NEURO-FUZZY MODELING OF SUPERHEATING SYSTEM OF A STEAM POWER PLANT

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1 NEURO-FUZZY MODELING OF SUPERHEAING SYSEM OF A SEAM POWER PLAN A. R. Mehraban, A. Yousef-Koma School of Mechancal Engneerng College of Engneerng Unversty of ehran P.O.Box: , ehran Iran armehraban@gmal.com M. Mohammad-Zaher Department of Engneerng Islamc Aad Unversty Shahr-e-Ray branch P.O.Box: , ehran Iran mmahery@gmal.com A. Ghaffar, D. Mehrab Department of Mechancal Engneerng K. N. oos Unversty of echnology ehran Iran ghaffar@kntu.ac.r ABSRAC In ths paper superheatng system of a 325MW steam power plant s modeled based on the recurrent neurofuy networks and subtractve clusterng. he expermental data are obtaned from a complete set of feld experments under varous operatng condtons. Nne neuro-fuy models are constructed and traned for seven subsystems of the superheatng unt. hen, these nne fuy models are put together mergng seres and parallel unts accordng to the real power plant subsystems, to obtan the global model of the superheatng process. Comparng the tme response of the nonlnear neuro-fuy model of a subsystem wth the tme response of ts lnear model based on the Least Square Error (LSE) method, ndcates that the nonlnear neurofuy model s more accurate and relable than the lnear model n the sense that ts response s closer to the response of the actual superheatng system. KEY WORDS Fuy sets, Neuro-fuy systems, Nonlnear modelng, Steam power plant, Nonlnear systems, PID controller and neuro-fuy networks are of the most common approaches [4], [5]. In ths paper superheatng system of a 325MW unt of a steam power plant, contanng seven subsystems s modeled, usng recurrent neuro-fuy networks, as a connected set of seres and parallel fuy models. 2. Modelng Strategy One of the most common structures of neuro-fuy network s dentfed as adaptve neuro-fuy nference systems (ANFIS) [], [6], [7], [8]. Fgure shows a scheme of a lnear Sugeno-type FIS (fuy nference system) [], [6], [7]. In ths structure, antecedent of rules contans fuy sets (as membershp functon) and consequent s a frst order polynomal (a crsp functon). he structure shown n Fgure can be transformed to the neuro fuy network as shown n Fgure 2. Usng ths A B. Introducton Model-based control scheme requres the exstence of a sutable process model. Proper models are, furthermore, needed to test new controllers. It s mathematcally proven that the least square error (LSE) method s the most sutable modelng method for lnear systems [], [2]. For nonlnear plants, n addton to mathematcal modelng based on the physcs of the system, there are a number of data drven (I/O data based) methods, as well. Data drven methods offer dfferent approaches, such as mult-layer perceptron neural networks (MLP), radal bass functon neural networks (RBF) and fuy systems (FS) [3]. A dynamcally unknown-system can be expressed by fuy rules by means of fuy modelng, where fuy rules are formed manly by lngustc varables. here are dfferent methods for obtanng fuy rules of the unknown-model, for nstance fuy genetcs (b) x y f =p x+q y+r w wf + w 2f 2 f = X Y w + w 2 A 2 B 2 = w f + w 2 f2 f 2 =p 2 x+q 2 y+r 2 w 2 X Y x y Fgure : A Sugeno-type fuy nference system Layer A Layer 2 Layer 3 w N A 2 B N w 2 B 2 Layer 4 x y w w f Layer 5 SUM f w 2 f w 2 2 x y Fgure 2: A Sugeno-type neuro-fuy network

2 method, a fuy nference system s desgned based on system specfcatons. hs ntal model s transformed to a neuro-fuy network and then traned by expermental recorded data from the actual system. In fuy nference systems the number of fuy rules s equal to number of membershp functons powered by number of nputs. Sometmes, to cover all nput space, so many rules are needed. ranng such FIS s s too tme consumng or practcally mpossble. In order to reduce the number of fuy rules wth mnmum accuracy loss, a method called subtractve clusterng s appled [], [7]. Usng ths algorthm, a lmted number of fuy-rules wth most probable antecedents n hstorcal data of actual system are generated. hen, the model derved from subtractve clusterng s used as ntal model for tranng. he tranng procedure nvolves both gradent error backpropagaton to adust membershp functon coeffcents, and LSE to adust lnear Sugeno-type output parameters. he mentoned modelng methods can be appled to model both statc and dynamc systems. If the output of the model at a moment s appled as ts nput at the next moment; the model s called dynamc (recurrent) model. In other words, n recurrent models, output of the model at the moment, s nfluenced by the output of the model, at prevous moments. For example, n ths research, current outlet temperature of a de-superheater model s dependent on ts outlet temperature n earler tmes. he nonlnear dynamc model can be descrbed by the dscrete tme equaton: y(k) = f(u(k ),..., u(k nu), y(k ),..., y(k ny)) () Dynamc systems can only be acceptably modeled by recurrent (dynamc) neural or neuro-fuy networks (see Fgure 3) not by statc (memory-less) networks. 