Generator Thermal Sensitivity Analysis with Support Vector Regression

Youliang Yang and Qing Zhao*

Abstract Generator thermal sensitivity issue is studied inthis paper. Currently, thermal sensitivity test is usually adoptedin industries to determine if a generator has been experiencingthermal sensitivity problem. However, this kind of tests has itsown disadvantages. In this paper, Support Vector Regressionis utilized to provide some valuable information regardingthermal sensitivity in a rotating machine based on the normaloperational data of the machine. Experimental results on thesteam turbine generators show that the proposed method canbe used to track the generator condition related to the thermaleffects and make a recommendation to the on-site engineerswhether or not a thermal sensitivity test should be performed.

I. INTRODUCTIONElectrical machine condition monitoring plays an impor-

tant role in modern industries and it has been an activeresearch topic. Traditionally, electrical machines are allowedto run until failure then they are either repaired or replaced.Very limited information regarding the machine condition isknown before the machine is shutdown and hence resulting inlong machine downtime and great economic lost. Recently,predictive maintenance strategy is adopted in many indus-tries. In predictive maintenance, machine condition is moni-tored continuously, and hence valuable information regardingmachine condition can be obtained before the machine isshutdown and repaired and the machine downtime can begreatly reduced.

Predictive maintenance consists of various aspects. Forexample, fault analysis needs to be performed and classi-fication models can be built with artificial intelligence tech-niques to classify and identify different machine conditions.In addition, prognosis models can be built to predict thefuture machine conditions and determine if the machineis experiencing faults related condition degradation. Themachine condition trending based on importance machineperformance index can be carried out to determine when themachine should be shutdown or a major maintenance/repairshould be scheduled. This way the number of unexpectedshutdown can be greatly reduced and the reliability is greatlyimproved.

In this paper, a specific issue, generator rotor thermalsensitivity, is studied. Thermal sensitivity is a phenomenoncaused by uneven heat distribution around an axis, e.g.rotor, causing it to bend. Some common causes of generatorthermal sensitivity include shorted turns, blocked ventilationor unsymmetrical cooling, insulation variation, wedge fit,

Y. Yang and Q. Zhao are with the Dept. of Electrical and ComputerEngineering, University of Alberta, Edmonton, Alberta, T6G2V4 Canada.Email: @ualberta.ca, *: correspondingauthor

distance block fitting, etc. [1]. There are two types of thermalsensitivity, reversible and irreversible. Normally thermal sen-sitivity is confirmed and the severity is determined througha standard test procedure commonly adopted in industries.However, the thermal sensitivity test is destructive especiallywhen the machine has irreversible thermal sensitivity prob-lem.

Support Vector Regression (SVR) has been widely usedin the field of electrical machine condition monitoring. Justto name a few, in [2], a hybrid model is built with SVRto predict the future state of a turbo generator. In [3], theLeast-Square Support Vector Machine (LS-SVM) combiningwith wavelet decomposition is utilized to predict the futurevibration of a hydro-turbine generating unit. In this paper,a model for vibration analysis is built with SVR that canbe useful in tracking machine conditions. It is applied toanalyze the thermal sensitivity issue for a type of steamturbine generators. In this method, only normal machineoperational data are used to build the model. The resultscan be used to recommend whether and when a necessarythermal sensitivity test is needed. The rest of the paper isorganized as follows. The basic theory of SVR is reviewedin section II. In section III, the background of generatorthermal sensitivity and the procedure of a thermal sensitivitytest are introduced. In section IV, after some discussionson the industrial practice regarding thermal sensitivity andthe limitations, SVR models are built and the experimentalresults are presented. Finally, the conclusion is provided insection V.

