10-i

CHAPTER 10. NATIONAL IMPACT ANALYSIS

TABLE OF CONTENTS

10.1 INTRODUCTION ......................................................................................................... 10-1

10.2 NATIONAL ENERGY SAVINGS ............................................................................... 10-4

10.2.1 Overview ........................................................................................................................ 10-5

10.2.2 Inputs.............................................................................................................................. 10-6

10.2.2.1 Size Scaling of Losses and Costs ................................................................. 10-6

10.2.2.2 Mapping Design Line Data to Equipment Classes ...................................... 10-8

10.2.2.3 Mapping Efficiency Level to Trial Standard Level ................................... 10-10

10.2.2.4 Root Mean Square Load ............................................................................ 10-11

10.2.2.5 Load Growth .............................................................................................. 10-11

10.2.2.6 Affected Stock ........................................................................................... 10-13

10.2.2.7 Unit Energy Consumption ......................................................................... 10-13

10.2.2.8 Site-to-Source Electricity Conversion ....................................................... 10-14

10.3 NET PRESENT VALUE ............................................................................................. 10-15

10.3.1 Overview ...................................................................................................................... 10-16

10.3.2 Inputs............................................................................................................................ 10-17

10.3.2.1 First Cost .................................................................................................... 10-18

10.3.2.2 Operating Costs .......................................................................................... 10-19

10.3.2.3 Peak Responsibility Factor ........................................................................ 10-20

10.3.2.4 Initial Peak Load ........................................................................................ 10-20

10.3.2.5 Scalar for Electricity Price Projections ...................................................... 10-21

10.3.2.6 Marginal Electricity Costs ......................................................................... 10-21

10.3.2.7 Discount Rate ............................................................................................. 10-21

10.3.2.8 Projection of Future Product Prices ........................................................... 10-22

10.4 RESULTS .................................................................................................................... 10-22

10.4.1 National Energy Savings and Net Present Value for Trial Standard Levels ............... 10-22

10.4.1.2 Results for Liquid-Immersed Distribution Transformers .......................... 10-23

10.4.1.3 Results for Low-Voltage Dry-Type Distribution Transformers ................ 10-24

10.4.1.4 Results for Medium-Voltage Dry-Type Distribution Transformers .......... 10-24

10.5 ANNUALIZED NATIONAL COSTS AND BENEFITS ........................................... 10-25

10.5.1 Calculation Method ...................................................................................................... 10-26

10.5.2 Results for the Considered Standards .......................................................................... 10-27

LIST OF TABLES

Table 10.2.1 Mapping of Design Line to Equipment Class .................................................... 10-9

Table 10.2.2 Mapping of Efficiency Levels to Trial Standard Levels for LiquidImmersed Transformers ................................................................................... 10-11

Table 10.2.3 Mapping of Efficiency Levels to Trial Standard Levels for Low-Voltage 

Dry-Type Transformers ................................................................................... 10-11
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Table 10.2.4 Mapping of Efficiency Levels to Trial Standard Levels for MediumVoltage Dry-Type Transformers...................................................................... 10-11

Table 10.2.5 Average Site-to-Source Conversion Factors for No-Load Losses and Load 

Losses ............................................................................................................... 10-15

Table 10.3.1 First Cost of Distribution Transformers by Trial Standard Level and 

Equipment Class (2011$/kVA) ........................................................................ 10-19

Table 10.3.2 Peak Responsibility Factors by Equipment Class ............................................ 10-20

Table 10.3.3 Initial Peak Loading by Equipment Class ........................................................ 10-20

Table 10.3.4 Marginal Energy and Capacity Costs by Equipment Class ............................. 10-21

Table 10.4.1 Results for Cumulative National Energy Savings (2016–2045) and Net 

Present Value (2016–2104).............................................................................. 10-23

LIST OF FIGURES 

Figure 10.1.1 Flowchart of National Impact Analysis ............................................................. 10-3

Figure 10.4.1 Liquid-Immersed Distribution Transformers: Impacts of Standards on 

National Energy Savings and Net Present Value ............................................. 10-23

Figure 10.4.2 Low-Voltage Dry-Type Distribution Transformers: Impacts of Standards 

on National Energy Savings and Net Present Value ........................................ 10-24

Figure 10.4.3 Medium-Voltage Dry-Type Distribution Transformers: Impacts of 

Standards on National Energy Savings and Net Present Value ....................... 10-25
10-1

CHAPTER 10. NATIONAL IMPACT ANALYSIS

10.1 INTRODUCTION

 The Energy Policy and Conservation Act of 1975, as amended, (EPCA) requires that any 

new or amended energy efficiency standard for distribution transformers shall be designed to 

achieve the maximum improvement in energy efficiency that is both technologically feasible, 

economically justified, and would save a significant amount of energy. (42 U.S.C. 6295(o)(2)(A) 

and (B), and 6317(a)(1). In determining whether a standard is economically justified. the U.S. 

Department of Energy (DOE) is required to determine whether the benefits of the potential 

standard outweigh its burdens. Key factors in the determination are (1) the total projected 

amount of energy savings likely to result directly from the imposition of the standard, and (2) the 

savings in operating costs throughout the life of the covered equipment when compared to any 

increase in its price, initial charges, such as installation costs, or maintenance−any of which are 

likely to result from promulgation of the standard. 

To satisfy the above EPCA requirements and more fully understand the overall impact of 

potential energy efficiency standards for distribution transformers, DOE conducted a national 

impact analysis (NIA). The NIA assessed future national energy savings (NES) from energy 

conservation standards for distribution transformers and the national economic impact using the 

net present value (NPV). This chapter describes the methodology DOE used to estimate the 

national impacts of trial standard levels (TSLs) for medium-voltage liquid-immersed distribution 

transformers, and low- and medium-voltage dry-type distribution transformers. The analyses that 

preceded the shipments analysis in chapter 9 of the Technical Support Document (TSD) (e.g., the 

engineering analysis (chapter 5) and the life-cycle cost analysis (chapter 8) examined

transformers by design-line, which accounts for the 14 distinct design options found in 

transformers. Additionally for the NIA, DOE is required to examine impacts as they relate to 

equipment classes, because the final standards will apply to equipment classes, not design-lines. 

DOE evaluated the following impacts: (1) NES attributable to each potential standard, (2) 

monetary value of the NES to purchasers of the considered equipment, (3) increased total 

installed cost of the equipment because of standards, and (4) NPV of energy savings (the 

difference between the operating cost savings and increased total installed cost). 

 To conduct its NIA, DOE determined both the NES and NPV for each trial standard level

being considered for distribution transformers. DOE performed all calculations for each 

considered equipment class using a Microsoft Excel spreadsheet model. The national impact 

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

http://www1.eere.energy.gov/buildings/appliance_standards/product.aspx/productid/66. 

The spreadsheets combine the calculations for determining the NES and NPV for each 

considered equipment class with input from the appropriate shipments model that DOE used to 

forecast future purchases of transformers. Chapter 9 provides a detailed description of the 

shipments model, including customers’ sensitivities to total installed cost, operating cost, and 

income, and how DOE captured those sensitivities within the model. The NES and NPV together 
10-2

constitute the NIA model. Additional details, along with instructions for using the NIA 

spreadsheet, are provided in appendix 10A of this TSD. 

