Energy Conversion and Management 73 (2013) 226–233

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Energy Conversion and Management

journal homepage: www.elsevier .com/locate /enconman

Discrete model-based operation of cooling tower basedon statistical analysis

0196-8904/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enconman.2013.04.025

⇑ Corresponding authors. Fax: +886 3 571 5408.E-mail addresses: sss@mail.cjcu.edu.tw (S.-S. Shieh), ssjang@mx.nthu.edu.tw

(S.-S. Jang).

Jian-Guo Wang a, Shyan-Shu Shieh b,⇑, Shi-Shang Jang c,⇑, Chan-Wei Wu d

a School of Mechatronical Engineering and Automation, Shanghai University, Shanghai Key Lab of Power Station Automation Technology, Shanghai 200072, Chinab Department of Occupational Safety and Health, Chang Jung Christian University, Tainan 71101, Taiwanc Department of Chemical Engineering, National Tsing-Hua University, Hsin-Chu 30013, Taiwand Energy & Air Pollution Control Section, New Materials R&D Department, China Steel Corporation, Kaohsiung 81233, Taiwan

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 December 2012Accepted 19 April 2013Available online 24 May 2013

Keywords:Statistical analysisCooling capability indexModel-based operationCooling towerEnergy conservation

This study is aimed to utilize the operation data to build a physical-meaningful and precise-enoughmodel to assist the operation of a cooling tower. To do so, this work introduces a dimensionless index,which can describe the cooling capability of a cooling tower in terms of effective power utilization. Inthe first phase of this study, principal component analysis, one of factor analysis methods, is used toinvestigate effects of ambient air temperature and relative humidity on the cooling capability of a coolingtower. Based on the proposed cooling capability index, the operation data are partitioned into differentgroups by the fuzzy c-mean clustering algorithm. The resulted groups are distinctly categorized by theconditions of ambient air temperature and relative humidity. In the second phase of the study, datawithin the same mode of a set of fans are partitioned by the fuzzy c-mean clustering algorithm. Theresulted groups of data are then modeled by linear regression. The acquired multiple models are highlyaccurate in predicting the output temperature of cooling water from the cooling tower. The acquiredmodels assist the operator to accurately select the proper fan mode when process conditions, e.g., coolingloading, or environment conditions, e.g., ambient air temperature, change. It results in electricity saving.This study is concluded by the presentation of a discrete model-based approach to determine the fanmode. The application to a real cooling tower in an iron and steel plant is promising in saving electricityconsumed by the fan set.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The cooling tower is an important unit in many industrial pro-cesses, such as: power generation systems, chemical and petro-chemical plants, refrigeration and air-conditioning systems, etc. Itdissipates the process heat absorbed from hot streams into theenvironment by virtue of mass and heat transfer between coolingwater and ambient air at the expense of electrical energy con-sumed to drive the fan set. The operation of cooling water has beentroubled by the large system time and strict prohibition of no over-shoot in some plants. Without the accurate-enough-model, thecontrol of the cooling water is done manually and conservativelyat the expense of energy wastefulness. This study is aimed to con-serve energy consumption by improving the operation of a typicalcooling tower serving in the iron and steel plant via the building ofa good model. A typical iron and steel plant usually has tens ofcooling tower units.

The conceptual design of the cooling tower can be traced backto Merkel’s work [1], which firstly developed a theory for the ther-mal calculation with some simplifying assumptions. Afterward,effectiveness-NTU method [2] and Poppe method [3] were pro-posed to improve Merkel’s approximations. Kloppers and Kröger[4] presented a comprehensive review on those works. In the lastdecade, based on the rapid development of software simulation,researchers studied the cooling tower design in more details [5–11], including the effect of special fill material and fill style to cool-ing performance [6,8–10].

