INSTITUTE OF INTEGRATED ELECTRICAL ENGINEERS 1

Transformer Loss Cost EvaluationR. F. Corpuz, G. R. Pagobo

Abstract—This paper establishes the monetary value of Na-tional Grid Corporation’s (NGCP) transformer losses. Based onIEEE Standard C57.120-1991, the results could be used to assessthe relative economic benefits of investment on capacity of say,a high-first-cost1, low-loss unit over one with low-first cost butwith higher losses. The use of the results in this paper facilitateswhat could be a tedious, perplexing optimization process enablingNGCP as a buyer and even its potential supplier to respectivelypurchase and manufacture transformers economically.

Index Terms—Loss evaluation, No-Load Loss, Load Loss,Auxillary Power Loss, Copper Loss, Core Loss

I. INTRODUCTION

TRANSFORMER losses evaluated using IEEE Std.C57.120-1991 fall into three categories namely No-Load

Loss (NLL), Load Loss (LL) and Auxiliary Power Loss (APL).No-Load Losses are inherent transformer losses and are morecommonly referred to as excitation losses. These losses includedielectric loss, conductor loss in the winding due to excitationcurrent, conductor loss due to circulating current in parallelwindings and core loss. Load Losses are transformer lossesthat are dependent on the transformer loading. Commonlyreferred to as “copper losses” these include losses due totransformer loading, eddy currents, leakage flux in the wind-ings, core clamps and circulating currents in parallel windings.Mathematically load losses are expressed as I2R. AuxiliaryPower Loss are losses that are required in order to operate thetransformer. These include power required for cooling fans,oil pumps and other ancillary equipment.

NLL, LL and APL are factors and come in the form of$/kW. NGCP uses these values in evaluating supplier’s totalbid for transformers. These factors multiplied by its respectivesupplier’s guaranteed loss will be added to transformer bid toarrive at the total supplier’s bid. To understand the concepts,an example is shown in Table I.

The total bid in Table I represents the total suppliers’bid which take into account the transformer losses. For theexample above, the most economical transformer to purchaseis Bid 4 despite having a relatively high initial cost.

The values of the factors NLL, LL, APL1 and APL2which are respectively $4,500/kW, $3,200/kW, $1,750/kW and$1,300/kW are the “rate” currently used by NGCP. Such valueshowever need to be updated to reflect the present economicfactors. To make it consistent with IEEE Standard C57.120-1991, NLL, LL, APL1 and APL2 will be referred to asrespectively, No-Load Loss Cost Rate (NLLCR), Load LossCost Rate (LLCR) and Auxiliary Load Cost Rate (ALCR1 andALCR2). Numerical indexes 1 and 2 in ALCR1 and ALCR2correspond to loss cost rates for stage 1 and stage 2 cooling,respectively.

1Unless otherwise specified, all costs appearing in this paper is in US$.

Table IINCLUSION OF LOSSES IN BID EVALUATION

Notes:NLL =$4,500/kWLL = $3,200/kWAPL1 = $1,750/kWAPL2 = $1,300 /kWColumn G = NLL x Column CColumn H = LL x Column DColumn I = APL1 x Column EColumn J = APL2 x Column F

In this paper the principles of loss evaluation is first pre-sented, followed by the assessment of each of the cost rates,defining and supplying values to variables along.

II. LOSS EVALUATION PRINCIPLE

In evaluating the cost of transformer losses, the cost ofenergy actually consumed by the losses, the generator invest-ment needed to supply the energy and the transmission line totransmit the generation shall be considered. As such, it consistsof a demand portion and energy portion.

Mathematically, the loss cost rate is formulated as follows;

LCR =(GIC × FCRG+ SIC × FCRS) + ( $

kwh × h)

FCRT

Where:(GIC×FCRG+SIC×FCRS)

FCRT is the demand portion( $kwh×h)

FCRT is the energy portionLCR the Loss Cost RateGIC is the cost of installing a kW of power plant

INSTITUTE OF INTEGRATED ELECTRICAL ENGINEERS 2

SIC is the cost installing transmission line with a kW ofcapacity

Loss Cost Rate refers to NLLCR or LLCR orALCR1/ALCR2

FCRG is the Fixed Charge Rate of Generating PlantFCRT is the Fixed Charge Rate of TransformerFCRS is the Fixed Charge Rate of Transmissionh is the number of hours per year that transformer is

energized

The Fixed Charge Rate of Plant/Transformer refers to thatportion of investment needed per year to support the capitalinvestment. In its simplest form, it represents the requiredyearly income from the investment. Its components are asfollows;

1) Minimum Acceptable Rate of Return2) Annual Cost of Depreciation and3) Taxes

For purposes of this study, FCRT and FCRS are equatedto NGCP’s Weighted Average Cost of Capital (WACC) forthe second regulatory period which is 15.87%. FCRG is setequivalent to 15%, NEDA’s Social Discount Rate.