3. Superheatng System Modelng he structure of a superheatng system n a steam power generatng plant s shown n Fgure 4. he steam flow enters to the superheater, then after passng through the heat exchangers t goes to the hgh pressure turbne. For normal operaton of the plant, whle the capacty of the Fgure 3: A scheme of a typcal recurrent model, u and y are nput and output power plant s over 30% of ts nomnal value, the desred output temperature of superheater s 540 Celsus degree ( o C). hs temperature s adusted at the de-superheater by sprayng coolng water through sprayng valves. In ths paper st order (lnear) Sugeno-type fuy nference systems are used [], [6], [7]. -norm s algebrac product and membershp functons are Gaussan, expressed: x c 2 Membershp grade = exp[ ( ) ] (2) 2 σ where x s the nput and c and σ are membershp functon varables []. he modelng s performed usng a complete set of data, ncludng 4000 data sets of Shaand power plant (located n the cty of Arak, Iran) recorded at Aug 2004, wth the samplng tme equal to second. Addtonally, 400 seconds of data are used as the checkng data. In order to model the superheatng system, for each subsystem a neuro-fuy nference system s constructed by subtractve clusterng and traned by hybrd learnng method of ANFIS. Superheatng system conssts of three superheaters and four de-superheaters (totally seven subsystems). Snce the frst and second superheaters are MIMO systems, they are modeled as two parallel MISO models wth same nputs (ncreasng the number of the neuro-fuy models to nne). Consequently, nne FIS s are constructed and traned for seven superheatng subsystems. Models have 8~ nputs and one output. hen, all these components are put together as parallel or seres elements, whereas n the fnal system, nputs of the Sprayng water comes from hgh pressure feed-water Left hand st V Left hand 2 nd Saturated steam from drum (Inlet steam) Frst super heater Rght hand st Second super heater f, b a Rght hand 2 nd hrd super heater Superheated steam to hgh pressure turbne (Outlet steam) Fgure 4: Superheatng system of the power plant 348

3 next subsystems are outputs of the precedng subsystems. In order to use recorded data for modelng, the followng ponts were consdered:. me delays are ncluded n modelng. For nstance, t takes 20 seconds for steam to pass through a superheater. herefore, when the temperature of nlet steam s appled n modelng the superheater, 20 seconds of tme delay should be consdered. 2. In order to mprove the speed of convergence of parameters and coeffcents of the neuro-fuy model, the senstvty of the neuro-fuy model to the varaton of nputs sgnals should be ncreased. o do so, elements of each column of tranng data are substtuted wth same elements subtracted from the mean value of elements n that column. It causes error ncrease of the quantty data magntude, where error n the numerator s the dfference between outputs of the model and the actual system. 3. Notng that the algorthm for adustng the neurofuy model depends on the magntude of data, all nputs are normaled. 4. In neuro-fuy modelng, mnmng of the checkng error s used as the crteron for successful modelng and avodng over tranng. In order to llumnate the modelng process, one subsystem of the superheatng system that s the second left-hand de-superheater, s selected to be comprehensvely offered n the next secton. 