Classification of Total Load Demand Profiles for War-ships based on Pattern Recognition Methods

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1 Recent Reseaches in Communications and IT Classification of Total Load Demand Pofiles fo Wa-ships based on Patten Recognition Methods 1 Depatment of Electical & Compute Science, Hellenic Naval Academy G.J. TSEKOURAS 1, I.S.KARANASIOU 2, F.D. KANELLOS 3 2 Infomatics and Compute Science LAB Depatment of Mathematics & Engineeing Sciences Univ. of Militay Education - Hellenic Amy Academy 3 Hellenic Tansmission System Opeato Tema Hatzikyiakou, Piaeus Vai 16673, Athens Kastoos 72, Piaeus GREECE tsekouas_geoge_@yahoo.g, ikaan@esd.ece.ntua.g, kanellos@mail.ntua.g Abstact: - The classification of total load demand pofiles fo evey type of wa-ships is cucial infomation, because it is the necessay base fo a seies of studies and opeations, such as load estimation, load shedding and powe management systems. In this pape a patten ecognition methodology is pesented, which is based on diffeent patten ecognition methods, such as k-means, modified k-means etc. Each method can popely be optimized by using diffeent adequacy measues, such as the atio of within cluste sum of squaes to between cluste vaiation. This methodology is applied to total load demand of Hellenic Navy MEKO type figate indicatively and the usefulness of the espective esults fo the powe system design and opeation is poved. Key-Wods: - Load pofiles, clusteing algoithms, patten ecognition, adequacy measues, waship 1 Intoduction The powe system of a waship, such as a figate o a covette, is a cucial paamete fo its fighting pepaedness. Especially, duing the last decade in the famewok of All Electic Ship (AES) a seies of advantages is offeed such as inceased safety, suvivability, manoeuvability, pecise and smooth speed contol, educed machiney space, low opeation and maintenance costs, low noise and low pollutant emission levels [1]. These benefits ae aleady obvious in waships such as aicaft-caies and submaines, which have a total electified powe system design based on nuclea eactos and batteies coespondingly. The powe system design and opeation unde diffeent ship opeating condition (ancho, floating, navigating, fighting, etc) is a complicated pocess, which equies the total load demand as data. The usual solution of this poblem is the estimation of the total load demand fo each opeating condition based on multiplicative factos fo each electic consume, such as powe efficiency, load facto, fo each ship opeating condition in ode to calculate the aveage daily equied load, as it has been analyzed in [2]-[3]. Altenatively, chaacteistic total load demand cuves fo each opeating condition can be estimated though classification pocess. In ode to cay out this classification, the chonological load cuves pe day o smalle time divisions can be used. Duing the last yeas, a significant eseach effot has been devoted to load cuves classification, in ode to solve the shot-tem load foecasting of anomalous days [4], to cluste the customes of the powe systems [5] and to estimate the total load pofile of powe systems fo the implementation of demand side management pogams [6-7]. The clusteing methods used so fa ae the k-means [4]- [6], the fuzzy k-means [4]-[6], the self-oganizing map [4]-[6], the modified follow the leade [4], and the hieachical methods [4]-[6]. These methods geneally belong to patten ecognition techniques [8]. The most commonly used espective adequacy measues ae the mean index adequacy [9], the clusteing dispesion indicato [4], [9], the similaity matix indicato [9], the Davies-Bouldin indicato [4], [9], the modified Dunn index [4], [9], the scatte index [4], the mean squae eo [9] and the atio of within cluste sum of squaes to between cluste vaiation [7]. The obective of this pape is to pesent a patten ecognition methodology fo the classification of the daily chonological total load demand cuves fo wa-ships powe systems. It compaes the esults obtained by cetain clusteing techniques (such as k- means with special weights initialization and adaptive vecto quantization) using the atio of within cluste sum of squaes to between cluste vaiation as adequacy measue. Following, the developed methodology is applied fo the active ISBN:

2 Recent Reseaches in Communications and IT total load demand of the Hellenic Navy MEKO type figate fo a peiod of 2 days. Finally, the implementations of the espective esults (typical days and epesentative load cuves) in navy aspects ae synoptically analyzed. 2 Patten Recognition Methodology fo the Classification of Total Load Demand Cuves of Waship s Powe System The classification of chonological load cuves fo powe system of a wa-ship is achieved by applying the patten ecognition methodology, as shown in Fig. 1. Main Pocedue Paametes optimization No Data selection Data pepocessing Fo each one of the clusteing algoithms Taining Pocess Evaluation Pocess End of optimization? Yes End of algoithms? Yes Typical load diagams & espective classes No Applications: I.e. Load shedding, automatic powe system management, powe system design, etc. Fig. 1. Flowchat of patten ecognition methodology fo the classification of chonological total load demand cuves of wa-ship s powe system The main steps ae the following: Data and featues selection: The active enegy E and eactive enegy E Q values ae egisteed (in kwh and kvah espectively) fo each time peiod in time steps Dt (which can be 1 hou, 15 mins, etc). The chonological load cuves ae detemined fo the study peiod, as the espective active powe P and eactive powe Q ae calculated by: E P= (1) Dt Q= (2) Dt Data pepocessing: The load diagams ae examined fo nomality, in ode to modify o delete the values that ae obviously wong. This pocess is known as noise suppession. Main pocedue of patten ecognition methods: Fo the load diagams, a numbe of clusteing algoithms can be applied, such as k- means, fuzzy k-means, adaptive vecto quantization, self-oganized map and hieachical clusteing. Hee, the study is limited to k-means and adaptive vecto quantization algoithms. Each algoithm can be tained fo the set of load diagams and evaluated accoding to diffeent adequacy measues, such as mean squae eo, mean index adequacy, clusteing dispesion indicato, similaity matix indicato, Davies-Bouldin indicato and atio of within cluste sum of squaes to between cluste vaiation. Hee, the study is limited to last one, because it is expected to be the most desciptive adequacy measue as it has been explained in [7]. The paametes of the algoithms ae optimized, if necessay. The developed methodology uses the clusteing method that povides the most satisfactoy esults. The esults of the developed methodology can have vaious applications, as it is analyzed in section 5. 3 Mathematical Base of Patten Recognition Methodology 3.1 Geneal Geneally N is defined as the population of the input vectos, which ae going to be clusteed. In this case study the input vecto is the chonological total load demand of a wa-ship s powe ship. The T x = x, x,... x,... x symbolizes the l -th input ( ) l l1 l2 li ld vecto and d its dimension, which equals to 24, if the load measuements ae taken evey hou, o 96, if the espective measuements ae taken evey 15 minutes. The coesponding set is given by X = x : l = 1,..., N. Each classification pocess { } l E Q ISBN:

3 Recent Reseaches in Communications and IT makes a patition of the initial N input vectos to M clustes. The -th cluste has a epesentative, which is the espective load pofile and is epesented by T w = w, w,..., w,... w of d the vecto ( 1 2 i d) dimension. The vecto w expesses the cluste cente. The coesponding set is the classes set, which is defined by W = { wk, k = 1,... M}. The subset of input vectos x l, which belong to the -th cluste, is Ω and the espective population of load diagams is N. Fo the study and evaluation of classification algoithms the Euclidean distance between l 1, l 2 input vectos of the set X is