Besides design work, performance assessment is anotherimportant issue in the research of the cooling tower. In general,CTI (cooling tower institute) standard specification [12] is recog-nized as a standard method to evaluate the performance of cool-ing tower. In addition, some performance assessment methodswere presented, namely, effectiveness-NTU based analysis [13],exergy analysis [14], software simulation [15,16], Poppe equationbased analysis [17,18], or fouling model development [19]. Con-sidering many long-in-service cooling towers whose operationconditions are far beyond the test conditions set by CTI method,such as ambient air conditions, entrance temperature of cooling

Nomenclature

Tcw,in inlet water temperature of cooling tower (�C)Tcw,out outlet water temperature of cooling tower (�C)Fcw water mass flow rate of cooling tower (103 kg/h)TD

air;in ambient air temperature, i.e., dry-bulb temperature ofinlet air to the cooling tower (�C)

MDair mass flow rate of dry air (kg/h)

RHair,in relative humidity of inlet air to the cooling tower (%)Wfan cooling tower fan power (kW)cct cooling capability indexCp Specific heat of water at constant pressure (kJ/(kg �C))

J.-G. Wang et al. / Energy Conversion and Management 73 (2013) 226–233 227

water, the authors presented a model-based assessment ap-proach to investigate the on-line performance of a cooling tower[20].

Besides design and performance assessment, some researchespay attention to the issue of optimal operation for a cooling tower[21,22]. Based on the mass/energy conservation laws and mass/heat transfer equations, CFD (computational fluid dynamics) mod-els were developed to simulate the cooling tower operation[16,23]. However, differences between the modeling world andthe actual operations keep the simulation models from being uti-lized in the real-time operation. In general, the model based onthe actual process data can reflect the actual process, but conven-tional linear model is not competent for the nonlinear and time-varying characteristic of a cooling tower. Artificial neural networksand bee colony algorithm were used for modeling cooling tower[24–27], but the results were beyond understanding and hardlyprovided any physical knowledge for reference. Recently, a linearmulti-model based approach is proposed by the authors with anautomatic clustering approach [28].

Although many authors have studied cooling tower operationsand optimization, following two issues have not been addressed:

(i) A data driven, physically meaningful model that is clear tothe operators has not been reported.

(ii) Application of a model based control to a real plant has notbeen addressed.

In this work, a dimensionless index is proposed to describe thecooling capability of a cooling tower in terms of unit consumedelectricity by the fan driver. Taking the cooling capability indexas dependent variables, the statistical analysis methods such asprincipal component analysis and correlation analysis are usedto reveal the roles of ambient air temperature and relativehumidity. In this study, ambient air temperature refers to dry-bulb temperature of inlet air to the cooling tower. Then, it isfound that operating data with same fan operating mode can becategorized into two distinct groups by fuzzy c-mean clustering(FCM) algorithm and the clustering results are analyzed to revealphysical meaning. The partitioned groups are subsequently usedto build a set of multiple linear models. A discrete model-basedapproach for selecting fan mode is presented and the implemen-tation of the proposed optimal operation is demonstrated by thestudied cooling tower.

The rest of the paper is organized as follows. The next sectiondescribes the studied system. In Section 3, a cooling capability in-dex is defined and statistical analysis methods are utilized toinvestigate the effect of ambient air temperature and relativehumidity on the cooling capability of a cooling tower. Fuzzy c-mean clustering (FCM) algorithm is used to categorize operatingdata into groups and the characteristics of the cooling tower aremodeled by multiple model method in Section 4. The implementa-tion of the proposed model-based operation for setting fan mode isdemonstrated in Section 5. Some remarks with a summary are con-cluded in the last section.

2. System background description

A pump draws water and sends it to the top of the fill and wateris evenly sprayed over the cooling tower fill, while ambient air ispulled into the tower from wall sides by fans. After absorbing heatfrom the hot water stream, the air stream is expelled through thetop of the cooling tower. As a result of rejecting heat to the airstream, temperature of the water stream drops, and then, air tem-perature rises.

The studied subject is one of cooling towers in a large ironand steel plant in Taiwan. Cooling water from the studied unitprovides service for tandem cold mill and continuous annealingline. The cooling tower unit has three fans. Each fan has 3operating modes, namely, closed, low speed and high speed.The fan set usually operates in one of the following sevenmodes from low to high level: three closed (C3_L0_H0), twoclosed and one low-speed (C2_L1_H0), one closed and twolow-speed (C1_L2_H0), three low-speed (C0_L3_H0), two low-speed and one high-speed (C0_L2_H1), one low-speed andtwo high-speed (C0_L1_H2), three high-speed (C0_L0_H3). Theoperation target is to not allow temperature of outlet waterto exceed 33.5 �C.

