CORE LOSS AFFECT OPERATING COSTS FOR TRANSFORMERS

HOW CORE LOSSES AFFECT OPERATING COSTS FOR TRANSFORMERS
DELIVERING NON-SINUSOIDAL LOADS
Optimized Program Service, LLC.
Strongsville, Ohio

ABSTRACT
Previous presentations by the authors have dealt with the costs of operating transformers where load losses were considered for both sinusoidal and non-sinusoidal loads. Core loss costs, however, were evaluated only for
sinusoidal loading. This paper will show that the presence of harmonic currents flowing in the windings does increase the core loss significantly and that these extra costs do affect the final transformer operating costs.
The paper will show that in the absence of a factor, such as the well known ‘K-factor’ that can be applied to core losses, calculations must be made for losses produced by each harmonic current present.
Costs of core losses and load losses will be developed for a specific set of three phase coils having cores made from several commonly used core materials. Using a transformer design software that is equipped
to calculate core losses for all harmonic currents present, design information will be developed for each of the selected core materials. The paper will compare the results obtained.

INTRODUCTION
Non-sinusoidal loading on transformers continues to be a major industry concern. It has led to changes in how transformers are designed and rated. Studies invoked by actions of the Department of Energy regarding energy savings possible with more efficient transformers have made both users
and producers of transformers more aware of the cost of operating them. One element of these costs that is rarely mentioned is the effect on these costs due to increased core losses incurred under non-sinusoidal loading. Testing of transformers under such loading conditions indicate increased losses are present besides the normal accountable losses. Furthermore some watt-hour tests have indicated significant differences in unaccountable losses for similar non-sinusoidal loading conditions for transformers with different core materials.
The following discussion will show the basic premise of how core losses are calculated for each harmonic current and how the values obtained affect the predicting of extra core losses due to the presence of harmonic
currents drawn by transformer loads.

BASIC ASSUMPTION
As harmonic currents flow in the windings they produce a voltage drop across the various reactive elements. Figure 1 illustrates the assumed circuit. Where:

Vhs = Harmonic voltage drop in secondary
Re = Equivalent resistance referred to the Sec.
Xls = Leakage reactance referred to the Sec.
RL = Load resistance.
Then: Vhs = Ih(Re + RL) + jlhxX1s
Where: Ih is the magnitude of each harmonic current. Then Vhs is converted to Vhp (Primary harmonic
voltage) by the turns ratio Np/Ns for the calculation of a flux density for each harmonic at it’s given frequency.
Core losses are then calculated for each harmonic and added to the core loss calculated for the fundamental
frequency.
Re
Vhs
Xls
RL

DISCUSSION
The study began with the selection of a basic transformer model having the following rating:
Primary: 480 Volts, 60 HZ.
Secondary: 208/120V 112.5 KVA
Connection: DYN11
Allowable Temperature Rise: 110C
Construction: Open Ventilated
Core materials and structures selected were:

MATERIAL THICKNESS CORE STRUCTURE
M19 .018 3 Leg Laminated Strip
M6 .014 3 Leg Laminated Strip
M4 .011 3 Leg Laminated Strip
Amorphous
Alloy (SA1) .0018 3 Leg Distributed Gap

DESIGN PROCEDURE
The coils were designed for the SAI core since it was expected to have the largest core cross-section. Crosssections
for the other core materials were adjusted to give operating flux densities for these materials near
values normally used. The coil inside dimensions were maintained the same for each design so that turns, mean
turns, and wire lengths were identical in every design.

DEVELOPMENT OF DATA
The designs were run for each core material for two cases. They were:

Case 1: Sinusoidal load at a secondary RMS current of 311 amperes.
Case 2: Non-sinusoidal load with the following load harmonic currents.

Harmonic Current (Amperes)
1 244
3 140
5 100
7 80
9 35
11 20
This loading gives a current distortion level (THCD) of 80% and a K factor of 9.8.
All losses were evaluated at a reference temperature of 130C (Allowable Rise + 20C).
Therefore, since the coils were identical, the load losses are assumed to be the same for each design.

Loss Comparisons
Since the load losses and coil costs are assumed to be the same for all designs this study will focus on cost of
the cores and the cost of core losses for comparison of core costs the following prices were used:

Core Material Price Per Pound
M19 .68
M6 .8
M4 .88
SA1 1.70
The SA1 cost is for a complete core. Therefore, 20 cents per pound will be added for M19, M6 and M4.
The cost of the core for each material is given in Table 1.

Table 1
Core Material Core Weight Core Cost
(Pounds) ($)
M19 708 623
M6 682 682
M4 656 708
SA1 731 1242
Core losses for Case 1 (Sinusoidal Loading) are
shown in Table 2.