II. SUPPORT VECTOR REGRESSIONIn SVR, the goal is to find a function f(x), which maps the

input to the output, while minimizing the difference betweenthe predicted value yi and the actual value yi based onthe loss function [4]. Suppose that there are training data(x1, y1), (x2, y2), ..., (xN , yN), where xi is the input and yiis the output. In a linear case, f(x) can be expressed as

y = f(x) = wx + b (1)where w is the weighted vector and b is a constant. Whiletrying to minimize the difference between the predicted valueand the actual value, in SVR, it is also desirable to keepthe function f(x) as flat as possible [4], which means wshould be as small as possible. One way to find a small wis to minimize the norm, i.e. ||w||2 =< w,w >. Thus, theregression problem becomes to

min.1

2

Nn=1

(yi yi)2 +

1

2||w||2 (2)

2010 American Control ConferenceMarriott Waterfront, Baltimore, MD, USAJune 30-July 02, 2010

WeB05.3

978-1-4244-7425-7/10/$26.00 2010 AACC 944

xx

x

x

x

x

x

x

x

x

x

xx

xx

x

x

x

x

i

i

x

x

y

+y

y

x

)( xy

Fig. 1. Linear SVR with slack variables

Quadratic error function is used in Eq. (2) to calculate theerror between the predicted value and the actual value. Inpractice, the -insensitive error function is often used, whichcan be mathematically expressed as

E(yi yi) =

{0, if |yi yi| < |yi yi| , otherwise

(3)

Readers can refer to [5] for more details on error functions.With the -insensitive error function, the regression problembecomes to minimize

C

Nn=1

E(yi yi) +1

2||w||2 (4)

Where C is the trade-off between the flatness of f(x) and theprediction error. In cases that with the optimal f(x), someactual values may not lie within the region [y, y+], slackvariables and need to be introduced so that for any givenactual value yi, it lies within the region [yii, yi++i](Please refer to Fig. 1). When yi lies above yi + , i > 0and i = 0. On the other hand, when yi lies below yi ,i = 0 and i > 0. Thus, the objective function of the SVRproblem can be rewritten as

min. CNi=1

(i + i) +1

2||w||2 (5)

subject toi 0 (6)i 0 (7)yi yi + + i (8)yi yi i (9)

The above optimization problem can be transformed intoa Lagrangian dual problem and the final predicted value isgiven by [6]:

yi =

Ni=1

(i i)k(x, xi) + b (10)

where i and i are the Lagrange multipliers, and k is thekernel function. Common kernel functions include linear,polynomial, and radial basis functions (RBF) [7].

III. GENERATOR THERMAL SENSITIVITYA. Causes of thermal sensitivity

As stated in [1], even for a rotor that has thermal sensitivityissue, it is not affected much when the generator is operatingwith low VAR. On the other hand, when the generator is op-erating with a power factor lower than 0.85 lagging, a thermalsensitive rotor will be affected and its vibration profile willchange. The rotor vibration may increase, decrease, or itsphase angle may change. Therefore, even with a thermalsensitive rotor, a generator may not have any issues whenoperating with low field current; however, its operation maybe greatly restricted at high field currents or VAR loads asthe rotor vibration excesses the acceptable limit.

Generator rotor thermal sensitivity can be classified intotwo types: reversible and irreversible. When the thermalsensitivity is reversible, rotor vibration changes as fieldcurrent varies. That is, when the field current increases, therotor vibration increases. Later on, when the field currentdecreases, the rotor vibration will decrease as well. This typeof thermal sensitivity usually does not cause major problemsin practice and the rotor can be balanced so that its maximumvibration will not excess the limit. If the rotor vibration doesnot decrease after the field current is reduced, this type ofthermal sensitivity is called irreversible. This type of thermalsensitivity is troublesome since the rotor vibration will keepincreasing, and the rotor may have to be taken off-line andrepaired in order to reduce the vibration. Readers can referto [1] for more details on some common causes of generatorthermal sensitivity and their thermal sensitivity types.

