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CHAPTER 9: SHIPMENTS ANALYSIS

TABLE OF CONTENTS

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

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

9.3 MODEL INPUTS ...................................................... 9-3

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

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

9.3.3 Shipments Forecast ....................................... 9-10

9.3.4 Long-Term Purchase Elasticity .............................. 9-11

9.3.4.1 Elasticity Estimates for Liquid-Immersed and Dry-Type 

Transformers ...................................... 9-12

9.3.5 Liquid-Immersed/Dry-Type Market Shares ..................... 9-12

9.3.6 Stock Accounting ........................................ 9-14

9.3.7 Retirement Function ...................................... 9-15

9.3.8 Refurbishments and Rewinds ............................... 9-16

9.3.9 Initial Stock ............................................. 9-17

9.3.10 Effective Date of Standard .................................. 9-17

9.3.11 Affected Stock ........................................... 9-17

9.4 RESULTS ........................................................... 9-18

LIST OF TABLES

Table 9.3.1 Distribution Transformer Shipment Estimates for 2001 .................. 9-5

Table 9.3.2 Liquid-Immersed Distribution Transformer Shipment Estimates, 2001 ...... 9-6

Table 9.3.3 Dry-Type, Low-Voltage Distribution Transformer 

Shipment Estimates, 2001 ......................................... 9-7

Table 9.3.4 Dry-Type, Medium-Voltage Distribution Transformer Shipment 

Estimates, 2001 ................................................. 9-8

Table 9.4.1 Cumulative Shipments of Transformers by Trial Standard 

Level, 2010–2038 ............................................... 9-18

LIST OF FIGURES

Figure 9.2.1 Shipments Model Flowchart ....................................... 9-2

Figure 9.3.1 Age Distribution of Liquid-Immersed In-Service Transformer 

Stock in 2004 .................................................. 9-10

Figure 9.3.2 Fraction of Original Shipment Retiring .............................. 9-16

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CHAPTER 9: SHIPMENTS ANALYSIS

9.1 INTRODUCTION

 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 meeting the trial

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

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

of aging transformers that are gradually replaced. An estimate of the rate at which transformers

are purchased and replaced is a key input to the Department’s estimate of the national impacts of

trial standards for distribution transformers. 

In addition to using estimates of distribution transformer shipments as an input for the

national energy savings (NES) analysis (see Chapter 10 of this Technical Support Document) for

the Notice of Proposed Rulemaking (NOPR), the Department will use the shipments estimates as

input to the manufacturer impact analysis (MIA). That analysis estimates the impact of potential

efficiency standards on businesses (see Chapter 12).

9.2 MODEL OVERVIEW

The Department uses 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 includes the age distribution of transformers for each transformer type

(classified according to product classes) and each transformer size. The model uses the annual

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

the net present value (NPV) and energy use for the NES, respectively. The Department chose an

accounting model method to prepare shipment scenarios for the base case and several trial

standard cases. 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 flows from these inputs, it may be integrated into intermediate results

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

outputs that are shown as boxes having curved bottom edges. 

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Total Shipments

Retirement Function

New Capacity

Shipments

Stock Accounting

Affected Stock

Marginal

Energy Prices

Source Energy

Savings

NPV NES

Total

Shipments -

Retirements

Marginal Heat

Rates from

NEMS

Discount

Rate

Peak

Responsibility

Factor

Initial Peak

Loading

HVOLT

2001Shipments

BEA Quality

Index

EIA Electricity

Market Share

First Cost

Elasticity

Retirements

First Cost by

Design Line

First Cost by

Product Class

Rated Losses

by Product

Class

Rated

Losses by

Design Line

Design Line to

Product Class

Conversion

Σ

Fractional

Load Growth

RMS Loading

from LCC

Site Energy

Savings

Annual Equipment

Costs

Actual Electricity

Use: Peak & Average

Electricity

Price

Forecast

Scalar

Σ

Annual Operating

Cost Savings

Figure 9.2.1 Shipments Model Flowchart

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As illustrated in the flow diagram, the Department 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 trial standard on future shipments. 

6. Accounting of sales and in-service stocks – Provides an annual age distribution of

in-service transformer stock from shipments estimates and the retirement function. 

