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OPTIMIZING ENERGY EFFICIENCY STANDARDS
FOR LOW VOLTAGE DISTRIBUTION TRANSFORMERS
A Thesis
Submitted to the Faculty
of
Purdue University
by
Kenneth Duane Harden
In Partial Fulfillment of the
Requirements for the Degree
of
Master of Science in Engineering
May 2011
Purdue University
Fort Wayne, Indiana
ii
For people everywhere pursuing energy conservation to protect the resources of our
planet.
iii
ACKNOWLEDGMENTS
I thank Dr. Steven Walter for his many hours of assistance and guidance
throughout the preparation of this research, and for his courses of instruction in System
Engineering. I also thank Dr. Carlos Pomalaza-Raez and Dr. Omonowo D Momoh for
their participation as advisory committee members for this research, and Barbara Lloyd
for her assistance in the format of this research. I thank my employer for their support of
my continuing education and for providing access to data in support of this research.
Additionally, I thank my parents for their encouragement of personal development and
the importance of education in my formative years. I also thank my sons for their
discussions and assistance. I especially thank my wife for all of her patience, support,
and encouragement through my continuing education.
iv
TABLE OF CONTENTS
Page
LIST OF TABLES ............................................................................................................. vi LIST OF FIGURES ......................................................................................................... viii LIST OF ABBREVIATIONS ........................................................................................... xii ABSTRACT ..................................................................................................................... xiii 1. INTRODUCTION ......................................................................................................... 1 2. GENERAL INFORMATION ........................................................................................ 4
2.1 Power Distribution Overview .................................................................................. 4 2.2 Overview of Transformer Operation ....................................................................... 7 2.3 Overview of Transformer Efficiency ..................................................................... 11 2.4 Overview of the Current Rulemaking .................................................................... 14
3. TRANSFORMER ENERGY EFFICIENCY ............................................................... 17
3.1 Transformer Calculations and Model .................................................................... 17
3.1.1 Transformer loss and efficiency calculations ................................................. 17 3.1.2 Transformer coil temperature calculation ....................................................... 21 3.1.3 Transformer temperature rises other than 150°C ............................................ 24
3.2 Impact of Temperature Correction on Transformer Efficiency ............................. 27 3.3 Design Considerations ........................................................................................... 29 3.4 Design Trade Space ............................................................................................... 31
4. ENERGY EFFICIENCY CALCULATION METHODS ............................................ 36
4.1 Single Point Efficiency Calculation Method ......................................................... 36 4.2 Multi-Point Efficiency Calculation Method .......................................................... 37 4.3 Composite Efficiency Calculation Method ............................................................ 43 4.4 Dual Criteria Efficiency Calculation Method ........................................................ 45
v
Page
4.5 Evaluation of Energy Efficiency Calculation Methods ......................................... 52 5. TRANSFORMER LOAD LEVELS ............................................................................ 53
5.1 Basis for the Current Federal Rulemaking............................................................. 53 5.2 Existing Load Level Research ............................................................................... 54 5.3 Schneider Electric Power Data .............................................................................. 55 5.4 Typical Power Data................................................................................................ 60 5.5 Transformer Load Profile ...................................................................................... 64
6. TRANSFORMERS AS PART OF A SYSTEM .......................................................... 71
6.1 Transformer Capacity ............................................................................................ 71 6.2 Transformer Operational Life ................................................................................ 71 6.3 National Electrical Code Recommendations for Sizing a Transformer ................. 72 6.4 Liability Inherent in Transformer Specification .................................................... 73 6.5 Impact of Transformer Applications on their Load Levels ................................... 74 6.6 Impact of Energy Conservation Initiatives on Transformer Loss .......................... 75
7. RECOMMENDATIONS ............................................................................................. 77
7.1 Recommendations for Improving Energy Efficiency ............................................ 77 7.2 Recommendations for Further Study ..................................................................... 81
8. SUMMARY AND CONCLUSIONS .......................................................................... 82 LIST OF REFERENCES .................................................................................................. 84 APPENDIX ....................................................................................................................... 86
vi
LIST OF TABLES
Table Page 2.1 Transformer Line Currents for Common Transformer Power Ratings ....................... 8 2.2 Minimum Requirements for the Efficiency of Transformers Dictated by
10 CFR Part 431........................................................................................................ 15 3.1 Losses for Designs Selected for Efficiency Calculation Comparisons ...................... 33 4.1 Efficiencies Calculated for a Multi-Point Method with Efficiency Criteria of
96%@10% Load, 98%@40% Load and 96.8%@90% Load ................................... 40 4.2 Comparison of the Implementation of the Single Point and Multi-Point
Methods of Specifying Transformer Efficiency ....................................................... 42 4.3 Composite Case CC43 Test Case .............................................................................. 44 4.4 Approaches for Dual Criteria Methods ...................................................................... 46 4.5 Comparison of the Implementation of the Single Point and Dual Criteria
Methods..................................................................................................................... 51 Appendix Table A.1 Temperature Corrected Efficiency for Designs A, B, and C at Loads of 10%,
40% and 90% ........................................................................................................... 87 A.2 Composite Cases CC01-CC70 .................................................................................. 88 A.3 Temperature Corrected Efficiency for Designs A, B, and C at Loads of 20%,
40% and 80% ........................................................................................................... 91 A.4 Composite Cases CC71-CC140 ................................................................................ 92 A.5 Comparing Discriminating Case Composite Weighting Factors .............................. 97
vii
Appendix Table Page A.6 Discriminating Case Strength ................................................................................... 98 A.7 Composite Case CC43 Test Case.............................................................................. 99
viii
LIST OF FIGURES
Figure Page 1.1 Summary of Requirements Identification, Analysis and Synthesis Processes
for Transformer Design............................................................................................... 2 1.2 Objective of the Government Rulemaking regarding Energy Efficiency of
Distribution Transformers ........................................................................................... 3 2.1 Generation, Transmission, and Distribution of Power from the Power Plant
to the Point of Use....................................................................................................... 4 2.2 A Use Case for the Design of a Power Distribution Network at an Industrial
or Commercial Facility ............................................................................................... 6 2.3 A Diagram showing the Coupling between a Transformer Coils and its Core ........... 7 2.4 Transformer Loss Curve for a Typical 75 kVA Transformer .................................... 10 2.5 Transformer Power Curve for a Typical 75kVA Transformer illustrating the
Loss as the Divergence between the Input and Output Power Curves ..................... 11 2.6 Typical Transformer Efficiency Curve ...................................................................... 12 2.7 Magnified View of a Typical Transformer Efficiency Curve ................................... 13 2.8 Efficiency Characteristics as a Function of Load for Eleven Low Voltage,
Dry Type Transformers with Power Ratings from 15kVA to 1000kVA.................. 16 3.1 Comparison of Coil Temperature Approximation Methods for a 150°C
Rise Transformer ...................................................................................................... 22 3.2 Magnified View of the Comparison of Coil Temperature Approximation
Methods for a 150°C Temperature Rise Transformer .............................................. 23
ix
Figure Page 3.3 Comparison of Coil Temperature Approximations for 150°C, 115°C, and
80°C Rise Transformers ............................................................................................ 25 3.4 Magnified View of the Comparison of Coil Temperature Approximations
for 150°C, 115°C, and 80°C Rise Transformers ....................................................... 26 3.5 Impact of Temperature Correction on Transformer Efficiency assuming Two
Different Load-Independent Operating Temperatures compared to a Simple Temperature Adjusted Model that Exhibits more Realistic Behavior ...................... 28
3.6 Typical Categories of System Level Transformer Requirements .............................. 29 3.7 Typical Design Variables Available to Transformer Designers ................................ 30 3.8 Typical Trade Study Criteria used to Optimize Transformer Design ........................ 31 3.9 Twenty Five Designs for Aluminum, 150°C Rise, 75kVA Transformers
of Various Voltages or other Requirements.............................................................. 32 3.10 Efficiency Curves for Designs Selected for Efficiency Calculation
Comparisons ........................................................................................................... 34 4.1 Illustration of the Multi-Point Energy Efficiency Calculation Method ..................... 38 4.2 Solution Set for Multi-Point Method Efficiency Criteria of 96%@10%
Load, 98%@40% Load, and 97%@90% Load ........................................................ 39 4.3 Solution Set for Multi-Point Method Efficiency Criteria of 96%@10%
Load, 98%@40% Load, and 96.8%@90% Load ..................................................... 41 4.4 Composite Case CC43 Test Case Efficiency Curve .................................................. 45 4.5 Solution Set for a Dual Criteria Method using Approach A’s Method of
Specifying Transformer Efficiency ........................................................................... 47 4.6 Solution Set for a Dual Criteria Method using Approach B’s Method of
Specifying Transformer Efficiency ........................................................................... 48 4.7 Solution Set for a Dual Criteria Method using Approach C’s Method of
Specifying Transformer Efficiency ........................................................................... 49 4.8 Efficiency Curve representing One Solution for a Dual Criteria Method
of Specifying Transformer Efficiency using Approach C ........................................ 50
x
Figure Page 5.1 Daily, Weekly, and Seasonal Power Variations at a Schneider Electric
Facility in Indiana ..................................................................................................... 57 5.2 Daily, Weekly, and Seasonal Power Variations at a Schneider Electric
Facility in North Carolina ......................................................................................... 58 5.3 Daily, Weekly, and Seasonal Power Variations at a Schneider Electric
Facility in Tennessee................................................................................................. 59 5.4 Daily, Weekly, and Seasonal Power Variations at a Schneider Electric
Facility in Texas ........................................................................................................ 60 5.5 Typical Power Data cannot be used to determine Transformer Load Levels ............ 61 5.6 Vector Representation of Real Power, Apparent Power, and Power Factor ............. 62 5.7 Transformer Operating Load Level will Increase if there is a Reactive
Component to the Load ............................................................................................. 63 5.8 Vector Illustration of how Reducing the Reactive Load will Reduce the
Transformer Load Level and Increase the Power Factor .......................................... 63 5.9 Daily, Weekly, and Seasonal Power Factor Variations at a Schneider
Electric Facility in Texas .......................................................................................... 64 5.10 Illustration of Load Level Terminology .................................................................. 65 5.11 Transformer Load Profile Scenarios based on the Schneider Electric
Indiana Facility using an Assumed Summer Weekday Load and Calculated Transformer Power Output ................................................................... 66
5.12 Transformer Load Profile Scenarios based on the Schneider Electric
North Carolina Facility using an Assumed Summer Weekday Load and Calculated Transformer Power Output ................................................................... 67
5.13 Transformer Load Profile Scenarios based on the Schneider Electric
Tennessee Facility using an Assumed Summer Weekday Load and Calculated Transformer Power Output ................................................................... 68
5.14 Transformer Load Profile Scenarios based on the Schneider Electric
Texas Facility using an Assumed Summer Weekday Load and Calculated Transformer Power Output ................................................................... 69
xi
Figure Page 6.1 Illustration of NEC Requirements for Calculating the Size of an
Industrial Feeder Circuit ........................................................................................... 73 Appendix Figure A.1 Composite Cases CC01 through CC70, Efficiency Differences............................... 95 A.2 Composite Cases CC71 through CC140, Efficiency Differences............................. 96 A.3 Composite Case CC43 Test Case Efficiency Curve ............................................... 100
xii
LIST OF ABBREVIATIONS
A Ampere
A.C. Alternating Current
°C Degrees Celsius
CFR U.S. Code of Federal Regulations
D Delta (Three Phase Delta Configuration)
D.C. Direct Current
DOE US Department of Energy
EIA U.S. Energy Information Administration
°F Degrees Fahrenheit
I Current
IEEE Institute of Electrical and Electronics Engineers
kVA Kilo Volt Ampere (1000 VA)
NEC National Electrical Code
NEMA National Electrical Manufacturers Association
R Resistance
UL Underwriters Laboratories Inc.
U.S. United States of America
V Volt
VA Volt Ampere
VAC Volts A.C.
W Watt
Y Wye (Three Phase Wye Configuration)
xiii
ABSTRACT
Harden, Kenneth Duane. M.S.E., Purdue University, May 2011. Optimizing Energy Efficiency Standards for Low Voltage Distribution Transformers. Major Professor: Steven J. Walter.
The energy efficiency of low voltage, dry type, distribution transformers is
influenced primarily by the imposition of energy efficiency regulations and by the
operational conditions imposed on the transformers. This study, in part, examines the
energy efficiency regulations that govern the measurement and specification of energy
efficiency for low voltage, dry type, distribution transformers and evaluates whether the
requirement used to certify the transformer efficiency is optimized for minimizing power
loss. In the U.S., regulations are mandated for transformer efficiency. With the demand
for electricity increasing every year, improvement in transformer efficiency at the point
of use under operational conditions will conserve energy.
This study investigates whether the current energy efficiency rulemaking, that
establishes transformer efficiency at only one point on the load curve, provides the level
of energy savings expected by government rulemakings, and evaluates alternate methods
for specifying transformer efficiency. This study also attempts to characterize the
operational load levels experienced by these transformers, including seasonal and daily
load variations, and relates the operational load levels to the efficiency standard and
alternate methods. The study also demonstrates the importance of considering
transformers and distribution networks as part of a system when evaluating the
implementation of other energy efficiency improvements, and how it impacts the
optimization of power consumption within commercial facilities. Recommendations are
xiv
presented for improving transformer rulemakings and for system considerations to realize
higher energy savings in commercial and industrial facilities.
1
1. INTRODUCTION
Low voltage, dry type, distribution transformers are typically utilized in
commercial and industrial applications to step down local utility distribution voltages to
provide power to facility panelboards or specific equipment within those facilities. The
term “low voltage” indicates that the supply voltage to the transformer is 600 VAC or
less. The term “dry type” indicates that the transformer is air cooled, and is not immersed
in liquids such as oil. The term “distribution” indicates that the transformer is on the
distribution side of the power grid.
The generation, transmission, and distribution of electricity to the point of use
consumes approximately two-thirds of the energy [1]. Accordingly, delivering one unit
of power to an end user requires approximately two units of power to generate, transmit,
and distribute that one unit of power. Alternatively, saving one unit of power at the end
user avoids the two units of power lost to generation, transmission, and distribution for a
three-fold impact on energy savings. Therefore, an improvement in transformer
efficiency at the point of use will have a three-fold, multiplicative impact on energy
savings.
Figure 1.1 summarizes the requirements identification, analysis and synthesis
processes associated with transformer design and selection. Various requirements
imposed by the customer, the government, and industry create a set of design
requirements for each transformer. Multiple designs can be developed to meet the
requirement set. Trade studies, which will consider factors such as cost, ease of
production, and reliability, are utilized by the manufacturer to select the desired design
for manufacture.
2
DesignA
DesignB
DesignC
TransformerRequirements
CustomerRequirements
IndustryRequirements
GovernmentRequirements
ManufacturerTrade Study
Design Selectedfor Manufacture
Fig. 1.1 Summary of Requirements Identification, Analysis and Synthesis Processes for Transformer Design
This study presents a general understanding of transformer operation and the
major sources of loss for a transformer to provide a basis for examining the U.S.
government energy efficiency rulemaking [2] that governs and certifies distribution
transformer efficiencies. Figure 1.2 presents the general objective of the rulemaking to
ensure that transformers released for use in the U.S. meet certain levels of efficiency to
maximize the energy savings.
3
Design meetsRequirements
GovernmentRequirements
MaximizesEnergy Savings
StandardLoad
Fig. 1.2 Objective of the Government Rulemaking regarding Energy Efficiency of Distribution Transformers
Inherent in the government rulemaking is a method for calculating the energy
efficiency of distribution transformers at a specified load. In reality, the transformer
loads vary dynamically within each installation, and will vary from application to
application. This study will show that transformer energy efficiency is a function of load
level. Accordingly, proper selection of the load profile is key to properly evaluating the
energy efficiency of transformers. This study evaluates the dynamics of operational load
levels in comparison to the load level specified by the rulemaking. This study also
provides recommendations for improving the calculation of energy efficiency, and also
considers other variables present in the transformer application, as part of a larger system,
which affect load levels and energy efficiency.