 Figure 10.1.1 presents a flow diagram of the model and spreadsheets used to perform the 

NIA (NES and NPV) for distribution transformers. In the diagram, arrows show the direction 

that information flows when the calculation is performed. The process begins with inputs (shown 

as parallelograms). As information flows from the inputs, it 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 NIA calculation starts with the shipments model (chapter 9), which is shaded in the 

flow diagram. For transformers, the model integrated the inputs of estimates of 2001 and 2009 

shipments from DOE’s contractor,1,2 the U.S. Bureau of Economic Analysis (BEA) transformer 

quantity index,3 electricity market shares from DOE’s Energy Information Administration 

(EIA),4,5 and equipment price estimates from DOE’s life-cycle cost (LCC) analysis. The model 

produced both a backcast and a forecast of total shipments. DOE used the total shipments and a 

retirement function to produce an accounting of in-service transformers (stocks), thereby 

enabling DOE to estimate the stock that would be affected by trial standard levels and 

transformer retirements. 

 DOE used a scaling factor (described in section 10.2.2.1) to estimate the national impacts 

of new standards for all the equipment classes considered in this rulemaking. The scaling factor 

is applied to the equipment cost and annual energy consumption of each representative 

transformer size so they can describe all sizes within that equipment class. 
10-3

Figure 10.1.1 Flowchart of National Impact Analysis 

 Following the calculation of shipments, the calculations of NES and NPV begin. For both 

calculations, key inputs from the LCC analysis are the average rated no-load and load losses and 

the cost of transformers, including installation. DOE adjusted the losses and equipment costs for 

transformer size and type to convert the applicability of the data from representative design-lines 

in to average equipment classes. Additional inputs on average and peak losses—including root 

mean square (RMS) loading, peak loading, and peak responsibility factor—enabled DOE to 
10-4

convert rated losses into actual losses. At this point, the information flow for the NES and NPV 

calculation splits into two paths. 

 On one path, the NES calculation sums the kilowatt-hours of energy consumed by the 

affected stock, taking the difference between the base-case and standards scenario to calculate 

site-energy savings. DOE converted site-energy savings to energy savings at the source (i.e., at 

the power plant), using average heat rates for base load and peak load generation from DOE’s 

National Energy Modeling System (NEMS).

6 The average heat rates from NEMS include 

transmission and distribution losses. Summing the annual energy savings for the forecast period, 

which extends from 2016 through 2045, provides the final NES result. 

 On the other path, the NPV calculation starts with marginal price inputs from the LCC 

analysis for both energy and capacity costs and for both load and no-load losses. The marginal 

prices, combined with the actual peak and average losses, provide estimates of operating costs. 

Meanwhile, the adjusted cost of installed equipment times the annual shipments provides the 

estimate of the total annual equipment costs. DOE calculated three differences to assess the net 

impact of each TSL. The first difference was between equipment costs in each TSL scenario and 

the base case to obtain the net increase in equipment cost attributable to the TSL. The second 

difference was between operating costs under the base-case scenario and each TSL to obtain the 

net operating cost savings from the TSL. The third difference was between the net operating cost 

savings and the net increase in equipment cost, which provides the net expense or savings for 

each year. To obtain the NPV impact of a TSL, DOE discounted the net expenses or savings to 

2011$ and summed them for 2016–2105a (the year the last unit shipped in 2045 retires from 

service) for transformers purchased during 2016–2045. 

 The two models that comprise the NIA are described below—the NES model in section 

10.2, and the NPV model in section 10.3. Each description begins with a summary of the model, 

followed by an overview of how DOE performed that model’s calculations. Then model inputs 

are summarized. The final subsections of the two sections describe each of the major inputs and 

computational steps in detail and with equations when appropriate. After the technical 

descriptions of the models, this chapter presents the results of the NIA calculations.

10.2 NATIONAL ENERGY SAVINGS

 DOE developed the NES model to estimate the total NES using results from the 

shipments model combined with information from the LCC on energy savings. The savings 

shown in the NES reflect decreased energy losses resulting from the installation of new, more 

efficient transformer units nationwide, in comparison to a base case in which there are no 

national standards. Positive values of NES correspond to net energy savings, specifically a 

decrease in energy consumption after implementation of a standard, in comparison to the energy 

consumption in the base-case scenario.

 

a The analysis period for NPV is based on the cumulative operating cost savings of the last unit shipped (2045 + 

maximum transformer life -1).
10-5

10.2.1 Overview

DOE calculated the cumulative incremental energy savings from each potential 

transformer efficiency standard relative to a base-case scenario of the current efficiency standard. 

It calculated NES, in units of quads, throughout the forecast period for standards that it assumed 

will be effective in 2016. The NES calculation started with estimates of transformer shipments 

and stocks (in-service transformers), which are outputs of the shipments model (chapter 9). DOE 

then obtained estimates of transformer energy losses from the LCC analysis (chapter 8), and 

calculated the total energy use by the stock of transformers for each year for both a base case and 

a standards case. In each standards case, as more efficient transformers replace less efficient ones

that retire from service, the energy per unit capacity used by the stock of transformers gradually 

decreases relative to the base case. DOE used a site-to-source conversion factor to convert the 

amount of energy used by the transformers into the amount of energy consumed at the source of 

electricity generation (the source energy). The site-to-source conversion factor accounts for 

transmission, distribution, and generation losses. For each year analyzed, the difference in source 

energy use between the base case and the standards scenario is the annual energy savings. DOE 

summed the annual energy savings from 2016 through 2045 to calculate the total NES for the 

forecast period. 

 In calculating the NES, DOE did not assume any trends in transformer nameplate 

efficiency besides the incremental improvement indicated by the LCC calculation. In examining 

proprietary shipments data provided by the transformer industry, DOE found that the data 

revealed no conclusive trends in improved efficiency. Deciding that future efficiency trends 

generally are indeterminate, DOE chose to use fixed baseline efficiency. DOE also assumed that 

the efficiency of transformers does not degrade over time. Therefore the annual energy savings 

can be described in terms of an affected stock, as described in section 9.3.11 of the shipments 

chapter. Annual energy savings therefore are described by the following equation. 

AES(y) = (UECBase − UECStd) × Aff_Stock(y) 

Where: 

AES(y) = the annual energy savings in year y, 

UECBase = the site unit energy consumption for the base case, 

UECStd = the site unit energy consumption for the standards case, and 

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

 Given the annual energy savings, the cumulative NES can then be calculated as a simple 

sum. 

NES= � SiteToSource(y) × AEC(y)

2045

y=Stdyear
10-6

Where: 

Stdyear = the year standards come into effect,

SiteToSource(y) = the site-to-source conversion factor in year y, and

AEC = the annual energy consumption. 

After the shipments model provides the estimate of affected stock, the NES calculates

UECBase and UECStd using the output from the LCC analysis and including the site-to-source 

conversion factor. The following section summarizes the inputs necessary for the NES 

calculation and then describes each input individually. 

10.2.2 Inputs 

Inputs to the NES model fall into three broad categories: (1) those that help convert the 

data from the LCC into data relevant to the equipment classes and transformer size distributions 

used in the NES; (2) those that help calculate the unit energy consumption; and (3) the site-tosource conversion factor, which enables the calculation of source energy consumption from site 

energy use. The specific NES model inputs are: 

1. size scaling of losses and costs, 

2. mapping of LCC design line data to equipment classes, 

3. root mean square loading, 

4. load growth, 

5. affected stock, 

6. effective date of standard, 

7. unit energy consumption, and

8. electricity site-to-source conversion. 

 Each input is described further below. 

10.2.2.1 Size Scaling of Losses and Costs 

Transformers are produced over a broad range of capacities, only a few of which are 

modeled explicitly in this analysis. The modeled designs are referred to as representative units. 

Any given equipment type includes 2-4 representative units at different capacity, or kVA values. 