The numerator in the equation for the Loss Cost Raterepresents the cost per year to provide a continuous kWof loss. The first term (GIC × FCRG + SIC × FCRS)represents that portion of investment cost on a generation andtransmission needed per year to support transformer losseswhile the second term represents the cost of the energy underthe present prevailing energy cost. For Luzon, the current yearenergy cost, CYEC, is set to $0.1444/kWh This is based onP7.04/kWh2 energy rate and P48.65/$13 peso-dollar exchangerate.

III. NO LOAD LOSS COST RATE

Following the principles in Section II, the No Load LossCost Rate is determined as follows;

NLLCR =(GIC×FCRG+ SIC×FCRS) + LECN

ET×FCRT×IF

Except for ET and IF terms in the denominator, the for-mula for NLLCR is similar to the equation for transformerloss in Section II. Note that LECN, the Levelized No LoadEnergy cost, is the energy portion in Section II equivalentto US$ 1,573.43/kWyear for Luzon. LECN is determined inSection VI. ET and IF are dimensionless factors introducedto reflect the Efficiency of Transmission and Increase Factorrespectively. ET is determined through power flow simulationsand is set to 0.9783 for Luzon Grid. To simplify calculations,IF is set to 1.0074 and only reflects project overhead cost.By introducing ET, the calculated energy, in terms of costis marked-up to include other costs dissipated through ineffi-ciency. IF further increments this cost in proportion to project’soverhead cost.

2Figures from PSALM3Exchange rate forecast from Economist Intelligence Unit as used by NGCP

in the 3rd Reg. Filing4Based on actual budget

Values for other variables are as follows;

Generation Installation Cost GIC = $1,600/kWGeneration Installation Cost SIC = $2.74/kW 5

Solving for NLLCR for Luzon Grid;

NLLCR =(1, 600×0.15 + 2.74×0.1444) + 1, 573.43

(0.9783×0.1587×1.007)

NLLCR = $11, 601.60/kW

IV. LOAD LOSS COST RATE

For the Load Loss Cost Rate, there is a need to removethe impact of the Availability Factor AF6 from LECN, ascalculated in Section VI since for this loss rate TransformerLoading Factor TLF will be used. Modifying LECN in thismanner results to LECL or the Levelized Load Energy Cost,LECL is determined as follows:

LECL =LECN

AF=

1, 573.43

0.9897=

1, 589.8

kWyear

With the denominator remaining the same as that for No-Load Loss Cost Rate, the equation for the Load Loss CostRate is:

LLCR =(GIC×FCRG+ SIC×FCRS)×PRF 2×PUL2

(ET×FCRT×IF )

+LECL×TLF 2

(ET×FCRT×IF )

The new terms in the numerator are dimensionless adjust-ment factors introduced to enable realistic assessment. ThePeak-Per Unit Load (PUL) relates demand-associated losses tofull rated transformer and not to the peak transformer load7 . Itis the average of yearly peaks over the lifetime of transformerdivided by the rating at which the load losses are guaranteedto be tested. For this study, load losses are assumed to betested at full-load transformer rating. Using load forecast datafor 2009, PUL is set to 1.114 for Luzon.

The Peak Responsibility Factor (PRF) is the transformer’sload during system peak8, divided the transformer’s peak load.This factor is intended to compensate for the transformerpeak load losses not occurring at the system peak losses.The rationale is, if the entire transformer peak does notoccur during the system peak, then there is no need to putup additional generation since the transformer load and itslosses could be supplied by the system. That is reason behindinclusion of PRF in the demand portion of the loss assessmentequation. The data used in the determination of this parameter

5Based on $27,365.00/km, 2008 Price Level of 5km, 69kV ST/SC, 1-336.4MCM ACSR

6Availability Factor AF is the expected percentage of time the transformerwill be energize. AF = 0.9897

7Guide for the Evaluation of Large Power Transformer Losses, USDA8System Peak assumed to occur at 1900H

INSTITUTE OF INTEGRATED ELECTRICAL ENGINEERS 3

was surveyed from various NGCP substations. Using the data,PRF for Luzon is set to 0.8643.

The Transformer Loading Factor is the ratio of the averagetransformer losses to the peak transformer losses during aspecific period of time . To simplify calculations, it is assumedconstant and does not change significantly over the life oftransformer. It is formulated as;

TLF = 0.8× LF 2 + 0.2× LF

Where:LF is the Load Factor

Using the equation above and the surveyed data fromvarious NGCP substations, the average TLF for Luzon Gridis 0.6480.

