6.14.1
SELECTION OF DISTRIBUTION TRANSFORMER BASED ON ECONOMIC CRITERIA
S. U. Ahn
ELETROPAULO
J. A. Jardini
C. M. V. Tahan
E. L. Ferrari
Escola Polithica da Universidade de S%oPaulo
Centro de ExcelCncia em Distribuiqilo de Energia Elttrica / BRAZIL
ABSTRACT
This paper presents considerations related to tlie loss of
life calculation and to the determination of tlie
distribution transformers loading, with technical and
economical consideratioiis and applying daily load
curves obtained from measurements in typical
transformers.
Loss of life estimation is done applying probabilistic
daily load curves and their probability of occurrence.
The transformer loading rnanagement criteria is then
compared to tlie methodology presently in use by Silo
Paulo State utilities. Finally a transformer loading
analysis is done through an economic criteria that
consists on the calculation of tlie investment cost,
losses, and the loss of life cost, all during its
operational life.
INTRODUCTION
Daily Load Curve
The transformer daily load curve expresses the power
through it and is made up here of tlie average demands
in 15-minute-intervals.
To establish a representative load curve of the
residential distribution transformer, tlie major scope of
this work, a population of 802 measurement days in the
transformers of three Silo Paulo State utilities were
performed.
The measured transformers are from various rated
power and a conversion of the demands in PU vilues
was necessary in order to have homogeneous curves
(6). So all the measurement values of demands were
then divided by a Base Power, the monthly average
power of the transformer (Phase), equal to
[kWNmontlily/(24 x 30 h)]. Figure 1 shows the
mean(p) and standard deviation
for one transformer.
The distribution transformer is an equipment applied in
large number, therefore its adequate rating selection
results in saving company’s costs, in the reduction of
equipment not adequately used in tlie system, and in
adequate losses during transformers operational life.
1.6-
2
1.u-
0.5 -
0.0 J
A+B
v =1
0 T
In this formulae, A and B are values, typical of tlie
transformer insulating material, T (“K) is considered
the hot spot temperature. However, depending on tlie
reference, of tlie values of the constants are different.
(1) (2) (3) (4) (5).
fl - mean load ci
.L
0
LOSS OF LIFE CALCULATION
The transformer life expectancy V, is estimated based
on tlie “Arrhenius’ law” that relates the insulating
material ageing due to temperature T. The equation is:
curves obtained
2.0 -
This paper aims at recomniending a policy for
transformers rating selection considering to technical
and economical factors. Besides transformers cost and
losses, this methodology consider the estimated loss of
life in transformer, based on daily load curves obtained
from measurement.
The load in tlie transformer heats it and cause
temperature increase. This temperature may lead to a
degradation in tlie insulating material, reducing its life.
(0)
3
6
9
12
15
JB
21
HOW
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Figure 1 Mean and standard deviation load curve.
Ambient Temperature.
I n general for the calculation of the loss of life, tlie
annual average teniperature is applied.
However, the peak load, for instance, in certain case,
llappens at night when the ambient temperature is
lower and in other cases during the day. To tqke this
fact into consideration, a daily curve temperature
expressed by a mean (ptZ,,,,,)
and a standard deviation
(ol,,,,,)curve are used in tlie calculation (Figure 2). ,
ClRED 97,2-5 June 1997, Conference Publication No. 438, 0 IEE, 1997
6.14.2
25
20
B J5
(3temp
10
- standard deviation
51
0
9
I
9
le
15
18
21
24
Hour
3
'0
6
12
9
15
21
18
24
Hour
Figure 2- Ambient temperature curve
Figure 4 - Set of temperature curve
Development of the Load and Temperature Curves
Once known the p and the (3 values, curves with a
certain P% probability of not being exceeded, can be
calculated by:
V(P) = p + k cs
Where k is taken from the Gaussian probability table
(ex: P=90% , k=l.28). The transformers load curve
measurements showed that the demand values are
distributed in a Gaussian curve (7).
A set of 11 curves was determined (P=2.5%; 10%;
20%; 30%; 40%; 50%; 60%; 70%; 80%; 90%; 97.5%).
to represent the load occiirence (Figure 3), and
similarly a set of 11 curves for the temperature (Figure
4).
Note that the 20% curve will be used to represent those
curves included in the range of P from 15% to 25%,
which occurs 10% of the time. The same applies to the
others, except for those with P=2.5% and 97.5% which
occurs 5% of the time.
