Fellow, IEEE
Member, EEE
Member, IEEE
Escola Politknica USP
CED
-
Centro de Excelencia em DistribuiGSo de Energia ElCtrica
SSo Paulo, BRASIL
E.L.
Member, IEEE
Abstract- A methodology for residential distribution transformer loading evaluation is presented here. The daily load profiles are used to determine the expected loss of life. Different calculation alternatives are used and compared. A methodology that includes the load curve shape obtained by measurements is proposed.
I. INTRODUCTION
The procedure used in Brazil for distribution transformer loading management is based on the expected loss of life calculation, and on statistical approach to determine the kVAs (statistical kVA) function. In order to develop the kVAs function, samples of transformers in operation are selected to be measured. The monthly energy
(kW) 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 installing eletronic recorders over a 2 day-period. The peak power determined 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 function provides its expected peak 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 from the standards tables [ 11 and used in the rating evaluation. This factor is taken as F = 1.5; for the SSo Paulo area and was determined by visual inspection of some typical load profile in some transformers. The ratio
[R=kVAs/F] is used to attribute to the transformer one of the following classifications: underloaded, normally loaded, overloaded, or critically loaded (ratio R range: below 0.75,
0.75 to 1.25, 1.25 to 1.5, and above 1.5, respectively). An appropriate action is taken, like relocation of loads or substitution of the transformer 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 now being re-examined, and new calculation procedures that will be hereinafter presented, are being considered.
11.
MEASUREMENTS
A field investigation was carried out, and the daily load profiles for transformers in residential areas were recorded using eletronic storage equipment. Measurements of the 15 minute-average load (96 points per day) were taken within
15 to 30 day-periods per transformer.
For a common analysis the kW-time curves were reduced to p.u.-time curves using the average monthly power
(energy/72O hours) as base power. For each transformer the mean curve (average of values within each interval for the
15-30 day period) and the standard deviation (std) curve were calculated. One example of these curves is shown in
Fig. 1, where it can be seen that the std values are about 20% of the mean value. The mean curves for 6 transformers are shown in Fig. 2. It can be seen that the mean curves have the same format and are reasonably similar.
20

25 T
O C
2.5
1 P.U. standard deviation
0 2 4 6 8 10 12 14 16 18
20
22
24
how
Fig. 1. Mean and std curves for one transformer Fig. 4. Temperature daily profile (mean and std curves)
T 111. LOSS OF LIFE CALCULATION
Transformer (TI)
\ T 2
In the first attempt the loss of life calculation was performed using the selected load profile curve, represented
the
and std curves. The daily temperature profile was also represented
their mean and std curves (Fig. 4).
Once known the mean M and the std S values, curves with a certaun P% probability of not being exceeded, can be calculated by:
0 4 :
0 2
: : : I : :
: : : :
I
4 6 8 10 12 14 16 18
20
22
24
hour
Fig. 2. Mean curves of 6 transformers
Considering a sample with these mean curves, the mean and std of the means were calculated and the curves are shown in Fig. 3. The low std values indicate a good similarity of the means. So one of them can be selected to be representative of then all. The curve selected is the one with the earliest peak time that leads to a larger loss of life because a higher demand occurs along with a higher day temperature, and so leading to a conservative figure.
2.5
5
2.5
2
V(P)= M +
S where
is taken from the Gaussian probability table (ex:
P=90%, k=1.28). The transformers load curve measurements showed that the demand values are distributed in a Gaussian curve [2].
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 occurence (Fig. 5A) and a set of 11 curves fiw the temperature (Fig.
97.5%
90%
-
0 ;
0
, - : :
2 4 6 8 10 12 14 16 18
20
22
24
how
Fig. 3. Mean and std of the means sample
1.5
1
0.5
0 4 8 12 16
HOUR
Fig. 5A. Set of load curves
20
--I
24
21

