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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 5, MAY 2012 2329

Power Transformer Economic Evaluation inDecentralized Electricity Markets

Eleftherios I. Amoiralis, Member, IEEE, Marina A. Tsili, Member, IEEE, and Antonios G. Kladas

Abstract—Owing to deregulation, privatization, and compe-tition, estimating financial benefits of electrical power systemprojects is becoming increasingly important. In other words, itis necessary to assess the project profitability under the lightof new developments in the electricity market. In this paper, adetailed methodology for the least cost choice of a distributiontransformer is proposed, showing how the higher price of a facilitycan be traded against its operational cost over its life span. Theproposed method involves the incorporation of the discountedcost of transformer losses to their economic evaluation, providingthe ability to take into account variable energy cost during thetransformer operating lifetime. In addition, the influence of thevariability in the energy loss cost is investigated, taking intoaccount a potential policy intended to be adopted by distributionnetwork operators. The method is combined with statistical andprobabilistic assessment of electricity price volatility in order toderive its impact on the transformer purchasing policy.

Index Terms—Electricity supply industry deregulation, powerdemand, power distribution, power grids, power system eco-nomics, probability density function, statistical analysis, trans-formers.

NOMENCLATURE

AF Annuity factor.BP Bid price (C).C Copper (load) loss (in kilowatts).CLk,j Total cost of energy losses for the kth period

of the jth day.CLL1 Total cost of energy losses for period L1 (C).CLL2 Total cost of energy losses for period L2 (C).CLL3 Total cost of energy losses for period L3 (C).CLL4 Total cost of energy losses for period L4 (C).CLop Cost of energy corresponding to load losses

and no-load losses of off-peak rate (C).CLp Cost of energy corresponding to load losses

and no-load losses of peak rate (C).ECk,j Energy cost during the kth period of the jth

day (C).ECL1 Energy cost during period L1 (C).

Manuscript received December 15, 2010; revised February 19, 2011 andApril 24, 2011; accepted May 9, 2011. Date of publication May 23, 2011; dateof current version February 3, 2012.

E. I. Amoiralis is with the Department of Production Engineering andManagement, Technical University of Crete, GR-73100 Chania, Greece(e-mail: [email protected]).

M. A. Tsili and A. G. Kladas are with the Faculty of Electrical and ComputerEngineering, National Technical University of Athens, GR-15780 Athens,Greece (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TIE.2011.2157291

ECL2 Energy cost during period L2 (C).ECL3 Energy cost during period L3 (C).ECL4 Energy cost during period L4 (C).ECop Energy cost during off-peak load hours

(C/kilowatthours).ECp Energy cost during peak load hours

(C/kilowatthours).L1, L2, L3, L4 Time periods of the day (hours).LLk Annual energy corresponding to load loss

values of the kth period of the day (in kilo-watthours).

LLL1 Annual energy corresponding to load lossvalues of the period L1 (in kilowatthours).




LF Loss factor.lf Load factor.LLp Annual energy corresponding to peak load

loss value (in kilowatthours).LLop Annual energy corresponding to off-peak

load loss value (in kilowatthours).NLLk Annual energy corresponding to no-load loss

values of the kth period of the day (in kilo-watthours).

NLLL1 Annual energy corresponding to no-load lossvalues of the period L1 (in kilowatthours).




NLLop Annual energy corresponding to off-peak no-load loss value (in kilowatthours).

r Discount rate (in percent).

I. INTRODUCTION

PROJECTS in the electrical power systems live for a longtime. Usually, 25 to 30 years is a normal useful life for

a conventional transformer, which is one of the three mainconstitutive components of a power system (power stations andlines are the remaining ones). For power generation projects,most expenditure, in the form of operational cost, i.e., fuel and

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2330 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 5, MAY 2012

so on, as well as income, occurs after commissioning. Suchfuture financial flows will take place during different times andcircumstances. Correspondingly, these will have different valueof money than flows occurring during project evaluation. Thus,the time value of money and the choice of a proper discount rateare highly important for capital-intensive long-life projects withlarge operational cost, like those of an electrical power system.True equipment cost is defined as the total of the initial capitalexpenditures plus the operating costs, which include energyand maintenance. Even though the foremost requirement for apiece of equipment is its performance in the production chain,the justification for selecting one piece over another should bebased upon the initial capital cost plus operating expenses [1].

Since transformers constitute key energy-consuming compo-nents in power systems (contributing to both variable and fixednetwork losses), the cost-effective potential from the selectionof improved energy efficiency criteria during the installationof new transformers or the retrofitting of existing transformerscan result to significant benefits for electric utilities [2], [3].This trend is also enhanced by the recent developments intransformer technology, able to provide high-efficient designsat a nonrestrictive manufacturing cost. The decision to pur-chase the best transformer for a specific application between alow-cost inefficient transformer and a more expensive energy-efficient one primarily involves economic issues [4]. On theother hand, in order to overcome the loss problem, as wellas other issues imposed by the use of transformers, severaltransformerless configurations are investigated, particularly inthe case of dispersed renewable energy source connection tothe grid [5], [6].