4. Second Left-hand De-superheater Modelng he nputs and output sgnals of the second left-hand desuperheater are shown n Fgure 5, where the three nputs are: the steam temperature before sprayng water b (nlet temperature), the sprayng water mass rate V and the steam mass rate f. he output s the steam temperature after sprayng water a (outlet temperature). Fgure 6 llustrates the nput-output sgnals of the neurofuy model for the de-superheater n the dscrete tme doman. In ths Fgure, the values of b, V and f at present tme, ther values at two steps before (for b and V) and one step before (for b, V and f) and also the values of a at the past two tme ncrements construct the array of the nput sgnals. he output of the neuro-fuy model s the output temperature of the de-superheater a (k). he relaton between the ten nputs and one output of Fgure 6 for each fuy rule s gven by the followng dscrete equaton: a ( k) = αb( k) + α2b( k ) + α3b( k 2) + α4v( k) + α5v( k ) + α6v( k 2) + α7 f( k) + α8f( k ) + α9a ( k ) + α ( k 2) + α 0 a where parameters α, =,..., and coeffcents of Gaussan membershp functons for all assocated fuy rules are adusted n neuro-fuy model. Note that (3) s wrtten for each fuy rule, whle for smplcty the subscrpt of the assocated fuy rule s omtted n ths equaton. If the left hand sde of (3) for the th fuy rule s shown by a (k), then the output of the global neurofuy model s: a η ( k) (3) ( k) = (4) η a where η s the frng strength of the th rule. For neurofuy modelng, all quanttes a, b, V and f are measured and are putted together n a column vector. b (k) - b V Plant a f Fgure 5: Inputs and output of a de-superheater V (k) f (k) Neuro-fuy model a (k) he steam mass rate (f) s summaton of two other sgnals. he frst sgnal s half of the total mass flow of water extng the drum, (after drum the steam flow s dvded nto two branches) and the second sgnal s the frst step sprayng water mass rate whch s added the to man steam flow (see Fgure 3). he de-superheater system s nfluenced by both of these sgnals wth dfferent tme delays (Fgure 7). a (k) Fgure 6: Inputs and output of de-superheater neurofuy model 349

4 INPU b Inlet steam temperature INPU2 V Mass flow rate of the sprayng water INPU3 Feed water mass flow INPU4 Frst de-superheater sprayng water mass flow rate f DE-SUPER HEAER FUZZY MODEL INLE SEAM EMPRAURE 20 5 Fgure 7: Input and output sgnals of neuro-fuy model 4000 s tranng plus 400 s checkng tranng area checkng area 0 δ [deg. Celsus] hs torcal data LS E neuro-fuy tme(s ) Fgure 8: Neuro-fuy and L SE modelng result, both for tranng and checkng area Fgure 7 shows a schematc dagram of ths desuperheater neuro-fuy model. Note that the number of nputs n ths model equals to 0, assgnng only 3 lngustc varables (.e. postve low, postve medum or postve large) for each nput, as a consequence, wll result to enormous number of 3 0 rules. In order to reduce the number of rules, subtractve clusterng was employed that prunes unnecessary rules [], [7]. When usng ths method, the number of rules reduces only nto 22. Note that for each rule n addton to parameters α, =,...,, coeffcents σ and c n all membershp functons of 0 nputs must be fne-tuned. hus for all rules a total sum of 682 parameters and coeffcents are adusted. Usng the same measured data, a lnear model of ths desuperheater s also derved based on the least square error (LSE) method n the form of a thrd order transfer functons: ( a ) = ( ) 3 2 b V () f() where ndcates Z transform. 5. Smulaton Results In ths secton, we frst nvestgate the smulaton results of mplemented neuro-fuy approach for the modelng the second left-hand de-superheater of power generatng plant. hen, the results of mplementng ths modelng method for the whole superheatng system wll be studed. Fgure 8 llustrates the response of the second left-hand de-superheater, obtaned from hstorcal data. It also shows the responses obtaned from smulatons result for both LSE and neuro-fuy models. Fgure 9 shows smlar responses of the actual plant and the models for specfc operatng regon. Both Fgures 8 and 9 ndcate that the (5) 350

5 neuro-fuy model s more accurate than the LSE model, n the sense that, ts response s closer to the response of the actual plant. he smulaton results confrm that the de-superheater s a nonlnear system LS E and neuro-fuy es tmated data vers us actual data, s mulaton s tarted at 500s represents temperature (constructed from seven dfferent sgnals). Fgure shows the smulaton result of the global model, formed by nne seres and parallel fuy models mentoned above, for both for tranng and checkng areas. It s clear from the Fgures 9 and that the obtaned model s very accurate and trustful. -4 δ [deg. Celsus] actual data LS E neuro-fu y tme (s ) Fgure 9: Neuro-fuy and LSE modelng result, under specal operatng condton A scheme of the whole superheatng model of the power plant s shown n fgure 0 (sgnals that represent order or tme delay and recurrent dynamc are avoded). Sgnal f s steam mass rate passng through the th superheater. Note that the sprayng water s also beng ntroduced to the steam n each de-superheater. VL, V2L, VR and V2R are the mass rate of sprayng water n the frst and the second left and rght