8-i

CHAPTER 8. LIFE-CYCLE COST AND PAYBACK PERIOD ANALYSES

TABLE OF CONTENTS

8.1 INTRODUCTION ........................................................................................................... 8-1

8.1.1 General Approach to Analyses ........................................................................................ 8-1

8.1.2 Base Case Scenario .......................................................................................................... 8-2

8.1.2.1 Design Limitation in the Base Case ............................................................... 8-2

8.1.3 Total Owning Cost ........................................................................................................... 8-3

8.2 LIFE-CYCLE COST ANALYSIS METHOD................................................................. 8-3

8.2.1 Definition ......................................................................................................................... 8-3

8.2.2 Key Steps in Life-Cycle Cost Analysis ........................................................................... 8-4

8.2.2.1 Step 1: Select Parameters A and B ................................................................ 8-6

8.2.2.2 Step 2: Select Designs that Meet a Chosen Efficiency Level ........................ 8-6

8.2.2.3 Step 3: Select Load and Price Profile ............................................................ 8-7

8.2.2.4 Step 4: Calculate Cost of Losses .................................................................... 8-7

8.2.2.5 Step 5: Project Losses and Costs into the Future ........................................... 8-7

8.2.2.6 Step 6: Select Discount Rate .......................................................................... 8-8

8.2.2.7 Step 7: Calculate Present Value of Future Cost of Losses............................. 8-8

8.2.2.8 Step 8: Report Results .................................................................................... 8-8

8.2.2.9 Step 9: Repeat Process and Report Results.................................................... 8-8

8.3 INPUTS TO LIFE-CYCLE COST ANALYSIS ............................................................. 8-8

8.3.1 A and B Distribution Transformer Selection Parameters ................................................ 8-9

8.3.1.1 A and B Parameter Selection for Liquid-Immersed Distribution 

Transformers ................................................................................................ 8-10

8.3.1.2 A and B Parameter Selection for Dry-Type Distribution Transformers ...... 8-12

8.3.2 Database of Distribution Transformer Designs ............................................................. 8-14

8.3.3 Markup and Installation Costs ....................................................................................... 8-14

8.3.3.1 Projection of Future Equipment Prices ........................................................ 8-14

8.3.4 Distribution Transformer Loading ................................................................................. 8-16

8.3.4.1 Loading Levels for Utilities Serving Low Population Densities ................. 8-16

8.3.5 Electricity Price Analysis ............................................................................................... 8-17

8.3.5.1 Hourly Marginal Electricity Price Model for Liquid-Immersed 

Distribution Transformers ............................................................................ 8-17

8.3.5.2 Capacity Costs ............................................................................................. 8-17

8.3.5.3 Energy Costs ................................................................................................ 8-23

8.3.5.4 Monthly Marginal Electricity Price Model for Dry-Type Distribution 

Transformers ................................................................................................ 8-24

8.3.6 Trends in Load Growth .................................................................................................. 8-25

8.3.7 Electricity Cost and Price Trends .................................................................................. 8-25

8.3.8 Discount Rate ................................................................................................................. 8-27

8.3.9 Effective Date of Standard ............................................................................................. 8-32

8.3.10 Transformer Service Life ............................................................................................... 8-32

8.3.11 Maintenance Costs ......................................................................................................... 8-33

8.3.12 Power Factor .................................................................................................................. 8-33
8-ii

8.3.13 Default Scenario............................................................................................................. 8-33

8.4 RESULTS OF LIFE-CYCLE COST ANALYSIS ........................................................ 8-33

8.4.1 Results for Design Line 1 .............................................................................................. 8-36

8.4.2 Results for Design Line 2 .............................................................................................. 8-37

8.4.3 Results for Design Line 3 .............................................................................................. 8-37

8.4.4 Results for Design Line 4 .............................................................................................. 8-38

8.4.5 Results for Design Line 5 .............................................................................................. 8-38

8.4.6 Results for Design Line 6 .............................................................................................. 8-39

8.4.7 Results for Design Line 7 .............................................................................................. 8-39

8.4.8 Results for Design Line 8 .............................................................................................. 8-40

8.4.9 Results for Design Line 9 .............................................................................................. 8-40

8.4.10 Results for Design Line 10 ............................................................................................ 8-41

8.4.11 Results for Design Line 11 ............................................................................................ 8-41

8.4.12 Results for Design Line 12 ............................................................................................ 8-42

8.4.13 Results for Design Line 13A.......................................................................................... 8-42

8.4.14 Results for Design Line 13B .......................................................................................... 8-43

8.5 LIFE-CYCLE COST SENSITIVITY ANALYSIS ....................................................... 8-43

8.5.1 Sensitivity Results for Design Line 1 ............................................................................ 8-44

8.5.2 Sensitivity Results for Design Line 7 ............................................................................ 8-45

8.5.3 Sensitivity Results for Design Line 12 .......................................................................... 8-47

8.6 PAYBACK PERIOD ..................................................................................................... 8-49

8.6.1 Definition ....................................................................................................................... 8-49

8.6.2 Inputs to Payback Period ............................................................................................... 8-49

8.6.3 Issues Regarding Baseline Scenario .............................................................................. 8-50

8.6.4 Results of Payback Period Analysis .............................................................................. 8-51

8.6.5 Results for Design Line 1 .............................................................................................. 8-52

8.6.6 Results for Design Line 2 .............................................................................................. 8-53

8.6.7 Results for Design Line 3 .............................................................................................. 8-54

8.6.8 Results for Design Line 4 .............................................................................................. 8-54

8.6.9 Results for Design Line 5 .............................................................................................. 8-55

8.6.10 Results for Design Line 6 .............................................................................................. 8-55

8.6.11 Results for Design Line 7 .............................................................................................. 8-56

8.6.12 Results for Design Line 8 .............................................................................................. 8-57

8.6.13 Results for Design Line 9 .............................................................................................. 8-57

8.6.14 Results for Design Line 10 ............................................................................................ 8-58

8.6.15 Results for Design Line 11 ............................................................................................ 8-59

8.6.16 Results for Design Line 12 ............................................................................................ 8-59

8.6.17 Results for Design Line 13A.......................................................................................... 8-60

8.6.18 Results for Design Line 13B .......................................................................................... 8-61

8.7 REBUTTABLE PRESUMPTION ................................................................................. 8-61

LIST OF TABLES

Table 8.3.1 A Parameter Model and Historical Data ............................................................ 8-11

Table 8.3.2 A and B Parameter Evaluation Scenarios .......................................................... 8-14
8-iii

Table 8.3.3 Generation Fixed Charge Rates ......................................................................... 8-19

Table 8.3.4 Regional Capacity Cost Factors ......................................................................... 8-22

Table 8.3.5 AEO 2012 Capacity by Fuel Type ..................................................................... 8-23

Table 8.3.6 Average Seasonal Marginal Energy and Demand Prices by Census 

Division .............................................................................................................. 8-25

Table 8.3.7 Typical Owners of Various Types of Transformers .......................................... 8-29

Table 8.3.8 Variables Used to Estimate Discount Rates for the C&I Sector ........................ 8-30

Table 8.3.9 Real Discount Rates by Transformer Ownership Category ............................... 8-31

Table 8.3.10 Transformer Ownership by Design Line ........................................................... 8-32

Table 8.4.1 Efficiency Levels Evaluated for Each Design Line ........................................... 8-34

Table 8.4.2 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 1 ....... 8-36

Table 8.4.3 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 2 ....... 8-37

Table 8.4.4 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 3 ....... 8-37

Table 8.4.5 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 4 ....... 8-38

Table 8.4.6 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 5 ....... 8-38

Table 8.4.7 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 6 ....... 8-39

Table 8.4.8 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 7 ....... 8-39

Table 8.4.9 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 8 ....... 8-40

Table 8.4.10 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 9 ....... 8-40

Table 8.4.11 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 10 ..... 8-41

Table 8.4.12 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 11 ..... 8-41

Table 8.4.13 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 12 ..... 8-42

Table 8.4.14 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 

13A ..................................................................................................................... 8-42

Table 8.4.15 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 

13B ..................................................................................................................... 8-43

Table 8.5.1 Effects of Changed Variables on Life-Cycle Cost Savings for 

Representative Unit, Design Line 1 (2011$) ..................................................... 8-45

Table 8.5.2 Effects of Changed Variables on Life-Cycle Cost Savings for 

Representative Unit, Design Line 7 (2011$) ..................................................... 8-46

Table 8.5.3 Effects of Changed Variables on Life-Cycle Cost Savings for 

Representative Unit, Design Line 12 (2011$) ................................................... 8-48

Table 8.6.1 Possible ΔFC and ΔOC Combinations for Payback Period Analysis ................ 8-51

Table 8.6.2 Results of Payback Period Analysis: Representative Unit, Design Line 1 ........ 8-53

Table 8.6.3 Results of Payback Period Analysis: Representative Unit, Design Line 2 ........ 8-53

Table 8.6.4 Results of Payback Period Analysis: Representative Unit, Design Line 3 ........ 8-54

Table 8.6.5 Results of Payback Period Analysis: Representative Unit, Design Line 4 ........ 8-55

Table 8.6.6 Results of Payback Period Analysis: Representative Unit, Design Line 5 ........ 8-55

Table 8.6.7 Results of Payback Period Analysis: Representative Unit, Design Line 6 ........ 8-56

Table 8.6.8 Results of Payback Period Analysis: Representative Unit, Design Line 7 ........ 8-56

Table 8.6.9 Results of Payback Period Analysis: Representative Unit, Design Line 8 ........ 8-57

Table 8.6.10 Results of Payback Period Analysis: Representative Unit, Design Line 9 ........ 8-58

Table 8.6.11 Results of Payback Period Analysis: Representative Unit, Design Line 10 ...... 8-58

Table 8.6.12 Results of Payback Period Analysis: Representative Unit, Design Line 11 ...... 8-59

Table 8.6.13 Results of Payback Period Analysis: Representative Unit, Design Line 12 ...... 8-60
8-iv

Table 8.6.14 Results of Payback Period Analysis: Representative Unit, Design Line 

13A ..................................................................................................................... 8-60

Table 8.6.15 Results of Payback Period Analysis: Representative Unit, Design Line 

13B ..................................................................................................................... 8-61

Table 8.7.1 Average Transformer Efficiency % ................................................................... 8-62

Table 8.7.2 Average Transformer Efficiency for Fractional Efficiency Levels % ............... 8-63

Table 8.7.3 Average Transformer Installed Cost (2011$) .................................................... 8-63

Table 8.7.4 Average Transformer Installed Cost for Fractional Efficiency Levels

(2011$) ............................................................................................................... 8-63

Table 8.7.5 Payback Period for Rebuttable Presumption (years) ......................................... 8-64

Table 8.7.6 Payback Period for Rebuttable Presumption for Fractional Efficiency 

Levels ................................................................................................................. 8-64

LIST OF FIGURES 

Figure 8.2.1 Flowchart of Spreadsheet Model for Calculating Transformer Life-Cycle 

Cost ...................................................................................................................... 8-5

Figure 8.3.1 Cumulative Distribution of Historical A Parameter and Model A 

Parameter ........................................................................................................... 8-10

Figure 8.3.2 Distributions of Load Loss (B) Values versus No- Load Loss (A) Values 

for Liquid-Immersed Distribution Transformers ............................................... 8-12

Figure 8.3.3 Historical Nominal and Deflated Producer Price Indexes for Electric 

Power and Specialty Transformer Manufacturing ............................................. 8-15

Figure 8.3.4 Historical Deflated Producer Price Indexes for Copper Smelting, Steel 

Mills Manufacturing and Electric Power and Specialty Transformer 

Manufacturing .................................................................................................... 8-16

Figure 8.3.5 Real Weighted-Average Cost of Capital and Generation Fixed Charge 

Rate .................................................................................................................... 8-20

Figure 8.3.6 Price Duration Curves for New York Independent System Operator (ISO) 

and ISO New England, 1999 versus 2008 ......................................................... 8-21

Figure 8.3.7 Combined Natural Gas and Steam Coal Price Forecast from AEO2012 ........... 8-26

Figure 8.3.8 Natural Gas Price Forecast from AEO2012 ....................................................... 8-26

Figure 8.3.9 Electricity Price Forecasts from AEO2012 ........................................................ 8-27

Figure 8.4.1 Design Load Losses versus No-Load Losses in the Base Case and 

Efficiency Level 1 for Design Line 1 ................................................................ 8-35

Figure 8.4.2 Distribution of Life-Cycle Cost Results for Design Line 2, Efficiency 

Level 2 ............................................................................................................... 8-36

Figure 8.5.1 Average Life-Cycle Cost Savings (2011$) by Scenario for Design Line 1 ....... 8-45

Figure 8.5.2 Average Life-Cycle Cost Savings (2011$) by Scenario for Design Line 7 ....... 8-47

Figure 8.5.3 Average Life-Cycle Cost Savings (2011$) by Scenario for Design Line 12 ..... 8-48

Figure 8.6.1 Distribution of Payback Period Results for Design Line 2, Efficiency 

Level 2 ............................................................................................................... 8-52
8-1

CHAPTER 8. LIFE-CYCLE COST AND PAYBACK PERIOD ANALYSES

8.1 INTRODUCTION

This chapter of the technical support document (TSD), prepared in support of potential 

energy efficiency standards for distribution transformers, presents the U.S. Department of 

Energy’s (DOE’s) life-cycle cost (LCC) and payback period (PBP) analyses. It describes the 

method DOE used for analyzing the economic impacts of possible energy efficiency standards 

on customers−purchasers and users of distribution transformers. The effect of efficiency 

standards on customers includes a change in operating expense (usually a decrease) and a change 

in purchase price (usually an increase). The LCC and PBP analyses produce two basic outputs to 

describe the effect of efficiency standards on customers.

• LCC is the total (discounted) cost that a customer pays over the lifetime of the 

equipment, including purchase price, installation cost, and operating expenses. 

• PBP measures the amount of time it takes customers to recover the estimated higher 

purchase price of more energy efficient equipment through lower operating costs. 

This chapter presents inputs and results for the LCC and PBP analyses, as well as key 

variables, assumptions, and computational equations. DOE performed the calculations discussed 

here using a series of Microsoft Excel spreadsheets, which are accessible on DOE's website 

(http://www1.eere.energy.gov/buildings/appliance_standards/rulemaking.aspx/ruleid/44,

http://www1.eere.energy.gov/buildings/appliance_standards/rulemaking.aspx/ruleid/43). 

Appendix 8A of the TSD contains details and instructions for using the spreadsheets. There are 

five appendices to this chapter, among which are appendix 8C, which presents a complete set of 

analytical results; appendix 8B, which discusses uncertainty and variability; and appendix 8D, 

which contains a complete set of sensitivity results for transformer design lines 1 through 5, 7, 

and 12. 

8.1.1 General Approach to Analyses 

Recognizing that each distribution transformer customer is unique, DOE calculated the 

LCC and PBP for a representative sample (a distribution) of individual customers who purchase 

individual transformers. In this manner, DOE’s analyses explicitly recognized that there is both 

variability and uncertainty in the inputs. DOE developed the LCC model using Excel 

spreadsheets combined with Crystal Ball, a commercially available add-in program. DOE used 

Monte Carlo simulations to model the distributions of inputs. The Monte Carlo process 

statistically captures input variability and distribution without testing all possible input 

combinations. The results are expressed as the number of distribution transformers that engender

economic impacts of varying magnitudes. Appendix 8B provides a detailed explanation of the 

Monte Carlo simulation process and the use of probability distributions in the analyses. 
8-2

 The LCC results are displayed as distributions of impacts compared to baseline 

conditions (no new standards). The tabular results presented later in this chapter are based on 

10,000 samples per Monte Carlo simulation run. 

DOE developed two approaches for the LCC calculations: one for liquid-immersed 

distribution transformers, and one for low-voltage and medium-voltage, dry-type distribution 

transformers. Because most owners of the liquid-immersed transformers are utilities, the LCC 

calculations for liquid-immersed transformers used utility marginal costs and distribution 

markups that do not include wholesaler or contractor markups. In contrast, because most owners 

of the dry-type transformers are commercial and industrial enterprises, DOE used monthly 

marginal electricity costs and complete distribution markups for calculating the LCC of dry-type 

transformers. For simplicity, DOE used only one type of LCC calculation for each design line of 

transformer, based on the type of owner that was the majority in that category.

8.1.2 Base Case Scenario

 In developing appliance standards, DOE used the existing standard under Title 10 of the 

Code of Federal Regulations, Part 431 (10 CFR Part 431) as a baseline from which it calculates 

the impact of any efficiency level. This approach focused on the mix of selection criteria that 

customers are known to use when purchasing a distribution transformer. Those criteria include 

first cost and what is known in the transformer industry as total owning cost (TOC), a criterion

some customers use in place of first cost. Purchasers of distribution transformers, especially in 

the utility sector, have long used TOC to determine which transformer to purchase.1,2

To establish the baseline scenario for the LCC, DOE used distributions of efficiencies 

and an estimated percent of distribution transformers currently being purchased using the TOC 

method. That scenario represents the range of transformer costs and efficiencies that transformer 

purchasers likely would face without national energy efficiency standards in place. 