defined: d 1 ( l, ) ( ) 1 l = 2 l1i l2i d x x x x d i = 1 2 (3) In ode to evaluate the pefomance of the clusteing algoithms and to compae them with each othe, the atio of within cluste sum of squaes to between cluste vaiation () this measue is going to be used as it has been poposed in [7]. It is also noted that the basic theoetical advantage of the indicato is that it combines the distances of the input vectos fom the epesentative clustes and the distances between clustes coveing also the mean squae eo and clusteing dispesion indicato chaacteistics. Specifically, depends on the sum of the distance squae between each input vecto and its cluste epesentative vecto, as well as the similaity of the clustes centes: d w x d w w M 2 M = (, ) 2 k l ( p, q) k= 1 xl Ω k 1 q< p (4) The success of the vaious algoithms fo the same final numbe of clustes is expessed by having small values of. By inceasing the numbe of clustes the espective measue deceases. An additional adequacy measue could be the numbe of the dead clustes, fo which the sets ae empty. It is intended to minimize this numbe. It is noted that in eq. (4) M is the numbe of the clustes without the dead ones. The basic chaacteistics of the thee clusteing methods (classical k-means, modified k-means, adaptive vecto quantization) being used ae the following. It is noted that a moe extended analysis is pesented in [9]. 3.2 K-means model The k-means clusteing method goups the set of the N input vectos to M clustes using an iteative pocedue. Initially the weights of the M clustes ae detemined. In the classical model a andom choice among the input vectos is used [4]. In the developed algoithm the w i of the -th cente is initialized as: () w = a+ b ( 1) ( M 1) (5) i whee a and b ae popely calibated paametes. Duing epoch t fo each taining vecto x l its d x w ae calculated fo all Euclidean distances ( l, ) ( ) centes. The l-th input vecto is put in the set Ω t, fo which the distance between x l and the espective cente is minimum. When the entie taining set is fomed, the new weights of each cente ae calculated as: ( t+ 1) 1 w = x ( t) N l (6) ( t ) whee ( t ) ( t ) xl Ω N is the population of the espective set Ω duing epoch t. This pocess is epeated until the maximum numbe of iteations is used o the vaiation of the weights is not significant. The algoithm s main pupose is to minimize the eo function: N 1 2 J = d ( x, w k : x Ω ) k N l (7) l l= 1 The main diffeence compaed to the classical model is that the pocess is epeated fo diffeent pais of (a,b) and the esults of the pai (a,b) with the best ae ecoded. 3.3 Adaptive vecto quantization This algoithm is a vaiation of the k-means method, which belongs to the unsupevised one-laye neual netwoks. It classifies input vectos into clustes by using a competitive laye with a constant numbe of neuons. Duing epoch t each input vecto x l is andomly pesented and its espective Euclidean distances fom evey neuon ae calculated. The weights of the winning neuon (with the smallest distance) ae updated as: t t t w n+ 1 = w n + η t x w n (8) ( ) ( ) ( ) ( ) ( ) ( ( ) l ( )) whee n is the numbe of input vectos, which have been pesented duing the cuent epoch, ( ) w.5,, i η t is the leaning ate i = and ( ) accoding to: η t = η exp t T η > η (9) ( ) ( ) min whee η, ηmin and T η ae the initial value, the minimum value and the time paamete espectively. The emaining neuons ae unchangeable fo x l, as intoduced by the Kohonen winne-take-all leaning ule [1]. This pocess is epeated until eithe the maximum numbe of epochs is eached o the ISBN:

4 Recent Reseaches in Communications and IT weights convege o the appopiate eo function is not impoving. 4 Application of the Poposed Methodology 4.1 Case study The developed methodology is applied fo the total load demand of the Hellenic Navy MEKO type figate. The active enegy of ship s geneatos was egisteed by the contol and monitoing system NAUTOS evey 15 minutes fo a peiod of 2 days (8-31 Januay 1998) with the ship at shoe condition. This load is equal to the total load demand povided no electic powe connection with the shoe. The espective daily vecto dimension is equal to 96. In the next paagaphs the application of each clusteing method is analyzed. 4.2 Application of the k-means The poposed model of the k-means method is executed fo diffeent pais (a,b) fom 2 to 2 clustes, whee a={.,.11,,.45} and a+b={.55,.56,,1.}. Fo each cluste 2116 diffeent pais (a,b) ae examined and the pai with the smallest is selected. In Fig. 2 the measue fo 2 to 2 clustes is pesented fo the set of 2 taining pattens of the total load demand Numbe of clustes Fig. 2. measue of the k-mean fo 2 to 2 clustes fo the set of 2 taining pattens of the total load demand The numbe of the clustes, which povides satisfactoy esults fo the study of the figate s total load demand, coesponds to the knee of the espective cuve [5], as it is shown in Fig. 3. In this case the espective numbe is supeio than 3, so the poposed numbe of clustes is 4. If the axis of changes so that the espective scale is extended, Fig. 4 will be aisen and the espective numbe of clustes should be equal to 7. This poves that the gaphical solution is not unique and the use s knowledge is also necessay Numbe of clustes Fig. 3. The use of tangents fo the estimation of the knee based on measue of the k-mean fo 2 to 2 clustes fo the set of 2 taining pattens of the total load demand Numbe of clustes Fig. 4. The use of tangents fo the estimation of the knee based on measue of the k-mean fo 2 to 2 clustes fo the set of 2 taining pattens of the total load demand with enlagement of Fig. 3 The altenative model is the classical one with the andom choice of the input vectos duing the centes initialization. Fo the k-means model 1 executions ae caied out and the best esults fo each index ae egisteed. The supeioity of the poposed model applies in all cases of neuons, while a second advantage is the convegence to the same esults fo the espective pais (a,b), which can not be achieved using the classical model. The espective supeioity is pesented in Fig Application of adaptive vecto quantization (AVQ) The initial value η, the minimum value ηmin and the time paamete T η of leaning ate must be popely ISBN:

5 Recent Reseaches in Communications and IT calibated. In this case the espective values of the paametes ae η ={.1,.2,,.9}, η min = {.1,.5,.1,.1} and the time paamete T η ={5, 1,, 5}. It is noted that the η min value does not pactically impove the neual netwok s behavio assuming that it anges between 1-5 and 1-6. In Fig. 5 the measue fo 2 to 2 clustes is pesented fo the espective data set fo the best combination ( η, T η, η min ) of each cluste. 4.4 Compaison of clusteing models In Fig. 5 the best esults achieved by each clusteing method (poposed k-means, classical k-means, adaptive vecto quantization) fo measue ae depicted. The poposed k-means model has the smallest values in the whole width of the clustes inteval Numbe of clustes poposed k-means classical k-means AVQ Fig. 5. measue of the poposed k-means technique, the classical k-means technique and adaptive vecto quantization algoithm fo 2 to 2 clustes fo the set of 2 taining pattens of the total load demand The impovement of the measue is significant until 1 clustes. Afte this value the behavio is pactically stabilized. It is noted that dead clustes ae appeaed ove 11 clustes. Afte 15 clustes a small impovement is pesented. Having also taken into consideation that the analogy of the computational taining time fo the unde study methods is.8:1:3 (classical k- means: poposed k-means: AVQ), the use of the k- means model is poposed. It is mentioned that the computational taining time fo the poposed k- means method is appoximately 1.5 minutes fo a Pentium 4, 1.7 GHz, 768 MB. 4.5 Repesentative daily total load demand cuves of the HN MEKO type figate powe system at shoe condition The esults of the espective clusteing fo 4, 7 and 1 clustes using the poposed k-means model with the optimization