The operation variables used in this cross-flow induced drafttower can be partitioned into two parts, i.e., (1) cooling water re-lated: water mass flow rate Fcw, inlet water temperature Tcw,in

and outlet water temperature Tcw,out; (2) ambient air related: drybulb temperature of inlet air TD

air;in, relative humidity of inlet airRHair,in, mass flow rate of dry air MD

air and fan power of coolingtower Wfan.

Fig. 1 shows historical data of some important variables. Thedata of 60,250 samples used in this study were collected within7 months from March, 2011, and December 2011 to May, 2012.The operating data are taken every 5 min. After removing theabnormal or erroneous samples, 60,000 samples remain.

Cooling duty of cooling water varies along with change of pro-duction phase. Operators tend to keep the outlet temperature ofcooling water much lower than the targeted temperature in orderto make sure that even when production phase changes to causehigh cooling duty demand, the cooling water temperature wouldnot exceed the target. As a result, the operation of the coolingtower usually ends up with the over consumption of electrical en-ergy. The objective of this paper is to investigate how to performa tight temperature control in operating the cooling tower andfulfill the need of the process ends for the cooling water. The en-ergy consumption of the cooling unit is hence significantlyreduced.

3. Statistical analysis of cooling capability

In this section, principal component analysis (PCA) and fuzzy c-mean clustering (FCM), are utilized to examine the effect of ambi-ent air temperature and its relative humidity on the cooling capa-bility of the studied cooling tower.

Table 1Correlation analysis results for cct and other variables.

Variable R2 (%)

TDair;in

19.6

RHair,in 7.0Tcw,in 1.5DTcw 3.31st PC 6.22nd PC 32.1

-4 -3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

RHair,in

TD air,i

n

1st PC2nd PC

Fig. 2. The first and second PC of TDair;in and RHair,in.

0 10000 20000 30000 40000 50000 600002000

40006000

F cw

0 10000 20000 30000 40000 50000 6000020

3040

T cw,in

0 10000 20000 30000 40000 50000 6000020

3040

T cw,o

ut

0 10000 20000 30000 40000 50000 600000

50

TD air,i

n

0 10000 20000 30000 40000 50000 600000

50

100

RH ai

r,in

0 10000 20000 30000 40000 50000 600000

100200300

Wfa

n

Data number

Fig. 1. Historical data of main operation variables at the sampling interval of 5 min.

228 J.-G. Wang et al. / Energy Conversion and Management 73 (2013) 226–233

3.1. PCA analysis for ambient air and cooling capability

In order to precisely describe the cooling capability in termsof unit energy consumption, the following dimensionless indexis defined as the ratio of rejected thermal energy from coolingwater to consumed electric energy by the fan driver. The dimen-sionless cooling capability index is termed as cct and defined asfollows:

cct ¼ðTcw;in � Tcw;outÞFcwCP

Wfanð1Þ

At the beginning of this study, correlation analysis was straightfor-wardly conducted on the relationship between the cooling capabil-ity index cct and the plain properties of ambient air, i.e., TD

air;in andRHair,in, in the cooling tower operation. It resulted in unimpressive19.6% of R2 between cct and TD

air;in, and 7.0% of R2 between cct andRHair,in.

Aimed to further explore the hidden factors in the data, prin-cipal component analysis (PCA) was applied to treat the dataregarding ambient air properties. Two principal components wereobtained. The 1st PC scores 68% while the 2nd PC 32%. Correlationanalysis was then conducted to investigate the relationship be-tween the cooling capability index cct and the two PCs. It turnedout with an impressive 32.1% of R2 between cct and 2nd PC. Fig. 2shows the results of PCA. It means that the 1st PC could explain68% of variations of the data regarding TD

air;in and RHair,in while the2nd PC accounts for the remained 32%. Table 1 summarizes cor-relation analysis results. The above analysis reveals that the majorvariation of data is along the line of from the points of high TD

air;in,and low RHair,in to the points of low TD

air;in, and high RHair,in, butwhat matters on the cooling capability of a cooling tower opera-tion is the linear combination of low TD

air;in, and low RHair,in, whichis 2nd PC.

