RBF NN Based Marine Diesel Engine Generator Modeling

Transcription

1 005 Amercan Control Conference June 8-0, 005. Portland, OR, USA ThB4.6 RBF Based Marne Desel Engne Generator Modelng Wefeng Sh, Janmn Yang, Tanhao Tang, Member, IEEE Abstract For buldng a real tme marne power system smulator, models of fast calculaton and hgh precson of marne power system are needed. Because there are abltes of learnng and batch operaton wth artfcal neural networks (A), t s ft for usng A to buld a real tme marne desel generator model for marne power system smulator. In ths paper, radal bass functon neural networks (RBF ) was used for buldng model of marne desel engne generator. RBF s unversal approxmaton neural network. There s ablty to approxmate a nonlnear functon wth RBF. Accordng to workng prncples of desel generator, parameters of exctaton current/voltage and desel engne mechancal torque are as nputs of RBF, parameters of termnal voltage current and frequency of generator are as outputs for RBF tranng. The type of supervsed learnng of center selecton strategy was used for the RBF learnng method. An approxmated model of marne desel generator s bult n hgh precson result wth 99 hdden neurons of RBF. calculatng by DSP. A provdes opportunty for mprovng the precson and fast calculaton speed to real tme marne desel generator model. Radal bass functon neural network (RBF ) s broad to unformly approxmate any contnuous functon [4]. There s ablty to approxmate nonlnear model wth RBF. In the paper, RBF was used for marne desel generator modelng of real tme power system smulator. II. EURO MODEL AD ETWORK ARCHITECTURE OF RBF euron model of RBF s showed n Fg. wth p nputs. Here R s number of elements n nput vector. The dst box n ths fgure accepts the nput vector p and the sngle row nput weght matrx, and produces the dot Input layer Radal Bass euron I. ITRODUCTIO CCORDIG to STCW78/95 nternatonal conventon, Aestablshed by the Internatonal Martme Organzaton (IMO), marne engneers on automatc ocean-shps must be advance through marne power system smulator tranng. Marne power system s dfferent wth shore power system because the generator s drove by large capacty desel engne. For buldng a real tme marne power system smulator, mathematcal model of marne desel generator s needed. Two factors about the real tme model are consdered. One factor s calculaton speed of model. Another factor s precson of model. The factors are mportant to response characterstcs of real tme marne power system smulator. Because theory model of electrcal generator s so complex, t s not ft for smulator Wefeng Sh, Assocate Prof., Dept. of Electrc Automaton. SMU. Pudong Dadao 550 hao, 064 #. 0035, Shangha, Chna. Tel: , Fax: , e-mal: wfsh@shmtu.edu.cn, Janmn Yang, Dept. of Electrc Automaton. SMU. Shangha PuDong DaDao 550 Hao, 0035, Shangha, Chna. Tel: , e-mal: yang.an.mn@63.com, Tanhao Tang, Prof. Dept. of Electrc Automaton. SMU. Member of IEEE. Pudong Dadao 550 hao. 0035, Shangha, Chna. Tel: , Fax: , e-mal: thtang@eee.org, product of the two []. The net nput to the transfer functon s the vector dstance between ts weght vector w and the nput vector p, multpled by bas b. The relatonshp between nput and output s: p = [p p p 3 p R ] w = [w, w, w,3 w,r ] a = f [( w p b)] Select Gaussan functon as transfer functon. The functon for a radal bass neuron s: n f( n) = e () The output of a s: a = exp[ ( w p b) ] b = Fg.. euron model of RBF m d max Here, m s the number of centers and d max s the maxmum dstance between the chosen centers /05/$ AACC 745