4
2. GENERAL INFORMATION
2.1 Power Distribution Overview
The demand for electricity increases every year. In the U.S., the demand in the
year 2035 is expected to be 30% above the 2008 levels [3]. Globally, the demand for
energy will increase at a much higher rate with the industrialization of underdeveloped
nations [4].
Electricity generated at power plants from resources (such as coal), is transmitted
across long distances at high voltages and is distributed in local areas among the users at
medium and low voltages. Figure 2.1 illustrates these three primary portions of a power
grid: Generation, Transmission, and Distribution.
Generation
High VMedium V
Low V
Transmission
D i s t r i b u t i o n
Low Voltage Distribution Transformer
typ 765kV-138kV
typ 69kV-4kV
< 600V
Fig. 2.1 Generation, Transmission, and Distribution of Power from the Power Plant to the Point of Use
5
To deliver power to the point of use, the gross power generated from power
generating facilities is ‘stepped-up’ to high voltages, exceeding 100,000 volts. As
electricity is distributed through the power grid to users, it is ‘stepped-down’ to lower
voltages. Stepping voltages up and down is accomplished through the use of
transformers which ‘transform’ input power from one voltage to another. The arrow in
Figure 2.1 illustrates the relative location of low voltage, dry type, distribution
transformers in the power grid. These transformers are typically located at, or very near,
the consumer’s point of use.
Given that per phase resistive power loss (I2R) in a transmission line is directly
related to the square of the current flowing in a transmission line and the amount of
resistance of the transmission line. By utilizing transformers to transform voltages to a
much higher level, distribution at high voltage requires much less current which reduces
the transmission losses. High voltage and medium voltage transformers are used
throughout the transmission and distribution network, eventually stepping the line
voltages down to 600 volts or less at the point of use.
Low voltage, distribution transformers commonly transform from a supply line
voltage of 480 VAC Delta to a facility voltage of 208 VAC Wye (or 120 VAC to
neutral), although many other voltage combinations are utilized as dictated by available
supply voltages and the voltages necessary to power systems and equipment at the point
of use. User needs determine the system requirements. Figure 2.2 is an example
illustration of one transformer use case in one facility.
6
FacilityMainPowerPanel480V
Transformer480D-
208Y/120
Transformer480D-415Y
Transformer480D-208D
PowerPanel
PowerPanel
Equipment415Y/240V
Equipment208V
Lights277V
Lights &Receptacles
120V
Fig. 2.2 A Use Case for the Design of a Power Distribution Network at an Industrial or Commercial Facility
The demand for power is initiated by the consumer. Turning on lights or
machinery in a facility (the point of use) creates a demand for electricity. This demand
establishes the transformer loads which result in loads on, or demands from, the electric
utility power grid, which results in a demand from the power generation facility (the
point of power generation). From the point of reference of the power generating
facilities, they must produce enough power over and above the user requirements to
overcome the power losses occurring throughout the power delivery system in order to
satisfy the demand at the point of use. One source indicates 62% of power is lost in
generation and an additional 2% is lost in transmission and distribution [5]. The U.S.
Energy Administration reports 65.8% of energy is wasted in generation, transmission and
distribution losses [1]. With approximately two thirds of power lost in generation,
transmission and distribution, improvements in the energy efficiency of low voltage, dry
type, distribution transformers at the point of use will reduce the burden on generating
capacity at the point of power generation approximately three times the energy savings.
7
2.2 Overview of Transformer Operation
Transformers are used to ‘transform’ power from one voltage level to another
voltage level. They use A.C. power in a coil of wire to create magnetic lines of flux
which pass through a core and induce a voltage across the output coil. The primary
components of a transformer are the coils and the core as shown in Figure 2.3.
Magnetic Flux
Transformer Core
Primary Coil
Secondary Coil
Fig. 2.3 A Diagram showing the Coupling between a Transformer Coils and its Core
The transformer coils are identified as “primary” and “secondary” coils. Power is
applied to the transformer’s primary coil. This is the “input” power, or “power in” 1. The
“output” power is available at the transformer’s secondary coil. The secondary is also
considered the “load” side of the transformer. The output power is equal to the input
power less the power consumed by the transformer. The efficiency of a transformer is
the ratio of output power to input power.
1 It may also be referred to as the ‘line’ side of the transformer.
8
The power ratings of transformers2 are directly related to the voltage across the
coils and the current through the coils. Table 2.1 identifies some standard transformers
and their associated current levels.
Table 2.1
Transformer Line Currents for Common Transformer Power Ratings
Single Phase Transformer Three Phase Transformer
Power Rating (kVA)
Line Currents @ 480V
Line Currents @ 120V
Power Rating (kVA)
Line Currents @ 480V
Line Currents @ 208V
15 31.3 A 125.0 A 15 18.0 A 41.6 A
25 52.1 A 208.3 A 30 36.1 A 83.3 A
37.5 78.1 A 312.5 A 45 54.1 A 124.9 A
50 104.2 A 416.7 A 75 90.2 A 208.2 A
75 156.3 A 625.0 A 112.5 135.3 A 312.3 A
100 208.3 A 833.3 A 150 180.4 A 416.4 A
167 347.9 A 1391.7 A 225 270.6 A 624.5 A
250 520.8 A 2083.3 A 300 360.8 A 832.7 A
333 693.8 A 2775.0 A 500 601.4 A 1387.9 A
750 902.1 A 2081.8 A
1000 1202.8 A 2775.7 A
The currents identified in Table 2.1 are calculated from either Equation (2.1) or
Equation (2.2) depending on power phasing.
( )
( )( )
Power VASinglePhaseCurrent A
Voltage V= (2.1)
( )
( )3 ( )
Power VAThreePhaseCurrent A
LineVoltage V=
⋅ (2.2)
2 Low voltage, power distribution transformer power capacities are usually specified in kVA as the unit of power, and typically range from 15 kVA to 1000 kVA.
9
The power consumed by a transformer is termed the transformer loss. The major
sources of loss in a transformer are the core losses and the load losses. Core losses are
due to the power required to magnetize the core. Core losses are related to the type of
core material, core size, configuration of the core, and assembly of the core. Load losses
are primarily composed of coil losses, which are lost to resistive heating of the wire in the
coil due to the coil resistance. Coil losses vary as the square of the electric current
passing through the coils. The impedance of the coils is related to the characteristics of
the conductor, the size and length of the conductor, and the geometry of the conductor
windings. The current passing through the coils is determined by the load on the
secondary coil and the ratio between the primary and secondary voltages. Other less
significant load losses include stray losses, which are caused by the magnetic field lines
that are drawn away from the primary path in the core towards other objects, such as
mounting clamps, other transformer hardware, and the transformer enclosure. In short,
the core losses occur continuously (even without a load) and are relatively independent of
load levels, while the load losses are proportional to the square of the load current.
Figure 2.4 provides a typical transformer loss curve3 to illustrate this general relationship.
3 Assumes a core loss of 250 VA and a coil loss, at full load, of 2335 VA.
10
0
500
1000
1500
2000
2500
3000
0% 10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Transformer Load
Tra
nsfo
rmer
Los
s (V
A)
Core Loss
Coil Loss
Total Loss
Fig. 2.4 Transformer Loss Curve for a Typical 75 kVA Transformer
Transformers are rated according to the output power. As such, a 75kVA
transformer is rated to provide 75kVA of power on the output. Consequently, the
required input power for a transformer is equal to the rated power output of the
transformer plus the power losses of the transformer. Using the transformer loss curve of
Figure 2.4, a 75kVA transformer (rated output power) will require an additional 2585VA
(approximately 2.6kVA) at the input to overcome the internal transformer losses. This is
illustrated in Figure 2.5.
11
0
10000
20000
30000
40000
50000
60000
70000
80000
0% 5% 10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
Transformer Load
Pow
er (
VA
)
Rated Power Output Required Power Input
Fig. 2.5 Transformer Power Curve for a Typical 75kVA Transformer illustrating the Loss as the Divergence between the Input and Output Power Curves
2.3 Overview of Transformer Efficiency
The power output of a transformer is equal to the power input to a transformer
less any losses incurred by the transformer. Since transformer efficiency (η) is the ratio
of output power to input power, it is therefore affected by transformer losses. A typical
transformer efficiency curve is represented in Figure 2.6 based on equation (2.3) and an
output power rating of 75kVA.
12
100%
out out
in out losses
out
out CoreLoss CoilLoss
Power Power
Power Power Power
Power
Power Power Power
η
η
= =+
= ⋅+ +
(2.3)
Figure 2.7 is a magnified view of Figure 2.6 that focuses on the range of loading
values from 10% to 100%.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0%
10
%
20
%
30
%
40
%
50
%
60
%
70
%
80
%
90
%
10
0%
Transformer Load
Eff
icie
ncy
Fig. 2.6 Typical Transformer Efficiency Curve
13
94%
95%
96%
97%
98%
99%
100%
10
%
20
%
30
%
40
%
50
%
60
%
70
%
80
%
90
%
10
0%
Transformer Load
Effi
cie
ncy
Fig. 2.7 Magnified View of a Typical Transformer Efficiency Curve
Typically at low loads, the core losses dominate the transformer loss, and at high
loads the coil losses dominate the transformer loss.
Additional factors affect the specification and design of a transformer, such as
temperature rise above the ambient temperature and the amount of acoustic “hum” or
noise. Higher flux densities in the core usually contribute to higher vibrations and,
consequently, higher noise levels4. Higher coil losses usually contribute to higher coil
temperatures. Typical temperature rise specifications are 80°C, 115°C, and 150°C. A
transformer operating at 10% load is using a low level of current and will not generate
much heat. As the load on that transformer increases to 100%, or full load, the current
also increases and generates much more heat as the full load currents flow through the
coil conductors. A temperature rise specification of 150°C allows the transformer
temperature to rise 150°C above the ambient temperature (typically 20°C). A fully
loaded commercial transformer can exceed 300°F.
4 Flux density is a measure of magnetic field intensity.
14
Transformer design engineers have a variety of parameters and materials that can
be used to produce transformers tailored to the requirements that satisfy specific
applications. Transformer manufacturers have to control materials, processes, and
configurations to ensure transformers are built to meet the specifications.
2.4 Overview of the Current Rulemaking
The U.S. Department of Energy is required to set rulemakings that maximize the
energy efficiency. These rulemakings are required to be both technically feasible and
economically justified [6]. The energy efficiency of major appliances and equipment are
governed in the U.S. by the Code of Federal Regulations, Title 10, Chapter II, Part 4315
[7]. Subpart K of 10 CFR Part 431 which directly concerns Distribution Transformers6
and specifies certain definitions and requirements related to transformer efficiency,
testing procedures, manufacturer’s compliance, and DOE specified enforcement testing.
For reference, the energy efficiency requirements for low voltage, dry type,
distribution transformers are reproduced herein in Table 2.2 [8]. Because a transformer’s
characteristics vary with load levels, the rulemakings also specify, in a footnote to the
table, that (a) the core losses are evaluated at no-load and 20°C, and (b) the load losses
are evaluated at a 35% load and a temperature of 75°C 7.
5 Federal Register Volume 75, page 56796, is a Notice of Proposed Rulemaking which includes restructuring 10 CFR Part 431 into 10 CFR Part 429, but does not propose to change the energy efficiency performance requirements of distribution transformers. 6 Appendix A of Subpart K is derived from transformer energy efficiency guidelines prepared by the National Electrical Manufacturers Association (NEMA). 7 An operating temperature of 75°C indicates an ambient temperature of 20°C and a transformer temperature rise of 55°C.
15
Table 2.2 Minimum Requirements for the Efficiency of Transformers
Dictated by 10 CFR Part 431
Single Phase Three Phase
Power Rating (kVA)
Efficiency (%)
Power Rating (kVA)
Efficiency (%)
15 97.7 15 97.0
25 98.0 30 97.5
37.5 98.2 45 97.7
50 98.3 75 98.0
75 98.5 112.5 98.2
100 98.6 150 98.3
167 98.7 225 98.5
250 98.8 300 98.6
333 98.9 500 98.7
750 98.8
1000 98.9
An analysis of manufacturer published data across the full kVA range for
common three phase transformers is presented in Figure 2.8 [9]. This data is represented
at a full temperature of 170°C for all load levels. A more extensive model is developed
in the next section. Figure 2.8 illustrates the variation in efficiency requirements as
identified in Table 2.2 and also suggests that transformers are designed to meet the
requirements of the rulemaking.
16
94.00%
95.00%
96.00%
97.00%
98.00%
99.00%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100
%
Transformer Load
Tra
nsfo
rmer
Eff
icie
ncy
15 kVA
30
45
75
112.5
150
225
300
500
750
1000
Fig. 2.8 Efficiency Characteristics as a Function of Load for Eleven Low Voltage, Dry Type Transformers with Power Ratings from 15kVA to 1000kVA
17
3. TRANSFORMER ENERGY EFFICIENCY
3.1 Transformer Calculations and Model
The efficiency calculations used in this and subsequent chapters mirror the
calculations used in 10 CFR Part 431 Subpart K Appendix A. In short, the no-load core
losses are adjusted for temperature, and the load losses are adjusted for load level,
material type, and temperature. The calculations specified in the rulemaking are oriented
towards the use of measured data.
The intent of the analysis of this section is to identify approximations that can be
used to derive simplified equations that can be applied to commonly available
transformer and load data to draw conclusions about the effectiveness of transformer
design criteria and efficiency rulemakings. The first subsection will derive the simplified
equations for transformer losses and efficiency. The second subsection will derive the
simplified equation for estimating transformer coil temperatures.
3.1.1 Transformer loss and efficiency calculations
Equation (3.1) [2, Appendix A, eq. (5-3)] calculates the transformer efficiency (η)
at any specified load level.
100%os
os ts
P
P Pη = ⋅
+ (3.1)
Pos is the power output at the specified load level and Pts is the corrected total
power loss adjusted to the specified load level. Equation (3.2) [2, Appendix A, sec. 5.1]
calculates the output power at the specified load.
os orP P L= ⋅ (3.2)
18
Por is the rated transformer output power (ex: 75kVA) and L is the per unit load
level (ex: L=0.35 for a 35% loading level).
Equation (3.3) [2, Appendix A, eq. (5-2)] calculates the corrected total power loss
as a function of core loss and load loss.
ts nc lcP P P= + (3.3)
Pnc is the no-load core loss corrected to 20°C and Plc is the adjusted load loss
power at a specified load level (L). Equation (3.4) [2, Appendix A, eq. (4-2)] is used for
temperature correction of the no-load core loss. (The DOE rulemaking states that the no-
load core loss does not need to be adjusted for temperature when the no-load core loss
data is attributed to a measurement of no-load core loss within the core temperature range
of 10°C to 30°C 8.)
( )1 1 0.00065nc nc nm nrP P T T= ⋅ + − (3.4)
Pnc1 is the no-load core loss at the temperature Tnm (the temperature at which the
data is obtained), corrected for waveform distortion9, and Tnr is the reference temperature
of 20°C (the temperature the data is being adjusted to).
Equation (3.5) [2, Appendix A, eq. (5-1)] calculates the adjusted load losses.
2
22 2
oslc lc lc
or
PP P P L
P
= = ⋅
(3.5)
Plc2 is the temperature (and material) corrected load loss. These load losses are
comprised of stray losses, Ps, in addition to ohmic (resistive) losses, Pe,.and are
represented in Equations (3.6) [2, Appendix A, eq. (4-8)], (3.7) [2, Appendix A, sec.
4.5.3.3] and (3.8) [2, Appendix A, eq. (4-10)].
