Economic Analysis of Power Transformer Selection in Electrical Power Systems

Transcription

1 Eoomi Aalysis of ower Trasformer eletio i Eletrial ower ystems Alexader Mészáros Departmet of Eletri ower egieerig Tehial Uiversity of Košie Košie, lovakia alexader.meszaros@tuke.sk Vladimír Gáll Departmet of Eletri ower egieerig Tehial Uiversity of Košie Košie, lovakia vladimir.gall.@studet.tuke.sk Abstrat the proper seletio ad operatio of the trasformer is importat i the power idustry. Also this artile shows the whole eergy system ifluee o the operatio of the trasformer. At the same time, here is show, how sigifiat are the relatios betwee tehial ad eoomial parameters of trasformer. The aim of this researh work is represet ew omprehesive approah to the trasformers as oe the most importat part of whole power system. Keywords: aual osts; eoomy; eletri eergy; power idustry; speifi osts; trasformers; I. INTRODUCTION ower trasformers belog to the most used devies i power idustry i eletriity trasmissio ad distributio o the eoomially most appropriate voltages. The proper seletio ad operatio of trasformer a greatly otribute to the eoomy of etire power system. Cotiuous irease of trasmitted power ad irease the voltage levels makes ostrutio of trasformers more omplex ad more expesive. To solve the problem eoomy of trasformers has a major sigifiae the method of priig of the losses eletri eergy, whih i trasformers our durig their operatio. I this ase as solutio, we a use the equatio for aual produtio osts ad equatio for relative osts for trasformatio []. At the same, it is eessary to kow the power losses, relative power losses ad power effiiey of trasformer. Whe we alulate the power losses of trasformer i differet times, we a osider the kowledge about his eergy losses, relative eergy losses ad eergy effiiey. All of these issues reate extremely omplex tissue of relatio to ahievig the proper seletio ad operatio of the trasformer i the power idustry. I the fial result it is a eed for a ew omprehesive approah to the trasformers as well as the eoomy of the whole power system [] [3] [4]. II. DERIVATION OF EUATION FOR TRANFORMER Relative ost for ad for power losses are defied with biompoet expressio, where st is fixed value ad po is variable value of prie of the eletri eergy. st + Tpr st + τ po po () () Where T pr is a operatio time ad is a time of full losses. The apparet o-load losses 0 ad the apparet shortiruit losses k are defied by equatios: 0 i0 k uk Where i o is the relative o-load urret, u k is the relative short-iruit voltage, ad is the omial apparet power of trasformer. The reative o-load losses 0 ad the reative short-iruit losses k are defied by equatios: k (5) k k (6) Where 0 meas ative o-load losses ad k ative short-iruit losses. Also we a defie tg 0 ad tg k : tg ξ 0 tg ξ k 0 0 ( 0 + k 0 0 ) 0 + k 0 0 k ( k + k k k ) k + k k k Where is umber of idetial parallel trasformers, whih have the same parameters, k 0 is a speifi loss fator for oload ru, ad k k is a speifi loss fator for short-iruit ru of trasformer. Trasmitted eergy A is defied by equatio: A τ (9) m Where m is trasferred power ad is is a time of usig the maximum. Aual osts N tr for idetial parallel trasformers we a alulate like this N tr ( N k + ( + k ) T ) i pr + k ( + k ) k k k m τ os ϕ (3) (4) (7) (8) (0) Where N i is iitial osts, k is aual quota ad os is power fator [] [5]. For speifi osts tr we a defied equatio for idetial parallel trasformers like this N tr i k + ( 0 + k0 0 ) Tpr ( + k ) τ m + k k k m τ () τ os ϕ Aordig trasferred power m we a alulate losses ad relative losses p for idetial parallel trasformers ( + k ) ( + k ) k k k os ϕ m ()