A common practice used for determining the cost effective-ness of distribution transformers is based on the total owningcost (TOC) method, where TOC is equal to the sum of trans-former purchasing price plus the cost of transformer lossesthroughout the transformer lifetime [7], [8]. The cost of own-ership method is applied to other electric devices as well, as ameans of their economic assessment [9]. The TOC technique isthe most widely used transformer evaluation method for deter-mining the cost effectiveness of energy-efficient transformers,providing a balance between cost of purchase and cost of energylosses. The TOC evaluation method has been developed as ahandy tool to reflect the unique financial environment faced byeach electric utility when purchasing distribution transformers.According to this method, the variability of the cost of electricenergy, capacity, and financing is expressed through two evalu-ation factors, called A and B factors, corresponding to the unitcost of no-load and load losses, respectively [10]. It is importantto note that the method that defines these two factors variesaccording to the role of the transformer purchaser in the energymarket (two major categories can be considered: electric utili-ties [11] and industrial users [12]) and the depth of the analysis(depending on the accuracy of the representation of the trans-former loading characteristics). It is important to recognize thatthe perspective of the electric utility is different from the per-spective of the industrial and commercial users of transformers.The transformer loss evaluation procedure for the electric utilityinvolves understanding and assessing the total cost of gener-ating, transmitting, and distributing transformer losses, while

the transformer loss evaluation procedure for industrial andcommercial users requires an understanding and assessment ofthe electric rates they pay to the electric utility. An importantpart of the transformer cost optimization research is devoted tothe TOC minimization, as described in the followings. Distrib-ution transformer TOC optimization is analyzed in [13]–[15].Since the load losses are directly linked to the type of theconsidered load and the specific details of the network at thetransformer installation point, a number of versatile factorsshould be incorporated in the TOC analysis. Such an analysis isperformed in depth in [16] and [17]. Transformer energy effi-ciency optimization, taking into account the specific constraintsset by national distribution regulation policies, has also beenpresented in [18], with the main aim to achieve the objectivesof the utility when installing new transformers. Energy andenvironment, particularly the global warming problem due toman-made greenhouse gases, have become a major concern inthe past few decades [19]. Recently, the impact of transformerenvironmental externalities (i.e., the costs that are associatedwith various types of emissions resulting from the combustionof fossil fuels so as to compensate for transformer losses) andthe contribution of losses to the greenhouse gas emissions gen-erated by the global power generation mix have been addressed[20], and new methodologies to quantify this impact have beendeveloped [21], [22].

The main drawback of the TOC method is that it has to takeinto account a constant annual levelized cost of energy for allyears of the study. In this paper, an assessment of the benefits re-sulting from the installation of energy-efficient transformers indistribution networks is realized through an improved economicevaluation method. The proposed method involves the incor-poration of the discounted cost of transformer losses to theireconomic evaluation, similarly to the TOC method, providingthe ability to take into account variable energy cost during thetransformer operating lifetime. Therefore, different loss costduring peak and off-peak load hours can be used for the overallenergy loss cost calculation, instead of a mean energy loss costvalue that is usually adopted in the TOC method. Moreover,a combination of the method to statistical and probabilisticassessment of electricity price volatility results to more realisticconclusions. The method is applied in real-life case studies, andsensitivity analysis is carried out, yielding detailed results of thesubstantial overall economic profit resulting from the invest-ment in high-efficiency transformers. Economic assessment oftransformer losses is realized:

1) considering four different scenarios for energy pricing,as shown in Fig. 1; more specifically, different electricitypricing is considered for the following:a) two time periods per day, namely, 8 h of peak load and

16 h of off-peak load (first scenario—Section II);b) four time periods per day, namely, 6 h of peak load,

two 6-h periods of intermediate load, and 6 h of lowload (second scenario—Section III);

c) four time periods per day, with varying duration ofhours, in order to better approximate the real dailyvariations of the electricity price, in conjunction withvarying transformer load factor during these periods,

AMOIRALIS et al.: POWER TRANSFORMER ECONOMIC EVALUATION IN DECENTRALIZED ELECTRICITY MARKETS 2331

Fig. 1. Different scenarios of electricity pricing examined in this paper.

so as to provide better representation of its operationalcharacteristics. The analysis is conducted for highand low electricity price scenarios (third and fourthscenario-Section IV).

2) considering detailed hourly electricity pricing P1–P24,based on historical market data and detailed load char-acteristics (Section V, fifth scenario in Fig. 1);

3) by probabilistic assessment for the hourly energy pricevariation P1–P24, providing respective distributions oftransformer cost variation, so as to take into accountthe influence of energy price volatility to the results(Section VII, sixth scenario in Fig. 1).

The policy of variable energy pricing in distribution net-work end users will be adopted shortly by the distributionsystem operators, if it has not already been applied in somecountries. Introducing the microgrid concept [23], as a partof the next-generation electricity grid or “smart” grid policies[24], diversification of microgeneration energy resources andprice-sensitive consumers at local low-voltage (LV) level wouldyield the creation of local energy markets at each mediumvoltage (MV)/LV transformer level. Therefore, the electricitycost for the end users may vary in compliance with the cost ofthe microgeneration and the willingness of the price-sensitiveconsumers (if demand side bidding is considered) to pay fortheir load at each microgrid level, or, in other words, the costof the electricity for the LV consumers will vary in accordancewith the retail market electricity price. Bearing this in mind, weinvestigate the behavior of the suggested economic evaluationmethod by considering multiple levels of different energy costsduring the day (two in the case study in Section II and four inthe case studies in Sections III and IV) as well as hourly energypricing variation (Sections V and VI).

This paper is organized as follows: Section II presents thebasics of the proposed economic evaluation methodology andits application for a daily electricity schedule divided into twoperiods (peak and off-peak load hours). Section III expandsthe methodology by dividing the daily period into four in-tervals and investigating their influence on the results of the

economic assessment for the same transformers considered inSection II. In Section IV, different electricity price scenarios areinvestigated while the analysis in Section III is expanded, con-sidering more accurate representation of transformer loadingvariation. In Section V, hourly variation of electricity pricingand load characteristics is considered in the analysis, while,in Section VI, the methodology is combined with probabilisticassessment of energy price fluctuation. Section VII presents aqualitative comparison of the results in Sections II–VI, whileSection VIII comprises the conclusions of this paper.