2
( ) ( )2 1( ) ( ) ( )
( ) 2 ( )
k p lr k s lre lm p dc p dc s
k p dc k s dc
T T T TNP I R R
T T N T T
+ + = ⋅ ⋅ + ⋅ ⋅ + +
(3.6)
2
( ) ( )2 11 ( ) ( ) ( )
( ) 2 ( )
k p lm k s lm k lms lc lm p dc p dc s
k p dc k s dc k lr
T T T T T TNP P I R R
T T N T T T T
+ + + = − ⋅ ⋅ + ⋅ ⋅ ⋅ + + + (3.7)
8 No-load core loss data in this research does not need temperature adjustment 9 Assumed the waveform is not distorted in the values used
19
2
2
( ) ( )2 1( ) ( ) ( )
( ) 2 ( )
2
( ) ( )2 11 ( ) ( ) ( )
( ) 2 ( )
lc e s
k p lr k s lrlm p dc p dc s
k p dc k s dc
k p lm k s lmlc lm p dc p dc s
k p dc k s dc
P P P
T T T TNI R R
T T N T T
T T T TNP I R R
T T N T T
= +
+ + = ⋅ ⋅ + ⋅ ⋅ + +
+ + + − ⋅ ⋅ + ⋅ ⋅ + +
k lm
k lr
T T
T T
+ ⋅ +
(3.8)
Equation (3.6) for ohmic losses is based on the D.C. resistances of the primary
(Rdc(p)) and the secondary (Rdc(s)) coils. It also includes the turns ratio of primary to
secondary (N1/N2), and the temperature adjustments. The critical temperatures (Tk) of the
primary winding material (Tk(p)) and secondary winding material (Tk(s)) are 225°C for
aluminum and 234.5°C for copper. The temperature at the time the load loss is measured
(Tlm) and the temperature at the time the D.C. resistances are measured (Tdc) are also
included, in addition to the current in the primary (Ilm(p)) and the temperature to correct
the load loss to (Tlr). The data in this research utilizes transformers where the primary
and secondary windings are made of the same material. This assumption simplifies
Equation (3.6) into Equation (3.9). The form of Equation (3.9) clarifies the relationship
between the overall transformer energy loss and the ohmic based power loss of the
primary and secondary coils as well as the temperature correction factor.
2
2 1( ) ( ) ( )
2
2
2 2 1( ) ( ) ( ) ( )
2
2 2( ) ( ) ( ) ( )
k lre lm p dc p dc s
k dc
k lrlm p dc p lm p dc s
k dc
k lrlm p dc p lm s dc s
k dc
T TNP I R R
N T T
T TNI R I R
N T T
T TI R I R
T T
+ = ⋅ + ⋅ ⋅ +
+ = ⋅ + ⋅ ⋅ ⋅ +
+ = ⋅ + ⋅ ⋅ +
(3.9)
Consequently, the temperature correction factor for ohmic losses (TCorrOhmic) is
expressed in Equation (3.10).
k lrCorrOhmic
k dc
T TT
T T
+= +
(3.10)
Stray losses are typically determined by measuring the total coil losses and
subtracting the ohmic losses as identified in Equation (3.7). Consequently, the
20
temperature correction factor for stray losses (TCorrStray) can be expressed as a
multiplicative factor in Equation (3.11).
k lmCorrStray
k lr
T TT
T T
+= +
(3.11)
Typical data available usually provides total load losses, which includes both
ohmic and stray losses. The temperature correction factors for ohmic and stray losses are
different as is evident in Equations (3.10) and (3.11). This research utilizes a common
estimate that stray losses are 10% of the coil losses and ohmic losses are 90% of the coil
losses. Given that the load losses are the sum of ohmic and stray losses, the temperature
adjusted losses will be calculated according to Equation (3.12).
( )
2
90% 10%
90% 10%
lc e s
CoilLoss CorrCoil CoilLoss CorrOhmic CoilLoss CorrStray
CoilLoss CorrCoil CorrOhmic CorrStray CoilLoss
P P P
P T P T P T
P T T T P
= +
⋅ = ⋅ ⋅ + ⋅ ⋅
⋅ = ⋅ + ⋅ ⋅
(3.12)
Consequently, the coil loss temperature correction factor can be estimated by
Equation (3.13).
90% 10%
90% 10%
CorrCoil CorrOhmic CorrStray
k lr k lm
k dc k lr
T T T
T T T T
T T T T
= ⋅ + ⋅
+ += ⋅ + ⋅ + +
(3.13)
The temperature correction factor formulas can be used to translate data from one
temperature reference to another temperature reference.
The formulae for transformer efficiency Equations (3.1), (3.2) and (3.13) will be
used in the remainder of this research. Additionally, the corrected total power loss,
Equation (3.3), will be approximated by Equation (3.14) based on the evaluation of, and
assumptions associated with, Equations (3.4) through (3.12).
2ts CoreLoss CorrCoil CoilLossP P T P L= + ⋅ ⋅ (3.14)
21
3.1.2 Transformer coil temperature calculation
The rulemaking established a reference temperature of 75°C at a coil load level of
35%. This research evaluates losses and efficiencies at load levels in addition to 35%
from no load to full load and, accordingly, a relationship between temperature and load is
formulated to allow the application of the temperature correction factor at each point the
losses and/or efficiencies are calculated.
Figure 3.1 presents three possible temperature models. One establishes a point at
55°C and a linear approximation from 0°C at 0% load and a 150°C at100% load10, with
the point at 55°C based on the government rulemaking of 75°C less an ambient of 20°C
which is indicative of a 55°C transformer temperature rise. Another method establishes a
linear approximation from 0°C at 0% load to 150°C at 100% load, again spanning the
temperature rise of the transformer. The third model approximates the temperature based
on prorated input power. This model recognizes a relationship between the power
coursing through the transformer at that load level and the temperature rise. It is
calculated based on the total input power11. Figure 3.1 illustrates the reasonably linear
approximation of each method. Figure 3.2 magnifies the portion of the models at the
DOE reference temperature.
10 150°C is the standard temperature rise of a standard transformer 11 Rated output power and losses at the specified load level
22
0
20
40
60
80
100
120
140
0%
5%
10
%
15
%
20
%
25
%
30
%
35
%
40
%
45
%
50
%
55
%
60
%
65
%
70
%
75
%
80
%
85
%
90
%
95
%
10
0%
Transformer Load
Tem
pe
ratu
re R
ise
55°C@35% Linear 150°C Rise Prorated Input Power
Fig. 3.1 Comparison of Coil Temperature Approximation Methods for a 150°C Rise Transformer
23
46
48
50
52
54
56
58
60
30
%
35
%
40
%
Transformer Load
Tem
per
atu
re R
ise
55°C@35% Linear 150°C Rise Prorated Input Power DOE
Fig. 3.2 Magnified View of the Comparison of Coil Temperature Approximation Methods for a 150°C Temperature Rise Transformer
Using these temperature approximation models at a 35% load, the first method
(aligned with methods that support the DOE rulemaking) is 55°C, the second method
(linear) is 52.5°C, and the third method (prorated power) is 51.8°C. Due to the similarity
in the methods and the simplification afforded by the second method, the author chose to
utilize the second method for approximating the temperature of the coils at various load
levels. Equation (3.15) defines this relationship as a proportion of the rated rise of the
transformer, TRatedRise, and Equation (3.16) solves for the transformer coil temperature
rise, TRise.
100%
Rise RatedRiseT T
L= (3.15)
Rise RatedRiseT L T= ⋅ (3.16)
24
Accordingly, the values of Tlr and Tlm can now be established at any load level per
Equations (3.17) and (3.18).
20lr Ambient Rise RiseT T T C T= + = ° + (3.17)
20lm Ambient RatedRise RatedRiseT T T C T= + = ° + (3.18)
3.1.3 Transformer temperature rises other than 150°C
Transformers are designed not to exceed a specified temperature rise at full load.
The most common temperature rise is 150°C. As observed in the previous section, the
rulemaking is consistent with a 150°C temperature rise. However, other temperature rise
requirements may be imposed by customers. Other temperature rises commonly include,
but are not limited to, a 115°C rise and an 80°C rise. The government rulemaking does
not adjust the 75°C temperature at 35% load for transformers with different temperature
rise requirements.
Figure 3.3 illustrates a linear relationship of temperature rise to load level for
common 80°C and 115°C rise transformers for comparison to the first model of section
3.1.2. Figure 3.4 magnifies Figure 3.3 near the 35% load level.
25
0
20
40
60
80
100
120
140
0%
5%
10
%
15
%
20
%
25
%
30
%
35
%
40
%
45
%
50
%
55
%
60
%
65
%
70
%
75
%
80
%
85
%
90
%
95
%
10
0%
Transformer Load
Te
mp
era
ture
Ris
e
DOE 150°C Rise (55°C@35%) Linear 115°C Rise Linear 80°C Rise
Fig. 3.3 Comparison of Coil Temperature Approximations for 150°C, 115°C, and 80°C Rise Transformers
26
20
25
30
35
40
45
50
55
60
30
%
35
%
40
%
Transformer Load
Tem
per
atu
re R
ise
DOE 150°C Rise (55°C@35%) Linear 115°C Rise Linear 80°C Rise
Fig. 3.4 Magnified View of the Comparison of Coil Temperature Approximations for 150°C, 115°C, and 80°C Rise Transformers
A linear approximation of the temperature rise of an 80°C rise transformer at 35%
load is 28°C. The government rulemaking requires that the efficiency be evaluated at
35% load at 75°C 12. This disparity should be investigated in further rulemakings as it
implies that an 80°C rise transformer will rise 55°C at 35% load instead of 28°C.
This remainder of this research will focus on data for 150°C rise transformers and
recommends that DOE further re-evaluate calculation of operating temperature in future
rulemakings.
12 A 20°C ambient and a 55°C rise
27
3.2 Impact of Temperature Correction on Transformer Efficiency
Figure 3.5 illustrates the impact of the temperature correction factor on
representations of transformer efficiency. If transformer efficiency is calculated using
full load loss values and adjusted for load level without adjusting for temperature, the
implication is that the transformer coils maintain the 170°C 13 across the load range of
the transformer. In other words, the transformer stays at a constant 170°C. This curve is
represented in Figure 3.5 and indicates that energy efficiency is understated. Similarly, if
one approximates the operating temperature at 72.5°C 14 across the load range, as
represented in Figure 3.5, the efficiency is overstated at higher load levels.
Figure 3.5 also plots the efficiencies for losses which are adjusted for temperature
across the load range. For accurate efficiency determinations or loss calculations, it is
necessary to utilize a temperature adjustment method across the load range.
13 150°C rise over a 20°C ambient 14 52.5°C rise over a 20°C ambient using the linear approximation of the previous section at a 35% load
28
95.00%
95.50%
96.00%
96.50%
97.00%
97.50%
98.00%
98.50%
99.00%
0% 5% 10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
Transformer Load
Effi
cie
ncy
170°C Losses 72.5°C Losses Temperature Adjusted Losses
Fig. 3.5 Impact of Temperature Correction on Transformer Efficiency assuming Two Different Load-Independent Operating Temperatures compared to a Simple Temperature
Adjusted Model that Exhibits more Realistic Behavior
29
3.3 Design Considerations
As indicated earlier, design engineers and manufacturers have various materials
and processes available to accommodate various customer requirements. As a result,
multiple compliant designs may be available and used in trade studies for design
selection. Figure 3.6 identifies some of the requirements that may be imposed on
transformer designs.
Voltages Temperature RiseSize (kVA)
Operating Hum (Sound Level)
TypicalTransformerRequirements
Ambient Temperature
Winding Material Enclosure
Tap Configuration
Temperature Sensors
Shields
Fig. 3.6 Typical Categories of System Level Transformer Requirements
Typical transformer design variables available to a design engineer are listed in
Figure 3.7.
30
Cooling DuctsPrimary
ConductorsCore Material
Core Height
TypicalDesign Variables
Secondary Conductors
Core Width Coil Length
Core ThicknessManufacturing
Processes# of Turns per
Winding
Volts per Turn
Temperature Sensors
Fig. 3.7 Typical Design Variables Available to Transformer Designers
Design engineers often employ trade studies to choose between multiple designs
that meet the transformer requirements. Those trade studies may include the criteria
noted in Figure 3.8.
31
Energy Efficiency ScheduleProduct Cost
WeightTypical
Trade Study Criteria
Special Mfg Processes
Material Inventory
Customized Parts
ReliabilityEquipment Resources
Manpower Resources
Temperature Sensors
Fig. 3.8 Typical Trade Study Criteria used to Optimize Transformer Design
The trade study criteria and weighting of these criteria to select among multiple
candidate designs is not regulated. As such, manufacturers may choose designs to
improve competitiveness or increase profitability, even though these design approaches
may be counter to the emphasis on energy efficiency. Stated differently, each design may
meet minimum efficiency requirements, but a manufacturer has the option to choose a
design from the trade space which may be less efficient than another for a specific
application.
3.4 Design Trade Space
A focus of this research is to ascertain whether changes to the energy efficiency
requirements are appropriate for reducing energy losses. Accordingly, these
recommendations may serve to reduce the number of design options to be evaluated in a
manufacturer’s trade study. To test additional energy efficiency calculation methods,
three designs will be chosen and applied to the calculation methods presented in the next
chapter.
32
Design data was obtained from a prominent manufacturer15 in the U.S. of low
voltage, dry type, distribution transformers for basic 75kVA transformers built using
aluminum coils and a temperature rise requirement of 150°C. The no-load core loss and
full load coil loss data was obtained for 25 different combinations of input and output
voltages16. This data is plotted in a scatter diagram in Figure 3.9 comparing core and coil
loss data. The mathematical averages of the core losses and the coil losses is also
represented in addition to a “best-fit” line through the data17.
266, 2553.84
2000
2100
2200
2300
2400
2500
2600
2700
2800
2900
3000
230 240 250 260 270 280 290 300
Core Loss (No Load)
Coi
l Lo
ss (
Fu
ll Lo
ad)
Mfr Designs Average of Mfr Designs Best Fit Line of Mfr Designs
Fig. 3.9 Twenty Five Designs for Aluminum, 150°C Rise, 75kVA Transformers of Various Voltages or other Requirements
15 Schneider Electric (Square D brand) 16 Input voltages from 208 Delta to 480 Delta, and output voltages from 208 Wye/120 to 480 Wye/277 17 The “best fit” line is based on the least squares method
Design A
Design B
Design C
33
Three designs were chosen from this data set for further evaluation. The chosen
designs were the designs with the lowest core loss, the highest core loss, and the point
represented by the computed averages. The data for these designs are listed in Table 3.1.
Table 3.1
Losses for Designs Selected for Efficiency Calculation Comparisons
Type of Loss Design A Design B Design C
Core Loss (VA) (no load) 238 266 297
Coil Loss (VA) (full load) 2997 2554 2203
Computing the transformer efficiency of each of these designs across the load
range with temperature correction yields the curves in Figure 3.10.
34
SinglePtReqmt
95.50%
96.00%
96.50%
97.00%
97.50%
98.00%
98.50%
0%
5%
10
%
15
%
20
%
25
%
30
%
35
%
40
%
45
%
50
%
55
%
60
%
65
%
70
%
75
%
80
%
85
%
90
%
95
%
10
0%
Transformer Load
Eff
icie
ncy
Design A Design B Design C
Fig. 3.10 Efficiency Curves for Designs Selected for Efficiency Calculation Comparisons
Although these designs yield similar efficiency characteristics at approximately
32% load and meet the regulated efficiency at 35% load, they vary significantly at low
loads and high loads. Design A transformers with low core losses and high load losses
perform better at low loads. Design C transformers with high core losses and low load
losses perform better at high loads. If these designs had represented the options for one
set of transformer requirements, the manufacturer can select the design of their choice
according to their trade study criteria and decisions.
The three designs selected are based on data from one manufacturer using the
materials and processes they have established. Presumably a wider variation of designs,
in terms of core and load losses and therefore efficiency curves, is available by
considering the collective data from other manufacturers. Additionally, more options
may be available with further adjustment of manufacturer processes and materials. The
35
three designs selected will be considered representative of the trade space for 75kVA
transformers with aluminum windings and a 150°C rise and applied to the energy
efficiency calculation methods presented in the next chapter.
