National Renewable Energy Laboratory 

Innovation for Our Energy Future 

A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 

Nexant Parabolic Trough Solar 

Power Plant Systems Analysis 

Task 2: Comparison of Wet and Dry 

Rankine Cycle Heat Rejection 

January 20, 2005 – December 31, 2005 

B. Kelly 

Nexant, Inc. 

San Francisco, California 

Subcontract Report 

NREL/SR-550-40163 

July 2006 
Nexant Parabolic Trough Solar 

Power Plant Systems Analysis 

Task 2: Comparison of Wet and Dry 

Rankine Cycle Heat Rejection 

January 20, 2005 – December 31, 2005 

B. Kelly 

Nexant, Inc. 

San Francisco, California 

NREL Technical Monitor: H. Price 

Prepared under Subcontract No. LDC-5-55014-01 

Subcontract Report 

NREL/SR-550-40163 

July 2006 

National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393 

303-275-3000 • www.nrel.gov 

Operated for the U.S. Department of Energy 

Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337
This publication was reproduced from the best available copy 

Submitted by the subcontractor and received no editorial review at NREL

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Contents 

1. Introduction............................................................................................................................................ 1 

2. Dry Heat Rejection ................................................................................................................................ 3 

2.1 Rankine Cycle.................................................................................................................................. 3 

2.2 Air Cooled Condenser Sizes ............................................................................................................ 3 

2.3 Dry Bulb Temperature Distribution................................................................................................. 3 

2.4 Parametric Studies ........................................................................................................................... 6 

2.5 Additional GateCycle Calculations.................................................................................................. 9 

3. Wet Heat Rejection.............................................................................................................................. 11 

3.1 Rankine Cycle................................................................................................................................ 11 

3.2 Wet Cooling Tower Capacity ........................................................................................................ 11 

3.3 Annual Performance Calculations ................................................................................................. 13 

4. Annual Plant Performance ................................................................................................................... 15 

4.1 Dry Heat Rejection ........................................................................................................................ 15 

4.2 Wet Heat Rejection........................................................................................................................ 17 

4.3 Annual Performance Comparison.................................................................................................. 17 

5. Economic Analysis .............................................................................................................................. 19 

6. References............................................................................................................................................ 22 

- - iii
Task 2 

Wet/Dry Heat Rejection Analysis 

Task 2 

Comparison of Wet and Dry Rankine Cycle Heat Rejection 

1. Introduction 

The efficiency of a Rankine cycle is defined, in large part, by the pressure and the temperature of the steam 

both entering and leaving the turbine. The cycle efficiency can be improved either by raising the pressure 

and the temperature at the inlet to the turbine, or decreasing the pressure and the temperature at the outlet. 

The steam conditions at the turbine outlet are defined by the temperature at which the steam is condensed 

and the latent heat of vaporization can be transferred to the environment. The lowest ambient temperature 

available is the wet bulb temperature; thus, most power plants use an evaporation process to provide the 

cooling water source for the condenser. However, the principal heat transfer mechanism in a wet cooling 

tower is evaporation. As a result, approximately 1 pound of water must be evaporated for each pound of 

steam condensed, and the water consumption in a large power plant can be significant. For example, an 

80 MWe parabolic trough solar plant, operating with a capacity factor of 27 percent, will consume about 

725,000 tons of water per year. 

For sites which have a limited supply of water, heat can be rejected to the environment by condensing 

turbine exhaust steam at the dry bulb, rather than the wet bulb, temperature. For desert sites, design values 

for the dry bulb and the wet bulb temperatures are about 104 °F and 68 °F, respectively. Compared with a 

turbine inlet temperature of 703 °F, a difference of 36 °F in the steam condensation temperature does not 

appear significant. However, the work performed in the turbine expansion process is defined as ∫ν dP, where 

ν is the fluid specific volume and dP is the change in pressure. With a turbine inlet pressure of 1,450 lbf/in2

, 

and an outlet pressure of 1.07 lbf/in2

 defined by a condensation temperature of 104 °F, a theoretical overall 

pressure ratio of 1,360 can be achieved. However, an outlet pressure of 0.34 lbf/in2

, defined by a 

condensation temperature of 68 °F, results in an overall pressure ratio of 4,260. Granted, the theoretical 

pressure ratios cannot be achieved due to economic limits on heat exchange area. Nonetheless, it is clear that 

small changes in the condensation temperature can have a large influence on the expansion ratio, and 

therefore the work performed by the steam. 

