optimization of the cooling tower condenser water leaving temperature using a component-based model

934 ASHRAE Transactions

ABSTRACT

This study investigates the optimization of the coolingtower condenser-water leaving temperature using a compo-nent-based model. This model consists of a chiller, acondenser-water pump, and two cooling towers. The chiller ismodeled with a Gordon-Ng model for vapor-compressionchillers with variable-condenser flow. The cooling tower issimulated with an effectiveness-NTU model. The pump poweris calculated from the pump flow rate, pump head, and effi-ciency. This optimization problem is formulated as that of mini-mizing the total power of the chiller, pump, and fans byselecting an optimal cooling tower condenser-water leavingtemperature at given weather conditions, chiller load, chilled-water leaving temperature, and condense-water flow rate. Themodel is applied in an example chiller CW system, and a gener-alized reduced gradient solver is used to search the optimalcooling tower approach setpoint. Simulation results show thatthe optimal cooling tower approach reset schedule can beapproximated with two straight lines. Significant energysavings could be achieved if compared with the scenario witha constant cooling tower condenser-water leaving tempera-ture. Further simulations show that the chilled-water leavingtemperature, chiller part-load ratio, and the climate zones theplant locates in have a minor effect on the optimal approachreset schedule. A higher condenser-water flow rate per coolington leads to a higher optimal cooling tower approach, but thiseffect can be neglected for a system with a constant CW flowrate. The approach setpoint reset schedule that yields optimalcontrol depends on the performance characteristics of thechiller and the cooling tower.

INTRODUCTION

A condenser water (CW) loop consists of chillers,condenser-water pumps (CWP), and cooling towers (CT). Theelectricity consumption of these components accounts for themajority of total electricity consumption in a chiller plant. Fora water-cooled chiller system, it is typically designed aroundentering condenser-water temperatures of 85F (29.4C) witha nominal CW flow of 3.0 gallon per minute (gpm) per ton(0.1937 m3/h per kW cooling) and a 10F (5.6C) range(Furlong and Morrison 2005). However, most of the time, thesystem could be operated under nondesign load and weatherconditions. How to optimize the operation of the condenser-water loop is of great interest.

Supervisory control is typically applied in the chillerplant. The CWP control is dedicated to the chiller control toprovide relatively constant flow for individual chillers. It ismore and more popular to apply variable-speed devices (VSD)to cooling tower fans to reduce their cycling frequency andallow better temperature control for any given chiller load andweather conditions. The CT condenser-water leaving temper-ature (CWLT) setpoint is maintained by modulating the CTfan speed. A dead band for the CWLT setpoint is adopted toavoid fan cycling. Braun and Diderrich (1990) demonstratedthat feedback control for cooling tower fans could be elimi-nated by using an open-loop supervisory control strategy. Thisstrategy requires only measuring chiller loading to specify thecontrol and is inherently stable.

Optimization of the cooling tower CWLT setpoint isintensively studied by some researchers. This setpoint and theCWP flow rate are the main inputs that are directly related tothe optimization of the condenser side. Some engineers keepthe setpoint at the lower limit at any time to minimize chiller

Optimization of the Cooling Tower Condenser Water Leaving Temperature Using a Component-Based Model

Zhiqin Zhang, PhD Hui Li, PhDStudent Member ASHRAE Associate Member ASHRAE

William D. Turner, PhD, PE Song Deng, PE Member ASHRAE

Zhiqin Zhang is a PhD student in the Department of Mechanical Engineering and a graduate research assistant in the Energy Systems Labo-ratory, Hui Li is a post-doctorate and Song Deng is an associate director in the Energy Systems Laboratory, and William D. Turner is a profes-sor in the Department of Mechanical Engineering, Texas A&M University, College Station, TX.

LV-11-027

2011. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 117, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAE'S prior written permission.