36
4. ENERGY EFFICIENCY CALCULATION METHODS
Design and manufacturing flexibility exists that can significantly affect the
efficiency of transformers across the load range, thus various energy efficiency
calculation methods are proposed to allow further control of the efficiency across the load
range. The methods considered are termed herein as Single Point, Multi-Point,
Composite, and Dual Criteria.
Of primary interest is the capability for an energy efficiency calculation method to
discern between design alternatives. Methods which discern between design alternatives
in the trade space present an opportunity for the DOE to implement an energy efficiency
calculation method which impacts design selection to improve the energy efficiency of
transformers. The designs represented in Table 3.1 and Figure 3.10 are used as a
reference set to test the calculation methods. Of secondary interest is the simplicity of a
method to be implemented in rulemakings across the range of transformer power levels
(kVA’s) 18 and the ability to interpolate between stated power levels for a power level not
specified in a rulemaking.
4.1 Single Point Efficiency Calculation Method
The existing rulemaking for transformer efficiency is based on a single point
energy efficiency calculation. It specifies the efficiency of a transformer at one point on
the load curve, specifically 35%. In the previous chapter we explored the inability of this
method to distinguish between a reference set of design alternatives. All of the designs
18 See Table 2.2
37
represented in Figure 3.9 satisfied the current rulemaking, yet with significantly different
efficiency variations across the load range as was illustrated in Figure 3.10.
The representation of required efficiencies across the power range is relatively
simplistic and represented in Table 2.2. The ability to interpolate for power levels not
stated in the rulemaking is also relatively simplistic by utilization of a simple linear
interpolation method on adjacent values as represented in Equation (4.1) where ηx is the
desired efficiency at a power level of Pwrx based on adjacent values in the table with “a”
representing the point above and “b” representing the point below.
x b x b
a b a b
Pwr Pwr
Pwr Pwr
η ηη η
− −=
− − (4.1)
Accordingly for example, a 60kVA transformer would require an efficiency of 97.9%.
As referenced earlier, NEMA had prepared guidelines for transformer energy
efficiency which were eventually utilized by the DOE in establishing the current
rulemaking. Late in 2010, NEMA prepared new guidelines regarding a “Premium 30”
[10] category of transformer with higher energy efficiencies, but continues to utilize a
single point method for calculating energy efficiency19.
4.2 Multi-Point Efficiency Calculation Method
A multiple point efficiency standard can be considered by establishing minimum
efficiencies at several specific load values. For example, Figure 4.1 illustrates a multi-
point efficiency criteria of 96.0% efficiency at 10% loading, 98.0% efficiency at 40%
loading, and 97.0% efficiency at 90% loading, as compared to the single point method
which would only specify efficiency at 35%. This multi-point method clearly
differentiates the design alternatives and, in this example, suggests that Design C would
provide the most efficient alternative for transformers that are routinely loaded at greater
than 35%.
19 NEMA members choosing to include “Premium 30” transformers in their product offering certify that the “Premium 30” transformers operate with 30% less power loss at a 35% load than required by the current rulemaking and are thereby a higher efficiency transformer
38
95.50%
96.00%
96.50%
97.00%
97.50%
98.00%
98.50%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
Transformer Load
Effi
cien
cy
Design A Design B Design C MultiPtReqmt SinglePtReqmt
Fig. 4.1 Illustration of the Multi-Point Energy Efficiency Calculation Method
Applying this efficiency scenario of 96%@10% load, 98%@40% load, and
97%@90% load to the trade space of 25 transformer designs of Figure 3.9 reveals that
Design C does not quite meet the requirements20. One design that did qualify is
illustrated in Figure 4.2.
20 Design C failed by only 0.01% at the 10% load level
39
266, 2553.84
2000
2100
2200
2300
2400
2500
2600
2700
2800
2900
3000
230 240 250 260 270 280 290 300
Core Loss (No Load)
Coi
l Lo
ss (
Fu
ll Lo
ad)
Mfr Designs Average of Mfr Designs Best Fit Line of Mfr Designs
Fig. 4.2 Solution Set for Multi-Point Method Efficiency Criteria of 96%@10% Load, 98%@40% Load, and 97%@90% Load
This method is sensitive to the criteria that are chosen. Table 4.1 identifies the
temperature adjusted efficiencies at each load level for each of the 25 designs and
indicates the ten which are acceptable if the criteria is changed slightly to 96.8% (instead
of 97%) at a 90% load. Figure 4.3 identifies the qualifying designs.
Qualifying Design
40
Table 4.1 Efficiencies Calculated for a Multi-Point Method with Efficiency Criteria of 96%@10%
Load, 98%@40% Load and 96.8%@90% Load
10% 40% 90% 10% 40% 90%
96.0% 98.0% 96.8%Acceptable?96.35% 98.01% 96.68% 1 1 096.46% 98.09% 96.82% 1 1 1 OK96.39% 97.99% 96.58% 1 0 096.45% 98.06% 96.73% 1 1 096.65% 97.94% 96.30% 1 0 096.39% 98.00% 96.62% 1 1 096.22% 98.08% 96.94% 1 1 1 OK95.99% 98.08% 97.08% 0 1 196.30% 98.04% 96.79% 1 1 096.08% 98.12% 97.13% 1 1 1 OK96.01% 98.03% 96.92% 1 1 1 OK96.29% 98.01% 96.71% 1 1 096.41% 98.11% 96.89% 1 1 1 OK96.12% 98.04% 96.89% 1 1 1 OK96.38% 97.94% 96.46% 1 0 096.49% 98.04% 96.66% 1 1 096.52% 98.00% 96.55% 1 1 096.36% 98.07% 96.81% 1 1 1 OK96.63% 97.96% 96.37% 1 0 096.13% 98.03% 96.84% 1 1 1 OK96.42% 98.07% 96.79% 1 1 096.23% 98.06% 96.88% 1 1 1 OK96.52% 98.05% 96.67% 1 1 096.39% 98.00% 96.62% 1 1 096.35% 98.07% 96.84% 1 1 1 OK
Load LevelEfficiency @
Load Level Load Level
Required Efficiency
41
266, 2553.84
2000
2100
2200
2300
2400
2500
2600
2700
2800
2900
3000
230 240 250 260 270 280 290 300
Core Loss (No Load)
Coi
l Lo
ss (
Fu
ll Lo
ad)
Mfr Designs Average of Mfr Designs Best Fit Line of Mfr Designs
Fig. 4.3 Solution Set for Multi-Point Method Efficiency Criteria of 96%@10% Load, 98%@40% Load, and 96.8%@90% Load
Regarding the secondary point of interest with respect to the simplicity of
implementing the method in a rulemaking across the power range, the existing single
point method is compared to the multi-point method in Table 4.2. The values used for
Table 4.2 were selected for representation purposes only. Detailed analysis is necessary
to arrive at the appropriate values, which would involve both the analysis of the industry
design trade space and an analysis to determine the emphasis of a new method (for
example, towards Design A or Design C?).
Qualifying Designs
Qualifying Designs
Qualifying Designs
42
Table 4.2 Comparison of the Implementation of the Single Point and Multi-Point Methods of
Specifying Transformer Efficiency
kVA @35% Load kVA @10% Load @40% Load @90% Load15 97.7 15 95.7 97.7 96.525 98.0 25 96.0 98.0 96.8
37.5 98.2 37.5 96.2 98.2 97.050 98.3 50 96.3 98.3 97.175 98.5 75 96.5 98.5 97.3100 98.6 100 96.6 98.6 97.4167 98.7 167 96.7 98.7 97.5250 98.8 250 96.8 98.8 97.6333 98.9 333 96.9 98.9 97.7
kVA @35% Load kVA @10% Load @40% Load @90% Load15 97.0 15 95.0 97.0 95.830 97.5 30 95.5 97.5 96.345 97.7 45 95.7 97.7 96.575 98.0 75 96.0 98.0 96.8
112.5 98.2 112.5 96.2 98.2 97.0150 98.3 150 96.3 98.3 97.1225 98.5 225 96.5 98.5 97.3300 98.6 300 96.6 98.6 97.4500 98.7 500 96.7 98.7 97.5750 98.8 750 96.8 98.8 97.61000 98.9 1000 96.9 98.9 97.7
Three Phase Efficiency %
Implementation of the Multi-Point Method
Three Phase Efficiency %
Single Phase Efficiency % Single Phase Efficiency %
Implementation of the Single Point Method
The ability to interpolate for power levels not stated in the rulemaking remains
relatively simplistic using a simple interpolation method on adjacent values as
represented in Equation (4.1), but the efficiency needs to be calculated for each reference
load. The overall representation of the Multi-Point method in a rulemaking is similar to
the existing method. The difficulty of using this method is in the measurement and data
collection, rather than the representation and applicability of the method in a rulemaking.
43
4.3 Composite Efficiency Calculation Method
A composite efficiency method is similar to the multi-point efficiency method
given that efficiencies are computed at specific reference points, but the requirement is
based on a composite weighted average rather than mandating the efficiency at each
point. This can be represented as shown in Equation (4.2).
% % %comp a b cx y zη η η η= ⋅ + ⋅ + ⋅ (4.2)
The values of x, y, and z are weighting factors applied to the efficiencies
calculated at load levels a%, b%, and c%. For each power level, only the composite
efficiency, ηcomp, is specified. For example, the rulemaking could require that all power
levels are evaluated with Equation (4.3).
10% 40% 90%.20 .65 .15compη η η η= ⋅ + ⋅ + ⋅ (4.3)
This method provides for evaluation of efficiency at multiple load levels, like the
multi-point method, with the simplicity of a single efficiency requirement, like the single
point method, and the simple interpolation of a single reference point, like the single
point method.
The California Energy Commission [11] utilizes a composite efficiency method
for establishing the requirements for inverters (converting D.C. solar energy to A.C.) For
reference, their composite efficiency is represented in Equation (4.4).
. 10% 20% 30% 50% 75% 100%.04 .05 .12 .21 .53 .05CEC inverterη η η η η η η= ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ (4.4)
A variety of composite cases were created to test this method. Each composite
case, named CC##, establishes the values of x, y, z, a%, b%, and c% for Equation (4.2) as
applied to the reference data of Table 3.1. An initial set of 19 composite cases were
considered. Following review of the 19 composite cases, 51 additional cases were
evaluated. These 70 cases utilized a%, b%, and c% of 10%, 40%, and 90%. The
analyses of these 70 cases were then repeated using 20%, 40%, and 80% for a%, b%, and
c%.
The 140 composite cases are identified and reviewed in Appendix A. Whereas
the data suggests that composite case CC43 may be an option for a two-point composite
method for evaluating efficiency, a simple test suggests otherwise. The composite case
44
sought to discriminate between Designs B and C, but as acknowledged in the Appendix,
the sample trade space of designs has a fundamental bias at a 35% load level due to the
existing need to satisfy the current DOE rulemaking. Table 4.3 introduces the test case,
Test 1, which mathematically achieves the same composite efficiency using case CC43.
Table 4.3
Composite Case CC43 Test Case
Design B (VA)
Design C (VA)
Test 1 (VA)
Core Loss 266 297 375 Load Loss 2554 2203 2100
Load Temperature Corrected Load Loss (VA)
40% 335.085 289.034 275.52 90% 2006.68 1730.9 1649.97
Efficiency 40% 98.04% 98.08% 97.88% 90% 96.74% 97.08% 97.09%
Composite Efficiency CC43 96.81% 97.13% 97.13%
Figure 4.4 graphs the efficiency of the Design B, Design C, and Test 1. Case
CC43 uses the efficiencies at 40% and 90% load levels to calculate the composite
efficiency. Also depicted in Figure 4.4 is the current DOE rulemaking of 98% at a 35%
load. With the high weighting of 0.95 at the 90% load level, the Test 1 test case can
satisfy CC43 but obviously underperform across the majority of the load range.
45
95.50%
96.00%
96.50%
97.00%
97.50%
98.00%
98.50%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100
%
Transformer Load
Eff
icie
ncy
Design B Design C Test 1 CC43 Load Levels Current DOE
Fig. 4.4 Composite Case CC43 Test Case Efficiency Curve
Review of the 140 composite cases tested on this data suggests that this method is
a significantly less viable approach than originally conceived. Further evaluation of this
method is summarily dismissed due to its inability to adequately discriminate between
designs.
4.4 Dual Criteria Efficiency Calculation Method
In addition to the single point, multi-point, and the composite efficiency methods,
a dual criteria method can be considered. Recognizing that transformer efficiency is
directly related to input power and output power, and that output power is directly related
to input power and power losses, as noted in Equations (2.3) and (3.1) , one can choose to
establish a method which directly involves power loss. Three Approaches for dual
criteria methods are noted in Table 4.4.
46
Table 4.4 Approaches for Dual Criteria Methods
Minimum
Efficiency Maximum Core Loss
Maximum Load Loss
Approach A ● ●
Approach B ● ●
Approach C ● ●
Table 4.4 defines a set of approaches to specifying transformer efficiencies that
establishes maximum component losses to meet proposed efficiency requirements.
Utilizing a dual criteria to specify transformer efficiency, Approach A specifies the
maximum core loss and minimum efficiency to control the number of acceptable design
options. Similarly, dual criteria Approach B and Approach C can also be used to limit
the number of acceptable design options. The overall purpose is not to control the
number of design options, it is to reduce the trade space of design options to achieve
selected efficiency profiles that will reduce energy loss under operational conditions. For
example, Design A has lower core losses and better efficiencies at lower load levels.
Conversely, Design C has lower load losses and better efficiencies at higher load levels.
Establishing permissive values, such as a maximum core loss of 300VA or
maximum load loss of 3000VA will not provide a method of discriminating between the
efficiency curves illustrated in Figure 3.9. Rather, restrictive values of a maximum core
loss of 260VA with a 98% efficiency at a load of 35% (Approach A), or a maximum load
loss of 2500VA with a 98% efficiency at a load of 35% (Approach B), or a maximum
core loss of 265VA with a maximum load loss of 2550VA (Approach C), can be used to
discriminate between design options. Using these specific examples on the data set of 25
design options represented in Figure 3.9, Approach A yields eight solutions, Approach B
yields 11 solutions, and Approach C yields four solutions. These selection results are
illustrated in Figures 4.5, 4.6, and 4.7.
47
266, 2553.84
2000
2100
2200
2300
2400
2500
2600
2700
2800
2900
3000
230 240 250 260 270 280 290 300
Core Loss (No Load)
Coi
l Lo
ss (
Fu
ll Lo
ad)
Mfr Designs Average of Mfr Designs Best Fit Line of Mfr Designs
Fig. 4.5 Solution Set for a Dual Criteria Method using Approach A’s Method of Specifying Transformer Efficiency
Qualifying Designs
48
266, 2553.84
2000
2100
2200
2300
2400
2500
2600
2700
2800
2900
3000
230 240 250 260 270 280 290 300
Core Loss (No Load)
Coi
l Lo
ss (
Fu
ll Lo
ad)
Mfr Designs Average of Mfr Designs Best Fit Line of Mfr Designs
Fig. 4.6 Solution Set for a Dual Criteria Method using Approach B’s Method of Specifying Transformer Efficiency
Qualifying Designs Qualifying
Designs
49
266, 2553.84
2000
2100
2200
2300
2400
2500
2600
2700
2800
2900
3000
230 240 250 260 270 280 290 300
Core Loss (No Load)
Coi
l Lo
ss (
Fu
ll Lo
ad)
Mfr Designs Average of Mfr Designs Best Fit Line of Mfr Designs
Fig. 4.7 Solution Set for a Dual Criteria Method using Approach C’s Method of Specifying Transformer Efficiency
Figure 4.8 illustrates one solution from Approach C which utilizes a core loss of
261VA and a load loss of 2422VA such that the efficiency of the selected transformer is
above average across the load range.