II. TRANSFORMER ECONOMIC EVALUATION

METHODOLOGY CONSIDERING TWO

LEVELS OF ELECTRICITY PRICING

A. Input Data of the Case Study

In this section, a real-life example of a detailed analysis forthe least cost choice of a transformer is presented. It shows howthe higher price of a facility can be traded against its opera-tional cost over its life span. The example considers two offersfor distribution transformers. The considered transformers are1000 kVA, rated primary voltage (HV) 20 kV delta connected,rated secondary voltage (LV) 400 V star connected, three-phase, wound core, oil-immersed, distribution transformers.Different transformer designs can be developed to meet therequirements of a particular transformer specification. Thesedesigns will have varying amounts of core steel and copper oraluminum conductors with differing no-load and load losses.The lowest cost design that meets all the applicable perfor-mance standards and requirements is generally referred to asthe standard efficiency design [25]–[27]. In general, improvedefficiencies in transformers can be achieved at the manufac-turing level through increases in material and engineering ex-penditures, but this results inevitably in premium prices [28].In the examined case study, the first transformer offer is thestandard efficiency design, corresponding to lower bid price buthigher losses. The two transformer offers have the technicalcharacteristics presented in Table I.


TABLE ITRANSFORMER TECHNICAL SPECIFICATIONS

Fig. 2. Transformer load factor variation for a period of study equal to30 years.

TABLE IIINPUT DATA

The transformers are assumed to be loaded at 50% of fullload in the first year, and each year, there is 3.7% increaseof the load. Fig. 2 shows the transformer load factor variationduring the study period. In this case study, the expected life ofthe project is 30 years, and a discount rate of 6% is considered.

In order to choose the least cost solution, it is required toconsider the total cost of the project over its expected life span.This includes the bid price BP of the two transformers plustheir discounted cost of losses, i.e., no-load losses and loadlosses. It is assumed that the reliability of the transformers willbe the same as well as their maintenance cost. For the sake ofsimplicity, these were ignored from the comparison. The inputdata of this case study are illustrated in Table II.

B. Transformer Loss Measurement Setup

The no-load and load loss values reported in Table I areextracted from the type tests specified by International Elec-trotechnical Commission 60076-1 [29], concerning the mea-surement of no-load and load losses. Figs. 3 and 4 describe themeasurement setup. All tests are carried out in the manufac-turing unit as part of the transformer validation and acceptancetesting.

No-load losses are measured from the LV side using anadjustable three-phase voltage source with neutral (Fig. 3). Thevoltage and frequency should be steady and at rated values.The LV side is energized at the rated tap at rated voltage.Phase voltage, current, and power are measured by amp meters

Fig. 3. Transformer no-load loss measurement setup.

Fig. 4. Transformer load loss measurement setup.

(Ia, Ib, and Ic), voltmeters (Va, Vb, and Vc), and watt meters(Wa,Wb, and Wc), respectively. The no-load loss value is thesum of the three readings of Wa, Wb, and Wc.

The load loss measurement test (Fig. 4) is done by energizingthe HV side at a suitable voltage, much lower than the nominalvalue, while shorting the LV side. The applied voltage isadjusted to pass the nominal current in the primary/secondarywinding (measured by amp meter I in Fig. 4). The load lossvalue is determined by the sum of the readings in watt metersW1 and W2 in Fig. 4.

C. Transformer Loss Cost

It has to be realized that copper (load) losses at any time(denoted C in the following equation) are equal to full-loadcopper losses (in kilowatts) multiplied by the square of thetransformer’s utilization factor, according to

C = load losses ·(

demand

rated capacity

)2

. (1)

Therefore, the load losses of the two examined transformersfor each year of the study (based on the respective load growthrate) are shown in Fig. 5. For example, the load losses ofthe transformer offer A for the first year of the study at halfload are

C = 9 kW ·(

0.5 · 1000 kVA1000 kVA

)2

= 2.25 kW.


Fig. 5. Load losses of the two transformer offers, based on the load factor inFig. 2.

Likewise, the load losses of the transformer offer B for thefirst year of the study at half load are

C = 7.6 kW ·(

0.5 · 1000 kVA1000 kVA

)2

= 1.9 kW.

To work out the annual energy losses, the load factor andshape of the load curve play a significant role. The loss factor isalso used, as an expression of the average power factor over agiven period of time. Usually, the loss factor (LF ) is derivedfrom the load factor (lf ), i.e., the mean transformer loadingover its lifetime, represented as equivalent percentage of itsnominal power, with the use of (2), as follows:

LF = 0.15 · lf + 0.85 · l2f . (2)

With a load factor of 70%, the loss factor will be equivalentto 0.52.

In order to compute the value of losses, these have to bemultiplied by the marginal cost of the energy at the substationsite. This may be significantly lower than the tariff if thetransformer is part of the utility system. Usually, a two-partenergy cost is considered: a “peak” energy cost during the 16 hof peak load and an “off-peak” energy cost for the 8 h of off-peak load. The peak cost was chosen based on the mean valueof the energy cost in the Greek power system for the year 2008,as provided by the hourly data for the system marginal priceof the Hellenic Transmission System Operator [30], yielding avalue of 0.087 C/kWh. A peak/off-peak load cost ratio equalto two is considered (i.e., the off-peak energy cost is consideredhalf of the peak energy cost, namely, 0.043 C/kWh).

Last but not the least, a very important finance factor duringthe economic evaluation of the transformer selection is theannuity factor (AF ), yielded by (3). This factor depicts thepresent value at a discount rate r of an annuity of 1 C paidat the end of each n period

AF (n) =1r− 1

r · (1 + r)n. (3)

Taking into consideration the input data in Table II, thevariation of the annuity factor for a study period equal to 30years is shown in Fig. 6.