Transformers Life
If one load curve and one temperature curve are t<aken
for the calculation, then the hot-spot and consequently
the loss of life Lif (load, temperature) can be evaluated
( 6 ) , once a transformer rating is selected. In the
calculation here the load curves are in PU of the
average power (Pbnse),so the transformer rating should
be converted to PU using the same base power. Now,
combining all load curves i and temperature curves j,
all the Lifii values can be determined. The total loss of
life is obtained by the weighted average of the values.
Liftot= LifijP(loadi) P(tem1q)
where the P values are the probabilities (5% or 10% ;,I
this case).
For comparison the transformers loss of life in this
investigation was also calculated, by applying only the
temperature mean curve and all 1 1 load curves,
obtaining close results.
However if only the mean curve of the load is applied,
in the calculation, the error is unacceptable.
Figure 5 show the results obtained with all this
approaches.
3.0 2.5 -
l.OWO0
Set of load and temperature curves
k 2*ol.5-
Set of load and illeat1 temperature
1.00.5
-
0.0 -4
0
3
6
0
12
15
18
21
I
Hour
Figure 3 - Set of load curves
f.0CM
. 18. 2.0.
1.1 1.8
.
E.2
,
2.4
. 2.8. 3.0. 3..2
2.6
,
3.4
,
3.6
,
3.1
4.0
PU of Rsting
Figure 5
-
Loss of life with diKerents calculations
procedures.
6.14.3
Other experiments in the calculation were made like:
considering the set of load curves tninkated at +20; or
considering in the calculation all the measured daily
load curves. All these alternatives led to close results
within a 10% accuracy.
So calculations with the set of I1 load curves and tlie
temperature mean curve will froin now on be applied
and its results are simply named “statistical loss of
life”.
To makc the calculation easier, the loss of life results
are represented by an equation, function of ratings
obtained through linear regression of calculated points.
The chosen fitting curve is the exponential with
polynomial exponent of 7th order. A correlation index
of 0.999 and an average standard error of 0.03% was
obtained.
TRANSFORMER LOAD MANAGEMENT
The procedure used in Brazil for already installed
distribution transformer loading management is based
on the expected loss of life calculation, and on
statistical approach to determine the KVAS
function(statistica1 LVA). In order to develop the
KVAS function, samples of transformers in operation
are selected to be measured. The n~onthlyenergy (kWh)
in each transformer is calculated by adding the energy
consumption of all customers connected to it.
Measurements of the peak load (kVA) in the
transformers are taken by iiiskilling electronic recorders
over 2 day-period. The peak power measured for each
transformer of the sample is the average power within
15 minute-intervals. The set of pairs kWh x kVA is
used to determine a correlation curve (exponential or
straight line), based on the least square fitting.
The KVAS function is the result of this very curve
fitting by considering a criterion of 90% probability of
the curve not being exceeded.
Now, if the energy through a certain transformer in the
area not included in the sample is known, the KVAS
fimction provides its expected pe‘ak demand. Then the
expected loss of life is assessed by taking into account
the average yearly temperature, and considering that
the load profile is a two power step-curve.
The continuous through power equivalent to the two
step-curve is obtained froin the standards tables (3) and
used in the rating evaluation (kVAN). This factor is
t‘aken as F=1.5, for the Silo Paul0 area and was
determined by visual inspection of some typical load
profiles in some transformers. The ratio
R=KVAS/( 1.5,kVAN) is used to attribute to the
transformer one of the following classifications:
underloaded, normally loaded, overloaded, or critically
loaded (ratio R ranges are: bellow 0.75, 0.75-1.25,
1.25-1.5, and above 1.5, respectively). An appropriate
action is kaken, like relocation of loads or substitution
of the transfornier by another in a different size, when
the transformer load is above normal.
This criterion and methodology were established a long
time ago and are being re-examined, and new
calculation procedures are being considered.
This new procedure considers the loss of life
calculation as presented in the previous section which
results are shown on Figure 5.
To understand the new procedure, first it should be
noted froin Figure 5 that, if for instance it is desired a
life expectancy of 150 year for a transformer, then the
rating should be 1.78 PU. Table 1 shows how the
ratings change as function of the life expectancy
criteria.