Qualifying Designs
50
95.50%
96.00%
96.50%
97.00%
97.50%
98.00%
98.50%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100
%
Transformer Load
Eff
icie
ncy
Design A Design B (Ave) Design C Approach C
Fig. 4.8 Efficiency Curve representing One Solution for a Dual Criteria Method of Specifying Transformer Efficiency using Approach C
It is not appropriate to conclude that Approach C is a better method for improving
efficiency. Approaches A, B, and C will all exert more control over the solution space
than the single point method if properly specified, and in so doing, influence the
efficiency of the transformer based on the criteria utilized.
Regarding the secondary point of interest which is the simplicity of implementing
the method in a rulemaking across the power range, the existing single point method is
compared to the dual criteria method in Table 4.5. The values used for Table 4.5 were
selected for representation purposes only. Detailed analysis is necessary to arrive at the
appropriate values, which would involve both the analysis of the industry design trade
space and an analysis to determine the emphasis of a new method (for example, towards
Design A or Design C?).
51
Table 4.5 Comparison of the Implementation of the Single Point and Dual Criteria Methods
Implementation of the Single Point Method
Implementation of the Dual Criteria Method
Single Phase Efficiency % Single Phase
kVA @35% Load kVA Efficiency @35% Load
Maximum Core Loss @No-Load
15 97.7 15 97.7 200.0
25 98.0 25 98.0 260.0
37.5 98.2 37.5 98.2 380.0
50 98.3 50 98.3 500.0
75 98.5 75 98.5 650.0
100 98.6 100 98.6 900.0
167 98.7 167 98.7 1300.0
250 98.8 250 98.8 1900.0
333 98.9 333 98.9 2200.0
Three Phase Efficiency % Three Phase
kVA @35% Load kVA Efficiency @35% Load
Maximum Core Loss @No-Load
15 97.0 15 97.0 100.0
30 97.5 30 97.5 150.0
45 97.7 45 97.7 200.0
75 98.0 75 98.0 260.0
112.5 98.2 112.5 98.2 380.0
150 98.3 150 98.3 500.0
225 98.5 225 98.5 650.0
300 98.6 300 98.6 900.0
500 98.7 500 98.7 1300.0
750 98.8 750 98.8 1900.0
1000 98.9 1000 98.9 2200.0
The ability to interpolate between power levels not stated in a rulemaking remains
relatively simplistic and relies on a simple interpolation method between adjacent values
as represented in Equation (4.1), but needs to be calculated for each criterion that is
specified.
52
4.5 Evaluation of Energy Efficiency Calculation Methods
Four methods of calculating energy efficiency have been evaluated in this
analysis. The single point method is currently utilized by the rulemaking and is
satisfactory for maintaining the efficiency at the specified load level of 35%. To exercise
further control over the efficiency of transformers at other load levels requires the
utilization of other criteria. The multi-point method allows a clear and consistent
definition. The composite method is inadequate as investigated herein. The dual criteria
method may use one of various approaches, any of which are adequate for exercising
further control on design selection. As with the current single point method, both the
multi-point and dual criteria methods can be easily represented in a rulemaking and can
utilize standard linear interpolation methods for power levels not specifically identified in
a rulemaking.
Before defining specific details of an energy efficiency calculation method, it is
important to determine the objectives of establishing a new method. Given that the
overall objective is to reduce energy consumption, and understanding that the energy
efficiency of transformers is linked to core losses and load losses, it is necessary to define
the specific load level(s) at which transformers typically operate to maximize the energy
savings.
53
5. TRANSFORMER LOAD LEVELS
The efficiency of transformers is affected by loading. As noted in the previous
chapters, Federal rulemaking establishes a single point criterion for evaluating the energy
efficiency of low voltage dry type transformers. The government assesses efficiency for a
35% load at 75°C, which provides transformer designers and manufacturers, flexibility in
determining the transformer efficiency at other load levels. Other methods of calculating
energy efficiency were evaluated in the previous chapter to further constrain the
transformer efficiency over the range of potential loads. Before further consideration is
given to alternative efficiency calculation methods, it is appropriate to determine typical
transformer load levels to provide appropriate discrimination between design alternatives.
This chapter will explore the basis for the current federal rulemaking, other load level
research, typical power data, and transformer load profiles.
5.1 Basis for the Current Federal Rulemaking
The current Federal rulemaking establishes a load level of 35%. The Federal
rulemaking itself does not explain the selection for the 35% load level, but does reference
[2, subpart 196 (a)] a source of NEMA TP-1-2002 [12] which was developed by the
NEMA Transformer Products Section which was comprised of 21 members at the time
(in 2002). The NEMA TP 1 document [12] does not provide any insight into the
establishment of a load level of 35%.
It is likely that the 35% load requirement originated in an Oak Ridge National
Laboratory report [13] that was prepared in response to NEMA TP 1-1996, a predecessor
to NEMA TP 1-2002. The supplementary report indicated a lack of data for transformer
loading levels, but suggested that most low voltage dry type transformers have a peak
54
load of 50-60% of their rated capacity and that an average load of 35% was a “reasonable
assumption.” This report utilized NEMA base cases, and, although admitting a lack of
data, suggested that the 35% load levels were “not inconsistent with the available data.”
5.2 Existing Load Level Research
Internet searches were unsuccessful for data specific to the loads experienced by
low voltage transformers. Instead of low voltage data, general power utilization data is
available which is typically generated by utility companies and is appropriate to medium
voltage distribution transformers. Discussion with Phil Hopkinson, Power Transformer
Consultant [14] and Chairperson of the IEEE Distribution Transformer Energy Efficiency
Task Force, who was a participant in the aforementioned NEMA and Oak Ridge studies,
has indicated that recent data is not available for load levels of low voltage distribution
transformers.
In 1999, The Cadmus Group, Inc. prepared a study [15] which specifically
focused on low voltage dry-type distribution transformer load levels. The study
monitored 89 transformers in 43 different buildings in the northeast, taking measurements
every 10 minutes continuously for a two week period, and concluded that the average
load experienced was 16%. The study also reports that the transformers exceeded a 50%
load only 3% of the time. Discussion with David Korn, Principal of The Cadmus Group,
Inc., indicated the NEMA load level of 35% was based only on day time spot metering in
one DOE facility. He also indicated that The Cadmus Group did additional work in a
DOE building in the D.C. area with nearly identical results to the earlier Cadmus study
(<20% load).
Although the NEMA and Cadmus Group studies have apparently significantly
different results, they may indeed be compatible. The Cadmus Group study reports a
load of 16% as an average load over daytime, nighttime, and weekend hours. If the
NEMA data represented daytime loads only, it is possible to construct a compatible
scenario as shown in Equation 5.1 which suggests a daytime load of 35% for 5 days a
week with 10% nighttime and weekend loads.
55
( ) 10 4
9 15 2435% 10% 10 10% 4
16.7%
Daytime Nighttime WeekendAveLoad Load Load days Load days
hrs hrs hrsAveLoad days days
day day day
AveLoad
= + ⋅ + ⋅
= ⋅ + ⋅ ⋅ + ⋅ ⋅
=
(5.1)
Although this construct appears to reconcile the NEMA and Cadmus studies, it is
merely a hypothesis21. While technology has been available to collect and monitor low
voltage transformer loads, it has not been applied to characterize regional, daily, weekly
and seasonal loading patterns. It is clear that there is a need for additional data regarding
load levels for low voltage dry-type transformers in order to optimize the regulations for
transformer energy savings.
5.3 Schneider Electric Power Data
Schneider Electric, a global specialist in energy management, is also a leading
manufacturer of low voltage, dry-type, distribution transformers in the U.S. and has
successfully implemented energy conservation measures in its facilities. As part of the
process, power monitoring equipment was installed in some of their facilities throughout
North America which captures data every 15 minutes, 24 hours a day. This data
collection rate yields 35,040 data points per year per meter. Since this was part of a total
energy conservation initiative of Schneider Electric facilities, these meters were not
specifically placed on the load side of low voltage transformers. Similarly, since the
initiative focused on facility power and primary subfeeds at major manufacturing sites,
the meter data may more closely align with medium voltage distribution transformers
rather than low voltage transformers that are distributed at the facilities.
Schneider Electric did provide the author with access to the 2010 data for the U.S.
facilities to evaluate trends in actual overall power data which may mirror trends in low
voltage transformer data. The volumes of data available from the 88 meters are not
included in this report. The author selected four meters from the last week of January
21 Although it is possible to discuss an Average Load to convey a sense of typical load level, it is not appropriate to use an average load calculated in this manner to calculate the power losses due to the I2R nature of the power loss curve
56
and the last week of July to illustrate the daily, weekly, and seasonal variations at four
locations in the country as shown in Figures 5.1 through 5.4.
In comparing these figures, it is obvious that there are daily, weekly and seasonal
periodicities. The period of reduced usage at nighttime is dependent on the number and
length of shift operations. For example, the Indiana facility was operating two extended
major shifts Monday through Thursday, two shorter major shifts on Friday, and shorter
minor shifts on Saturday and Sunday. Accordingly, the Indiana facility experiences
fewer hours of nighttime load levels than the others represented here. Weekday and
weekend variations are more apparent in the North Carolina and Tennessee facilities.
Although there are significant variations in the Indiana facility between January and July
usage, it is more significant in the Tennessee and Texas facilities. (These could be
explained by summer time requirements for air conditioning.) Also noted are the similar
nighttime seasonal load levels in both the Indiana and Texas facilities.
57
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Last Week of the Month (Jan25-Jan31, and Jul26-Aug01)
Ap
par
ent P
ow
er (
kVA
)
Indiana facility Jan Indiana facility July
Fig. 5.1 Daily, Weekly, and Seasonal Power Variations at a Schneider Electric Facility in Indiana
58
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Last Week of the Month (Jan25-Jan31, and Jul26-Aug01)
App
aren
t P
ower
(kV
A)
North Carolina facility Jan North Carolina facility July
Fig. 5.2 Daily, Weekly, and Seasonal Power Variations at a Schneider Electric Facility in North Carolina
59
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Last Week of the Month (Jan25-Jan31, and Jul26-Aug01)
App
aren
t Po
we
r (k
VA
)
Tennessee facility Jan Tennessee facility July
Fig. 5.3 Daily, Weekly, and Seasonal Power Variations at a Schneider Electric Facility in Tennessee
60
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Last Week of the Month (Jan25-Jan31, and Jul26-Aug01)
App
aren
t P
ower
(kV
A)
Texas facility Jan Texas facility July
Fig. 5.4 Daily, Weekly, and Seasonal Power Variations at a Schneider Electric Facility in Texas
5.4 Typical Power Data
Typical power data available is often expressed as an amount of power used,
rather than as a percentage of the rated supply power. Figures 5.1 through 5.4 reflect the
dynamic amount of power used throughout the day, week, and seasons. However the
data does not reference the associated transformer loading. Using the power data content
of Figure 5.4 as a reference, Figure 5.5 illustrates this issue. One can approximate the
summer daytime load at 430kVA, but is the 430kVA supplied by a 500kVA, 750kVA, or
1000kVA transformer, and thus, does it represent a summer daytime load of 86%, 57%,
or 43% respectively?
61
0
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00:
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Last Week of the Month (Jan25-Jan31, and Jul26-Aug01)
App
aren
t P
ower
(kV
A)
Texas facility Jan Texas facility July
Fig. 5.5 Typical Power Data cannot be used to determine Transformer Load Levels
Typical power data may also include reference to the power factor, which by
definition is the ratio of real power to apparent power. Apparent power is the absolute
value of complex power, which is the vector sum of real power and reactive power. Real
power is the component of power that actually performs work, the useful power, and is
rated in watts or kilowatts. Reactive power is the power, rated in kVAR, required to
overcome the inductive and capacitive dynamics of an A.C. circuit, but does not provide
useful power to the load. Figure 5.6 illustrates that apparent power is a sum vector of real
and reactive power. Accordingly, transformers are rated in terms of apparent power,
kVA, which is the total power necessary to provide the power to overcome the capacitive
and inductive losses (reactive power) to provide the useful power (real power). The
power factor, being the ratio of real power to apparent power, is always less than or equal
to one. The power is one for a resistive load without a reactive component. Reactive
loads such as elevators with inductive motors can be characterized by much lower power
factors.
What is the % load of rated load?
Is this 86%, 57%, or 43% load?
Is this 42%, 28%, or 21% load?
Is this 10%, 7%, or 5% load?
62
Apparent Power = |Complex Power|Complex Power (kVA)
Total power required.Reactive Power (kVAR)Due to system capacitance and inductance.
Real Power (kW)Does work.
Power Factor = Real Power / Apparent Power
Fig. 5.6 Vector Representation of Real Power, Apparent Power, and Power Factor
The transformer load level, is the load level at which the transformer is operating
as a ratio to the rated load of the transformer. Figure 5.7 extends the model of Figure 5.6
to illustrate the capacity or rated load of a transformer. Figure 5.8 illustrates the effect of
a dynamically changing reactive power in a circuit on the vector diagrams. A
transformer with a rated load that experiences a reduction in reactive power while
maintaining a constant real power to the transformer load yields an increased or improved
power factor and a reduction in apparent power which is a reduction in load level on the
transformer.
63
TransformerRated Power Level
OperatingLoad Level
kVA kVAR
kW
Fig. 5.7 Transformer Operating Load Level will Increase if there is a Reactive Component to the Load
kVA kVAR
kW
Same Rated Power Level
Reduced Reactive Power
Same Real Power & increased Power Factor
Lower Apparent Power required & transformer load level is reduced
Fig 5.8 Vector Illustration of how Reducing the Reactive Load will Reduce the Transformer Load Level and Increase the Power Factor
As a sidebar, Figure 5.9 is presented which illustrates the power factor based on
the data received for the Texas facility. One can observe similar daytime and nighttime
patterns in the graphs. Since the power factor increases during the daytime in this
dataset, one can assume that daily activities rely on a proportionally higher level of
resistive devices as compared to night time uses of energy that rely on inductive devices.
64
0.500
0.600
0.700
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0.900
1.000
Mo
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:00
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:00
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n 12
:00
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n 18
:00
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06:
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12:
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18:
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00
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:00
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:00
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00
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Mo
n 00
:00
Last Week of the Month (Jan25-Jan31, and Jul26-Aug01)
Pow
er F
acto
r
Texas facility Jan Texas facility Jan
Fig. 5.9 Daily, Weekly, and Seasonal Power Factor Variations at a Schneider Electric Facility in Texas
5.5 Transformer Load Profile
Returning to the daily, weekly, and seasonal variations in power utilization
illustrated in Figures 5.1 through 5.5, it can be concluded that the relationship between
the transformer load profiles associated with this type of power data is unknowable
without reference to the rated power level of the transformers used to supply this power.
However, casual observation of Figures 5.1 through 5.4 do suggest a dynamically
changing transformer load profile. Figure 5.10 represents a simplified model of a typical
weekday or weekend and illustrates a summer and winter season.
65
100%Summer Day Load Rate
??% Summer Night Load RateWinter Day Load Rate
??% Winter Night Load Rate
??%
??%
??%
??%
??%
??%
??%
0%
0:00
2:00
4:00
6:00
8:00
10:0
0
12:0
0
14:0
0
16:0
0
18:0
0
20:0
0
22:0
0
0:00
2:00
4:00
6:00
8:00
Day Duration
Night Duration
Tra
nsfo
rmer
Loa
d Le
vel
Time of Day
Fig. 5.10 Illustration of Load Level Terminology
For a typical week, there are four transformer load levels corresponding to the
business week daytime load, the business week nighttime load, the weekend daytime
load, and the weekend nighttime load. Additionally, there are corresponding loads for
each season to model. Hence, in a two season model there are eight transformer load
levels, and in a four season model there are 16 transformer load levels.
The current DOE rulemaking specifies transformer efficiency at a 35% load level.