2 h? N AMi`M ibm H a+bmib}+ avktbbmk GEh_L_:hAE kyrd- RkX@R9X NX kyrd- ai ` GbM - ahp F _Tm#HB+ ( 0 + k 0 0 ) + m m ( k + kk p k ) m os ϕ (3) Aordig trasferred power m we a alulate reative losses for idetial parallel trasformers ( 0 + k 0 0 ) tg ξ 0 + ( k + k k k ) m tg ξ k os ϕ (4) ower effiiey tr of trasformer is defied [6] as the ratio of the trasferred power m ad the iput power vst (5) m m vst m + ηtr After substitutio of equatio () ito equatio (5) we get equatio for power effiiey tr (6) m η tr m + ( 0 + k 0 0 ) + ( k + k k k ) m A ( 0 + k 0 0 ) T pr + a ( k + k k k ) τ m Mark hysial quatity Tpr 8760 h.year (7) Time of usig maximum 540 h.year Time of full losses 3579 h.year Fixed ompoet of osts st Variable ompoet of osts po Ivestmet osts of trasformer Ni Aual quota k rimary voltage U 0, year 0 kv eodary voltage U kv kva os 3,774.kW.year 0,448.kWh ,95 Relative o-load urret i0 0,0009 Relative short-iruit voltage uk 0,4 Ative o-load losses 0 3 kw Ative short-iruit losses k 48 kw os ϕ A A ( 0 + k0 0 ) Tpr ( k + kk k ) τ m + A m τ m τ τ os ϕ (8) Aordig trasferred power m we a alulate reative losses of eergy Aj for idetial parallel trasformers Name of value Operatio time ower fator Aordig trasferred power m we a alulate losses of eergy A ad relative losses of eergy a for idetial parallel trasformers Table. Iput parameters of trasformer Nomial apparet power os ϕ For ext umerial alulatio is eessary to asertai properties of atual trasformer [9] [0] []. All eessary iput values for this trasformer we a see i the table. Aj ( 0 + k0 0 ) Tpr tg ξ0 + ( k + kk k) τ m tg ξk os ϕ We a see alulated aual osts Ntr o Figure ad speifi osts tr o Figure. These graphs are made for differet loads m of trasformer. (9) Eergy effiiey Atr of trasformer is defied [6] as the ratio of the trasferred eergy A ad the iput eergy Avst η Atr A A m τ Avst A + A m τ + A (0) After substitutio of equatio (7) ito equatio (0) we get equatio for eergy effiiey Atr () Figure. The aual osts o trasformers m τ η Atr m τ + ( 0 + k 0 0 ) T pr + III. ( k + k k k ) τ m os ϕ NUMERICAL CALCULATION FOR THE TRANFORMER For the umerial alulatio were osidered four ases of k 0 as speifi loss fator for o-load ru, ad k k as speifi loss fator for short-iruit ru of trasformer, whih are show i the table. For trasformatio we are used two or three trasformers [7] [8]. Table. Variats the values of speifi loss fators Number of ase k 0 (kw.kvar ) k k (kw.kvar ) Case 0,0433 0,0433 Case 0,0507 0,0507 0,0083 0,08 0,0066 0,074 Figure. The speifi osts o trasformers We a see alulated losses o Figure 3, relative losses p o Figure 4, reative losses o Figure 5 ad power effiiey tr Figure 6. The reative losses are idepedet RNR

3 h? N AMi`M ibm H a+bmib}+ avktbbmk GEh_L_:hAE kyrd- RkX@R9X NX kyrd- ai ` GbM - ahp F _Tm#HB+ of the speifi loss fator for o-load ru k 0 ad the speifi loss fator for short-iruit ru k k. These graphs are made for differet loads m of trasformer. We a see alulated losses of eergy A o Figure 7, relative losses of eergy a o Figure 8, reative losses of eergy Aj o Figure 9 ad eergy effiiey Atr o Figure 0. The reative losses of eergy Aj are idepedet of the speifi loss fator for o-load ru k 0 ad the speifi loss fator for short-iruit ru k k. These graphs are made for differet loads m of trasformer. Figure 3. The losses o trasformers Figure 7. The losses of eergy o trasformers Figure 4. The relative losses o trasformers Figure 8. The relative losses of eergy o trasformers Figure 5. The reative losses o trasformers Figure 9. The reative losses of eergy o trasformers Figure 6. The power effeiey o trasformers RNk