J.-G. Wang et al. / Energy Conversion and Management 73 (2013) 226–233 229

3.2. FCM analysis for data of different levels of cooling capability

With the knowledge acquired in the above section, this studyfurther investigate what the roles of ambient air temperatureand relative humidity play on the cooling capability of the coolingtower by conducting Fuzzy c-mean clustering (FCM) on the opera-tion data.

Fuzzy c-mean clustering is based on the minimization of dis-tances between data points and the prototype of cluster centers[29]. For the purpose of minimization, the following cost functionis used:

JFCMðU;V ;UÞ ¼XN

k¼1

Xc

i¼1

u2ikk/ðkÞ � v ik2 ð2Þ

where N is the number of all the data points, c is the given clusternumber,U ¼ uik 2 ½0;1�j

Pci¼1uik ¼ 1;

PNk¼1uik > 0; k ¼ 1; . . . ;N; i ¼ 1; . . . ; c

n ois a membership matrix, V = {v1, . . . , vc} is a cluster center set. For agiven cluster number, the objective function is minimized by analternating optimization algorithm [30].

The FCM partitioning was made based on the cooling capabilitylevel, i.e., cct After several trials, it was found that the partitioningof eight groups provided the best and clear results. The eight clus-tering central points within obtained groups of data are plotted inFig. 3. With descending order, eight cooling capability levels aredenoted as from cct,1 to cct,8. The value inside the parenthesis isthe dimensionless cooling capability index. It is found that thecooling tower has the high cooling capability in the area withlow temperature and low humidity ðTD

air;in < 22:5 �C;RHair;in < 74:5%Þ while low cooling capability groups appear inthe opposite direction. With the increase of temperature andhumidity, the cooling capability becomes poor. The cooling capa-bility in the highest group, i.e., 475 is four times of that in the low-est level, 116.

The scattering plot of these eight center points has the sametrend as what 2nd PC shows in Fig. 2. Both figures reflect the samephenomenon in physics. The ambient air with less saturated mois-ture and lower temperature a cooling tower bring in is more capa-ble to absorb the heat from cooling water. In other words, thetemperature difference between inlet cooling water and ambientair as well as the less saturation condition are the two major driv-ing forces to effectively reject the heat from cooling water. Duringthe real operation, operators may not timely change the fan mode

73 73.5 74 74.5 75 75.5 76 76.5 77 77.521

22

23

24

25

26

27

28

1(475)

2(313)

3(266)

4(232)

5(197)6(174)

7(151)

8(116)

TD air,i

n

RHair,in

Fig. 3. Clustering centers of eight groups with different cooling capability level.

responding to the weather change. Lack of physical knowledge,operators tend to be conservative in coping with the requirementof keeping outlet cooling tower temperature below the certainpoint demanded by the users. As a result, operators would ineffi-ciently set all fans in high mode in the hot humid summer dayswhile wastefully start many fans in the cold dry winter days. Thelocal weather has distinctive characteristic in temperature differ-ence between summer and winter, but less distinguishable inhumidity conditions. The 1st PC in Fig. 2 reflects the above-men-tioned characteristics. With those data, Fig. 3 shows a distorted linewith both opposite ends, instead of being a straight line as shownby the 2nd PC in Fig. 2.

4. Discrete model-based operation of cooling tower

Imbedded with the knowledge revealed in the previous sec-tions, the model-based operation of the cooling tower will be de-scribed and demonstrated in this section. Ambient airtemperature and relative humidity have been proved to be corre-lated to the cooling capability index in the last section. Subse-quently, it is reasonably supposed that the fan operating modeshould be associated with the cooling capability index. After cate-gorizing the data by the fan operating mode and calculating theiraverage values of air temperature, relative humidity and coolingcapability index, it is found that each fan operating mode had dis-tinct averaged air temperature and cooling capability index, butindistinguishable relative humidity. By investigating the datagroups partitioned by fan operating mode, the same characteristicscan be found as those by FCM method. Therefore, this studydecided to build the multiple models by partitioning the databased the fan operating mode. In this way, it would be easy to buildthe models and then implement the model-based approach in realoperation.