DOE used a scaling relationship, or equation, to project the economic results from a given 

transformer design line to similar transformers of different sizes. This relationship is a key 

element in adjusting losses and costs from a representative transformer in the LCC to the 

distribution of transformer sizes incorporated in the calculation of NES and subject to potential 

standards. The Department uses the 0.75 scaling rule to scale the cost and efficiency results for 

the modeled kVA values to the full capacity range for each type, the 0.75 scaling rule is 

discussed in greater detail in chapter 5. This rule assumes that both the physical and cost 

characteristics are determined by the quantity of material required to build the transformer, and is 

approximately true. In practice, if the kVA-range over which cost and efficiency data are to be 

scaled is large, the 0.75 rule is less accurate. This manifests as kinks or angles in the curve of 

efficiency as a function of capacity for a given equipment type. 
10-7

The Department has implemented a correction to the 0.75 scaling rule to produce 

smoother curves of efficiency versus capacity. This correction adjusts the value of the exponent 

(the 0.75 of the scaling rule) so that the curve extrapolates correctly between any two 

representative units. Mathematically, the efficiency of a transformer is equal to the ratio: 

Eff = Load

(Load + Losses)

Where:

Eff = transformer efficiency

Load = the load on the transformer 

Losses = the transformer’s combined no-load and load losses. 

 

 Load is proportional to capacity kVA, and if the 0.75 scaling rule is valid, losses are 

proportional to (kVA)

0.75. This expression can thus be written as, 

Eff = 1

(1 + Constant × (kVA)−0.25)

 Defining the loss function as 

Losses = 

1

Eff − 1 ,

Losses = Constant × (kVA)−0.25

 For two representative units labeled 1 and 2, 

Log �

Losses1

Losses2

� = −0.25 Log �

kVA1

kVA2

�

 The validity of the 0.75 scaling rule can thus be tested by evaluating the ratio,

x =

−Log �

Losses1

Losses2 � �

Log �

kVA1

kVA2 � �

 The Department uses the exponent x calculated through the above equation, instead of the 

value -0.25 implied by the scaling rule, to interpolate the efficiency between any two 

representative units. The DOE uses the unmodified scaling rule to extrapolate efficiency values 

to capacities below the minimum representative unit, or above the maximum representative unit.
10-8

The DOE calculated an adjustment factor using the exponent x to account for the fact that 

the representative design-line unit used in the engineering analysis is not the “average” size for 

the set of transformers that the design line represents. This adjustment factor is given by the 

following equation. 

AdjFactor = 

∑ [Shipi × Capi i 1+X]

(CapDL1+X × ∑ Shipii )

Where: 

AdjFactor = the adjustment factor that, when multiplied by the design line losses or 

costs, gives the shipment-weighted losses or costs per transformer; 

Shipi = the shipments in the i-th size category; 

Capi = the rated capacity of the transformers in the i-th size category; and

CapDL = the rated capacity of the representative unit of the design line. 

 DOE also used the shipment-weighted average size of transformers represented by a 

particular design line to calculate the average loss per capacity (AvgLossPerCapDL), as described 

by: 

AvgLossPerCapDL = LossPerCapDL × AdjFactor × CapDL

Capavg

Where: 

LossPerCapDL = the loss, or cost per unit capacity, for the design line unit from the 

LCC analysis, and

Capavg = the shipment-weighted average size of transformers represented by a 

particular design line.

After the losses and costs from the LCC were adjusted to represent the correct size 

distribution, they needed a further adjustment to represent the appropriate equipment classes, as 

described in the following section. 

10.2.2.2 Mapping Design Line Data to Equipment Classes

The calculations of NES and NPV use the LCC calculations (chapter 8) as the source of 

most input data. DOE performed the LCC calculations by design line, whereas any standard will 

be promulgated by equipment class. As a first step, therefore, the NES calculation aggregates the 

LCC design line data into equipment classes. DOE used this aggregation method to prepare for 

estimating economic impacts by equipment class.
10-9

To represent the range of designs in some distribution transformer equipment classes, 

DOE often analyzed several design lines per equipment class. For example, equipment class 1B 

(single-phase, medium-voltage, pole-mounted, liquid-immersed transformers) is represented by 

two design lines, as is equipment class 2A (three-phase, medium-voltage, liquid-immersed 

transformers) which is also represented by two design lines. DOE did not specifically examine 

some equipment classes. For three-phase, liquid-immersed, equipment class 2B, DOE used 

factors for the appropriate single-phase design lines multiplied by three. For single-phase, 

medium-voltage, dry-type design lines, equipment classes 5, 7, and 9, DOE used factors for the 

appropriate three-phase design lines divided by three. Table 10.2.1 presents the mapping of 

design line (DL) to equipment class (EC).

Table 10.2.1 Mapping of Design Line to Equipment Class

Equipment Class BIL* kV Capacity kVA Mapping

1 Liquid-immersed, medium-voltage, single-phase < 200 10–833 DL 1 + DL2 + DL3 

2 Liquid-immersed, medium-voltage, three-phase < 200 15–2,500 DL4 + DL5

3 Dry-type, low-voltage, single-phase ≤ 10 15–333 DL6

4 Dry-type, low-voltage, three-phase ≤ 10 15–1,000 DL7+DL8

5 Dry-type, medium-voltage, single-phase 20–45 15–833 (DL9 + DL10)/3

6 Dry-type, medium-voltage, three-phase 20–45 15-2,500 DL9 + DL10

7 Dry-type, medium-voltage, single-phase 46–95 15–833 (DL11 + DL12)/3

8 Dry-type, medium-voltage, three-phase 46–95 15–2,500 DL11 + DL12

9 Dry-type, medium-voltage, single-phase > 95 75–833 (DL13A + DL13B)/3

10 Dry-type, medium-voltage, three-phase > 95 225–2,500 DL13A + DL13B

* BIL = basic impulse insulation level in kilovolts (kV).

 To aggregate losses from more than one design line, DOE applied the average of 

shipments weighted by capacity of the per-kilovolt-ampere (kVA) transformer characteristics 

from the economic analysis of the design lines to the estimated capacity shipped for each 

equipment class. DOE’s contractor1,2 provided the capacity shipped for each design line (and 

each equipment class). The LCC analysis provided the economic results for each design line, and 

DOE used the scaling method described in section 10.2.2.1 to estimate the scaled cost and loss 

estimates for each size category represented by each design line. The following equation 

provides the average loss per unit capacity for an equipment class (AvgLossPerCapEC) as derived 

from the average loss per unit capacity for a design line. The equation sums those design lines 

that constitute an equipment class.

AvgLossPerCapEC = ∑ [AvgLossPerCapDL × MSDL DL ]

∑ MSDLDL

.
10-10

Where: 

AvgLossPerCapDL = the average loss per unit capacity for the design line, and 

MSDL = the design line’s market share by capacity. 

The AvgLossPerCapEC represents the average loss per unit capacity of the transformer 

load. No further adjustment is needed for no-load losses. For load losses, however, the losses at 

rated load must be converted to losses at actual loading. Root mean square (RMS) loading is a 

key factor used in estimating load losses at actual loading. The following section describes the 

RMS loading input to the NES. 

10.2.2.3 Mapping Efficiency Level to Trial Standard Level 

DOE conducted the LCC analysis for up to seven energy efficiency levels (EL) for each 

representative unit in the 14 design lines. DOE selected the ELs for each design line by applying 

a set of economic and design criteria to intermediate LCC analyses as discussed in chapter 5, 

resulting in unique sets of EL efficiencies for each design line. It mapped these LCC analysis 

results to trial standard levels (TSLs) for the 10 equipment classes. 

 For liquid-immersed distribution transformers the efficiency levels in each TSL can be 

characterized as follows: TSL 1 represents an increase in efficiency where a diversity of 

electrical steels are cost-competitive and economically feasible for all design lines; TSL 2 

represents EL1 for all design lines; TSL 3 represents the maximum efficiency level achievable 

with M3 core steel; TSL 4 represents the maximum NPV with 7 percent discounting; TSL 5 

represents EL 3 for all design lines; TSL 6 represents the maximum source energy savings with 

positive NPV with 7 percent discounting; and TSL 7 represents the maximum technologically 

feasible level (max tech).

 For low-voltage, dry-type distribution transformers, the efficiency levels in each TSL can 

be characterized as follows: TSL 1 represents the maximum efficiency level achievable with M6 

core steel; TSL 2 represents base efficiency for DL 6, EL 3 for DL 7, and EL2 for DL 8; TSL 3 

represents the maximum EL achievable using butt-lap miter core manufacturing for single-phase 

distribution transformers, and full miter core manufacturing for three-phase distribution 

transformers; TSL 4 represents the maximum NPV with 7 percent discounting; TSL 5 represents 

the maximum source energy savings with positive NPV with 7 percent discounting; and TSL 6 

represents the max tech.

 For medium-voltage, dry-type distribution transformers, the efficiency levels in each TSL 

can be characterized as follows: TSL 1 represents EL1 for all design lines; TSL 2 represents an 

increase in efficiency where a diversity of electrical steels are cost-competitive and economically 

feasible for all design lines; TSL 3 represents the maximum NPV with 7 percent discounting; 

TSL 4 represents the maximum source energy savings with positive NPV with 7 percent 

discounting; and TSL 5 represents the max tech. 
10-11

Table 10.2.2 Mapping of Efficiency Levels to Trial Standard Levels for LiquidImmersed Transformers

Design Line TSL1 TSL2 TSL3 TSL4 TSL5 TSL6 TSL7

1 Liquid-Immersed, 50kVA, single-phase EL 1 (EL 0.4 actual) EL 1 EL 1 EL 2 EL 3 EL 4 EL 7

2 Liquid-Immersed, 25kVA, single-phase Base (EL 0.5 actual) EL 1 EL 1 EL 2 EL 3 EL 4 EL 7

3 Liquid-Immersed, 500kVA, single-phase EL 1 (EL 1.1 actual) EL 1 EL 2 EL 4 EL 3 EL 5 EL 7

4 Liquid-Immersed, 150kVA, three-phase EL 1 EL 1 EL 1 EL 2 EL 3 EL 4 EL 7

5 Liquid-Immersed, 1500kVA, three-phase EL 1 EL 1 EL 2 EL 4 EL 3 EL 5 EL 7

Table 10.2.3 Mapping of Efficiency Levels to Trial Standard Levels for Low-Voltage 

Dry-Type Transformers

Design Line TSL1 TSL2 TSL3 TSL4 TSL5 TSL6

6 LVDT, 25kVA, single-phase Base Base EL 4 EL 6 EL 6 EL 7 

7 LVDT, 75kVA, three-phase EL 2 EL 3 EL 4 EL 6 EL 6 EL 7 

8 LVDT, 300kVA, three-phase EL 2 EL 2 EL 4 EL 6 EL 7 EL 7 

Table 10.2.4 Mapping of Efficiency Levels to Trial Standard Levels for MediumVoltage Dry-Type Transformers

Design Line TSL1 TSL2 TSL3 TSL4 TSL5 

9 MVDT, 300kVA, three-phase, 45kV BIL EL 1 EL 1 EL 2 EL 2 EL 7 

10 MVDT, 1500kVA, three-phase, 45kV BIL EL 1 EL 2 EL 2 EL 2 EL 7 

11 MVDT, 300kVA, three-phase, 95kV BIL EL 1 EL 1 EL 4 EL 4 EL 7 

12 MVDT, 1500kVA, three-phase, 95kV BIL EL 1 EL 2 EL 4 EL 4 EL 7 

13A MVDT, 300kVA, three-phase, 125kV BIL EL 1 EL 1 EL 2 EL 4 EL 6 

13B MVDT, 2000kVA, three-phase, 125kV BIL EL 1 EL 2 EL 2 EL 2 EL 5 

10.2.2.4 Root Mean Square Load 

 Energy losses in transformers follow the RMS load, not the arithmetic average load. DOE 

calculated the RMS load as the RMS of the transformer load divided by the transformer rated 

capacity, then multiplied by the power factor. (As explained in chapter 6 of the TSD, although 

DOE’s analytical method can derive results for varying power factors, for the analysis presented 

here DOE set the power factor to a value of one.) DOE used the average national RMS load for 

each design line as calculated for the LCC analysis. Those values range from 22.1 percent to 

41.2 percent for the various design lines. 

10.2.2.5 Load Growth 

 The load growth is the fraction by which the load increases after a transformer is 

installed. DOE investigated load growth as a sensitivity analysis (described in appendix 10B). 

Load growth occurs when new equipment, new appliances, or additional activities increase the 
10-12

energy loads on the circuits served by distribution transformers. Load growth increases the load 

losses relative to those estimated to have occurred during the first year of installation. 

DOE calculated the fractional load growth from an estimated rate that it used as an input 

to the LCC analysis. There is a maximum load growth, LGRMax, which DOE set at 50 percent

for liquid-immersed transformers. The 50-percent value represents the approximate amount of 

growth in load that can occur without overloading the transformer beyond a reasonable point. 

When overloading occurs, DOE assumed that the transformer would be installed in a new 

location where the initial peak loading would be the same as when originally installed.7 See 

Institute of Electrical and Electronics Engineers, Inc. (IEEE) Standard C57.91-1995, Guide for 

Loading Mineral-Oil-Immersed Transformers and Step-Voltage Regulators,8 for details on 

permissible electrical overloading of mineral-oil-immersed transformers. Because IEEE does not 

report data on permissible overloading of dry-type units, DOE used the same values for both 

liquid-immersed and dry-type transformers. The age at which a transformer load switches back 

to initial peak load is given by the following equation. 

ageMax = ln (1 + LGRMax)

ln(1 + LGR) .

Where: 

ageMax = the maximum age of the transformer after which time the load switches back 

to initial peak load (years), and 

LGR = the annual load growth rate (%). 

Thus, the equation for the load growth as a function of the age of the transformer is:

LGrwth(age) = (1 − LGR)(age) − 1

for age < ageMax, and 

LGrwth(age) = (1 − LGR)(age−ageMax) − 1

for age >= ageMax. 

Where: 

LGrwth (age) = the fractional load growth, and 

age = the age of the transformer (years).

 DOE then used the load growth to adjust the estimate of RMS load for the affected stock. 

The mathematical equation for this adjustment is:
10-13

LAdjust(y) = � � [Stock(y, age) × (1 + LGrwth(age))2]

Aff_Stock(y)

y−Std_year

age=1

,

where LAdjust(y) is the load adjustment factor in year y. All other variables were defined for

previous equations. DOE applied a load adjustment factor to RMS loading to incorporate load 

growth into the unit energy consumption, as described in section 10.2.2.7. 

10.2.2.6 Affected Stock

The affected stock, an output of the shipments model (chapter 9), is a key input for the 

NES and NPV calculations. The affected stock represents that part of the transformer stock that 

would be impacted by a standard. It consists of those transformers purchased in or after the year 

the standard takes effect, as described by the following equation. 

AffStock(y) = Ship(y) + � Stock(age)

y−Stdyear

age=1

.

Where: 

Aff_Stock(y) = stock of affected transformers of all vintages that are operational in

year y, 

Ship(y) = shipment of new transformers in year y, 

Std_year = year the standard becomes effective, and

Stock(age) = age in years of the stock of transformers. 

10.2.2.7 Unit Energy Consumption

One of the final quantities DOE calculated to estimate the NES was the unit energy 

consumption for affected stock. The unit energy consumption multiplied by the capacity shipped 

and the site-to-source conversion factor equals the annual site energy consumption from which 

DOE derived total NES.