4 h? N AMi`M ibm H a+bmib}+ avktbbmk GEh_L_:hAE kyrd- RkX@R9X NX kyrd- ai ` GbM - ahp F _Tm#HB+ I followig ase, whe is equality of speifi osts tr betwee differet umber of idetial trasformers ad, we a asertai boudary power h from the equality of speifi osts. h os ϕ Ni k + ( 0 + k0 0 ) Tpr (5) τ ( k + kk k ) I followig ase, whe is equality of power effiiey tr betwee differet umber of idetial trasformers ad, we a asertai boudary power h from the equality of power effiiey. Figure 0. The eergy effeiey o trasformers ηh osϕ Miimum of speifi osts tr o the trasformer is whe trasformer is loaded by eoomi power e. Eoomi power e for miimum of speifi osts tr is defied by equatio e osϕ Ni k + ( 0 + k0 0 ) Tpr ( k + kk ηah os ϕ Maximum of power effiiey tr o the trasformer is whe trasformer is loaded by power max. ower max for maximum of power effiiey tr is defied by equatio η max osϕ ( 0 + k0 0 ) ( k + kk k ) (3) ( 0 + k0 0 ) Tpr ( k + kk k ) τ (6) ( 0 + k0 0 ) Tpr ( k + kk k ) τ (7) O the table 5 we a see alulated values of trasferred power h, h ad Ah betwee two ad three idetial trasformers [] [5]. Table 5. The alulated values of trasferred power Number of ase h (kw) Case 5886, , , Case 57854, , , , , , , , , Maximum of eergy effiiey Atr o the trasformer is whe trasformer is loaded by power Amax. ower Amax for maximum of eergy effiiey Atr is defied by equatio ηa max os ϕ 0 ) k ) I followig ase, whe is equality of eergy effiiey Atr betwee differet umber of idetial trasformers ad, we a asertai boudary power Ah from the equality of eergy effiiey. () k ) τ ( 0 + k0 ( k + kk h (kw) Ah (kw) (4) IV. CALCULATION FOR THE TRANFORMER WITH DIFFERENT LOAD O the table 3 we a see alulated values of trasferred power e, max ad Amax for umber of idetial trasformers is two. The alulatios a be proved by the foreast trasferred power m. O the Figure we a see the example of trasferred power m i time t for the ext five days [6] []. Table 3. The alulated values of trasferred power Number of ase e (kw) Case 47590, , max (kw) 45743, Amax (kw) Case 4737, , , , , , , , , O the table 4 we a see alulated values of trasferred power e, max ad Amax for umber of idetial trasformers is three. Table 4. The alulated values of trasferred power Number of ase e (kw) Case 7385, , max (kw) 6865, Amax (kw) Case 70856, , , , , , , , , Figure. The foreast of trasferred power O the Figure we a see alulated speifi osts tr. This graph is made aordig the example of trasferred power m whih flow through trasformers. RNj

5 h? N AMi`M ibm H a+bmib}+ avktbbmk GEh_L_:hAE kyrd- RkX@R9X NX kyrd- ai ` GbM - ahp F _Tm#HB+ Figure 5. The relative losses of eergy o trasformers Figure. The speifi osts o trasformers O the Figure 3 we a see alulated relative losses p ad o the Figure 4 we a see alulated power effiiey tr. These graphs are made aordig the example of trasferred power m whih flow through trasformers. Figure 6. The eergy effeiey o trasformer Whe we osider speifi osts tr o the Figure for five days, it is appropriate to osider usig two trasformers. I this ase, if here is foreasted the rise of trasferred power m i the future, it is appropriate to osider usig of three trasformers. Whe we osider relative losses p o the Figure 3 or power effiiey tr o the Figure 4 for five days, we a see approximate equality of these values, so we a use two or three trasformers. I this ase, if better tehial parameters are eessary, it is appropriate to osider usig of three trasformers. Whe we osider relative losses of eergy a o the Figure 5 or eergy effiiey Atr o the Figure 6 for five days, it is appropriate to osider usig two trasformers. I this ase, if here is foreasted the rise of trasferred power m i the future, it is appropriate to osider usig of three trasformers. The proposed aalysis a be easily expaded to take ito aout differet searios of priig of the losses eletri eergy i trasformers ad variatio of trasferred power m aordig to the oditios, that our durig witer or summer seaso ad the type of the demad for eletri power m [3]. Figure 3. The relative losses o trasformers Figure 4. The power effeiey o trasformers O the Figure 5 we a see we a see alulated relative losses of eergy a ad o the Figure 6 we a see we a see alulated eergy effiiey Atr. These graphs are made aordig the example of trasferred power m whih flow through trasformers. RN9 V. CONCLUION A key problem of the eoomis of the power idustry is the variatio i the demad for eletri power durig eah day, eah week ad throughout year [6]. O the other side, eletri eergy is versatile, uiversal, lea to use ad easy to distribute ad supreme to otrol. That is importat, it is ow established that eletri eergy has better produtivity i may appliatios i idustries tha most other eergy forms [4]. Uderstadig these alulatios is deisive if they are to be used i makig deisios how to solve proper seletio ad operatio of the trasformer i the power idustry. At the same, it is equally importat to reogize that the maximum of power i the

