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INSTITUTE OF INTEGRATED ELECTRICAL ENGINEERS 1
Transformer Loss Cost Evaluation
R. F. Corpuz, G. R. Pagobo
Abstract—This paper establishes the monetary value of National
Grid Corporation’s (NGCP) transformer losses. Based on
IEEE Standard C57.120-1991, the results could be used to assess
the relative economic benefits of investment on capacity of say,
a high-first-cost 1 , low-loss unit over one with low-first cost but
with higher losses. The use of the results in this paper facilitates
what could be a tedious, perplexing optimization process enabling
NGCP as a buyer and even its potential supplier to respectively
purchase and manufacture transformers economically.
Index Terms—Loss evaluation, No-Load Loss, Load Loss,
Auxillary Power Loss, Copper Loss, Core Loss
Table I
INCLUSION OF LOSSES IN BID EVALUATION
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 more
commonly referred to as excitation losses. These losses include
dielectric loss, conductor loss in the winding due to excitation
current, conductor loss due to circulating current in parallel
windings and core loss. Load Losses are transformer losses
that are dependent on the transformer loading. Commonly
referred to as “copper losses” these include losses due to
transformer loading, eddy currents, leakage flux in the windings,
core clamps and circulating currents in parallel windings.
Mathematically load losses are expressed as I 2 R. Auxiliary
Power Loss are losses that are required in order to operate the
transformer. 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 total
bid for transformers. These factors multiplied by its respective
supplier’s guaranteed loss will be added to transformer bid to
arrive 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 the
example above, the most economical transformer to purchase
is Bid 4 despite having a relatively high initial cost.
The values of the factors NLL, LL, APL1 and APL2
which are respectively $4,500/kW, $3,200/kW, $1,750/kW and
$1,300/kW are the “rate” currently used by NGCP. Such values
however need to be updated to reflect the present economic
factors. To make it consistent with IEEE Standard C57.120-
1991, NLL, LL, APL1 and APL2 will be referred to as
respectively, No-Load Loss Cost Rate (NLLCR), Load Loss
Cost Rate (LLCR) and Auxiliary Load Cost Rate (ALCR1 and
ALCR2). Numerical indexes 1 and 2 in ALCR1 and ALCR2
correspond to loss cost rates for stage 1 and stage 2 cooling,
respectively.
1 Unless otherwise specified, all costs appearing in this paper is in US$.
Notes:
NLL =$4,500/kW
LL = $3,200/kW
APL1 = $1,750/kW
APL2 = $1,300 /kW
Column G = NLL x Column C
Column H = LL x Column D
Column I = APL1 x Column E
Column J = APL2 x Column F
In this paper the principles of loss evaluation is first presented,
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 of
energy actually consumed by the losses, the generator investment
needed to supply the energy and the transmission line to
transmit the generation shall be considered. As such, it consists
of a demand portion and energy portion.
Mathematically, the loss cost rate is formulated as follows;
LCR =
(GIC × F CRG + SIC × F CRS) + (
$
kwh × h)
F CRT
Where:
(GIC×F CRG+SIC×F CRS)
F CRT
( $
kwh ×h)
is the demand portion
F CRT
is the energy portion
LCR the Loss Cost Rate
GIC 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 of
capacity
Loss Cost Rate refers to NLLCR or LLCR or
ALCR1/ALCR2
FCRG is the Fixed Charge Rate of Generating Plant
FCRT is the Fixed Charge Rate of Transformer
FCRS is the Fixed Charge Rate of Transmission
h is the number of hours per year that transformer is
energized
The Fixed Charge Rate of Plant/Transformer refers to that
portion of investment needed per year to support the capital
investment. In its simplest form, it represents the required
yearly income from the investment. Its components are as
follows;
1) Minimum Acceptable Rate of Return
2) Annual Cost of Depreciation and
3) Taxes
For purposes of this study, FCRT and FCRS are equated
to NGCP’s Weighted Average Cost of Capital (WACC) for
the second regulatory period which is 15.87%. FCRG is set
equivalent to 15%, NEDA’s Social Discount Rate.