4.1. FCM analysis

According to the previously described seven fan operatingmodes, denoted with corresponding fan power as Wfan,1 to Wfan,7,all the operation data are divided into seven groups and every datahas five variables, namely ambient air temperature TD

air;in, its rela-tive humidity RHair,in, inlet water temperature Tcw,in and watermass flow rate Fcw and fan operating mode Wfan. Within eachgroup, fuzzy c-mean clustering (FCM) is conducted on the datawith cluster number, c set as 2. The data in the resulted partitionedgroups in every one of seven fan operating modes are distinctlyscattered in the Cartesian coordinates of ambient air temperatureTD

air;in and relative humidity, RHair,in.Taking the examples of two fan operating modes, C3_L0_H0 and

C1_L2_H0, the data with degree of membership u1k and u2k largerthan 70% are plotted as shown in Figs. 4 and 5. It is found thatthe data within the same fan operating mode are divided distinctlyinto two groups, one with high temperature and low humidity, andthe other with low temperature and high humidity. It reflects thelocal weather characteristics imbedded in the data.

4.2. Cooling tower modeling

From the mass and energy conservative laws, outlet tempera-ture of cooling water Tcw,out is known to be the function of inletcooling water temperature Tcw,in, cooling water flow rate Fcw, ambi-ent air temperature TD

air;in, relative humidity RHair,in and air flow rateMD

air . Because the data are partitioned by their fan operating mode,7 in this case, the air flow rate, being the same within each group ofdata, is not treated as variable. Since two clusters are made by FCMin each fan operating mode, the total number of the multiple mod-

40 50 60 70 80 90 10012

14

16

18

20

22

24

26

28

30

32

TD air,i

n

RHair,in (%)

Group1Group2

Fig. 4. Clustering result with fan operating mode C3_L0_H0.

40 50 60 70 80 90 10014

16

18

20

22

24

26

28

30

32

TD air,i

n

RHair,in (%)

Group1Group2

Fig. 5. Clustering result with fan operating mode C1_L2_H0.

230 J.-G. Wang et al. / Energy Conversion and Management 73 (2013) 226–233

els is 14 in this case. They are constructed by the followingequations.

bT mcw;outðkÞ ¼

X2

i¼1

qið/ðkÞÞ � f̂ iðXðkÞÞ ðm ¼ 1; . . . ;7Þ ð3Þ

where /ðkÞ ¼ ½FcwðkÞ; Tcw;inðkÞ; TDair;inðkÞ;RHair;inðkÞ�, the cluster num-

ber c = 2, m indicates the different fan operating mode, k is the timestep with interval of 5 min and

qið/ðkÞÞ ¼exp � ð/ðkÞ�v iÞT ð/ðkÞ�v iÞ

S2i

� �P2

i¼1 exp � ð/ðkÞ�v iÞT ð/ðkÞ�v iÞS2

i

� � ð4Þ

where vi (i = 1,2) is the cluster center, which is obtained by the min-imization of the cost function shown in Eq. (2), and Si is the width ofGaussian function. For the case of cluster number c = 2,

s1 ¼ s2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðv1 � v2Þðv1 � v2ÞT

q. XðkÞ ¼ ½1;/ðkÞ� and

f̂ ðXðkÞÞ ¼ XðkÞ � bi, and bi = [bi,0,bi,1,bi,2,bi,3,bi,4]T are coefficients ofthe ith local model.

Among 60,000 samples, seven batches of 500 samples randomlywere taken from them for each fan operating mode. The 500 sam-ples were partitioned into two groups by FCM method and used to

build two local models in the formats of linear equations. The de-tailed procedures of the FCM-based multiple-model method can bereferred to the authors’article [31]. The rest of the sampled datawere used to test the prediction accuracy with two indexes,namely mean square error (MSE) and R2 as shown below:

MSE ¼ 1N

XN

k¼1

ðTcw;outðkÞ � bT cw;outðkÞÞ2 ð5Þ

R2 ¼ 1�PN

k¼1ðTcw;outðkÞ � bT cw;outðkÞÞ2PNk¼1ðTcw;outðkÞ � Tcw;outðkÞÞ2

ð6Þ

The prediction capability of the acquired multiple models are dem-onstrated in the cases of fan operating mode C3_L0_H0 andC1_L2_H0. Both of Figs. 6 and 7 show the model prediction results.Fig. 6 is for the case of fan operation mode C3_L0_H0 while Fig. 7 forC1_L2_H0. Both figures consist of a comprehensive picture showingthe prediction result of the testing set of 7000 points, and a close-uppicture showing that of 1000 points. They illustrate that the outlettemperatures of cooling water are well fitted by the models.

