Economic Evaluation of Transformer Selection in Electrical Power Systems

Transcription

1 Economic Evaluation of Transformer Selection in Electrical Power Systems Eleftherios I. Amoiralis, Marina A. Tsili, Antonios G. Kladas Φ Abstract Owning to deregulation, rivatization and cometition, estimating financial benefits of electrical ower system rojects is becoming increasingly imortant. In other words, it is necessary to ensure that a roject is rofitable. In this work, a real-life examle of a detailed analysis for the leastcost choice of a transformer is carried out, showing how the higher rice of a facility can be traded against its oerational cost over its life san. Index Terms-- Distribution transformers, Power system economics. I. INTRODUCTION ROJECTS in the electrical ower systems live for a long P time. Usually, 5 to 3 years is a normal useful life for a conventional transformer, which is one of the three main arts of a ower system (ower station and lines are the remaining elements). For ower generation rojects most exenditure, in the form of oerational cost, i.e. fuel and so on, as well as income occur after commissioning. Such future financial flows will take lace during different times and circumstances. Corresondingly, these will have different value of money than flows occurring during roject evaluation. Thus, the time value of money and the choice of a roer discount rate are highly imortant for caital intensive long-life rojects with large oerational cost, like those of an electrical ower system. Since transformers consist some of key energyconsuming roducts in ower systems (contributing to both variable and fixed network losses), the cost-effective otential from the selection of imroved energy efficiency during the installation of new transformers or the retrofitting of existing transformers can result to significant benefits for electric utilities [1]-[3]. This trend is also enhanced by the recent develoments in transformer technology, able to rovide high efficient designs at a non restricting manufacturing cost. The decision as to whether to urchase a low-cost, inefficient transformer or a more exensive, energy-efficient transformer, is rimarily an economic one [4]. A common ractice used for determining the costeffectiveness of distribution transformers is based on the total owning cost (TOC) method, where TOC is equal to the sum of transformer-urchasing rice lus the cost of transformer losses throughout the transformer lifetime [5]. Different imlementations of the TOC method are encountered in the relevant bibliograhy, adoted by electric utilities [6]-[8] or industrial and commercial transformer users [9],[1]. In the resent aer, an assessment of the benefits resulting from the installation of energy efficient transformers in distribution networks is realized through a roer economic evaluation method. The roosed method involves the incororation of the discounted cost of transformer losses to their economic evaluation, similarly to the TOC method, roviding the ability to take into account variable energy cost during the transformer oerating lifetime. Therefore, different loss cost during eak and off eak load hours can be used for the overall energy loss cost calculation, instead of a mean energy loss cost value that is usually adoted in the TOC method. The method is alied in real-life study cases and sensitivity analysis is carried out, yielding detailed results of the substantial overall economic rofit resulting from the investment to high efficiency transformers. II. TRANSFORMER ECONOMIC EVALUATION A. Inut Data of the Study Case In this section, a real-life examle of a detailed analysis for the least-cost choice of a transformer is resented. It shows how the higher rice of a facility can be traded against its oerational cost over its life san. The examle considers two offers for distribution transformers. Different transformer designs can be develoed to meet the requirements of a articular transformer secification. These designs will have varying amounts of core steel and coer or aluminum conductors with differing no-load and load losses. The lowest cost design that meets all the alicable erformance standards and requirements is generally referred to as the standard efficiency design [11]. In the examined case study. the first transformer offer is the standard efficiency design, corresonding to lower bid rice but higher losses. The two transformer offers have the technical characteristics resented in Table I. Transformer TABLE I TRANSFORMER TECHNICAL SPECIFICATIONS Size (kva) Bid Price ( ) No load losses (kw) Offer A Offer B Load losses (kw) The transformers are assumed to be loaded at 5% of full load at the first year, and each year there is 3.7% increase of the load. Fig. 1 illustrates the transformer load factor variation during the study eriod. In this study case, the exected life of the roject is 3 years and a discount rate of 6% is considered. Φ E. I. Amoiralis is with the Deartment of Production Engineering & Management, Technical University of Crete, GR-731, Chania, Greece ( eamir@tee.gr). M. A. Tsili and A. G. Kladas are with the Faculty of Electrical & Comuter Engineering, National Technical University of Athens, GR- 1578, Athens, Greece ( mtsili@central.ntua.gr, kladasel@central.ntua.gr).