An economic analysis was conducted to determine 1) the preferred design conditions for a dry cooling tower, 

and 2) the anticipated increase in the levelized cost of energy due the selection of a dry, rather than a wet, 

cooling tower. For the purposes of the analysis, the power plant was assumed to be an 80 MWe parabolic 

trough facility located near Barstow, California. The study was conducted through the following steps: 

• A model of an 80 MWe Rankine cycle using an air cooled condenser was developed using the GateCycle 

program (Reference 1). Six models were developed, with initial temperature differences between 24 °F 

and 49 °F. (Initial temperature difference is defined as Dry bulb temperature - Steam condensation 

temperature.) For each of the six models, estimates of turbine output and cooling fan power demand were 

made for dry bulb temperatures between 40 °F and 130 °F. 

- - 1
Task 2 

Wet/Dry Heat Rejection Analysis 

• A histogram of the hourly dry bulb temperatures, at direct normal radiation values above 250 W/m2

, was 

assembled for Barstow. For each of the six models, the predicted turbine output and fan power demand at 

each of the 21 ambient temperatures in the histogram was multiplied by the number of hours at each 

temperature, and the outputs summed to estimate the annual plant performance. 

• Capital cost estimates for the air cooled condenser in each of the six models were developed. The relative 

economic benefits among the six models were plotted for a range of energy values between $60/MWhe 

and $140/MWhe to determine the sensitivity of the preferred initial temperature difference on the selling 

price of electric energy. 

• A second model of an 80 MWe Rankine cycle, this using a wet cooling tower, was developed with the 

GateCycle program. One case was developed, with a condenser cooling water temperature range of 22 °F 

and a cooling tower approach to the wet bulb temperature of 12 °F. 

• A histogram of the hourly dry bulb temperatures and coincident relative humidities, at direct normal 

radiation values above 250 W/m2

, was assembled for Barstow. From these data, an equation relating dry 

bulb temperature and annual average relative humidity was developed. 

• Estimates of turbine output, cooling fan power, and water consumption for the wet heat rejection case 

were made for combinations of dry bulb temperatures between 40 °F and 130 °F and the corresponding 

relative humidities. From this, equations for estimating Rankine cycle performance were developed for 

use in the Excelergy computer program. The annual net electric output and water consumption of the 

plant were then estimated. 

• Estimates of the capital costs and the operating costs for the six plants with a dry heat rejection system, 

and the one plant with the wet heat rejection system, were developed. The costs were used as inputs to an 

annual cash flow analysis to determine the levelized energy costs for the seven cases. 

• For the dry heat rejection case with the lowest energy cost, additional GateCycle calculations were 

performed to estimate the turbine output if the maximum exhaust pressure was limited to 8 in. HgA 

during those periods in which the dry bulb temperature exceeded 110 °F. Equations of turbine output and 

fan power demand as a function of dry bulb temperature were incorporated in the Excelergy computer 

program, from which the annual net electric output and levelized energy cost were estimated. 

- - 2
- - 3

A list of the hourly dry bulb temperatures was derived from the Excelergy weather file DAG_TMY2_hr. 

The list was sorted into a series of 21 bins representing 5 °F increments in temperature between 20 °F and 

125 °F. The summations were limited to those hours in which the plant was in operation by selecting 

temperatures only for direct normal radiation values above 250 W/m2

. The resulting histogram is shown in 

Figure 2. 

2.3 Dry Bulb Temperature Distribution 

The design parameters for the heat exchangers are listed in Table 1, and the calculated areas and fan power 

requirements are shown in Table 2. As expected, both the heat transfer areas and the fan power requirements 

are inversely proportional to the initial temperature difference. 

Air cooled condenser heat transfer areas were calculated for the 6 initial temperature differences of 24 °F, 

29 °F, 34 °F, 39 °F, 44 °F, and 49 °F. The calculations were based on a dry bulb temperature of 106 °F, 

which is not exceed for all but 1 percent of the hours each year at Barstow. An allowance for subcooling the 

water leaving the condenser by 2 °F is provided to ensure the flow to the condensate pump is single-phase. 

2.2 Air Cooled Condenser Sizes 

Task 2

Wet/Dry Heat Rejection Analysis

2. Dry Heat Rejection 

The procedure for determining the performance and the operating cost for the air cooled condenser in a plant 

with dry heat rejection is outlined below. 

2.1 Rankine Cycle 

The Rankine cycle design closely followed that developed by Fichtner for the 55 MWe AndaSol project in 

Spain. The cycle is a conventional, single reheat design with 5 closed and 1 open extraction feedwater 

heaters. The live steam pressure and temperature are 1,450 lbf/in2

 and 703 °F, respectively, and the reheat 

steam temperature is 703 °F. The GateCycle flow diagram is shown in Figure 1. 

Cold and hot reheat steam pressures, feedwater heater extraction pressures, feedwater heater terminal 

temperature differences, and feedwater heater drain cooler approach temperatures were taken from the 

Fichtner flow diagram. Pressure losses in the steam lines to the feedwater heaters were set to zero, as 

implied in the Fichtner diagram. The condenser pressure was set to 1.23 lbf/in2

, or 2.5 in. HgA. 