The results of prediction accuracy for all seven fan operatingmodes are summarized in Table 2. All of the operating modes sharethe similar prediction accuracy. It means that the proposed ap-proach is stable and reliable in the whole range of the operation.

Table 3Comparison among three different partitioning ways.

Prediction MSE Prediction R2 (%)

c = 5 0.4263 64.24c = 14 0.3145 70.62Combination way in this study 0.2050 73.65

0 1000 2000 3000 4000 5000 6000 700025

30

35

Data number (k)

Tcw

,out

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 200025

30

35

Data number (k)

Tcw

,out

MeasuredPredicted

MeasuredPredicted

Fig. 7. Prediction result of the fan operating mode C1_L2_H0.

0 1000 2000 3000 4000 5000 6000 700020

25

30

35

Data number (k)

T cw,o

ut

MeasuredPredicted

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 200020

25

30

35

Data number (k)

T cw,o

ut

MeasuredPredicted

Fig. 6. Prediction result of the fan operating mode C3_L0_H0.

Table 2Prediction accuracy in seven fan modes.

Fan operatingmode

Number ofall data

Number ofmodeling data

PredictionMSE

PredictionR2 (%)

C3_L0_H0 6077 500 0.205 74.81C2_L1_H0 11401 500 0.188 75.56C1_L2_H0 12803 500 0.175 74.72C0_L3_H0 14049 500 0.151 76.32C0_L2_H1 7251 500 0.153 76.47C0_L1_H2 6922 500 0.161 73.65C0_L0_H3 1497 500 0.101 74.15

J.-G. Wang et al. / Energy Conversion and Management 73 (2013) 226–233 231

The proposed approach of partitioning the data shown above is thecombination way based on knowledge and FCM. The knowledge ofidea is inspired by physical sense and verified by statisticalanalysis.

To justify the proposed way of partitioning, the above resultsare compared to those by the FCM method only. Two cases of plainFCM partitioning are made, i.e., setting clustering number c = 5 andC = 14 respectively. The first number, 5, is arbitrarily chosen while

14 is the total model number of the proposed approach in thisstudy. To make the comparison fair, both cases randomly take3500 samples from all 60,000 data to build multiple models basedon FCM clustering.

Table 3 summarizes the comparisons of both prediction in-dexes among three ways. Because MSE tells the absolute preci-sion of the prediction capability, it is commonly used as anindex to address the accuracy of the model for prediction. Inthis table, the improvement of the proposed approach is53.4% over plain partitioning by FCM in terms of MSE (i.e.,(0.3145–0.2050)/0.2050). If we take the square root of MSE asthe index, then the improvement is 24%.

232 J.-G. Wang et al. / Energy Conversion and Management 73 (2013) 226–233

The plain partitioning by FCM is no match to the proposed way,not to mention that the former way provides messy and hard-to-figure-out-meaning clustered groups.

4.3. Discrete model-based operation strategy and implementation

As the models of outlet temperature of cooling water Tcw,out areacquired with good precision in previous section, the next task isthe formulation of model-based optimal operation for the coolingtower. The objective of the optimal operation is to keep the coolingwater temperature below the certain point demanded by the pro-cess end users with the minimizing the consumed electrical power.The temperature of cooling water is demanded below the level of34 �C by the end user and the upper temperature bound is set at33.5 �C by utility operators in this study. The control scheme isto predict the outlet temperature of cooling water based on thepresent conditions of operation variables. All possible modes forthe next operation are reviewed based on the above model, andthe optimal mode that can make the outlet temperature fall belowthe target with the least electricity can be acquired.