Back to Figure 3, the pe‘ak demand of tlie mean curve is
2.08 PU. and the peak demand with 90% probability of
not being exceeded is 2.8 PU. If this last value is t.akei1
as the KVAS value, the transformer rztiiig should
2.8/1.5=1.87 PU., by using the existing criterion. If the
KVAS value is adopted at 97.5%, then KVAS=3.2 and
the rating reaches 2.2 PU. From figure 5, the above
ratings 1.87 PU and 2.2 PU, represent lives of 400 and
3500 years respectively. The criterion is then strongly
dependent on the probability of the KVAS figure, as
can be observed in Table I.
TABLE 1 - Transformer rated power as function of life
criterion.
Life criterion
Rating
I .45
1.62
3
30
1so
300
3.000
I .78
1.82
2.18
I
It is reconmended that the transformer loading
management be based on life criterion as follows:
TABLE 2 - Recommended transformer loading
management criteria
> 300 year
30 to 300 year
3 to 30 year
< 3 year
underloaded
normally loaded
overloaded
critically loaded
If a 150 year-life is t<aken as a basis for classification
(loo%), then iinderloaded, normal, overloadcd,‘critical
represent loads of: bellow 0.95; 0.95-1.10; 1.10-1.23;
over 1.23; respectively, above base power, values
deducted from Table 1. The ranges are though
narrower than the ranges of today’s criterion.
It should be remembered that this criteria can be used
for transformer loading management, since no
econoniic criteria is considered.
6.14.4
ECONOMIC CRITERIA
In order to select the trarlsfornler by economic criteria,
the following cost aspects should be considered:
Transformer rating cost.
Iron losses, and copper losses costs.
0
Installation cost and eventually removal cost.
0
Residual transformer cost at the renioval date.
Transformer Cost
0
where: PCV= copper losses for rated power (PU).
To calculate the energy lost in the copper all curves in
Figure 3 must be used with their probabilities. For the
mean curve “p” the losses in a day shall be :
In the first year the transformer purchase cost (CTO)is
given by:
where:
CTO”CTRPN
being : Cm = Cost per kVA in the initial year
PN = Rated Power (kVA)
The annual cost, payment in installments (CAT)), in N
years of loan that covers the cost (CT,)witli a discount
rate “ d and an inflation rate “i”, in the year “J” is:
n = the number of 15min. intervals in a day.
Pn = are the power values in the mean cuwe in PU of
the base power Phase.
For the other curves like (a, a’) one above and the other
below the mean, equidistant of the mean of (k..o), the
copper losses are.
AP, = B.C ( P, +
AP,. = B.C ( P, kaon)*
At = is the time interval in hours (lSmid60min).
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Removal and Installation Cost
The removal cost at the date of the removal (CRJ)in
relation to the cost (C,) in the initial year shall be:
cRJ=cR( 1 + i ) ’
In similar manner the installation cost at the removal
date, in relation to the cost (C,) in the initial year is:
~ ~ ~ = ~ ~ ( l + i ) ~
Transformer Losses Cost
Transformer the losses cost is made up of two parts:
one due to the iron losses; and the other to the copper
losses.
The annual iron loss cost ( C p ~ ~is) evaluated
considering the related peak and the energy value as:
C p ~=
j (Cd +8766.Ce). Pfe. PN . ( 1 + i)’
where: Cd = pe<akcost $/kW in the initial year
Ce = cost of energy $/kWh in the initial year
Pfe = the iron loss in pu of rating PN.
The copper losses depend on the transformer daily load
curve. This cost is also evaluated considering the pe‘ak
and the energy values and unit prices.
To calculate the transformer annual pe,ak demand of
the copper losses, the transformer peak delnand (Pp)
must be used. From Figure 3, it can be adopted for
instance
P,, = 3.4 Phase (value at 2 CT )
where: Ph,is the base power (kW).
The correspondent copper losses cost (Cpcu),valued at
peak unit cost, is then
APa + AP,. = 2.B.C ( Pn2-t k:n:)
For example: a maybe the 60% and a’ the 40% curves.
For is done in Figure 3 with 10% of probability, except
the extremes that have S%, results.
r
-I
~Pn2+0.2~~~,2(k,2+~2+k,2+k,,2+0.5~k2e)
The total annual cost of copper losses (peak and
energy) C ~ Cof
J the transformers is then:
Transformer Residual Cost at Removal Date.
The transformer operating with rated temperature (95’)
have a life duration of N years (say 30 years).
When loaded above the rated temperature, the loss of
life rate (DVJ)is higher. The additional loss of life
&VI),
a relative value is then:
DDVI= ( Dvr -1 )
This value of additional loss of life can be converted
into cost in the year “J” having it multiplied by the
transformer annual cost (CATJ).