Given the potential for numerous load levels by considering daily, weekly, and seasonal
variations, it is hard to assess the relevance of the 35% load level. In the absence of a
comprehensive data set, sample scenarios can be constructed to constrain the applicability
of the 35% load level specified in the Federal rulemakings. The scenarios depicted in
Figures 5.11 through 5.14 are based upon review of the Schneider Electric data of Figures
5.1 through 5.4 and are based on the assumption that the data is representative of a low
voltage distribution transformer. In Figures 5.11 through 5.14 the scenarios are based on
assumptions that the summer daytime load rate is 80%, 60%, 50%, 35%, 25%, or 15% of
the rated transformer output with the weekend and night time loads being extrapolated
from the corresponding summer daytime load level.
66
0%
10%
20%
30%
40%
50%
60%
70%
80%
80% 60% 50% 35% 25% 15%
Transformer Load Period Using Assumed Summer Weekday Load Rate
Tra
nsf
orm
er L
oad
Le
vel
Summer Weekday Load Rate Summer Weeknight Load Rate Summer Weekend Day Load Rate
Summer Weekend Night Load RateWinter Weekday Load Rate Winter Weeknight Load Rate
Winter Weekend Day Load Rate Winter Weekend Night Load Rate
Fig. 5.11 Transformer Load Profile Scenarios based on the Schneider Electric Indiana Facility using an Assumed Summer Weekday Load and Calculated Transformer Power
Output
35% DOE Load Level
67
0%
10%
20%
30%
40%
50%
60%
70%
80%
80% 60% 50% 35% 25% 15%
Transformer Load Period Using Assumed Summer Weekday Load Rate
Tra
nsf
orm
er L
oad
Lev
el
Summer Weekday Load Rate Summer Weeknight Load Rate Summer Weekend Day Load Rate
Summer Weekend Night Load RateWinter Weekday Load Rate Winter Weeknight Load Rate
Winter Weekend Day Load Rate Winter Weekend Night Load Rate
Fig. 5.12 Transformer Load Profile Scenarios based on the Schneider Electric North Carolina Facility using an Assumed Summer Weekday Load and Calculated Transformer
Power Output
35%DOE Load Level
68
0%
10%
20%
30%
40%
50%
60%
70%
80%
80% 60% 50% 35% 25% 15%
Transformer Load Period Using Assumed Summer Weekday Load Rate
Tra
nsfo
rmer
Loa
d L
evel
Summer Weekday Load Rate Summer Weeknight Load Rate Summer Weekend Day Load Rate
Summer Weekend Night Load RateWinter Weekday Load Rate Winter Weeknight Load Rate
Winter Weekend Day Load Rate Winter Weekend Night Load Rate
Fig. 5.13 Transformer Load Profile Scenarios based on the Schneider Electric Tennessee Facility using an Assumed Summer Weekday Load and Calculated Transformer Power
Output
35%DOE Load Level
69
0%
10%
20%
30%
40%
50%
60%
70%
80%
80% 60% 50% 35% 25% 15%
Transformer Load Period Using Assumed Summer Weekday Load Rate
Tra
nsfo
rmer
Loa
d L
evel
Summer Weekday Load Rate Summer Weeknight Load Rate Summer Weekend Day Load Rate
Summer Weekend Night Load RateWinter Weekday Load Rate Winter Weeknight Load Rate
Winter Weekend Day Load Rate Winter Weekend Night Load Rate
Fig. 5.14 Transformer Load Profile Scenarios based on the Schneider Electric Texas Facility using an Assumed Summer Weekday Load and Calculated Transformer Power
Output
It is appropriate to consider the observations from the daily, weekly and seasonal
variability that were illustrated in Figures 5.1 through 5.4, and Figures 5.11 through 5.14,
in the context of the load-dependent, transformer loss curve illustrated in Figure 2.4. If a
typical 12 hour daytime load is 80% and a typical 12-hour nighttime load is 20%, the
average load may be considered 50% and one can discuss the “average” load as 50%.
However the value of 50% cannot be used to properly evaluate transformer losses since
the relationship between transformer losses and loading is non-linear. Thus, the loss
averaged at 80% load and 20% load may not correspond to the loss at 50% load. For
example, Figure 2.4 illustrates 350VA losses at 20% load and 1750VA losses at 80%
load for an average of 1050VA losses. 1050 VA loss corresponds to approximately 60%
load , not 50% load; the “50% average” corresponds to roughly 875VA in losses.
Consequently, a more detailed loss analysis needs to be utilized to determine the actual
losses rather than averages of loading percentages as represented in Equation (5.1).
35%DOE Load Level
70
One can deduce from Figures 5.11 through 5.14 that the DOE’s 35% load level
may be high. These figures also indicate that it is important to obtain accurate data for
low voltage distribution transformer loading levels. Generalizing from this data,
efficiency calculation methods should be selected to improve transformer efficiency at
lower load levels. Multi-point and dual criteria efficiency calculation methodologies both
permit the development of energy efficiency specifications to minimize the total power
loss of transformers.
71
6. TRANSFORMERS AS PART OF A SYSTEM
Low voltage dry type distribution transformers are an integral part of the
distribution and voltage/current transformation of electrical power to, and within,
commercial and industrial facilities. Once installed, they are often overlooked and taken
for granted as they typically require no maintenance. Various considerations affect the
load levels typically experienced by the transformers, such as application (i.e., powering
HVAC, manufacturing equipment, commercial lighting and/or elevators). These
considerations determine their actual energy efficiency. Selected considerations are
noted in this chapter.
6.1 Transformer Capacity
Transformers generally are capable of operating beyond their rated capacity for
short periods of time. To be safe, they should not be operated to temperature levels
beyond the limits of their insulation system. For example, a transformer may be rated for
a 150°C temperature rise above a 40°C ambient and utilize a UL approved insulation
system rated to 220°C which results in a thermal margin of 30°C. The main consequence
of routinely operating transformers beyond their ratings is accelerating the deterioration
of the insulation, and ultimately, reducing their operational life.
6.2 Transformer Operational Life
Transformers do not have moving parts or power switches, and, according to the
general rule of thumb, they are expected to have an operational life of 30 years. They sit
quietly (figuratively speaking) and perform their intended purpose without interruption
72
for many years. Because a transformer is a 30-year investment, it is plausible that
transformers are “oversized” to allow for future growth opportunities. Oversizing, or
installing a larger than necessary transformer, will ensure a lower load level on the
transformer until such time when expansion projects do require additional capacity.
6.3 National Electrical Code Recommendations for Sizing a Transformer
Distribution transformers are installed by qualified electricians in accordance with
local electrical codes. Typically, localities adopt the National Electrical Code (NEC) and
may add additional, more stringent, requirements for their locality. In the context of
transformers, review of the widely accepted National Electrical Code [16] provides
requirements related to the over current protection for transformers and panelboards and
the recommended process for specifying a transformer.
The maximum load on a transformer cannot be expected to exceed the level at
which circuit breakers or other over current protection devices will “trip”, or break the
circuit, to stop the flow of current. When over current protection is installed on both
sides of the transformer, protection on the secondary side is to be established at 125% of
the transformer’s secondary current rating, and the over current protection on the primary
side can be set as high as 250% of the primary current rating. When over current
protection is only installed on the primary side of a transformer, it is to be set at 125% of
the transformer’s primary current rating. Accordingly, a transformer’s over current
protection devices can easily allow operation at 100% of the transformer rating and still
allow short periods of higher, inrush current, that occur when high loads are switched into
a branch circuit that is powered by the transformer.
Determining the size of a transformer for a building load or branch circuit is based
on the expected load of the building or branch circuit. In simple terms, a transformer
should be able to provide at least as much current as the rated panelboard or load(s) that it
supplies. For example, a 400A panelboard will have over current protection that will trip
at 400A. Accordingly the transformer which feeds the panelboard should be capable of
at least 400A. The NEC prescribes requirements for the sizing of over current protection
73
as a function of expected continuous and non-continuous loads. For example, the over
current protection for an industrial feeder circuit is usually calculated as the sum of all of
the non-continuous loads, which assumes that they may all be switched in
simultaneously, plus 125% of the sum of the continuous loads. This sum of continuous
and non-continuous loads is then rounded up to the next standard size of over current
protection devices. This will result in a higher panelboard rating with an excess of 25%
margin in the expected loads. This will likely lead to selection of an oversized
transformer for the circuit in question. This, in turn, will lead to a transformer that will
nominally operate at a fairly low load level.
NonContinuousLoads∑
( ) 125%ContinuousLoads ⋅∑
IncreaseToNextStdPanelSize
Fig. 6.1 Illustration of NEC Requirements for Calculating the Size of an Industrial Feeder Circuit
6.4 Liability Inherent in Transformer Specification
Even though transformers are capable of operating at higher than their rated loads,
presumably most professionals, for liability reasons, will not recommend transformers
rated for less than the apparent load for which they supply. For example, an architect is
not likely to recommend a transformer rated at 350A to feed a 400A panelboard.
Intentionally undersizing a transformer raises liability concerns and presents a risk to the
Sum of all Noncontinuous Loads
Next Larger Panel Size
Sum of all Continuous Loads
Plus 25% of all Continuous Loads
Transformer sized as if everything is running at the same time.
Typical transformer load
74
architects and builders. Thus, it is common practice for architects and electricians to
recommend using the NEC recommendations for sizing transformers or adding additional
margin to the NEC recommendations.
6.5 Impact of Transformer Applications on their Load Levels
Low voltage, dry-type, distribution transformers are used for a wide range of
applications and are configured and specified to meet the requirements of those
applications. For example, a single transformer may be installed to provide power to the
main service panel for a building, such as a 480V, 600A panel, which could power a
small store or office. Alternately, transformers may be used within a facility to transform
voltages from major supply lines to other panels. For example, a transformer may be
dedicated to powering 277V commercial lighting circuits and thus, be specified to
transform from 480V delta power service to 480Y/277V suitable for commercial lighting
systems. Also, transformers may be utilized to provide dedicated power to industrial
equipment. For example, a metal press may require 415V at 120A which will likely
require a transformer to transform from 600V or 480V line voltage to 415V. Since low-
voltage, dry-type, distribution transformers typically do not provide integrated switches
to power them on and off, safety switches or large knife switches can be used to break the
power between a transformer and its supply or load.
Since power utilization has daily, weekly and seasonal periodicities, transformers
supplying power to facility service mains or panelboards within facilities also likely
experience load profiles similar to the ones presented in Chapter 5. Transformers
connected to industrial equipment may also exhibit similar daily, weekly, and possibly
seasonal variations. However, the more directly related a transformer is to its load, such
as a dedicated transformer feeding a specific set of industrial manufacturing equipment,
the more likely it is sized appropriately for the load. The load may still vary significantly
with repetitive press operations, with equipment on/off cycles, or with work shifts. In
some cases though, transformers may have a fairly consistent load if used to power
75
continuous equipment such as newspaper printing presses. In a scenario where the load
is well defined, transformers may be sized to run at higher load levels.
It is also worth noting that energy utilization in the workplace has been changing
with the introduction of new technology and government efficiency standards. For
example, commercial refrigeration is much more efficient than it was just a decade ago.
In the last two decades, hand cranked mills and lathes have been replaced by 5-axis
computer numerically controlled (CNC) mills. While desktop computer power
consumption is down, the number of computers and monitors in the work place has
proliferated. Large screen TVs instead of poster boards are now used to provide
information to employees. Thus it is more important than ever to characterize transformer
load levels.
Finally in typical applications, a panelboard’s over current protection does not trip
which indicates that the current levels do not reach the rated load of the panelboard, and
similarly they do not reach the rated load of the transformer. Thus, this sets an upper
bound on transformer load levels. The facility data provides evidence that the load
profiles of most transformers can be modeled using the modeling scheme proposed in
section 5.5 and illustrated in Figure 5.10. While actual data is needed to reveal the load
levels experienced by transformers in various applications, it is anticipated that the
majority of applications will involve significant variations in transformer load levels with
respect to time of day, day of the week, season and application.
6.6 Impact of Energy Conservation Initiatives on Transformer Loss
In recent years it has been common for facilities or companies to undertake
initiatives to reduce energy consumption. Companies may install higher efficiency
ballasts and bulbs, lighting occupancy sensors, adjust the thermostats, reduce heat or air
conditioning transfer through loading docks, install solar devices, install doors on
commercial freezers and refrigerators, etc. The net effect of nearly all of these initiatives
is a reduction in the electrical usage. Typically these actions directly reduce the
transformer load level. Depending on the load levels experienced by a transformer, it
76
likely pushes the transformers into a less efficient operating range which reduces the
effectiveness of the energy savings measures. For example, if a company decides to turn
off lights at night, the loading of the transformer may drop from 15% to 5%. Due to the
dominance of core losses at low load levels, the transformer efficiency might be 95%
with a 15% load and drop to 45% at a 5% load, thereby significantly counteracting the
electric savings. As was discussed in Chapter 2, the core losses which are independent of
load are used to magnetize the core, thus at load levels below 10%, transformers become
very inefficient.
77
7. RECOMMENDATIONS
Various observations were noted throughout this research that represents viable
opportunities to develop rulemakings and improve design practices that can increase
energy efficiency. This chapter collects, identifies, develops and offers a comprehensive
list of opportunities as recommendations that could ultimately improve the energy
efficiency of commercial buildings utilizing dry-type, low voltage distribution
transformers.
7.1 Recommendations for Improving Energy Efficiency
1. Obtain Load Profile Data
a. There is a critical need for a contemporary data set that would allow the
loads experienced by low voltage, dry type distribution transformers to be
characterized. The analysis of resulting load profiles for various classes of
customers and transformer applications is needed to search for
commonality in profiles to optimize the national efficiency objectives.
The technology is available to monitor and record the input and output
power of transformers and to correlate it to the transformer ratings. The
DOE should sponsor an initiative to collect multi-year, high temporal
resolution load data for low voltage, dry-type transformers to support
optimization of future rulemakings for transformer efficiency standards.
78
b. The availability of transformer load profile data could spur development
of a more detailed loss analysis model to determine actual losses over time
rather than utilizing averages of loading percentages.
2. Revise Efficiency Calculation Criteria
a. As discussed in chapter four, the current rulemaking that mandates
efficiency be specified at a 35% load specification needs to be revised to
incorporate a multiple point or dual point criteria for calculating
efficiency. This will optimize the reduction of energy losses over a larger
range of transformer loads.
b. Implementation of a dual point or multi-point criteria for specifying
energy efficiency should include an assessment of the impact of these
types of specifications on the design trade space used to tailor
transformers to the needs of specific applications, such as applications that
require the transformer emit low noise, produce low stray fields, or
moderate the temperature rise with load.
3. Incorporate Temperature Rise Modeling
a. The current rulemaking establishes a reference of 75°C at 35% load. This
temperature specification is reasonable for a transformer rated for a 150°C
rise. However, it is not practical to assume a transformer rated with a
maximum rise of 80°C will rise 55°C, or 68% of full temperature rise,
when operating at 35% of rated capacity. Updating the rulemaking to use
a linear interpolation or extrapolation from the specification temperature
to approximate the actual transformer temperature will improve the
appropriateness of the rulemaking to low-rise transformers.
79
4. Establish Transformer Load Classes
a. It is anticipated that load data results from Recommendation 1 will affirm
typical low voltage, dry type transformers generally operate at loading
levels below 35% and that the criteria for efficiency calculations methods
referenced in Recommendation 2 should be biased for energy efficiency
for loads that are less than 35%. These criteria should be defined in
rulemakings as a “Low Load Class”.
b. The DOE should consider establishing a rulemaking to improve the energy
efficiency of a “High Load Class” of transformers used in high load
applications such as powering continuously operating equipment.
5. Avoid Over-Sizing of Transformers
a. The DOE and professional and trade organizations should provide general
awareness and education to consumers, consultants, and contractors that
specifying transformers using large power margins is wasteful. Energy
loss could be reduced if architectural practices and codes encouraged the
allocation of space and/or accommodations within facilities to allow
upgrading the electrical distribution with additional transformer(s) when
power needs grow rather than specifying an over-sized transformer at the
outset.
b. Additionally when transformers near the end of their useful life, the
circuits and loads they serve should be characterized to provide data to
ensure that replacement transformers are properly sized.