30 T°C
25 --
20
--
15
-- l o -. wg..\ g7'r
TABLE I
LOSS OF LIFE VALUE3 (p.u./yr)
CONTRIBUTION OF EACH LOAD CURVE
I
Load Curve Probability of not being exceeded
1
P W )
TRANSFORMER 1
RAT1NGm.U.) I
1 3
1
2,06
1
' ' ' ' ' ' ' ' ' " ' 1 0
0 4 0 12
HOUR
16 20
Fig. 5B. Set of temperature curves
24
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.
If one load and one temperature curves are taken for calculation, then the hot spot temperature and the loss of life Lif (load,temp) can be evaluated [ 11, once a transformer rating is selected. In the calculation the load curves are in p.u. d / 720 h), and the transformer rating should be converted to p.u. using the same base power. Now, combining all load curves i, and temperature curves j, all the Lif ij values can be determined.
The total loss of life is obtained by the weighted average of the values.
Lif tot = Lif ij P(1oad i ) P(temp j) where the P values are the probabilities (5% or 10% in this
It should be mentioned that the calculation carried out
as 11 load curves and only one temperature curve, the
50% one, offered the same results.
Table I shows the loss of life figures for each load curve combined with the 50% temperature curve and two transformer ratings. It should be mentioned, at this point, that the load curve used for the calculation refers to active power only and considers no phase load unbalance. To take care of those facts, a safety margin should be added to the rating (e.g. 10%).
The major contribution is due to the upper load curve
(97.5%). Therefore the result is highly dependent on this curve.
M+1,28S
M+1,96 S
I
90
I
97.5
I
TOTAL WEIGHTED AVERAGE
I
10
I
10,83091
I
5 195,36233
I
I
0,05422
0,15742
I
6,38
I
0,0226
I
It may be questioned that the average and the others derived curves are not actual ones. Therefore the results might not be valid because, at a given time, the hot spot temperature is dependent on the previous instant temperature and the load. Also there should be a truncation point where from the values can be disregarded. In order to check this procedure, all actual daily load curves and the curves M
+ k S (with k=0,+1,+2,+3,-1,-2,-3) were plotted in the same graph. It was verified that only few points of few curves fall off the range (-2 S to + 2 S). An example is shown in Fig. 6.
P.U.
Fig.6. One daily load curve and the truncation range -2S, 2s
22

Lou of Life
@.U.
I uur)
AS
TABLE Il
TRANFORMER RATED POWER
FUNCTION OF LIFE CRlTERION
I
Life criterion
I - I ear) (P.U.)
30 1.4
L
3.000
I
2.02
Table I1 was obtained for the more conservative calculation procedure. No safety margin due to power factor and phase loading unbalance was used. Back to Fig. 1, the ]peak demand of the mean curve is 2.05 p.u. and the corresponding std is 0.25 P.u.. The peak demand with 90% probability of not being exceeded is 2.05
+
1.3 x 0.;!5 =
2.375 p.u. If this value is taken
the kVAs value, the transformer irating should be 2.37Y1.5 = 1.58 P.u., by using the existing criterion. If the kVAs value is adopted at :I std above mean the rating reaches 1.87 P.u.. From Table [I or
Fig. 7, the above ratings (1.58 p.u. and 1.87 P.u.) represent lives of 100 and 1500 years respectivilly. The criterion is then strongly dependent on the probability of the kVAs figure.
IV. TRA.NSFORMER
The loss of life was then calculated considering the truncation at
+
2 s to be compared with the result without truncation.
Finally the loss of life was 'calculated using all actual daily curves ( and the 50% temperature curve) and averaging the results to define the expected annual loss of life. The values obtained with all procedures described above are shown in Fig. 7 for comparison sake.
It can be noted that the values are close to each other in the range of a transformer life from 3 to 300 years. In fact if, for instance, a 300 year life is chosen as a selecting criterion, the related rating will fall in the range 1.5 to 1.65 p.u. depending on the calculation procedure (difference <
10%).
Table I1 shows some key figures taken from Fig.
7.
It is suggested that the transformer loading management be based on life criterion as follows:
TABLE E
SUGGESTED TRANSFORMER LOADING MANAGEMENT
130
Life
F-
> 300 yr
Classification underloaded
I normallv loaded
I to 300 vr overloaded critically loaded
23

If a 150 year-life is taken as a basis for classification
(100%), then underloaded, normal, overloaded, critical represent loads of: <.95, 0.95 to 1.15, 1.15 to 1.3, >1.3 respectively, above base power. The total range is though narrower than the range of todays criterion.
VI. REFERENCES
[ l ] IEC 354, "Loading guide for transformers",JEC publication, 1991. oil immersed v.
[2] J.A. Jardini, C.M.V. Tahan, S.U. Ahn, S.L.S. Cabral,
"Determination of the Typical Daily Load Curve for
Residential Area Based on Field Measurements",
IEEE
-
Transmission and Distribution Conference and Exposition ApriV94 Chicago
-
USA.
The procedure discussed here is a good tool to evaluate transformer loss of life, offering more accurate results, profiles. The load profiles
be obtained by a number of measurements and statistical evaluation to determine a certain number of patterns. Those patterns can included residential commercial or industrial loads. A good representation of load profiles is necessary to fully profit from it.
[3] A. M. Lockie, "Loding Distribution Tranformers
Beyond Name Plate Rating" IEEE Tutorial Course
Application of Distribution Transformers.
[4] ANSI "Guide for Loading Mineral-Oil-Immersed
Overhead and Pad-Mounted Distribution
Transformers (rated 500 kVA and less with 65°C or
55°C average winding rise)"
-
(257.91.1981.
24