2 RBF conssts of three layers nclude nput layer wth networks. Fg. shows network archtecture of radal bass networks. The nput layer s made up of source nodes that MSB D/G D/G D/G3 D/G4 EG ESB Input layer Radal Bass layer Lnear layer AC450V 3 AC450V 3 60Hz500kW 60Hz60kW AH-40C AH-40C AH-40C AH-40C AME-6 REF. General Contaner Feed VA 440/0V o. Steer gear GSP ~3 3VA 440/3300V VA 440/0V o. Steer gear ST Fg.. etwork archtecture of RBF (L) 0V F P M SIDE THRUSTER 00kW 465A (A) 0VF P connect the network to ts envronment. The second layer, the only hdden layer, t s radal bass layer of S neurons. Here S s number of neurons n hdden layer. It apples a nonlnear transformaton from the nput space to the hdden space, n most applcatons the hdden space s of hgh dmensonalty. The dst box n ths fgure accepts the nput vector p and the nput weght matrx IW, and produces a vector havng S elements. The elements are the dstances between the nput vector and vector IW, formed from the rows of the nput weght matrx []. And another s output lnear layer of S neurons. The output layer s lnear layer. Accordng to network archtecture of RBF n Fg., the output of radal bass layer and lnear layer can be calculate as: = exp [ ( IW p b ) ] a, a y = = f ( LW + In Fg., R s number of elements n nput vector, S s number of neurons n radal bass layer, S s number of neurons n lnear layer. a s the th element of a. IW, s a vector made of the th row of IW,. f s a lnear functon. An mportant pont s the fact that the dmenson of the hdden space s drectly related to the capacty of the network to approxmate a smooth nput-output mappng; the hgher the dmenson of the hdden space, the more accurate the approxmaton wll be [3]. III. MARIE ELECTRIC POWER SYSTEM ITRODUCE The power supply and control system are becomng more complex now the electrcal capacty of automated ocean-gong shps s growng larger. Fg. 3 shows the confguraton of electrc power system of a large marne contaner shp. Ths s an AC440V (3-60Hz) power network system. The capacty of each desel generator s 850kVA, 3657A. There s an emergency desel generator (35kVA, 47A) wth the system. About electrc loads, there are sde-thruster (00kW, 465A), steerng gear, refrgerated contaner and so on. The dynamc characterstc of marne power system depends on the desel, a b ) Fg. 3 Confguraton of the electrc power system engne generator. For power system smulator, model of the desel engne generator s the most mportant secton. IV. MARIE DIESEL EGIE GEERATOR MODELIG BASED O RBF A. Desel Generator Modelng Method Three layers networks were formed wth one nput layer one hdden layer and one output layer as Fg.. The neural networks based model of generator depends on the weghts between neural elements. Supervsed learnng s used n the system tranng. We can tran a neural network by adustng the values of the weghts accordng to error. After that an nput tend to a specfc target output. A supervsed neural network was pursued n a varety of weghts. The supervsed tranng of the neural networks can be vewed as a curve-fttng process. For approach to the marne desel generator model, a confguraton dagram of RBF of desel generator modelng and tranng s shown n Fg. 4. Frst step s to select nput and output parameters of generator. We selected that the nput parameters are exctaton current/voltage (v t ) and desel engne mechancal torque (P m ). The output parameters are termnal voltage (v), current () and frequency ( f ) of generator. Through measurng and recordng, a set of data wll be obtaned as samplng data for tranng. The measured data vector s x. Fg. 4. Confguraton dagram of RBF tranng 746

3 The nput p connected to RBF through a tapped delay lne. The nput vector p of RBF s: p = [v t P m v' ' f ' ] The output vector y of RBF s: y = [v f ] Such nput value and desre value par vectors were used for tranng a network n supervsed learnng. The network s adusted, based on error of output vector y = [v f ]and desred response vector d = [v f ], untl the network output matches the desred response. So the number of elements n nput vector (R) s fve. The number of neurons n lnear layer (S ) s three. B. Learnng Strateges of RBF There are dfferent learnng strateges that we can follow n tranng of a RBF, dependng on how the centers of the radal-bass functons of the network are specfed. Here supervsed selecton of centers learnng strateges was used. The centers of the radal bass functons and other parameters of the network n supervsed learnng process. We defne the value of cost functon as: ε = e () = Here s the sze of the tranng sample used to do the learnng, and e s the error defned by: S * e = = d y d F ( p ) d wg p (3) = C The requrement s to fnd the parameters w, t, and - (the latter beng related to the norm-weghtng matrx C ) so as to mnmze. Here, w s lnear weghts, t s postons of centers of a radal-bass functon, - s spread of centers. The results of ths mnmzaton are summarzed as follow: () Lnear weghts (output layer) = e ϕ( p ) (4) C w = w ( n + ) = w S, =,,, w (5) () Postons of centers (hdden layer) = w e ϕ' ( p ) [ p ] (6) C t = t ( n + ) = t, =,,, S (7) t (3) Spreads of centers (hdden layer) = w e '( ) Q ϕ p (8) C = T ( n ) = [ p ( n )][ p ( n )] (9) Q ( n + ) = (0) 3 Here, n s steps number of teraton. e (n) s the error sgnal of output unt at step n. The ϕ '( ) s frst dervatve of the Green s functon ϕ( ) wth respect to ts argument. The, and 3 are three coeffcents of learnng. The learnng-rates were depended on the value of them respectvely. The tranng process of RBF modelng as follow: () Endow wth ntal values to all weghts and bas. () Present nput and output sample data for RBF tranng. (3) Calculate the outputs of RBF accordng to nputs, weght and bas. When the value of cost functon between sample data to output of RBF s lttle than permsson value, the tranng process fnshes. Otherwse shft to step (4). (4) Accordng to dfference between RBF output value and expectaton value, the weghts and bas wll be adusted. (5) Go back to step (). C. Modelng Results of Marne Desel Generator The parameters of nput and output were measured as samplng data, and used for RBF offlne tranng. We selected some dfferent runnng states of marne power system, such as desel engne generator startng, a general pump (40kW, 440V) of power system runnng, a sde-thruster (00kW, 3300V) startng and three-phases short crcut ground fault. After tranng, the desel engne generator model of RBF was bult n network weghts functon. There are 99 (S ) hdden neurons wth one RBF model for normal operatng model. As example, termnal voltage parameter of generator s selected to demonstrate the precson of model n normal operatng. The parameter of termnal voltage s per unt value n dagram. The error s desred value mnus output value of RBF model. The axs of horzontal s tme (t). It s a relatonshp between perod tme (T) of samplng and sze () of the tranng samples. There s t = T. Some approxmated results were obtaned. The frst approxmated result s desel engne startng. Fg. 5 shows voltage of generator and ts error between desred value and output value of RBF model when desel engne generator startng. Fg. 6 shows termnal voltage of generator and error when lubrcaton pump s startng. Fg. 7 shows termnal voltage of generator and error when sde-thruster motor s startng. For power system three-phases short crcut ground fault, the fault process lkes ths. A ground fault occurs from a general pump. A large overload current was produced, and termnal voltage of generator was full down. After that the protecton unt cut off ths general pump because of overload current. In the end, the termnal voltage of generator was recovered. Fg. 8 shows termnal voltage of generator and error wth RBF model when three-phase grounded fault happened. From the recorded data and error curve all above, the error value s lmted n So the 747