Copyright American Society of Heating, Refrigerating and Air-Conditioning EngineProvided by IHS under license with ASHRAE Licensee=Istanbul Teknik Universtesi/5956919001

Not for Resale, 12/26/2014 01:00:35 MSTNo reproduction or networking permitted without license from IHS

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2011 ASHRAE 935

compressor power or at 6.0F8.0F (3.3C4.4C) above thedesigned wet-bulb (WB) temperature to limit tower fan power.An alternative method is to keep the cooling tower setpoint toa constant value (7F to 11F [4C to 6C]) above the WBtemperature (this value is called cooling tower approachtemperature) to provide near-optimal tower operation (Burger1993). Stout (2003) showed that the fixed-approach towersetpoint method of optimization was not as effective as an opti-mization technique based on tower range. In colder climates,the potential savings increase by 25% to 40% when the rangeincreases from 10F to 40F (5.6C to 22.2C). Yet the chillerpower is not considered. None of these temperature controls isa proven technique to achieve minimum energy use of chillersand cooling towers. Few of them consider the interactionbetween chillers and cooling towers. Braun et al. (1989)showed the trade-off between the chiller and cooling tower fanpower associated with increasing tower airflow for variable-speed fans. It is pointed out that the minimum total poweroccurs at a point where the rate of increase in fan power withairflow is equal to the rate of decrease in chiller power. Nearthe optimum, the total power is not very sensitive to thecontrol. In general, it is better to have too high rather than toolow a fan speed. A linear relationship between airflow and loadis presented for an open-loop linear control. The reset sched-ule of the optimal cooling tower CWLT is not discussed.

Cassidy and Stack (1988) showed that VSD-equipped CTfans could reduce energy consumption at part-load conditions.Braun and Diderrich (1990) proposed a systematic approachto find a near-optimal VSD fan speed based on parametersestimated from design data. Schwedler (1998) used a simpleevaluation method to compare chiller-tower energy consump-tion and claimed that providing the coldest leaving watertemperature possible was not optimal under all conditions.Benton et al. (2002) explored most of the available coolingtower models and selected five of them for further investiga-tion. Each model computed the approach temperature as afunction of WB temperature, cooling range, water flow rate,and fan power. The maximum error in computed approachover the entire range of data was from 1.6F to 4.0F (2.2Cto 0.9C) for all of the cooling tower models except for theNTU-effectiveness model. The optimization of cooling towerswas not discussed.

Graves (2003) presented a thermodynamic model for ascrew chiller and cooling tower system for the purpose ofdeveloping an optimized control algorithm for the chillerplant. The chiller model was coupled with an effectiveness-NTU model for evaluating the cooling tower performance. AWB temperature and cooling tower setpoint correlationcoupled with a fan speed and condenser-water pump speedcorrelation obtained a 17% reduction in the energy consump-tion. Yet the tower model discounted the water loss due toevaporation, and a single NTU value was assumed to representthe tower performance at different water and airflow rates,ranging from 50% to 100% of their nominal levels. Lu et al.(2004) presented a model-based optimization strategy for the

CW loop of centralized heating, ventilating, and air-condition-ing (HVAC) systems. A modified generic algorithm for thisparticular problem was proposed to obtain the optimalsetpoints of the process. Simulations and experimental resultson a centralized HVAC pilot plant showed that the operatingcost of the CW loop could be substantially reduced comparedwith conventional operation strategies. Yet they did notexplain what setpoint should be used for the CWLT to controlthe fan speed for optimizing the system. Yu and Chan (2008)presented the use of load-based speed control to enhance theenergy performance of water-cooled chiller systems. The opti-mal cooling tower CWLT and CWP speed were expressed asa function of ambient WB temperature and chiller part loadratio (PLR). The system performance under the optimalcontrol could increase by 1.4%16.1% relative to the equiva-lent system with fixed temperature and flow rate controls forthe cooling water leaving from cooling towers.

This paper presents the optimization of the cooling towerCWLT by coupling an effectiveness-NTU cooling towermodel and a Gordon-Ng model for vapor-compression chillerswith variable-condenser flow. An example chiller system isused and the total power of the chiller compressor, condenser-water pump, and fan motors are minimized by selecting anoptimal cooling tower approach setpoint. The factors thatcould affect the form of the optimal reset schedule arediscussed, such as CW flow rate, chiller PLR, chiller chilled-water (ChW) leaving temperature, chiller and tower charac-teristics, and climate zones.

