9-i

CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

9.1 INTRODUCTION ........................................................................................................... 9-1

9.2 MODEL OVERVIEW ..................................................................................................... 9-2

9.3 MODEL INPUTS ............................................................................................................ 9-4

9.3.1 Shipments Data ................................................................................................................ 9-4

9.3.2 Shipments Backcast ......................................................................................................... 9-6

9.3.3 Shipments Forecast .......................................................................................................... 9-7

9.3.4 Long-Term Purchase Elasticity ........................................................................................ 9-8

9.3.4.1 Elasticity Estimates for Liquid-Immersed and Dry-Type Transformers ....... 9-9

9.3.5 Liquid-Immersed and Dry-Type Market Shares .............................................................. 9-9

9.3.6 Stock Accounting ........................................................................................................... 9-10

9.3.7 Retirement Function....................................................................................................... 9-11

9.3.8 Refurbishments and Rewinds ........................................................................................ 9-13

9.3.9 Initial Stock .................................................................................................................... 9-13

9.3.10 Effective Date of Standard ............................................................................................. 9-14

9.3.11 Affected Stock ............................................................................................................... 9-14

9.4 RESULTS ...................................................................................................................... 9-14

LIST OF TABLES

Table 9.3.1 Distribution Transformer Shipment Estimates for 2009 ...................................... 9-5

Table 9.3.2 Liquid-Immersed Distribution Transformer Shipment Estimates, 2009 ............. 9-5

Table 9.3.3 Dry-Type, Medium-Voltage Distribution Transformer Shipment 

Estimates, 2009 .................................................................................................... 9-6

Table 9.4.1 Cumulative Shipments of Transformers by Candidate Standard Level 

(CSL), 2016 - 2045 ............................................................................................ 9-15

LIST OF FIGURE

Figure 9.2.1 Shipments Model Flowchart ................................................................................ 9-3

Figure 9.3.1 Fraction of Original Shipment Retiring ............................................................. 9-12
9-1

CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

The U.S. Department of Energy (DOE) analyzes shipments of affected products as a part of 

every rulemaking regarding new or amended energy efficiency standards for products that 

impact national energy use. Estimates of product shipments are a necessary input to calculating 

national energy savings (NES) and net present value (NPV) of the investment in a more efficient 

product; both of these calculations are required to analyze the impact of proposed new or 

amended energy efficiency standards. Shipments also are a necessary input to the manufacturer 

impact analysis (MIA), which DOE conducts to prepare its notice of proposed rulemaking 

(NOPR). The MIA estimates the impact of potential efficiency standards on manufacturers of the 

affected products, in this case distribution transformers, and assesses the direct impact of such 

standards on employment and manufacturing capacity. This chapter describes the method DOE

used to project annual shipments for liquid-immersed and dry-type distribution transformers 

under base- and standards-case efficiency levels and the results obtained. 

DOE developed a shipments model to predict shipments of distribution transformers. The 

shipments model provides an estimate of the rate at which an in-service stock of existing 

transformers may be replaced by new, more efficient transformers after the enactment of an 

energy conservation standard. The core of the shipments analysis is an accounting model that 

DOE developed to simulate how existing and future purchases are incorporated into an in-service 

stock of aging transformers that are gradually replaced. In estimating the effects of potential new 

standard levels on product shipments, the model accounts for the combined effects on the 

purchase decision of increases in purchase price, decreases in annual operating costs, and 

consumer income.

To estimate total product shipments, the model estimates shipments for specific market 

segments and then aggregates those results. DOE accounted for two market segments: (1) 

shipments to new construction; and (2) replacement shipments going into existing buildings. 

The shipments models are prepared as Microsoft Excel spreadsheets that are accessible 

on the Internet (http://www.eere.energy.gov/buildings/appliance_standards/). Appendix 10A 

discusses how to access the shipments model and other related spreadsheets and provides basic 

instructions for using them. The rest of this chapter explains the shipments model in more detail. 

Section 9.2 describes the methodology that underlies development of the model. Section 9.3 

describes the data inputs and model calibration, the effects on shipments of changes in purchase 

price, operating costs, and consumer income, and the affected stock of products. Section 9.4 

presents the model results for both liquid-immersed and dry-type distribution transformers for 

the seven efficiency levels that were identified as candidate standard levels (CSLs) for this 

rulemaking. 
9-2

9.2 MODEL OVERVIEW

DOE used forecasts of shipments for a base case and a standards case to provide an 

estimate of the annual sales and in-service stock of transformers for the forecast period. The 

estimate included the age distribution of transformers for each transformer type (classified 

according to equipment classes) and each transformer size. DOE chose an accounting model 

method to prepare shipment scenarios for the base case and several CSLs. The model uses 

annual transformer sales and the age distribution of the in-service stock to calculate equipment 

costs for the NPV and energy use for the NES, respectively. The model keeps track of the age 

and replacement of transformer capacity, given a projection of future transformer sales growth. 

Figure 9.2.1 presents a graphical flow diagram of the shipments model portion of the 

distribution transformer national impact (NES and NPV) model and spreadsheet. In the diagram, 

the arrows show the interconnectivity of data exchanges between calculations. Inputs are shown 

as parallelograms. As data flow from these inputs, they may be integrated into intermediate 

results (shown as rectangles) or, through integrating sums or differences (shown as circles), into 

major outputs (shown as boxes with curved bottom edges). 

As illustrated in the flow diagram, DOE organized shipments into two categories: 

replacements and new capacity. Replacements occur when transformers break down, corrode, 

are struck by lightning, or otherwise need to be replaced. New capacity purchases occur due to 

increases in electricity use that may be driven by increasing population, commercial and 

industrial activity, or growth in electricity distribution systems. The model starts with an 

estimate of the overall growth in transformer capacity and then estimates shipments for particular 

design lines using estimates of the relative market share for different design and size categories. 

The steps for the shipments calculation are: 

1. Collection of available data – Acquisition and processing of available transformer 

shipments data. 

2. Construction of aggregate shipments backcast – Provides an annual estimate of historical 

total capacity shipped using available shipments and electricity consumption data. 

3. Construction of aggregate shipments forecast – Provides a future base case annual 

shipments estimate by applying a shipments growth rate. 

4. Development of liquid-immersed and dry-type market shares – Disaggregates the total 

capacity shipped into liquid-immersed and dry-type transformers. 

5. Modeling of purchase price elasticity – Models the impact of higher purchase prices due 

to a standard on future shipments. 

6. Accounting of sales and in-service stocks – Provides an annual age distribution of inservice transformer stock from shipments estimates and the retirement function. 
9-3

Figure 9.2.1 Shipments Model Flowchart
9-4

9.3 MODEL INPUTS

 The shipments model inputs flow from the shipments calculation steps described in the 

previous section. The shipments model takes both internal and external inputs. Internal inputs 

comprise quantities that are calculated from previous steps in the model. External inputs are data 

sets acquired exogenously. The final outputs of the shipments calculation are the annual 

shipments estimates and the age distribution of in-service transformer stock. The list of specific 

inputs is as follows: 

1. Shipments data – Include external estimates of transformer shipments and the quantity 

index of transformers manufactured. The external estimates of transformer shipments in 

this analysis include sales data for 2001 and 2009. The quantity index of transformers 

manufactured is available for the years from 1977-2008. 

2. Shipments backcast – Provides an estimate of total transformer capacity shipped before 

2009. 

3. Shipments forecast – Provides an estimate of total transformers shipped after 2009. 

4. Long-term purchase elasticity – Estimates the price sensitivity of transformers shipped 

over the long term. 

5. Dry-type/liquid-immersed market shares – Provides the annual capacity-based market 

shares of dry-type and liquid-immersed transformers shipped. 

6. Stock accounting – Provides the age distribution of the current year’s in-service 

transformer stock based on the previous year’s in-service stock and shipments. 

7. Retirement function – Provides an estimate of the probability that a transformer will be 

replaced as a function of its age.

8. Initial stock – Provides the age distribution of the in-service stock of transformers at the 

start of the stock-accounting calculation (i.e., in 1950). 

9.3.1 Shipments Data

DOE uses historical transformer shipments data to calibrate a forecast of future shipments 

and in-service stocks. These data are key inputs to the national impact analysis because changes 

in shipments and in-service stock create nearly proportional changes in the estimate of the energy 

savings from a standard. 

DOE obtained an estimate of sales (for the entire market) for the year 2009, 

disaggregated by type and kilovolt-ampere (kVA) rating.

1

 DOE also used a similar sales 

estimate for the year 2001, which was completed by the same source. Market shares for both 

liquid-immersed and dry-type distribution transformers, by product type and kVA rating, came 

from the 2001 and 2009 shipments estimates. In the absence of historical shipments data for 

other years, DOE explored other means of getting at transformer sales estimates. The historical 

series of the power distribution and specialty transformer manufacturing (North American 

Industry Classification System (NAICS) code 335311) quantity index for 1977–2008 is available 

from the U.S. Bureau of Economic Affairs (BEA). The BEA transformer manufacturing quantity 

index provides information on changes to aggregate shipments from 1977 to 2008.2 Using the 

sales estimates for 2001 and 2009 as reference points and the BEA quantity index data, DOE 

estimated aggregate transformer shipments from 1977 to 2008. 
9-5

Table 9.3.1 presents the shipment estimates in both units and megavolt-amperes (MVA) 

shipped, and the approximate value of these shipments. The total sales for the distribution 

transformer industry were about $1.9 billion in 2009. 

Table 9.3.1 Distribution Transformer Shipment Estimates for 2009 

Distribution Transformer Equipment Class Units 

Shipped

MVA 

Capacity 

Shipped

Shipment 

Value (2009 

US$ million)

Liquid-immersed, medium-voltage, single-phase 683,726 21,994 714.8

Liquid-immersed, medium-voltage, three-phase 49,739 32,266 786.0

Dry-type, low-voltage, single-phase 17,740 647 22.0

Dry-type, low-voltage, three-phase 206,929 15,778 394.4

Dry-type, medium-voltage, single-phase, 20-45 kV BIL 709 23 0.7

Dry-type, medium-voltage, three-phase, 20-45 kV BIL 522 257 6.2

Dry-type, medium-voltage, single-phase, 46-95 kV BIL 546 23 0.8

Dry-type, medium-voltage, three-phase, 46-95 kV BIL 2,074 3,655 98.7

Dry-type, medium-voltage, single-phase, ≥96 kV BIL 202 9 0.3

* BIL = Basic impulse insulation level

Tables 9.3.2 and 9.3.3 present the disaggregated shipment estimates for 2009 by product 

type and kVA rating. 

Table 9.3.2 Liquid-Immersed Distribution Transformer Shipment Estimates, 2009 

Liquid-Immersed, Medium-Voltage, 

Single-Phase

Liquid-Immersed, Medium-Voltage, 

Three-Phase

kVA Units Shipped kVA Units Shipped

10 58,090 15 -

15 169,083 30 -

25 243,583 45 1,438

37.5 41,755 75 3,753

50 119,455 112.5 790

75 26,338 150 7,426

100 18,679 225 1,969

167 4,357 300 7,340

250 1,905 500 6,650

333 238 750 3,502

500 238 1000 3,171

667 5 1500 2,941

833 - 2000 2,497

- 2500 2,260

Total Units 683,726 Total Units 43,736

Total MVA 21,994 Total MVA 28,372
9-6

Table 9.3.3 Dry-Type, Medium-Voltage Distribution Transformer Shipment 

Estimates, 2009

Dry-Type, Medium-Voltage, Single-Phase Dry-Type, Medium-Voltage, Three-Phase

kVA

Units Shipped

kVA

Units Shipped

20-

45kVBIL

46-

95kVBIL >96kVBIL 20-45kVBIL

46-

95kVBIL >96kVBIL

15 242 182 61 15 4 - -

25 42 182 61 30 7 - -

37.5 61 42 18 45 7 - -

50 61 42 18 75 10 2 -

75 30 18 12 112.5 34 4 -

100 30 18 12 150 30 5 -

167 12 18 6 225 36 12 -

250 7 8 2 300 91 30 25

333 12 18 6 500 121 85 74

500 12 18 6 750 121 121 75

667 - - - 1000 61 242 194

833 - - - 1500 - 363 244

- - - - 2000 - 605 280

- 182 61 2500 - 605 394

Total Units 709 546 202 Total Units 522 2,074 1,286

Total MVA 23 23 9 Total MVA 257 3,655 2,206

There are two major assumptions inherent in the shipments model. The first is that the 

relative market shares of the different transformer product classes and size categories are 

constant over time. In actuality, there is probably a gradual increase in the average size of 

transformers as the electricity demand per customer increases, but DOE does not have sufficient 

data to characterize such transformer size trends. 

The second assumption concerns the use of the BEA quantity index data. The BEA index 

data actually include shipments of transformers other than those covered by this rulemaking. 

The use of the BEA Standard Industrial Classification (SIC) code 3612 (NAICS code 335311) 

quantity index to estimate shipments for products under this rulemaking assumes that the 

quantity market share of distribution transformers relative to all NAICS code 335311 

transformers is relatively constant over the period 1977–2009. DOE made this assumption 

because quantity index data that are more disaggregated were not available.

9.3.2 Shipments Backcast

The shipments backcast is the estimate of previous aggregate transformer shipments 

based on limited historical data. The backcast of transformers shipments is a key element in 

estimating age distributions of future in-service transformer stock. 

The shipments backcast begins with the estimate of transformer shipments in the year 

20011

 and uses BEA’s NAICS code 335311 quantity index to estimate total shipments in the 

period 1977 to 2008.3

 Specifically, DOE used the following equation to backcast shipments 

from 2008 to 1977: 
9-7

TotShip(y) = TotShip(2001) × BEA(y)/BEA(2001) Eq. 9.1 

where:

TotShip(y) = the total capacity of transformer shipments estimated for year y 

where 1977 ≤ y < 2008 (MVA),

TotShip(2001) = the total transformer capacity shipped, from the shipments estimate 

(MVA), and

BEA(y) = the BEA quantity index for year y. 

 Annual shipments of transformer capacity for the years prior to 1977 are backcast to 1950 

using annual growth of electricity consumption from Table 8.9 of DOE’s Energy Information 

Administration (EIA)’s Annual Energy Review 2009, a proxy for growth of transformer sales 

during this period.4 Using this method, the shipments for the years 1950 to 1977 are given by the 

following equation: 

TotShip(y) = TotShip(1977) × AllElec(y) / AllElec(1977) Eq. 9.2 

where:

TotShip(y) = the total capacity of shipments estimated for year y where 1950 ≤ y 

< 1977 (MVA), and

AllElec(y) = national electricity consumption in year y according to EIA's 

Annual Energy Outlook 2010 (AEO2010) (W-hr).5

9.3.3 Shipments Forecast

After constructing a shipments backcast and calibrating it with shipments data, DOE 

constructed a forecast of transformer shipments. This forecast provided the necessary input for 

equipment expense and in-service transformer stock accounting.

DOE constructed a simplified forecast of transformer shipments for the base case 

scenario based on the assumption that long-term growth in electricity consumption will drive 

transformer shipments. The detailed dynamics of transformer shipments are highly complex. 

This complexity can be seen in the fluctuations in the total quantity of transformers 

manufactured, as expressed by the BEA transformer quantity index. DOE examined the 

possibility of modeling the fluctuations in transformers shipped using a bottom-up model in 

which the shipments are triggered by retirements and new capacity additions, but found 

insufficient data to calibrate model parameters within an acceptable margin of error. Hence, 

DOE decoupled the overall shipments and retirements in the construction of the shipments 

forecast and maintained the age distribution of the in-service transformer stock using a 

retirement function. 
9-8

 DOE constructed the transformer shipments forecast assuming that transformer 

shipments growth is equal to forecasted growth in electricity consumption, as given by the 

AEO2010 forecast up to the year 2035.5 For the years 2036–2045, DOE extrapolated the AEO 

2010 forecast, using its growth rate of electricity consumption between 2025 and 2035. 

Specifically, DOE used the following equation for the shipments forecast: 

TotShip(y) = TotShip(2009) × AllElec(y) / AllElec(2001) Eq. 9.3 

where:

TotShip(y) = the total capacity of shipments estimated for year y where 2011 < y 

≤ 2045 (MVA), and

AllElec(y) = national electricity consumption forecasted for year y by AEO2010 

(or by an extrapolation of AEO2010 data) (W-hr).

The next section describes how DOE adjusted its base case scenario forecast to account 

for price increases arising from a standard.

9.3.4 Long-Term Purchase Elasticity

DOE used purchase elasticity to adjust the base case shipments forecasts for potential 

transformer price increases due to a standard. The long-term purchase elasticity is a measure of 

how sensitive transformer shipments are to potential increases in price. Elasticity is defined as 

the percentage change in quantity purchased divided by the percentage change in price (or some 

other factor that influences purchase behavior). 

The basic formula DOE used to determine price elasticity is:

e= (dQ/Q) / (dP/P) Eq. 9.4 

where:

dQ/Q = a small percentage change in quantity purchased (Q), and

dP/P = a small percentage change in price.

If the elasticity is constant, then the quantity purchased can be written in terms of the 

price, a reference price, a reference quantity, and the elasticity. Specifically, the following 

equation holds true when the elasticity is constant:

Q(P) = Q0 × (P/P0) e Eq. 9.5 

where:

Q(P) = the quantity purchased as a function of price, 

Q0 = a reference quantity at a reference price P0, and
9-9

e = the elasticity, which is almost always negative or zero (i.e., non-positive) 

with respect to price.

For the forecast, the reference price and the reference quantity are the price and quantity 

from the base case scenario. A change in price due to a standard then has an impact on the 

quantity purchased, Q(P), as described by the above equation. 

9.3.4.1 Elasticity Estimates for Liquid-Immersed and Dry-Type Transformers

To model utility and customer decision-making, DOE constructed a model employing a 

standard econometric logit equation, used for general applications of market response to costs 

and perceived utility. For liquid-immersed transformers, DOE fitted the model to transformer 

purchase data from U.S. Federal Energy Regulatory Commission (FERC) Form No. 15 to 

determine the parameters of the logit equation. This resulted in a value of -0.04 for price 

elasticity. DOE assigned -0.04 as the medium scenario and incremented the elasticity to -0.2 to 

implement a high sensitivity to price change. The low scenario assumes zero elasticity, or no 

impact on purchase decisions from a price change. For dry-type transformers, historical 

purchase data were not available. Since dry-type units are primarily used in commercial and 

industrial applications, as are unitary air conditioners, DOE used sales and price data for air 

conditioners to estimate price elasticity for dry-type transformers. DOE fitted the model to the 

Air-Conditioning and Refrigeration Institute's sales data and real Producer Price Index (PPI) of 

unitary air conditioners.6

9.3.5 Liquid-Immersed and Dry-Type Market Shares

 The resulting value of elasticity was -0.02. DOE assigned -0.02 as the 

medium scenario and incremented the elasticity to -0.2 to implement a high sensitivity to price 

change. The low scenario assumes zero elasticity, or no impact on purchase decisions from a 

price change.

 The shipments forecast and backcast described above provided an aggregate estimate of 

the total capacity of transformers shipped from 1950 to 2045. To disaggregate the total capacity 

into the capacity for different types of transformers, DOE applied capacity market share 

estimates. To distinguish between liquid-immersed and dry-type transformers, DOE applied a 

liquid-immersed and dry-type market share, respectively. To distinguish between different 

equipment classes and size categories within each equipment class, DOE used 2001 market 

shares estimates. DOE used trends in electricity consumption from EIA’s retail sales data to 

estimate market share trends for liquid-immersed and dry-type transformers.4

 Assuming that 

transformer sales over the long term track electricity sales for the sectors served by those 

transformers, DOE derived the following market share model: 

LiqShip(y) = CL × AllElec(y); 

where CL = LiqShip(2001) / AllElec(2001) ∀ y≤2008

CL = LiqShip(2009) / AllElec(2009) ∀ y≥ 2009 Eq. 9.6 

DryShip(y) = CD × CIElec(y); 

where CD = DryShip(2001) / CIElec(2001) for all y≤2008

CD = DryShip(2009) / CIElec(2009) for all y≥ 2009 Eq. 9.7 
9-10

DryMS( y) = CD × CIElec( y) / (CL × AllElec( y) + CD× CIElec( y)) Eq. 9.8

LiqMS(y) = 1 − DryMS(y) Eq. 9.9 

where:

CL = the constant of proportionality between the electricity consumption 

and the sales of liquid-immersed transformers in the year 2001, 

CD = the constant of proportionality between the electricity consumption 

and the sales of dry-type transformers in the year 2001, 

LiqShip(2001) = the capacity of liquid-immersed transformers shipped in 2001 

(MVA),

DryShip(2001) = the capacity of dry-type transformers shipped in 2001 (MVA), 

LiqShip(2009) = the capacity of liquid-immersed transformers shipped in 2009 

(MVA),

DryShip(2009) = the capacity of dry-type transformers shipped in 2009 (MVA), 

AllElec(y) = the total consumption of electricity in year y (W-hr),

CIElec(y) = the consumption of electricity by the commercial and industrial 

sectors in year y (W-hr),

LiqMS(y) = the capacity market share of liquid-immersed transformers in year y 

(%), and

DryMS(y) = the capacity market share of dry-type transformers in year y (%).

 The key assumption behind the market share equations is that transformer capacity 

market shares follow the relative electricity consumption of the end users of the electricity that 

passes through the transformers. The dynamics of liquid-immersed and dry-type market shares 

are likely to be fairly complicated, but DOE believes this is the best way to capture long-term 

average trends in market share, given the lack of detailed market share data over long time 

periods. 

 For the market shares of different kVA ratings and equipment classes, DOE assumed that 

the relative market share within each transformer type (i.e., liquid-immersed or dry-type) is 

constant over time. Given a lack of detailed, long-term market share data, an alternative 

assumption regarding kVA ratings and equipment class market shares may not be supportable. 

Once it had fully specified the shipments backcast, forecast, elasticity, and market shares, 

DOE had completely specified the characteristics of transformer shipments. The next step was to 

provide an accounting of in-service transformer stocks, as described in the next section.

9.3.6 Stock Accounting

The stock accounting took transformer shipments, a retirement function, and initial inservice transformer stock as inputs and provided an estimate of the age distribution of in-service 

transformer stocks for all years. The age distribution of in-service transformer stocks is a key 

input to both the NES and NPV calculations, because the operating costs for any year depend on 
9-11

the age distribution. The dependence of operating cost on the transformer age distribution occurs 

because, under a candidate standard scenario that produces increasing efficiency over time, 

older, less efficient transformers will have higher operating costs, while younger, more efficient 

transformers tend to have lower operating costs. 

DOE calculated total in-service stock of distribution transformers by integrating historical 

shipments, starting from 1950. As transformers are added to the in-service stock, some of the 

older ones retire and exit the stock. 

 To estimate the shipment forecasts, DOE developed a series of equations that define the 

dynamics and accounting of in-service transformer stocks. For new units, the equation is: 

Stock( y,age = 1) = Ship( y − 1) Eq. 9.10 

where:

Stock (y, age) = the population of in-service transformers of a particular age 

(MVA),

y = the year for which the in-service stock is being estimated, and

Ship (y) = the number of transformers purchased in a particular year (MVA).

 This equation indicates that the number of one-year-old units is simply equal to the 

number of new transformer units purchased the previous year. The slightly more complicated 

accounting equations are those that describe the accounting of the existing in-service stock of 

transformer units:

Stock(y+1,age+1) = Stock(y,age) × [1 − ProbRetire (age)] Eq. 9.11 

 This equation says that, as time goes on, only a fraction of the in-service stock exists in 

the next year. As the year is incremented and goes from y to y+1, the age is also incremented 

from age to age+1. Also, as time moves forward, a fraction of the in-service stock is removed, 

and that fraction is determined by a retirement probability function, ProbRetire(age), which is 

described in the next section.

9.3.7 Retirement Function

The accounting of in-service transformer stock requires specification of a retirement 

probability function. DOE derived the retirement probability function from a modified version of 

a transformer reliability function. The reliability function for determining the lifetime of the 

transformer is a Weibull distribution and is adapted from an earlier study for DOE, ORNL 

6804/R1, p. D-1.7

r(age) = exp �− �age

d �

d

� ((1 − constfail)age × (1 − constfail)age−15) Eq. 9.12 

where:
9-12

r(age) = the reliability of a transformer of a certain age, where reliability is 

defined as the probability that a transformer will last to a particular 

age,

d and e = parameters used for fitting the reliability data, 

constfail = a constant failure rate of 0.5 percent per yeara

corrfail = a corrosive failure rate of 0.5 percent per year at age 15 and above.

, and 

DOE adjusted the parameters of the Weibull distribution to maintain an average lifetime 

of 32 years. It adapted the failure rates and the lifetime from ORNL 6804/R1, p. D-1. 

DOE converted the reliability function into an annual retirement probability function by 

dividing the incremental reliability at a given age by the fraction of transformers that last to that 

age, as shown in Equation 9.13 below. 

ProbRetire(age) = [r(age − 1) − r(age)] / r(age) Eq. 9.13 

where:

ProbRetire (age) = the probability that a transformer of a particular age will be 

retired. 

Figure 9.3.1 shows the retirement rate of distribution transformers. 

Figure 9.3.1 Fraction of Original Shipment Retiring

 

 

a Constant failure could be due to lightning or other random events.

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 10 20 30 40 50 60

Probability of Failure in Year t to t+1

Age of Unit
9-13

DOE considered the possibility that more efficient transformers may operate at lower 

temperatures, which could alter the retirement function for these transformers. Upon review of 

the engineering data, DOE found that the more efficient transformers that are made with an 

amorphous core material were the transformers that had a significant drop in operating 

temperatures. Theoretically, lower operating temperatures should lower the degradation rate of 

electrical insulation in the transformer and lead to fewer failures of these transformers as they 

age. However, because amorphous core technology is a relatively recent technology (within the 

last couple of decades), and because use of this technology can result in larger, bulkier 

transformers, this type of transformer may have features that contribute to more frequent 

replacements over the long term. Such features may include larger size and weight, which can 

lead to increased failures during storms or replacement due to size or space constraints. DOE did 

not have enough information to determine if such transformers would have longer or shorter 

system lifetimes relative to baseline efficiency transformers and therefore estimated that the 

transformer lifetime function should be largely independent of transformer efficiency.

 Once DOE specified the retirement probability function, the remaining input to the stockaccounting equation was the initial in-service stock of transformers, as described in the following

sections. 

9.3.8 Refurbishments and Rewinds

 Transformers that are not retired can be refurbished and returned to the stock. Minor 

refurbishments may include replacement of connectors, bushings, or the oil. Major 

refurbishments could include the rewinding of the transformer, a function often performed by a 

rewinding firm. ORNL-6804/R1 reported annual refurbished capacity, including rewound units, 

to be approximately one percent of the in-service transformer capacity. DOE carried out further 

research, including discussions with owners of transformers to ascertain the estimated annual 

refurbishments. The findings were inconclusive. Major refurbishment appears to represent a 

small fraction of the distribution transformer market; however, that share could potentially grow 

with the imposition of an energy efficiency standard. Transformer users expressed hesitancy 

regarding widespread adoption of rewound transformers. Not finding a consensus regarding 

transformer refurbishment, DOE did not include major refurbishments in the current analysis. 

Minor refurbishment is widespread and already is captured in the retirement function. 

9.3.9 Initial Stock

DOE initialized the stock-accounting model in the year 1950, which was the first year for 

which electricity consumption data were available.4

 For simplicity, DOE set the in-service transformer stock in the first year at zero.a

 

a Note that transformer stocks in 1950 were quite small compared to transformer stocks in 2001.

This number 

does not affect the analysis because most of the transformer stock from the year 1950 would no 

longer be in service after 2001. 
9-14

9.3.10 Effective Date of Standard

 A key output of the shipments model is the in-service stock of transformers that may be 

affected by a standard. To calculate this affected stock, the effective date of the standard must be 

defined. DOE assumed for this analysis that any new energy efficiency standard for distribution 

transformers will become effective in 2015. The exact effective date of the standard is January 1, 

2015, so all distribution transformers manufactured or imported starting on the first day of the 

year 2015 are affected by the standard.

9.3.11 Affected Stock

 The affected stock is an output of the shipments model and a key input for the NES and 

NPV calculations. The affected stock consists of that portion of the in-service transformer stock 

that is potentially impacted by a standard. It therefore consists of those in-service transformers 

that are purchased in or after the year the standard has taken effect, as described by the following 

equation: 

AffStock(y) = Ship(y) + ∑ Stock(age) y−StdYear

age=1 Eq. 9.14 

where: 

AffStock(y) = stock of transformers of all vintages that are operational in year y 

(MVA),

Ship (y) = shipments in year y (MVA), and

age = the age of the transformer (years).

 Once DOE had specified the shipments, in-service stocks, and affected stocks of 

transformers, it was able to proceed to the NES and NPV models and calculations; these 

calculations are described in chapter 10. 

9.4 RESULTS

 The main output of the shipments model is the total capacity of distribution transformers 

shipped annually from 2016 through 2045. Total shipments depend on transformer lifetime, the 

market elasticity of transformer purchases with respect to price, and growth in new electricity 

demand. Total shipments for all CSLs for liquid-immersed and dry-type distribution transformers 

are shown in Table 9.4.1. 
9-15

Table 9.4.1 Cumulative Shipments of Transformers by Candidate Standard Level 

(CSL), 2016 - 2045 

 

Candidate Standard Level

Base-case 1 2 3 4 5 6 7

Liquid-Immersed 1.98 1.97 1.97 1.97 1.96 1.95 1.95 1.95 

Low-Voltage Dry-Type 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 

Medium-Voltage Dry-Type 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23

 An important factor that influences the size of the potential standards-induced change in 

shipments is the actual equipment price increase due to standards. If price increases are large, the 

shipments volume will decrease almost proportionally to the price increase, but because the price 

elasticity of transformers is less than one, price increases will result in increased gross sales 

dollar volume to the transformer manufacturer. The net financial impact of these opposing 

effects is examined in the MIA, found in chapter 12 of the NOPR. 

The national impact spreadsheet is available as an Excel file on the DOE website: 

http://www.eere.energy.gov/buildings/appliance_standards/commercial/distribution_transformer

s.html. Instructions for using the spreadsheet are in Appendix 10-A of this technical support 

document. 
9-16

REFERENCES

1. Hopkinson, P. & Puri, J. Distribution Transformer Market Shipment Estimates for 2001. 

(HVOLT Consultants Inc.: 2003). 

2. U.S. Department of Commerce. Bureau of Economic Analysis U.S. Department of 

Commerce. Bureau of Economic Analysis. at 

<http://www.bea.gov/national/nipaweb/DownSS2.asp>

3. Bureau of Economic Analysis Industry Economic Accounts Information Guide. Annual 

Industry Accounts. Gross Domestic Product (GDP) by Industry. (2005). 

4. U.S. Department of Energy-Energy Information Administration Annual Energy Review 2009, 

Chapter 8: Electricity, Table 8.9 Electricity End Use, 1949-2009. (U.S. Department of 

Energy: Washington DC, 2010). 

5. U.S. Department of Energy – Energy Information Administration Annual Energy Outlook 

2010: With Projections Through 2035. (U.S. Department of Energy: Washington DC, 2010). 

6. U.S. Department of Labor-Bureau of Labor Statistics Producer Price Index. Industry: 

Refrigeration and Heating Equipment-Product: Unitary Air Conditioners-Series ID: 

PCU3585#2 (N). (2005). 

7. Barnes, P., Van Dyke, J.W., McConnell, B.W. & Das, S. Determination Analysis of Energy 

Conservation Standards for Distribution Transformers. (Oak Ridge National Laboratory: 

1996).