4 desel engne generator model approxmated by RBF wth hgh precson results. V. APPLICATIO OF MARIE DIESEL EGIE GEERATOR MODEL TO AREAL TIME SIMULATOR For buldng a real tme marne power system smulator, A model of synchronous generator has been obtaned. * output of * output of Tme(s) Tme(s) Tme(s) Fg. 5. Voltage and ts error wth RBF model when desel engne generator s startng * output of Tme(s) Fg. 7. Voltage and ts error wth RBF model when sde-thruster motor s startng Tme(s) Tme(s) Fg. 6. Voltage and ts error wth RBF model when lubrcaton pump s startng Tme(s) Fg. 8. Voltage and ts error wth RBF model when three-phase grounded fault happened 748

5 After that the model operaton program s downloaded to a dgtal sgnal processor (DSP). Fg. 9 shows a part of confguraton between controller and models for real tme marne power system smulator. Logcal controller s used for desel engne startng and stoppng. Speed controller s used for constant value control of desel engne rotatonal Fg. 9. Part structure of real tme smulator speed. Voltage regulator s used for termnal voltage control of generator. Generally the rule of regulators are PID controllers. Through testng by TMS30LF407 DSP (30MIPS), the operatng perod tme of model s lttle than 58 mcroseconds wth 99 hdden neural nodes of RBF. In the real tme marne power system smulator system, the control computer was an ndustral mcrocomputer. A data acquston and control system s used for sgnals nput and output. Generally the nput sgnals are rotatonal speed (rpm) of desel engne, voltage (V) and current (A) of generator. The output sgnals are ol supply, exctaton voltage or current. The RBF generator model produces voltage sgnal and current sgnal to voltage regulator. All parameters were dsplay through control computer. VI. COCLUSIO Because generator system s a nonlnear system, the RBF was used for marne desel engne generator modelng, the model approxmated wth good precson. The calculaton speed s satsfactory usng RBF generator model. The advantage of usng RBF to buld a marne generator model s that the algorthm s smple and fast. It s ft for DSP calculatng. The dsadvantage of the method s that the generalzaton of system s not so satsfactory. The ablty of RBF generalzaton s not enough for all status of generator n one model especally for falure runnng state of generator. In normal operatng mode and fault operatng mode of real tme power system smulator, we had to use two dfferent models. One model s used for normal operatng. Other model s used for fault operatng. REFERECES [] Martn T. Hagan, Howard B. Demuth, Mark Beale. eural network desgn, Frst publshed by PWS Publshng Company, a dvson of Thomson Learnng, Unted States of Amerca. Reprnted for People s Republc of Chna by Thomson Asa Pte Ltd and Chna Machne Press and CITIC Publshng House under the authorzaton of Thomson Learnng. 00. pp(7-)-pp(7-30). [] Smon Haykn. eural networks a comprehensve foundaton (Second edton). Orgnal Englsh language edton publshed by Prentce-Hall, Inc. Copyrght 999 by Prentce-Hall, Inc. pp [3] Fredrc M. Ham, Ivca Kostanc. Prncples of eurocomputng for scence & engneerng. Orgnal language publshed by The McGraw-Hll Companes, Inc. 00. Authorzed Englsh language reprnt edton ontly publshed by McGraw-Hll educaton (Asa) Co. and Chna Machne Press pp40-6. [4] Lu Me-qn, Shen Y, Lao Xao-xn. Applcaton of a Class of ew RBF eural etworks to Modelng onlnear Systems. Control and Decson, Vol.6. o.3. May 00. pp [5] L Yan-un, Wu Te-un, Zhao Mng-wang. A ovel onlnear Dynamc System Modelng Approach Usng Radal Bass Functon eural etworks. Theory and Practce of System Engneerng, o.3. March 00. pp [6] Song Bao qang, Fu qong, Song Tong. Improved RBF eural network and ts applcaton. Computng Technology And Automaton. Vol.0, o.3 Sep. 00. pp [7] Xu Shanglng. Marne Engne Automaton. Dalan martme affars unversty press. Chna. 00.pp [8] Wefeng Sh, Tanhao Tang, Hangyng We. Marne power system modelng and smulator. IFAC PPS003, Seoul, Korea. Vol.. pp