80
c. Similarly, since panelboard sizes are often directly related to transformer
sizes, panelboards should be loaded to safe maximum levels, rather than
selected for excess capacity that may or may not be required at a future
date.
6. Conserve Energy During “Off Hours”
a. In applications where there is no power utilization during off hours, such
as transformers that feed manufacturing equipment, architectural practices
and codes should encourage the implementation and use of switchgear to
de-energize (“turn off”) transformers to eliminate energy consumption by
the core.
b. Commercial facilities should be architected to provide electrical layouts
that allow main transformers to be disabled during “off-shifts”. Utilize
small transformers to power circuits required to provide for “24/7” service
such as maintenance lighting, emergency lighting, security systems and air
circulators.
7. Include Transformers when Evaluating Energy Conservation Initiatives
a. Companies, organizations, consultants and architects should consider the
efficiency of transformers for the reduction of energy savings when
evaluating energy conservation measures. Specifically, when transformers
operate at less than 10% load, their efficiency drops precipitately reducing
the energy savings associated with load reductions. Thus, considering
transformer loads will allow companies to choose reduction strategies that
will maximize the benefit of energy saving investments.
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7.2 Recommendations for Further Study
In addition to the need for commercial and industrial load data, the underlying
data for much of the analysis in this thesis relied on 75kVA-class transformers designed
and manufactured by Schneider Electric. The results of this study can be strengthened by
obtaining and analyzing a wider range of design data for transformers built by multiple
manufacturers.
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8. SUMMARY AND CONCLUSIONS
Improvement in the energy efficiency of low voltage, dry type, distribution
transformers has a multiplicative effect on total energy savings. Current rulemaking
provides a minimum standard for manufacturers, which has been in effect since 2007.
This study examined the energy efficiency regulations that govern the measurement and
specification of energy efficiency for low voltage, dry type, distribution transformers and
made recommendations to improve and further optimize the rulemaking used to certify
the transformer efficiency to meet national energy efficiency objectives.
This thesis documents how the current energy efficiency rulemaking specifying
transformer efficiency at only one point on the load curve does not provide the expected
energy savings and that alternate methods of specifying efficiency are available that
could reduce transformer energy loss. Secondly, this thesis provides data and analysis
that demonstrates that additional energy savings can be achieved by considering
transformers and distribution networks as part of a system when evaluating or specifying
transformers for use in commercial and industrial facilities. Consideration of load
variability, methods used to determine power margins, implementation of line-side
switchgear, and future expansion plans could improve selection of a transformer that
minimizes wasted energy. These results led to a series of recommendations for
improving transformer standards and designs that could realize greater energy savings in
commercial and industrial facilities.
As the demand for electricity increases every year, improvement in transformer
efficiency and the way transformers are implemented at the point of use will be
increasingly important in conserving energy. Numerous recommendations have been
proposed to further refine this study and to improve energy efficiency by acknowledging
the impact of developer, contractor and user decisions which can decrease energy losses
83
in typical power systems through informed design and operations. Additional research
regarding the load profiles of low voltage, dry type transformers will confirm and
optimize criteria for specifying transformer efficiency and maximize energy savings. The
DOE has an opportunity to improve the energy efficiency of transformers and reduce the
nation’s energy usage without inconvenience to users.
LIST OF REFERENCES
84
LIST OF REFERENCES
[1] EIA Annual Energy Review 2009. Report # DOE/EIA-0384(2009). 19 Aug 2010. U.S. Energy Information Administration. [On-line] 29 Jan 2011 Electricity/Electricity Flow 2009 <http://www.eia.doe.gov/emeu/aer/pdf/pages/sec8_3.pdf>
[2] Code of Federal Regulations, Title 10, Chapter II, Part 431, Subpart K. 64 FR 54141, 05 Oct 1999. 29 Jan 2011.
[3] EIA Annual Energy Outlook 2010 with Projections to 2035. Report # DOE/EIA-0383(2010). 11 May 2010. U.S. Energy Information Administration. [On-line] 28 Nov 2010 Electricity Projections <http://www.eia.doe.gov/oiaf/aeo/electricity.html>
[4] EIA Energy Explained, Your Guide To Understanding Energy. 01 Oct 2009. U.S. Energy Information Administration. [On-line] 28 Nov 2010 Secondary Sources/Electricity/Use of Electricity <http://tonto.eia.doe.gov/energyexplained/index.cfm?page=electricity_use>
[5] What You Need to Know About Energy. Board on Energy and Environmental Systems (BEES). 2008 The National Academies Press. [On-line] 31 Jan 2011. Pg 8. <http://www.nap.edu/openbook.php?record_id=12204&page=8>
[6] DOE Energy Efficiency & Renewable Energy, Building Technologies Program, Appliances & Commercial Equipment, About Standards. DOE Mandatory Energy Conservation Standards. 27 Jun 2008. U.S. Department of Energy. [On-line] 29 Nov 2010 <http://www1.eere.energy.gov/buildings/appliance_standards/ about_standards.html>
[7] Federal Register Volume 75, page 56796. 16 Sep 2010. U.S. Department of Energy
[8] Low Voltage Dry Type Distribution Transformer Efficiency Standards. 10 CFR Part 431, 431.196. [On-line] 02 Feb 2011. <http://ecfr.gpoaccess.gov>
85
[9] Schneider-Electric Energy Efficient Transformer Technical Data. Data Bulletin 7400DB0702R07/09. Jul 2009. Schneider-Electric. [On-line] 29 Nov 2010. Pg 4, 480D-208Y Aluminum and 150°C rise. <http://products.schneider-electric.us/support/technical-library/?event=detail&oid=09008926803e354e&cat= 0b008926801a1545>
[10] NEMA Premium Efficiency Transformers Program. 2010. National Electrical Manufacturers Association. [On-line] 19 Feb 2011. <http://www.nema.org/prod/pwr/trans/transformersProgram.cfm>
[11] California Energy Commission Emerging Renewables Program. CEC-300-2006-001-ED8F-CMF, Eighth Edition. Dec 2006. California Energy Commission. [On-line] 29 Nov 2010 <http://www.energy.ca.gov/2006publications/CEC-300-2006-001/CEC-300-2006-001-ED8F.PDF>
[12] NEMA Standards Publication TP 1-2002. 2002. National Electrical Manufacturers Association. [On-line] 12 Sep 2010. <http://www.nema.org/stds/tp1.cfm>
[13] Supplement to the “Determination Analysis” (ORNL-6847) and Analysis of the NEMA Efficiency Standard for Distribution Transformers. ORNL-6925. Sep 1997. Oak Ridge National Laboratory and Lockheed Martin Energy Research Corporation. [On-line] 29 Nov 2010. <http://www.ornl.gov/~webworks/cpr/v823/rpt/94260.pdf>
[14] Phil Hopkinson, CEO. HVOLT Inc. [On-line] 27 Feb 2011. <http://www.hvolt.com>
[15] Metered Load Factors for Low-Voltage, Dry-Type Transformers in Commercial, Industrial, and Public Buildings. 07Dec 1999. The Cadmus Group, Inc. [On-line] 15 Nov 2010. <http://www.cee1.org/ind/trnsfm/neep-rpt.pdf>
[16] NEC 2008 Handbook, 11th ed., National Fire Protection Association, Quincy, MA, 2008
APPENDIX
86
APPENDIX. EVALUATION OF THE COMPOSITE EFFICIENCY
CALCULATION METHOD OF DETERMINING THE ENERGY
EFFICIENCY OF A LOW VOLTAGE, DRY TYPE DISTRIBUTION
TRANSFORMER
A composite efficiency method is evaluated as a possible alternative to the single
point method currently used for determining the energy efficiency of low voltage, dry
type distribution transformers in the United States. In the composite efficiency method,
efficiencies are computed at specific reference points, but the requirement is based on a
composite calculation rather than an efficiency mandate at each point. This can be
represented as shown below.
% % %comp a b cx y zη η η η= ⋅ + ⋅ + ⋅
The values of x, y, and z are weighting factors applied to the efficiencies
calculated at load levels a%, b%, and c%. For each power level, only the composite
efficiency, ηcomp, is specified. The rulemaking could specify an equation to be applied to
all power levels as shown in the example that follows.
10% 40% 90%.20 .65 .15compη η η η= ⋅ + ⋅ + ⋅
This method provides for evaluation of efficiency at multiple load levels, like a
multi-point method, with the simplicity of a single efficiency requirement, like a single
point method, and the simple interpolation of a single reference point, like a single point
method.
A variety of composite cases were created to test the Composite Efficiency
Method. Each composite case, named CC##, establishes the values of x, y, z, a%, b%,
and c% as follows:
% % %comp a b cx y zη η η η= ⋅ + ⋅ + ⋅
87
The composite cases are applied to the temperature corrected efficiency reference
data of Table A.1.
Table A.1
Temperature Corrected Efficiency for Designs A, B, and C at Loads of 10%, 40% and 90%
Efficiency
Load Design A Design B Design C 10% 96.65% 96.34% 95.99% 40% 97.94% 98.04% 98.08% 90% 96.30% 96.74% 97.08%
The composite cases and composite efficiencies are shown in Table A.2. All of
the composite cases in Table A.2 utilize the load levels of 10%, 40%, and 90% (for a%,
b%, and c%). The weighting factors of x, y, and z are identified next to the case number.
To clarify the data represented in the table, explanations for one composite case,
CC03, are discussed. CC03 applies a weighting factor of 0.25 to the efficiency at a 10%
load, a weighting factor of 0.50 to the efficiency at a 40% load, and a weighting factor of
0.25 to the efficiency at a 90% load. The result of applying these weighting factors at the
corresponding loads to the efficiencies of Design A, as noted in Table A.1, is identified as
97.21% in the Design A column. Similarly, the composite efficiency results are shown
for Designs B and C. Typically the composite efficiency result for Design B falls in
between Design A and Design C. As such, the absolute value of the simple difference
between Design C and Design A composite efficiencies is presented in the last column.
88
Table A.2 Composite Cases CC01-CC70
Load Level and Weighting Composite Efficiency Design C
minus Design A
Case 10% 40% 90% Design A
Design B
Design C
CC01 0.33 0.34 0.33 96.97% 97.05% 97.06% 0.0905% CC02 0.30 0.40 0.30 97.06% 97.14% 97.16% 0.0954% CC03 0.25 0.50 0.25 97.21% 97.29% 97.31% 0.1036% CC04 0.20 0.60 0.20 97.35% 97.44% 97.47% 0.1118% CC05 0.15 0.70 0.15 97.50% 97.59% 97.62% 0.1200% CC06 0.10 0.80 0.10 97.65% 97.74% 97.77% 0.1282% CC07 0.05 0.90 0.05 97.79% 97.89% 97.93% 0.1364% CC08 0.40 0.30 0.30 96.93% 96.97% 96.95% 0.0152% CC09 0.50 0.25 0.25 96.88% 96.86% 96.79% -0.0968% CC10 0.60 0.20 0.20 96.84% 96.76% 96.63% -0.2089% CC11 0.70 0.15 0.15 96.79% 96.66% 96.47% -0.3209% CC12 0.80 0.10 0.10 96.74% 96.55% 96.31% -0.4330% CC13 0.90 0.05 0.05 96.69% 96.45% 96.15% -0.5451% CC14 0.30 0.30 0.40 96.90% 97.01% 97.06% 0.1592% CC15 0.25 0.25 0.50 96.80% 96.97% 97.06% 0.2631% CC16 0.20 0.20 0.60 96.70% 96.92% 97.06% 0.3669% CC17 0.15 0.15 0.70 96.60% 96.88% 97.07% 0.4708% CC18 0.10 0.10 0.80 96.50% 96.83% 97.07% 0.5746% CC19 0.05 0.05 0.90 96.40% 96.79% 97.08% 0.6785% CC20 0.50 0.50 0.00 97.29% 97.19% 97.04% -0.2562% CC21 0.40 0.60 0.00 97.42% 97.36% 97.25% -0.1761% CC22 0.30 0.70 0.00 97.55% 97.53% 97.46% -0.0959% CC23 0.25 0.75 0.00 97.62% 97.61% 97.56% -0.0558% CC24 0.20 0.80 0.00 97.68% 97.70% 97.67% -0.0157% CC25 0.15 0.85 0.00 97.75% 97.78% 97.77% 0.0244% CC26 0.10 0.90 0.00 97.81% 97.87% 97.87% 0.0645% CC27 0.05 0.95 0.00 97.87% 97.95% 97.98% 0.1046% CC28 0.50 0.50 0.00 97.29% 97.19% 97.04% -0.2562% CC29 0.60 0.40 0.00 97.16% 97.02% 96.83% -0.3364% CC30 0.70 0.30 0.00 97.03% 96.85% 96.62% -0.4166% CC31 0.75 0.25 0.00 96.97% 96.76% 96.51% -0.4567% CC32 0.80 0.20 0.00 96.91% 96.68% 96.41% -0.4968% CC33 0.85 0.15 0.00 96.84% 96.59% 96.30% -0.5369% CC34 0.90 0.10 0.00 96.78% 96.51% 96.20% -0.5769% CC35 0.95 0.05 0.00 96.71% 96.43% 96.09% -0.6170%
89
Table A.2 Composite Cases CC01-CC70
Load Level and Weighting Composite Efficiency Design C
minus Design A
Case 10% 40% 90% Design A
Design B
Design C
CC36 0.00 0.50 0.50 97.12% 97.39% 97.58% 0.4635% CC37 0.00 0.40 0.60 96.96% 97.26% 97.48% 0.5273% CC38 0.00 0.30 0.70 96.79% 97.13% 97.38% 0.5910% CC39 0.00 0.25 0.75 96.71% 97.07% 97.33% 0.6229% CC40 0.00 0.20 0.80 96.63% 97.00% 97.28% 0.6548% CC41 0.00 0.15 0.85 96.55% 96.94% 97.23% 0.6867% CC42 0.00 0.10 0.90 96.46% 96.87% 97.18% 0.7186% CC43 0.00 0.05 0.95 96.38% 96.81% 97.13% 0.7505% CC44 0.00 0.50 0.50 97.12% 97.39% 97.58% 0.4635% CC45 0.00 0.60 0.40 97.28% 97.52% 97.68% 0.3997% CC46 0.00 0.70 0.30 97.45% 97.65% 97.78% 0.3360% CC47 0.00 0.75 0.25 97.53% 97.71% 97.83% 0.3041% CC48 0.00 0.80 0.20 97.61% 97.78% 97.88% 0.2722% CC49 0.00 0.85 0.15 97.69% 97.84% 97.93% 0.2403% CC50 0.00 0.90 0.10 97.78% 97.91% 97.98% 0.2084% CC51 0.00 0.95 0.05 97.86% 97.97% 98.03% 0.1765% CC52 0.50 0.00 0.50 96.47% 96.54% 96.54% 0.0626% CC53 0.40 0.00 0.60 96.44% 96.58% 96.65% 0.2066% CC54 0.30 0.00 0.70 96.40% 96.62% 96.76% 0.3505% CC55 0.25 0.00 0.75 96.39% 96.64% 96.81% 0.4225% CC56 0.20 0.00 0.80 96.37% 96.66% 96.86% 0.4945% CC57 0.15 0.00 0.85 96.35% 96.68% 96.92% 0.5664% CC58 0.10 0.00 0.90 96.34% 96.70% 96.97% 0.6384% CC59 0.05 0.00 0.95 96.32% 96.72% 97.03% 0.7104% CC60 0.50 0.00 0.50 96.47% 96.54% 96.54% 0.0626% CC61 0.60 0.00 0.40 96.51% 96.50% 96.43% -0.0813% CC62 0.70 0.00 0.30 96.54% 96.46% 96.32% -0.2253% CC63 0.75 0.00 0.25 96.56% 96.44% 96.26% -0.2973% CC64 0.80 0.00 0.20 96.58% 96.42% 96.21% -0.3692% CC65 0.85 0.00 0.15 96.60% 96.40% 96.15% -0.4412% CC66 0.90 0.00 0.10 96.61% 96.38% 96.10% -0.5132% CC67 0.95 0.00 0.05 96.63% 96.36% 96.04% -0.5852% CC68 0.00 1.00 0.00 97.94% 98.04% 98.08% 0.1446% CC69 1.00 0.00 0.00 96.65% 96.34% 95.99% -0.6571% CC70 0.00 0.00 1.00 96.30% 96.74% 97.08% 0.7824%
90
Composite cases CC01 through CC07 illustrate a transition from nearly equal
weighting to heavily weighting the 40% load. Composite cases CC08 through CC13
transition to heavily weighting the 10% load. Composite cases CC14 through CC19
transition to heavily weighting the 90% load. The first seven cases only exhibit a spread
of 0.14% or less between the Design A and Design C results. In the first 13 cases, CC13
and CC19 show the most ability to discern between Design A and Design C. These two
cases share a high weighting of 0.90 for either the 10% or 90% loads and yields a spread
of 0.54% or 0.68%.