Table 2
Core Material Core Loss Watts
M19 1520
M6 760
M4 511
SA1 87
Core losses for each harmonic for Case 2 (nonsinusoidal
loading) are shown in Tables 3a, 3b, 3c and
3d.
Table 3a
Core Losses for M19
Frequency AC Voltage Flux Density Core Loss
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
60.0 480.000 15.584 1480.763
180.0 68.457 2.875 267.458
300.0 49.115 1.238 115.723
420.0 39.551 .712 66.901
540.0 17.453 .244 13.635
660.0 10.079 .115 4.618
– – – – – – –
1949.098
Table 3b
Core Losses for M6
Frequency AC Voltage Flux Density Core Loss
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
60.0 480.000 16.216 736.393
180.0 68.608 2.992 167.698
300.0 49.222 1.288 79.179
420.0 39.636 .741 48.489
540.0 17.490 .254 9.918
660.0 10.100 .120 3.390
– – – – – – –
1045.067
Table 3c
Core Losses for M4
Frequency AC Voltage Flux Density Core Loss
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
60.0 480.000 16.878 495.992
180.0 68.671 3.115 116.139
300.0 49.267 1.341 53.232
420.0 39.672 .771 32.013
540.0 17.506 .265 6.429
660.0 10.109 .125 2.262
– – – – – – –
706.067
Table 3d
Core Losses for Amorphous Alloy (SA1)
Frequency AC Voltage Flux Density Core Loss
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
60.0 480.000 13.567 85.731
180.0 68.674 2.504 16.492
300.0 49.269 1.078 8.972
420.0 39.673 .620 7.487
540.0 17.507 .213 1.702
660.0 10.109 .101 .625
– – – – – – –
121.011
As can be seen by comparing the data in Table 2 with the respective data in Tables 3a, 3b, 3c and 3d there are
large differences in total core losses among the various core materials and these differences among the selected
core materials increase in the presence of harmonic currents.

Cost Comparisons
Two methods of evaluating the cost of core losses are:
1. Using an “A Factor” as normally used in
Total Ownership Cost (TOC) calculations.
“A Factor” is typically 3.5.
2. Calculating the annual cost of losses as
follows:
Annual Cost = $Kwhr. x Core Loss x Factor
Where: $/Kwhr is the cost of power in dollars
per kilo-watt hour.
Factor = Hours Per Year = 8.76
1000
Then:
Annual Cost = .07 x Core Loss x 8.76
Cost comparisons using the above methods are shown in Table 4a and 4b.
Table 4a
Loss Costs TOC Method
A Factor = 3.5
Sinusoidal Load Non-Sinusoidal Load
M19 $5320 $6822
M6 $2660 $3658
M4 $1778 $2471
SA1 $305 $424
Table 4b
Annual Cost Method
Sinusoidal Load Non-Sinusoidal Load
1Year 10 Years 1 Year 10 Years
M19 932 9320 1195 11950
M6 466 4660 641 6410
M4 313 3130 433 4330
SA1 54 540 74 740
The data in Tables 4a and 4b shows that there is a
significant increase in core loss costs when the load is
non-sinusoidal.

Core Cost Premium Payback Times
If the M6 design was considered to be standard for comparison and M19 design was eliminated because of
its high losses the payback times for the higher cost of M4 and SA1 cores could be calculated as follows:
Payback Time = Core Cost Premium
Annual Cost of Loss Difference
These comparisons are shown in Table 5. For this comparison the core costs were multiplied by 1.6 to
reflect their selling price value.

Table 5
Payback Times for Premium Core Costs for
Non-Sinusoidal Loads
Core Core Premium Annual Loss Payback
Material Cost Cost Loss Cost Savings Years
M6 1091 —- 641 —-
M4 1133 42 433 208 .2
SA1 1987 896 74 567 1.6
The data in Table 5 shows that premiums paid for M4 and SA1 materials over M6 can be recovered in rather
short times due to lower loss costs under non-sinusoidal loading conditions.

OBSERVATIONS
In reviewing the data generated during this study the following notable observations are made:
1. Core losses increase when the load on a transformer goes from sinusoidal to non-sinusoidal.
2. The differences between core losses for the core materials selected increase under non-sinusoidal
loading.
3. Under non-sinusoidal loading the premiums paid for better core materials can be recovered in a
relatively short period of time.
4. Perhaps a new way of evaluating the increased core loss costs should be developed because they are only
present when the load is present.

CONCLUSION
This paper has described one method for calculating core loss-costs for non-sinusoidal loading.
The data obtained during this design study demonstrates that harmonic currents drawn by the load cause voltage
distortion that results in increased core losses. In the near future an extension of this study will be made with
enhanced loss separation data for a range of core materials.