2 load factor (%) study eriod (years) Fig. 1. Transformer load factor variation for a eriod of study equal to 3 years. In order to choose the least-cost solution it is required to consider the total cost of the roject over its exected life san. This includes the bid rice of the two transformers lus their discounted cost of losses, i.e. no load losses and load losses. It is assumed that reliability of the transformers will be the same as well as their maintenance cost. For the sake of simlicity, these were ignored from the comarison. The inut data of this case study are illustrated in Table II. TABLE II INPUT DATA Inut data Values Discount rate (%) 6 Load factor (%) 7 Average losses (LF).5 Energy cost 16h of eak ( /kwh).87 Energy cost 8h of eak ( /kwh).43 Study eriod (yr) 3 B. Transformer loss cost It has to be realized that coer losses at any time are equal to full load coer losses kw (denoted C) multilied by the square of the transformer s utilization factor, i.e.: demand C = load losses (1) rated caacity Therefore, in the case of the two transformers their combined annual load losses based on the load are resented in Fig.. For examle, the annual load losses of the transformer offer A for the first year of the study at half load are:.5 1 kva C= 9kW =.5kW 1kVA Likewise, the annual load losses of the transformer offer B for the first year of the study at half load are:.5 1kVA C= 7.6 kw = 1.9 kw 1 kva Annual load losses (kw) Offer A Offer B load factor (%) Fig.. Annual load losses of the two transformer offers, based on the load factor of Fig. 1. TABLE III ANNUAL LOAD LOSSES OF THE TWO TRANSFORMER OFFERS Year Load factor (%) Annual load losses of Offer A (kw) Annual no load losses of Offer B (kw) To work out the annual energy losses, the load factor and shae of the load curve lays a significant role. Usually, the loss factor (LF) derives from the load factor (l f ), i.e. the mean transformer loading over its lifetime, reresented as equivalent ercentage of its nominal ower, as follows: LF =.15 lf +.85 lf () With a load factor of 7%, the loss factor will be equivalent to.5. In order to comute the value of losses, these have to be multilied by the marginal cost of the energy at the substation site. This may be significantly lower than the tariff if the transformer is art of the utility system. Usually, a two-art energy cost is considered: a eak energy cost during the 16 hours of eak load and an off-eak energy

3 cost for the off-eak load 8 hours. The eak cost was chosen based on the mean value of the energy cost in the Greek ower system for the year 8, as rovided by the hourly data for the system marginal rice of the Hellenic Transmission System Oerator [1], yielding a value of.87 /kwh. A eak/off-eak load cost ratio equal to is considered (i.e. the off-eak energy cost is considered half of the eak energy cost, namely.43 /kwh). Last but not least, a very imortant finance factor during the economic evaluation of the transformer selection is the annuity factor. This factor deicts the resent value at a discount rate r of an annuity of 1 aid at the end of each n eriods: 1 1 Annuity factor = r r (1 + r) n () Taking into consideration the inut data of Table II, the variation of the annuity factor for a study eriod equal to 3 years is resented in Fig. 3. annuity factor study eriod (years) Fig. 3. Annuity factor variation, based on the inut data of Table II. C. Economic evaluation of offer A Costs of no load losses and load losses are calculated at the eak (16 hours) and off-eak rate (8 hours). Since no load losses are constant through the study eriod, the annual eak and off-eak no load loses values, NLL and NLL o resectively, are comuted as follows: NLL = 1.1kW 16h 365 = 644kWh NLL = 1.1kW 8h 365 = 31kWh o In order to comute the annual eak and off-eak load loses values, transformer loading should be taken into account. To be more recise, based on Table II, the annual eak and off-eak load loss values are calculated (Table IV). TABLE IV ANNUAL LOAD LOSSES OF OFFER A Year Annual eak load Annual off-eak load For examle, at the first year of the study, the annual eak load losses, LL (kwh), as well as the annual off-eak load losses, LL o (kwh), are comuted as follows: LL =.5kW 16h = 6853kWh LL =.5kW 8h = 346kWh o Therefore, the total losses, i.e. load losses and no load losses, of eak (TL in kwh) and off-eak rate (TL o in kwh), are given based on the following equations: n [ ( () ()) TL = LL i + NLL i i= 1 ( annuity factor() i annuity factor( i 1) ) ] n [ ( () ()) TL = NLL i + LL i o o o i= 1 ( annuity factor() i annuity factor( i 1) ) ] where the index i refers to the current year of the study (i.e. NLL o (3) are the off-eak no load losses of the third year), and annuity factor (-1) is equal to zero. Using eq. (3) and eq. (4), we get: TL = kWh and TLo = 31539kWh The cost of losses of eak (CL in ) and off-eak rate (CL o in ) are: = 31539kWh.87 euros / kwh = 743euros and = kWh.43 euros / kwh = 6779euros Thus, the total cost of offer A is the summation of the cost of losses (eak and off eak rate) and the rice of the transformer A, namely: Offer Acost = Offer Acost = 4385euros D. Economic evaluation of offer B Costs of no load losses and load losses are calculated at the eak (16 hours) and off-eak rate (8 hours). Since no load losses are constant through the study eriod, the annual eak and off-eak no load loses values, NLL and NLL o resectively, are comuted as follows: (3) (4)