Fig. 6. Annuity factor variation, based on the input data in Table II.

D. Economic Evaluation of Offer A

The costs of no-load losses and load losses are calculated atthe peak (16 h) and off-peak rates (8 h).

Since no-load losses are constant through the study period,the annual energies corresponding to peak and off-peak no-load loss values, NLLA

p (in kilowatthours) and NLLAop (in

kilowatthours), respectively, are computed as follows:

NLLAp = 1.1 kW · 16 h · 365 = 6424 kWh

NLLAop = 1.1 kW · 8 h · 365 = 3212 kWh.

In order to compute the energy corresponding to the peakand off-peak load loss values, the transformer loading per yearshould be taken into account. To be more precise, based onTable II, the annual energy losses corresponding to peak andoff-peak load losses for offer A are calculated (Fig. 7).

For example, in the first year of the study, the annual energycorresponding to peak load losses LLA

p (in kilowatthours) andthe annual energy corresponding to off-peak load losses LLA

op

(in kilowatthours) are computed as follows:

LLAp = 2.25 kW · 16 h · 365 · 0.522 = 6853 kWh

LLAop = 2.25 kW · 8 h · 365 · 0.522 = 3426 kWh.

Therefore, the total cost for the energy loss for the 30years of the considered time period, i.e., the cost of energycorresponding to load losses and no-load losses of peak (CLA

p

in C) and off-peak rates (CLAop in C), is given based on

CLAp =ECp ·

n∑i=1

[(LLA

p (i)+NLLAp (i)

)·(AF (i)−AF (i−1))]

(4)

CLAop =ECop·

n∑i=1

[(LLA

op(i)+NLLAop(i)

)·(AF (i)−AF (i−1))]

(5)

where ECp is the energy cost during peak load hours, ECop

is the energy cost during off-peak load hours, index i refersto the current year of the study (i.e., NLLA

op(3) is the energycorresponding to the off-peak no-load losses of the third year),and AF (−1) is equal to zero.


Fig. 7. Annual energy corresponding to peak and off-peak load losses ofoffers A and B.

Given that

(AF (i)−AF (i−1)) =[1r− 1

r·(1+r)i

]−

[1r− 1

r·(1+r)i−1

]

=1

(1+r)i(6)

the cost of energy losses of peak (CLAp in C) and off-peak rates

(CLAop in C) is finally derived from

CLAp =

n∑i=1

[(NLLA

p (i) + LLAp (i)

) · ECp

(1 + r)i

](7)

CLAop =

n∑i=1

[(NLLA

op(i) + LLAop(i)

) · ECop

(1 + r)i

]. (8)

The cost of energy losses of peak (CLAp in C) and off-peak

rates (CLAop in C) is:

CLAp = 315309 kWh · 0.087 C/kWh = 27432 C

CLAop = 157655 kWh · 0.043 C/kWh = 6779 C.

Thus, the total cost of offer A is the summation of the costof energy losses (peak and off-peak rates) and the price of thetransformer A, namely

CostA =CLAP +CLA

op+BPA =27432+6779+9074=4328 C.

E. Economic Evaluation of Offer B

The energies corresponding to annual peak and off-peak no-load loss values, NLLB

p (in kilowatthours) and NLLBop (in

kilowatthours), respectively, are computed as follows:

NLLBp = 0.94 kW · 16 h · 365 = 5490 kWh

NLLBop = 0.94 kW · 8 h · 365 = 2745 kWh.

As in the case of offer A, based on Table II, the annual energylosses corresponding to peak and off-peak load losses for offerB are calculated (Fig. 7). For example, in the first year of thestudy, the annual energy corresponding to peak load losses

Fig. 8. Cost results for transformer offers A and B.

LLBp (in kilowatthours) and the annual energy corresponding

to off-peak load losses LLBop (in kilowatthours) are

LLBp = 1.9 kW · 16 h · 365 · 0.522 = 5787 kWh

LLBop = 21.9 kW · 8 h · 365 · 0.522 = 2893 kWh.

The cost of energy losses of peak (CLBp in C) and off-peak

rates (CLBop in C) is

CLBp = 267154 kWh · 0.087 C/kWh = 23242 C

CLBop = 133577 kWh · 0.043 C/kWh = 5744 C.

Thus, the total cost of offer B is the summation of the costof energy losses (peak and off-peak rates) and the price of thetransformer B, namely

CostB =CLBp + CLB

op + BPB

= 23242 + 5744 + 11362 = 40348 C.

For the aforementioned analysis, it is clear that the life spancost of the first alternative offer A is 43285 C, while that ofoffer B is 40348 C. These values correspond to a difference of7.3% between the cost of offer A and offer B. Fig. 8 shows theparticipation of bid price and peak and off-peak rate loss costsin the overall costs of the two offers.

Therefore, offer B is the least cost alternative, although itis more expensive in terms of bid price. This real-life ex-ample shows how the operational costs of almost all energy-consuming facilities in the electrical power system play a moresignificant role in the overall life span cost than the investmentcost.