Denote the model of outlet cooling water temperature as fm(�),with m indicating the different level of the fan operating mode.The model-based approach of fan operation is formulated asfollows:

moptionalðkÞ ¼ arg min jbT mcw;outðkÞ � 33 �Cj ðm ¼ 1; . . . ;7Þ

s:t: bT mcw;outðkÞ ¼

X2

i¼1

qið/ðkÞÞ � f̂ ið½1 /ðkÞ�Þ

/ðkÞ ¼ ½FcwðkÞ; Tcw;inðkÞ; TDair;inðkÞ;RHair;inðkÞ�bT m

cw;outðkÞ < 33:5 �C

ð7Þ

The experiment was demonstrated in the period of from 8:15 to14:50 on May 22, 2012. An off-line PC implemented with thebuilt-in model was temporarily connected to the distributed controlsystem. The suggested fan mode was presented based on the calcu-lation of the model, and passed to the operator to adjust the fanmode of the cooling tower during the period of the experiment.Fig. 8 shows the historical data of inlet temperature of cooling

08:00 09:00 10:00 11:0026

28

30

32

34

36

38

40

Tim

TDair,in

Tcw,inTcw,out,measured33Tcw,out,predicted

C0 L2 H1 C2 L1 H0 C0 L3C3 L0 H0

Fig. 8. Model-based operation res

tower Tcw,in, ambient air temperature TDair;in, predicted outlet tem-

perature bT cw;out and measured outlet temperature Tcw,out.Before the implementation of model-based operation, the on-

duty operator set the cooling fan mode at C0_L2_H1. The movewas a bit conservative and wasteful because outlet temperaturewas 28 �C, almost 5.5 �C below the set point of 33.5 �C. After check-ing the prediction accuracy, the operation was switched to themodel-based control. A series of actions were taken in the 6-hexperiment. The actions included the adjustment to operatingmode C2_L1_H0, C3_L0_H0 and C0_L3_H0 at time 8:15, 9:20 and11:20, respectively. The outlet temperature Tcw,out is accuratelypredicted by the cluster-based models and the outlet temperaturesmoothly approached the set point and stayed in the proximity of33.5 �C.

Taking the original fan mode of C0_L2_H1 mode and the associ-ated power as the baseline, 72.36% of the electricity consumption,i.e., 608 kW h, was saved. The resulted benefit/cost ratio is signifi-cant, considering that almost no fixed cost is needed in the imple-mentation of model-based optimal operation. In our study, weestimate that the energy saving would be up to 114 MW h/monthin the summer while 16 MW h/month in the winter. It is reason-able that operators used to operate cooling fan conservatively oreven wastefully in order to fulfill their duty of providing low tem-perature cooling water. The proposed model-based approach pro-vides the best practical opportunity to conserve energy in theoperation of a cooling tower.

5. Conclusion

This paper proposed a dimensionless cooling capability index toinvestigate how the operation variables affect the power efficiencyof the fan operation. The analysis of PCA and FCM partitioning re-vealed the similar results that ambient air temperature and rela-tive humidity played the important role. Taking the fact that theoperation data within the same fan operating mode have the sim-ilar cooling capability index, the multiple models were constructedbased on the combination way of partitioning data, first by the ac-quired knowledge and then by FCM clustering.

A discrete model-based operation was demonstrated in anexperimental trial. The experiment showed the promising result

12:00 13:00 14:00 15:00e

H0

ults for actual cooling tower.

J.-G. Wang et al. / Energy Conversion and Management 73 (2013) 226–233 233

of saving 72% of electric power. Comparing the effort taking toimplement the proposed model-based operation to the effectshown in the test trial, the resulting improvement was good en-ough to convince the operator to shift the present practice to mod-el-based operation. As a matter of fact, it is hard for any operator tomake the optimal decision without precise knowledge on how toadjust the fan mode. The proposed approach provides the bestpractical opportunity in the operation of a cooling tower. Further-more, once the operation shifts to the proposed approach, the mul-tiple models to be further refined based on the future operationdata is to be more accurate because the operation is close to opti-mal. The whole approach becomes a positive cycle to conserve en-ergy in the cooling fan operation.

Acknowledgements

S.S. Jang would like to thank the financial support provided byMinistry of Economic Affairs, Taiwan, under the Grant 101-EC-17-A-09-S1-198, and the support of Grant 101N2027E1 from Cen-ter for Energy and Environmental Research, National Tsing-HuaUniversity, Taiwan. J.G. Wang would like to acknowledge the sup-port of National Nature Science Foundation of China under theGrants 61171145 and 61104061.

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