4 NLL =.94kW 16h 365 = 549 kwh NLLo =.94kW 8h 365 = 745kWh In order to comute the annual eak and off-eak load loses values, transformer loading should take into account. To be more recise, based on Table II, comute the annual eak and off-eak load loses values are calculated (Table V). TABLE V ANNUAL LOAD LOSSES OF OFFER B Year Annual eak load Annual off-eak load For examle, at the first year of the study, the annual eak load losses, LL (kwh), as well as the annual off-eak load losses, LL o (kwh), are comuted as follows: LL = 1.9kW 16h = 5787 kwh LLo = 1.9kW 8h = 893kWh Using eq. (3) and eq. (4), we get: TL = 67154kWh and TLo = kWh The cost of losses of eak (CL in ) and off-eak rate (CL o in ) are: = 67154kWh.87 euros / kwh = 34euros and = kWh.43 euros / kwh = 5744euros Thus, the total cost of offer B is the summation of the cost of losses (eak and off eak rate) and the rice of the transformer B, namely: Offer Acost = Offer Acost = 4348euros For the above analysis it is clear that the life san cost of the first alternative Offer A is 4385, while that of Offer B is These values corresond to a difference of 7.3% between the cost of Offer A and Offer B. Fig. 4 resents the articiation of bid rice and eak and off-eak rate loss costs in the overall costs of the two offers. Cost ( ) Transformer A Fig. 4. Cost results for transformer offers A and B. Cost of off-eak rate losses ( ) Cost of eak rate losses ( ) Bid rice ( ) Transformer B Therefore, Offer B is the least-cost alternative, although it is more exensive. This real-life examle shows how oerational costs of almost all energy consuming facilities in the electrical ower system lay a more significant role in the overall life san cost that the investment cost. E. Sensitivity analysis The discount rate is one of the major arameters determining the outcome of an economic evaluation rocess. Other factors such as the daily fluctuation of the energy loss cost or the load factor influence significantly the results of the analysis. For a comrehensive overview of this influence, a sensitivity analysis has been carried out, concerning these factors. Considering as base case the results of the revious subsections (difference between the cost of Offer A and Offer B equal to 7.3%, for a discount rate equal to 6% and eak to off-eak energy cost ratio equal to ), Fig. 5 resents the sensitivity arameter analysis results, based on various arameter values. Each time, one arameter is modified, while the other arameters are assumed to remain at their base case values. For examle, by changing the discount rate by +1%, the difference between Offer A and Offer B changes by -8.6% in comarison to the base case. The sloe of each curve of the sensitivity grah of Fig. 4 indicates the relative degree of sensitivity of the result to each arameter: the steeer the sloe of a curve, the more sensitive the cost difference is to the arameter, [13]. Given the results of Fig. 5, the load factor is the arameter that influences the most the results. It must also be noted, that in case that a constant energy loss cost is considered in the analysis (i.e. the value of.87 /kwh is the same for eak and off-eak load hours), the difference between Offer A and Offer B becomes equal to 8.6%. Therefore, the benefit from the installation of transformer B aears to be 19.44% greater comared to the more realistic aroach of adoting a reduced energy loss cost during off-eak load hours, a difference that alters significantly the ersective of the