The numerator in the equation for the Loss Cost Rate
represents the cost per year to provide a continuous kW
of loss. The first term (GIC × F CRG + SIC × F CRS)
represents that portion of investment cost on a generation and
transmission needed per year to support transformer losses
while the second term represents the cost of the energy under
the present prevailing energy cost. For Luzon, the current year
energy cost, CYEC, is set to $0.1444/kWh This is based on
P7.04/kWh 2 energy rate and P48.65/$1 3 peso-dollar exchange
rate.
III. NO LOAD LOSS COST RATE
Following the principles in Section II, the No Load Loss
Cost Rate is determined as follows;
NLLCR =
(GIC×F CRG + SIC×F CRS) + LECN
ET ×F CRT ×IF
Except for ET and IF terms in the denominator, the formula
for NLLCR is similar to the equation for transformer
loss in Section II. Note that LECN, the Levelized No Load
Energy cost, is the energy portion in Section II equivalent
to US$ 1,573.43/kWyear for Luzon. LECN is determined in
Section VI. ET and IF are dimensionless factors introduced
to reflect the Efficiency of Transmission and Increase Factor
respectively. ET is determined through power flow simulations
and is set to 0.9783 for Luzon Grid. To simplify calculations,
IF is set to 1.007 4 and only reflects project overhead cost.
By introducing ET, the calculated energy, in terms of cost
is marked-up to include other costs dissipated through inefficiency.
IF further increments this cost in proportion to project’s
overhead cost.
2 Figures from PSALM
3 Exchange rate forecast from Economist Intelligence Unit as used by NGCP
in the 3rd Reg. Filing
4 Based on actual budget
Values for other variables are as follows;
Generation Installation Cost GIC = $1,600/kW
Generation 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 remove
the impact of the Availability Factor AF 6 from LECN, as
calculated in Section VI since for this loss rate Transformer
Loading Factor TLF will be used. Modifying LECN in this
manner 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
=
kW
year
With the denominator remaining the same as that for No-
Load Loss Cost Rate, the equation for the Load Loss Cost
Rate is:
LLCR = (GIC×F CRG + SIC×F CRS)×P RF 2 ×P UL 2
(ET ×F CRT ×IF )
2
LECL×T LF
+
(ET ×F CRT ×IF )
The new terms in the numerator are dimensionless adjustment
factors introduced to enable realistic assessment. The
Peak-Per Unit Load (PUL) relates demand-associated losses to
full rated transformer and not to the peak transformer load 7 . It
is the average of yearly peaks over the lifetime of transformer
divided by the rating at which the load losses are guaranteed
to be tested. For this study, load losses are assumed to be
tested at full-load transformer rating. Using load forecast data
for 2009, PUL is set to 1.114 for Luzon.
The Peak Responsibility Factor (PRF) is the transformer’s
load during system peak 8 , divided the transformer’s peak load.
This factor is intended to compensate for the transformer
peak load losses not occurring at the system peak losses.
The rationale is, if the entire transformer peak does not
occur during the system peak, then there is no need to put
up additional generation since the transformer load and its
losses could be supplied by the system. That is reason behind
inclusion of PRF in the demand portion of the loss assessment
equation. The data used in the determination of this parameter
5 Based on $27,365.00/km, 2008 Price Level of 5km, 69kV ST/SC, 1-336.4
MCM ACSR
6 Availability Factor AF is the expected percentage of time the transformer
will be energize. AF = 0.9897
7 Guide for the Evaluation of Large Power Transformer Losses, USDA
8 System 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 average
transformer losses to the peak transformer losses during a
specific period of time . To simplify calculations, it is assumed
constant and does not change significantly over the life of
transformer. It is formulated as;
Where:
LF is the Load Factor
T LF = 0.8 × LF 2 + 0.2 × LF
Using the equation above and the surveyed data from
various NGCP substations, the average TLF for Luzon Grid
is 0.6480.
