Applied Mthemticl Sciences, Vol. 1, 2007, no. 42, 2091-2099 Neuro-Fuzzy Modeling of Superheting System of Stem Power Plnt Mortez Mohmmdzheri, Ali Mirsephi, Orng Asef-fshr nd Hmidrez Koohi The University of Adelide Islmic Azd University (Szevr nd Amol Brnches) Astrct In this pper the superheting system of 325MW stem power generting plnt is modeled y usge of recurrent neuro-fuzzy networks nd sutrctive clustering. The experimentl dt re otined from complete set of field experiments under vrious operting conditions. Neuro-fuzzy models re constructed for ech susystem of the superheting unit. The nine fuzzy models re then constructed in comintion of series nd prllel units in ccordnce with rel power plnt susystems. Compring the response of nonliner neuro-fuzzy model of susystem with the response of its liner model otined sed on LSE method; shows tht the nonliner neuro-fuzzy model is more ccurte thn liner model in the sense tht its response is closer to the response of the ctul system. Since LSE is optimum modeling method for liner systems, it cn e concluded tht some of power plnt susystems re of nonliner processes. Keywords: Fuzzy logic, Modeling, Neuro-fuzzy, Stem power plnt Introduction Model-sed control schemes require the existence of suitle process model. Proper models re, furthermore, needed to test new controllers. It is mthemticlly proved tht the lest squre error (LSE) method is the optimum modeling method for liner systems [1,2]. For nonliner plnts, in ddition to physics sed modeling, there re some I/O dt sed methods, s well. I/O dt sed methods offer different models, such s perceptron neurl networks nd
2092 M. Mohmmdzheri et l fuzzy models [3]. Neurl networks re usully considered s lck oxes, ut systems cn e expressed in fuzzy rules with using fuzzy modeling. Fuzzy rules re formed minly y linguistic vriles. There re some methods for fuzzy modeling such s fuzzy genetics nd neuro-fuzzy networks [4, 5]. Neuro-fuzzy networks re one of the most fvorle structures for fuzzy modeling. In this pper superheting system of 325MW unit of stem power plnt, including seven susystems is modeled, using recurrent neuro-fuzzy networks; s connected set of series nd prllel fuzzy models. Modeling Strtegy In this pper one of the most common structures of neuro-fuzzy network identified s dptive neuro-fuzzy inference systems (ANFIS) [1,6,7,8] is considered. Figure1 shows scheme of liner sugeno type FIS (fuzzy inference system) [1, 6, 7]. In this structure, ntecedent of rules contins fuzzy sets (s memership functions) nd consequent is first order polynomil ( crisp function). The structure shown in Figure1 cn e trnsformed to the neuro fuzzy network shown in Figure2. Figure1: A Sugeno-type FIS Figure2: Sugeno-type neuro-fuzzy network In this method, fuzzy inference system is designed sed on system specifictions. This initil model is trnsformed to neuro-fuzzy network nd then trined y experimentl recorded dt of the system. The trining procedure involves oth grdient error ck propgtion (to djust memership function coefficients) nd LSE (to djust liner output prmeters). In fuzzy inference systems, fuzzy rules numer is equl to numer of memership functions powered y numer of inputs. Sometimes, to cover ll input spce, so mny rules re needed. Trining such FIS s is too time consuming or prcticlly impossile. In order to reduce fuzzy rules numer with minimum ccurcy loss, method nmely sutrctive clustering is pplied [1, 7]. In this method, rules with most prole ntecedents in recorded dt of ctul system re selected. The model derived from sutrctive clustering is used s initil model for trining. All mentioned modeling methods cn e pplied to model oth sttic nd dynmic systems. If the output of the model t moment is pplied s its input t
Neuro-fuzzy modeling 2093 the next moment; the model is dynmic (recurrent) model. In other words, in recurrent models, output of the model t the existing moment, is influenced y the output of the model, t previous moments. For exmple, in this reserch, current outlet temperture of de-superheter model is dependent on its outlet temperture in erlier times. The nonliner dynmic model cn e descried y the discrete time eqution: y(k)=f(u(k),..., u(k nu), y(k),..., y(k ny)) (1) Dynmic systems cn only e modeled stisfctorily y recurrent (dynmic) neurl or neuro-fuzzy networks (i.e. Fig2) not y sttic (memory-less) networks. Figure3: A scheme of typicl recurrent model, u nd y re input nd output Superheting system modeling The structure of superheting system in stem power generting plnt is shown in Fig 4. The stem flow inters to the superheter nd fter pssing through the het exchngers it inters to the high pressure turine. For norml opertion of the plnt nd when the cpcity of the power plnt is over 30% of its nominl vlue, the desired output temperture of superheter is 540 Celsius degree ( o c ).This temperture is djusted t the de-superheter y sprying wter through sprying vlves. Fig4: Super heting system of the power plnt In this pper 1st order (liner) Sugeno type fuzzy inference systems re used [1, 6, 7]. T-norm is lgeric product nd memership functions re Gussin, expressed: 1 x c 2 Memership grde = exp[ ( ) ] (2) 2 σ
