DETERMINATION OF OPTIMAL HYDRO GENERATING UNIT COMBINATION IN OPERATION

Transcription

1 International Journal on Inmation Technoloies & Security,, 07 5 DETERMINTION OF OTIML HYDRO GENERTING UNIT COMINTION IN OERTION Sofija Nikolova-oceva, nton Chaushevski, Dimitar Dimitrov Faculty of Electrical Enineerin & Inmation Technoloies Ss. Cyril and Methodius University in Skoje s: nsofija@feit.ukim.edu.mk, caus@feit.ukim.edu.mk, ddimitar@feit.ukim.edu.mk R. Macedonia bstract: In this aer a method determinin the otimal combination of areates in a iven hydroower lant is resented. s a secific case a hydroower lant with a roer number of installed hydro eneratin units is considered. Moreover, in this aer, the efficiency of the hydroower lant all ossible unit combinations in oeration is determined. For this urose the characteristic of efficiency of each unit is defined. The otimal unit combination is determined all individual ower ranes of the oeratin rane of the lant. Key words: Hydroower lant, Efficiency Characteristic, Otimal Unit Combination.. INTRODUCTION Of reat imortance hydroower lant (H) oeration is the achievement of the required electricity roduction at satisfactory efficiency of hydroower lant. To achieve maximum efficiency of a certain hydroower lant requires ood knowlede of the oeratin modes of the lant and the number of roduction units in oeration [], []. On the efficiency of the hydroower lant, at articular ower, affects the number of hydro eneratin units in oeration. Theree it is essential to consider the variation of the efficiency in various combinations of installed units, in order to achieve the required electricity roduction more efficiently. For each articular load corresonds most favorable combination of hydro eneratin units that ensure maximum ower lant efficiency. So, each combination it is need to determine the ower roduction interval which is best hydroower lant to oerate []. Oeration of a certain hydroower lant should be such that the lant oerates at ranes of hih efficiency while ensurin minimal water consumtion. nother roblem is to determine the otimal amounts of eneration ower of the eneratin units, in oeration, over the study eriod in order some iven

2 54 International Journal on Inmation Technoloies & Security,, 07 criteria to be fulfilled. In [5], the authors resent an otimization solution to solve this roblem an actual lant, usin Genetic lorithms. While the aer [6] resents strateic lannin otimal oeration of lare hydroelectric ower lants. This aer resents a method determinin the otimal combination of hydro eneratin units to be ut into oeration in order to ensure maximum ower lant efficiency in satisfyin the secified load. This method we alied on hydro ower lant with 4 installed units. For each ossible combinations of available units, analytical and rahic, we determined the hydroower lant efficiency characteristic as a function of load. Further we determined which hydro eneratin unit combination rovides the reatest ower lant efficiency certain oeratin ower ranes. The method based on knowlede of the characteristics of the efficiency of installed units in H.. HYDROOWER LNT EFFICIENCY The hydro eneratin unit efficiency is iven by [4]: j = j () j j where j are active ower losses in the ј-th hydro eneratin unit, and j is active enerated ower by the ј-th hydro eneratin unit. From the revious equation the active ower losses in the ј-th hydro eneratin unit can be exressed as [4]: j j = j () j If n hydro eneratin units are in oeration in the H, then the hydroower lant efficiency is determined by the exression: v e= () where vv v... n is the total H ower roduction, while v v vn is the total H inut ower. y relacin in relation () the vv... hydroower lant efficiency the followin relation is obtained:... n e= (4)... v v vn Takin into account the exressions () and () we obtained that:... n e= (5)... or n n

3 International Journal on Inmation Technoloies & Security,, e=... n... n n ecause the hydroower lant should meet a certain load, then the n hydro eneratin units which are in oeration is necessary to roduce as much ower as it has satisfied followin relationshi:... n (7) = e y relacin (7) in (6)... n n e we obtained that: From the last exression can be noted that the determination of the hydroower lant efficiency e, at articular load of the lant, it is necessary to know the efficiency of each of the eneratin units at their aroriate load. The efficiency characteristic of hydro eneratin units that are installed in a articular H, commonly is modeled by olynomial of second order []: = + + (9) j j j. RCTICL EXMLE In this section, analytically and rahically, the efficiency characteristic each available combination of hydro eneratin units in iven ower rane will be determined. Furthermore the otimal unit combination, which rovides the hihest efficiency, is determined all individual ower ranes of the lant ower oeratin rane. Microsoft Excel is used calculation. The H which is analysed is consistin of 4 units whose efficiency characteristics are modeled by olynomial of second order. The efficiency characteristic of unit and unit is rahically resented in fiure and is iven by: = - 0, , ,588 (0) The efficiency characteristic of unit and unit 4 is rahically resented in fiure and is iven by: -5-4, , ,7948 () = n n (6) (8)

4 56 International Journal on Inmation Technoloies & Security,, 07 Fi.. Characteristic f ( ) Fi.. Characteristic f ( ) = = From the characteristics f ( ) and f ( ) it is noted that the = minimum ower outut of the units and is = 40 MW and unit m m and 4 is 5 MW, while the maximum ower outut is m 4m M M 0 MW and 50 MW. Thus the H total ower oeratin rane is M 4M m 5 MW M M 40 MW. The ossible combinations of units in oeration are iven in Table. Table. ossible combinations of units in oeration Combination Unit Unit Unit Unit ecause the units and, as well as the units and 4 are with same characteristic the number of ossible combinations of units in oeration is reduced to 8 and are iven in Table. ccordin to the value of the efficiency the