5 economic analysis. Variation of difference betwee Offer A and B (%) d Peak/Off-Peak 4 Energy Loss Cost load factor Fig. 5. Sensitivity Analysis Parameters variation (%) III. CONCLUSIONS In the resent article, the imortance and the otentials to imrove ower systems efficiency through the installation of energy efficient transformers was investigated. The analysis was erformed through roer transformer economic evaluation methods, taking into account the energy loss consumtion and its daily rice fluctuation, revealing new asects that must be taken into account during the definition of the transformer urchasing olicy of electric utilities. The main conclusions of the study can be summarized as follows: i) investment to low efficiency decreases the initial caital cost, but results to higher energy costs during the transformer lifetime, yielding transformers with low manufacturing cost non-rofitable in the long term, ii) the choice of the most rofitable among transformers with high degrees of efficiency must be based on the otimum balance between the initial urchasing cost and the energy savings through the transformer lifetime. IV. REFERENCES [1] Leonardo Energy, Analysis of insufficient regulatory incentives for investments into electric networks. An udate, Final Reort submitted to Euroean Coer Institute (ECI), KEMA, Bonn, January 9. [] M. McNeil, M. Iyer, S. Meyers, V. Letschert, J. McMahon, "Potential benefits from imroved energy efficiency of key electrical roducts: The case of India," Energy Policy, vol. 36, , 8. [3] Euroean Commission, The scoe for energy saving in the EU through the use of energy-efficient electricity distribution transformers, Euroean Communities, [4] B. W. Kennedy, Energy efficient transformers. McGraw-Hill, [5] P. S. Georgilakis, E. I. Amoiralis, Distribution Transformer Cost Evaluation Methodology Incororating Environmental Cost, IET Generation, Transmission & Distribution (submitted). [6] D. L. Nickel, and H. R. Braunstein, Distribution transformer loss evaluation: I Proosed techniques, IEEE Trans. Power Aaratus and Systems, vol. 1, no., , [7] D. L. Nickel, and H. R. Braunstein, Distribution transformer loss evaluation: II Load characteristics and system cost arameters, IEEE Trans. Power Aaratus and Systems, vol. 1, no., , [8] E. Amoiralis, P. Georgilakis, M. Tsili, Utility-based economic assessment of distribution transformers considering secific load characteristics and environmental factors, Journal of Otoelectronics and Advanced Materials, Vol. 1, No. 5, May 8, [9] S. Merritt, and S. Chaitkin, No load versus load loss, IEEE Industry Alications Magazine, vol. 9, no. 6,. 1-8, 3. [1] E. Amoiralis, M. Tsili, P. Georgilakis, A. Kladas, Energy efficient transformer selection imlementing life cycle costs and environmental externalities, Proc. 9th International Conference on Electrical Power Quality and Utilisation (EPQU 7), Barcelona, Sain, 9-11 October 7. [11] N. Haggerty, T. Malone, J. Crouse, Alying high efficiency transformers, IEEE Industry Alications Magazine, vol. 4, no. 6,. 5-56, Nov [1] Hellenic Transmission System Oerator. Load, System Marginal Price and Interconnection Data. Available: htt:// [13] W. G. Sullivan, E. M. Wicks, and J. T. Luxhoj, Engineering Economy. Prentice Hall, 13th edn., 6. V. BIOGRAPHIES Eleftherios I. Amoiralis was born in Greece, in 198. He received the Diloma in Production and Management Engineering, the M.Sc. in Industrial Engineering, and the Ph.D. degree in the field of Electric Power Systems from the Technical University of Crete (TUC), Greece, in 4, 5, and 8, resectively. From 5 to resent, he is with Schneider Electric AE as a freelancer. In 1 and, he has worked as an intern at the Public Power Cooeration, of Greece. Since 4, he has been occuied as research associate in many research rojects. His current research interests include transformer cost evaluation, energy-efficient transformers, otimal transformer sizing, transformer design otimization as well as artificial intelligence. Dr. Amoiralis is member of IEEE and the Technical Chamber of Greece. Marina A. Tsili was born in Greece, in She received the Diloma in Electrical and Comuter Engineering in 1 and the Ph.D. degree in 5 from the National Technical University of Athens, Greece. From 5 to 6 she worked for the Distribution Division of the Public Power Cororation of Greece, in high and medium voltage substation studies. In 7, she joined the Hellenic Transmission System Oerator as a ower systems engineer. Her research interests include transformer and electric machine modeling as well as analysis of generating units by renewable energy sources. She is a member of IEEE and the Technical Chamber of Greece. Antonios G. Kladas was born in Greece, in He received the Diloma in Electrical Engineering from the Aristotle University of Thessaloniki, Greece in 198 and the DEA and Ph.D. degrees in 1983 and 1987, resectively from the University of Pierre and Marie Curie (Paris 6), France. He served as Associate Assistant in the University of Pierre and Marie Curie from During the eriod he joined the Public Power Cororation of Greece, where he was engaged in the System Studies Deartment. Since 1996 he joined the Deartment of Electrical and Comuter Engineering of the National Technical University of Athens (NTUA), where he is now Professor. His research interests include transformer and electric machine modeling and design as well as analysis of generating units by renewable energy sources and industrial drives.