8.1.2.1 Design Limitation in the Base Case

 During the negotiated rulemaking process for distribution transformers, DOE received 

comments from the Energy Efficiency and Renewable Energy, Energy Advisory Committee 

(ERAC) subcommittee members who noted that currently ZDMH core steel is not used in 

significant quantities in the U.S. market. Therefore, DOE screened out designs using this 

material in the base case selection. For higher efficiency levels, the LCC analysis samples from 

all design options are identified in the engineering analysis. 

ERAC subcommittee members provided to DOE data about market share as a function of 

efficiency. For some design lines, the lower boundary of the price-efficiency curve produced in 

the engineering analysis (see chapter 5 of the TSD) is quite flat, so that the customer choice 

algorithm (see section 8.2.2.2) in the LCC analysis showed units being selected in the base case 

with efficiencies substantially higher than the current minimum standard required under 10 CFR 

431.196. DOE modified its approach so that the fraction of units selected in the base case at 

different efficiency levels is consistent with the provided market share data.
8-3

8.1.3 Total Owning Cost 

The utility industry developed TOC evaluation software as an easy-to-use tool to reflect 

the unique financial environment faced by each distribution transformer purchaser. To express 

variation in such factors as the costs of electric energy, energy capacity, and financing, the utility 

industry developed a range of factors, called A and B values, to use in its evaluations. A and B 

are the equivalent first costs of a distribution transformer’s no-load losses and load losses, 

respectively, in dollars per watt ($/W). No-load losses refer to the core losses that remain 

roughly constant after the transformer is energized; load losses are the coil losses that vary 

roughly with the square of the load on the transformer. 

After assigning an economic value to the A and B parameters of distribution transformer 

losses, purchasers add those costs to the first cost of acquiring the transformer, thereby deriving 

TOC. Throughout the LCC analysis, DOE expresses monetary values in units of year 2010 real 

dollars (2011$). The equation for calculating transformer TOC is:

TOC = FC + (A × NLL) + (B × LL).

Where: 

FC = first cost of acquiring the distribution transformer, including purchase price 

and installation cost (2011$);

A = the no-load loss valuation parameter in dollars per watt ($/W);

NLL = the no-load loss at nameplate load (W);

B = the load loss valuation parameter ($/W); and

LL = the load loss at nameplate load (W).

8.2 LIFE-CYCLE COST ANALYSIS METHOD

The following sections present the LCC equation and define its terms, then describe the 

nine key steps DOE used in performing the LCC for distribution transformers. 

8.2.1 Definition

The LCC equation serves as the basis for both the LCC analysis and the LCC spreadsheet 

model. The LCC equation reflects both the first cost of a distribution transformer and the present 

value of the operating costs throughout the service life of that transformer. The LCC equation is: 

LCC = FC + � � OCn

(1+Drate)n

� .

Lifetime

1

Where: 

FC = the first cost (2011$);
8-4

n = the index for the year of operation (yr); 

Lifetime = the service life of the transformer; 

OCn = the operating cost in year n, including the value of the losses and 

maintenance costs (2011$/yr); and 

Drate = the discount rate applied to the calculation (%). 

8.2.2 Key Steps in Life-Cycle Cost Analysis 

Although the LCC relies on a simple equation, DOE's LCC spreadsheet model accounts 

for the dynamic nature of numerous inputs throughout the service life of a distribution 

transformer. A simplified flowchart (Figure 8.2.1) illustrates the key steps implemented in the 

LCC spreadsheet: the primary inputs, the key computational steps, and the important outputs. 

The LCC spreadsheet is available as an Excel file on the DOE website at 

http://www1.eere.energy.gov/buildings/appliance_standards/rulemaking.aspx/ruleid/44 and 

http://www1.eere.energy.gov/buildings/appliance_standards/rulemaking.aspx/ruleid/43. 
8-5

Figure 8.2.1 Flowchart of Spreadsheet Model for Calculating 

Transformer Life-Cycle Cost

Sections 8.2.2.1 through 8.2.2.11 describe the analytical steps of the LCC model shown 

in the flowchart. Following this description, this chapter presents the specific inputs that DOE 

developed and then used in the LCC model for this rulemaking (section 8.3). Next, the chapter 

presents the results of the LCC model runs for the various design lines (section 8.4), and the key 

sensitivities to those results (section 8.5). 
8-6

The calculation of LCC determines the financial impact of energy efficiency standards 

for distribution transformers from the perspective of the customer, or the owner of the 

transformer. Several types of information are necessary for the calculation: the first-cost of 

transformers with and without standards, operating costs of transformers with and without 

standards, the year the standard would become effective, and the lifetime of transformers. 

Section 8.3 explains in more detail DOE’s inputs to the LCC. 

8.2.2.1 Step 1: Select Parameters A and B 

The spreadsheet user selects customer choice of A and B parameters from the choices on 

the A & B Dist worksheet. This step establishes the current environment for the purchasing 

decision. For liquid-immersed distribution transformers, DOE assumed that 90 percent are 

purchased based on lowest first cost and 10 percent are purchased using the TOC evaluation. 

When deciding on which dry-type distribution transformers to purchase, commercial and 

industrial (C&I) entities also may use an evaluation based on parameters A and B. Although C&I 

purchasers use a different analytic process for determining A and B values from that used by 

electric utilities, the fundamental meanings of A and B are the same for both groups of 

purchasers. 

The LCC spreadsheet uses two different models of A and B to simulate the two different 

distribution transformer purchase decisions. One model is used for all liquid-immersed 

transformer design lines, and a different model for dry-type design lines. The specific inputs to

the two scenarios are given in section 8.3 of this TSD chapter, as well as in the A & B Dist

worksheet of the LCC spreadsheets for liquid-immersed and the Demand and Usage worksheet 

for dry-type units. These scenarios can be selected using the “Transformer Customer A’s and 

B’s” pull-down menu on the Summary worksheet. Step 2 below explains the application of the A 

and B distributions when selecting transformer designs.

8.2.2.2 Step 2: Select Designs that Meet a Chosen Efficiency Level

Step 2a: The spreadsheet model selects a efficiency level (EL) and its associated 

distribution transformer designs to evaluate. DOE developed as many as seven ELs for each 

design line based on information obtained from the engineering analysis (see chapter 5). The 

engineering analysis yielded a cost-efficiency relationship in the form of manufacturer selling 

prices, no-load losses, and load losses for a range of realistic transformer designs. This set of 

data provided the LCC model with a distribution of transformer design choices. (The Design 

Table worksheet provides a condensed version of the engineering analysis output.) After the user 

chooses a EL, the spreadsheet selects from its database of designs the subset of designs that 

satisfy the selected EL and another set of designs that satisfy the baseline scenario.

In addition to the economic value of load and no-load losses, other factors may affect 

design selection. DOE accounted for such factors by adding a random factor to the distribution 

transformer’s first cost. By incorporating this factor, DOE captured the range of typical realworld variation in the first cost of a transformer. DOE modeled this random cost factor as a 

uniformly distributed random number that can either increase or decrease the first cost of the 
8-7

transformer by as much as 5 percent. The spreadsheet selects the transformer design that has the 

lowest TOC (including the random cost factor) for the customer. For each iteration cycle, a 

design is chosen based on distributions of A and B parameters from Step 1. 

Step 2b: The spreadsheet model calculates markup and installation costs. For liquidimmersed distribution transformers, which typically are purchased directly by utilities from 

manufacturer representatives, DOE considered the transformer purchase price to be the 

manufacturer selling price plus a distributor markup and sales tax. It added installation costs 

separately. For dry-type distribution transformers, the distribution channel includes various 

intermediaries who add their own costs to the manufacturer selling price. Those costs include a 

manufacturer markup, distributor markup, contractor markup, installation costs, and sales tax. 

For this step key inputs include markup and installation costs. DOE presents its specific values 

for those inputs in chapter 6 of this TSD. 

8.2.2.3 Step 3: Select Load and Price Profile

The spreadsheet model dynamically selects a sample distribution transformer load profile 

from distributions derived from available data. For liquid-immersed distribution transformers, 

DOE developed an hourly transformer load simulation model to capture the dynamics and 

economics of transformer loads. DOE then used the marginal cost for the cost of electricity. 

To estimate the impact of distribution transformer losses on C&I companies’ electricity 

bills, DOE modeled the relationship between monthly transformer load characteristics and 

customer demand and usage. It developed a method to calculate customer monthly bills and 

derived distributions of load parameters from available hourly load data. 

The load profiles and characteristics are provided in the Price Load Model worksheet of 

the LCC spreadsheet for liquid-immersed distribution transformers and in the Demand & Usage

worksheet of the LCC spreadsheet for dry-type distribution transformers. For both types of

transformers, DOE calculated the total cost of electricity both with and without transformer 

losses and used the difference to calculate incremental electricity costs. Section 8.3.5 provides a 

detailed discussion of the electricity price analysis. 

8.2.2.4 Step 4: Calculate Cost of Losses 

The spreadsheet model estimates the incremental impacts of no-load and load losses from 

the loss coefficients of the design, the monthly customer load characteristics (demand and 

usage), and the cost of electricity. In this step, the spreadsheet combines the no-load losses, load 

losses, and electricity price information for each distribution transformer in the baseline scenario 

and in the chosen standards scenario. Subsequent steps project the costs of losses into the future 

and then convert them back to present values. 

8.2.2.5 Step 5: Project Losses and Costs into the Future

The spreadsheet model projects losses and costs into the future based on assumptions 

regarding load growth and a forecast of future changes in electricity price. Spreadsheet users can 
8-8

select various scenarios for load growth and future electricity price. The model applies the 

selected options to the initial cost of losses that were calculated in Step 4. DOE presents its 

specific load growth and electricity price trends in the LCC inputs section (section 8.3) of this 

chapter.

8.2.2.6 Step 6: Select Discount Rate

To discount the future stream of costs into a present value, the spreadsheet model selects 

a discount rate from a distribution. The LCC spreadsheet selects a discount rate from a weighted 

sample of discount rate inputs derived from the financing costs of purchasing transformers. DOE 

presents its specific discount rates in the LCC inputs section (section 8.3) of this chapter. 

8.2.2.7 Step 7: Calculate Present Value of Future Cost of Losses

The spreadsheet model calculates the present value of future operating costs and losses 

and the present worth per watt of no-load and load losses. This step applies the discount rate 

selected in Step 6 to the future costs of losses from Step 5 to produce a single, present-valued 

number. In addition to the costs from Step 5, the calculation uses as inputs the effective date of 

the standard, the transformer lifetime, maintenance costs, and a power factor. 

8.2.2.8 Step 8: Report Results

The spreadsheet model provides the LCC, LCC savings, payback period, and other 

results for inclusion in the distribution of results. 

8.2.2.9 Step 9: Repeat Process and Report Results

When applying the Monte Carlo simulation, the model performs a user-defined number 

of iterations and reports the results as distributions. The specific number of iterations for the 

Monte Carlo simulation is specified through the “Repeat Process” decision box. Based on DOE’s 

rulemaking experience with expressing results as distributions, 10,000 iterations in a Monte 

Carlo simulation capture sufficient variability. When the specified number of iterations has been 

reached, the model ends the simulation process and generates result reports.

8.3 INPUTS TO LIFE-CYCLE COST ANALYSIS

This section describes the LCC inputs used in the spreadsheet model and provides 

definitions and data sources for each input. This section also elaborates on how the LCC 

spreadsheets apply certain user-chosen inputs to the model. The specific inputs to the model, in 

the order in which they appear on the left-hand side of the LCC flowchart (Figure 8.2.1), are:

• transformer selection A and B parameters 

• database of transformer designs

• markup and installation costs

• transformer loading 
8-9

• electricity costs and prices

• load growth trends 

• electricity growth and price trends 

• discount rates 

• effective date of standard

• transformer service life

• maintenance costs

• power factor

8.3.1 A and B Distribution Transformer Selection Parameters

The A and B distribution transformer selection parameters that DOE used in calculating

total owning cost (TOC) characterize the value that transformer purchasers place on reducing noload and load losses, expressed in terms of dollars per watt of reduced losses. Using A and B 

parameters to represent a customer’s choice of transformer implies that the value of loss 

reduction is proportional to the amount by which losses are reduced. Given the wider 

applicability of the TOC formulation to the expression of loss valuations, DOE used A and B 

parameters to formulate a customer choice model. 

To represent the potential range of purchasers’ valuation of losses, DOE developed three 

customer choice scenarios for each LCC calculation. The difference among the three scenarios is 

the fraction of purchasers who place a value on reducing transformer losses. Those who place a 

value on reducing losses are described as evaluators; those who do not consider transformer 

losses during a purchase decision are termed non-evaluators. The scenario representing nonevaluation for all purchases has 0 percent evaluators, while the scenario representing evaluation 

for all purchases has 100 percent evaluators. 

For liquid-immersed distribution transformers, DOE’s default scenario is an evaluation 

rate of 10 percent. Because few purchasers consider transformer losses as part of the purchase 

decision for low and medium-voltage, dry-type distribution transformers, DOE assumed a 

default evaluation rate of 2 percent. 

DOE used the 0-percent and 100-percent evaluation scenarios to test the LCC sensitivity 

to changes in the percentage of distribution transformers purchased using TOC. It estimated the 

mean value of A for evaluators from public transformer purchase bids available on the 

Internet.2,3,4,5,6,7,8,9,10 Then, recognizing that there is substantial variability in the value that 

transformer purchasers may place on reducing losses, DOE created separate statistical models for 

A and B for liquid-immersed and dry-type transformers.

For each value of A that a distribution transformer purchaser may use, there is a range of 

possible B values that are consistent with the particular A parameter. (B parameters relates to the 

value associated with load losses.) In general, the ratio of B to A is a measure of the relative 

importance of load losses and no-load losses. For a distribution transformer that is constantly 

loaded at 100 percent of rated capacity, the values of B and A should be the same, because both 

load and no-load losses will always be at their rated values. Load losses increase with the square 

of the load, and transformer mean loads are almost always less than 100 percent. Therefore, in 
8-10

practice, B is always less than A, and is approximately equal to A times the square of the 

expected load (not considering peak loads).

8.3.1.1 A and B Parameter Selection for Liquid-Immersed Distribution 

Transformers

DOE collected A and B parameter values from distribution transformer purchase bids 

available on the Internet and combined these with the sample used in the previous final rule.3

The bid documents were published in various years. In order to evaluate the data, DOE therefore 

normalized the A and B values to 2010$ using the U.S. Bureau of Labor Statistics’ Producer 

Price Index for power generation, transmission, and control.11

A Parameter: To model the distribution of A values in the data, DOE developed a 

piecewise linear fit to the empirical distribution. Figure 8.3.1 shows the cumulative distribution 

function for both the data and the model. 

Figure 8.3.1 Cumulative Distribution of Historical A Parameter

and Model A Parameter 

 Table 8.3.1 lists midpoints for the A parameter and the cumulative probability of each 

midpoint estimated by the model, along with the probability derived from the historical data. 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Probability

A Value $/W (2010$)

Cumulative Distribution of A Values

Historical Data

Model
8-11

Table 8.3.1 A Parameter Model and Historical Data

A Parameter Midpoint

$/W 

Cumulative Probability, 

Model

%

Cumulative Probability, 

Historical Data

%

2.5 0.20 0.2051

3.5 0.30 0.2821

4.5 0.60 0.5897

5.5 0.70 0.6667

6.5 0.80 0.7949

7.5 0.90 0.9231

8.5 0.95 0.9487

9.5 0.96 0.9487

10.5 0.97 0.9744

11.5 0.98 0.9744

12.5 0.99 1.0000

B Parameter: The data show that the value of the B parameter depends somewhat on the 

value of A used by the purchaser, with most of the data points lying in two distinct clusters. The 

clusters, which represent different ratios of B to A, likely reflect the different technologies used 

to serve base load and peak load. The first cluster, consisting of approximately 40 percent of the 

sample, has a B:A ratio of 0.24 and represents utilities that place relatively low economic value 

on load losses. The second cluster has a B:A ration of 0.46 and represents utilities that place 

relatively higher economic value on load losses. Figure 8.3.2 illustrates the two clusters. Each 

cluster is modeled as a linear fit plus a random increment. In the LCC model, purchasers are 

assigned randomly to one or the other category of B to A ratio, in the same proportion as seen in 

the data.
8-12

Figure 8.3.2 Distributions of Load Loss (B) Values versus NoLoad Loss (A) Values for Liquid-Immersed

Distribution Transformers

8.3.1.2 A and B Parameter Selection for Dry-Type Distribution Transformers

 DOE developed models of A and B parameters for dry-type distribution transformers that 

differ from those used for liquid-immersed distribution transformers. The C&I building owners 

of dry-type transformers pay for the energy dissipated by the transformer at a price specified by 

their electricity tariff. DOE estimated that 60 percent of dry-type distribution transformers are 

installed in commercial buildings, and 40 percent in industrial buildings.12 The LCC accounts for 

this distribution by adjusting the weights of individual buildings. For each design line, only 

buildings having a peak load larger than the transformer capacity are included in the customer 

sample.