 Annual unit energy consumption (UEC(y)) for affected stock is the annual energy 

consumption per unit capacity for transformers shipped after the effective date of a standard. 

DOE calculated the losses per transformer as the sum of no-load losses plus load losses. It 

calculated the load losses as the rated load loss times the square of the RMS load, adjusted for 

load growth. Average energy consumed per unit capacity for affected stock varies from year to 

year because of load growth effects. The annual unit energy consumption for affected stock of 

distribution transformers is given by the following equation. 

UEC(y) = ENL + ELL × [RMS × LAdjust(y)]2

.
10-14

Where: 

ENL = rated no-load losses per kVA capacity,

ELL = rated load losses per kVA capacity,

RMS = root mean square, and

LAdjust(y) = load adjustment factor for year y. 

After DOE defined the unit energy consumption for affected stock, only one more input 

was necessary to complete the NES calculation: the site-to-source conversion factor. 

10.2.2.8 Site-to-Source Electricity Conversion 

The site-to-source conversion factor for electricity is the factor by which site energy (in 

kilowatt-hours (kWh)) is multiplied to obtain primary (source) energy (in quadrillion British 

thermal units (quads). Because the NES estimates the change in energy use of the resource (e.g., 

at the power plant), this conversion factor is necessary to account for losses in generation, 

transmission, and distribution. After calculating energy consumption at the site of use—the 

installed transformer—DOE multiplied the site energy consumption by the conversion factor to 

obtain primary energy consumption, expressed in quads. This conversion permitted comparison 

across (source) fuels by taking into account the heat content of various fuels and the efficiency of 

various energy conversion processes. The annual conversion factors are the United States

averages for generating electricity for both peak and base loads. DOE used average heat rates 

corresponding to base load for no-load losses (or core losses), and average heat rates 

corresponding to peak load for load losses (or coil losses). It used different rates because load 

losses are higher during transformer peak loads, whereas no-load losses occur at all times. DOE 

developed conversion factors using a variant of the NEMS5 called NEMS-BT.b Table 10.2.5

presents the average annual conversion factors DOE used. 

 

b DOE/EIA approved use of the name NEMS to describe only an official version of the model without any 

modification to code or data. Because this analysis entailed some minor code modifications and the model is run 

under policy scenarios that are variations on DOE/EIA assumptions, the name NEMS-BT refers to the model as used 

here (BT is DOE’s Building Technologies Program, under whose aegis this work was performed).
10-15

Table 10.2.5 Average Site-to-Source Conversion Factors for No-Load Losses and Load 

Losses

Year No-Load Losses Load Losses

2015 1.890 2.443

2016 1.888 2.446

2017 1.885 2.444

2018 1.883 2.443

2019 1.883 2.444

2020 1.886 2.446

2021 1.896 2.452

2022 1.900 2.450

2023 1.907 2.447

2024 1.915 2.448

2025 1.915 2.439

2026 1.916 2.425

2027 1.920 2.414

2028 1.921 2.395

2029 1.920 2.377

2030 1.919 2.355

2031 1.920 2.345

2032 1.920 2.330

2033 1.919 2.308

2034 1.920 2.294

2035 1.923 2.289

2036–2045 1.923 2.289

 The conversion factors change over time to account for the changes in electricitygenerating sources. The NES spreadsheet model includes the conversion factors for each year of 

the projection. DOE and interested parties can examine the effects of alternative assumptions by 

revising the conversion factors in the NES spreadsheet. 

 The conversion of site energy savings to source energy savings and the summation of 

energy savings throughout the forecast period complete the calculations needed to estimate the 

NES. The next section (section 10.3) describes the technical details of the NPV calculation. 

Section 10.4 presents the NES and NPV results from the NIA spreadsheet model. 

10.3 NET PRESENT VALUE

DOE used a national net present value (NPV) accounting component in the NIA 

spreadsheet to estimate the national financial impact on customers from the imposition of 

potential energy efficiency standards. DOE combined the output of the shipments model with 

energy savings and financial data from the LCC analysis to calculate an annual stream of costs 

and benefits resulting from trial standard levels (TSLs) for distribution transformers. It 
10-16

discounted this time series to 2010 and summed the result for 2016–2105 (the year the last unit 

shipped in 2045 retires from service), yielding the national NPV.

10.3.1 Overview

The NPV is the present value of the incremental economic impact of a TSL. Like the 

NES, the NPV calculation started with distribution transformer shipments and stocks, estimates 

of which are outputs of the shipments model. DOE then obtained estimates of distribution 

transformer first costs, losses, and average marginal electricity costs from the LCC analysis. It 

calculated the costs of transformer purchases and installation, then the corresponding operating 

costs for both a base case and a standards case, by applying marginal prices to the energy (both 

energy and electricity system capacity) used by the stock of transformers for each year. In the 

standards case, more expensive, but more efficient, transformers gradually replace less efficient 

units. Thus, the operating cost per unit capacity for the stock of transformers gradually decreases

in the standards case relative to the base case, while equipment costs increase.

DOE used a simple national average discount factor to discount purchases, expenses, and 

operating costs for distribution transformers. The discount factor converts a future expense or 

benefit to a present value. The difference in present value of all expenses and benefits between 

the base-case and standards scenario represents the impact on national NPV. DOE calculated the 

NPV impact for transformers purchased during the forecast period (between the effective date of 

the standard and 2104, inclusive). Mathematically, NPV is the value in the present of a time 

series of costs and savings, described by the equation: 

NPV = PVS – PVC.

Where: 

PVS = the present value of electricity savings, and

PVC = the present value of equipment costs including installation. 

PVS and PVC are determined according to the following three equations. 

 

PVS = � �

OCBase

Cap (y) ×

OCStd

Cap (y)� × AffStock(y) × Discount Factor(y).

2104

y=Std_year

Where: 

OCBase/Cap(y) = operating cost in year y per unit capacity of transformer for the 

base case,

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

y, 

y = the year (from effective date of the standard to the year when

units purchased in 2045 retire (in 2104), and 
10-17

Discount Factor(y) = discount factor for year y, defined in the next equation. 

Discount Factor(y) = 

1

(1 + Discount Rate)(y−reference year)

Where:

reference year = 2016, and 

discount rate = the discount rate, as described in section 10.3.2.7. 

PVC is determined as follows.

PVC = Std_year2104 �

FCstd

Cap (y) − FCBaseCap (y)� × Ship(y) × DiscountFactor(y).

Where: 

FCBase/Cap (y) = first cost of the transformer per unit of capacity in the Base case for a 

EL Base in year y (first cost is described in section 10.3.2.1); 

FCStd/Cap (y) = first cost of the transformer per unit of capacity in the Standards case 

for a EL Std in year y (first cost is described in section 10.3.2.1);

Std_year = the year the standard comes into effect, and

Ship(y) = shipments of transformers in year y for the standards case.

 DOE calculated NPV using its projections of national expenditures for distribution 

transformers, including purchase price (equipment and installation price) and operating costs 

(electricity and maintenance costs). It calculated costs and savings as the difference between a 

TSL and a base case lacking national standards. It discounted future costs and savings to the 

present (2012$). DOE calculated a discount factor from the discount rate and the number of 

years between the year to which the sum is being discounted (2012) and the year in which the 

costs and savings occur. The NPV is the sum over time (2016–2104) of the discounted net 

financial savings.

 The following sections describe inputs to the NPV calculation that are not described 

elsewhere. 

10.3.2 Inputs

 Inputs to the NPV model include cost inputs, inputs important for detailing electricity 

capacity costs, and several of the inputs used by the NES calculation. This section provides 

details on those inputs that were not described for the NES or shipments model. The specific 

inputs for the NPV are: 

1. first cost, 

2. operating cost, 
10-18

3. peak responsibility factor, 

4. initial peak load, 

5. scalar for electricity price forecast, 

6. marginal electricity costs, and

7. discount rate. 

Each input is described in detail below. 

10.3.2.1 First Cost

The first cost includes all the initial costs incurred with the installation of a distribution 

transformer. DOE expresses first cost in terms of cost per unit capacity. Specifically, it defines 

the first cost of acquiring a transformer with the following equation. 

FC/Cap = (P + Install)/Cap. 

Where: 

FC = first cost; 

Cap = rated capacity of the transformer; 

P = price of the transformer including shipping, and taxes; and

Install = installation cost of the transformer.

 The above values were obtained from the LCC calculation as the averages for individual 

design lines. DOE converted the first cost of a representative design to an estimated average first 

cost for a distribution of sizes within a particular equipment class. The adjustment incorporates 

the 0.75 scaling rule and the mapping of design line to equipment class discussed in sections 

10.2.2.1 and 10.2.2.2. Costs are expressed in units of 2011$ per kVA of rated transformer 

capacity. Table 10.3.1 shows the resulting mean first costs per kVA for distribution transformers 

by EL and equipment class. 
10-19

Table 10.3.1 First Costc

Equipment 

Class

of Distribution Transformers by Trial Standard Level and

Equipment Class (2011$/kVA)

Base TSL 1 TSL 2 TSL 3 TSL 4 TSL 5 TSL 6 TSL 7

1 99.98 102.50 107.97 107.99 111.64 113.59 118.19 164.42

2 30.60 32.84 95.49 95.52 98.80 100.67 103.97 151.11

3 75.31 75.31 75.31 95.54 110.81 110.81 153.61

4 55.78 61.60 61.62 65.13 72.81 79.39 103.53

5 41.85 42.12 44.10 44.63 44.63 72.26

6 33.03 33.22 35.46 35.56 35.56 59.34

7 55.12 57.51 59.54 69.61 69.61 94.96

8 39.59 41.09 43.39 51.00 51.00 71.01

9 51.03 51.93 57.01 57.01 57.01 81.11

10 39.48 40.17 44.10 44.11 44.11 62.76

10.3.2.2 Operating Costs 

 Transformer operating costs are the annual cost of transformer losses. Operating costs are 

a complex, yet essential, part of calculating the national economic impact of a standard. DOE 

used distinct costs to calculate the value of various types of losses and peak capacity savings. 

Potential load growth also requires an adjustment factor. Peak loading, peak load coincidence, 

and average loading require additional factors to characterize load losses. Finally, DOE used a

scalar for the electricity price forecast to characterize future trends in electricity prices consistent 

with the EIA’s AEO2012forecast.

4

 

In calculating transformer operating costs, DOE assumed zero incremental maintenance 

costs. It used the following formula to capture the diversity of factors that can affect annual 

operating costs.

OC/Cap = EPFS(y) × (ENL × (NLLMCC + 8760 × NLLMEC) + ELL × (LAdjust(y))2

× (PRF × PL2 × LLMCC + 8760 × RMS2 × LLMEC))/Cap.

Where: 

OC = the operating cost,

Cap = the rated capacity of the transformer,

EPFS(y) = the scalar for the electricity price forecast for year y, 

ENL = the no-load losses at rated load, 

NLLMCC = the marginal cost of capacity for no-load losses, 

NLLMEC = the marginal cost of energy for no-load losses, 

 

c First cost includes installation cost.
10-20

ELL = the load losses at rated load,

LAdjust(y) = the load growth adjustment factor in year y, 

PRF = the peak responsibility factor, 

PL = the initial peak load,

LLMCC = the marginal cost of capacity for load losses, 

RMS = the root mean square loading of the transformer, and 

LLMEC = the marginal cost of energy for load losses. 

 DOE expressed the operating costs in 2011$ per kVA of rated capacity. When calculating 

the NES (sections 10.2.2.1 and 10.2.2.2), DOE also used an adjustment factor to scale to ENL and 

ELL to convert from design-line data to equipment class estimates.

10.3.2.3 Peak Responsibility Factor 

 The transformer peak responsibility factor (PRF) is the fraction of the distribution 

transformer peak load that is coincident with the system peak, calculated by taking the square of 

the ratio of the transformer load at the time of the customer peak load to the transformer peak 

load. In combination with the initial peak load, the PRF is necessary for estimating impacts on 

capacity costs of transformer load losses. DOE used the average PRF from the hourly and the 

monthly load analyses for liquid-immersed and dry-type transformers, respectively, as reported 

in the LCC analysis. Table 10.3.2 presents the PRFs used in the analysis of the 12 equipment 

classes (ECs). 

Table 10.3.2 Peak Responsibility Factors by Equipment Class

EC 1 EC 2 EC 3 EC 4 EC 5 EC 6 EC 7 EC 8 EC 9 EC 10

PRF 0.28 0.36 0.23 0.23 0.46 0.46 0.46 0.46 0.46 0.46

10.3.2.4 Initial Peak Load 

 The initial peak load is the annual per-unit peak load on the distribution transformer 

during the first year of operation. This factor, in combination with the PRF, is necessary for 

calculating impacts on capacity costs from transformer load losses. The initial peak load is 

estimated as a percentage of the rated peak load of the transformer. The IEEE Draft Guide for 

Distribution Transformer Loss Evaluation (2001)7 defines a similar, but different, measure of 

peak transformer load called an “Equivalent Annual Peak Load” that accounts for changes in 

peak load during the life of the transformer. Rather than use the equivalent annual peak load, 

DOE used a distribution to characterize a range of initial peak loads. Chapter 6, sections 6.2.3.3 

and 6.3.3.3, further describe DOE’s method. Table 10.3.3 presents the initial peak loads used in 

the NPV analysis for the 12 equipment classes.

Table 10.3.3 Initial Peak Loading by Equipment Class

EC 1 EC 2 EC 3 EC 4 EC 5 EC 6 EC 7 EC 8 EC 9 EC 10

Initial Peak Load 0.88 0.88 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80
10-21

10.3.2.5 Scalar for Electricity Price Projections 

The scalar for forecasting electricity prices converts current electricity costs into 

projected costs for 2010 through 2105. The scalar is the ratio of the unit cost of electricity in real 

dollars in a given year to the real cost of electricity in 2011. DOE used projections from

AEO20124 to obtain the scalar for electricity price projections. For the period beyond 2035, 

DOE extrapolated the scalar based on the EIA real dollar price trend for 2025–2035. 

10.3.2.6 Marginal Electricity Costs

DOE needed to characterize four distinct marginal electricity costs to calculate the 

operating costs of distribution transformers and the financial impact of potential efficiency 

standards. The four marginal costs are: the marginal capacity cost for no-load losses, (the 

marginal capacity cost for load losses, the marginal energy cost for no-load losses, and the 

marginal energy cost for load losses. An electricity system has both energy costs and capacity 

costs. Depending on the shape of a particular load, the average value of capacity costs may differ 

from those of energy costs. Because no-load losses and load losses have distinct load shapes, and 

because different customers experience different load shapes, costs vary both by loss type and by 

the equipment class of a transformer. DOE therefore used distinct marginal energy and capacity 

costs for no-load losses and load losses for each transformer equipment class. No transformer 

size scaling is necessary for the marginal costs, although DOE needed to map design lines to

equipment classes (as described in section 10.2.2.2) to convert the design line output from the 

LCC to equipment class information for calculating the NPV. DOE calculated capacity costs in 

units of 2011$/kilowatt (kW)/year, and energy costs in units of 2011$/kWh. Table 10.3.4 

summarizes the four marginal costs for the 12 equipment classes. 

Table 10.3.4 Marginal Energy and Capacity Costs by Equipment Class

Marginal Energy Cost by Equipment Class $/kWh

EC 1 EC 2 EC 3 EC 4 EC 5 EC 6 EC 7 EC 8 EC 9 EC 10

NLL 0.067 0.067 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 

LL 0.073 0.073 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 

Marginal Capacity Cost by Equipment Class $/kW/year

EC 1 EC 2 EC 3 EC 4 EC 5 EC 6 EC 7 EC 8 EC 9 EC 10

NLL 264.97 266.15 142.62 142.62 142.62 142.62 142.62 142.62 142.62 142.62 

LL 164.37 165.64 114.40 114.86 101.46 101.46 101.69 101.47 101.46 101.46 

10.3.2.7 Discount Rate

 The discount rate, which is the final input to the NPV calculation, expresses the time 

value of money. DOE used real discount rates of 3 percent and 7 percent, as established by the 

Office of Management and Budget guidelines on regulatory analysis.9

 The discount rates DOE 

used in the LCC differ from those used in the NPV calculations, in that the NPV discount rates 

represent the societal rate of return on capital, whereas LCC discount rates reflect the owner cost 

of capital and the financial environment of electric utilities and commercial and industrial 

entities.
10-22

10.3.2.8 Projection of Future Product Prices

 For reasons discussed in chapter 8 (Section 8.2.1.1), DOE used a constant price 

assumption for the default forecast in the NIA. To investigate the impact of different product 

price forecasts on the consumer NPV for the considered TSLs for medium electric motors, DOE 

also considered two alternative price trends. Both trends are based on a power-law fit on the 

deflated producer price index for electric power and specialty transformer manufacturing. 

Details on how these alternative price trends were developed are in appendix 10B of the TSD, 

which also presents the results of the sensitivity analysis. 

10.4 RESULTS

The following sections summarize the results of the NES and NPV calculations 

performed for the NIA. 

10.4.1 National Energy Savings and Net Present Value for Trial Standard Levels

Table 10.4.1 presents the NES and NPV results from the spreadsheet model for TSLs 1–5 

for medium-voltage liquid-immersed and dry-type distribution transformers and TSLs 1–6 for 

low-voltage dry-type transformers. It should be reiterated that the NES spreadsheet model uses 

discrete point values rather than a distribution of values for all inputs. 
10-23

Table 10.4.1 Results for Cumulative National Energy Savings (2016–2045) and Net 

Present Value (2016–2104) 

 Discount 

Rate (%)

Trial Standard Level

1 2 3 4 5 6 7 

Liquid-Immersed

Cumulative Source Savings 2044 (Quads) 0.92 1.56 1.76 3.31 3.30 4.09 7.01 

Net Present Value (billion 2011$) 3 2.00 3.00 4.00 5.00 6.00 7.00 -8.50

7 0.58 0.69 0.91 1.92 1.60 0.74 -12.97

Low-Voltage Dry-Type

Cumulative Source Savings 2044 (Quads) 2.28 2.43 3.05 4.39 4.48 4.94 

Net Present Value (billion 2011$) 3 8.38 9.04 10.38 13.65 11.80 5.17

7 2.45 2.67 2.82 3.34 2.22 -1.92 

Medium-Voltage Dry-Type

Cumulative Source Savings 2044 (Quads) 0.15 0.29 0.53 0.53 0.84 

Net Present Value (billion 2011$) 3 0.49 0.79 1.12 1.12 -0.20

7 0.13 0.17 0.12 0.12 -0.89 

10.4.1.2 Results for Liquid-Immersed Distribution Transformers

 Figure 10.4.1 illustrates the typical pattern of source energy savings and costs resulting 

from standards for liquid-immersed distribution transformers. The figure shows the nature of net 

savings for all six TSLs relative to the base case. The figure also shows the NPV at both a 3- 

percent and a 7- percent discount rate. 

Figure 10.4.1 Liquid-Immersed Distribution Transformers: 

Impacts of Standards on National Energy Savings 

and Net Present Value

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

1 2 3 4 5 6 7

Net Present Value (Billion US$)

Cumulative Source Energy Savings (Quads)

Trial Standard Levels

Cumulative Source Energy Savings and NPV for Liquid-Immersed Units

Cumulative Source Savings 2105 (Quads) Net Present Value ($Billions) discounted at 7%

Net Present Value ($Billions) discounted at 3%
10-24

 Figure 10.4.1 shows that, although the savings in energy (quads) are greatest at TSLs 7 

(max tech), the associated financial savings decrease at either the 3-percent or 7-percent discount 

rate. At a discount rate of three percent, the NPV of cumulative source savings for liquidimmersed transformers are highest at TSL 4. At a discount rate of seven percent, the NPV is 

highest at TSL 4. 

10.4.1.3 Results for Low-Voltage Dry-Type Distribution Transformers

 Figure 10.4.2 shows the pattern of source energy savings and costs resulting from 

potential standards for low-voltage dry-type distribution transformers. The figure shows the 

nature of net savings for the six TSLs relative to the base case. The figure also shows the NPV at 

both a 3-percent and a 7-percent discount rate.

 Figure 10.4.2 Low-Voltage Dry-Type Distribution Transformers: 

Impacts of Standards on National Energy Savings 

and Net Present Value 

 Figure 10.4.2 shows that the cumulative savings in energy (quads) is highest under TSLs 

6, the associated financial savings decrease dramatically at either discount rate. At a discount rate 

of three percent, the NPV of cumulative source savings for dry-type transformers are highest 

under TSL4. At a discount rate of seven percent, the savings are highest under TSL 4. 

10.4.1.4 Results for Medium-Voltage Dry-Type Distribution Transformers

 Figure 10.4.3 illustrates the typical pattern of source energy savings and costs resulting 

from standards for medium-voltage dry-type distribution transformers. The figure shows the 

nature of net savings for all five TSLs relative to the base case. The figure also shows the NPV at 

both a 3-percent and a 7-percent discount rate. 

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

1 2 3 4 5 6

Net Present Value (Billion US$)

Cumulative Source Energy Savings (Quads)

Trial Standard Levels

Cumulative Source Energy Savings and NPV for Low-Voltage Dry-Type Units

Cumulative Source Savings 2105 (Quads) Net Present Value ($Billions) discounted at 7%

Net Present Value ($Billions) discounted at 3%
10-25

 Figure 10.4.3 Medium-Voltage Dry-Type Distribution 

Transformers: Impacts of Standards on National 

Energy Savings and Net Present Value 

 Figure 10.4.3 shows that, although the savings in energy (quads) are greatest at TSLs 5 

(max tech), the associated financial savings decrease dramatically at either the 3-percent or 7-

percent discount rate. At a discount rate of three percent, the NPV of cumulative source savings 

for medium-voltage dry-type distribution transformers are highest at TSL 4. At a discount rate of 

seven percent, the NPV is highest at TSL 3. 

10.5 ANNUALIZED NATIONAL COSTS AND BENEFITS

 The benefits and costs of the proposed standards for distribution transformers can be 

expressed in terms of annualized values over the analysis period. The annualized monetary 

values are the sum of (1) the annualized national economic value of the benefits from operating 

products that meet the proposed standards (consisting primarily of operating cost savings from 

using less energy, minus increases in equipment purchase costs, which is another way of 

representing consumer NPV), and (2) the monetary value of the benefits of emission reductions, 

including CO2 emission reductions. The emissions reductions for each TSL are described in 

chapter 15, and the derivation of the monetary value of the benefits of emission reductions is 

described in chapter 16 of this TSD. The value of the CO2 reductions, otherwise known as the 

social cost of carbon (SCC), is calculated using a range of values per metric ton of CO2

developed by a recent interagency process. The derivation of the time series of SCC values is 

discussed in Appendix 16-A of this TSD. 