CHILLER-COOLING TOWER SYSTEM

System Configuration

Figure 1 shows an example condenser-water loop consid-ered to characterize and compare annual electricity energy andcost savings when applying various tower CWLT controlmethods. It consists of one constant-speed water-cooledcentrifugal chiller, one constant-speed condenser-waterpump, and two VSD-equipped induced draft-type coolingtowers. The two towers are staged on at the same time, and the

Figure 1 Schematic of a condenser water loop.



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condenser-water flow is equally split by the towers. The fanspeed is modulated to maintain the tower CWLT setpoint. TheCW flow rate can be varied by adjusting the flow control valve.The chiller is controlled to maintain a constant chilled-waterleaving temperature.

The objective function is to minimize the instant totalpower of the chiller compressor, condenser-water pump, andfan motors. This is a static optimization problem. The inputsare the ambient dry-bulb (DB) and WB temperatures, chillerload and ChW leaving temperature, and condenser-water flowrate. An initial value of the cooling tower CWLT setpoint isselected at the beginning of simulations. For each givenCWLT, iterations are performed to reach a converged solutionof the cooling tower airflow rate by solving the Equations 1through 5. The function F1 is the cooling tower model, and thefunction G is the chiller model. The objective function is mini-mized using a generalized reduced gradient (GRG2) methodto find an optimal cooling tower CWLT.

(1)

(2)

(3)

(4)

(5)

(6)

Upper and lower limits are defined for the cooling towerCWLT according to the system chiller requirements:

(7)

If the tower airflow rate found by the solver correspond-ing to the optimal CWLT is higher than the maximum airflowrate of the fan, the following equation is used to find the cool-ing tower CWLT at the maximum airflow rate:

(8)

The minimum fan speed could be down to 20% of therated fan speed.

Chiller Modeling

In this study, a Gordon-Ng model for vapor-compressionchillers with variable condenser flow is selected. It can applyto unitary and large chillers operating under steady-state vari-able condenser flow conditions. This model is strictly appli-cable to inlet guide vane capacity control (as against cylinder

unloading for reciprocating chillers, or VSD for centrifugalchillers). It is in the following form (Jiang and Reddy 2003):

(9)

The independent variables x1, x2, and x3 can be expressedas a function of chiller load, ChW leaving temperature, andCW entering temperature. The coefficients can be found inTable 1. The chiller motor power can be calculated with thefollowing formula:

(10)

The trended historical data for the chiller are used to iden-tify the coefficients of the model with the ordinary least-squares linear regression method. Figure 2 is a comparisonbetween measured and predicted motor power using theGordon-Ng model. Statistical analysis shows that the root-mean-square error (RSME) of the predictions is 102.5 kW andthe coefficient of variation (CV) is 2.96%. Table 1 shows therated chiller parameters as well as the chiller model coeffi-cients.

Cooling Tower Modeling

The mass and heat transfer process in a cooling tower isfairly complicated. The effectiveness-NTU model is the mostpopular model in CT simulations, but iterations are required toobtain a converged solution (Braun 1989). The details of themodel can be found in the original paper. Particularly, theoverall number of transfer units (NTU) can be correlated withthe following form:

(11)

The value of c is between 1.0 and 3.0 for towers, and nranges between 0.4 and 0.8 (Kreider et al. 2002). Thismodel can be reformulated in two forms. The F1 form calcu-lates the fan airflow rate at the given cooling tower CWLT.

(12)

The F2 form calculates the cooling tower CWLT at thegiven fan airflow rate.

minPtot PCHLR PCWP Pfan+ +=

Vfan F1 VCT CW, TDB TWB TCT CW E,, TCT CW L,,, , , ,( )=

TCHLR CW L,, =G QCHLR VCHLR CW, TCHLR ChW L,, TCHLR CW E,,, , ,( )

TCHLR CW E,, TCT CW L,,=

TCT CW E,, TCHLR CW L,,=

VCT CW, VCHLR CW, 2=

TCHLR CW E min, ,, TCHLR CW E,, TCHLR CW E max, ,,

TCT CW L,, =F2 VCT CW, TDB TWB TCT CW E,, Vfan max,, , , ,( )

y c0 c1x1 c2x2 c3x3+ + +=

PCHLR 3.517QChW=

c0 c1x1 c2x2 1+ + +( )