F. Sensitivity Analysis

The discount rate is one of the major parameters determiningthe outcome of an economic evaluation process. Other factorssuch as the daily fluctuation of the energy loss cost or the loadfactor influence significantly the results of the analysis. For acomprehensive overview of this influence, a sensitivity analysishas been carried out, concerning these factors. Consideringas base case the results of the previous sections (differencebetween the cost of offer A and offer B equal to 7.3%, for a


Fig. 9. Sensitivity analysis.

discount rate equal to 6%, and peak-to-off-peak energy costratio equal to 2), Fig. 9 shows the sensitivity parameter analysisresults, based on various parameter values. Each time, oneparameter is modified, while the other parameters are assumedto remain at their base case values. For example, by changingthe discount rate by +10%, the difference between offer A andoffer B changes by −8.6% in comparison to the base case. Theslope of each curve of the sensitivity graph in Fig. 9 indicatesthe relative degree of sensitivity of the result to each parameter:The steeper the slope of a curve, the more sensitive the cost dif-ference is to the parameter [31]. Given the results in Fig. 9, theload factor is the parameter that influences the results in a moresignificant way. It must also be noted that, in case that a constantenergy loss cost is considered in the analysis (i.e., the value of0.087 C/kWh is the same for peak and off-peak load hoursand the peak-to-off-peak energy cost ratio is equal to 1), thedifference between the cost of offer A and offer B becomesequal to 8.6% (instead of 7.3%). Therefore, the benefit fromthe installation of transformer B appears to be 17.8% greatercompared to the more realistic approach of adopting a reducedenergy loss cost during off-peak load hours, a difference thatalters significantly the perspective of the economic analysis.This difference is not visible in Fig. 9, since it correspondsto peak-to-off-peak energy cost ratio variation equal to −50%,which is outside the limits of the sensitivity graph.

III. TRANSFORMER ECONOMIC EVALUATION

METHODOLOGY CONSIDERING FOUR

LEVELS OF ELECTRICITY PRICING

In this section, a second case study is investigated where,instead of two different time periods (peak and off-peakload—first case study), four different time periods and respec-tive energy loss costs are considered. This potential strategy isintended to be implemented by distribution system operators. Inthis case and due to energy deregulation, the cost of electricitycan be varied because it is produced by different ways, suchas photovoltaic systems, wind turbines, and so on, creatingvarious costs of electricity energy price (following the next-generation electricity grid strategy, known as the “smart grid”or “intelligent grid”).

Taking the aforementioned electricity market volatility intoconsideration, we investigate the behavior of the suggestedeconomic evaluation method of the first case study by dividingthe electricity cost time period to four different parts (Table III).It is assumed that a 24-h day is divided into four equal timeperiods, i.e., four periods, and each period is equal to 6 h. Theenergy cost of each period is shown in Table III. It is importantto mention that the load losses of transformer offer A and B, theload factor variation and the annuity factor variation (shown inFigs. 2, 5, and 6, respectively) are the same as in the first casestudy.

A. Economic Evaluation of Offer A

The costs of energy corresponding to no-load losses and loadlosses are calculated at the four different time periods, i.e., 6 hof peak load (designated as L1 period), 6 h of intermediateload level 1 (designated as L2 period), 6 h of intermediate loadlevel 2 (designated as L3 period), and 6 h of off-peak load(designated as L4 period).

Since no-load losses are constant through the study period,the annual energies corresponding to no-load loss values ofthe four periods, NLLA

L1, NLLAL2, NLLA

L3, and NLLAL4,

respectively, are computed as follows:

NLLAL1 =NLLA

L2 = NLLAL3 = NLLA

L4

=1.1 kW · 6 h · 365 = 2409 kWh.

In order to compute the annual energy corresponding to theload loss values at the four different time periods, transformerloading should be taken into account. More precisely, basedon Table III, the annual energy corresponding to the load lossvalues for the four time periods are calculated and shown inFig. 10. As expected, since the time periods are equal, theenergies corresponding to them are equal.

Therefore, the total cost of the energy loss for the 30 yearsof the considered time period, i.e., the energy correspondingto load losses and no-load losses, for period L1 (CLA

L1 in C),period L2 (CLA

L2 in C), period L3 (CLAL3 in C), and period L4

(CLAL4 in C) can be determined by

CLAL1 =ECL1 ·

n∑i=1

[(LLA

L1(i) + NLLAL1(i)

)

· (AF (i) − AF (i − 1))] (9)

CLAL2 =ECL2 ·

n∑i=1

[(LLA

L2(i) + NLLAL2(i)

)

· (AF (i) − AF (i − 1))] (10)

CLAL3 =ECL3 ·

n∑i=1

[(LLA

L3(i) + NLLAL3(i)

)

· (AF (i) − AF (i − 1))] (11)

CLAL4 =ECL4 ·

n∑i=1

[(LLA

L4(i) + NLLAL4(i)

)

· (AF (i) − AF (i − 1))] (12)


TABLE IIIINPUT DATA FOR THE TWO TRANSFORMER OFFERS IN TABLE I

Fig. 10. Annual energy corresponding to load losses of L1, L2, L3, and L4periods for offer A.

where ECL1 is the energy cost during period L1, ECL2 is theenergy cost during period L2, ECL3 is the energy cost duringperiod L3, ECL4 is the energy cost during period L4, index irefers to the current year of the study (i.e., NLLA

L1 (3) denotesthe energy corresponding to no-load losses of period L1 of thethird year), and AF (−1) is equal to zero.

Combining (9)–(12) with (6), the total costs of energy lossesfor period L1 (CLA

L1 in C), period L2 (CLAL2 in C), period L3

(CLAL3 in C), and period L4 (CLA

L4 in C) are finally derivedfrom

CLAL1 =

n∑i=1

[(NLLA

L1(i) + LLAL1(i)

) · ECL1

(1 + r)i

](13)

CLAL2 =

n∑i=1

[(NLLA

L2(i) + LLAL2(i)

) · ECL2

(1 + r)i

](14)

CLAL3 =

n∑i=1

[(NLLA

L3(i) + LLAL3(i)

) · ECL3

(1 + r)i

](15)

CLAL4 =

n∑i=1

[(NLLA

L4(i) + LLAL4(i)

) · ECL4

(1 + r)i

]. (16)

The cost of energy losses of period L1 (CLAL1 in C), period

L2 (CLAL2 in C), period L3 (CLA

L3 in C), and period L4 (CLAL4

in C) is as follows:

CLAL1 = 118241 kWh · 0.091 C/kWh = 10760 C

CLAL2 = 118241 kWh · 0.043 C/kWh = 5084 C

CLAL3 = 118241 kWh · 0.075 C/kWh = 8868 C

CLAL4 = 118241 kWh · 0.062 C/kWh = 7331 C.