5 International Journal on Inmation Technoloies & Security,, combinations shown in Table the combinations with the same efficiency are and ; and 4; 7, 8, 9 and 0; and ; 4 and 5 resectively. Table. ossible combinations of units in oeration Combination Unit Unit Unit Unit 4 Sin For the combinations and, from the Table, the efficiency characteristic is resented in fiure and resectively ( f ( ) and f ( ) ). = 4 = For the combinations, the efficiency characteristic f ( ) = f ( ) is obtained by: = -6 = , 80 MW 40 MW () and is resented in fiure. When in oeration are the unit and 4 (the combination 4) the efficiency characteristic f ( ) = f ( ) is iven by: = -5 = , 0 MW 00 MW () and is resented in fiure 4. Fi.. Characteristic f ( ) =

6 International Journal on Inmation Technoloies & Security,, Fi. 4. Characteristic ) ( f = When in oeration are the unit (or ) and (or 4), which corresonds to a combined 5 of Table, the efficiency characteristic can be obtained by: (4) M M m m Secifically in our case, the efficiency characteristic of the combination 5 is rahically reresented in Fiure 5 and is determined by the followin analytical exression: = (5) MW 70 MW 55 When in oeration are all 4 units (combination 6), the efficiency characteristic can be obtained by: (6) M M m m from which it follows that: ) ( ) ( f f (7) Secifically in our case, the efficiency characteristic of the combination 6 is rahically reresented in Fiure 6 and is determined by the followin analytical exression: = (8)

7 International Journal on Inmation Technoloies & Security,, MW 40 MW Fi. 5. Characteristic f ( ) Fi. 6. Characteristic f ( ) For the combination 7, when in oeration are the units (or ), and 4, the efficiency characteristic can be obtained by: (9) m m M M Secifically in our case, the efficiency characteristic of the combination 7 is rahically reresented in Fiure 7 and is determined by the followin analytical exression: -6 = (0) 70 MW 0 MW

8 60 International Journal on Inmation Technoloies & Security,, 07 For the combination 8, when in oeration are the units, and (or 4), the efficiency characteristic can be obtained by: () m m M M In our case, the efficiency characteristic of the combination 8 is rahically reresented in Fiure 8 and is determined by the followin exression: -6 = () 95 MW 90 MW Fi. 7. Characteristic f ( ) Fi. 8. Characteristic f ( ) The otimal combination of units in oeration, certain ower rane, under the exosed method is that one that rovides the hihest efficiency. This roblem could be easily solved if in the common rahic are resented the efficiency characteristic all ossible combinations iven in Table. The H efficiency characteristic all observed 8 combinations of areates, of the lant ower

9 International Journal on Inmation Technoloies & Security,, 07 6 oeratin rane ( m 5 MW M M 40 MW ), is iven on fiure 9. From the results can be seen which unit combination rovides the reatest lant efficiency certain ranes of ower. Fi. 9. Efficiency characteristic all observed combinations of areates 4. CONCLUSION This aer resents method determinin the otimal combination of hydro eneratin units to be ut into oeration in a hydro ower lant, in order to ensure maximum ower lant efficiency in satisfyin the secified load. The method based on knowlede of the efficiency characteristics of each of the units installed in the lant. The method is alied to hydro ower lant with 4 installed units. ll ossible combinations of units are considered and each combination the efficiency as a function of load is obtained. From the resented rahic results, the ower oeration ranes of certain unit combinations, the most favourable unit combination that meet the set criteria is established. The H efficiency will have different values different ower distribution between hydro eneratin units. However certain load of the H there is a secific ower distribution between available units in which the H efficiency is maximized. For future research can be solvin the otimization roblem aimed at determinin the ower distribution between the hydro units in which the H efficiency is the hihest and met the aroriate oerational constraints.

10 6 International Journal on Inmation Technoloies & Security,, REFERENCES [] rce, T. Ohishi, S. Soares. Otimal Disatch of Generatin Units of the Itaiu Hydroelectric lant. IEEE Trans. ower Systems, (vol. 7), 00, [] C.V. Camian, D. Nedelcu. Otimize system of the hydro units oeration H Rueni. roc. of the nd IHR international Meetin of the Workrou on Cavitation and Dynamic roblems in Hydraulic Machinery and Systems, Romania, October 007, [] H. ozar. ower and enery in ower systems (in Croatian), Inmator, Zareb, Croatia, 98. [4] Milan S. Calovic, ndrija T. Saric. ower System Oeration (in Serbian), eores, eorad, Serbia, 999. [5] Carolina, G. M., et al. Otimal Disatch rorammin of Hydroelectric ower Generation with the use of Genetic lorithms. INFOCOM, (vol. ), 0,. -. [6] Shambhu, R.., Vishnu,., Saroj R. Strateic lannin Oeration of Lare Hydroower lants. HYDRO NEL, Issue no. 4, January 04, Inmation about the authors: Sofija Nikolova-oceva, h.d. is assistant rofessor at the Faculty of Electrical Enineerin & IT, Ss. Cyril and Methodius University in Skoje, R. Macedonia. Her areas of interest include: Electric ower System Oeration and Control, Modellin and Otimization in ower lants and Systems, Enery Efficiency, Renewable Enery Sources. nton Chaushevski, h.d. is a full rofessor at the Faculty of Electrical Enineerin & IT, Ss. Cyril and Methodius University in Skoje, R. Macedonia. His areas of interest include: ower lants Oeration in a Comlex ower System, Enery Efficiency, Environmental Imacts of Enery Technoloies and ower lants Oeration. Dimitar Dimitrov, h.d. is associate rofessor at the Faculty of Electrical Enineerin & IT, Ss. Cyril and Methodius University in Skoje, R. Macedonia. His areas of interest include: Renewable Enery Sources, Enery Efficiency, ower lants Oeration. Manuscrit received on 09 July 07