B. Thermal sensitivity testA standard procedure for determining generator thermal

sensitivity is normally adopted. The purpose of this test is toisolate the machine vibration which is caused by MW (realpower) loading from that caused by VAR loading (reactivepower). Vibration changing with MW loading does notindicate thermal sensitivity problem. The thermal sensitivitytest consists of 3 parts:

1) The thermal sensitivity test is started by loading thegenerator with small MW and MVAR, 10MW and0MVAR for example, and then MW gradually in-creases to about 60% of its rated value and MVARwill be reduced. At each stage, all the important read-ings, such as the machine vibration, voltage, current,temperature, etc. are recorded.

2) In the second step of the test, the generator MW is keptconstant while the field current continuously increasesto its rated value, so MVAR increases correspondingly.It is important that the MVAR is high enough so thatthe generator operates with a power factor lower than0.85 lagging.

3) The last step of the thermal sensitivity test is thereverse of the first 2 parts. The generator MVARdecreases while the MW is kept constant, and thenthe MW decreases and MVAR increases so that thefinal generator MW and MVAR are back to the same

945

10

-20

-10

40

30

20

10

706050403020

0 MW

MVAR

Fig. 2. Typical plot of machine output power during a thermal sensitivitytest

Stream

TurbineGenerator

Bearing 1X, 1Y Bearing 4X, 4YBearing 3X, 3YBearing 2X, 2Y

A

X YA

Axial view

Fig. 3. Typical layout of a BPSTG

values as when the test is started. The complete processof the thermal sensitivity test is illustrated in Figure 2.If the final machine vibration is similar to the vibrationwhen the test is started, it can be concluded that thethermal sensitivity is reversible. Otherwise, if the finalmachine vibration remains high, the thermal sensitivityis irreversible and further maintenance actions mayneed to be taken.

IV. SVR MODEL BASED ON MACHINE VIBRATIONTRACKING FOR THERMAL SENSITIVITY ANALYSIS

A. Experimental setupTwo back pressure steam turbine generators (BPSTG) used

in a local oil-sand company are investigated in this paper.They are labeled as G1 and G2. Figure 3 shows a typicallayout of the BPSTG, which consists of a steam turbine anda generator. They are 4 bearings in total for each generatorand two vibration sensors are installed on each bearing alongx and y axes of 90 degrees apart. During normal operation,the machines are running at 3600 RPM and the vibrationwaveform for each bearing is captured and updated every 2hours.

B. Thermal componentThe thermal sensitivity test serves 2 purposes. The first one

is to determine if there exists irreversible thermal sensitivity.The other purpose is to determine the size of the thermalcomponent, i.e. the difference between the vibration when thegenerator is operating at the low MW and MVAR loading atthe beginning of the test and the vibration when the generatoris operating at the highest MW and MVAR during the test.The difference has to be within a certain limit otherwisethe generator will not be able to run with its full capacity.The method used to calculate the thermal component is asfollows:

0 20 40 60 80 100 120 1401

0

1

Time (ms)

mil

(a)

0 20 40 60 80 100 120 1401

0

1

Time (ms)

mil

(b)

Fig. 4. Machine vibration waveform, (a) unfiltered, (b) 1X only

During the thermal sensitivity test, at each stage, themachine vibration peak-to-peak value and its phase can berecorded. However, it is believed that the vibration due tothermal bow is mainly shown on 1X (one times) speed, whichis 60 Hz in this case; therefore, in order to eliminate the othereffects, the 1X vibration peak-to-peak value is used. Figure4 shows a typical machine vibration waveform together with1X component only. Thus, every cycle in the 1X vibrationwaveform in the x and y direction can be expressed by:

Vx =1

2Axcos( x)

Vy =1

2Aycos( y)

0 < 2 (11)where Ax, Ay , x, and y are the 1X vibration peak-to-peakvalue and phase angle in the x and y direction, respectively,and they can all be recorded during the thermal sensitivitytest.y is subtracted by /2 (or added by 3/2 if y/2 < 0)

since the vibration sensor x and y are 90o degree apart. Thus,

y = y /2

Vy =1

2Aycos( y) (12)

To ensure Vx and Vy are larger than 0, constant terms, 12Axand 1

2Ay will be added to Vx and Vy , respectively. Hence,

Vx =1

2Ax +

1

2Axcos( x)

Vy =1

2Ay +

1

2Aycos( y) (13)

Finally, by iteration, a can be found which maximizesthe following equation,

VT =

Vx

2+ Vy

2 (14)The corresponding phase angle can be denoted as T . Atthis point, the overall maximum machine vibration can beexpressed by a vibration vector with magnitude VT and phaseangle T .