A Parameter: DOE used the following equation to convert the customer’s marginal 

electricity prices to the appropriate A parameter.

A = HPW × MPEW + HPS × MPES + MW × MPDW + MS × MPDS

FCR .

Where:

MPEW = the winter marginal energy charge ($/kilowatt-hour (kWh)) (see section 

8.3.5.4; 

MPDW = the winter marginal demand charge ($/kW) (see section 8.3.5.4); 

MPES = the summer marginal energy charge ($/kWh) (see section 8.3.5.4); 

MPDS = the summer marginal demand charge ($/kW) (see section 8.3.5.4)

HPW = the number of hours in the winter period; 

y = 0.23x + 0.00

R2 = 0.91

y = 0.45x + 0.02

R2 = 0.61

0 

1 

2 

3 

4 

5 

0 2 4 6 8 10 12 14

Load Losses (B) $/W ( 2010$)

No-load Losses (A) $/W (2010$)

Line 1

Line 2

Linear (Line 1)

Linear (Line 2)
8-13

HPS = the number of hours in the summer period; 

MW = the number of months in the winter period, defined as October through 

April; 

MS = the number of months in the summer period, defined as May through 

September; and

FCR = the fixed charge rate, here equal to 0.2.13

 

B Parameter: The equation for B is similar to that for A, modified to account for the fact 

that load losses depend on the square of the load on the transformer. The transformer load loss 

rate is defined assuming the transformer is fully loaded; in reality most of the time a transformer 

is only partly loaded. This situation is accounted for by the transformer loss factor (LSF), which 

is equal to the average of the square of the transformer load divided by the square of the peak 

transformer load. The building peak load is reduced by an amount equal to the square of the load 

on the transformer at the time of the building peak; this effect is accounted for by the transformer 

peak responsibility factor. The formula for the B parameter is:

B = LSF(HPW × MPEW + HPS × MPES) + RF(MW × MPDW + MS × MPDS)

FCR

Where: 

LSF = the transformer energy loss factor, which is equal to the square of the 

transformer root mean square (RMS) load; and

RF = the transformer peak responsibility factor, which is equal to the square of the 

ratio of the transformer load during the hour of the building peak to the peak 

transformer load. 

 For both A and B parameters, the fixed charge rate is used to convert the annual cost of 

load losses to a net present value. 

To summarize, DOE characterized distribution transformer purchases with respect to 

efficiency in terms of two economic valuation parameters. The parameter A expresses the value 

that a customer gives to reducing no-load losses in dollars per watt, while the parameter B 

expresses the value given to reducing load losses at rated load. DOE described purchase 

behavior in terms of evaluators who place a value on reducing losses, and non-evaluators who 

place no value on reducing losses. DOE investigated four scenarios as sensitivities: (1) liquidimmersed, (2) small-capacity low-voltage dry-type, (3) small-capacity medium-voltage dry-type 

and (4) large-capacity medium-voltage dry-type. The A and B parameter evaluation rates for the 

low, medium and high sensitivities for each of those scenarios are shown in Table 8.3.2. For 

evaluators, DOE used a distribution of A and B values to characterize the economic criteria used 

in the purchase decision. 
8-14

Table 8.3.2 A and B Parameter Evaluation Scenarios 

Percentage of Evaluators %

Low Medium High

Liquid-immersed 0 10 100

Low-voltage dry-type 0 2 100

Medium-voltage dry-type 0 2 100

8.3.2 Database of Distribution Transformer Designs

Establishing a relationship between cost and efficiency is an integral part of DOE’s 

rulemaking process. For distribution transformers, DOE derived this relationship from a database 

developed during the engineering analysis (chapter 5 of the TSD) of selling prices, no-load 

losses, and load losses for the range of realistic distribution transformer designs contained in the 

LCC spreadsheets. DOE used a commercial transformer design software company, Optimized 

Program Service Inc., and its software to create the database of designs. The database comprises

a wide range of efficiencies and manufacturer selling prices (including a predetermined 

manufacturer markup) to represent the variability of designs in the marketplace. Chapter 5 

provides more detail on the method DOE used to generate the database of transformer designs

and the database structure. 

8.3.3 Markup and Installation Costs

Bringing a newly manufactured distribution transformer into service as an installed piece 

of electrical equipment entails costs for markups, sales tax, and installation. 

For liquid-immersed distribution transformers, which a utility typically purchases directly 

from a manufacturer, DOE considered the transformer purchase price to be the manufacturer 

selling price plus, in some cases, a distributor markup and sales tax. DOE added installation costs 

separately. For dry-type distribution transformers, the distribution channel includes 

intermediaries who add their own costs to the manufacturer’s selling price. Costs therefore 

include a manufacturer markup, distribution markup, contractor markup, installation cost, and 

sales tax. See chapter 6 of this TSD for a detailed discussion of the markup calculations. 

8.3.3.1 Projection of Future Equipment Prices 

To derive a price trend for distribution transformers, DOE obtained historical Producer 

Price Index (PPI) data for electric power and specialty transformer manufacturing spanning the 

time period 1969-2011 from the Bureau of Labor Statistics’ (BLS).a

Figure 8.3.3

The PPI data reflect nominal 

prices, adjusted for product quality changes. An inflation-adjusted (deflated) price index for 

specialty transformers was calculated by dividing the PPI series by the Gross Domestic Product 

Chained Price Index (see ).

 

a

 Series ID PCU335311335311; http://www.bls.gov/ppi/ 
8-15

Figure 8.3.3 Historical Nominal and Deflated Producer Price 

Indexes for Electric Power and Specialty

Transformer Manufacturing

 From the mid-1970s to 2005, the deflated price index for transformers was in decline. 

Since then, the index has risen sharply, primarily due to rising prices of copper and steel products 

that go into manufacturing transformers (see Figure 8.3.4). The rising prices for copper and steel 

products were primarily a result of strong demand from China and other emerging economies. 

Given the slowdown in global economic activity in 2011, DOE believes that the extent to which 

the trends of the past five years will continue is very uncertain. DOE performed an exponential 

fit on the deflated price index for transformers, but the R2 was relatively low (0.21). 

 Given the above considerations, DOE decided to use a constant price assumption as the 

default price factor index to project future distribution transformer prices in 2016. Thus, prices 

forecast for the LCC and PBP analysis are equal to the values from the engineering analysis 

(chapter 5) for each efficiency level in each equipment class.

0

50

100

150

200

250

300

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1967 1972 1977 1982 1987 1992 1997 2002 2007

Nominal PPI (1983=100)

Deflated PPI (2011=1)

Deflated Electric Power and Specialty Transformer Manufacturing PPI

Nominal Electric Power and Specialty Transformer Manufacturing PPI
8-16

Figure 8.3.4 Historical Deflated Producer Price Indexes for 

Copper Smelting, Steel Mills Manufacturing and 

Electric Power and Specialty Transformer 

Manufacturing

8.3.4 Distribution Transformer Loading

To estimate the economic burdens and benefits of efficiency improvements, DOE 

characterized the energy use and losses of distribution transformers by estimating the loads on 

them. Because the applications for distribution transformers vary significantly by type of 

transformer (liquid-immersed or dry-type) and ownership (95 percent of electric utilities own 

liquid-immersed; C&I entities primarily use dry-type), DOE performed two separate load 

analyses to evaluate the efficiency of the two types of distribution transformers. Chapter 7 of this 

TSD, Energy Use and End-Use Load Characterization, describes the two separate load analyses.

8.3.4.1 Loading Levels for Utilities Serving Low Population Densities 

DOE recognizes that rural areas the number of customers per distribution transformer is 

likely to be significantly lower than in urban or suburban areas, which in turn results in lower 

root-mean-square (RMS) loads. To account for this effect, DOE performed an analysis to 

determine an average population density in the territory served by each of the utilities 

represented in the LCC simulation. This analysis is implemented for liquid-immersed designlines 1through 5. For each utility, EIA Form 861 data were used to generate a list of counties 

served by the utility. Census data were used to determine the average housing unit density in 

0 

0.2

0.4

0.6

0.8

1 

1.2

1.4

1.6

1960 1970 1980 1990 2000 2010 2020

Deflated Commodity Price Index (2011=1)

Year

Primary Copper Smelting PPI

Iron and Steel Mills PPI

Delfated Distribuiton Transformers PPI
8-17

each county. An average over counties was then used to assign the utility to a low density, 

average density or high density category, with the cutoff for low density set at 32 households per 

square mile. For those utilities serving primarily low density residential areas the median of the 

RMS load distribution is reduced from 35 percent by 25 percent. 

8.3.5 Electricity Price Analysis

This section describes the electricity price analysis DOE performed to determine the 

energy portion of the annual operating expenses for distribution transformers. DOE performed 

two types of analyses: one investigated the nature of hourly transformer loads, their correlation 

with the overall utility system load, and their correlation with hourly electricity costs and prices; 

another estimated the impacts of transformer loads and resultant losses on monthly electricity 

usage, demand, and electricity bills. DOE refers to the two analyses as hourly and monthly

analyses, respectively. DOE used the hourly analysis for liquid-immersed distribution 

transformers, which are owned predominantly by utilities that pay costs that vary by the hour. 

DOE used the monthly analysis for dry-type distribution transformers, which typically are owned 

by C&I establishments that receive monthly electricity bills. 

8.3.5.1 Hourly Marginal Electricity Price Model for Liquid-Immersed 

Distribution Transformers

To evaluate the electricity costs associated with liquid-immersed distribution 

transformers, DOE used marginal electricity prices. Marginal prices are those utilities pay for the 

last kilowatt-hour of electricity produced. A utility’s marginal price may be higher or lower than 

its average price, depending on the relationships among capacity, generation, transmission, and 

distribution costs. The general structure of the hourly marginal cost equation divides the costs of 

electricity into (1) capacity components and (2) energy cost components. For each component 

DOE estimated the economic value for both no-load losses and load losses. The capacity 

components include generation and transmission capacity. Capacity components also include a 

reserve margin for ensuring system reliability, along with factors that account for system losses. 

Energy cost components include a marginal cost of supply that varies by the hour. 

8.3.5.2 Capacity Costs 

 DOE developed a methodology to calculate marginal costs for the set of regions defined 

in the Energy Information Administration’s (EIA’s) National Energy Modeling System (NEMS) 

electricity market module (EMM).14 The method depends on the type of generation that is built, 

DOE developed the same capacity costs formula for both types of losses. 

Capacity costs are defined as follows.

CC = ∆P(βCM(CCadj (CGFG + CTFT) + FOM) − RCV)

Where:

∆P = the reduction in system peak load; 

β = a load adjustment factor, which is one plus the estimated system losses;
8-18

CM = the reserve capacity margin; 

CCadj = a capacity construction cost adjustment factor, which accounts for variation in 

construction costs by region, 

CG = the overnight cost in $/kW of building new generation capacity; 

FG = the fixed charge rate, used to convert the overnight cost to an annual carrying 

cost; 

CT = the overnight cost in $/kW of new transmission capacity; 

FT = the fixed charge rate for transmission investments;

FOM = the fixed operations and maintenance cost for new capacity in $/kW 

RCV = the residual capacity value; this is the amount of annual revenue a generator is 

expected to earn when market prices or system lambdas are above the 

operating cost of that unit, expressed in $/kW

DOE calculated the various inputs of this equation as follows. 

Peak Load Reduction (∆P): This reduction results from improved transformer efficiency. 

DOE used a statistical model to estimate the reduction consistent with the methodology used to 

model transformer hourly loads.

Loss Adjustment Factor (β): The loss adjustment factor represents the fraction of 

electricity that is dissipated by the transmission and distribution system. It is equal to one plus 

the fractional losses in the system. DOE used a constant average value of 1.08, based on the 

regional transmission and distribution loss factors from the NEMS planning model.2 The 

regional transmission and distribution loss factors are given in Table 8.3.4. 

Capacity Margin (CM): This factor represents the fraction of planning reserve capacity 

needed to ensure system reliability, per unit of additional capacity requirement. DOE used the 

industry standard of 15 percent. 

Capacity Construction Cost Adjustment Factor (CCadj): These factors account for the 

fact that construction costs vary by region. They are applied to the overnight cost of new 

generation to estimate the cost of constructing new power plants by NEMS region. The factors 

were developed using representative costs of labor, materials and equipment by the U.S. Army 

Corps of Engineers Civil Works Construction Cost Index System.15 The regional capacity 

construction cost adjustment factors are given in Table 8.3.4. 

Unit Generation Capacity Cost (CG): This factor represents the overnight cost of 

building new generating capacity, as provided by NEMS.14 The costs do not include financing 

charges; DOE added the cost of financing to the overnight costs assuming a cost of capital of 5 

percent. Table 8.3.4 shows the rates for generating no-load loss and load loss capacity for 

regulated systems. 

 Generation Fixed Charge Rate (FG): A fixed charge rate is used to convert the overnight 

capital cost of new generation to an annualized (or amortized) cost. 
8-19

Table 8.3.3 shows the FG for each of the average discount rate and plus/minus two 

standard deviation scenarios for the investor owned utilities (IOUs) and publically owned 

utilities (POUs). 

Table 8.3.3 Generation Fixed Charge Rates

 

IOU POU

Average 

Case - 2 S.D. + 2 S.D. Average Case - 2 S.D. + 2 S.D.

Fixed Charge Rate 0.131 0.113 0.149 0.095 0.077 0.114 

System Design

Installed System Cost per kW $1,300.00 $1,300.00 $1,300.00 $1,300.00 $1,300.00 $1,300.00

Plant Cost

O&M Costs ($/kW) $8.00 $8.00 $8.00 $8.00 $8.00 $8.00 

O&M Costs Escalator (%/yr) 2.50% 2.50% 2.50% 2.50% 2.50% 2.50% 

Financing

Financing Lifetime (years) 20 20 20 20 20 20 

% Equity Financed 50% 50% 50% 0% 0% 0% 

% Debt Financed 50% 50% 50% 100% 100% 100% 

Debt Interest rate 5.96% 3.34% 8.58% 5.96% 3.34% 8.58% 

Cost of Equity 10.51% 9.07% 11.95% 10.51% 9.07% 11.95% 

Pre-tax WACC 8.23% 6.20% 10.26% 5.96% 3.34% 8.58% 

After tax WACC 7.05% 5.54% 8.57% 5.96% 3.34% 8.58% 

Tax Assumptions

Federal Tax Rate 35.00% 35.00% 35.00% 0.00% 0.00% 0.00% 

State Tax Rate 7.00% 7.00% 7.00% 0.00% 0.00% 0.00% 

DOE select a FG consistent with the discount rates described in section 8.3.8. As shown 

in Figure 8.3.5, the relationship between the real weighted-average cost of capital (WACC) and 

FG is nearly linear:
8-20

Figure 8.3.5 Real Weighted-Average Cost of Capital and 

Generation Fixed Charge Rate

 Given this relationship, the appropriate FG rates can be closely estimated using the 

following equations: 

FG for IOUs = 1.122 × Real Discount Rate + 0.070, and

FG for POUs = 0.715 × Real Discount Rate + 0.0672

By applying these equations for each of the discount rates for IOUs and POUs ensures 

that the discount rate and FG are properly aligned. 

 Unit Transmission Capacity Cost (CT): This overnight cost per unit for an increment of 

new transmission capacity is provided by NEMS.15

 Transmission Fixed Charge Rate (FT): The fixed charge rate is used to convert the 

overnight cost of new investment in transmission into an annual (amortized) cost. DOE used a 

value of 0.12.14

 Fixed Operating and Maintenance Cost (FOM): This factor is used to capture the fixed 

operating and maintenances costs of new capacity.

Residual Capacity Value (RCV): The residual capacity value represents the additional 

revenue a generation owner would earn whenever their operating cost is below the market 

clearing price or system lambda. This annual revenue offsets, to some extent, the cost of building 

new generation capacity. The operating cost is estimated as the fuel cost times the heat rate plus 

the variable O&M. The residual capacity value is expressed in $/kW-year, and is calculated as 

follows: 

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00%

Generation Fixed Charge Rate (FG) 

Real Weighted -- Average Cost of Capital

IOU

POU

Linear (IOU)

Linear (POU)
8-21

1. In each hour, the difference between the operating cost and the hourly price is 

calculated; a small threshold of 3 percent is applied to the hourly price to ensure that 

the calculation is not overly sensitive to the hourly price 

2. For peaking capacity, if the difference is above zero, then the unit is assumed to be 

dispatched and the revenues for that hour are added to the annual sum 

3. For base-load capacity, if the difference is above zero during a period of 3 hours or 

more, the unit is assumed to be dispatched and the revenues for that period are added 

to the annual sum. 

For both capacity types, it is assumed that the fuel used is natural gas. The estimated RCV

will depend on both wholesale electricity prices and natural gas prices during the analysis period. 