Turbine expansion efficiencies, and the required live and reheat steam flow rates to achieve a gross output of 

88.0 MWe, were calculated by GateCycle. Simultaneously, the low pressure turbine exhaust loss was 

adjusted manually to yield a gross cycle efficiency of 0.377. 
W

- 4 - 

MODEL:CASE:POWER:HR:EFF:

80PTDC80PTDC 87.99 0.00 0.00

ST1

CN

FWH4

FDWPMP

ST2

FWH5

485.59 79259

466.421206.7

P T

W H

202.91 34863

664.711356.0

P T

W H

DA1 FWH0

FWH1

 3.26

 17100

144.701053.7

P T

W H

IPST

268.30

675690

407.261163.0

P T

W H

 89.65

 34037

489.451275.0

P T

W H

 75.00

606790

454.141258.8

P T

W H

FWH2

 44.11

 33106

361.141216.5

P T

W H

 16.93

 42516

219.231149.8

P T

W H

 25.00

4.95E6

1500.0369.63

P T

W H

 25.00

4.95E6

1084.2256.81

P T

W H

VRHTR

VSUHTR

STMGEN

V2

 89.65

 34037

489.451275.0

P T

W H

 89.65

770434

320.02290.41

P T

W H

 3.4741Exh loss

1460.1

770434

455.03436.39

P T

W H

135.00

622775

137.50105.76

P T

W H

1470.1

770434

374.04348.99

P T

W H

1450.5

754948

703.401294.8

P T

W H

239.29

675690

703.401373.9

P T

W H

S4

S7

S8

S11

S12

S15

S16

S26

S27

S28

S32

S33

S1

S18

S19

S22

S30

S6

S13

S14

S3

S31

S21 S39

S25

S38

88 MWe Rankine Cycle with Dry Heat Rejection 

Figure 1 GateCycle Flow Diagram 
Task 2 

Wet/Dry Heat Rejection Analysis 

Table 1 

Air Cooled Condenser Design Parameters 

Parameter Value

 Condenser pressure, in. HgA 2.5 

 Tubes 

 - Diameter, in. 1.0 

 - Wall thickness, in. 0.05 

 - Arrangement Staggered 

 - Rows perpendicular to air flow 3 

 Fins 

 - Type Round 

 - Diameter, in. 2.74 

 - Thickness, in. 0.04 

 - Fins per inch, each 9 

 Air velocity, ft/sec 11.5 

 Overall heat transfer coefficient, Btu/hr-ft2-F 7.79 1

 Exit subcooling, °F 2 

Note 1: Based on sum of outside tube surface area and fin area 

Table 2 

Air Cooled Condenser Surface Areas and Fan Power 

 Initial temperature Heat transfer Total fan 

difference, °F area 1, ft2 power, kWe

 24 4,378,469 4,561 

 29 3,596,010 3,752 

 34 3,046,976 3,181 

 39 2,644,881 2,751 

 44 2,325,841 2,430 

 49 2,078,986 2,167 

Note 1: Sum of outside tube surface area and fin area 

- 5 - 
- 6 - 

For each of the air cooled condenser areas listed in Table 2, the performance of the turbine was modeled for 

a series of dry bulb temperatures in the range of 40 °F to 130 °F. From this, equations were developed for 

estimating turbine output as a function of the dry bulb temperature. Gross turbine outputs and fan power 

demands were then calculated for each of the 21 temperature bins. The gross power outputs and the fan 

power demands were multiplied by the hours in each bin, and then summed over the year to estimate the 

annual gross output, the annual fan energy demand, and the net plant output. The results are shown in 

Table 3. 

2.4 Parametric Studies 

The line labeled “Net incremental output, MWhe” is the net output compared to the net output at a selected 

reference initial temperature difference of 44 °F. The line labeled “Allowable incremental capital cost, $” is 

calculated as follows: 

The gross output increases uniformly as the initial temperature difference decreases. However, the highest 

net output occurs with an initial temperature difference of 29 °F; the incremental increase in the fan energy 

demand at 24 °F compared to 29 °F is higher than the incremental increase in gross output. 

0

50

100

150

200

250

300

350

400

450

500

82 87 92 97 102 107 112

o

F

Annual Period, hours 

27 32 37 42 47 52 57 62 67 72 77

Dry Bulb Temperature, 

Figure 2 Dry Bulb Temperature Distribution for Barstow, California 

rate charge Fixed

output, lincrementa (Net MWhe)(Ene $/MWhe) value,rgy 

Task 2

Wet/Dry Heat Rejection Analysis
W

- 7 - 

Table 3 

Air Cooled Condenser Parametric Studies 
Task 2 

Wet/Dry Heat Rejection Analysis 

For the purposes of the study, a fixed charge rate of 0.15 has been assumed. 

The line labeled “Condenser cost, $” is derived from the data shown in Figure 4 (Reference 2). 

y = 79.09605x2 - 8870.05650x + 322033

$70,000

$90,000

$110,000

$130,000

$150,000

$170,000

$190,000

20 25 30 35 40 45 50 55 60

Initial Temperature Difference, o

F

Unit ACC Cost, $/MWt

Figure 4 Unit Air Cooled Condenser Cost as a Function of Initial Temperature Difference 

The “Incremental capital cost, $” is the capital cost of the condenser compared to the capital cost of the 

condenser at the selected reference initial temperature difference of 44 °F. The “Net cost benefit” is the 

incremental capital cost minus the allowable incremental capital cost. 

The results for the six initial temperature differences, at each of five energy values between $60/MWhe and 

$140/MWhe, are illustrated in Figure 5. The ordinate locations of the curves are arbitrary since the adoption 

of a reference initial temperature difference of 44 °F was also arbitrary. The curves show the optimum initial 

temperature difference is likely to be in the range of 35 °F to 40 °F. Further, the curves show the optimum 

temperature difference is, to a large degree, insensitive to the selling price of the electric energy. 

As noted in Table 3, the analyses assumed the Rankine cycle operated at full load throughout the year. This 

simplifying assumption was made to determine the sensitivity of the preferred initial temperature difference 

on the overall plant economics. A more detailed performance and economic analysis, based on the 

Excelergy program, is discussed in Section 4. 

- 8 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

-$4,000,000

-$3,000,000

-$2,000,000

-$1,000,000

$0

$1,000,000

$2,000,000

$3,000,000

20 25 30 35 40 45 50

Initial Temperature Difference, o

F

Net Value, $

$60 $80 $100 $120 $140

Figure 5 Net Value to Plant as a Function of Initial Temperature Difference 

2.5 Additional GateCycle Calculations 

With an air cooled condenser area of 2,645,000 ft2

, corresponding to the nominal preferred initial 

temperature difference of 39 °F, the condenser pressure reaches 8 in. HgA with an ambient temperature of 

about 108 °F. With an ambient temperature of 130 °F, the condenser pressure reaches (on a theoretical 

basis) 14.2 in. HgA. 

In practice, the condenser pressure is likely to be limited to a value of about 8 in. HgA to prevent excessive 

aerodynamic loads on the last stage blades. To model the effect of this constraint on the output of the 

turbine, a series of additional GateCycle calculations were made at ambient temperatures of 110 °F, 120 °F, 

and 130 °F with the main steam flow rate reduced to the point where the condenser pressure does not exceed 

8 in. HgA. 

The results are illustrated in Figure 6. The upper lines represents the turbine output with no constraints on 

the condenser pressure, and the lower line shows the turbine output with the pressure limited to 8 in. HgA. 

With ambient temperatures of 120 °F and 130 °F, the turbine output must be reduced by a significant 

31 percent and 55 percent, respectively. However, a review of the dry bulb temperature histogram for 

Barstow in Figure 2 shows only a limited number of hours with temperatures above 110 °F. As a result, the 

- 9 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

effect on the annual plant output due a constraint on the condenser pressure should be minor. The effect is 

explored on a quantitative basis in Sections 4 and 5 below. 

30

40

50

60

70

80

90

100

40 50 60 70 80 90 100 110 120 130

Dry Bulb Temperature, o

F

Gross Cycle Output, MWe

14 in. HgA 8 in. HgA

Figure 6 Gross Turbine Output 

with Allowable Condenser Pressures of 14 in. HgA and 8 in. HgA 

- 10 - 
- 11 - 

Task 2

Wet/Dry Heat Rejection Analysis

3. Wet Heat Rejection 

The procedure for estimating the performance of a plant with a wet mechanical draft cooling tower is 

outlined below. 

3.1 Rankine Cycle 

The Rankine cycle design for a plant with a wet heat rejection system follows very closely the design for a 

plant with a dry heat rejection system. The principal changes are the deletion of the air cooled condenser, 

and the addition of a surface condenser, the wet cooling towers, a circulating water pump, and a makeup 

water source. The GateCycle flow diagram is shown in Figure 7. 

The design condenser pressure is 1.23 lbf/in2

 for both the dry and the wet heat rejection systems; thus, the 

gross cycle efficiency is 0.375 for both plants. 

3.2 Wet Cooling Tower Capacity 

The capacities of the wet cooling tower were selected by the GateCycle program, based on a dry bulb 

temperature of 106 °F and a coincident wet bulb temperature of 68 °F. This combination of temperatures is 

not expected to be exceeded for all but 1 percent of the hours each year. The characteristics of the cooling 

tower are summarized in Table 4. 

Table 4 

Wet Cooling Tower Design Parameters 

Parameter Value

 Condenser pressure, in. HgA 2.5 

 Approach to wet bulb temperature, °F 12.3 

 Circulating water range, °F 21.1 

 Cells, each 3 

 Total fan power, kWe 881 

 Water consumption, lbm/hr 

 - Blowdown 154,694 

 - Evaporation 531,620 

 - Drift 22,513 

 ---------- 

 - Total 708,827 
W

- 12 - 

ST1 

 1.23

520142

108.721012.7

P T

W H

CND1

CNDPMP

FWH4

FDWPMP

ST2

FWH5

485.59 80099

466.371206.7

P T

W H

202.91 35231

664.701356.0

P T

W H

DA1

FWH0

FWH1

 5.37

 27834

165.261081.1

P T

W H

IPST

268.30

682820

407.261163.0

P T

W H

239.29

682820

703.401373.9

P T

W H

 89.65

 34392

489.441275.0

P T

W H

 75.00

613198

454.121258.8

P T

W H

FWH2

 44.11

 33455

361.161216.5

P T

W H

 16.93

 31767

219.231149.8

P T

W H

 25.00

5.14E6

1500.0369.63

P T

W H

 25.00

5.14E6

1096.2260.00

P T

W H

VRHTR

VSUHTR

STMGEN

1450.5

762920

703.401294.8

P T

W H

V2

 89.65

 34392

489.441275.0

P T

W H

 89.65

778569

320.02290.41

P T

W H

 8.406Exh loss

1460.1

778569

455.03436.39

P T

W H

135.00

629347

158.06126.31

P T

W H

1470.1

778569

374.04348.99

P T

W H

????????????

????????????

P T

W H

S2

S4

S5

S7

S8

S9

S11

S12

S15

S16

S26

S27

S28

S1

S32

S33

S35

S1

S18

S19

S22

S24

S30

S6

S13

S14

S3

S31

S20

S39

S25

Figure 7 GateCycle Flow Diagram 

88 MWe Rankine Cycle with Wet Heat Rejection 
Task 2 

Wet/Dry Heat Rejection Analysis 

3.3 Annual Performance Calculations 

The performance of a wet cooling tower is calculated by the GateCycle program using a combination of the 

dry bulb temperature and the relative humidity. However, the data contained in the Excelergy weather file 

DAG_TMY2_hr lists dry bulb temperature and dew point temperature. The relative humidities were 

calculated from the dew point temperatures using the standard expression, as follows: 

2

f

2

f

Steam temperatur bulbdry at pressure n saturatio /inlb e,

Steam temperatur point dew at pressure n saturatio /inlb e,

φ =

For the hours in which the direct normal radiation exceeded 250 W/m2

, the dry bulb temperatures were 

plotted against the corresponding relative humidities, which yielded the distribution shown in Figure 8. 

y = 0.00010001x2 - 0.02455648x + 1.61571832

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

30 40 50 60 70 80 90 100 110 120

Dry Bulb Temperature, oF

Relative Humidity .

Figure 8 Dry Bulb Temperatures and Calculated Coincident Relative Humidities 

Using the equation shown in Figure 8, a representative annual relative humidity was developed for each dry 

bulb temperature. From this information, the gross plant output and cooling tower water consumption were 

calculated for a series of dry bulb temperatures between 40 °F and 120 °F. The results, summarized in 

Table 5, show the plant output to be essentially invariant with the ambient temperature. However, the 

cooling tower water use varies inversely with the ambient temperature. 

- 13 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

Table 5 

Gross Plant Output as a Function of Dry Bulb Temperature 

Wet Heat Rejection 

 Dry bulb Relative Gross turbine Cooling tower 

temperature, °F humidity output, MWe makeup 1, lbm/hr

 40 0.79 88.5 383,000 

 50 0.64 88.5 456,000 

 60 0.50 88.5 527,000 

 70 0.39 88.4 584,000 

 80 0.29 88.4 635,000 

 90 0.22 88.3 686,000 

 100 0.16 88.2 737,000 

 110 0.12 88.1 789,000 

 120 0.11 88.0 841,000 

Note 1: Sum of blowdown, evaporation, and drift losses. 

Strictly speaking, numerous relative humidities are associated with each dry bulb temperature, as illustrated 

in the data points of Figure 8. Fortunately, for sites with low relative humidities during the summer, the 

performance of the Rankine cycle is essentially invariant with the dry bulb temperature. As a result, 

assigning only one relative humidity to each dry bulb temperature should result in an annual energy estimate 

which is very close to a more complex analysis involving a three-dimensional surface fit of gross output as a 

function of dry bulb temperature and relative humidity. 

A combination of an essentially constant turbine output and an inverse relationship between ambient 

temperature and water use should be characteristic of a desert location. In essence, the cooling tower always 

transfer heats to the environment under favorable conditions: When the ambient temperature is high, the 

relative humidity is low; and when the relative humidity is high, the ambient temperature is low. However, 

at other plant locations in which the relative humidity is not a strong function of the ambient temperature, the 

turbine output is likely to decline on hot days. 

- 14 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

4. Annual Plant Performance 

The net electric outputs for the plants with dry and wet heat rejection were estimated using the Excelergy 

computer program. The plant designs were based on the characteristics listed in Table 6. 

Table 6 

Plant Design Parameters for Use In Excelergy 

Parameter Value

 Collector type LS-2+ 

 Collector field aperture area, m2 534,230 

 Solar multiple 1.45 

 Gross plant output, MWe 88.0 

 Gross cycle efficiency 0.377 

 Solar field design parameters Default 

 Solar field parasitic power demand Default 

 Power block design parameters Default 

 Power block parasitic power demand Default 1

Note 1: With separate calculations for cooling tower and circulating water pump 

auxiliary power consumption 

4.1 Dry Heat Rejection 

The gross output of the Rankine cycle was calculated using the standard Excelergy format, as follows: 

 Nth = .Qtpb / Qdesign 

 Nel = T2EPLF0 + (T2EPLF1)(Nth) + (T2EPLF2)(Nth)2

 + (T2EPLF3)(Nth)3 + (T2EPLF4)(Nth)4

 .EgrSol = Edesign * Nel 

where .Qtpb is the thermal power to the steam generator at each time step, Qdesign is the design thermal 

power to the steam generator, .EgrSol is the gross turbine output at each time step, and Edesign is the design 

gross turbine output. The part load thermal-to-electric coefficients T2EPLF0 through T2EPLF4 are the 

default Excelergy values; i.e., the ratio of part load to full load Rankine cycle efficiency is assumed to be 

independent of the heat rejection system. 

The effect of the ambient temperature on the gross cycle output is also modeled using the standard Excelergy 

format, as follows: 

 Ntc = TempCorr0 + TempCorr1 * Ttc + TempCorr2 * Ttc2

 + TempCorr3 * Ttc3 + TempCorr4 * Ttc4

 .EgrSol = .EgrSol * Ntc 

- 15 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

where Ttc is the dry bulb temperature, and the five coefficients TempCorr0 through TempCorr4 are derived 

from a fourth order polynomial fit of GateCycle calculations of the gross turbine output plotted as a function 

of the dry bulb temperature. 

The gross turbine output assumes all 14 cooling tower fans are in operation when the turbine is operating at 

or near full load, regardless of the ambient temperature. In principal, it may be possible to turn off some of 

the fans at low ambient temperatures to reduce the parasitic energy demand. To explore the potential energy 

savings, a series of GateCycle calculations were performed for the following conditions: 60 °F ambient 

temperature; 50 percent relative humidity; and 8 to 14 fans in operation. The results are illustrated in 

Figure 9. With 11 to 14 fans in operation, the reduction in parasitic energy demand associated with isolating 

a fan was essentially equal to the reduction in the gross output of the turbine due to an increase in the 

condenser pressure, and the net output of the plant remained nearly constant. However, with fewer than 11 

fans in operation, the performance degradation due to the increase in the condenser pressure was larger than 

the savings in fan energy, and the net output decreased. For the purposes of the study, the fan power 

calculation assumed that all fans were in operation whenever the turbine was in operation at or near full load. 

80

82

84

86

88

90

8 9 10 11 12 13 14

Fans in Operation, Each

Net Cycle Output, MWe

0.0

0.5

1.0

1.5

2.0

2.5

Condenser Pressure, lbf/in2

Output Pressure

Figure 9 Plant Performance and Air Cooled Condenser Operation 

On a related point, the GateCycle calculations for fan power consumption are based on an air velocity at the 

entrance to the tube bank of 11.5 ft/sec. As such, the mass flow rate and fan power consumption are 

inversely related to the ambient air temperature. For example, with an ambient temperature of 40 °F, the 

- 16 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

power demand of each fan is 219 kWe; at 140 °F, the demand falls to 182 kWe. A polynomial expression is 

included in the Excelergy parasitic block calculations to model this effect, as follows: 

.EparCt = (CtPar)[(CtParF0 + (CtParF1)(AmbTemp(D, H, T)) + (CtParF2)(AmbTemp(D, H, T))2)] (.PbLoad) 

where .EparCt is the cooling tower energy demand at each time step, CtPar is the fan power demand at the 

design point, the coefficients CtParP0 through CtParF2 adjust the fan power demand with the ambient 

temperature, and .PbLoad is the ratio of gross electric output at each time step to the design electric output. 

As such, the number of cooling tower fans in operation is assumed to be proportional to the turbine output. 

4.2 Wet Heat Rejection 

The gross output of the Rankine cycle was calculated using a modified Excelergy format for wet cooling 

towers. The effect of the wet bulb temperature on the Rankine output was modeled as follows: 

 Ntc = TempCorr0 + TempCorr1 * Ttc + TempCorr2 * Ttc2

 .EgrSol = .EgrSol * Ntc 

where Ttc is the dry bulb temperature, and the three coefficients TempCorr0 through TempCorr2 are derived 

from a second order polynomial fit of GateCycle calculations of the gross turbine output plotted as a function 

of the dry bulb temperature. Each dry bulb temperature is assumed to have a corresponding relative 

humidity, as illustrated in the trend line of Figure 8. 

At the design point, the parasitic energy consumption was estimated to be 881 kWe for the cooling tower 

fans, and 653 kWe for the circulating water pumps. For combinations of ambient temperature and Rankine 

cycle output other than the design point, the energy demand was calculated as follows: 

.EparCt = (CtPar)[(CtParF0 + (CtParF1)(AmbTemp(D, H, T)) + (CtParF2)(AmbTemp(D, H, T))2)] (.PbLoad) 

where the coefficients CtParP0 through CtParF2 are based on GateCycle calculations which adjust the fan 

and the circulating water pump power demands with the ambient temperature. 

4.3 Annual Performance Comparison 

The results of the annual performance calculations for the dry and the wet heat rejection cases are shown in 

Table 7. Cases 1 through 6 use dry heat rejection systems, with initial temperature differences of 24 °F to 

49 °F, respectively. Case 7 is the same as Case 4, but with the condenser pressure limited to 8 in. HgA.. 

Case 8 uses a wet heat rejection system. 

The dry heat rejection cases deliver 91 to 96 percent of the annual electric energy supplied by the wet heat 

rejection case, and have annual solar-to-electric efficiencies 0.5 to 0.7 percentage points lower. However, 

the annual water use for the dry cases is only about 8 percent of that for the wet case. 

- 17 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

Table 7 

Annual Energies for Plants with Dry and Wet Heat Rejection 

Case 1 2 3 4 5 6 7 8

Type of cooling tower Dry Dry Dry Dry Dry Dry Dry Wet

Initial temperature difference, F 24 29 34 39 44 49 39 1 N/A

Fan power, kWe 4,541 3,800 3,194 2,724 2,399 2,194 2,724 1,559

Cooling tower fan energy, MWhe 11,820 9,823 8,138 6,857 5,901 5,311 6,860 4,124

Net energy generation, MWhe 192,933 193,282 191,651 190,263 186,324 183,506 190,346 201,177

Annual solar-to-electric efficiency 0.1294 0.1296 0.1285 0.1276 0.1249 0.1231 0.1276 0.1349

Raw water use, m3 57,451 57,140 56,485 55,957 54,972 54,285 55,974 742,368

Note 1: Maximum condenser pressure limited to 8 in. HgA 

- 18 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

5. Economic Analysis 

Levelized energy costs were calculated for the plants with dry and wet cooling using the year-by-year cash 

flow analysis within Excelergy. The input financial parameters to the model are listed in Table 8. 

Table 8 

Financial Parameters for Levelized Energy Cost Calculations 

Parameter Value

 Interest during construction 

 - Construction period, years 2 

 - Interest rate, percent 7 

 Operation and maintenance cost, $ million 

 - Dry cooling 1 4.720 to 4.793 

 - Wet cooling 4.778 

 Cost of water, $/1000 gallons 1.40 

 Effective income tax rate, percent 40.0 

 Debt financing 

 - Interest rate, percent 6 

 - Period, years 20 

 - Minimum coverage ratio 1.4 

 - Nominal fraction of total investment, percent 2 56 

 Investment tax credit, percent 10 

 Depreciation period, years 5 

 Equity financing 

 - Required return, percent 15 

 - Nominal fraction of total investment, percent 2 44

 Discount rate, percent 

 - Nominal 10.1 

 - Real 7.6 

Notes: 

 1) Varies with the size and capital cost of the air cooled condenser 

 2) Actual value varies by plant, based on debt coverage ratio, depreciation 

schedule, investment tax credit, and equity financing requirements 

The capital cost for the plant with wet cooling was developed from the default values in Excelergy. As a 

point of reference, the default estimate within Excelergy for ‘General Balance of Plant and Cooling’ was 

compared with an independent estimate of the wet heat rejection system from References 2 and 3. The 

results are shown in Table 9. 

- 19 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

Table 9 

Comparison of Wet Heat Rejection System Costs 

Excelergy Refs. 2 and 3

 General BOP and Cooling $6,792,000 

 Surface condenser $1,650,000 

 Wet cooling tower $1,316,000 

 Cooling tower basin $553,000 

 Circulating water pumps $60,000 

 Circulating water pipe $81,000 

 Raw water well and well field $496,000 

 Evaporation pond $1,561,000 

 -------------- -------------- 

 Total $6,792,000 $5,717,000 

Assuming the Excelergy estimate includes balance of plant items other than the wet heat rejection system, 

such as a compressed air system, the two estimates are in reasonable agreement. 