7. Consistency check with purchase and replacement data – Confirms that shipments

model forecasts are consistent with available data on utility transformer purchases

and replacements.

9.3 MODEL INPUTS

The shipments model inputs parallel the shipments calculation described in the previous

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

quantities that are calculated from previous steps in the model. 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 – Includes external estimates of transformer shipments and

quantity index of transformers manufactured. 

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

before 2001.

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

2001. 

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 upon 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 

The Department 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 trial standard. 

The Department obtained an estimate of sales (for the entire market) for the year 2001,

disaggregated by product class and kilovolt-ampere (kVA) rating.1 The historical series of the

power distribution and specialty transformer manufacturing (North American Industry

Classification System (NAICS) code 335311) quantity index for 1977 to 2003 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 2003.2 Market shares for

both liquid-immersed and dry-type distribution transformers came from the 2001 shipments

estimate by product type and kVA rating. Using the sales estimate for 2001 as a reference point

and the BEA quantity index data, the Department estimated aggregate transformer shipments

from 1977 to 2003.

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

shipped and the approximate value of these shipments. The distribution transformer industry's

total sales were about $1.6 billion dollars in 2001.

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Table 9.3.1 Distribution Transformer Shipment Estimates for 2001

Product Class (PC) Units 

Shipped

MVA

Capacity

Shipped

Shipment Value

2001$ million

Liquid-Immersed, Medium-Voltage, Single-Phase, (PC 1) 977,388 36,633 698.8

Liquid-Immersed, Medium-Voltage, Three-Phase, (PC 2) 79,367 42,887 540.4

Dry-Type, Low-Voltage, Single-Phase, (PC 3) 23,324 983 17.8

Dry-Type, Low-Voltage, Three-Phase, (PC 4) 290,818 21,909 235.0

Dry-Type, Medium-Voltage, Single-Phase, 20-45 kV BIL,* (PC 5) 119 18 0.5

Dry-Type, Medium-Voltage, Three-Phase, 20-45 kV BIL, (PC 6) 650 776 13.5

Dry-Type, Medium-Voltage, Single-Phase, 46-95 kV BIL, (PC 7) 121 22 0.6

Dry-Type, Medium-Voltage, Three-Phase, 46-95 kV BIL, (PC 8) 2,371 3,913 68.1

Dry-Type, Medium-Voltage, Single-Phase, >96 kV BIL, (PC 9) 20 4 0.1

Dry-Type, Medium-Voltage, Three-Phase, >96 kV BIL, (PC 10) 187 367 6.4

Total 1,374,366 107,512 1,581.2

* BIL = Basic Impulse insulation Level

Tables 9.3.2 through 9.3.4 present the disaggregated shipment estimates for 2001 by

product class and kVA rating. 

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Table 9.3.2 Liquid-Immersed Distribution Transformer Shipment Estimates, 2001

Liquid-Immersed, Medium-Voltage,

Single-Phase

Liquid-Immersed, Medium-Voltage,

Three-Phase

kVA Units Shipped kVA Units Shipped

10 114,594 15 -

15 167,234 30 -

25 277,581 45 605

37.5 66,977 75 1,816

50 242,931 112.5 4,842

75 44,214 150 9,078

100 49,696 225 9,078

167 9,762 300 17,552

250 2,158 500 17,552

333 1,188 750 6,219

500 1,040 1000 4,523

667 4 1500 3,769

833 8 2000 1,884

- - 2500 2,450

Total Units 977,388 Total Units 79,367

Total MVA 36,633 Total MVA 42,887

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Table 9.3.3 Dry-Type, Low-Voltage Distribution Transformer Shipment Estimates, 2001

Dry-Type, Low-Voltage,

Single-Phase*

Dry-Type, Low-Voltage,

Three-Phase

kVA Units Shipped kVA Units Shipped

15 2,554 15 24,484

25 4,573 30 56,511

37.5 4,396 45 65,474

50 9,759 75 85,354

75 1,108 112.5 24,150

100 929 150 17,265

167 - 225 9,505

250 4 300 5,460

333 - 500 2,190

- - 750 420

- - 1000 5

Total Units 23,324 Total Units 290,818

Total MVA 983 Total MVA 21,909

*Note: These estimates do not include sand-resin (epoxy-potted) units.

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Table 9.3.4 Dry-Type, Medium-Voltage Distribution Transformer Shipment Estimates,

2001

Dry-Type, Medium-Voltage,

Single-Phase

Dry-Type, Medium-Voltage,

Three-Phase

kVA Units Shipped kVA Units Shipped

20-45kV

BIL

46-95kV

BIL

>96kV

BIL

20-45kV

BIL

46-95kV

BIL

>96kV

BIL

15 3 2 - 15 2 1 -

25 7 3 - 30 4 2 -

37.5 10 5 - 45 4 2 -

50 17 8 - 75 7 3 -

75 20 25 5 112.5 20 11 -

100 20 25 5 150 18 11 -

167 12 15 3 225 20 19 1

250 6 8 1 300 59 60 2

333 12 15 3 500 76 150 5

500 12 15 3 750 80 177 5

667 - - - 1000 80 320 10

833 - - - 1500 80 390 32

- - - - 2000 100 575 56

- - - - 2500 100 650 76

Total Units 119 121 20 Total Units 650 2,371 187

Total MVA 18.4 22.1 4.1 Total MVA 776 3,913 367

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

assumption 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 the Department does

not have sufficient data to characterize such transformer size trends. 

The second major 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

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

transformers is relatively constant over the period from 1977 to 2003. The Department made this

assumption because more 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 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 2003.2 Specifically, the Department used the following equation to backcast

shipments from 2003 to 1977: 

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 < 2003 (MVA), 

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

(MVA), and 

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

Annual shipments of transformer capacity for 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) Annual Energy Review 2003, a proxy for growth of transformer sales

during this period.3 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 2005 (AEO2005) (W-hr).

4

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0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

0369

1215182124273033363942454851545760

Age (years)

Capacity (MVA)

Figure 9.3.1 Age Distribution of Liquid-Immersed In-Service Transformer Stock in 2004

9.3.3 Shipments Forecast 

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

Department constructed a forecast of transformers shipments. This forecast provides the

necessary input for equipment expense and in-service transformer stock accounting.

The Department 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 is 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. The Department examined the possibility

of modeling the fluctuations in transformers shipped using a bottom-up model where 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, the Department

de-coupled 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. Figure 9.3.1 shows the estimated age distribution of the in-service stock of liquidimmersed transformers in 2004. The Department developed similar age distributions for lowvoltage and medium-voltage dry-type transformers.

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The Department constructed the transformer shipments forecast assuming that

transformer shipments growth is equal to forecasted growth in electricity consumption as given

by the AEO2005 forecast up to the year 2025.4 For the years from 2026 to 2038, DOE

extrapolated the AEO 2005 forecast using its growth rate of electricity consumption between

2015 and 2025. Specifically, the Department used the following equation for the shipments

forecast: 

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

where: 

TotShip(y) = the total capacity of shipments estimated for year y where 2003 < y

# 2038 (MVA), and 

AllElec(y) = national electricity consumption forecasted for year y by AEO2005

(or by an extrapolation of AEO2005 data) (W-hr).

The next section describes how the Department adjusted its base case scenario forecast to

account for price increases arising from a trial standard.

9.3.4 Long-Term Purchase Elasticity

The Department used a purchase elasticity to adjust the base case shipments forecasts for

potential transformer price increases due to a trial 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 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

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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 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 trial 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

The Department constructed a model employing a standard econometric logit equation,

used for general applications of market response to costs and perceived utility, to model utility

and customer decision-making. For liquid-immersed transformers, the model was fitted to

transformer purchase data from FERC Form No. 15 to determine the parameters of the logit

equation. This resulted in a value of -0.04 for price elasticity. The Department 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 was not available. Since dry-type

units are primarily used in commercial and industrial applications, as are unitary air conditioners,

the Department used sales and price data for the latter for estimating price elasticity. The model

was fitted to the Air-Conditioning and Refrigeration Institute's sales data6 and real Producer Price

Index (PPI) of unitary air conditioners.7 The resulting value of elasticity was -0.02. The

Department 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.

9.3.5 Liquid-Immersed/Dry-Type Market Shares

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

the total capacity of transformers shipped from 1950 to 2038. In order to disaggregate the total

capacity into the capacity for different types of transformers, the Department applied a capacity

market share estimate. To distinguish between liquid-immersed and dry-type transformers, the

Department applied a liquid-immersed and dry-type market share, respectively. To distinguish

between different product classes and size categories within each product class, the Department

used 2001 market shares estimates.

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The Department used trends in electricity consumption from EIA’s retail sales data to

estimate market share trends for liquid-immersed and dry-type transformers.3 Assuming that

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

transformers, the following market share model can be derived: 

LiqShip(y) = CL × AllElec(2001); where CL = LiqShip(2001) / AllElec(2001) Eq. 9.6

DryShip(y) = CD × CIElec(2001); where CD = DryShip(2001) / CIElec(2001) Eq. 9.7

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), 

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 the Department 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 product classes, the Department

assumed that the relative market share within each transformer type (i.e., liquid-immersed or drytype) is constant over time. Given a lack of detailed, long-term, market share data, an alternative

assumption regarding kVA ratings and product class market shares may not be feasible.

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

the characteristics of transformer shipments are completely specified. The next step is to provide

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

9.3.6 Stock Accounting 

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

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

input to both the NES and NPV calculations, since the operating costs for any year depend on the

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

because under a trial standard scenario that produces increasing efficiency over time, older, lessefficient transformers may have higher operating costs, while younger, more-efficient

transformers will have lower operating costs.

The Department calculated total in-service stock of distribution transformers by

integrating historical shipments starting from the year 1950. As transformers are added to the inservice stock, some of the older ones retire and exit the stock. 

To estimate the shipment forecasts, the Department 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 1 ) ( ) Ship y 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 transformer purchased in a particular year (MVA).

This equation says 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 which describe the accounting of the existing in-service stock of transformer

units:

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

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a

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

b

 The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering. It is used to

model material strength, times-to-failure of electronic and mechanical components, equipment or systems. 

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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. The Department 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 adapted from an earlier study for the Department, ORNL

6804/R1, p. D-1.8

r age ( ) ( ) Eq. 9.12

age

d

e

constfail age corrfail age ( ) = − exp





























− ⋅ −

 −









1 1 

15

where: 

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% per yeara, and

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

The parameters of the Weibullb distribution are adjusted to maintain an average lifetime of 32

years. The failure rates and the lifetime are adapted from ORNL 6804/R1, p. D-1.

The Department 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 below:

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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

Age of Unit (years)

Probability of Failure in Year t to t+1 (%)

Figure 9.3.2 Fraction of Original Shipment Retiring

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.

Figures 9.3.2 shows the retirement rate of distribution transformers.

Once the retirement probability function is specified, the remaining input to the stockaccounting equation is the initial in-service stock of transformers as described in the next section.

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a

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

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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 1% of the in-service transformer capacity. The Department carried out

further research and had 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, the Department did not include major

refurbishments in the current analysis. Minor refurbishment is widespread and is already

captured in the retirement function. 

9.3.9 Initial Stock 

The Department initialized the stock-accounting model in the year 1950 which was the

first year that electricity consumption data was available.3 For simplicity, the Department set the

in-service transformer stock in the first year at zero.a This number does not affect the analysis

because most of the transformer stock from the year 1950 will no longer be in service post-2001.

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 trial standard

must be defined. The Department assumed for this analysis that any new energy-efficiency

standard for distribution transformers will become effective in 2010. The exact effective date of

the standard is January 1, 2010, so that all distribution transformers purchased starting on the

first day of the year 2010 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 trial standard level. It therefore consists of those in-service

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transformers that are purchased in or after the year the trial standard level has taken effect, as

described by the following equation:

Aff Stock y Ship y Stock age Eq. 9.14

age

y Std year

_ ( ) ( ) ( )

_

= +

=

−

∑

1

where:

Aff_Stock(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 the shipments, in-service stocks, and affected stocks of transformers have been

completely specified, it is possible to proceed to the NES and NPV models and calculations, as

described in the Chapter 10. 

9.4 RESULTS

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

shipped annually from 2010 through 2038. Total shipments depend on transformer lifetime and

growth in new electricity demand. The Department does not expect any direct effect on total

shipments in the long term from energy-efficiency standards. Total shipments for all trial

standard levels (TSLs) for liquid-immersed and dry-type distribution transformers are shown in

Table 9.4.1.