Fig. 11. Approximation of electricity price daily fluctuation for a high MMPscenario.

Thus, the total cost of offer A is the summation of the costof energy losses (for the four periods) and the price of thetransformer A, namely

CostA = CLAL1 + CLA

L2 + CLAL3 + CLA

L4 + BPA ⇒CostA = 10760 + 5084 + 8868 + 7331 + 9074 = 41117 C.

B. Economic Evaluation of Offer B

Following the same methodology, already presented for theeconomic evaluation of offer A, we derive that the total cost ofoffer B is

CostB =CLBL1 + CLB

L2 + CLBL3 + CLB

L4 + BPB ⇒CostB = 9117 + 4308 + 7514 + 6211 + 11 362=38 512 C.

From the aforementioned analysis, it is clear that the life spancost of the first alternative offer A is 41 117 C, while that ofoffer B is 38 512 C. These values correspond to a difference of6.7% between the cost of offer A and offer B.

IV. DIFFERENT SCENARIOS OF ELECTRICITY PRICING

The marginal market price (MMP) in a free electricity marketcannot be adequately estimated for large time intervals, mainlydue to the ambiguity on the generation availability and cost.In this section, two different MMP scenarios are investigated,and their results are compared in order to derive the respectiveconclusions on the MMP variation influence on the results ofthe economic evaluation. Moreover, this section expands theanalysis in Section III, considering more accurate representa-tion of transformer loading variation.

The daily electricity price variation is investigated, for highand low MMP scenarios, based on the data provided by the


Fig. 12. Approximation of electricity price daily fluctuation for a low MMPscenario.

Fig. 13. Transformer daily load curve.

TABLE IVINPUT DATA FOR HIGH AND LOW MMP SCENARIOS

transmission system operator. The MMP variation is approxi-mated by four levels of electricity pricing; however, the timeperiods of each level are not equal, as in the case in Section III.This division provides an accurate representation of the realvariation as can be seen in Figs. 11 and 12. Moreover, basedon the transformer load curve in Fig. 13, an average load factorfor each one of the four time periods is considered (instead ofthe constant load factor used in Sections II and III). Therefore,two sets of input data for the high and low MMP scenarios aregenerated, presented in Table IV.

TABLE VCOMPARISON OF TRANSFORMER OFFERS A AND B FOR

DIFFERENT ELECTRICITY PRICING SCENARIOS

The results of the analysis for transformer offers A and B aresummarized in Table V. According to Table V, transformer Bremains the most cost-efficient one in both scenarios. However,the difference in the profit derived by its installation, comparedto transformer A, varies significantly according to the MMPscenario, yielding a value of 4.95% for the high MMP scenarioand 2.59% for the low MMP scenario. Moreover, a significantdifference in both transformer costs for the two scenarios(namely, 21.08% between high and low MMP scenarios fortransformer A and 18.34% between high and low MMP sce-narios for transformer B) is observed.

V. TRANSFORMER ECONOMIC EVALUATION

METHODOLOGY CONSIDERING HOURLY VARIATION

OF ELECTRICITY PRICING AND LOAD

This section expands the proposed methodology so as to takeinto account the detailed characteristics of transformer loadingand electricity pricing. In order to model the electricity pricevolatility as realistically as possible, the historical MMP data offive years (24 hourly values for 1826 days, i.e., 43 824 energycost values) [30] have been used as input to the transformereconomic analysis (Fig. 14), in order to produce distributionsof the total cost of the considered transformers. The costs ofenergy corresponding to no-load losses and load losses of offersA and B are calculated at each kth period of the 24 hourly timeperiods considered, using the hourly energy prices of each jthday of the considered 1826 days included in the 2006–2010historical market data. The annual energies corresponding tono-load loss values of each kth hourly period for offers A andB, NLLA

k and NLLBk , respectively, are computed as follows:

NLLAk = 1.1 kW · 1 h · 365 = 401.5 kWh

NLLBk = 0.94 kW · 1 h · 365 = 343.1 kWh.

The annual energy corresponding to the load loss values foreach kth hourly period for offers A and B is calculated asfollows:

LLAk = 2.25 kW · 1 h · 365 · LFk

LLBk = 1.9 kW · 1 h · 365 · LFk

where LFk is the loss factor of the kth hourly period, which iscalculated based on the hourly load factor in Fig. 13, while 2.25and 1.9 kW correspond to the load losses of offers A and B forthe first year of the study at half load, calculated in Section II-B.


Fig. 14. Average daily MMP variation based on historical market data for theperiod 2006–2010 [30].

Therefore, by proper modification of (9)–(12) and (13)–(16),the total cost of the energy loss for the 30 years of the study,corresponding to the kth hourly period and the hourly energyprices of the jth day from the considered 1826 days includedin the 2006–2010 historical market data for offers A and B, i.e.,the cost of the energy corresponding to load losses and no-loadlosses, CLA

k,j (in C) and CLBk,j (in C), respectively, can be

determined by

CLAk,j =ECk,j ·

n∑i=1

[(LLA

k (i) + NLLAk (i)

)

· (AF (i) − AF (i − 1))] (17)

CLBk,j =ECk,j ·

n∑i=1

[(LLB

k (i) + NLLBk (i)

)

· (AF (i) − AF (i − 1))] (18)

where ECk,j is the energy cost during each kth hourly periodof the day j and index i refers to the current year of the study(i.e., CLA

5,1300 denotes the energy loss cost of offer A for thefifth hour corresponding to the hourly energy prices of day1300 from the considered 1826 days included in the 2006–2010historical market data).