To estimate the degree of variation, RCV values were calculated for 2016 and 2035. Wholesale 

electricity prices were scaled from the 2008 data year to the calculation year using the generation 

price trend in AEO 2012. The natural gas fuel price for electric power generation was taken from 

AEO 2012. 

For a base-load natural gas combined-cycle (NGCC) plant, the RCV is equal to about 95 

$/kW in 2016 and 80 $/kW in 2035; for simplicity an average of 90 $/kW is used to estimate a 

typical annual value. For a peaking natural gas combustion turbine, the RCV is equal to 27 $/kW 

in 2016 and 21 $/kW in 2035. An average of 25 $/kW is used to represent a typical annual value. 

Figure 8.3.6 Price Duration Curves for New York Independent 

System Operator (ISO) and ISO New England, 1999 

versus 2008 
8-22

Table 8.3.4 Regional Capacity Cost Factors 

EMM 

Regiona CCadj

Construction cost 

adjustment factor

β

TD Loss 

Factor

RCV

Annualized Capacity 

Cost Savings

NLL LL NLL LL

Code Name (2011$/kW) 

1 ECAR 1.02 1.070 90 25 228 142

2 ERCOT 0.87 1.065 90 25 185 119

3 MAAC 1.1 1.072 90 25 258 160

4 MAIN 1.06 1.068 90 25 239 148

5 MAPP 0.99 1.088 90 25 225 140

6 NY 1.16 1.080 90 25 278 172

7 NE 1.06 1.080 90 25 248 155

8 FL 0.94 1.068 90 25 206 130

9 SERC 0.89 1.068 90 25 191 122

10 SPP 0.91 1.081 90 25 201 127

11 NPP 1 1.093 90 25 256 169

12 RA 0.97 1.093 90 25 240 157

13 CA 1.18 1.093 90 25 329 218

No-Load Losses 

DOE assumed that these losses are served by base-load capacity. The capacity cost is 

estimated by assuming that marginal capacity is added in the proportions 40 percent coal, 40 

percent NGCC, and 20 percent wind. These proportions are based on the capacity mix estimated 

in the AEO 2012 projection to 2035, summarized below in Table 8.3.5. A small decrease in the 

fraction of capacity served by coal is compensated by an increase in the fraction served by oil 

and gas, but otherwise the proportions remain approximately constant from 2015 through 2035. 

AEO does not separately itemize capacity additions and retirements; it only itemizes net 

additions. If the typical lifetime of a power plant is T in years, then approximately 1/T of total 

capacity should be retired each year. This will vary somewhat according to the age of the 

standing stock. If all lifetimes were equal, then the fact that the proportion of capacity by fuel 

type is constant would mean that new capacity is being added in the same constant proportions. 

Although coal plants have a longer lifetime and might therefore be added more slowly than 

NGCC, the standing stock of coal plants is also older, which conversely implies a greater 

retirement rate. 

Based on AEO estimates of capacity factors, coal serves predominantly base load, while 

natural gas and renewables serve a mix of base, mid-merit and peaking loads. Hence, the 

fraction of oil and natural gas is raised from approximately 46 percent to 50 percent to represent 

its greater contribution to base load. For simplicity, onshore wind costs are used to represent all 

renewables, and the proportion is increased to 20 percent to represent the additional penetration 

of other types of renewables (wind has the lowest cost). This proportion also reflects the fact that 

 

a Regions are defined in the U.S. Energy Information Administration (EIA), National Energy Modeling System 

(NEMS) Electricity Market Module (EMM)
8-23

current incentive programs require wind to be dispatched first. The remaining 30 percent of new 

base load is assumed to come from coal and nuclear. 

Table 8.3.5 AEO 2012 Capacity by Fuel Type 

Fuel Type AEO 2012 Applied 2015 2035

Steam Coal 28% 25% 25%

Oil and Natural Gas 43% 47% 50%

Renewable Generation (including Hydro) 17% 18% 20%

Nuclear 11% 10% 5%

Load Losses 

 For load losses, the additional capacity is assumed to be a simple combustion turbine. 

8.3.5.3 Energy Costs 

 DOE developed two sets of energy costs to be applied to the two types of losses: 

ECNLL = the value of the capacity costs associated with no-load losses, and

ECLL = the value of the capacity costs associated with load losses.

These terms can be further expressed as:

ECNLL = β ∈NLL ∑ P(h) h , 

and

ECLL = β ∈LL ∑ P(h)e2(h) h . 

Where:

β = a load adjustment factor, which is one plus the estimated system losses; 

∈NLL = the no-load (constant) loss rate; 

∈LL = the load loss rate; 

P(h) = the hourly electricity price; and

e

2

(h) = the hourly transformer load. 

Hourly Electricity Price (P(h)): To calculate the hourly price of electricity, DOE used 

the day-ahead market clearing price for regions having wholesale electricity markets, and system 

lambda values for all other regions. System lambda values, which are roughly equal to the 

operating cost of the next unit in line for dispatch, are filed by control area operators under 

Federal Energy Regulatory Commission (FERC) Form 714.16 DOE used the most recent data 

available, from 2008, for both market prices and system lambdas. 
8-24

Hourly Transformer Load (e2(h)): DOE used a statistical model to represent hourly 

variations in transformer loading and the correlation with hourly-varying system electricity 

prices. The hourly load model is discussed in detail in chapter 7 of this TSD. 

No-load Loss Rate (∈NLL): This parameter, which provides the no-load loss rate of the 

selected transformers, is imported from the database of transformer design options developed in 

the engineering analysis (chapter 5). 

Load Loss Rate (∈LL): This parameter, which provides the load loss rate of the selected 

transformers, is imported from the database of transformer design options. The load loss rate is 

estimated while the transformer is fully loaded. 

8.3.5.4 Monthly Marginal Electricity Price Model for Dry-Type Distribution 

Transformers

For C&I owners of dry-type distribution transformers, DOE developed average marginal 

electricity prices from an analysis of marginal energy prices from tariffs for commercial 

buildings.17, 18

 Electricity tariffs for C&I customers can be complex, incorporating block rates, seasonal 

rates, demand charges, and time-of-use rates. To calculate commercial electricity bills requires 

both the monthly consumption and demand; if the supplying utility levies mandatory time-of-use 

(TOU) tariffs, consumption and demand data are required for each TOU period. Monthly billing 

data, consisting of electricity consumption, demand, and expenditures, are available from the 

EIA’s Commercial Building Energy Consumption Survey for 1992 and 1995 survey years.a

Those monthly data were processed using Coughlin et al.’s tariff bill calculation tools17 to 

generate the corresponding monthly utility bill. DOE used the baseline utility bills to calculate 

average prices. Because the customer bill depends on both energy consumption and demand, 

separate marginal prices are needed to represent the effect of independently varying those two 

quantities. The monthly price of marginal electricity consumption (or demand) is calculated by 

decrementing the electricity consumption (or demand) and recalculating the bill. DOE calculated 

seasonal marginal energy prices (MPE) and marginal demand prices (MPD) for each building in 

the sample. The summer season is defined as the months May through September, and the winter 

season all other months. 

DOE’s tariff data were updated most recently in 2004. To convert to 2011 dollars, DOE 

used two datasets: (1) the report, Average Regulated Retail Price of Electricity19 for 2004–2007, 

and (2) the Edison Electric Institute (EEI) Typical Bills and Average Rate reports for 200720

through 2010.21,22 Based on those data, DOE used customer counts to calculate a weightedaverage price escalation factor for each region. The customer counts came from the most recent 

EIA Form 861 data.12 The EEI data only covers publicly owned companies. An analysis of EIA 

data for 2003–2006 showed that the rate of price escalation does not differ significantly for 

publicly versus privately owned utility companies, so DOE used the same escalation factors for 

 

a See: Chapter 7, Energy Use and End-Use Load Characterization, for details regarding DOE’s treatment of the 

CBECS sample.
8-25

both market sectors. Table 8.3.6 provides the average marginal energy and demand prices by 

season for the U.S. Census divisions. DOE dived the census divisions 8 (Mountain) and 9 

(Pacific) into North and South sub regions to account for the impacts of climate on electricity 

prices. 

Table 8.3.6 Average Seasonal Marginal Energy and Demand Prices by Census 

Division 

Census Division

Marginal Energy Price 

2011$/kWh

Marginal Demand Price 

2011$/kW

Summer Winter Summer Winter

1 (New England) 0.11 0.10 16.46 12.98

2 (Mid-Atlantic) 0.09 0.09 14.90 13.15

3 (East North Central) 0.06 0.05 14.04 12.70

4 (West North Central) 0.05 0.05 7.10 5.65

5 (South Atlantic) 0.07 0.07 10.12 9.83

6 (East South Central) 0.06 0.06 9.24 8.87

7 (West South Central) 0.09 0.07 7.18 5.89

8 (Mountain)North 0.05 0.05 3.97 3.94

8 (Mountain) South 0.07 0.08 9.90 9.49

9 (Pacific) North 0.06 0.06 3.48 3.48

9 (Pacific) South 0.11 0.11 9.97 4.54

8.3.6 Trends in Load Growth 

The LCC analysis examines a cross-section of distribution transformers. As part of an 

LCC sensitivity analysis, DOE applied a load growth trend to each new transformer. Spreadsheet 

users can choose among three scenarios using the “Transformer Load Growth/Year” drop-box on 

the Summary worksheet. The three scenarios are: no growth, one-half-percent-per-year growth, 

and one-percent-per-year growth. As the default scenario DOE used a growth trend of 0.5 

percent for liquid-immersed and no growth trend for dry-type distribution transformers. 

8.3.7 Electricity Cost and Price Trends

For the relative change in electricity prices for future years, DOE used the price trends 

from the three forecast scenarios in the EIA’s AEO 2012.

23 The default price trend scenario that 

DOE used in the LCC analysis is the trend in the AEO 2012 reference case. LCC spreadsheet 

users have the choice of using electricity price trends from the AEO 2012 low-growth scenario, 

reference scenario, or high-growth scenario. 

Figure 8.3.7 and Figure 8.3.9 shows the trends for the three AEO 2012 price projections. 

Because AEO 2012 does not forecast beyond 2035, DOE extrapolated the values in later years 

from the price trends of the forecast from 2015 to 2035. This method of extrapolation is in line 

with methods the EIA currently uses to forecast fuel prices for the Federal Energy Management 

Program. 
8-26

For liquid-immersed distribution transformers, which are primarily owned by utilities, the 

price trend applied is of the fuels (natural gas and steam coal) that are consumed by power 

plants, since the operating costs are largely determined by the price of fuel. Base load would be 

fueled by an average coal and gas, while peak loads would likely be fueled primarily by gas. 

These trends are shown in Figure 8.3.8 and Figure 8.3.9. 

Figure 8.3.7 Combined Natural Gas and Steam Coal Price 

Forecast from AEO2012 

Figure 8.3.8 Natural Gas Price Forecast from AEO2012 

Compliance 

Year, 2016

60%

80%

100%

120%

140%

160%

180%

2005 2010 2015 2020 2025 2030 2035 2040

Real Price Relative to 2012

Year

Reference Case

High Growth

Low Growth

Compliance 

Year, 2016

60%

80%

100%

120%

140%

160%

180%

2005 2010 2015 2020 2025 2030 2035 2040

Real Price Relative to 2012

Year

Reference Case

High Growth

Low Growth
8-27

For dry-type distribution transformers, which are primarily owned by C&I building the 

price trend applied is the national average of the retail cost of electricity to C&I customers for all 

losses. This trend is shown in Figure 8.3.9. 

 

 Figure 8.3.9 Electricity Price Forecasts from AEO2012

8.3.8 Discount Rate

The discount rate is the rate at which future expenditures are discounted to estimate their 

present value. DOE derived the discount rates for use in the distribution transformer LCC 

analysis from estimates of the cost of capital for companies that purchase transformers. 

Following financial theory, the cost of capital can be interpreted as (1) the discount rate that 

should be used to reduce the future value of cash flows to be derived from a typical company 

project or investment; (2) the economic cost to a firm of attracting and retaining capital in a 

competitive environment; or (3) the return that investors require from their investment in a firm’s 

debt or equity.24 DOE used primarily the first interpretation. Because most companies use both 

debt and equity capital to fund investments; for most companies, the cost of capital is the 

weighted average of the cost to the firm of equity and debt financing.25

DOE estimated the cost of equity financing using the Capital Asset Pricing Model 

(CAPM). Among the most widely used models to estimate the cost of equity financing, the 

CAPM assumes that the cost of equity is proportional to the amount of systematic risk associated 

with a firm. The cost of equity financing tends to be high when a firm faces a large degree of 

systematic risk, and low when the firm faces a small degree of systematic risk. The degree of 

systematic risk facing a firm and the subsequent cost of equity financing are determined by 

several variables, including the risk coefficient of a firm (beta, or B); the expected return on riskfree assets (Rf); and the additional return expected on assets facing average market risk (which is 

known as the equity risk premium, or ERP). The beta indicates the degree of risk associated with 

90%

95%

100%

105%

110%

115%

120%

2005 2010 2015 2020 2025 2030 2035 2040

Real Price Relative to 2012

Year

Average Commercail & Industiral Electricity Prices by Sales, 

Relative to 2012

Reference Case High Growth Low Growth
8-28

a given firm relative to the level of risk (or price variability) in the overall stock market. Betas 

usually fall between 0.5 and 2.0. A firm having a beta of 0.5 faces half the risk of other stocks in 

the market; a firm having a beta of 2.0 faces twice the overall stock market risk. Following this 

approach, the cost of equity financing for a particular company is given by the following 

equation. 

ke = Rf + (B × ERP). 

Where:

ke = the cost of equity for a company, 

Rf = the expected return of a risk-free asset,

B = the beta of the company stock, and 

ERP = the expected equity risk premium, or the amount by which investors expect the 

future return on equities to exceed that on a risk-free asset.

 The cost of debt financing (kd) is the yield or interest rate paid on money borrowed by a 

company (for example by selling bonds). As defined here, the cost of debt includes 

compensation for default risk and excludes deductions for taxes. DOE estimated the cost of debt 

for companies by adding a risk adjustment factor (Ra) to the current yield on long-term corporate 

bonds (the risk-free rate). DOE used this procedure to estimate current (and future) company 

costs to obtain debt financing. The adjustment factor is based on indicators of company risk, 

such as credit rating or variability of stock returns. 

The discount rate of companies is the weighted average cost of debt and equity financing, less 

expected inflation. DOE estimated the discount rate using the equation: 

k = (ke × we) + (kd × wd). 

Where:

 k = the (nominal) cost of capital,

 ke and kd = the expected rates of return on equity and debt, respectively, and 

 we and wd = the proportions of equity and debt financing, respectively. 

 The real discount rate deducts expected inflation from the nominal rate. The expected 

return on risk-free assets, or the risk-free rate, is defined by the current yield on long-term 

government bonds. The ERP represents the difference between the expected (average) stock 

market return and the risk-free rate.26 DOE adjusted the risk-free rate for inflation to arrive at the 

real risk-free rate, which it then used in the CAPM to estimate of the real discount rate as 

described above.27

Table 8.3.7 shows the typical owners of transformers, grouped by transformer type (the 

design lines DOE used in the engineering analysis). DOE used a sample of approximately 3,200 

companies drawn from the various owner categories to represent transformer purchasers. DOE 

took the sample from the list of companies included on the Damodaran Online website.28 DOE 
8-29

obtained the firm beta, the percent of debt and equity financing, the risk-free rate, and the equity 

risk premium from Damodaran Online. 

Table 8.3.7 Typical Owners of Various Types of Transformers

Design Line Typical Ownership Categories

1, 2, 3, 4, 5 Electric utilities, both publicly and investor owned

6, 7, 8 Electric utilities, commercial property owners, commercial and 

industrial

9, 10, 11, 12, 13A, 13B Companies, government offices

 Transformers are purchased and owned by electric utilities (publicly and investorowned), C&I companies, the owners of commercial buildings (property owners), and all levels of 

government. DOE estimated the cost of debt financing for these companies from the 40 year 

geometric average of the 10-year Treasury note annual rate and the standard deviation of the 

stock price. Publicly owned utilities, including municipals and cooperatives, do not issue stock 

and tend to be financed with debt. DOE obtained the cost of debt for those companies from 

information provided in FERC Form 1 filings. Finally, for owners of government offices, the 

discount rate represents an average of the Federal rate and the State and local bond rates. DOE 

drew the Federal rate directly from the U.S. Office of Management and Budget discount rate for 

investments in energy efficiency in government buildings.29 DOE estimated the State and local 

discount rates from the interest rates on State and local bonds between 1971 and 2010.30 

Table 8.3.8 shows the average values DOE used for the parameters related to cost of 

equity financing and discount rate for industrial companies, commercial companies, commercial 

property owners, and investor-owned utilities. The risk-free rate and equity risk premium are 

constant across sectors in each year, but the cost of debt, percent debt financing, and systematic 

firm risk vary by sector.
8-30

Table 8.3.8 Variables Used to Estimate Discount Rates for the C&I Sector

Sector Year β Rf % ERP % Ra % we % wd %

Industrial Companies 

(SIC 1–4) 

2005 1.03 3.47 3.89 1.50 79 21

2006 1.00 3.44 4.55 2.00 81 19

2007 1.03 3.74 3.80 2.00 78 22

2008 1.10 4.21 2.19 4.00 73 27

2009 1.06 4.15 3.20 4.00 76 24

2010 1.12 6.74 3.23 2.50 74 26

Commercial 

Companies 

(SIC 5–8) 

2005 0.88 3.47 3.89 1.25 80 20

2006 0.88 3.44 4.55 1.25 78 22

2007 0.90 3.74 3.80 1.25 75 25

2008 0.95 4.21 2.19 3.00 64 36

2009 0.94 4.15 3.20 4.00 68 32

2010 0.98 6.74 3.23 2.00 62 38

Commercial Property 

Owners

(SIC 6720) 

2005 0.70 3.47 3.89 0.25 77 23

2006 0.84 3.44 4.55 0.50 55 45

2007 0.91 3.74 3.80 0.50 60 40

2008 1.06 4.21 2.19 3.00 47 53

2009 1.22 4.15 3.20 3.00 56 44

2010 1.02 6.74 3.23 1.50 67 33

*SIC codes refer to the U.S. Standard Industrial Classification system.

 As mentioned above, the cost of capital may be viewed as the discount rate that should be 

used to reduce the future value of typical company project cash flows. It is a nominal discount 

rate, since anticipated future inflation is included in both stock and bond expected returns. 

Deducting expected inflation from the cost of capital provides estimates of the real discount rate 

by ownership category (Table 8.3.9). The mean real discount rate for these companies varies 

between 2.4 percent (government offices) and 5.4 percent (industrial companies). 
8-31

Table 8.3.9 Real Discount Rates by Transformer Ownership Category

Ownership Category SIC 

Code(s)*

Mean Real

Discount Rate 

%

Standard

Deviation 

%

Number of

Observations

Industrial Companies 1–4 5.4 0.4 1866

Commercial Companies 5–8 4.6 1.4 1303

Commercial Property Owners 6720 4.6 0.4 3

Utilities, Investor-Owned 49 3.5 0.4 61

Utilities, Publicly Owned n/a 3.8 0.3 7

Government Offices n/a 2.4 2.2 40

 *SIC codes refer to the U.S. Standard Industrial Classification system.

 Because IOUs purchase the bulk of many of the transformer design lines evaluated here, 

the discount rates calculated for that sector (Table 8.3.9) are particularly important. DOE 

estimated that the average IOU real discount rate is 3.5 percent. That figure is an after-tax 

discount rate, representing the return required by such utilities to attract financing. Private 

financial data companies, including Ibbotson Associates, offer similar estimates. Using Ibbotson 

Associates debt, equity, standard deviation of stock price, and company beta statistics for 2008 in 

the electric, gas, and sanitary services sector (SIC 49), DOE estimates a similar discount rate of 

3.84 percent.24 DOE used the value of 3.5 percent, estimated from the company-level 

Damodaran data, because it is tailored specifically to IOUs, not the broader SIC 49 sector. 

DOE’s approach to estimating the cost of capital provides a measure of the spread as well 

as the average of the discount rate. DOE inferred the spread of the discount rate by ownership 

category from the standard deviation, which ranges from 0.4 percent to 2.2 percent (Table 

8.3.10). Discount rates for publicly owned utilities and commercial property owners are narrowly 

concentrated around their mean values. Discount rates for C&I companies are dispersed across a 

broader range.
8-32

Table 8.3.10 Transformer Ownership by Design Line

Design 

Line

Property

Owners

%

Industrial

Companies

%

Commercial

Companies

%

InvestorOwned

Utilities

%

Publicly

Owned

Utilities

%

Government

Offices

%

1 0.4 0.5 0.9 72.0 26.0 0.2

2 0.4 0.5 0.9 72.0 26.0 0.2

3 2.1 2.4 4.5 80.0 10.0 1.0

4 0.4 0.5 0.9 72.0 26.0 0.2

5 9.5 9.5 27.0 35.0 15.0 4.0

6 19.0 19.0 54.0 0 0 7.9

7 19.0 19.0 54.0 0 0 7.9

8 19.0 19.0 54.0 0 0 7.9

9 19.0 19.0 54.0 0 0 7.9

10 19.0 19.0 54.0 0 0 7.9

11 19.0 19.0 54.0 0 0 7.9

12 19.0 19.0 54.0 0 0 7.9

13A 19.0 19.0 54.0 0 0 7.9

13B 19.0 19.0 54.0 0 0 7.9

Source: DOE contractors.

 Various combinations of commercial property owners and commercial, industrial, and 

utility buyers purchase the different transformer design lines included in the engineering analysis 

(chapter 5). Accordingly, DOE constructed the discount rates associated with any given design 

line from various combinations of discount rates for commercial property owners, commercial, 

industrial, and utility enterprises.

31 DOE estimated distributions of discount rates for the different 

design lines as a weighted average of the distributions for the ownership types. 

8.3.9 Effective Date of Standard

The effective date of the revised energy efficiency standard for distribution transformers 

is four years after DOE issues the final rule. DOE assumes that it will issue the final rule in 2012, 

so the new standard will take effect in 2016. DOE calculated the LCC for all users as if each 

purchase of a new distribution transformer occurs in the year the standard takes effect. It based 

the cost of the equipment on that year; as stated above, however, DOE expresses all dollar values 

in 2011$. 

8.3.10 Transformer Service Life

DOE defined distribution transformer service life as the age at which a transformer retires 

from service. DOE assumed, based on Barnes et al. (1996),32 that the average life of distribution 

transformers is 32 years. This lifetime includes a constant failure rate of 0.5 percent per year due 

to lightning and other random failures unrelated to transformer age, and an additional corrosive 

failure rate of 0.5 percent per year starting at year 15. DOE adjusted the retirement distribution to 

maintain an average life of 32 years.
8-33

8.3.11 Maintenance Costs

Maintenance costs are costs that the customer incurs to maintain equipment operation. 

Maintenance costs are not associated with the replacement or repair of components that fail, but 

rather with general maintenance. DOE assumed that the cost for general maintenance will not 

change with increased efficiency. In practice, there is little scheduled maintenance for 

transformers beyond brief annual checks for dust buildup, vermin infestation, and accident or 

lightning damage.

8.3.12 Power Factor

The power factor of a transformer is the real power divided by the apparent power. Real 

power is the time average of the instantaneous product of voltage and current. Apparent power is 

the product of the root mean square (RMS) voltage times the RMS current. Transformer 

efficiency specifications, such as NEMA's TP 1-2002, assume a power factor of 1.0.1 Therefore, 

DOE used a power factor of 1.0, both in calculating efficiency levels in the engineering analysis 

and when preparing efficiency levels.

In real-world installations, however, the loads experienced by distribution transformers 

are likely to have power factors of less than 1.0. Because the LCC analysis models transformers 

that are installed and operating in the field, DOE created the LCC spreadsheet with an adjustable 

power factor, enabling the incorporation of lower power factors. In the absence of any specific 

data or guidance on the appropriate power factor, DOE used 1.0 for this LCC analysis. 

8.3.13 Default Scenario

 DOE developed separate low, medium, and high scenarios for several key input 

parameters. For each of the key inputs, DOE chose the medium designation as the default 

scenario. The overall default scenario used in the LCC analysis has the following values. 

• Transformer load growth per year: medium (one percent) for liquid-immersed; low (zero 

percent) for dry-type. 

• Transformer loading (relative to current estimate): medium (zero percent).

• Electricity prices (relative to current estimate): medium (zero percent).

• Transformer customer A and B parameters: medium. 

• Future energy price trend: AEO2012 reference. 

Other scenarios can be used to explore the sensitivities to variations of these key 

variables.

8.4 RESULTS OF LIFE-CYCLE COST ANALYSIS

This section presents LCC results for the candidate efficiency improvement levels 

evaluated for all 14 transformer design lines. Table 8.4.1 summarizes the seven candidate 

standard efficiency levels DOE evaluated for each of the 14 design lines examined for the 
8-34

preliminary analysis. The lowest efficiency level (EL) is baseline and current standard, and the 

highest is the most efficient design identified in the engineering analysis. The other six efficiency 

levels fall between those two bounds. DOE expresses all ELs in terms of efficiency, assuming no 

explicit or implicit technology. The column labeled “Base +” shows by how much a given 

standard level exceeds the baseline. DOE based the results presented in this section on the inputs 

described in section 8.3. 

Table 8.4.1 Efficiency Levels Evaluated for Each Design Line 

EL Variable

Design Line

1 2 3 4 5 6 7 8 9 10 11 12 13A 13B 

Baseline (Current 

DOE Standard) % 99.08 98.91 99.42 99.08 99.42 98.00 98.00 98.60 98.82 99.22 98.67 99.12 98.63 99.15 

0.4 

Base + % 0.03 

Efficiency % 99.11 

0.5 

Base + % 0.04 

Efficiency % 98.95 

1 

Base + % 0.08 0.09 0.06 0.08 0.06 0.23 0.23 0.20 0.11 0.07 0.14 0.09 0.06 0.04 

Efficiency % 99.16 99.00 99.48 99.16 99.48 98.23 98.23 98.80 98.93 99.29 98.81 99.21 98.69 99.19 

1.1 

Base + % 0.07 

Efficiency % 99.49 

2 

Base + % 0.14 0.16 0.09 0.14 0.09 0.47 0.47 0.42 0.22 0.15 0.27 0.18 0.21 0.13 

Efficiency % 99.22 99.07 99.51 99.22 99.51 98.47 98.47 99.02 99.04 99.37 98.94 99.30 98.84 99.28 

3 

Base + % 0.17 0.20 0.12 0.17 0.12 0.60 0.60 0.54 0.33 0.23 0.39 0.27 0.34 0.23 

Efficiency % 99.25 99.11 99.54 99.25 99.54 98.60 98.60 99.14 99.15 99.45 99.06 99.39 98.97 99.38 

4 

Base + % 0.23 0.27 0.15 0.23 0.15 0.80 0.80 0.65 0.40 0.29 0.46 0.34 0.41 0.30 

Efficiency % 99.31 99.18 99.57 99.31 99.57 98.80 98.80 99.25 99.22 99.51 99.13 99.46 99.04 99.45 

5 

Base + % 0.34 0.40 0.19 0.34 0.19 0.93 0.93 0.72 0.57 0.36 0.65 0.41 0.62 0.37 

Efficiency % 99.42 99.31 99.61 99.42 99.61 98.93 98.93 99.32 99.39 99.58 99.32 99.53 99.25 99.52 

6 

Base + % 0.42 0.50 0.27 0.42 0.27 1.17 1.17 0.84 0.73 0.41 0.83 0.47 0.82 -99.15 

Efficiency % 99.50 99.41 99.69 99.50 99.69 99.17 99.17 99.44 99.55 99.63 99.50 99.59 99.45 

7 

Base + % 0.56 0.31 1.44 1.44 0.98 0.45 0.51 

Efficiency % 99.47 99.73 99.44 99.44 99.58 99.67 99.63 

One major impact of an energy efficiency standard is to change the set of transformer 

designs available for purchase and their corresponding loss characteristics: load losses (LL) and 

no-load losses (NL). This effect is illustrated in the “LL versus NL graph” (worksheet LL versus 

NL in the LCC spreadsheet). 

Figure 8.4.2 provides an example of the “LL versus NL graph” from the LCC spreadsheet 

for design line 1, using EL 1. Because each design line has a unique set of engineering 

constraints, the LL-versus-NL graph for each will be different. This graph plots results of a 
8-35

Crystal Ball run for LCC. It shows different sets of designs by their LL at rated load and by their 

NL. Potential designs are shown as both small dots and small triangles. The selected designs not 

subject to standard constraints are plotted as circles. The designs subject to standards constraints 

are plotted as dots. As the required efficiency level increases, the cluster of selected designs

moves to the left (to the area for lower losses. The efficiency level is defined at 50 percent load

liquid-immersed and medium-voltage dry-type, and 35 percent load for low-voltage dry-type 

transformers, while the LL and NL for the design assumptions are defined by nameplate loading 

(100 percent). For those designs having higher LL, the heating from losses causes the actual 

efficiency to drop, shifting the design to the right in the graph. 

Figure 8.4.1 Design Load Losses versus No-Load Losses in the 

Base Case and Efficiency Level 1 for Design Line 1

Figure 8.4.3 illustrates the distribution of results of the LCC analysis for one design line 

at one EL. The LCC spreadsheet tool can generate graphical representations such as Figure 8.4.3

for each design line and efficiency level. 

0

100

200

300

400

500

600

700

800

900

1,000

0 20 40 60 80 100 120 140 160 180

Load Losses (watts)

No Load Losses (watts)

Design Load Losses (LL) vs No-Load Losses (NL)

at rated load

Available Designs

Selected Designs, Base

Selected Designs, Standard
8-36

Figure 8.4.2 Distribution of Life-Cycle Cost Results for Design 

Line 2, Efficiency Level 2 

The 14 tables that follow summarize the results from DOE’s LCC analysis. For each 

evaluated design line and each EL, DOE presents the percent efficiency; the percent of evaluated 

transformer purchases that would experience negative, zero, and positive LCC savings when 

subject to the EL; and the mean LCC savings. 

8.4.1 Results for Design Line 1 

Table 8.4.2 summarizes results of the LCC analysis for the representative unit from 

design line 1, a 50-kVA, liquid-immersed, single-phase, pad-mounted transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 99.08 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $2,020; the installation cost was $2,129. 

Table 8.4.2 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 1

 

Efficiency Level

1 (actual 

EL 0.4) 1 2 3 4 5 6 

Efficiency (%) 99.11 99.16 99.22 99.25 99.31 99.42 99.50

Transformers with Net 

Increase in LCC (%) 37.33 44.23 6.98 6.98 11.18 14.07 42.58

Transformers with No 

Impact on LCC (%) 0.17 0.17 0.17 0.17 0.00 0.00 0.00

Transformers with Net 

LCC Savings (%) 62.50 55.60 92.85 92.85 88.82 85.93 57.42

Mean LCC Savings ($) 83 153 696 696 618 856 365

Median LCC Savings ($) 44 53 671 671 588 765 181
8-37

8.4.2 Results for Design Line 2

Table 8.4.3 summarizes results of the LCC analysis for the representative unit from 

design line 2, a 25-kVA, liquid-immersed, single-phase, pole-mounted transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 98.91 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $1,288; the installation cost was $1,636. 

Table 8.4.3 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 2

 

Efficiency Level

Base, 

Actual 

(EL 

0.5)

1 2 3 4 5 6 7 

Efficiency (%) 98.95 99.00 99.07 99.11 99.18 99.31 99.41 99.46

Transformers with Net Increase 

in LCC (%) 41.49 18.16 11.39 13.07 17.83 51.51 67.17 76.53

Transformers with No Impact 

on LCC (%) 3.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Transformers with Net LCC 

Savings (%) 55.16 81.84 88.61 86.93 82.17 48.49 32.83 23.47

Mean LCC Savings ($) 66 278 343 330 311 -332 -579 -792

Median LCC Savings ($) 22 260 323 317 300 -23 -301 -550

8.4.3 Results for Design Line 3 

Table 8.4.4 summarizes results of the LCC analysis for the representative unit from 

design line 3, a 500-kVA, liquid-immersed, single-phase distribution transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 99.42 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $7,708; the installation cost was $4,235. 

Table 8.4.4 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 3

 Efficiency Level

1 1.1 2 3 4 5 6 7

Efficiency (%) 99.48 99.49 99.51 99.54 99.57 99.61 99.69 99.73

Transformers with Net Increase 

in LCC (%) 13.90 14.48 11.98 5.28 4.03 4.04 8.04 29.93

Transformers with No Impact 

on LCC (%) 1.33 1.33 1.16 0.03 0.03 0.00 0.00 0.00

Transformers with Net LCC 

Savings (%) 84.77 84.19 86.86 94.69 95.94 95.96 91.96 70.07

Mean LCC Savings ($) 2407 2709 3526 5037 5527 6942 8075 4491

Median LCC Savings ($) 1918 2174 3170 4712 5246 6715 7517 3756
8-38

8.4.4 Results for Design Line 4 

Table 8.4.5 summarizes results of the LCC analysis for the representative unit from 

design line 4, a 150-kVA, liquid-immersed, three-phase distribution transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 99.08 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $5,512; the installation cost was $4,034. 

