dt_nopr_tsd_chp9 092211 DRAFT

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- i CHAPTER 9

. SHIPMENTS ANALYSIS

TABLE OF CO NTENTS

9.1 INTRODUCTION

................................ ................................ ................................ ........... 9

- 1

9.2 MODEL OVERVIEW

................................ ................................ ................................ ..... 9

- 1

9.3 INPUTS T O 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 Re tirement 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 FIGURE S

Figure 9.2.1 Flowchart of Shipments Model

................................ ................................ ............ 9

- 3 Figure 9.3.1 Percent of Original Stock Retiring

................................ ................................ ..... 9

- 13dt_nopr_tsd_chp9 092211 DRAFT

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- 1 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 savi ngs (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 impact s of proposed standards. Shipments are also a necessary input to the manufacturer impact anal ysis (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 estimate s the rate at which the in

- service stock of transformers may be rep laced by new, more efficient unit s 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 replac e 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

.

T he 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 10 A of this technical support document d escrib es how to access and utilize the spreadsheets that support the shipments model and other models rela ted 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

. S ection

9.3 describes the da ta inputs and mod el 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 f or 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 shipmentdt_nopr_tsd_chp9 092211 DRAFT

9

- 2 scenarios for the base case and several standard levels

. The estimate included the age distribution

of each transformer type (classified according to equipment c lass ) 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 capa city

, 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 structure s. Replacements occur when transformers break down, corrode, are struck by lightning, or otherwise need to be replaced. P urchases for n ew capacity occur due to increases in electricity use that m ay 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 p art of the NES and NPV spreadsheet s 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

p arallelograms. 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 star ts 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 li sted below.

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

transformer s

. 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.dt_nopr_tsd_chp9 092211 DRAFT

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- 3 Figure 9.2.1 Flowchart of Shipments Modeldt_nopr_tsd_chp9 092211 DRAFT

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- 4 9.3 INPUTS TO MODEL

The shipments model utiliz es 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 i nclude 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 200 9

. 4. Long

- term price elasticity of transformer purchase s

. 5. A nnual 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 refurbis hed/rewound.

9

. T he 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 k ey output of the shipments model that is an input for the NES/NPV calculation and represents that p ercentage 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 s tock create nearly proportional changes in the estimate d energy savings from a standard.

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

200 9 , disaggregated by transformer type (whether liquid

- immersed or dry

- t ype) and kilovolt

ampere (kVA) rating

. 1,2 D OE 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

– 200 8 is available from the U.S. Bureaudt_nopr_tsd_chp9 092211 DRAFT

9

- 5 of Economic Affairs (BEA). The BEA quantity index provides inf ormation on changes to aggregate shipments from 1977 to 200 8

. 3 Using the sales estimate s for 2001 an d 2009 as reference point s and the BEA quantity index data, DOE estimated aggregate transformer shipments from 1977 to 200 8

.

Table 9.3.1 presents DOE’s estimates of both units shipment and overall megavolt

amperes (MVA) shipped, and the approximate value of th o se shipments. T otal sales for the distribution transformer industry were about $1. 9 billion in 200 9

.

Table 9.3.1 Estimated Shipments of Distribution Transformer s, 200 9

Equipment Class Units Shipped Capacity Shipped

MVA Value of Shipment s

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 present s the shipment estimates for 200 9 for medium

- voltage liquid

immersed distribution transformers categorized by capacity and by equipment type whether single

- or three

- phase

.dt_nopr_tsd_chp9 092211 DRAFT

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- 6 Table 9.3.2 Estimated Shipments of Liquid

- Immersed , Medium

- Voltage

Transformer s , 200 9
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 200 9 for dry

- type medium

- voltage

distribution transformers categorized by capacity and by whether single

- or three

- phase

.

Table 9.3.3 Estimated Shipment s of Dry

- Type, Me dium

- Voltage Transformer s , 200 9

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 = b asic impulse insulation level

.dt_nopr_tsd_chp9 092211 DRAFT

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- 7 T he 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

dem and per customer increases, but DOE h as in sufficient 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 rule making. 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

– 200 9 . 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 shipment s 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

– 200 8

. 4 Specifically, DOE used the following equation to backcast shipments from 200 8 to 1977

.

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

.

W here :

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

1977 ≤ y < 200 8 (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 200 9

, a proxy for growth of transformer sale s during this period. 5 Using this method, the shipme nts for 1950

– 1977 are given by the following equation

.

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

.

W here :

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 20 10 ( AEO20 1 1 )

. 6dt_nopr_tsd_chp9 092211 DRAFT

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- 8 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 transformer s

. D OE 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 co mplex. This complexity can be seen in the

fluctuations in t he 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 bot tom

- 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 constructi ng the shipments forecast DOE decoupled

the overall shipments and retirements and us ed 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 forecaste d growth in electricity consumption, as given by the AEO201 1

forecast through 20 3 5

. 7 For 20 3 6

– 20 4 5 , DOE extrapolated the AEO 20 1 1 forecast, using its growth rate of electricity consumption between 20 2 5 and 20 3 5 . Specifically, DOE used the following equation for the shipments forecast

.