Combining (9)–(12) with (17) and (18), the cost of the energycorresponding to load losses and no-load losses, for each kthhourly period of jth day, CLA

k,j (in C) and CLBk,j (in C),

respectively, is finally derived from

CLAk,j =

n∑i=1

[(NLLA

k (i) + LLAk (i)

) · ECk,j

(1 + r)i

](19)

CLBk,j =

n∑i=1

[(NLLB

k (i) + LLBk (i)

) · ECk,j

(1 + r)i

]. (20)

Thus, the total cost of offers A and B, CostAj and CostBj ,respectively, corresponding to the hourly energy prices of jthday is the summation of the cost of energy losses (for the 24hourly periods) and the bid price, namely

CostAj =24∑

k=1

CLAk,j + BPA (21)

CostBj =24∑

k=1

CLBk,j + BPB. (22)

Fig. 15. Histogram of cost variation of offers A and B.

Fig. 16. Histogram of the variation of cost difference between offers A and B.

The results in (21) and (22) (yielding values for j = 1 to1826) are used to derive the total cost distributions for trans-former offers A and B.

Fig. 15 shows the distribution of the total cost of offer Aand offer B, while Fig. 16 shows the distribution of the costdifference for the economic analysis presented in this section.As can be observed, the mode value of the cost difference (i.e.,the prevailing value, corresponding to the largest probability)between offer A and offer B is equal to 1%; thus, the low losstransformer remains the most economic solution in the longterm. However, the benefit is significantly lower than the oneyielded in the analysis in the previous sections, while a highvolatility of the cost difference can be observed, rendering theprofitability of offer B rather marginal.

VI. PROBABILISTIC ASSESSMENT OF ELECTRICITY

PRICE VOLATILITY INFLUENCE ON TRANSFORMER

ECONOMIC EVALUATION

In this section, the proposed methodology is combined withprobabilistic assessment of MMP variation using the MonteCarlo analysis, in order to deal with its uncertainty and unpre-dictability. More specifically, each hourly MMP price is definedwith a probability distribution, derived based on the historicaldata in Fig. 14. Next, the detailed economic evaluation modelof the previous section is used with different input scenarios,produced by repeatedly sampling values from the probabilitydistributions of the hourly MMP values, producing cost distri-butions for offers A and B. The historical MMP data are fittedusing the generalized extreme value distribution, the extremevalue distribution, or the normal distribution, according to thevariation characteristics of each hourly MMP profile. Eachdistribution was used to produce 4000 hourly samples, yieldingan MMP input data set of 4000 ∗ 24 = 96 000 values.


Fig. 17. Histogram of the cost variation of offers A and B, yielded by theMonte Carlo analysis.

Fig. 18. Histogram of the variation of cost difference between offers A and B,yielded by the Monte Carlo analysis.

Fig. 17 shows the distribution of the total cost of offer A andoffer B, while Fig. 18 shows the distribution of the cost dif-ference for the probabilistic analysis presented in this section.As can be observed, the mode value of the cost difference (i.e.,the prevailing value, corresponding to the largest probability)between offer A and offer B is equal to 4.5%, enhancing theprofitability of the low loss transformer.

VII. DISCUSSION OF THE RESULTS

Sections II and III presented the results of the economicassessment of transformer losses for two offers of the samerating, considering different energy pricing: Two time periods,namely, 8 h of peak load and 16 h of off-peak load during theday (first case study), in the first step and four time periods,namely, 6 h of peak load, two six-hour periods of intermediateload, and 6 h of low load (second case study), in the secondstep have been considered, respectively. As it can be observed,the percentage between the two transformer offers of the firstcase study (7.3%) is better in comparison to the second case(6.7%). Based on these two case studies, we can reach crucialconclusions, evaluating financial benefits of electrical powersystem projects, as follows.

1) The overall energy loss cost of the more efficient trans-former yielded in the second case study is higher than theone yielded in the first case study, resulting to a decreaseof the overall cost benefit. This happens because the aver-age energy price is more important in the first case studyinvolving two time periods (0.072 C/kWh) in comparisonto the one in the second case study (0.068 C/kWh)involving four time periods.

2) The division into time periods with different energy priceof the 24-h daily time is important. The energy costcould be lower than 0.068 C/kWh, if the number oftime periods was different. For example, if the day timewas divided into the following time periods, namely, 2 h(0.091 C/kWh), 6 h (0.043 C/kWh), 8 h (0.075 C/kWh),and 8 h (0.062 C/kWh), then the average energy pricewould be 0.064 C/kWh. In this case, the percentage in thecost variation between the two transformer offers wouldbe 6.3% (in comparison to the percentage of 6.7% yieldedin the case in Section III). Therefore, the difference inthe time periods with different energy price may resultto variations of the final benefit. In any case, the energy-efficient transformer is still better than the conventionalone of the first case; however, its potential economicbenefit can be highly variable according to the consideredeconomic indices. As a result, one of the vital points inthe correct definition of energy price is the division of the24-h daily time into periods as well as the energy priceconsidered for each period.

3) The aforementioned observation is verified by the resultsin Section IV, where a more realistic representation ofMMP daily fluctuation leads to smaller differences be-tween the transformer offers, in comparison to the resultsin Section III. More specifically, in the case of the highMMP scenario, where the average daily electricity price(0.064 C/kWh) is very close to the one in Section III(0.068 C/kWh), the percentage of difference betweenoffer A and offer B is reduced from 6.7% to 4.95%. Thisresult is also influenced by the different transformer loadfactors considered during the four time periods. Importantdifferences can be observed between the high and lowMMP scenarios: the difference between A and B for thelow MMP scenario (which corresponds to average dailyelectricity price 0.056 C/kWh) reduces to 2.59%.