Table 8.4.5 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 4

 Efficiency Level

1 1.5 2 3 4 5 6 7

Efficiency (%) 99.16 99.19 99.22 99.25 99.31 99.42 99.50 99.60

Transformers with Net Increase 

in LCC (%) 6.59 7.58 2.49 2.49 2.49 2.65 5.86 23.81

Transformers with No Impact 

on LCC (%) 0.62 0.62 0.62 0.62 0.62 0.18 0.00 0.00

Transformers with Net LCC 

Savings (%) 92.79 91.80 96.89 96.89 96.89 97.17 94.14 76.19

Mean LCC Savings ($) 977 1212 3603 3603 3603 3755 4349 2806

Median LCC Savings ($) 768 2396 3546 3546 3546 3694 4135 2396

8.4.5 Results for Design Line 5 

Table 8.4.6 summarizes results of the LCC analysis for the representative unit from 

design line 5, a 1,500-kVA, liquid-immersed, three-phase distribution transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 99.42 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $25,391; the installation cost was $8,438. 

Table 8.4.6 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 5

 Efficiency Level

1 1.5 2 3 4 5 6 

Efficiency (%) 99.48 99.49 99.51 99.54 99.57 99.61 99.69

Transformers with Net Increase in 

LCC (%) 30.50 28.30 19.89 14.76 9.83 9.05 41.91

Transformers with No Impact on 

LCC (%) 0.39 0.35 0.09 0.01 0.00 0.00 0.00

Transformers with Net LCC 

Savings (%) 69.11 71.35 80.02 85.23 90.17 90.95 58.09

Mean LCC Savings ($) 3668 4486 6852 8616 10382 12014 4619

Median LCC Savings ($) 4304 3015 6763 8095 9681 11190 3015
8-39

8.4.6 Results for Design Line 6 

Table 8.4.7 summarizes results of the LCC analysis for the representative unit from 

design line 6, a 25-kVA, low-voltage, dry-type, three-phase transformer with a 10-kV basic 

impulse insulation level (BIL). The average efficiency of the baseline units selected during the 

LCC analysis was 98.00 percent. The customer equipment cost before installation, which 

includes the manufacturer selling price, distributor markup, contractor markup, and sales tax, 

was $1,192; the installation cost was $943. 

Table 8.4.7 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 6 

 Efficiency Level

1 2 3 4 5 6 7 

Efficiency (%) 98.23 98.47 98.60 98.80 98.93 99.17 99.44

Transformers with Net Increase in 

LCC (%) 56.21 71.32 78.08 15.65 16.47 37.80 96.60

Transformers with No Impact on 

LCC (%) 43.59 28.68 21.92 84.35 83.53 62.20 3.40

Transformers with Net LCC 

Savings (%) 0.20 0.00 0.00 0.00 0.00 0.00 0.00

Mean LCC Savings ($) -76 -104 -182 305 325 148 -992

Median LCC Savings ($) -44 -133 -215 278 308 129 -1026

8.4.7 Results for Design Line 7 

Table 8.4.8 summarizes results of the LCC analysis for the representative unit from 

design line 7, a 75-kVA, low-voltage, dry-type, three-phase transformer with a 10-kV BIL. The 

average efficiency of the baseline units selected during the LCC analysis was 98.00 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $2,843; the installation cost was 

$1,854. 

Table 8.4.8 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 7 

 Efficiency Level

1 2 3 4 5 6 7 

Efficiency (%) 98.23 98.47 98.60 98.80 98.93 99.17 99.44

Transformers with Net Increase in 

LCC (%) 1.5 1.5 1.3 1.7 2.6 3.3 45.6

Transformers with No Impact on 

LCC (%) 0.1 0.1 0.1 0.0 0.0 0.0 0.0

Transformers with Net LCC 

Savings (%) 98.4 98.4 98.7 98.3 97.4 96.7 54.4

Mean LCC Savings ($) 1526 1526 1678 1838 2045 2280 212

Median LCC Savings ($) 1471 1471 1661 1809 1987 2250 137
8-40

8.4.8 Results for Design Line 8 

Table 8.4.9 summarizes results of the LCC analysis for the representative unit from 

design line 8, a 300-kVA, low-voltage, dry-type, three-phase transformer with a 20-kV BIL. The 

average efficiency of the baseline units selected during the LCC analysis was 98.60 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $6,748; the installation cost was 

$2,758. 

Table 8.4.9 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 8 

 Efficiency Level

1 2 3 4 5 6 7 

Efficiency (%) 98.80 99.02 99.14 99.25 99.32 99.44 99.58

Transformers with Net LCC Cost 

(%) 6.50 4.70 10.42 13.30 9.01 8.96 79.34

Transformers with Net LCC Benefit 

(%) 93.50 95.30 89.58 86.70 90.99 91.04 20.66

Transformers with No Change in 

LCC (%) 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Mean LCC Savings ($) 1091 2588 2530 2724 4253 4261 -2938

Median LCC Savings ($) 984 2490 2392 2578 4128 4132 -3191

8.4.9 Results for Design Line 9

Table 8.4.10 summarizes results of the LCC analysis for the representative unit from 

design line 9, a 300-kVA, medium-voltage, dry-type, three-phase transformer with a 45-kV BIL. 

The average efficiency of the baseline units selected during the LCC analysis was 98.82 percent. 

The customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $14,251; the installation cost was 

$3,294. 

Table 8.4.10 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 9 

Efficiency Level

1 2 3 4 5 6 

Efficiency (%) 98.93 99.04 99.15 99.22 99.39 99.55

Transformers with Net LCC Cost 

(%) 3.56 5.87 23.75 5.60 8.38 57.39

Transformers with Net LCC Benefit 

(%) 83.17 94.13 76.25 94.40 91.62 42.61

Transformers with No Change in 

LCC (%) 13.27 0.00 0.00 0.00 0.00 0.00

Mean LCC Savings ($) 787 1514 1464 3872 3875 -299

Median LCC Savings ($) 732 1352 1236 3681 3626 -728
8-41

8.4.10 Results for Design Line 10

Table 8.4.11 summarizes results of the LCC analysis for the representative unit from 

design line 10, a 1,500-kVA, medium-voltage, dry-type, three-phase transformer with a 45-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 99.22 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $43,361; the installation 

cost was $6,433. 

Table 8.4.11 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 10 

Efficiency Level

1 2 3 4 5 6 

Efficiency (%) 99.29 99.37 99.45 99.51 99.58 99.63

Transformers with Net LCC Cost 

(%) 0.68 17.89 46.52 63.73 70.79 88.84

Transformers with Net LCC Benefit 

(%) 98.80 82.11 53.48 36.27 29.21 11.16

Transformers with No Change in 

LCC (%) 0.52 0.00 0.00 0.00 0.00 0.00

Mean LCC Savings ($) 4604 4455 1463 -2205 -4654 -14727

Median LCC Savings ($) 4438 3911 610 -2805 -5575 -15943

8.4.11 Results for Design Line 11

Table 8.4.12 summarizes results of the LCC analysis for the representative unit from 

design line 11, a 300-kVA, medium-voltage, dry-type, three-phase transformer with a 95-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 98.67 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $21,469; the installation 

cost was $3,942. 

Table 8.4.12 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 11 

Efficiency Level

1 2 3 4 5 6 

Efficiency (%) 98.81 98.94 99.06 99.13 99.32 99.50

Transformers with Net LCC Cost 

(%) 21.85 55.29 33.20 25.89 42.44 82.65

Transformers with Net LCC Benefit 

(%) 78.14 44.71 66.80 74.11 57.56 17.35

Transformers with No Change in 

LCC (%) 0.01 0.00 0.00 0.00 0.00 0.00

Mean LCC Savings ($) 996 -155 1283 1849 879 -4166

Median LCC Savings ($) 881 -266 1210 1655 651 -4539
8-42

8.4.12 Results for Design Line 12

Table 8.4.13 summarizes results of the LCC analysis for the representative unit from 

design line 12, a 1,500-kVA, medium-voltage, dry-type, three-phase transformer with a 95-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 99.12 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $54,971; the installation 

cost was $7,196. 

Table 8.4.13 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 12 

 Efficiency Level

1 2 3 4 5 6 7 

Efficiency (%) 99.21 99.30 99.39 99.46 99.53 99.59 99.63

Transformers with Net LCC Cost 

(%) 7.08 7.56 23.38 17.13 24.86 50.42 85.39

Transformers with Net LCC Benefit 

(%) 0.01 0.00 0.00 0.00 0.00 0.00 0.00

Transformers with No Change in 

LCC (%) 92.91 92.44 76.62 82.87 75.14 49.58 14.61

Mean LCC Savings ($) 4537 6790 6048 8594 7858 828 -14496

Median LCC Savings ($) 4301 6414 5402 8074 7250 -163 -15669

8.4.13 Results for Design Line 13A 

Table 8.4.14 summarizes results of the LCC analysis for the representative unit from 

design line 13, a 2,000-kVA, medium-voltage, dry-type, three-phase transformer with a 125-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 98.63 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $27,141; the installation 

cost was $4,645. 

Table 8.4.14 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 

13A 

 Efficiency Level

1 2 3 4 5 6 

Efficiency (%) 98.69 98.84 98.97 99.04 99.25 99.45

Transformers with Net LCC Cost (%) 54.22 45.52 78.38 66.30 67.20 98.46

Transformers with Net LCC Benefit (%) 45.76 54.48 21.62 33.70 32.80 1.54

Transformers with No Change in LCC (%) 0.02 0.00 0.00 0.00 0.00 0.00

Mean LCC Savings ($) -27 311 -1592 -1019 -1430 -12053

Median LCC Savings ($) -91 154 -1766 -1292 -1660 -12367
8-43

8.4.14 Results for Design Line 13B

Table 8.4.14 summarizes results of the LCC analysis for the representative unit from 

design line 13, a 2,000-kVA, medium-voltage, dry-type, three-phase transformer with a 125-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 99.15 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $70,884; the installation 

cost was $8,783. 

Table 8.4.15 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 

13B 

Efficiency Level

1 2 3 4 5 

Efficiency (%) 99.19 99.28 99.38 99.45 99.52

Transformers with Net LCC Cost (%) 30.53 27.33 60.68 53.69 70.44

Transformers with Net LCC Benefit (%) 69.27 72.67 39.32 46.31 29.56

Transformers with No Change in LCC (%) 0.20 0.00 0.00 0.00 0.00

Mean LCC Savings ($) 2494 4346 -1501 -169 -6823

Median LCC Savings ($) 2185 3751 -2427 -1056 -7690

8.5 LIFE-CYCLE COST SENSITIVITY ANALYSIS

DOE recognizes that all engineering and economic analyses involve some uncertainty. To 

minimize that uncertainty, DOE strives to use the best techniques and the best data at its 

disposal. To account for the widest possible set of scenarios, DOE used distributions of values 

for key inputs to the analysis. For some variables, DOE went one step further by incorporating in 

the LCC spreadsheet the ability to repeat a given LCC analysis using values different from the 

default set used to produce DOE’s results. 

Detailed descriptions of all of the LCC input variables are included in the discussion of 

inputs in section 8.3, with additional information in chapters 6 and 7. This section focuses on 

seven key variables and the effect on the LCC results if they are assigned different values. The 

five variables and the location of their descriptive materials are:

1. percentage of transformers purchased using evaluation of parameters A and B (see 

section 8.3.1);

2. transformer loading relative to current estimate (see chapter 7); 

3. electricity price (see chapter 7); 

4. load growth trends (see section 8.3.6); 

5. equipment price (see chapter 6); 

6. electricity price trends (see section 8.3.7); and

7. the exclusion of transformers designed with ZDMH, H1 and amorphous core steels 

(SA1). 
8-44

This analysis examines how sensitive the LCC results are to changes in key DOE 

assumptions. For this final rule, DOE conducted the sensitivity analysis on design lines 1, 7, and 

12. Because the analysis treats each variable independently, the default values remain in effect 

for all variables except the one being examined. Sensitivity results should always be compared to 

default results. 

The variable that characterizes the percentage of transformers purchased using evaluation 

of parameters A and B uses the same set of low and high values, but different medium values, for 

liquid-immersed and dry-type transformers. The low value represents a scenario in which no 

transformer purchases are evaluated (the non-evaluating scenario). The high value represents a 

scenario in which all transformer purchases are evaluated. The medium value for liquidimmersed transformers represents a scenario in which 10 percent of purchases are evaluated. The 

medium value for low-voltage dry-type transformers represents a scenario in which 2 percent of 

purchases are evaluated. The medium value for medium-voltage, dry-type transformers 

represents a scenario in which 2 percent of purchases are evaluated. 

For transformer loading, the medium scenario represents the output of the load simulation 

described in chapter 7. The low scenario for liquid-immersed and medium-voltage dry-type 

distribution transformers decreases the median RMS load to 25 percent; the high scenario 

increases it to 50 percent; for low-voltage dry-type distribution transformers the low scenario 

decreased the median RMS load to 16 percent, the high scenario increases it to 35 percent. For 

load growth, the annual low, medium, and high scenarios are 0 percent, 0.5 percent, and 1 

percent, respectively, the default case for liquid-immersed distribution transformers is the 

medium case, the default for both low-voltage and medium-voltage dry-type transformers is the 

low case. Electricity price trends use the AEO 2012 low, reference, and high growth scenarios. 

8.5.1 Sensitivity Results for Design Line 1 

The representative unit from design line 1 is a 50-kVA, liquid-immersed, single-phase, 

pad-mounted transformer. The average efficiency of the baseline units selected in the base case 

during the LCC analysis was 99.08 percent. The customer equipment cost before installation, 

which includes the manufacturer selling price, shipping costs, distributor markup, and sales tax,

was $2,020; the installation cost was $2,129. 

Table 8.5.1 and Figure 8.5.1 illustrate the LCC sensitivity to changes in the six userselectable variables. For all variables, each sensitivity run causes some change in the LCC 

results. For design line 1, the change in percentage of transformer loading results in the most 

significant changes in LCC savings for all ELs examined. The reason that transformer loading is 

so important is that it is related directly to the amount of electricity that passes through a 

transformer. When the load on a transformer is increased, the load losses also increase. Thus at 

higher loading levels the economic gains from the reduction in losses are significant compared to 

the baseline. 
8-45

Table 8.5.1 Effects of Changed Variables on Life-Cycle Cost Savings for 

Representative Unit, Design Line 1 (2011$) 

Scenario

Efficiency Level

0.4 1 2 3 4 5 6

Efficiency (%) 99.11 99.16 99.22 99.25 99.31 99.42 99.50

Baseline 83 153 696 696 618 856 365

Low A & B Distribution 61 110 695 695 617 857 366

High A & B Distribution 267 544 698 698 622 842 347

Low Loading -48 -118 704 704 545 475 -273

High Loading 363 732 678 678 776 1672 1730

Low Electricity Price 64 109 560 560 473 659 148

High Electricity Price 102 197 832 832 763 1053 581

No Load Growth 40 64 699 699 594 731 157

High Load Growth 136 264 692 692 649 1012 626

Low Equipment Price 88 207 755 755 708 1002 638

High Equipment Price 22 32 487 487 344 473 -298

Low Electricity Price Trend 61 105 629 629 540 723 197

High Electricity Price Trend 92 173 742 742 670 931 452

Materials Exclusion 45 108 -173 -363 NA NA NA

*The higher ELs cannot be met without amorphous steel

Figure 8.5.1 Average Life-Cycle Cost Savings (2011$) by 

Scenario for Design Line 1

8.5.2 Sensitivity Results for Design Line 7 

The representative unit from design line 7 is a 75-kVA, low-voltage, dry-type, threephase transformer with a 10-kV basic BIL. The average efficiency of the baseline units selected 

in the base case during the LCC analysis was 98.00 percent. The customer equipment cost 
8-46

before installation, which includes the manufacturer selling price, distributor markup, contractor 

markup, and sales tax, was $2,843; the installation cost was $1,854. 

Table 8.5.2 and Figure 8.5.2 illustrate the LCC sensitivity to changes in the six userselectable variables for design line 7. For all variables, each sensitivity run causes some change 

in the LCC results. For design line 7, high electricity price trend results in significantly larger

LCC savings. Greater LCC savings are realized when the future price of electricity generation is 

assumed to grow at high rate. 

Table 8.5.2 Effects of Changed Variables on Life-Cycle Cost Savings for 

Representative Unit, Design Line 7 (2011$)

Scenario

Efficiency Level

1 2 3 4 5 6 7

Efficiency (%) 98.23 98.47 98.60 98.80 98.93 99.17 99.44

Baseline 1526 1526 1678 1838 2045 2280 212

Low A & B Distribution 1486 1486 1677 1832 2006 2276 171

High A & B Distribution 1608 1608 1608 1811 1935 2174 63

Low Loading 1386 1386 1579 1712 2027 2109 -203

High Loading 1716 1716 1883 2073 1948 2635 1017

Low Electricity Price 1281 1281 1448 1569 1669 1892 -224

High Electricity Price 1694 1694 1900 2087 2339 2652 559

Medium Load Growth 1532 1532 1713 1874 1996 2339 322

High Load Growth 1578 1578 1759 1929 1982 2421 515

Low Equipment Price 1632 1632 1805 2046 2406 2718 1035

High Equipment Price 1258 1258 1404 1251 1491 1628 -1473

Low Electricity Price Trend 1439 1439 1619 1767 1927 2183 61

High Electricity Price Trend 1541 1541 1736 1898 2088 2376 284

Materials Exclusion 1487 1487 1676 1584 1035 NA* NA*

*The higher ELs cannot be met without amorphous steel
8-47

Figure 8.5.2 Average Life-Cycle Cost Savings (2011$) by 

Scenario for Design Line 7

8.5.3 Sensitivity Results for Design Line 12 

The representative unit from design line 12 is a 1500-kVA, medium-voltage, dry-type, 

three-phase transformer with a 95-kV BIL. The average efficiency of the baseline units selected 

in the base case during the LCC analysis was 99.12 percent. The customer equipment cost before 

installation, which includes the manufacturer selling price, distributor markup, contractor 

markup, and sales tax, was $54,971; the installation cost was $7,196. 

Table 8.5.3 and Figure 8.5.3 illustrate the LCC sensitivity to changes in the six userselectable variables for design line 12. For all the variables, each sensitivity run causes some 

change in the LCC results. The changes tend to increase with the efficiency of the EL. For design 

line 12, the change in percentage of transformer loading and equipment price results in the most 

significant increase in LCC savings for all ELs examined. Transformer loading is a measure the 

amount of electricity that passes through a transformer. When the load on a transformer is 

increased, the load losses also increase; at higher loading levels the economic gains from the 

reduction in losses are greater when compared to the baseline.

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

3000

98.23% 98.47% 98.60% 98.80% 98.93% 99.17% 99.44%

Average LCC Savings ($)

Transformer Efficiency (%)

Baseline

Low A & B Distribution

High A & B Distribution

Low Loading

High Loading 

Low Electricity Price

High Electricity Price

Medium Load Growth

High Load Growth

Low Equipment Price

High Equipment Price

Low Electricity Price Trend

High Electricity Price Trend

Materials Exclusion
8-48

Table 8.5.3 Effects of Changed Variables on Life-Cycle Cost Savings for 

Representative Unit, Design Line 12 (2011$)

Scenario

Efficiency Level

1 2 3 4 5 6 7

Efficiency (%) 99.21 99.30 99.39 99.46 99.53 99.59 99.63

Baseline 4537 6790 6048 8594 7858 828 -14496

Low A & B Distribution 4321 6439 5399 8108 7294 -115 -15615

High A & B Distribution 3131 4957 5499 6752 5630 -1795 -17426

Low Loading 3833 3984 2783 6310 2641 -7656 -24648

High Loading 5129 11808 7708 12077 18243 17921 6511

Low Electricity Price 3572 5126 3173 5134 3978 -3562 -19205

High Electricity Price 5028 7720 7580 11007 10556 3263 -12196

Medium Load Growth 4407 6955 5783 8489 8205 1495 -13764

High Load Growth 4493 7529 6115 8920 9286 3280 -11512

Low Equipment Price 4550 6331 10587 12970 13528 8702 -2719

High Equipment Price 2689 2299 -3354 -1370 -3900 -14765 -37672

Low Electricity Price Trend 4127 6094 4868 7405 6443 -1065 -16650

High Electricity Price Trend 4487 6786 5967 8856 8144 920 -14564

Materials Exclusion* 2951 653 -4361 -17644 NA NA NA

*The higher ELs cannot be met without amorphous steel

Figure 8.5.3 Average Life-Cycle Cost Savings (2011$) by 

Scenario for Design Line 12 
8-49

8.6 PAYBACK PERIOD

The payback period (PBP) analysis is commonly used to evaluate investment decisions. 

A more energy efficient device usually costs more to purchase than a device of standard energy 

efficiency. The more efficient device usually costs less to operate, however, because of its lower

energy consumption. The payback period is the time (usually expressed in years) it takes to 

recover the additional first cost of the efficient device through its energy cost savings. Because 

the LCC analysis uses distributions of inputs, DOE gives PBP results in the form of distributions. 

8.6.1 Definition 

The PBP is the ratio of the increase in purchase expense (for a more efficient design 

compared to a less efficient design) to the decrease in annual operating expenditures for the more 

efficient design. This calculation provides what is known as a simple payback period because it 

does not take into account changes in operating costs over time. PBP is found using the equation: 

PBP = 

∆FC

∆OC.

Where:

ΔFC = installed purchase price (first cost) of a transformer that satisfies the given EL

minus the first cost of a transformer in the absence of the standard (assumes the 

transformer meeting the standard is more expensive than the transformer not 

subject to the standard) (2011$), and 

ΔOC = operating cost of the transformer not subject to the standard minus operating 

cost of the transformer subject to the standard (assumes the transformer 

meeting the efficiency level has lower energy consumption, and hence lower 

operating cost). Because ΔOC is expressed in annual terms, PBP is expressed 

in years. 

DOE calculates the PBP both for a distribution of transformers and for an average 

transformer. For the national average transformer, the average values of the increase in first cost 

and the operating-cost savings are used to calculate the PBP.

8.6.2 Inputs to Payback Period 

The inputs to PBP are: (1) the purchase expense, otherwise known as the total installed 

customer cost, or first cost, for each selected design; and (2) the annual (first-year) operating 

expenditures for each selected design. The inputs to the purchase expense are the equipment 

price and the installation cost including appropriate markups. The inputs to operating costs are 

the annual (first-year) energy consumption and the electricity price. The distributional PBP uses 

the same inputs as the LCC analysis described in section 8.3, except that, because this is a simple 
8-50

payback, the electricity price DOE uses is only for the year the standard takes effect, assumed 

here to be 2016. 

8.6.3 Issues Regarding Baseline Scenario 

DOE’s default assumption for the baseline scenario was that some percentage of 

transformer purchase decisions are based on evaluating the total owning cost (TOC) through 

parameters A and B. Specifically, the default assumptions are that 50 percent of purchase 

decisions for liquid-immersed, 2 percent for low-voltage dry-type transformers, and 10 to 20 

percent for medium-voltage, dry-type transformers use TOC-type evaluations that incorporate 

various distributions of values for parameters A and B. Especially at the lower efficiency levels 

(ELs) that DOE evaluated, transformer purchases based on TOC may not satisfy the basic PBP 

assumptions of higher purchase price and lower operating costs for the transformers subject to 

the EL. When those basic assumptions are not satisfied, the traditional PBP calculation loses its 

validity.

For example, a current transformer purchase decision (subject to the current standards)

based on TOC may have a first cost (ΔFC = 0) that is identical to a transformer that just meets 

EL 1. In addition, the transformer that meets the standard may have a different operating cost 

from a transformer that does not. In such a situation, PBP = 0. In another example, a current 

transformer purchase decision based on TOC may result in a transformer that costs more to 

purchase and install but consumes less electricity than a transformer that just meets baseline. In 

this case, the PBP calculation for the standards case is nonsensical, because it would imply a 

negative payback period. 

DOE’s method of calculating PBP is shown below. 

ΔFC = FC(standard) - FC(baseline) 

(ΔFC usually is positive.) 

ΔOC = OC(standard) - OC(baseline) 

(ΔOC usually is negative.) 

PBP = - ΔFC/ΔOC

(For the usually positive ΔFC and the usually negative ΔOC, PBP is 

positive.) 

Because ΔFC can be 0 or negative, and because ΔOC also can be 0 or negative, there are 

nine possible situations, which can be grouped into five computational cases. Table 8.6.1 shows 

the possible relationships between ΔFC and ΔOC and the resultant effect on PBP. 
8-51

Table 8.6.1 Possible ΔFC and ΔOC Combinations for Payback Period Analysis 

Case # Possible Cases Effect on PBP Calculation

1 ΔFC > 0 and ΔOC < 0 Well-defined PBP.

2 ΔFC = 0 and ΔOC = 0 Unaffected by the standard.

3 ΔFC < 0 and ΔOC = 0, or

ΔFC > 0 and ΔOC = 0 Division by 0: PBP is undefined. 

4 ΔFC = 0 and ΔOC > 0, or

ΔFC = 0 and ΔOC < 0 PBP = 0. 

5 

ΔFC < 0 and ΔOC < 0, or

ΔFC > 0 and ΔOC > 0, or 

ΔFC < 0 and ΔOC > 0

Not valid: negative or double-negative PBP, 

PBP = 0. 

8.6.4 Results of Payback Period Analysis 

Tables 8.6.2 through 8.6.14 illustrate, for each of the 14 design lines and their 7 

efficiency levels, the mean PBP and the percentage of the 10,000 Monte Carlo simulations to 

which the PBP calculation applies. For every EL for each design line, the sum of the categories 

“Transformers Having Well-Defined Payback Period,” and “Transformers Having Undefined 

Payback Period” should equal 100 percent.a As the efficiency of the ELs increases, so does the 

percentage of purchase decisions in which the PBP is well defined. DOE calculates the PBP both 

for a distribution of transformers. The PBP for the national average transformer is calculated 

using the average values of the first cost increase and operating cost savings. 

Figure 8.6.1 illustrates the full PBP results from the Monte Carlo simulation as a 

histogram for one example design line and EL. The LCC spreadsheet tool can be used to 

generate similar histograms for all design lines and each EL. 

 

a

For simplicity of presentation, cases 3, 4, and 5, shown in Table 8.6.1, were combined into the “Transformers 

Having Undefined Payback Period” category in Tables 8.6.2 through 8.6.14.
8-52

Figure 8.6.1 Distribution of Payback Period Results for Design 

Line 2, Efficiency Level 2 

8.6.5 Results for Design Line 1 

Table 8.6.2 summarizes results of the PBP analysis for the representative unit from 

design line 1, a 50-kVA, liquid-immersed, single-phase, pad-mounted transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 99.08 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $2,020; the installation cost was $2,129. 
8-53

Table 8.6.2 Results of Payback Period Analysis: Representative Unit, Design Line 1 

Efficiency Level

1, 

Actual 

(EL 0.4)

1 2 3 4 5 6 

Mean Payback (Years) 25.5 35.7 11.4 11.4 14.3 15.9 25.7

Median Payback (Years) 17.7 24.7 10.8 10.8 13.7 15.2 24.6

Transformers having Well 

Defined Payback (%) 81.89 91.47 99.83 99.83 99.96 100.00 99.99

Transformers having Undefined 

Payback (%) 18.11 8.53 0.17 0.17 0.04 0.00 0.01

Mean Retail Cost ($) 2,110 2,247 2,447 2,447 2,550 2,804 3,335

Mean Installation Costs ($) 2,169 2,229 2,271 2,271 2,344 2,415 2,606

Mean Operating Costs ($) 205 197 159 159 157 139 134

Mean Incremental First Cost ($) 128 326 568 568 745 1,068 1,791

Mean Operating Cost Savings ($) 6 15 52 52 55 72 77

Payback of Average Transformer 20.8 22.4 10.9 10.9 13.6 14.9 23.2

8.6.6 Results for Design Line 2

Table 8.6.3 summarizes results of the PBP analysis for the representative unit from 

design line 2, a 25-kVA, liquid-immersed, single-phase, pole-mounted transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 98.91 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $1,288; the installation cost was $1,636. 

Table 8.6.3 Results of Payback Period Analysis: Representative Unit, Design Line 2 

Efficiency Level

Base, 

(actual 

EL 0.5)

1 2 3 4 5 6 7 

Mean Payback (Years) 23.1 12.9 12.7 14.7 17.3 35.0 40.5 44.4

Median Payback (Years) 5.92 9.9 11.1 13.0 15.5 24.9 31.6 36.6

Transformers having Well 

Defined Payback (%) 71.11 99.14 99.93 99.86 99.91 99.88 99.92 99.95

Transformers having Undefined 

Payback (%) 28.89 0.86 0.07 0.14 0.09 0.12 0.08 0.05

Mean Retail Cost ($) 1,288 1,437 1,480 1,530 1,598 1,846 2,052 2,577

Mean Installation Costs ($) 1636 1722 1761 1790 1859 2516 2678 2457

Mean Operating Costs ($) 144 120 115 113 109 101 97 93

Mean Incremental First Cost ($) 138 235 317 396 534 1,439 1,807 2,110

Mean Operating Cost Savings ($) 65 24 29 31 34 43 47 50

Payback of Average Transformer 2.1 9.8 11.0 13.0 15.5 33.6 38.5 42.0
8-54

8.6.7 Results for Design Line 3

Table 8.6.4 summarizes results of the PBP analysis for the representative unit from 

design line 3, a 500-kVA, liquid-immersed, single-phase distribution transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 99.42 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $7,708; the installation cost was $4,235. 

Table 8.6.4 Results of Payback Period Analysis: Representative Unit, Design Line 3 

 

Efficiency Level

1

1, 

Actual 

(EL 

1.1) 2 3 4 5 6 7

Mean Payback (Years) 11.2 11.4 8.7 7.3 7.3 7.9 12.2 22.2

Median Payback (Years) 8.3 8.5 5.8 6.4 6.5 7.2 11.0 19.1

Transformers having Well 

Defined Payback (%) 96.67 97.27 98.36 99.97 99.97 100.00 100.00 99.99

Transformers having Undefined 

Payback (%) 3.33 2.73 1.64 0.03 0.03 0.00 0.00 0.01

Mean Retail Cost ($) 8,549 8,719 8,943 9,535 9,678 10,279 12,499 15,917

Mean Installation Costs ($) 4,332 4,369 4,310 4,371 4,402 4,523 4,996 7,081

Mean Operating Costs ($) 946 923 866 780 759 693 578 523

Mean Incremental First Cost ($) 937 1,145 1,310 1,962 2,136 2,859 5,552 11,054

Mean Operating Cost Savings ($) 144 167 223 310 330 396 512 567

Payback of Average Transformer 6.5 6.9 5.9 6.3 6.5 7.2 10.8 19.5

8.6.8 Results for Design Line 4

Table 8.6.5 summarizes results of the PBP analysis for the representative unit from 

design line 4, a 150-kVA, liquid-immersed, three-phase distribution transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 99.08 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $5,512; the installation cost was $4,034. 
8-55

Table 8.6.5 Results of Payback Period Analysis: Representative Unit, Design Line 4

 

Efficiency Level

1 1.5 2 3 4 5 6 7

Mean Payback (Years) 8.9 10.6 5.8 5.8 5.8 6.1 10.7 19.5

Median Payback (Years) 7.0 9.1 5.6 5.6 5.6 5.8 10.2 18.7

Transformers having Well 

Defined Payback (%) 99.38 99.38 99.38 99.38 99.38 99.82 100.00 100.00

Transformers having Undefined 

Payback (%) 0.62 0.62 0.62 0.62 0.62 0.18 0.00 0.00

Mean Retail Cost ($) 5,892 6,122 6,434 6,434 6,434 6,490 7,569 10,600

Mean Installation Costs ($) 4,095 4,112 4,202 4,202 4,202 4,233 4,606 4,709

Mean Operating Costs ($) 558 539 420 420 420 413 352 297

Mean Incremental First Cost ($) 440 688 1,090 1,090 1,090 1,177 2,630 5,764

Mean Operating Cost Savings ($) 57 75 194 194 194 202 263 318

Payback of Average Transformer 7.7 9.1 5.6 5.6 5.6 5.8 10.0 18.1

8.6.9 Results for Design Line 5 

Table 8.6.6 summarizes results of the PBP analysis for the representative unit from 

design line 5, a 1,500-kVA, liquid-immersed, three-phase distribution transformer. The average 

efficiency of the baseline units selected during the LCC analysis was 99.42 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $25,391; the installation cost was $8,438. 

Table 8.6.6 Results of Payback Period Analysis: Representative Unit, Design Line 5 

 

Efficiency Level

1 1.5 2 3 4 5 6 

Mean Payback (Years) 10.6 9.9 9.2 10.1 10.1 12.2 23.7

Median Payback (Years) 6.5 6.3 6.5 8.5 9.1 11.4 22.5

Transformers having Well 

Defined Payback (%) 91.48 92.85 97.46 99.68 100.00 100.00 100.00

Transformers having Undefined 

Payback (%) 8.52 7.15 2.54 0.32 0.00 0.00 0.00

Mean Retail Cost ($) 28,575 28,608 29,043 30,875 31,982 35,306 56,798

Mean Installation Costs ($) 8,554 8,576 8,632 8,876 9,032 9,483 9,834

Mean Operating Costs ($) 2,840 2,800 2,716 2,586 2,491 2,321 1,809

Mean Incremental First Cost ($) 3,301 3,355 3,845 5,922 7,185 10,959 32,803

Mean Operating Cost Savings ($) 457 496 581 710 805 975 1,487

Payback of Average Transformer 7.2 6.8 6.6 8.3 8.9 11.2 22.1

8.6.10 Results for Design Line 6 

Table 8.6.7 summarizes results of the PBP analysis for the representative unit from 

design line 6, a 25-kVA, low-voltage, dry-type, three-phase transformer with a 10-kV basic 
8-56

impulse insulation level (BIL). The average efficiency of the baseline units selected during the 

LCC analysis was 98.00 percent. The customer equipment cost before installation, which 

includes the manufacturer selling price, distributor markup, contractor markup, and sales tax, 

was $1,192; the installation cost was $943. 