Table 9.4.1 Cumulative Shipments of Transformers by Trial Standard Level, 2010–2038

Distribution

Transformers

Transformer Capacity Shipments in Thousand MVA

Base Case TSL 1

(TP 1)

TSL 2 TSL 3 TSL 4 TSL 5 TSL 6

Liquid-Immersed 3501.3 3498.7 3494.7 3487.2 3484.4 3452.1 3420.7

Dry-Type 1290.6 1289.4 1288.2 1286.6 1283.7 1277.7 1277.6

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

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to the transformer manufacturer. The net financial impact of these opposing effects is examined

in the manufacturer impact analysis in Chapter 12.

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

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

.html. Instructions for using the spreadsheet are in Appendix 10A of this TSD.

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REFERENCES

1. HVOLT Consultants Inc., P. Hopkinson, and J. Puri. Distribution Transformer Market

Shipment Estimates for 2001. February 17, 2003. 3704 High Ridge Road, Charlotte, NC,

28270, tel: (704) 846-3290, e-mail: P.Hopkinson@hotmail.com. Prepared for Navigant

Consulting, Inc., Washington DC. 

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

Accounts Information Guide. Annual Industry Accounts. Gross Domestic Product (GDP)

by Industry. 2005. (Last accessed May 11, 2005.) This material is available in Docket

#83. Contact Ms. Brenda Edwards-Jones, U.S. Department of Energy, Building

Technologies Program, Mailstop EE-2J, 1000 Independence Avenue, SW, Washington,

DC, 20585-0121, telephone (202) 586-2945 for more information. <For download page,

see http://www.bea.gov/bea/dn2/iedguide.htm#gpo . For 1977-1997 data, go to

http://bea.gov/bea/pn/GDPbyInd_SHIP_SIC.xls . For 1998-2003 data, go to

http://bea.gov/bea/pn/GDPbyInd_SHIP_NAICS.xls .>>

3. U.S. Department of Energy-Energy Information Administration. Annual Energy Review

2003, Chapter 8: Electricity, Table 8.9 Electricity End Use, 1949-2003. 2004. (Last

accessed May 9, 2005.) This material is available in Docket #83. Contact Ms. Brenda

Edwards-Jones, U.S. Department of Energy, Building Technologies Program, Mailstop

EE-2J, 1000 Independence Avenue, SW, Washington, DC, 20585-0121, telephone (202)

586-2945 for more information. <http://www.eia.doe.gov/emeu/aer/txt/stb0809.xls>

4. U.S. Department of Energy - Energy Information Administration. Annual Energy Outlook

2005: With Projections Through 2025. January, 2005. Washington, DC. Report No.

DOE/EIA-0383(2005). <http://www.eia.doe.gov/oiaf/aeo/index.html>

5. U.S. Department of Energy - Federal Energy Regulatory Commission. Form No. 1 -

Electric Utility Annual Report. 2002. (Last accessed February 11, 2005.) This material is

available in Docket #83. Contact Ms. Brenda Edwards-Jones, U.S. Department of

Energy, Building Technologies Program, Mailstop EE-2J, 1000 Independence Avenue,

SW, Washington, DC, 20585-0121, telephone (202) 586-2945 for more information.

<http://www.ferc.gov/docs-filing/eforms/form-1/form1_blank.pdf>

6. Air-Conditioning and Refrigeration Institute. 1999 Statistical Profile of the AirConditioning, Refrigeration, and Heating Industry. 1999. Arlington, VA. 

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

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

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PCU3585#2 (N). 2005. (Last accessed April 11, 2005.) This material is available in

Docket #83. Contact Ms. Brenda Edwards-Jones, U.S. Department of Energy, Building

Technologies Program, Mailstop EE-2J, 1000 Independence Avenue, SW, Washington,

DC, 20585-0121, telephone (202) 586-2945 for more information.

<http://bls.gov/ppi/home.htm>

8. Barnes, P. R., J. W. Van Dyke, B. W. McConnell, S. M. Cohn, and S. L. Purucker. The

Feasibility of Replacing or Upgrading Utility Distribution Transformers During Routine

Maintenance. 1995. Oak Ridge National Laboratory. Oak Ridge, TN. Report No. ORNL6804/R1. < http://www.ornl.gov/~webworks/cpr/v823/rpt/78562.pdf>

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