4) Section V extends the economic evaluation methodologyin order to take into account the hourly energy pricing andload characteristics. Instead of using the MMP variationof one day, historical data of five years are used, provid-ing cost distributions for offers A and B. The influenceof the electricity price volatility in the results can beobserved in Fig. 16, where the cost difference betweenA and B varies from −8% to 6%, i.e., for certain com-binations of electricity pricing, transformer B may notbe the most profitable solution, although the probabilityfor this result is quite low. The mode cost differencevalue for this analysis is equal to 1%, which means thatoffer B remains statistically the most economic choice;however, the benefit is much smaller than the one yieldedin Sections II–IV.

5) Section VI comprises a probabilistic assessment of MMPprice variation, based on the Monte Carlo analysis,producing cost results for different input values forhourly MMP data (derived from fitted distributions ofthe available historical data). In this case, the cost dif-ference between A and B varies from 1% to 6.5%,and the mode value is equal to 4.5%; thus, the ben-efit from the installation of transformer B is more


significant than the one yielded in the statistical analysisin Section V.

6) Transformer loss cost incorporation to the final purchas-ing policy remains the most important issue in trans-former selection. As fuel costs continue to rise andpower outages become more prevalent around the coun-try, the necessity of utilizing energy-efficient products ofall types is becoming universally recognized. For years,electric utilities have been evaluating transformers forlosses when making purchase decisions on MV and high-voltage power transformers. However, in the commer-cial arena, the losses—and efficiencies—of distributiontransformers have received relatively little attention, duein part to the fact that the initial cost of a LV distrib-ution transformer is the primary driver in determiningwhich transformer to purchase. The total operating costof the transformer, over the life of the transformer, shouldbe taken into consideration. Therefore, energy-efficienttransformer is becoming an important mean to reducetransmission and distribution losses.

VIII. CONCLUSION

In this paper, the importance and the potentials to improvepower system efficiency through the installation of energy-efficient transformers have been investigated. The analysis hasbeen performed through proper transformer economic evalua-tion methods, taking into account the energy loss consumptionand its daily price fluctuation, revealing new aspects that mustbe taken into account during the definition of the transformerpurchasing policy of electric utilities. The main conclusionsof this paper can be summarized as follows: 1) investment tolow efficiency decreases the initial capital cost but results tohigher energy costs during the transformer lifetime, yieldingtransformers with low manufacturing cost non-profitable inthe long term; 2) the choice of the most profitable amongtransformers with high degrees of efficiency must be based onthe optimum balance between the initial purchasing cost and theenergy savings through transformer lifetime; 3) more detailedrepresentation of the daily energy price fluctuation results tomore refined results considering the profits derived from the in-stallation of energy-efficient transformers and can therefore al-ter significantly the final purchasing decisions; and 4) differentscenarios for the electricity price, investigated in Section IV, aswell as the sensitivity analysis in Section II-E, the statisticalanalysis in Section V, and the probabilistic assessment inSection VI, reflect the influence of its variation to the respectivecost evaluation results. As expected, higher electricity pricescenarios result to more significant differences in the costbetween the evaluated transformers. However, the benefit forthe most energy-efficient transformer is highly influenced bythe MMP volatility.

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Eleftherios I. Amoiralis (M’09) was born in Greecein 1980. He received the Diploma degree in pro-duction and management engineering„ M.Sc. degreein industrial engineering, and Ph.D. degree in thefield of electric power systems from the TechnicalUniversity of Crete, Chania, Greece, in 2004, 2005,and 2008, respectively.

Since 2010, he has been an Assistant Profes-sor with the Technological Educational Institute ofChalkida, Psachna, Greece. From 2005 to 2009, hewas with Schneider Electric AE as a Freelancer. He

was an Intern with the Public Power Cooperation (six months) in Athens,Greece. Since 2008 he is collaborating with the Technical University of Creteas a Research Associate. His current research interests include transformer costevaluation, energy-efficient transformers, transformer design optimization, ar-tificial intelligence, design and analysis of airfoils, and the design optimizationof aerodynamic shapes.

Dr. Amoiralis has been a member of the Technical Chamber of Greecesince 2005.

Marina A. Tsili (M’04) received the Diploma de-gree in electrical and computer engineering and thePh.D. degree from the National Technical Univer-sity of Athens, Athens, Greece, in 2001 and 2005,respectively.

From 2005 to 2006, she was with the Distribu-tion Division, Public Power Corporation of Greece,in high- and medium-voltage substation studies. In2007, she joined the Hellenic Transmission SystemOperator as a Power Systems Engineer. Since 2005,she is collaborating with the National Technical Uni-

versity of Athens as a Research Associate. Her research interests includetransformer and electric machine modeling and analysis of generating units byrenewable energy sources.

Dr. Tsili is a member of the Technical Chamber of Greece.

Antonios G. Kladas was born in Greece in 1959.He received the Diploma degree in electrical en-gineering from the Aristotle University of Thessa-loniki, Thessaloniki, Greece, in 1982 and the DEAand Ph.D. degrees from the Pierre and Marie CurieUniversity (Paris 6), Paris, France, in 1983 and 1987,respectively.

He was an Associate Assistant with the Pierre andMarie Curie University from 1984 to 1989. From1991 to 1996, he was with the System Studies De-partment, Public Power Corporation of Greece. Since

1996, he has been with the Department of Electrical and Computer Engineering,National Technical University of Athens, Athens, Greece, where he is currentlya Professor. His research interests include transformer and electric machinemodeling and design as well as analysis of generating units by renewable energysources and industrial drives.

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