2094 M. Mohmmdzheri et l x is the input nd c nd σ re memership function vriles[1]. The modeling is performed using complete set of dt, including 4000 dt sets of Shznd power plnt, the smpling time equls to 1 second. Additionlly, 1400 sets of dt re used s checking dt. Recording dte is 26 th Aug 2004. In order to model the superheting system, for ech susystem neuro-fuzzy inference system is constructed y sutrctive clustering nd trined y hyrid lerning method of ANFIS. Superheting system consists of three superheters nd four de-superheters. Since the first nd second superheters re MIMO systems, they re modeled s two prllel MISO systems. In totl, nine FIS s re constructed nd trined for seven superheting susystems. Models hve 8~11 inputs nd one output. Then, ll these components re put together s prllel or series elements, wheres in finl run, mny of inputs of susystems model re outputs of preceding susystems. In order to use recorded dt for modeling, the following points re considered; 1. Delys re included in modeling. For instnce, it tkes 20 seconds to stem psses through superheter. Therefore, when the temperture of inlet stem is pplied in modeling tht superheter, 20 seconds dely should e considered. 2. In order to improve the speed of convergence of prmeters nd coefficients in neuro-fuzzy model, their sensitivity to the vrition of inputs signls should e incresed. To do so elements of ech column of trining dt re sustituted with sme elements sutrcted from the men vlue of elements in tht column. It cuses tht the quntity error dt mgnitude increses, where, error in the numertor is the difference etween outputs of the model nd the ctul system. 3. Noting tht the lgorithm for djusting the neuro-fuzzy model depends on the mgnitude of inputs dt ; therefore, ll inputs re normlized. 4. In neuro-fuzzy modeling, minimizing of the checking error is the criterion of successful modeling nd over trining is voided. In order to clrify the modeling process, susystem of superheting system, the second left-hnd de-superheter is selected. Modeling process for this susystem is comprehensively offered. Second left-hnd de-superheter modeling Figure 5 shows the inputs nd output signls of the second left-hnd desuperheter, where the three inputs re; the stem temperture efore sprying wtert (inlet temperture), the wter mss rte V nd the stem mss rte f. The output is the stem temperture fter sprying wtert.
Neuro-fuzzy modeling 2095 Fig5: Inputs nd output of de-superheter: () plnt, The stem mss rte ( f ) is summtion of two other signls. The first is hlf of totl mss flow of wter entering the drum (fter drum the stem flow is divided into two rnches, Fig3) nd the second signl is the first step sprying wter mss rte which is dded to min stem flow. The de-superheter system is influenced y oth of these signls with dely (Fig 7). Figure 6 illustrtes the input-output signls of the neuro-fuzzy model for the desuperheter in the discrete domin. In this Figure, the vlues of T,V nd f t present time, their vlues t two steps efore (for T nd V) nd one step efore (for T,V nd f ) nd lso the vlues of T t the pst two time increments re ll input signls. The output of the neuro-fuzzy model is the output temperture of the de-superheter T (k). Fig6: Inputs nd output of de-superheter neuro-fuzzy model The reltion etween the ten inputs nd one output of Fig6 for ech fuzzy rule is given y the following eqution: T α V ( k 2) + α f ( k) 6 ( k) = α T ( k) + α T ( k ) + α T ( k 2) + α V ( k) + α V ( k ) + 1 7 2 8 3 + α f ( k ) + α T ( k ) + α T ( k 2) + α 9 4 10 5 11 (3) Prmeters α i, i = 1,..., 11 nd coefficients of Gussin memership functions for ll ssocited fuzzy rules re djusted in neuro-fuzzy model. Note tht Eq.(3) is written for ech fuzzy rule, while for simplicity the suscript of the ssocited fuzzy rule is omitted in this eqution. If the left hnd side of Eq.(3) for the jth fuzzy rule is shown y (k), then the output of neuro-fuzzy model is: T j