TCHLR CW E,, 32( )59--- + 273

3.517c3QChW

TCHLR ChW L,, 32( )59--- + 273+

3.517QChW

236.34VCWwcpw-------------------------------------------------

--------------------------------------------------------------------------------------------------- 1

NTU cm wm a-------

1 n+=

Va 60m w i, Tw i, Tref( )cpw m w o, Tw o, Tref( )cpw

a ha o, ha i,( )------------------------------------------------------------------------------------------------------------------------------=



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2011 ASHRAE 937

(13)

Other given inputs are CW flow rate, ambient DB and WBtemperatures, and cooling tower condenser-water leavingtemperature. Iterations are required to obtain a convergedsolution for these two forms. The cooling tower coefficient cand n can be identified with the trended historical coolingtower data, which are shown in Table 1. Figure 3 shows thecomparison between measured and predicted cooling towerCWLTs, and a good match can be found.

The power of the VFD-equipped cooling tower fan can becalculated with a model regressed from the trended fan speedand fan motor current:

(14)

(15)

Table 1. Parameters of the Chiller System

Variable Name SymbolI-P SI

Value Unit Value Unit

Capacity QCHLR,rate 5500 ton 15,474 kW

ChW leaving temperature TCHLR,ChW,L 36.0 F 2.2 C

CW flow rate VCHLR,CW 10,000 gpm 2271 m3/h

Chiller coefficient 0 c0 0.28100 0.28100




Fan rated airflow rate Vfan,rate 650,000 cfm 306.8 m3/s

Fan motor rated power Pfan,rate 150 hp 111.9 kW

CT coefficient 1 c 3.6152 3.6152

CT coefficient 2 n 0.6667 0.6667

Reference temperature Tref 32.0 F 0.0 C

CW pump rated power PCWP,rate 400 hp 298.3 kW

Pump motor efficiency motor 0.98 0.98 Pump shaft efficiency shaft 0.97 0.97

Pump head HCWP Head curve ft Head curve m

Pump efficiency cwp Efficiency curve % Efficiency curve %

Tw o, Trefm w i, Tw i, Tref( )cpw aVa ha o, ha i,( )

m w o, cpw-----------------------------------------------------------------------------------------------------------------+=

PfanPfan rate,-------------------------- =

0.4149 0.8305 PLR( ) 1.6959 PLR( )2 0.2831 PLR( )3+

PLRVa

Vfan rate,----------------------=

Figure 2 Comparison of chiller measured and predictedmotor powers.



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Pump Modeling

The pump power is calculated with the followingformula:

(16)

The head and efficiency of pumps can be simulated as afunction of pump flow rate, and is the overall efficiency,

including pump efficiency, motor efficiency, shaft efficiency,and VFD efficiency.

Weather Conditions

Weather conditions play an important effect on the oper-ation of a water-cool chiller plant. Six cities representing sixtypical climate zones in the United States are selected forsimulation: Houston, TX (hot and humid), Phoenix, AZ (hotand dry), Chicago, IL (cool and humid), Denver, CO (cool anddry), Los Angles, CA (warm and dry), and Miami, FL (hot and

Ppump0.746V H

3960all----------------------------=

Figure 3 Comparison of CT condenser water measured and predicted leaving temperatures; (a) I-P, (b) SI.

Table 2. Hour Number in Each DB and WB Bin for Houston, TX

Wet-Bulb Temperature, F (C)

Dry Bulb, F (C)

17(8)

24 (4)

30(1)

36(2)

43(6)

49(9)

55(13)

62(17)

68(20)

74(23)

81(27)