of the measue ae pesented in Table 1, whee the calenda of the time peiod unde study with the kind of cluste and the total numbe of days pe cluste ae egisteed. It is obseved that using 4 clustes fo the classification the thid cluste is the most populated one. Using 7 o 1 clustes fo the classification the thid cluste of the classification with 4 clustes has been divided in sepaate new clustes. This is obvious, as the fist cluste, the second one and the last one fo the thee diffeent classifications ae pactically unchangeable. TABLE 1 CLUSTERS CALENDAR OF THE TOTAL LOAD DEMAND CURVES FOR HN MEKO TYPE FRIGATE POWER SYSTEM Numbe of clustes Date (Januay 1998) Total numbe of days pe cluste 4 (1 st -4 th ) 4 (1 st -7 th ) 8 2 nd 2 nd 2 nd 9 3 d 4 th 6 th 11 2 nd 3 d 2 nd 12 3 d 4 th 6 th 14 4 th 7 th 1 th 16 3 d 3 d 3 d 17 3 d 4 th 4 th 18 3 d 4 th 6 th 2 3 d 5 th 8 th 21 3 d 6 th 9 th 22 3 d 5 th 7 th 23 3 d 5 th 7 th 24 3 d 5 th 5 th 25 3 d 5 th 5 th 26 3 d 4 th 7 th 27 2 nd 2 nd 2 nd 28 3 d 4 th 4 th 29 1 st 1 st 1 st 3 3 d 4 th 6 th 31 3 d 6 th 9 th 1 st nd d th (1 st -1 th ) 5 th th th th 1 9 th 2 1 th 1 In Fig. 6 the epesentative load cuves pe cluste ae pesented using the classification with 4 clustes. ISBN:

6 Recent Reseaches in Communications and IT Additionally the confidence limits of the vaiations (mean value ± standad deviation) ae pesented and this has a pobability of occuence equal to 68.27% assuming a nomal distibution. Active powe (kw) Active powe (kw) Active powe (kw) Active powe (kw) st cluste Mean value Mean value - standad deviation Mean value+standad deviation nd cluste Mean value Mean value - standad deviation Mean value+standad deviation d cluste th cluste Fig. 6. Daily chonological load cuve fo total load demand with the espective standad deviation using the poposed k-means technique algoithm with measue fo 4 clustes Specifically, the fist cluste epesents the load cuve of 29 Januay 1998, because the figate was supplied by shoe with powe fo 8 hous. This cluste emains unchangeable in all unde study classifications. The second cluste epesents days with small mean load demand, while the thid one is the most populated one with mean total load demand about 53 MW and with mean standad deviation about 4 MW. The fouth cluste is the last cluste, which epesents the load cuve of 14 Januay 1998, whee a powe system s failue was aisen at 1:45 p.m. This day always emains in a sepaate cluste, as it is a special day, which could be deleted duing the data pepocessing. Fom the analysis of this shot peiod it is likely that duing wokdays and no-wokdays the figate s powe system has not pesent diffeent behavio in opposition to what happens in intecontinental powe system [7]. 5 Pactical Application of Classification Methodology The esults of the developed methodology can be used eithe fo powe system design o fo powe system opeation. Moe specifically: the design of the waship s powe system estimating the espective total load demand moe accuately and selecting the geneatos popely. The optimized powe system s design inceases safety and suvivability, it educes machiney space, while it can allow low opeation and maintenance costs, low noise and low pollutant emission levels. the opeation of the waship s powe system succeeding moe pecise shot-tem load foecasting, inceasing the espective opeation eliability and deceasing the espective opeation cost. the impovement of powe facto taking into consideation the espective eactive load cuves. the load estimation afte the application of demand side management pogams fo total load demand, as well as the feasibility studies of the enegy efficiency which nomalize the total load demand and impove the total load facto. the impovement of the opeation of the automatic battle management and load shedding systems, because the automatic supply of the citical consumes in each opeating mode is facilitated in case of powe system s fault based on the available geneatos, the healthy pat of the powe distibution system and the load demand of each consume. This impoves the cucial paamete of ship s fighting pepaedness and ISBN:

7 Recent Reseaches in Communications and IT espective suvivability. 6 Conclusions This pape pesents a patten ecognition methodology fo the study of the total load demand behavio of wa-ships powe systems. The unsupevised clusteing methods can be applied, such as the k-means and adaptive vecto quantization. The pefomance of these methods is evaluated by the atio of within cluste sum of squaes to between cluste vaiation. Finally the epesentative daily load diagams along with the espective populations pe each typical day ae calculated. This infomation is valuable fo the shipbuilding companies and Navies, because it mainly facilitates (1) the design of the waship s powe system optimizing the geneatos selection and minimizing the machiney space, (2) the opeation of the waship s powe system though the coect load estimation inceasing the enegy efficiency and minimizing the opeation cost, (3) the opeation of the automatic battle management and load shedding systems inceasing fighting pepaedness and espective suvivability. By applying the poposed methodology to the active total load demand of the Hellenic Navy MEKO type figate fo a peiod of 2 days the espective pimay esults have been pesented. In futue moe extended data sets will be examined so that safe esults can be aisen. Contempoaneously, additional unsupevised clusteing methods can be applied, such as the fuzzy k-means, hieachical methods, mono-dimensional and bi-dimensional self oganizing maps, while thei pefomance can be evaluated by othe adequacy measues, such as mean squae eo, mean index adequacy, clusteing dispesion indicato, similaity matix indicato, Davies-Bouldin indicato. Additionally, diffeent time peiods of chonological load cuves (beyond the daily ones) can be also investigated. Acknowledgements The authos want to expess thei sincee gatitude to the Hellenic Navy fo poviding all the necessay data fo this application. Refeences: [1] J. M. Pousalidis, G. J. Tsekouas, F.D. Kanellos. New challenges emeged fom the development of moe efficient electic enegy geneation units. IEEE Electic Ship Technologies Symposium (IEEE ESTS '11), Westin Alexandia, Alexandia, Viginia, USA, Apil 1-13, 211. [2] US Navy. Electical system load and powe analysis fo suface ships. DOS 31-1, 198. [3] I.K. Hatzilau, G. J. Tsekouas, J. Pousalidis, I.K. Gypais. On Electic Load Chaacteization and Categoization in Ship Electic Installations. INEC-28, 1-3 Apil 28, Hambug, Gemany. [4] G.Chicco, R. Napoli, F. Piglione. Compaisons among clusteing techniques fo electicity custome classification. IEEE Tansactions on Powe Systems, Vol. 21, No. 2, May 26, pp [5] G. J. Tsekouas, N.D. Hatziagyiou, E. N. Dialynas. Two-Stage Patten Recognition of Load Cuves fo Classification of Electicity Customes. IEEE Tansactions on Powe Systems, Vol. 22, No. 3, August 27, pp [6] G. J. Tsekouas, C.A. Anastasopoulos, F.D. Kanellos, V.T. Kontagyi, I.S. Kaanasiou, A.D. Salis, N.E. Mastoakis. A Demand Side Management Pogam of Vanadium Redox Enegy Stoage System fo an Inteconnected Powe System. WSEAS Intenational Confeence on Enegy Planning, Enegy Saving, Envionmental Education, (EPESE '8), Cofu Island, Geece, Octobe 26-28, 28 [7] G. J. Tsekouas, F.D. Kanellos, V.T. Kontagyi, I.S. Kaanasiou, A.D. Salis, N.E. Mastoakis. A New Classification Patten Recognition Methodology fo Powe System Typical Load Pofiles. WSEAS Tansactions on Cicuits & Systems, Vol. 12, Issue 7, Decembe 28, pp [8] S. Theodoidis, K. Koutoumbas, Patten Recognition, 1st Edition, Academic Pess, New Yok, [9] G. J. Tsekouas, A. D. Salis, M. A. Tsaoucha, I. S. Kaanasiou. Load time-seies classification based on patten ecognition methods. 16 th chapte in the book of Peng- Yeng Yin. Patten Recognition; Techniques, Technology and Applications. 1st Edition, I- Tech Pess, Vienna, 28. [1] S. Haykin. Neual Netwoks: A Compehensive Foundation, Pentice Hall, NJ, ISBN: