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CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

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

9.2 MODEL OVERVIEW ..................................................................................................... 9-1

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

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

9.3.2 Shipments Backcast ......................................................................................................... 9-7

9.3.3 Shipments Forecast .......................................................................................................... 9-8

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

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

9.3.6 Stock Accounting ........................................................................................................... 9-11

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

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

9.3.9 Initial Stock .................................................................................................................... 9-14

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

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

9.4 RESULTS ...................................................................................................................... 9-15

LIST OF TABLES

Table 9.3.1 Estimated Shipments of Distribution Transformers, 2009 .................................. 9-5

Table 9.3.2 Estimated Shipments of Liquid-Immersed, Medium-Voltage 

Transformers, 2009 .............................................................................................. 9-6

Table 9.3.3 Estimated Shipments of Dry-Type, Medium-Voltage Transformers, 2009 ........ 9-6

Table 9.4.1 Cumulative Shipments of Transformers by Trial Standard Level, 2016–

2045 Billion kVA ................................................................................................ 9-15

LIST OF FIGURES 

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

Figure 9.3.1 Percent of Original Stock Retiring ..................................................................... 9-13
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CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

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

part of establishing a new or amended energy efficiency standard. Estimates of shipments are a 

necessary input to calculating the national energy savings (NES) and net present value (NPV) of 

an investment in more efficient equipment. Both the NES and NPV, discussed in chapter 10, are 

needed to analyze the impacts of proposed standards. Shipments are also a necessary input to the 

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

rulemaking. The MIA estimates the impact of potential efficiency standards on manufacturers of 

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

each potential standard on employment and manufacturing capacity. This chapter describes the 

method DOE used to project annual shipments of liquid-immersed and dry-type distribution 

transformers under base- and standards-case efficiency levels. It also presents results of the 

shipments analysis. 

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

shipments model estimates the rate at which the in-service stock of transformers may be replaced 

by new, more efficient units after an energy conservation standard becomes effective. The core 

of the shipments analysis is an accounting model that DOE developed to simulate how current

and future purchases are incorporated into and gradually replace the in-service stock. In 

estimating the effects of potential new standards on shipments, the model accounts for the 

combined effects on the purchase decision of increases in purchase price and decreases in annual 

operating costs, and consumer income. 

 The shipments model is prepared as a Microsoft Excel spreadsheet that is accessible on 

DOE’s website

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

s.html)

9.2 MODEL OVERVIEW

. Appendix 10A of this technical support document describes how to access and utilize the 

spreadsheets that support the shipments model and other models related to the national impact 

analysis (described in chapter 10). The rest of this chapter explains the shipments model in more 

detail. Section 9.2 describes the methodology that underlay development of the model. Section 

9.3 describes the data inputs and model calibration; the effects on shipments of changes in 

purchase price and operating costs, and consumer income; and the affected stock of transformers. 

Section 9.4 presents the model results for both liquid-immersed and dry-type distribution 

transformers for the seven trial standard levels identified for this rulemaking.

 In developing the shipments model, DOE used forecasts of shipments for a base case and 

each standards case to estimate the annual sales and in-service stock of transformers throughout 

the forecast period (2016–2045). DOE chose an accounting method to prepare shipment 
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scenarios for the base case and several standard levels. The estimate included the age distribution 

of each transformer type (classified according to equipment class) and size. 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 growth in transformer 

sales.

To estimate total transformer shipments, the model estimates shipments for specific 

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

new capacity, and (2) replacement shipments going into existing structures. Replacements occur 

when transformers break down, corrode, are struck by lightning, or otherwise need to be 

replaced. Purchases for new capacity occur due to increases in electricity use that may be driven 

by increasing population, commercial and industrial activity, or growth in electricity distribution 

systems. 

Figure 9.2.1 presents a flow diagram of the shipments model part of the NES and NPV 

spreadsheets that underlie the national impact analysis (chapter 10). 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, via integrating sums or differences (shown as circles), into major 

outputs (shown as boxes having wavy bottom edges). 

The model starts with an estimate of the overall growth in transformer capacity and then 

estimates shipments for particular equipment classes using estimates of the relative market share 

for various design and size categories. The steps for the shipments analysis are listed below. 

1. Collection and processing of available data on shipments of distribution 

transformers. 

2. Construction of an aggregate shipments backcast, based on shipments and electricity 

consumption data, to obtain an annual estimate of historical total capacity shipped. 

3. Construction of aggregate shipments forecast, to estimate future annual shipments in 

the base case. 

4. Development of separate market shares for liquid-immersed and dry-type

transformers from the total capacity shipped. 

5. Modeling of purchase price elasticity to evaluate the impact that higher purchase 

prices due to a standard will have on future shipments. 

6. Accounting of sales and in-service transformer stocks to develop an annual age 

distribution of in-service stock from shipments estimates and a retirement function. 
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Figure 9.2.1 Flowchart of Shipments Model 

BEA Quality 

Index 

EIA Electricity 

Market Share 

HVOL T 2001 & 2009 

Shipments 

First Cost 

Elasticity 

stock Accounting 

Affected Stock 

M ... [ gy Pr1CBI 

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F 

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Total ShlprrMlnts 

Retirement Function 

ReUremenm ,." Shl~­

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Shipments 

ttt 

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First Cost by 

DesignUne 

First Cost by 

ProductCl1lU 

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9.3 INPUTS TO MODEL

 The shipments model utilizes both internal and external inputs. Internal inputs comprise 

quantities that are calculated from the steps described above. External inputs are acquired 

exogenously. The outputs of the shipments analysis are estimates of annual shipments and the 

age distribution of in-service transformer stock. The specific inputs are listed below. 

1. Shipments data, which include external estimates of transformer shipments and the 

quantity index of transformers manufactured. The external estimates used in this 

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

manufactured is available for 1977–2008. 

2. Shipments backcast, an estimate of transformer capacity shipped before 2009. 

3. Shipments forecast, an estimate of distribution transformers shipped after 2009. 

4. Long-term price elasticity of transformer purchases. 

5. Annual market shares of liquid-immersed and dry-type transformers shipped, 

categorized by capacity. 

6. Stock accounting to develop the age distribution of the current year’s in-service 

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

7. Retirement function that provides an estimate of the probability that a transformer 

will be replaced as a function of its age.

8. Refurbishments and Rewinds, to accurately capture whether or not a unit is replaced 

upon failure or refurbished/rewound. 

9. The initial stock of transformers at the start of the stock-accounting calculation (in 

1950). 

9. Effective date of standard (2016) is a key input for determining the stock of 

transformers impacted by a standard.

10. Affected stock is a key output of the shipments model that is an input for the 

NES/NPV calculation and represents that percentage of the in-service transformer 

stock that may be impacted by a standard. 

Each of these inputs is described in detail in the following sections. 

9.3.1 Shipments Data

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

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

(chapter 10), because changes in shipments and in-service stock create nearly proportional 

changes in the estimated energy savings from a standard. 

DOE obtained an estimate of sales (for the entire market for distribution transformers) for 

2009, disaggregated by transformer type (whether liquid-immersed or dry-type) and kilovoltampere (kVA) rating.

1,2 DOE used a similar sales estimate, compiled by the same source, for 

2001. In the absence of data regarding historical shipments for years other than 2001 and 2009, 

DOE explored other means of developing estimates of transformer sales. The historical quantity 

index for power distribution and specialty transformer manufacturing (North American Industry 

Classification System [NAICS] code 335311) for 1977–2008 is available from the U.S. Bureau 
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of Economic Affairs (BEA). The BEA quantity index provides information on changes to 

aggregate shipments from 1977 to 2008.3 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. 

Table 9.3.1 presents DOE’s estimates of both units shipment and overall megavoltamperes (MVA) shipped, and the approximate value of those shipments. Total sales for the 

distribution transformer industry were about $1.9 billion in 2009. 

Table 9.3.1 Estimated Shipments of Distribution Transformers, 2009 

Equipment Class Units 

Shipped

Capacity 

Shipped

MVA

Value of 

Shipments 

million

2009$

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 

Source: HVOLT Inc.

* BIL = basic impulse insulation level. 

Table 9.3.2 presents the shipment estimates for 2009 for medium-voltage liquidimmersed distribution transformers categorized by capacity and by equipment type whether 

single- or three-phase. 
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Table 9.3.2 Estimated Shipments of Liquid-Immersed, Medium-Voltage 

Transformers, 2009 

Single-Phase Three-Phase

Capacity kVA Units Shipped Capacity 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 1,000 3,171

667 5 1,500 2,941

833 – 2,000 2,497

– 2,500 2,260

Total Units 683,726 Total Units 43,736

Total MVA 21,994 Total MVA 28,372

Source: HVOLT Inc.

Table 9.3.3 gives the shipment estimates for 2009 for dry-type medium-voltage 

distribution transformers categorized by capacity and by whether single- or three-phase. 

Table 9.3.3 Estimated Shipments of Dry-Type, Medium-Voltage Transformers, 2009 

Capacity 

kVA

Single-Phase Units Shipped by BIL* 

kV Capacity 

kVA

Three-Phase Units Shipped by 

BIL* kV

20-45 46-95 > 96 20-45 46-95 > 96

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 – – – 1,000 61 242 194

833 – – – 1,500 – 363 244

– – – – 2,000 – 605 280

– 182 61 2,500 – 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

Source HVOLT Inc.

* BIL = basic impulse insulation level.
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 The shipments model incorporates two major assumptions. The first is that the relative 

market shares of the various transformer equipment classes and size categories are constant over 

time. In actuality, the average size of transformers probably increases gradually as the electricity 

demand per customer increases, but DOE has insufficient data to characterize such size trends. 

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

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

the BEA’s SIC code 3612 (NAICS code 335311) quantity index to estimate shipments assumes 

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

transformers is relatively constant for 1977–2009. DOE made this assumption because 

disaggregated quantity index data 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 transformer shipments is a key element in 

estimating the age distributions of future in-service transformer stock. The shipments backcast 

begins with the estimate of transformer shipments in 2001,1 then uses BEA’s NAICS code 

335311 quantity index to estimate total shipments for 1977–2008.4 Specifically, DOE used the 

following equation to backcast shipments from 2008 to 1977. 

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

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 (MVA) based on the shipments 

estimate (MVA); and

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

 Annual shipments of transformer capacity prior to 1977 are backcast to 1950 using 

annual growth of electricity consumption from Table 8.9 of the DOE Energy Information 

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

during this period.5

 Using this method, the shipments for 1950–1977 are given by the following 

equation. 

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

Where: 

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

1977 (MVA); and

AllElec(y) = the national electricity consumption in year y (kWh) according to 

EIA's Annual Energy Outlook 2010 (AEO2011).6

 
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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 input necessary to 

develop equipment cost and the stock accounting of in-service transformers. 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 quantity of transformers manufactured, as expressed by the BEA transformer 

quantity index. DOE examined the possibility of modeling the fluctuations in number of 

transformers shipped using a bottom-up model in which shipments are triggered by retirements 

and additions of new capacity, but found insufficient data to calibrate model parameters within 

an acceptable margin of error. Hence, in the constructing the shipments forecast DOE decoupled 

the overall shipments and retirements and used a retirement function to maintain the age 

distribution of the in-service transformer stock. 

 DOE constructed the transformer shipments forecast assuming that growth in transformer 

shipments is equal to forecasted growth in electricity consumption, as given by the AEO2011

forecast through 2035.7 For 2036–2045, DOE extrapolated the AEO 2011 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). 

Where: 

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

2045 (MVA); and

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

AEO2011 (or by an extrapolation of AEO2011 data).

The following section describes how DOE adjusted its base-case forecast to account for 

price increases arising from each trial standard. 

9.3.4 Long-Term Price Elasticity

 Long-term price 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). 

Where: 

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

Where: 

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

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

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

respect to price.

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

and quantity from the base-case scenario. DOE used price elasticity to adjust forecasts of basecase shipments for potential price increases due to a standard. A change in price due to a 

standard has an impact on the quantity purchased, Q(P), as described by the above equation. 

To model the purchase decisions made by utilities and other customers, DOE constructed 

a model that employs a standard econometric logit equation, such as those used for general 

applications of market response to costs and perceived utility. To determine the parameters of the 

logit equation for liquid-immersed transformers, DOE fitted the model to transformer purchase 

data from U.S. Federal Energy Regulatory Commission Form No. 15. This procedure resulted in 

a value of -0.04 for price elasticity. DOE assigned -0.04 as the medium scenario for liquidimmersed transformers 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. No historical purchase data were available for dry-type transformers. Because

dry-type units are used primarily 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 the real Producer Price Index (PPI) of unitary air conditioners.8

 The resulting 

value of elasticity was -0.02. DOE assigned -0.02 as the medium scenario for dry-type 

transformers 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.

9.3.5 Market Shares of Liquid-Immersed and Dry-Type Transformers

 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 the two types of transformers, DOE assigned liquid-immersed and dry-type 

market shares by capacity. To distinguish between the various equipment classes and size 

categories within each equipment class, DOE used estimates of market shares from 2001. DOE 

used trends in electricity consumption from EIA’s retail sales data to estimate market share 
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trends for the two types of transformers.5 Based on the assumption 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 and 

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

DryShip(y) = CD × CIElec(y), 

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

CD = DryShip(2009) / CIElec(2009) for all y ≥ 2009. 

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

LiqMS(y) = 1 − DryMS(y). 

Where: 

CL = the constant of proportionality between the electricity consumption 

and the sales of liquid-immersed transformers in 2001, 

CD = the constant of proportionality between the electricity consumption 

and the sales of dry-type transformers in 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 (kWh),

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

sectors in year y (kWh),

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 dynamics that determine market shares of liquid-immersed and dry-type transformers 

likely are complicated, but DOE believes the process and equation described above represent the 

best way to capture long-term average trends in market share, given the lack of long-term, 

detailed market share data. The key assumption behind the market share equations is that market 

shares by transformer capacity follow the relative electricity consumption of the end users of the 

electricity that passes through the transformers. DOE also assumed that the relative market 

shares of various kVA ratings and equipment classes within each transformer type (i.e., liquidimmersed or dry-type) is constant over time. Given a lack of detailed, long-term market share 

data, an alternative assumption regarding market shares by kVA rating and equipment class may 

not be supportable. 
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After fully specifying 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 following section. 

9.3.6 Stock Accounting

DOE’s stock accounting used transformer shipments, a retirement function, and initial inservice transformer stock as inputs to develop 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 calculations of both the NES and NPV, because the operating costs for any year depend 

on the age distribution. The transformer age distribution affects operating costs because, under a 

trial standard scenario that produces increasing efficiency over time, the operating costs of older, 

less efficient transformers are higher than those of newer, more efficient transformers .

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

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

older ones retire and exit the stock. 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). 

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).

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

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

equations account for the existing in-service stock of transformer units: 

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

The above equation says that, as time passes, only a fraction of the in-service stock exists 

the following year. As the year is incremented from y to y + 1, the age is also incremented from 

age to age + 1. Also, as time passes, a fraction of the in-service stock is removed. That fraction 

is determined by a retirement probability function, ProbRetire(age), which is described in the 

following section. 

9.3.7 Retirement Function

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

probability function for distribution transformers. DOE derived this probability function from a 

modified version of a transformer reliability function. The reliability function for determining the 

lifetime of a transformer is a Weibull distribution adapted from an earlier study by Oak Ridge 

National Laboratory (ORNL) for DOE:

9

 
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9-12

r(age) = exp �− �age

d �

d

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

Where: 

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

as the probability that the transformer will last to that particular age;

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

constfail = a constant failure rate of 0.5 percent per year;a

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.7

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: 

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

Where: 

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

Figure 9.3.1 shows the retirement rate for distribution transformers. 

 

a Constant failure could be due to lightning or other random events.
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9-13

Figure 9.3.1 Percent of Original Stock Retiring

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

temperatures, which could alter their retirement function. After reviewing the engineering data, 

DOE found that more efficient transformers made with an amorphous core material demonstrate 

a significant drop in operating temperatures. Theoretically, lower operating temperatures should 

lower the degradation rate of electrical insulation in the transformer and result in fewer failures 

over time. Amorphous core technology is relatively recent (within the last couple of decades), 

however, and the technology can require larger, bulkier transformers, features that may 

contribute to more frequent replacements over the long term. The larger size and weight, for 

example, can lead to increased failures during storms or increased replacements because of size 

or space constraints. DOE did not have enough information to determine whether such 

transformers would have longer or shorter lifetimes relative to baseline transformers and 

therefore estimated that the transformer lifetime function should be independent of transformer 

efficiency.

9.3.8 Refurbishments and Rewinds

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

refurbishments may include replacing connectors, bushings, or the oil. Major refurbishments 

may include rewinding the transformer, an operation often performed by a specialized firm. 

ORNL reported annual refurbished capacity, including rewound units, to be approximately one 

percent of the in-service transformer capacity.7 DOE carried out further research, including 

discussions with owners of transformers, to finalize the estimate of annual refurbishments. The 

findings were inconclusive. Major refurbishment appears to represent a small fraction of the 

distribution transformer market; however, that share could increase in response to the imposition 

of an energy efficiency standard. Transformer users expressed hesitancy regarding widespread 

adoption of rewound transformers. Not finding a consensus regarding transformer refurbishment, 

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
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9-14

DOE did not include major refurbishments in the current analysis. Minor refurbishment is 

widespread and already is captured in the retirement function. 

After 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.

9.3.9 Initial Stock

DOE began applying the stock-accounting model for1950, the first year for which 

electricity consumption data were available.5 

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

9.3.10 Effective Date of Standard

This number 

does not affect the analysis because most of the transformer stock from 1950 would not be in 

service after 2001.

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

transformers would become effective in 2016. The exact effective date of the standard is January 

1, 2016, so all distribution transformers manufactured or imported starting on the first day of 

2016 are affected by the standard. 

9.3.11 Affected Stock

The affected stock is an output of the shipments model and a key input to the calculations 

of NES and NPV. The affected stock consists of that percentage of the in-service transformer 

stock that may be 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 .

Where: 

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

(MVA),

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

age = the age of the transformer (years).

 

a Note that transformer stocks in 1950 were small compared to those in 2001.
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 Section 9.4 summarizes results of DOE’s shipments analysis. After DOE specified the 

shipments, in-service stocks, and affected stocks of transformers, it was able to calculate the 

NES and NPV. Those calculations are described in chapter 10. 

9.4 RESULTS

The primary 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 price elasticity of transformer purchases, and growth in new electricity demand. 

Total shipments for all draft trial standard levels for liquid-immersed and dry-type distribution 

transformers throughout the forecast period are shown in Table 9.4.1. 

Table 9.4.1 Cumulative Shipments of Transformers by Draft Trial Standard Level, 

2016–2045 Billion kVA

Draft Trial Standard Level

Base case 1 2 3 4 5 6

Liquid-Immersed 1.95 1.94 1.94 1.94 1.94 1.91

Low-Voltage Dry-Type 0.62 0.62 0.62 0.62 0.62 0.61 0.61 

Medium-Voltage Dry-Type 0.22 0.22 0.22 0.22 0.22 0.22 

 The size of the potential standards-induced change in shipments is influenced greatly by 

the increase in equipment price due to standards. Given a large price increase, the volume of 

shipments 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, chapter 12 of the notice of proposed rulemaking. 
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REFERENCES

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

(HVOLT Consultants Inc.: Washington DC, 2003). 

2. Hopkinson, P. & Puri, J. Distribution Transformer Market Shipment Estimates for 2009. 

(HVOLT Consultants Inc.: Washington DC, 2010). 

3. U.S. Department of Commerce-Bureau of Economic Analysis National Economic Accounts: 

National Income and Product Accounts Tables (1969-Present). 

4. U.S Department of Commerce-Bureau of Economic Analysis Industry Economic Accounts 

Information Guide. Annual industry accounts: gross domestic product (GDP) by industry. 

(2010). 

5. 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). 

6. U.S. Energy Information Administration Annual Energy Outlook 2011, With Projections to 

2036. (U.S. Department of Energy: Washington DC, 2011). 

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

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

8. 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).

9. Barnes, P.R., Dyke, J.W.V., McConnell, B.W., Cohn, S.M. & Purucker, S.L. The Feasibility 

of Replacing or Upgrading Utility Distribution Transformers During Routine Maintenance. 

(Oak Ridge National Laboratory: 1995).