2096 M. Mohmmdzheri et l T j η T ( k) ( k) = (4) η j j j j Where η j is the firing strength of the jth rule. For neuro-fuzzy modeling, ll quntitiest, T, V nd f re mesured nd put in column vectors. Figure 7 shows the schemtic digrm of this de-superheter neuro-fuzzy model. Noting tht the numer of inputs in this model is 10, if only 3 linguistic vriles (ie, positive medium or positive lrge) re ssigned for ech input, the numer of rules would result in 3 10 rules. An lterntive pproch is sutrctive clustering [1, 7], with using this method, the numer of rules reduces to only 22 rules. Note tht for ech rule in ddition to prmeters αi, i = 1,..., 11, coefficients σ nd c in ll memership functions of 10 inputs must e djusted. Thus for ll rules totl sum of 682 prmeters nd coefficients re djusted. Using the sme mesured dt, liner model of this de-superheter is lso derived sed on the lest squre error (LSE) method in the form of third order trnsfer functions ; 0. 029z 0. 176z + 0. 154 T ( z) = T ( z) +. z. z. z 3 0 01 + 0 02 01 + 1 0. 059z 0. 084z + 0. 004 0. 005z + 0. 003z + 0. 002 V( z) f ( z). z. z. z +. z. z. z 3 3 0 01 + 0 02 01 + 1 0 01 + 0 02 01 + 1 In this eqution, the vriles T (z), T (z), V (z) nd f (z) re the Z trnsform of stem temperture fter nd efore sprying, wter mss rte nd stem mss rte, respectively. (5)
Neuro-fuzzy modeling 2097 Fig7: Input nd output signls of neuro-fuzzy model Simultion Results In this section, we first investigte the simultion results of implementing the neuro-fuzzy pproch for modeling the second left-hnd de-superheter of power generting plnt, nd then study the results of implementing this modeling method for whole superheting system. Figure 8 illustrtes the response of the second left-hnd de-superheter, otined from recorded dt of the ctul plnt. It lso shows the responses otined from simultion results for oth LSE nd neuro-fuzzy models. Figure 9 shows similr responses of the ctul plnt nd the models under specil operting conditions. Both Fig s 8 nd 9 indicte tht the neuro-fuzzy model is more ccurte thn the LSE model, in the sense tht, its response is closer to the response of the ctul plnt. Noting tht the LSE method is optimum for modeling liner systems, the simultion results confirm tht the de-superheter is nonliner susystem of power plnt. Figure 8: neuro-fuzzy nd LSE modeling result, oth for trining nd checking re
2098 M. Mohmmdzheri et l Figure9: neuro-fuzzy nd LSE modeling result, under specil operting condition Figure10 shows the simultion result of whole model, formed y 9 series nd prllel fuzzy models, for oth for trining nd checking res. Figure10: neuro-fuzzy modeling result, for integrted model (including nine su-models) Conclusion In this pper, neuro-fuzzy modeling is performed for power plnt superheting system, including three superheters nd four de-superheters. Then ll these models put together s totl model. In modeling, some significnt notes re considered, such s time delys. After ll considertions nd using sutrctive clustering, to reduce the numer of fuzzy rules, reltively good ccurcy is chieved for this set of complex models. Mny of inputs of totl model elements re outputs of other elements or their own outputs t erlier times. Also, it is indicted tht some of power plnt susystems re of nonliner nture, with comprison etween LSE modeling result nd neuro-fuzzy modeling.
Neuro-fuzzy modeling 2099 Acknowledgement Authors wish to thnk the stff of Shznd power plnt for their coopertion in this reserch. References [1] J. R. Jng, C. Sun, E. Mizutni. Neuro-Fuzzy nd Soft Computing. Prentice-Hll Inc.1997 [2] L. Ljung System Identifiction - Theory for the User, Prentice Hll, Upper Sddle River, N.J. 2nd edition, 1999. [3] J.Vieir, F. Morgdo Dis, A. Mot Artificil Neurl Networks nd Neurofuzzy Systems for Modeling nd Controlling Rel Systems: A Comprtive Study, Engineering Applictions of Artificil Intelligence 17 (2004) 265 273 [4] H. ghezelygh, K. Y.Lee, Trining Neuro-Fuzzy Boiler Identifier with Genetic Algorithm nd Error-Bck Propgtion Power Engineering Society Summer Meeting, 1999. IEEE, Volume: 2, 18-22 July 1999,pp978-982. [5] A. Afzlin, D.A. Linkens, Trining Of Neurofuzzy Power Systems Stilizers Using Genetic Algorithm, 22nd conference of Electricl Power nd Energy Systems(2003), pp93-102 [6] J. Jntzen,. Neurofuzzy Modeling, Technicl University of Denmrk, Deprtment of Automtion, Bldg 326, DK-2800 Lyngy, Denmrk, Tech. report no 98-H-874 (nfmod), 30 Oct. 1998 [7] J.R. Jng, Fuzzy Logic Toolox User s Guide,2 nd Version. MthWorks Inc.2000 [8] J.R. Jng, ANFIS: Adptive-network-sed Fuzzy Inference Systems.IEEE Trnsctions on Systems, Mn, nd Cyernetics 23 (3), 1993,pp665-685. [9]K. J. Astrom, T. Hgglund, PID Controllers: Theory, Design, nd Tuning, ISA, Reserch Tringle Prk, NC, 1995. Received: Jnury 18, 2007