Substituting values and calculating for the Load Loss Cost
Rate for Luzon Grid;
LLCR = (1, 600×0.15 + 2.74×0.1587)×0.86432 ×1.114 2 )
(0.97742×0.1587×1.007)
For Stage 2 Cooling:
3, 100
LAEC2 = 1, 573.43×
8, 669.77 = $562.605
kW
year
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 methodology
presented above.
Table II
TRANSFORMER LOSS EVALUATION FOR LUZON, VISAYAS AND
MINDANAO GRIDS
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 the
energy portion of the loss equation has to be modified. LECN
has to be proportionately adjusted to the average number
of hours that stage 1 cooling is expected to operate. The
Levelized Auxiliary Energy Loss Cost – Stage 1 Cooling
(LAEC1) is computed as follows;
LAEC1 = LECN ×
h stage1
8760×AF
Where:
h stage1 is the average hours stage 1 cooling is running
Substituting:
4, 700
LAEC1 = 1, 573.43 ×
8, 669.77 = $852.98
kW
year
Using the value determined for LAEC1, the Auxiliary Loss
Cost Rate Stage 1 (ALCR1) is calculated as follows:
ALCR1 =
ALCR1 =
(GIC×F CRG + SIC×F CRS)
(ET ×F CRT ×IF )
LAEC1
+
(ET ×F CRT ×IF )
(1, 600×0.15 + 2.74×0.1587) + 852.978)
(0.9783×0.1587×1.007)
ALCR1 = $6, 993.67/kW
VI. DETERMINATION OF LEVELIZED NO-LOAD ENERGY
COST
The cost of energy, as with any other commodity, is subject
to inflation. Economic studies, such as this transformer loss
evaluation, would require more complicated techniques to
assess exponential variables. One method of simplifying the
problem is to levelize the values of the variables, this way the
rate of energy would be equal during the entire booklife of
the transformer.
As an example consider a cost of $1/kWh escalating at
5% per annum, that is, its rate after a year is 1(1.05), after
two years 1(1.05)(1.05) and so on until N years when its rate
becomes 1(1.05)N. In the Figure 1 below the exponential cost
of energy is the increasing curve below. The dashed line results
after levelling.
Levelling is achieved by multiplying the Net Present Value
of 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 2.
Cash Flow. Concept of Net Present Value
Figure 1.
Illustration of Levelization
LECN =
$1, 573.32
kW
year
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 the
following equation:
Where:
∑35
NP V = (1 + r) −N (1 + i) N (CY EC)
N=1
r and N is as given in CRF calculation
i 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 energy
in the Nth year which is (1 + i) N (CY EC) in terms of the
present values. In other words it determines how much must
be 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:
The value 0.9897 appearing in the equation above is the
Availability Factor (AF). This figure was determined from
2005-2009 transformer outage statistics from System Operations.
Following the same methodology, LECN for Visayas and
Mindanao Grids are as follows:
LECN =
LECN =
$1, 367.81
kW
year
$2, 219.34
kW
year
Rex F. Corpuz is a former Sr. VP of the National Transmission Corporation
and a former President of National Grid Corporation of the Philippines
(NGCP). He is presently the Sr. Technical Adviser at the Office of the
President, NGCP. He is also a former Regional Governor of IIEE Region
1., e-mail: rfcorpuz@gmail.com
∑35
NP V = (1 + 0.1587) −N (1 + 0.03) N (0.1444) = 1.13697
N=1
The Calculated Levelized No-Load Energy Cost (LECN)
for Luzon Grid is equal to:
LECN = NP V ×CRF ×8760×AF
Gerald R. Pagobo is a Power System Consultant and formerly worked with
the research group of NGCP. He received his MS in Electrical Engineering
degree from the University of the Philippines in 2009. His research interests
include reliability engineering, power system dynamic stability, electricity
market optimization, and computer-based power system modeling and analysis.
Email: grpagobo@gmail.com
LECN = 1.13697×0.159621×8760×0.9897
9 Escalation rate for 2009 figures as used by Project Management. Note a
constant rate of 3% is assumed for the entire book life of transformer