6 power system is limited [5]. These pratial examples illustrate that the seletio of umber idetial parallel trasformers are based o omprehesive approah ad alulatio of differet loads of trasformer. At preset, this artile also disusses the problem eoomy of trasformer ad tehial parameters of trasformer. roper seletio ad operatio of the trasformer sietifially is beomig a effetive way to redue power losses ad losses of eergy i the power system [6]. Differet desigs of trasformer a be developed to meet the requiremets of a partiular speifiatio by the power system [3]. I the future, the power systems will ooperate with reewable resoures to a larger extet. Curretly, there is a hage to atural oditios ad is expeted to further irease i the temperature []. This meas, there will be less old witers, but hotter summers. It also hages the osumptio of eletri eergy, whih i witer will be the less heat, but i the summer the eletri eergy will be used to drive air oditioers for oolig buildigs. Experiee from outries where a large part of osumptio of eletri eergy is used to drive air oditioers show that ot all the problems assoiated resolved through example mart Grid i power systems [3]. O the other side, the variatios i the demad for eletri power have otributed to the eed to develop a ew tehology strategy alled the smart grid systems []. At the same, power systems are vulerable to extreme atmospheri pheomea, whih may destabilize i the ase disturbae of the power system ad ause power failure for huge areas [4]. ACKNOWLEDGMENT This work was supported by the ietifi Grat Agey of the Miistry of Eduatio of lovak Republi ad the lovak Aademy of iees uder the otrat No. VEGA /03/5. REFERENCE [] M. Kolu,. Bea, A. Mészáros, "Optimalizáia prevádzky elektrizaej sústavy", Tehial Uiversity of Košie, 009, IBN []. ta k,. Ivaová, "úasé tedeie ekoomikej globalizaie", Bratislava 05, IBN [3]. ta k,. Ivaová, "Štvrtá priemyselá revolúia a piaty ivilizaý zlom", Bratislava 06, IBN [4]. ta k,. Ivaová, "Európska úia a križovatke postrehy a išpirujúe riešeia", Bratislava 06, IBN [5] L. Varga,. Ilei,. Lešiský, "reos a rozvod elektrikej eergie", Tehial Uiversity of Košie, 003 [6] C. R. Dorf, "Eergy, resoures ad poliy", Addiso Wesley ublishig Compay I., 978, IBN [7] J. Chlebý,. Beeš, J. Lager, J. Král, M. Martiásková, "Automatizae a automatizaí tehika", Computer ress Bro, 04 [8] J. Desmet, G. Delaere, L. Lemeko, "Volba a dimezováí trasformátor", Tehial Uiversity of Ostrava, 006 [9] M. Kolu, V. Chladý, M. Mešter, R. Cimbala, J. Tká, M. Hvizdoš, J. Rusák, "Elektráre", Tehial Uiversity of Košie, 006, IBN [0]. Novák, "Elektriké teplo", Tehial Uiversity of Košie, 00, IBN [] A. ietriková, J. Baský, "Základy ižiierstva materiálov", Tehial Uiversity of Košie, 007, IBN [] M. Kolu, V. Griger,. Bea, J. Rusák, "revádzka elektrizaej sústavy", Tehial Uiversity of Košie, 007 [3] E. I. Amoiralis, M. A. Tsili, A. Kladas, "Eoomi evaluatio of trasformer seletio i eletrial power systems", Iteratioal Coferee o Eletrial Mahies, IEEE, 00 [4] H. Khatib, "Eoomi evaluatio of projets i the eletriity supply idustry", Lodo 008, [5] B. C. Lesieutre, J. H. Eto, "Eletriity trasmissio ogestio osts a review of reet reports", Uiversity of Califoria Berkeley, 003 [6] W. Jili,. Waxig, W. Li, Y. Hoglei, "tudy o tehial ad eoomial effiiey of amorphous alloy trasformer ad o-load apaity regulatig trasformer i distributio etwork appliatio", Chia Iteratioal Coferee o Eletriity Distributio, 04