21 (6) 5 7

29 (2) 26 66

37 (3) 2 118 227 25

46 (8) 4 147 395 78

54 (12) 18 158 503 272

62 (17) 19 202 432 681 18

70 (21) 42 152 380 915 239

78 (26) 48 111 467 1476 73

87 (31) 13 154 644 228

95 (35) 29 258 108

103 (39) 1 14 5

(a) (b)

all



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2011 ASHRAE 939

humid). The Typical Meteorological Year 3 (TMY3) hourlyweather data (NREL 2008) are used to generate a two-dimen-sion bin. One dimension is DB temperature and the other isWB temperature. In each bin, the hour number is counted andthe average DB and WB temperatures in each bin are calcu-lated. These data are used as inputs for the CW loop simulationprogram. Table 2 shows an 11 by 11 bin for the TMY3 weatherdata of Houston, TX. For example, for the bin of the DB is54F and the WB is 49F, the total hour number is 503. In thisstudy, to achieve a higher accuracy, the DB is divided into 46bins and the WB is divided into 39 bins.

OPTIMIZATION RESULTS

Optimal Cooling Tower Approach Temperature

In this simulation, the chiller part-load ratio is 80%(4400 ton [15,474 kW]), and the chiller ChW leaving temper-

ature is 36.0F (2.2C). The chiller CW flow rate is10,000 gpm (2271 m3/h). The system is located in Houston,TX, and it is a VSD-equipped fan. These are the default condi-tions for the following analysis. Figure 4 shows the optimalcooling tower CWLT setpoint versus the ambient WB temper-ature, and a strong linear correlation can be observed. Thisrelationship can be approximated with two straight lines toform a near-optimal fan control.

(17)

When the ambient WB is lower than 47.0F (8.3C), thetower CWLT is controlled at 55.0F (12.8C) to meet thelower limit of the chiller. When the WB is higher than 47F(8.3C), a higher WB temperature leads to a lower optimaltower CWLT. The slope and the intercept of the optimal reset

Figure 4 Optimal CT approach temperature versus ambient WB temperature; (a) I-P, (b) SI.

(a) (b)

Figure 5 Cooling tower approach temperatures under various fan control strategies; (a) I-P, (b) SI.

(a) (b)

TApp Twb 55 if Twb 47F+=TApp 0.1325Twb 13.56 if Twb 47F>+=



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schedule could be changed with many factors, which will bediscussed one by one in the following sections.

Energy Savings Potential

Figure 5 shows the simulated cooling tower approachversus the ambient WB temperature for different CT controlstrategies. For the scenario with 70.0F (21.1C) CWLTsetpoint, if the ambient WB is higher than 66.0F (18.9C), thefan speed reaches 100% and the approach setpoint cannot bemaintained. For the scenario with 4.0F (2.2C) constantapproach temperature, if the ambient WB temperature is lowerthan 68.0F (20.0C), the fan is running at full speed and theactual approach is higher than 4.0F (2.2C).

The scenario of controlling the cooling tower CWLTsetpoint at 70F (21.1C) is used as the baseline. The annualtotal electricity consumptions of the chiller, cooling towerfans, and CW pump are simulated. Another six CT fan controlstrategies are simulated and the energy savings percentages for

each strategy are shown in Table 3. The optimal control canreduce the chiller power consumption by 5.8%, but consume19.7% more of the fan power. The total electricity energysavings are 4.1%. The total power savings for the near-optimalcontrol are very close to that for the optimal control. If thecooling tower approach is 1F (0.6C) higher than the optimalvalue, less electricity is consumed by the fan but more isconsumed by the chiller. The change of the annual total powersavings is 0.3%. If a constant approach setpoint of 8.0F(4.4C) is selected, the annual energy savings is 2.6%, whichis 1.5% or 426,637 kWh per year less than the savings of theoptimal control. The energy consumption with a constantapproach setpoint of 4.0F (2.2C) is almost equal to that withthe optimal control, which means that the operation with alower constant approach temperature is closer to the optimaloperation. In other words, it is preferred to run cooling towerfans at a higher speed. This is consistent with the conclusiondrawn by Braun et al. (1989).

Figure 6 Optimal CT approach temperature under different CW flow rates; (a) I-P, (b) SI.