de-superheater respectvely. he fuel sgnal s the mass of the nected fuel and the sgnal 6. An Applcaton One of the man obectves of the de-superheater system dentfcaton s to acheve an adequate model of the process n order to desgn an effectve controller. Wth the purpose of showng effectveness of presented dentfcaton scheme, an llustratve control law was desgned for the second left-hand de-superheater. he controller s a PI-acton controller wth ant-wnd-up strategy [9]. Parameters of the controller are tuned by GA optmng technque (explaned n detals n [0], []). he controller command has the followng form: t () () ( τ) ( τ ) e τ (6) s u t = Kp e t + K 0 e + d t where et () s the error sgnal, K p and K are f VL the frst left f2 V2L the second left f fuel the frst super-heater m f2 fuel the second super-heater m f3 fuel the thrd super-heater VR f the frst rgh V2R f2 Fgure 0: Scheme of the total neuro-fuy model the second rght 550 tranng area checkng area 545 Outlet temprature [deg. Celsus ] ntegrated model output hstorcal data Fgure : Neuro-fuy modelng result, for ntegrated model (ncludng nne sub-models) tme(s ) 35

6 proportonal and ntegral gans respectvely, and t s the trackng tme constant. Employng GA optmaton followng values for controller parameters are obtaned [0], []: Kp = 0.748, K = 0.08, t = 0.2. me response of the closed-loop system s depcted n Fgure 2 for the sample nterval wth respect to operatng PI controller on the actual system. It can be clearly seen that the set-pont s followed by desgned controller closer than operatng PI controller. It s clear from the Fgure 2 that the controller command s subected to saturaton, whch obvously explans the necessty of mplementng ant-wnd-up strategy. o C] Value [ Mag [ton/hour] PI wth ant-wndup: u Current PID Set pont Outlet temperature tme response me [sec] Controller command PI wth ant-wndup: u 2 Current PID me [sec] Fgure 2: Dynamc tme response of the de-superheater PI controller wth ant-wndup 7. Concluson In ths research a neuro-fuy algorthm s employed for the modelng of power plant superheatng subsystems, ncludng three superheaters and four de-superheaters. me delays that exst n the real system are consdered n the modelng. After that, usng subtractve clusterng, n order to reduce the number of fuy rules, a model wth hgh accuracy s acheved for set of complex subsystems. hen, all these models are put together to reach the global model of the superheatng process. Many nputs of the global model subsystems are outputs of the other subsystems or ther own outputs at earler tmes, ndcatng necessty of use of recurrent structure. Also, t s llustrated that power plant subsystems have nonlnear nature, whch can be concluded by comparng results of LSE and neuro-fuy modelng. References [] J. R. Jang, C. Sun, E. Mutan, Neuro-fuy and soft computng (Englewood Clffs, NJ: Prentce-Hall, 997). [2] L. Lung, System dentfcaton - theory for the user (Upper Saddle Rver, NJ: Prentce Hall, 999). [3] J. Vera, F. Morgado Das, A. Mota, Artfcal neural networks and neuro-fuy systems for modelng and controllng real systems: a comparatve study, Engneerng Applcatons of Artfcal Intellgence, 7, 2004, [4] H. Gheelayagh, K. Y. Lee, ranng neuro-fuy boler dentfer wth genetc algorthm and error-back propagaton, Proc. IEEE Power Engneerng Socety Summer Meetng 2, 999, [5] A. Afalan, D. A. Lnkens, ranng of neuro-fuy power system stablsers usng genetc algorthms, Internatonal Journal of Electrcal Power & Energy Systems 22 (2), 2000, [6] J. Janten, Neuro-fuy modelng, ech. report no 98- H-874 (nfmod) (echncal Unversty of Denmark, Department of Automaton, Bldg 326, DK-2800, Lyngby, Denmark: 998). [7] J. R. Jang, Fuy logc toolbox user s gude, 2 nd verson, MathWorks, [8] J. R. Jang, ANFIS: Adaptve-network-based fuy nference systems, IEEE ransactons on Systems, Man, and Cybernetcs 23 (3), 993, [9] K. J. Astrom,. Hagglund, PID Controllers: heory, Desgn, and unng (Research rangle Park, NC: ISA, 995). [0] A. Ghaffar, A. R. Mehraban, M. Mohammad- Zaher, Identfcaton and Control of Power Plant De- Superheater Usng Soft Computng echnques, submtted to Engneerng Applcatons of Artfcal Intellgence, Specal Issue on Artfcal Intellgence Applcatons n Process Control. [] A. R. Mehraban, M. Mohammad-Zaher, A. Yousef-Koma, Desgn of a Genetc-Algorthm-Based Steam emperature Controller n hermal Power Plants, submtted to IEEE Internatonal Conference on Engneerng of Intellgent Systems, ICEIS Acknowledgements he authors wsh to thank the revewers of the paper for ther outstandng suggestons. 352