The capital costs for the seven plants with dry cooling were developed by subtracting the ‘General Balance 

of Plant and Cooling’ estimate from the default Excelergy values, and then adding the cost of the air cooled 

condensers. To this was added an allowance of $1 million for those items within ‘General Balance of Plant 

and Cooling’ which were not associated with the wet heat rejection system. 

The annual operation and maintenance costs for the plant with both dry and wet heat rejection systems were 

developed from the default values in Excelergy. 

The results of the levelized energy cost calculations are shown in Table 10. 

Table 10 

Levelized Energy Costs for Plants with Dry and Wet Heat Rejection Systems 

Case 1 2 3 4 5 6 7 8

Type of cooling tower Dry Dry Dry Dry Dry Dry Dry Wet

Capital cost, $ 1000 290,958 286,202 282,256 279,120 276,862 275,315 279,120 267,747

O&M cost, $ 1000 4,763 4,744 4,728 4,715 4,705 4,698 4,716 4,778

Levelized energy cost, $/kWhe 0.1400 0.1379 0.1375 0.1373 0.1393 0.1408 0.1373 0.1270

Energy cost penalty, percent 10.2 8.6 8.3 8.1 9.7 10.9 8.1 Base

Thus, the use of a dry heat rejection system imposes a nominal 8 to 9 percent penalty on the levelized cost of 

energy. 

- 20 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

With further optimization efforts, the expected penalty could perhaps be reduced to values in the range of 

7 to 8 percent. Potential improvements include the following: 

• Reducing the capital cost of the air cooled condenser by optimizing the tube and fin geometry in 

conjunction with the design air velocity and the fan power demand 

• Reducing the parasitic energy demand by optimizing a schedule for fan speed settings as a function of 

turbine output and ambient temperature. 

As noted in Table 8, the cost of raw water is estimated to be $1.40 per 1000 gallons. On a conceptual level, 

the cost for water could rise to the point where the cost of energy for a plant with wet cooling is equal to the 

cost of energy from a plant with dry cooling. A brief economic analysis shows the required cost of water to 

be $14.80 per 1000 gallons, which is about a factor of 10 higher than current prices. 

On a point related to the selection of the optimum initial temperature difference for the air cooled condenser, 

initial considerations might lead to the selection of a low value for the design initial temperature difference. 

The cost of energy from a solar project is higher than from a fossil-fired plant; thus, small approach 

temperatures for the heat exchangers should be justified. However, the capacity factor of a solar power plant 

without thermal storage is no higher than 28 percent. As a result, there are only a limited number of hours in 

a year in which the capital investment in the larger heat exchanger can be recovered. This characteristic, 

coupled with the limited number of hours in a year in which the ambient temperature exceeds 110 °F, leads 

to the selection of an air cooled condenser with a relatively high initial temperature difference, and relatively 

high turbine performance penalties on hot days. 

- 21 - 
Task 2 

Wet/Dry Heat Rejection Analysis 

6. References 

1) GateCycle Program, Version 5.20, GE Enter Software, Inc. and the Electric Power Research Institute 

2) Maulbetsch, John S., (Electric Power Research Institute, Palo Alto, California), “Comparison of 

Alternate Cooling Technologies for California Power Plants - Economic, Environmental, and Other 

Tradeoffs”, Public Interest Energy Research, California Energy Commission, Report 500-02-079F, 

February 2002 

3) Letter from Bill Powers (Powers Engineering, Los Angeles, California) to Kent Zammit (Electric Power 

Research Institute, Palo Alto, California), Subject: Comments on February 2002 CEC/EPRI Document - 

“Comparison of Alternate Cooling Technologies for California Power Plants - Economic, 

Environmental, and Other Tradeoffs”, March 29, 2003 

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January 20, 2005 – December 31, 2005 

5a. CONTRACT NUMBER

DE-AC36-99-GO10337 

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4. TITLE AND SUBTITLE

Nexant Parabolic Trough Solar Power Plant Systems Analysis: 

Task 2: Comparison of Wet and Dry Rankine Cycle Heat Rejection 

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NREL/SR-550-40163 

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CP06.1301 

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B. Kelly 

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Nexant, Inc. 

101 Second St., 11th Floor 

San Francisco, CA 94105-3672 

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Subcontract report by Nexant, Inc., regarding a system analysis comparing solar parabolic trough plants with wet and 

dry rankine cycle heat rejection. 

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concentrating solar power; solar parabolic trough; solar; solar thermal electricity 

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