To apply the data of CC01 through CC19, if one chooses to favor a design with a
low core loss, a design with a higher efficiency at low load levels, composite case CC13
could be selected with a required minimum composite efficiency of 96.6% for example
which would exclude Designs B and C. Conversely, if one chooses to favor a design
with a high core loss, a design with a higher efficiency at high load levels, composite case
CC19 could be selected with a required minimum efficiency of 97.0% for example which
would exclude Designs A and B.
Given that the review of cases CC01 through CC19 suggested that a high
weighting of 90% be used to differentiate the data, the author chose to consider
composite cases bases on only two points rather than three yielding cases CC20 through
CC67. In a few instances the cases are identical, such as CC20 and CC28, but they each
represent the point of departure for a series. For comparison, cases CC68 through CC70
were included to represent composite cases based on one point (or hence the single point
method) for each load level. Each subset of cases involves a trend to more heavily
weight one loading level over the other.
Cases CC20 through CC27 more heavily weight the 40% loading level show little
promise of differentiating between Designs A and C. The other two subsets, CC28
through CC35, and CC36 through CC43, each illustrate a similar ability to differentiate
between designs regardless of the weighting factors. A commonality between cases
CC44 through CC51 is the utilization of the 40% load level as one of the two data
references in the composite. Reviewing the corrected efficiencies of the 40% load level
in Table A.1 and observing the characteristics of the utilization of the 40% load level in
91
the composites, it reveals a fundamental bias in the data which was derived from a trade
space of designs meeting a 98% energy efficiency rating at a 35% load level. However
this bias does not discredit the analysis since the intent was to differentiate between
designs which met that rating. This observation suggests, if this method is to be
considered, that further research will be necessary with designs not meeting the current
efficiency requirement. As in the three point analysis in cases CC01 through CC19, the
remaining cases of Table A.1 often indicate that the best discernment occurs when an
extreme weighting factor is used in the composite. Conversely, the subsets beginning at
CC20 and CC44 suggest that the more even weighting factors are more discerning than
the extreme weighting ones. As such, it is not clear that one approach is favorable.
To further explore this method, composite cases CC01 through CC70 were
subjected to loading levels of 20%, 40%, and 80% (instead of 10%, 40%, and 90%) to
create composite cases CC71 through CC140. Table A.3 lists the corrected efficiencies
and Table A.4 identifies the composite cases and resultant efficiencies.
Table A.3
Temperature Corrected Efficiency for Designs A, B, and C at Loads of 20%, 40% and 80%
Efficiency
Load Design A Design B Design C
20% 97.85% 97.75% 97.63% 40% 97.94% 98.04% 98.08% 80% 96.71% 97.08% 97.37%
92
Table A.4 Composite Cases CC71-CC140
Load Level and Weighting Composite Efficiency Design C
minus Design A
Case 20% 40% 80% Design A
Design B
Design C
CC71 0.33 0.34 0.33 97.50% 97.63% 97.70% 0.1934% CC72 0.30 0.40 0.30 97.54% 97.67% 97.73% 0.1890% CC73 0.25 0.50 0.25 97.61% 97.73% 97.79% 0.1816% CC74 0.20 0.60 0.20 97.67% 97.79% 97.85% 0.1742% CC75 0.15 0.70 0.15 97.74% 97.85% 97.91% 0.1668% CC76 0.10 0.80 0.10 97.81% 97.91% 97.97% 0.1594% CC77 0.05 0.90 0.05 97.87% 97.97% 98.03% 0.1520% CC78 0.40 0.30 0.30 97.53% 97.64% 97.69% 0.1525% CC79 0.50 0.25 0.25 97.59% 97.66% 97.68% 0.0904% CC80 0.60 0.20 0.20 97.64% 97.68% 97.67% 0.0284% CC81 0.70 0.15 0.15 97.69% 97.70% 97.66% -0.0337% CC82 0.80 0.10 0.10 97.74% 97.72% 97.65% -0.0958% CC83 0.90 0.05 0.05 97.79% 97.73% 97.64% -0.1579% CC84 0.30 0.30 0.40 97.42% 97.57% 97.66% 0.2402% CC85 0.25 0.25 0.50 97.30% 97.49% 97.61% 0.3097% CC86 0.20 0.20 0.60 97.18% 97.41% 97.56% 0.3792% CC87 0.15 0.15 0.70 97.06% 97.33% 97.51% 0.4486% CC88 0.10 0.10 0.80 96.95% 97.25% 97.46% 0.5181% CC89 0.05 0.05 0.90 96.83% 97.16% 97.42% 0.5876% CC90 0.50 0.50 0.00 97.89% 97.89% 97.85% -0.0377% CC91 0.40 0.60 0.00 97.90% 97.92% 97.90% -0.0012% CC92 0.30 0.70 0.00 97.91% 97.95% 97.95% 0.0353% CC93 0.25 0.75 0.00 97.92% 97.97% 97.97% 0.0535% CC94 0.20 0.80 0.00 97.92% 97.98% 97.99% 0.0717% CC95 0.15 0.85 0.00 97.93% 97.99% 98.02% 0.0900% CC96 0.10 0.90 0.00 97.93% 98.01% 98.04% 0.1082% CC97 0.05 0.95 0.00 97.93% 98.02% 98.06% 0.1264% CC98 0.50 0.50 0.00 97.89% 97.89% 97.85% -0.0377% CC99 0.60 0.40 0.00 97.88% 97.87% 97.81% -0.0741% CC100 0.70 0.30 0.00 97.87% 97.84% 97.76% -0.1106% CC101 0.75 0.25 0.00 97.87% 97.82% 97.74% -0.1288% CC102 0.80 0.20 0.00 97.86% 97.81% 97.72% -0.1471% CC103 0.85 0.15 0.00 97.86% 97.80% 97.69% -0.1653% CC104 0.90 0.10 0.00 97.85% 97.78% 97.67% -0.1835% CC105 0.95 0.05 0.00 97.85% 97.77% 97.65% -0.2018%
93
Table A.4 Composite Cases CC71-CC140
Load Level and Weighting Composite Efficiency Design C
minus Design A
Case 20% 40% 80% Design A
Design B
Design C
CC106 0.00 0.50 0.50 97.32% 97.56% 97.73% 0.4009% CC107 0.00 0.40 0.60 97.20% 97.46% 97.65% 0.4521% CC108 0.00 0.30 0.70 97.08% 97.37% 97.58% 0.5033% CC109 0.00 0.25 0.75 97.02% 97.32% 97.55% 0.5290% CC110 0.00 0.20 0.80 96.96% 97.27% 97.51% 0.5546% CC111 0.00 0.15 0.85 96.89% 97.23% 97.47% 0.5802% CC112 0.00 0.10 0.90 96.83% 97.18% 97.44% 0.6058% CC113 0.00 0.05 0.95 96.77% 97.13% 97.40% 0.6314% CC114 0.00 0.50 0.50 97.32% 97.56% 97.73% 0.4009% CC115 0.00 0.60 0.40 97.45% 97.65% 97.80% 0.3496% CC116 0.00 0.70 0.30 97.57% 97.75% 97.87% 0.2984% CC117 0.00 0.75 0.25 97.63% 97.80% 97.90% 0.2728% CC118 0.00 0.80 0.20 97.69% 97.85% 97.94% 0.2471% CC119 0.00 0.85 0.15 97.75% 97.89% 97.98% 0.2215% CC120 0.00 0.90 0.10 97.82% 97.94% 98.01% 0.1959% CC121 0.00 0.95 0.05 97.88% 97.99% 98.05% 0.1703% CC122 0.50 0.00 0.50 97.28% 97.42% 97.50% 0.2185% CC123 0.40 0.00 0.60 97.16% 97.35% 97.47% 0.3062% CC124 0.30 0.00 0.70 97.05% 97.28% 97.44% 0.3939% CC125 0.25 0.00 0.75 96.99% 97.25% 97.43% 0.4378% CC126 0.20 0.00 0.80 96.94% 97.22% 97.42% 0.4817% CC127 0.15 0.00 0.85 96.88% 97.18% 97.41% 0.5255% CC128 0.10 0.00 0.90 96.82% 97.15% 97.39% 0.5694% CC129 0.05 0.00 0.95 96.77% 97.12% 97.38% 0.6132% CC130 0.50 0.00 0.50 97.28% 97.42% 97.50% 0.2185% CC131 0.60 0.00 0.40 97.39% 97.49% 97.52% 0.1308% CC132 0.70 0.00 0.30 97.50% 97.55% 97.55% 0.0431% CC133 0.75 0.00 0.25 97.56% 97.59% 97.56% -0.0007% CC134 0.80 0.00 0.20 97.62% 97.62% 97.57% -0.0446% CC135 0.85 0.00 0.15 97.68% 97.65% 97.59% -0.0884% CC136 0.90 0.00 0.10 97.73% 97.69% 97.60% -0.1323% CC137 0.95 0.00 0.05 97.79% 97.72% 97.61% -0.1761% CC138 0.00 1.00 0.00 97.94% 98.04% 98.08% 0.1446% CC139 1.00 0.00 0.00 97.85% 97.75% 97.63% -0.2200% CC140 0.00 0.00 1.00 96.71% 97.08% 97.37% 0.6571%
94
Review of this data yields similar, but less consistent, results than the data of
Table A.2.
Figures A.1 and A.2 utilize bar charts to reflect the absolute value of the
difference between Design A and C efficiencies for each composite case.
95
0.0000% 0.1000% 0.2000% 0.3000% 0.4000% 0.5000% 0.6000% 0.7000% 0.8000%
CC01
CC04
CC07
CC10
CC13
CC16
CC19
CC22
CC25
CC28
CC31
CC34
CC37
CC40
CC43
CC46
CC49
CC52
CC55
CC58
CC61
CC64
CC67
CC70
Co
mp
osite
Cas
e
Composite Efficiency Difference between Designs A and C
Fig. A.1 Composite Cases CC01 through CC70, Efficiency Differences
96
0.0000% 0.1000% 0.2000% 0.3000% 0.4000% 0.5000% 0.6000% 0.7000% 0.8000%
CC71
CC74
CC77
CC80
CC83
CC86
CC89
CC92
CC95
CC98
CC101
CC104
CC107
CC110
CC113
CC116
CC119
CC122
CC125
CC128
CC131
CC134
CC137
CC140
Co
mp
osite
Cas
e
Composite Efficiency Difference between Designs A and C
Fig. A.2 Composite Cases CC71 through CC140, Efficiency Differences
97
Comparison of Figures A.1 and A.2 indicates that the 20%, 40%, and 80% loads
have lower differences, or abilities to discern, between the reference designs.
Figure A.1 suggests the most discriminating cases may be CC13, CC19, CC35,
CC43, CC59 and CC70. Figure A.2 suggests the most discriminating cases may be
CC89, CC113, CC129 and CC140. Table A.5 lists the discriminating cases side-by-side
to compare the weighting factors. As such, it is obvious that CC19 and CC89 share the
same weighting factors, and similarly CC43 and CC113, and CC59 and CC129, and
CC70 and CC140. In each of these cases the higher load level (90% or 80%) has a high
weighting factor (.90, .95, or 1.00). Cases CC13 and CC67 are discriminating cases for
one set of load levels, but not the other.
Table A.5
Comparing Discriminating Case Composite Weighting Factors
Load Level and Weighting Load Level and Weighting Case 10% 40% 90% Case 20% 40% 80% CC13 0.90 0.05 0.05 CC19 0.05 0.05 0.90 CC89 0.05 0.05 0.90 CC43 0.00 0.05 0.95 CC113 0.00 0.05 0.95 CC59 0.05 0.00 0.95 CC129 0.05 0.00 0.95 CC67 0.95 0.00 0.05 CC70 0.00 0.00 1.00 CC140 0.00 0.00 1.00
Table A.6 lists the composite efficiencies of the discriminating cases. It also
calculates the absolute value of the difference between Designs A and C to indicate a
relative strength of discrimination.
98
Table A.6 Discriminating Case Strength
Composite Efficiency
Case Design A Design B Design C |Design C
minus Design A|
CC13 96.695% 96.445% 96.149% 0.545% CC19 96.400% 96.787% 97.079% 0.678% CC43 96.383% 96.807% 97.133% 0.750% CC59 96.318% 96.723% 97.029% 0.710% CC67 96.630% 96.360% 96.045% 0.585% CC70 96.301% 96.743% 97.083% 0.782% CC89 96.828% 97.165% 97.416% 0.588% CC113 96.772% 97.131% 97.403% 0.631% CC129 96.767% 97.117% 97.380% 0.613% CC140 96.710% 97.083% 97.367% 0.657%
This analysis indicates that CC70 and CC43 provide the strongest levels of
discrimination. Case CC70 represents a single point method, so case CC43 will be
evaluated one step further. Whereas the data has suggested that composite case CC43
may be an option for a two point composite method for evaluating efficiency, a simple
test suggests otherwise. The composite case sought to discriminate between Designs B
and C, but as acknowledged earlier, the sample trade space of designs has a fundamental
bias at a 35% load level based on meeting the current DOE rulemaking. Table A.7
introduces a test case, Test 1, which mathematically achieves the same composite
efficiency using case CC43.
99
Table A.7 Composite Case CC43 Test Case
Design B
(VA) Design C
(VA) Test 1 (VA)
Core Loss 266 297 375 Load Loss 2554 2203 2100
Load Temperature Corrected Load Loss (VA)
40% 335.085 289.034 275.52 90% 2006.68 1730.9 1649.97
Efficiency 40% 98.04% 98.08% 97.88% 90% 96.74% 97.08% 97.09%
Composite Efficiency CC43 96.81% 97.13% 97.13%
Figure A.3 graphs the efficiency of the Design B, Design C, and Test1. Case
CC43 uses the efficiencies at 40% and 90% load levels to calculate the composite
efficiency. Also depicted in Figure A.3 is the current DOE rulemaking of 98% at a 35%
load. With the high weighting of 0.95 at the 90% load level, the Test 1 test case can
satisfy CC43 but obviously underperform across the majority of the load range.
100
95.50%
96.00%
96.50%
97.00%
97.50%
98.00%
98.50%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100
%
Transformer Load
Eff
icie
ncy
Design B Design C Test 1 CC43 Load Levels Current DOE
Fig. A.3 Composite Case CC43 Test Case Efficiency Curve
Review of the 140 composite cases tested on this data suggests that this method is
a significantly less viable approach than originally conceived. Furthermore, when
evaluating the two point composite cases, such as CC52 through CC67, it should be noted
that there is a fundamental bias in the original data since the efficiency of these
transformer designs already exceed 98.0% at a 35% load level. Further evaluation of this
method is summarily dismissed due to its inability to adequately discriminate between
designs.