Substituting values and calculating for the Load Loss CostRate for Luzon Grid;

LLCR =(1, 600×0.15 + 2.74×0.1587)×0.86432×1.1142)

(0.97742×0.1587×1.007)

+1, 589.80×0.64802

(0.97742×0.1587×1.007)

LLCR = $5, 695.54/kW

V. AUXILIARY LOAD LOSS COST RATE

For the Auxiliary Loss Cost Rate Stage 1 (ALCR1), only theenergy portion of the loss equation has to be modified. LECNhas to be proportionately adjusted to the average numberof hours that stage 1 cooling is expected to operate. TheLevelized Auxiliary Energy Loss Cost – Stage 1 Cooling(LAEC1) is computed as follows;

LAEC1 = LECN × hstage1

8760×AF

Where:hstage1is the average hours stage 1 cooling is running

Substituting:

LAEC1 = 1, 573.43× 4, 700

8, 669.77=

$852.98

kWyear

Using the value determined for LAEC1, the Auxiliary LossCost Rate Stage 1 (ALCR1) is calculated as follows:

ALCR1 =(GIC×FCRG+ SIC×FCRS)

(ET×FCRT×IF )

+LAEC1

(ET×FCRT×IF )

ALCR1 =(1, 600×0.15 + 2.74×0.1587) + 852.978)

(0.9783×0.1587×1.007)

ALCR1 = $6, 993.67/kW

For Stage 2 Cooling:

LAEC2 = 1, 573.43×3, 100

8, 669.77=

$562.605

kWyear

ALCR2 =(1, 600×0.15 + 2.74×0.1587) + 562.60)

(0.9783×0.1587×1.007)

ALCR2 =$5, 136.38

kW

Table II is a summary of the Loss Cost Rate for Luzon,Visayas and Mindanao Grids determined through the method-ology presented above.

Table IITRANSFORMER LOSS EVALUATION FOR LUZON, VISAYAS AND

MINDANAO GRIDS

VI. DETERMINATION OF LEVELIZED NO-LOAD ENERGYCOST

The cost of energy, as with any other commodity, is subjectto inflation. Economic studies, such as this transformer lossevaluation, would require more complicated techniques toassess exponential variables. One method of simplifying theproblem is to levelize the values of the variables, this way therate of energy would be equal during the entire booklife ofthe transformer.

As an example consider a cost of $1/kWh escalating at5% per annum, that is, its rate after a year is 1(1.05), aftertwo years 1(1.05)(1.05) and so on until N years when its ratebecomes 1(1.05)N. In the Figure 1 below the exponential costof energy is the increasing curve below. The dashed line resultsafter levelling.

Levelling is achieved by multiplying the Net Present Valueof all yearly energy rates by the Capital Recovery Factor(CRF) given by the following equation:

CRF =r(1 + r)N

(1 + r)N − 1

Where:r is the Rate of Return, in the context of this study it is

equal to WACC = 15.87%N is equal to 35 years, the booklife of transformer

INSTITUTE OF INTEGRATED ELECTRICAL ENGINEERS 4

Figure 1. Illustration of Levelization

Applying the values and solving for CRF:

CRF =0.1587(1 + 0.1587)35

(1 + 0.1587)35 − 1= 0.159621

The Net Present Value (NPV) is determined using thefollowing equation:

NPV =

35∑N=1

(1 + r)−N (1 + i)N (CY EC)

Where:

r and N is as given in CRF calculationi is the escalation rate equivalent to 3%9

CYEC is the Current Year Energy Cost equivalent to$0.1444/kWh

The first term in the NPV equation equates the rate of energyin the Nth year which is (1 + i)N (CY EC) in terms of thepresent values. In other words it determines how much mustbe invested today at an interest rate “r” in order to have (1 +i)N (CY EC) in the future. Figure 2 illustrates the principle.The sum of these present values is the Net Present Value.

Substituting variables and solving for NPV:

NPV =

35∑N=1

(1+ 0.1587)−N (1+ 0.03)N (0.1444) = 1.13697

The Calculated Levelized No-Load Energy Cost (LECN)for Luzon Grid is equal to:

LECN = NPV ×CRF×8760×AF

LECN = 1.13697×0.159621×8760×0.9897

9Escalation rate for 2009 figures as used by Project Management. Note aconstant rate of 3% is assumed for the entire book life of transformer

Figure 2. Cash Flow. Concept of Net Present Value

LECN =$1, 573.32

kWyear

The value 0.9897 appearing in the equation above is theAvailability Factor (AF). This figure was determined from2005-2009 transformer outage statistics from System Oper-ations.

Following the same methodology, LECN for Visayas andMindanao Grids are as follows:

LECN =$1, 367.81

kWyear

LECN =$2, 219.34

kWyear

Rex F. Corpuz is a former Sr. VP of the National Transmission Corporationand a former President of National Grid Corporation of the Philippines(NGCP). He is presently the Sr. Technical Adviser at the Office of thePresident, NGCP. He is also a former Regional Governor of IIEE Region1., e-mail: rfcorpuz@gmail.com

Gerald R. Pagobo is a Power System Consultant and formerly worked withthe research group of NGCP. He received his MS in Electrical Engineeringdegree from the University of the Philippines in 2009. His research interestsinclude reliability engineering, power system dynamic stability, electricitymarket optimization, and computer-based power system modeling and analy-sis. Email: grpagobo@gmail.com