate and n the lifetime of the plant in years.

The values of above data assumed in our calculations, with the exception of the Capital Cost, are reported in Table 10.

Table 10. Cost data for the economic analysis

Table 11. Costs of Brayton Cycle Plant and LCOE

Table 12. Costs of CC Plant and LCOE

Table 13. Costs of Molten Salts Plant and LCOE

Table 11 shows the costs for the ground, the heliostats, the receiver, the tower and the total cost, the Capital Cost and the LCOE values, for the Brayton plant, at varying of solar multiple, evaluated by Eq. (34) and (35).

Table 12 reports the same data for the combined cycle plant, while Table 13 refers to the molten salts reference plant.

To obtain the Capital Cost values, the total costs of the plants were obtained as the sum of the cost of the ground, of the heliostats, the price of the receiver and of the power block.

The following assumptions were made [39, 40]:

Occupied ground area: $(\left.A_{e}=1.3+0.18\right) \mathrm{km}^{2}$  

Ground cost (land cost and construction costs for building and roads): $25.3 \$ / m^{2}$ The tower cost (\$) was calculated by the following formula:

$C_{T}=552,000 \cdot e^{H / 100}$     (36)

where, H is the height of the tower in meters.

Power Block costs:

• 850 \$/kW (600 \$/kW + 250 \$/kW of balance of the plant) for the Brayton cycle [39];
• 1500 \$/kW (1000 \$/kW+ 500 \$/kW of balance of the plant) for the Combined Cycle plant [40, 41];
• 940 \$/kW (590\$/kW+ 350 \$/kW of balance of the plant) for the Molten salts plant [36].

A calculation method was developed for the design and the estimation of the annual performance of two 50 MWe concentrating solar tower power plants that use atmospheric air as heat transfer fluid. In the first plant the air evolves in an open Brayton cycle; the second plant is a combined cycle. The annual performance of the two systems has been estimated, in terms of electricity, average annual efficiency of the heliostats field-receiver system, efficiency of the thermodynamic cycle and of the entire plant, comparing these parameters with those of a plant with molten salts of the same nominal power output. The technical-economic performance of the two proposed systems is superior to molten salt systems, currently widely established on a global scale. In fact, the specific annual electrical energy (per square meter of heliostat) is, in the Brayton cycle, 11.5% higher than that obtained with the system using molten salts, while in the combined cycle plant an increase of 38% was achieved. The cost of electricity, in terms of LCOE, amounted to 11.9 cent\$/kWh for the Brayton cycle, to 12.1 cent\$/kWh for combined cycle, against the value of 14 cent\$/kWh for the reference molten salts plant, with savings of 15% and 13.6%.