TotShip(y) = TotShip( 200 9 ) × AllElec(y) / AllElec(2001 )

.

W here :

TotShi p(y) = the total capacity of shipments estimated for year y where 201 1 < y ≤

20 4 5 (MVA) ; and AllElec(y) = the national electricity consumption for year y (kWh) forecasted by

AEO201 1 (or by an extrapolation of AEO201 1 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 P rice Elasticity

L ong

- 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)

.

W here :

dQ/Q = a small percentage change in quantity purchased ( Q ), anddt_nopr_tsd_chp9 092211 DRAFT

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- 9 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

.

W here :

Q(P) = the quantity purchased as a function of price, Q 0 = a reference quantity at a reference price P 0 , 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 el asticity to adjust forecasts of base

case 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 ma de by utilit ies and other customer s , DOE constructed

a model that employ s a standard econometric logit equation, such as those used for general applications of market response to costs and perceived utility. T o determine the parameters of the logit equatio n f or 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 f or liquid

immersed 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 hi storical purchase data were avail able f or 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 20 4 5 . To disaggregate the total capacity into the capacity for the two types of transformers, DOE assigned liquid

- immersed and dry

- type
market share s 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 sharedt_nopr_tsd_chp9 092211 DRAFT

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- 10 trends for the two type s of transformers. 5 Based on the a ssum ption that transformer sales over the long ter m track electricity sales for the sectors served by those transformers, DOE derived the following market share model

.

LiqShip(y) = CL × AllElec( y )

,

w here CL = LiqShip(2001) / AllElec(2001) **∀** y ≤ 2008 and

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

.

DryShip(y) = CD × CIElec( y )

,

w here 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)

.

W here :

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

, LiqShi p(2001) = the capacity of liquid

- immersed transformers shipped in 2001 (MVA )

, DryShip(2001) = the capacity of dry

- type transformers shipped in 2001 (MVA )

, LiqShip(200 9 ) = the capacity of liquid

- immersed transformers shipped in 200 9 (MVA )

, DryShip(200 9 ) = the capacity of dry

- type transformers shipped in 200 9 (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

share s of various kVA ratings and equipment class es 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 market shares by kVA rating and equipment class may not be supportable.dt_nopr_tsd_chp9 092211 DRAFT

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- 11 After fully specif ying 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 in

service transformer stock as inputs to develop an estimate of the age distribution of in

- service transformer stocks for all ye ars. The age distribution of in

- service transformer stocks i s a key input to calculations of both the NES and NPV, because the operating costs for any year depend

on the age distribution

. T he transformer age distribution affects operating costs because, un der a

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

less efficient transformers are higher than those of new er , more efficient transformers .

DOE calculated the total in

- service stock of distributio n 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)

.

W here :

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).

Th e above equation indicates that the number of one

- year

- old units is equal simply to the number of new transformer units purchased the p revious year. S lightly more complicated equations account for the existing in

- service stock of transformer units:

Stock(y + 1,age + 1) = Stock(y,age) × [1

− Prob Retire (age)]

.

Th e 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 . T hat fraction

is determin ed 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 specif ying a retirement probability function for distribution transformers

. DOE derived th is 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 Labora tory ( ORNL ) for DOE : 9dt_nopr_tsd_chp9 092211 DRAFT

9

- 12 r ( age ) = exp �

− � age

d � d � ( ( 1

− constfail ) age × ( 1

− constfail ) age

− 15 )

.

W here :

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 lif etime 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 :

Prob Retire (age) = [r(age

− 1)

− r(age)] / r(age)

.

W here :

Prob Retire (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.dt_nopr_tsd_chp9 092211 DRAFT

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 the ir retirement function. After review ing 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

. A morphous core technology is relatively recent (within the last couple of decades), however, and th e technology can re quire 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 replacement s because of size

or space c onstraints. 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 i ndependent of transfor mer efficiency.

9.3.8 Refurbishments and Rewinds

Transformers that are not retired can be refurbished and returned to the stock. Minor refurbishments may include repla cing connectors, bushings, or the oil. Major refurbishments

may include rewinding the transformer, a n 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

discus sions 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 re sponse 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 60Probability of Failure in Year t to t+1

Age of Unitdt_nopr_tsd_chp9 092211 DRAFT

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 stock

accounting 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 for 1950, 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 w ould no t 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. F or 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, 201 6 , so all distribution transformers manufactured or imported starting on the first day of

201 6 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 p ercentage 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 ) = S h ip ( y ) + ∑ Stock ( age ) y

− StdYear

age = 1 .

W here :

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.dt_nopr_tsd_chp9 092211 DRAFT

9

- 15 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 . T h o se calculations are described in c hapter 10

.

9.4 RESULTS

The primary output of the shipments model is the total capacity of distribution transformers shipped annually from 201 6 through 20 4 5 . Total shipments depend on transformer lifetime, the price elasticity of transformer purchases, and growth in new electricity demand.

T otal 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

, 201 6

– 204 5 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

T he 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 i mpact of these opposing

effects is examined in the MIA, chapter 12 of the notice of proposed rulemaking.dt_nopr_tsd_chp9 092211 DRAFT

9

- 16 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 Acc ounts: 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 Ou tlook 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, 2 010).

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).