(a) (b)

Table 3. Annual Electricity Consumption Change under Different CT Control Strategies

CT ControlCHLR Power,

kWhCT Fan Power,

kWhCW Pump Power,

kWhTotal Power,

kWh

Baseline

CT CWLT = 70F (21C) 24,611,417 1,325,921 2,245,375 28,182,713

TApp,sp = Optimal 5.8% 19.7% 0.0% 4.1%

TApp,sp = Near-optimal 5.7% 18.6% 0.0% 4.1%

Energy savings

percentage

TApp,sp = Optimal+1F (0.6C) 3.7% 12.8% 0.0% 3.8%

TApp,sp = 4F (2.2C) 5.8% 20.8% 0.0% 4.1%

TApp,sp = 6F (3.3C) 4.1% 1.3% 0.0% 3.6%

TApp,sp = 8F (4.4C) 2.0% 18.3% 0.0% 2.6%



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2011 ASHRAE 941

Condenser-Water Flow Rate

Based on the velocity limits of condenser water passingthrough the condenser, the acceptable range of varying CWflow rate would be 50%100% of the nominal flow rate. Thechiller load is 80% (4400 ton [15,474 kW]), and thecondenser-water flow is varying at 9000 gpm (2044 m3/h),10,000 gpm (2271 m3/h), 11,000 gpm (2498 m3/h), and12,000 gpm (2726 m3/h). Figure 6 shows the scatter plots ofthe optimal CT approach as a function of the ambient WBunder different CW flow rates. The slope of each plot is almostthe same, but a higher CW flow rate leads to a slightly higheroptimal CT approach temperature. The optimal CT approachdifference for these various CW flow rates is around 1.0F2.0F (0.6C1.1C). In Table 3, it is shown that, if theapproach setpoint is 1F (0.6C) higher than the optimal value,the total energy consumption increases 0.3%. Considering that

the CW flow rate is controlled at a constant value or in anarrow range, this difference could be neglected in designingan optimal cooling tower approach setpoint reset schedule.

Chiller Part-Load Ratio

To test the relation between the optimal CWLT resetschedule and the chiller PLR, the optimal cooling towerapproach setpoints when the chiller part-load ratio is 100%,80%, 60%, and 40% are plotted against the ambient WBtemperature in Figure 7. For 100% PLR, when the WB isbetween 45.0F (7.2C) and 60.0F (15.6C), the fan speedreaches 100% and the simulated setpoint is higher than theoptimal approach setpoint. A higher PLR leads to a lower opti-mal approach setpoint. These four scatter plots are overlappedwith each other in most areas, and the differences at the certainWB temperatures is within 1.0F. Consequently, a same

Figure 7 Optimal CT approach temperature under different chiller loads; (a) I-P, (b) SI.

(a) (b)

Figure 8 Optimal CT approach temperature under different chiller ChW leaving temperatures; (a) I-P, (b) SI.

(a) (b)



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approach optimal reset schedule can be applied at differentchiller PLRs.

Chilled-Water Leaving Temperature

The chiller chilled-water leaving temperature plays asignificant effect on the chiller performance. In practicality, itis typically reset based on the weather conditions or chillerload. Figure 8 shows the simulated optimal CT approachtemperature under different chilled-water leaving tempera-tures. The four scatter plots are overlapped with each other,which indicates that the chiller chilled-water leaving temper-ature has no effect on the optimal reset schedule.

Chiller and Tower Performance

The chiller sensitivity factor is defined as the incrementalincrease in chiller power for each degree increase incondenser-water temperature as a fraction of the power(ASHRAE 2003). A large sensitivity factor means the chillerpower is very sensitive to the CT control, favoring operation

at higher airflow rates or lower cooling tower approach. Thisvalue can be obtained by calculating the derivative of Equa-tion 10 to chiller condenser-water entering temperature. Atypical factor is between 0.01 and 0.03 per F (0.02 and 0.06per C). For this particular chiller, it is 0.02 per F (0.04 per C),which indicates the chiller is sensitive to the condenser-waterentering temperature. This explains why a lower than typicalapproach is selected for optimization.

The tower performance is determined by two coefficients,c and n, which are empirical constants specific to a particulartower design. A lower c indicates that the heat transfer area issmaller for the airflow, leading to a higher airflow rate for thesame CWLT. Figure 9 shows the optimal cooling towerapproach temperature under different cooling tower coeffi-cients of c. If the coefficient c decreases, the tower heat dissi-pation capacity drops and more airflow is required to achievethe same cooling tower CWLT. The plot indicates that a highercooling tower approach will make the system optimal. The

Figure 9 Optimal CT approach temperature under different CT coefficients; (a) I-P, (b) SI.