The maximum vibration vector can be calculated for themachine vibration at the start of the thermal sensitivity testand at the point when the machine is operating at the highestMW and MVAR during the test, and then the vibration

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1 2 3 4 50

-1

-2

-3

1

2

Low

Load

High Load

Thermal Component

mil

mil

-1

Fig. 5. Typical plot of the machine 1X vibration vector during a thermalsensitivity test

difference between those 2 conditions can be calculated.Figure 5 is a typical plot of the vibration vector during athermal sensitivity test indicating the thermal component.

The above analysis is focused on the vibration differencebetween the lowest load and the highest load of the machineoperation during the thermal sensitivity test. However, howthe machine vibration changes due to thermal sensitivity ina long term has not been taken into consideration. Also, ifthe machine thermal sensitivity is irreversible, the thermalsensitivity test can be destructive since the machine vibrationmay become worse after the test. Moreover, when a machineis undergone a thermal sensitivity test, it has to be removedfrom the production line, so the productivity is reduced. Itis therefore desirable to determine whether or not a machinehas been experiencing thermal sensitivity issue by analyzingnormal machine operational data. In this paper, the SVRtechnique is applied to build a model for this purpose.Many different techniques can be used to build a systemmodel, including building a physical model. However, thisusually requires an in-depth understanding of the machinestructure. Hence, artificial intelligence techniques are oftenpreferred. Based on [8] and [9], SVR seems to be a betterchoice over Neural Network (NN) and adaptive neuro-fuzzyinference system (ANFIS) and therefore it is selected inthis paper. The method is tested on the two BPSTG andsome valuable preliminary information about rotor thermalsensitivity problem is obtained.

C. SVR based vibration model

For tracking the machine vibration, a system model isneeded. In this case, the inputs of the model are the generatoroutput real power and reactive power, and the output of themodel is the machine 1X vibration. Other than the machineoutput power, many other factors, such as the temperature ofthe machine operating environment, may also have impactson the machine vibration. However, machine output powercan be directly controlled by the on-site engineers, and thisis why they are chosen as the inputs of the model. The modelbuilt to predict the machine vibration based on the generatoroutput power can be mathematically expressed as

y = f(P,Q) (15)

(a)

(b)

Fig. 6. Plots of (a) VTX and (b) VTY , G1

where P and Q are the machine real and reactive power,respectively, and y is the output related to machine 1Xvibration amplitude. If the model is properly trained andthe machine thermal sensitivity is irreversible, the differencebetween the predicted vibration and the real vibration can beshown in the thermal component analysis. Instead of usingthe magnitude or phase angle of the vibration vector as themodel output, the vibration vector is decomposed into twocomponents by projecting to X and Y axes:

VTX = VT cosT , VTY = VT sinT (16)Thus, any changes in the magnitude and phase angle of

the machine 1X vibration are reflected in VTX and VTY .

D. Case studies and the analysis resultsIn this section, SVR models are built for both G1 and G2

and used to track their vibrations. Based on previous thermalsensitivity test results from the plant, it is known that G1does not have serious problem since the thermal sensitivity isreversible. On the other hand, G2 may have serious thermalsensitivity issue and it is irreversible. Vibrations for bothgenerators are analyzed separately in the following sections.

Fig. 6 shows the plots of VTX and VTY of G1. Thevibration data is obtained during the period from Jan. to Aug.2003 on bearing 4 and there are 2761 data points in total.From Fig. 6, no obvious trend can be noticed. VTX and VTYdo not seem to increase or decrease as time progresses. Inorder to confirm that the machine condition did not changeduring that period, SVR models can be built to predict themachine vibration based on the machine output power. If themachine condition indeed did not change during that period,the model predicted vibration should be very close to thereal vibration as long as the model is properly trained.