CVJ= DDVICATJ
Note: When the relative loss of life comes to 1 PU(al1
life), in a certain year, a high value for the annual cost
of life is allocated in the formulae above.
Overall Economic Evaluation
For the overall economic evaluation, calculations of the
costs on “year per year” basis should be performed,
then all annual parcels has to be converted into
6.14.5
“present worth” and be added to reach the total cost in
the study period
So the economic evaluation is started from the load
average power at the initial year Po. In a given year “J”
the average power in considering of growth rate “r”
(PU), is estimated by:
J
PJ=PO(l+r)
The economic evaluation of the transformer in this year
is then done by calculating, using all the formulae
presented before for power Pj, and applying all the
standard rating transformers in the company.
CTAJ= CATJ+ (CPFJ+ CPCJ)+ CVJ
The values (CTN) are plotted in a graphic to check
which transformer has the lowest annual cost. Figure 6
shows an example of such costs.
In Figure 6 various alternatives (A,, A*, .. AN) were
established. They are shown at kqble 3.
I
I
I
I
CONCLUSIONS AND RECOMMENDATIONS
From the analysis performed in this paper, the
following conclusions can be drawn:
0
Transformers load curve can be represented by t k
mean and deviation being this model useful for the
transformer loading representation and its selection.
0
To have the adequate value of loss of life a set of
load curve and the temperature mean curve should
be applied in the calculation.
0
For transformer loading management a criteria
based on life duration is recommended as a
refinement of the existing criteria.
0
The economical evaluation methodology here
proposed is recommended for the use of the utilities.
This methodology includes transformer’s cost,
losses, loss of life and removdhstallation cost.
I
BIBLIOGRAPHICAL REFERENCES
1. Blake J.H. and Kelly E.J, 1969 “Oil-immersed
power transformer overload calculations by
computer” IEEE vol.PAS-88 no 8. August.
2. Montsinger V.M., 1930 “Loading Transformers by
Temperature” Transactions AIEE.
3. ANSI, 1981 “Guide for loading mineral-oi!
immersed overhead and pad-mounted distributhi
transformers (rated 500 kVA and less with 65OC or
55OC average winding rise)” ANSI (257.91.
4. “T, 1981 “Loading Power Transformers
Book”, WR-5416). Brazilian Standards
5. IEC 354, 1991 “Loading Guide for Oil Immersed
Transformers” ,IEC publication.
6. Jardini J.A. et all, 1996 “Daily Load Curves-Data
Base Established on Field Measurements” CIRED
Argentina 96 .Buenos A ires.
7. Jardini J.A., et allii, 1994 “Determination of the
Typical Daily Load Curve for Residential Area
Based on Field Measurements” IEEE Transmission
and Distribution Conference Chicapo. USA.
8. Ahn S.U., 1993 “Distribution Transformer Loading
Police ” - Msc dissertation. Siio Paulo Universitu.
9. McNutt
W.Jr., 1992 “Insulation Thermal Life
Consideration for Transformer Loading Guide”,
IEEE transation on Power Deliverv. January.
10.Lockie A.M., 1984 “Loading Distribution
Tranformcn beyond Name Plate Ratink”
Tutorial Course Application of Distribution
Transforms.
11.Jardini J.A , et allii, 1995 “Residential and
Commercial Daily Load Curve Representation by
Statistical Function for Engineering Studies
Purposes” CIRED Conference ‘95 Brussels
Belgium.
12. ELETROPAULO, 1993 “ND-2.005 Distribution
Transformer Loading”, Technical Guide 1993.
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5a
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Figure 6 Cost x Time
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TABLE 3 Alternatives of transformers
PN(LVA)
A,
A2
A3
A4
30
45
75
112.5
150
0-4
5-12
13- 19
20-26
26-30
0-12
0-12
13 19
2 0 - 2 6 13 - 2 6
2 6 - 3 0 ’ 26-30
-
0-12
13-30
To understand the figures on Table 3 note that,
alternative A, consider an alternative that starts with
3OkVA that remains in operation from year 0 to 4, then
change to 45kVA from years 5 to 12, then 75kVA from
years 13 to 19, etc...
For all selected alternatives, there should be calculated
the present worth of the parcels in the study period and
then add to it the removal and new installation costs.
It should be mentioned that alternative Az was the one
with lowest total cost, in the example of Figure 6.
Of course the most economic alternative to be selected
depend on the average power, in the initial year and on
the growing rate.
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