(a) (b)

(a) (b)

Figure 10 Optimal CT approach temperature in different climate zones; (a) I-P, (b) SI.



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2011 ASHRAE 943

tower performance plays a significant effect on the optimalresults.

Climate Zones

The scatter plots of the optimal CT approach tempera-tures at six typical climate zones are shown in Figure 10. Thechiller is loaded at 80% PLR, the chilled-water leavingtemperature is 36F (2.2C), and the condenser-water flowrate is 10,000 gpm (2271 m3/h). Except for the plots forDenver, these plots are overlapped with each other and asignificant correlation can be observed between the optimalcooling tower CWLT setpoint and the ambient WB tempera-ture. The atmospheric pressure in Denver is 0.824 atm and itis cool and dry. It is easier for water to evaporate. For the sameairflow rate or fan power, a lower tower CWLT can beachieved.

SUMMARY AND CONCLUSION

Resetting the cooling tower CWLT is one of the mostpopular measures to improve the performance of a chillerplant. It plays opposite effects on the efficiencies of the chillerand cooling tower. An optimal value exists for specific oper-ating conditions to minimize the power consumption of thechiller, cooling tower, and CW pump.

This paper introduces the optimization of the coolingtower CWLT using a component-based model. The model isapplied in an example chiller CW system and the coolingtower approach temperature setpoint is optimized to minimizethe total power of the chiller, pump, and fans at given weatherconditions, chiller load, chilled-water leaving temperature,and condenser-water flow rate. Simulation results show thatthe optimal cooling tower approach setpoint reset schedulecan be approximated with two straight lines. Significantenergy savings could be achieved if compared with thescenario with a constant cooling tower CWLT. Further simu-lations show that chiller PLR, chiller ChW leaving tempera-ture, and climate zones the plant locates in play minor effectson the coefficients of the optimal CWLT reset schedule. Ahigher condenser-water flow rate per cooling ton leads to ahigher optimal cooling tower approach, but this effect can beneglected for a system with a constant CW flow rate. The formof this reset schedule is determined by the performance char-acteristics of the chiller and cooling tower.

NOMENCLATURE

c = cooling tower or chiller model coefficients

cp = water heat capacity, Btu/lbmF (W/kgC)ChW = chilled water

CT = cooling tower

CV = coefficient of variation

CW = condenser water

CWP = condenser water pump

DB = dry bulb

gpm = gallons per minute

GRG = generalized reduced gradient

h = enthalpy, Btu/lbm (W/kg)

H = water head, ft (m)

HVAC = heating, ventilating, and air conditioning

m = mass, lbm (kg)

n = cooling tower model index

NTU = number of transfer units

P = power, kW

PLR = part load ratio

PPMP = primary pump

Q = cooling load, ton

RSME = root mean square error

T = temperature, F (C)

V = flow rate, gpm

VSD = variable speed drive

WB = wet bulb

x = independent variables

Greek Symbols

= efficiency = density, lbm/ft3 (kg/m3)Subscripts

a = air

App = approach

E = entering

i = inlet

L = leaving

max = maximum

min = minimum

o = outlet

ref = reference

sp = setpoint

tot = total

w = water

wb = wet bulb

REFERENCES

ASHRAE. 2003. ASHRAE HandbookHVAC ApplicationsChapter 41 Supervisory Control Strategies and Optimi-zation. Atlanta, GA: American Society of Heating,Refrigerating and Air-Conditioning Engineers, Inc.

Benton, D.J., C.F. Bowman, M. Hydeman, and P. Miller.2002. An improved cooling tower algorithm for theCoolToolsTM simulation mode. ASHRAE Transactions108(1).

Braun, J.E. 1989. Effectiveness models for cooling towersand cooling coils. ASHRAE Transactions 96(2): 16474.



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optimization of the cooling tower condenser water leaving temperature using a component-based model

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