When building the SVR models in this section, differentkernel functions have been tried, including linear and poly-nomial kernel functions with different degrees. By trial anderror while taking the model training time into considerationas well, polynomial kernel function with degree 2 is selected.The first 700 data points are used to train the SVR modelsand the prediction error is simply the difference between thepredicted vibration value and the real vibration value:

error = V ibrationT, actual V ibrationT, predicted (17)947

(a)

(b)

Fig. 7. (a) SVR model prediction results for VTX , predicted values (red),actual values (blue), and (b) prediction error, G1

(a)

(b)

Fig. 8. (a) SVR model prediction results for VTY , predicted values (red),actual values (blue), and (b) prediction error, G1

Fig. 7 and 8 shows the SVR model prediction results alongwith the real machine vibration and the prediction error. Itcan be seen that, for both VTX and VTY , the predictionresults are very close to the real values. The mean andthe standard deviation of the prediction error of VTX are0.024 and 0.2599, respectively, while they are 0.1202 and0.5018 for VTY . Also, from the error plots, there is noclear trend that the prediction error increases or decreasesas time progresses. Therefore, it can be concluded that thecondition of G1 did not change during the period from Jan. toAug. 2003, and a thermal sensitivity test around this periodmay not be necessary for G1. From the plots, it can alsobe concluded that there is a direct relationship between themachine output power and the machine 1X vibration. It ispossible to build an accurate model with machine real andreactive powers as the model inputs to predict the machine1X vibration.

Similar analysis can be applied to generator G2. Fig. 10shows the plots of VTX and VTY of G2. The vibration datais obtained from Jan. to Sep. 2003 on bearing 3 and there are3123 data points in total. SVR models are built with the samekernel function and parameter for VTX and VTY , and againthe first 700 data points are used to trained the models. Theprediction results and prediction errors are shown on Fig.11 and 12. From Fig. 11, it can be seen that the predictionresults are close to the actual values. The mean and standard

deviation of the prediction errors are 0.0114 and 0.2584,respectively. On the other hand, on Fig. 12, starting fromdata points around 1920, which corresponding to June 23,2003 in actual date, the actual vibration starts to increase,which causes the prediction error between the predicted VTYand the actual VTY to increase and finally settles down atdata points around 2200, which corresponding to July 16,2003 in actual date. The mean and standard deviation of theprediction errors are 0.5502 and 0.613, respectively. Hence,the mean of the prediction error is much larger than thosein the other 3 cases. The prediction error can be furtheranalyzed with the moving window method to show how themean and standard deviation change more clearly. The resultsare shown in Fig. 13, with 500 data points as the windowsize and 100 data points as the moving size. From Fig. 13,it is very clear that the mean of the prediction error starts toincrease rapidly after index 15, which is equivalent to index1900 in the actual data point. If the vibration vectors areplotted during the period from June 23 to July 16, the resultwould be similar to Fig. 9. VTX did not change too muchduring that period and it remained at about 2.5 mil, whileVTY increased approximately from -1 to 1 mil. Thus, thevibration vector moves from the forth quadrant to the firstquadrant.