 Although combining the values of operating savings and CO2 reductions provides a 

useful perspective, two issues should be considered. First, the national operating savings are 

-1.0

-0.5

0.0

0.5

1.0

1.5

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1 2 3 4 5

Net Present Value (Billion US$)

Cumulative Source Energy Savings (Quads)

Trial Standard Levels

Cumulative Source Energy Savings and NPV for Medium-Voltage Dry-Type Units

Cumulative Source Savings 2105 (Quads) Net Present Value ($Billions) discounted at 7%

Net Present Value ($Billions) discounted at 3%
10-26

domestic U.S. consumer monetary savings that occur as a result of market transactions while the 

value of CO2 reductions is based on a global value. Second, the assessments of operating cost 

savings and CO2 savings are performed with different methods that use quite different time 

frames for analysis. The national operating cost savings is measured for the lifetime of 

equipment shipped in the 30-year analysis period. The SCC values, on the other hand, reflect the 

present value of future climate-related impacts resulting from the emission of one ton of carbon 

dioxide in each year. These impacts go well beyond 2100. 

10.5.1 Calculation Method 

DOE uses a two-step calculation process to convert each time-series of costs and benefits 

into annualized values. First, DOE calculates a present value in the “present” year used in 

discounting the NPV of total consumer costs and savings.d

 For this calculation, DOE uses 

discount rates of three and seven percent for all costs and benefits except for the value of CO2

reductions. For the latter, DOE uses the discount rate appropriate for each SCC time-series (see 

chapter 16 for discussion). 

PVx = � (x(t) ∙ (1 + rx)yNPV−t)

t=y1,yT

Where:

x(t) = Time-series under evaluation, 

PVx = Present value of the time-series x, 

y1 = First year in the analysis period, 

yT = Last year in the analysis period,

yNPV = Year to which the NPV of consumers’ costs and savings are being discounted, 

rx = Discount rate used to discount the annual values of time-series x to year yNPV. 

 In the second step, DOE calculates, from the present values, the fixed annual payments 

over a 30-year period, starting in the first year of the analysis period (i.e., the compliance year), 

which yields the same present values with discount rates of three and seven percent. This 

requires projecting the present values in the “present” year ahead to the compliance year. The 

fixed annual payments are the annualized values. 

Annx,r = PVx ∙ fy1−yNPV,r ∙ a30,r = PVx ∙ (1 + r)y1−yNPV ∙

r ∙ (1 + r)30

(1 + r)30 − 1

Where:

Annx,r = Annualized value of the time-series x, 

 

d For the value of emissions reductions, DOE uses a time series that corresponds to the time period used in 

calculating the operating cost savings (i.e., through the final year in which products shipped are still operating).
10-27

fn,r = Factor to project a value n years aheade

n = Number of years between the “present” year and the compliance year, 

with r discount rate, 

a30,r = Factor to annualize present values over a 30-year period with r discount rate. 

 Although DOE calculates annualized values, this does not imply that the time-series of 

cost and benefits from which the annualized values were determined would be a steady stream of 

payments. 

10.5.2 Results for the Considered Standards

The notice associated with this TSD states that DOE is selecting amended energy 

conservation standards that correspond to TSL 1 for liquid-immersed distribution transformers, 

TSL 2 for low-voltage dry-type distribution transformers, and TSL 2 for medium-voltage drytype distribution transformers. Estimates of annualized benefits and costs for the proposed 

standards are shown in Table 10.5.1. 

The Primary Estimate, Low Net Benefits Estimate, and High Net Benefits Estimate 

utilize forecasts of energy prices from the AEO2012 Reference case, Low Economic Growth 

case, and High Economic Growth case, respectively. In addition, incremental equipment costs 

reflect no change in the Primary estimate, rising equipment prices in the Low Net Benefits 

estimate, and declining equipment prices in the High Net Benefits Estimate. 

 

e n is the number of years between the “present” year and the compliance year.
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Table 10.5.1 Annualized Benefits and Costs of Standards for Distribution Transformers

Discount Rate

% 

Primary 

Estimate*

Low Net Benefits 

Estimate*

High Net Benefits 

Estimate*

Million 2011$/year

Benefits

Operating cost savings 

7% 581 559 590

3% 983 930 1003

CO2 reduction monetized 

value ($4.9/t case)** 5% 57.7 57.7 57.7 

CO2 reduction monetized 

value ($22.3/t case)** 3% 237 237 237 

CO2 reduction monetized 

value ($36.5/t case)** 2.5% 377 377 377 

CO2 reduction monetized 

value ($67.6/t case)** 3% 721 721 721 

NOX reduction monetized 

value ($2,591/ton)** 

7% 8.60 8.60 8.60

3% 12.67 12.67 12.67

Total benefits†

7% plus CO2

range

648 to 1311 625 to 1288 656 to 1319

7% 827 805 836

3% plus CO2

range

1053 to 1716 1000 to 1663 1074 to 1737 

3% 1233 1179 1253

Costs

Incremental product costs

7% 266 300 257

3% 282 325 271

Net Benefits

Total† 7% plus CO2

range

381 to 1044 325 to 988 400 to 1063
10-29

7% 561 504 579

3% plus CO2

range

771 to 1434 675 to 1338 803 to 1466

3% 950 854 982

* This table presents the annualized costs and benefits associated with transformers shipped in 2016−2045. These 

results include benefits to customers that accrue after 2045 from equipment purchased in 2016−2045. Costs incurred 

by manufacturers, some of which may be incurred in preparation for the rule, are not directly included, but are 

indirectly included as part of incremental equipment costs. The Primary, Low Benefits, and High Benefits estimates 

utilize projections of energy prices from the AEO2012

** The CO2 values represent global monetized values of the SCC, in 2011$, in 2011 under several scenarios. The 

values of $4.9, $22.3, and $36.5 per metric ton are the averages of SCC distributions calculated using 5%, 3%, and 

2.5% discount rates, respectively. The value of $67.6/t represents the 95th percentile of the SCC distribution 

calculated using a 3% discount rate. The SCC time series used by DOE incorporate an escalation factor. The value 

for NOX (in 2011$) is the average of the low and high values used in DOE’s analysis.

Reference case, Low Estimate, and High Estimate, 

respectively. In addition, incremental equipment costs reflect a constant equipment price trend in the Primary 

Estimate, an increasing price trend in the Low Benefits Estimate, and a declining price trend in the High Benefits 

Estimate. The methods used to derive projected price trends are explained in section IV.F.2.

† Total Benefits for both the 3% and 7% cases are derived using the series corresponding to SCC value of $22.3/t. In 

the rows labeled “7% plus CO2 range” and “3% plus CO2 range,” the operating cost and NOX benefits are calculated 

using the labeled discount rate, and those values are added to the full range of CO2 values.

. 
10-30

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 Industry Economic Accounts 

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

(2010). 

4. U.S. Energy Information Administration Annual Energy Outlook 2012, With Projections to 

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

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. Energy Information Administration - Office of Integrated Analysis and Forecasting The 

National Energy Modeling System (NEMS): An Overview. (U.S. Department of Energy: 

Washington DC, 2009). 

7. Institute of Electrical and Electronic Engineers (IEEE) Draft Guide for Distribution 

Transfomer Loss Evaluation. (IEEE: 2001). 

8. Institute of Electrical and Electronic Engineers (IEEE) Guide for Loading Mineral OilImmersed Transformers. (Transformer Committee of the IEEE Power Engineering Society: 

1995). 

9. U.S. Office of Management and Budget Circular A-4: Guidelines and Discount Rates for 

Benefit-Cost Analysis of Federal Programs. (2003).