From the Fig. 12, it is noticed that the model predictionerrors are small for the first 1800 data points, it can beconfirmed that the SVR model has been trained properlyand it should generate outputs accordingly with the changinginput power. Therefore the difference shown after the indexnumber 1920, is mainly due to the reason that the machinecondition has changed. The machine condition may changedue to many mechanical reasons, such as the machine mayhave been taken off-line and maintenance work have beenperformed to the machine, or some machine componentsare worn out. However, it has been confirmed that G2 wascontinuously running for the whole period and there wasnot any maintenance work done to the machine. Also, ifthe machine condition is changed due to components wearout, the process should be slow and the vibration shouldchange slowly instead of increasing abruptly as it is shownin Fig. 12. Another possible cause for the machine conditionchange is irreversible thermal sensitivity. By checking thegenerator output powers, it is found out that, from June 23 to27, the generator was operating with very high MVAR, suchas 25MW and 30MVAR, 45MW and 30MVAR, etc. Also,G2 was considered running in the normal condition sinceits peak-to-peak vibration is under the pre-defined limit andthe change of vibration cannot be noticed if the vibrationdata was not processed by the method described previouslyin this paper. Thus, considering all the analysis above, itis believed that the vibration change is due to thermalsensitivity. Based on the results, one could then recommenda thermal sensitivity test to be scheduled to confirm this.Since the valuable information about thermal sensitivity canbe obtained before the severe machine condition degradationby analyzing past operational data, unexpected shutdownscan be avoided.

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1 2 3 4 50

-1

1

mil

mil

-1

June 23, 2003

July 16, 2003

Change of vibration vector

Fig. 9. Change of vibration vector, G2

(a)

(b)

Fig. 10. Plots of (a) VTX and (b) VTY , G2

(a)

(b)

Fig. 11. (a) SVR model prediction results for VTX , predicted values (red),actual values (blue), and (b) prediction error, G2

(a)

(b)

Fig. 12. (a) SVR model prediction results for VTY , predicted values (red),actual values (blue), and (b) prediction error, G2

0 5 10 15 20 25 300.5

0

0.5

1

1.5

mil

(a)

0 5 10 15 20 25 300.2

0.3

0.4

0.5

0.6

0.7

mil

(b)

Fig. 13. SVR model prediction results for VTY , (a) mean, and (b) standarddeviation, G2

V. CONCLUSIONGenerator thermal sensitivity is studied in this paper. Cur-

rently, in practice, a thermal sensitivity test can be performedto determine if a generator has thermal sensitivity issue ornot. However, thermal sensitivity test has some disadvantagesand it is preferred to determine the thermal sensitivity prob-lem based on the regular machine operational data. In thispaper, system model is built with SVR to predict the machinevibration based on the machine output power. The proposedmethod is applied to analyze the thermal sensitivity in 2BPSTGs and experimental results show that the proposedmethod can be used to keep track of the machine conditionand provide valuable information on whether the generatorhas thermal sensitivity issue.

REFERENCES[1] R.J. Zawoysky and W.M. Genovese. Generator Rotor Thermal

Sensitivity-Theory and Experience, GE Power Systems, New York,2001.

[2] L. Xiang, G.J. Tang, and C. Zhang. Simulation of time seriesprediction based on hybrid support vector regression, Proceedings- 4th International Conference on Natural Computation, Vol, 2, 2008,pp.167171.

[3] M. Zou, J. Zhou, Z. Liu, and L. Zhan, L. A Hybrid Model forHydroturbine Generating Unit Trend Analysis, Proceedings - ThirdInternational Conference on Natural Computation, Vol. 2, 2007,pp.570574.

[4] Alex J. Smola and B. Scholkopf, A tutorial on support vectorregression, Statistics and Computing, Vol. 14, 2004, pp.199222.

[5] S.R. Gunn, Support Vector Machines for Classification and Re-gression, Technical Report, Faculty of Engineering, Science andMathematics, School of Electronics and Computer Science, Universityof Southampton, 1998.

[6] C.M. Bishop, Pattern Recognition and Machine Learning, Springer,New York, 2006.

[7] S. Abe, Support Vector Machine for Pattern Classification, Springer,London, 2005.

[8] Jang, J.R. (1993) ANFIS: adaptive-network-based fuzzy inferencesystem, IEEE Transactions on Systems, Man, and Cybernetics,May/June, Vol. 23, No. 6, pp.665685.

[9] B. Samanta and C. Nataraj. Prognostics of machine condition usingsoft computing, Robotics and Computer-Integrated Manufacturing,Vol. 24, 2008, pp.816823.

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