Table 8.6.7 Results of Payback Period Analysis: Representative Unit, Design Line 6

 

Efficiency Level

1 2 3 4 5 6 7 

Mean Payback (Years) 28.0 31.3 29.8 12.5 12.7 16.3 32.8

Median Payback (Years) 17.6 23.8 25.5 12.1 12.4 15.7 31.7

Transformers having Well 

Defined Payback (%) 89.76 98.86 99.93 100.00 100.00 100.00 100.00

Transformers having Undefined 

Payback (%) 10.24 1.14 0.07 0.00 0.00 0.00 0.00

Mean Retail Cost ($) 1,208 1,272 1,403 1,683 1,743 1,977 2,864

Mean Installation Costs ($) 1,202 1,305 1,369 1,026 1,059 1,164 1,490

Mean Operating Costs ($) 136 128 121 99 92 82 75

Mean Incremental First Cost ($) 275 442 638 573 667 1,006 2,220

Mean Operating Cost Savings ($) 12 20 27 49 56 65 72

Payback of Average Transformer 23.7 22.5 24.1 11.7 12.0 15.4 30.6

8.6.11 Results for Design Line 7

Table 8.6.8 summarizes results of the PBP analysis for the representative unit from 

design line 7, a 75-kVA, low-voltage, dry-type, three-phase transformer with a 10-kV BIL. The 

average efficiency of the baseline units selected during the LCC analysis was 98.00 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $2,842; the installation cost was 

$1,854. 

Table 8.6.8 Results of Payback Period Analysis: Representative Unit, Design Line 7

 

Efficiency Level

1 2 3 4 5 6 7 

Mean Payback (Years) 4.1 4.1 3.8 4.3 5.6 6.6 17.4

Median Payback (Years) 3.9 3.9 3.6 4.1 5.4 6.3 16.8

Transformers having Well 

Defined Payback (%) 99.93 99.93 99.93 100.00 100.00 100.00 100.00

Transformers having Undefined 

Payback (%) 0.07 0.07 0.07 0.00 0.00 0.00 0.00

Mean Retail Cost 3,201 3,201 3,204 3,459 3,813 4,089 5,929

Mean Installation Costs ($) 1,912 1,912 1,912 1,786 1,734 1,839 2,362

Mean Operating Costs ($) 239 239 230 214 185 150 128

Mean Incremental First Cost ($) 416 416 419 548 851 1,231 3,594

Mean Operating Cost Savings ($) 108 108 117 133 162 197 219

Payback of Average Transformer 3.8 3.8 3.6 4.1 5.3 6.3 16.4
8-57

8.6.12 Results for Design Line 8

Table 8.6.9 summarizes results of the PBP analysis for the representative unit from 

design line 8, a 300-kVA, low-voltage, dry-type, three-phase transformer with a 20-kV BIL. The 

average efficiency of the baseline units selected during the LCC analysis was 98.60 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $6,748; the installation cost was 

$2,758. 

Table 8.6.9 Results of Payback Period Analysis: Representative Unit, Design Line 8 

 

Efficiency Level

1 2 3 4 5 6 7 

Mean Payback (Years) 8.5 8.0 10.7 11.7 10.5 10.5 23.4

Median Payback (Years) 8.0 7.7 10.2 11.3 10.1 10.1 22.5

Transformers having Well 

Defined Payback () 100.00 100.00 100.00 100.00 100.00 100.00 100.00

Transformers having Undefined 

Payback () 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Mean Retail Cost ($) 7,463 8,411 9,700 10,851 11,784 11,782 19,031

Mean Installation Costs ($) 2,850 2,999 3,126 3,221 3,158 3,158 3,905

Mean Operating Costs ($) 783 638 560 477 343 343 278

Mean Incremental First Cost ($) 807 1,905 3,321 4,567 5,437 5,435 13,430

Mean Operating Cost Savings ($) 107 252 331 413 547 547 612

Payback of Average Transformer 7.6 7.6 10.0 11.1 9.9 9.9 22.0

8.6.13 Results for Design Line 9 

Table 8.6.10 summarizes results of the PBP analysis for the representative unit from 

design line 9, a 300-kVA, medium-voltage, dry-type, three-phase transformer with a 45-kV BIL. 

The average efficiency of the baseline units selected during the LCC analysis was 98.82 percent. 

The customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $14,251; the installation cost was 

$3,294. 
8-58

Table 8.6.10 Results of Payback Period Analysis: Representative Unit, Design Line 9 

 

Efficiency Level

1 2 3 4 5 6 

Mean Payback (Years) 3.7 7.2 13.6 8.7 9.8 19.9

Median Payback (Years) 2.6 6.1 10.9 8.3 9.4 18.5

Transformers having Well 

Defined Payback (%) 85.38 99.98 99.92 100.00 100.00 100.00

Transformers having Undefined 

Payback (%) 14.62 0.02 0.08 0.00 0.00 0.00

Mean Retail Price ($) 14,388 14,994 16,391 17,256 18,027 23,021

Mean Installation Costs ($) 3,295 3,311 3,435 3,674 3,806 4,431

Mean Operating Costs ($) 873 795 710 509 456 373

Mean Incremental First Cost ($) 139 760 2,282 3,386 4,289 9,907

Mean Operating Cost Savings ($) 53 131 216 417 470 553

Payback of Average Transformer 2.6 5.8 10.6 8.1 9.1 17.9

8.6.14 Results for Design Line 10

Table 8.6.11 summarizes results of the PBP analysis for the representative unit from 

design line 10, a 1,500-kVA, medium-voltage, dry-type, three-phase transformer with a 45-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 99.22 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $43,361; the installation 

cost was $6,433. 

Table 8.6.11 Results of Payback Period Analysis: Representative Unit, Design Line 10 

Efficiency Level

1 2 3 4 5 6

Mean Payback (Years) 1.4 11.7 20.5 20.7 22.6 30.1

Median Payback (Years) 1.1 8.6 16.1 19.6 21.2 27.5

Transformers having Well 

Defined Payback (%) 99.42 98.87 99.81 100.00 100.00 100.00

Transformers having Undefined 

Payback (%) 0.58 1.13 0.19 0.00 0.00 0.00

Mean Retail Price ($) 43,657 46,918 54,571 65,497 70,424 81,370

Mean Installation Costs ($) 6,416 6,834 7,441 8,036 8,390 9,104

Mean Operating Costs ($) 2,599 2,394 2,083 1,622 1,453 1,335

Mean Incremental First Cost ($) 279 3,958 12,218 23,739 29,021 40,680

Mean Operating Cost Savings ($) 269 474 785 1,246 1,416 1,533

Payback of Average Transformer 1.0 8.4 15.6 19.1 20.5 26.5
8-59

8.6.15 Results for Design Line 11

Table 8.6.12 summarizes results of the PBP analysis for the representative unit from 

design line 11, a 300-kVA, medium-voltage, dry-type, three-phase transformer with a 95-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 98.67 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $21,469; the installation 

cost was $3,942. 

Table 8.6.12 Results of Payback Period Analysis: Representative Unit, Design Line 11 

 

Efficiency Level

1 2 3 4 5 6

Mean Payback (Years) 12.6 24.2 16.5 14.0 17.0 25.8

Median Payback (Years) 10.6 17.7 14.1 13.6 16.1 24.1

Transformers having Well 

Defined Payback () 98.86 98.02 99.98 100.00 100.00 100.00

Transformers having Undefined 

Payback () 1.14 1.98 0.02 0.00 0.00 0.00

Mean Retail Price ($) 22,724 24,638 26,367 26,683 29,377 35,473

Mean Installation Costs ($) 4,030 4,326 4,306 4,296 4,622 5,206

Mean Operating Costs ($) 963 899 722 673 553 445

Mean Incremental First Cost ($) 1,342 3,553 5,261 5,568 8,587 15,267

Mean Operating Cost Savings ($) 132 196 373 422 543 650

Payback of Average Transformer 10.2 18.1 14.1 13.2 15.8 23.5

8.6.16 Results for Design Line 12

Table 8.6.13 summarizes results of the PBP analysis for the representative unit from 

design line 12, a 1,500-kVA, medium-voltage, dry-type, three-phase transformer with a 95-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 99.12 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $54,971; the installation 

cost was $7,196. 
8-60

Table 8.6.13 Results of Payback Period Analysis: Representative Unit, Design Line 12 

 

Efficiency Level

1 2 3 4 5 6 7 

Mean Payback (Years) 7.2 9.3 13.8 12.7 14.0 18.3 26.1

Median Payback (Years) 6.0 8.5 12.7 12.3 13.3 17.4 24.7

Transformers having Well 

Defined Payback (%) 99.18 100.00 99.99 100.00 100.00 100.00 100.00

Transformers having Undefined 

Payback (%) 0.82 0.00 0.01 0.00 0.00 0.00 0.00

Mean Retail Price ($) 57,380 60,978 68,566 71,895 76,909 86,085 101,590

Mean Installation Costs ($) 7,113 7,231 7,971 8,316 8,637 9,318 10,270

Mean Operating Costs ($) 3,057 2,718 2,281 1,929 1,662 1,481 1,376

Mean Incremental First Cost ($) 2,326 6,042 14,370 18,045 23,379 33,236 49,694

Mean Operating Cost Savings ($) 384 722 1,160 1,512 1,779 1,960 2,065

Payback of Average Transformer 6.1 8.4 12.4 11.9 13.1 17.0 24.1

8.6.17 Results for Design Line 13A 

Table 8.6.14 summarizes results of the PBP analysis for the representative unit from 

design line 13, a 2,000-kVA, medium-voltage, dry-type, three-phase transformer with a 125-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 98.63 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $27,141; the installation 

cost was $4,645. 

Table 8.6.14 Results of Payback Period Analysis: Representative Unit, Design Line 

13A 

Efficiency Level

1 2 3 4 5 6 

Mean Payback (Years) 24.5 18.3 26.1 20.9 21.0 37.3

Median Payback (Years) 16.1 16.2 23.6 20.4 20.3 35.3

Transformers having Well

Defined Payback (%) 87.42 99.92 100.00 100.00 100.00 100.00

Transformers having Undefined 

Payback (%) 12.58 0.08 0.00 0.00 0.00 0.00

Mean Retail Price ($) 27,902 29,552 32,891 35,577 37,918 48,703

Mean Installation Costs ($) 4,752 4,832 5,103 5,093 5,309 6,280

Mean Operating Costs ($) 1,114 996 893 708 583 491

Mean Incremental First Cost ($) 868 2,598 6,207 8,884 11,441 23,197

Mean Operating Cost Savings ($) 49 167 270 455 580 672

Payback of Average Transformer 17.9 15.6 23.0 19.5 19.7 34.5
8-61

8.6.18 Results for Design Line 13B 

Table 8.6.14 summarizes results of the PBP analysis for the representative unit from 

design line 13, a 2,000-kVA, medium-voltage, dry-type, three-phase transformer with a 125-kV 

BIL. The average efficiency of the baseline units selected during the LCC analysis was 99.15 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $70,884; the installation 

cost was $8,783. 

Table 8.6.15 Results of Payback Period Analysis: Representative Unit, Design Line 

13B 

 

Efficiency Level

1 2 3 4 5 

Mean Payback (Years) 12.0 13.3 20.7 18.6 21.4

Median Payback (Years) 4.5 12.2 19.2 18.1 20.6

Transformers having Well 

Defined Payback (%) 86.89 100.00 100.00 100.00 100.00

Transformers having Undefined 

Payback (%) 13.11 0.00 0.00 0.00 0.00

Mean Retail Price ($) 72,108 80,007 91,898 103,613 116,322

Mean Installation Costs ($) 8,958 8,997 9,629 9,652 10,305

Mean Operating Costs ($) 4,219 3,661 3,261 2,515 2,111

Mean Incremental First Cost ($) 1,398 9,337 21,859 33,599 46,959

Mean Operating Cost Savings ($) 219 777 1,177 1,923 2,327

Payback of Average Transformer 6.4 12.0 18.6 17.5 20.2

8.7 REBUTTABLE PRESUMPTION

The rebuttable presumption is a simplified method of determining the economic 

justification of a proposed energy efficiency standard. In evaluating the rebuttable presumption, 

DOE estimates the additional cost of purchasing a more efficient, standard-compliant equipment, 

then compares that cost to the value of the energy savings during the first year of operation as 

determined by the applicable test procedure. The rebuttable presumption that such a standard 

level is economically justified is satisfied if the additional first cost is less than three times the 

value of the energy savings (when the rebuttable payback period is less than three years).

The payback period for the rebuttable presumption differs from payback periods 

presented in earlier parts of this chapter in two important ways. 

• The rebuttable presumption payback period uses test procedure loading levels to 

evaluate losses, rather than DOE’s estimate of in-service loading conditions. 

• The payback period considers only the value of energy savings, not total operating 
8-62

costs. In the case of distribution transformers, however, DOE estimates that the 

change in operating costs is due solely to energy savings.

There are three key inputs to calculation of the payback period for the rebuttable 

presumption: (1) average efficiency, (2) average installed cost, and (3) the cost of electricity. 

Given the average efficiency of a transformer, DOE calculated the losses on the transformer 

assuming the loading conditions from the test procedure. Multiplying the losses times the cost of 

electricity provided the operating cost. Then, dividing incremental operating costs into 

incremental installed cost provided the estimate of the rebuttable payback period. 

Tables 8.7.1 through 8.7.2 show the inputs to the calculation of the rebuttable 

presumption payback period. Table 8.7.1 shows the average transformer efficiency as a function 

of design line and standard level for EL 1 through EL 7. This is the average efficiency as 

determined by the customer choice model from the LCC calculation. The customer choice model 

provides a range of transformer design efficiencies that depends on a distribution of customer 

choices with respect to the value that customers place on reducing transformer design losses. 

Table 8.7.2 shows the average installed cost of the transformer as a function of both design line 

and EL. The average marginal cost of electricity is a function of transformer type: for liquidimmersed transformers it is estimated to be 0.67 $/kWh; for dry-type transformers, 0.06 $/kWh. 

The difference between the two marginal costs of electricity reflects the fact that liquidimmersed transformers tend to be owned by utilities, which pay the wholesale (rather than retail) 

cost of electricity. 

Table 8.7.1 Average Transformer Efficiency %

Design 

Line

Rated 

Capacity 

kVA

Efficiency Level

Base 1 2 3 4 5 6 7 

1 50 99.08 99.17 99.30 99.30 99.32 99.43 99.50

2 25 98.91 99.02 99.08 99.11 99.17 99.33 99.40 99.46

3 500 99.42 99.48 99.51 99.55 99.56 99.61 99.68 99.72

4 150 99.08 99.18 99.40 99.40 99.40 99.42 99.50 99.59

5 1500 99.42 99.48 99.51 99.54 99.56 99.60 99.68

6 25 98.01 98.32 98.49 98.64 98.80 98.93 99.17 99.44

7 75 98.02 98.65 98.65 98.69 98.81 98.94 99.17 99.43

8 300 98.62 98.81 99.02 99.15 99.26 99.45 99.45 99.58

9 300 98.88 98.95 99.05 99.16 99.33 99.40 99.55

10 1500 99.24 99.30 99.37 99.45 99.52 99.58 99.63

11 300 98.70 98.83 98.95 99.10 99.14 99.32 99.51

12 1500 99.14 99.22 99.31 99.40 99.46 99.53 99.59 99.63

13A 300 98.64 98.71 98.84 98.98 99.08 99.27 99.46

13B 2000 99.16 99.20 99.29 99.38 99.46 99.55 99.55
8-63

Table 8.7.2 Average Transformer Efficiency for Fractional Efficiency Levels %

Design Line Rated Capacity 

kVA Efficiency % Efficiency Level Average Efficiency

1 50 99.11 0.4 99.12

2 25 98.95 0.5 98.95

3 500 99.49 1.1 44.49

Table 8.7.3 Average Transformer Installed Cost (2011$)

Design 

Line

Rated 

Capacity 

kVA

Efficiency Level

Base 1 2 3 4 5 6 7 

1 50 4,150 4,476 4,718 4,718 4,895 5,218 5,940

2 25 2,924 3,159 3,241 3,320 3,457 4,346 4,731 4,670

3 500 11,943 12,881 13,254 13,905 14,080 14,802 17,496 22,998

4 150 9,546 9,986 10,636 10,636 10,636 10,723 12,175 15,310

5 1500 33,829 37,130 37,675 39,751 41,014 44,789 66,632

6 25 2,135 2,410 2,577 2,773 2,708 2,802 3,141 4,354

7 75 4697 5113 5113 5116 5245 5547 5928 8291

8 300 9,505 10,312 11,410 12,826 14,072 14,942 14,940 22,935

9 300 17,545 17,704 18,506 20,332 20,931 21,936 28,495

10 1500 49,796 50,510 54,698 65,502 73,850 79,271 94,669

11 300 25,411 26,754 28,964 30,672 30,979 33,999 40,678

12 1500 62,167 64,493 68,209 76,537 80,211 85,546 95,403 111,860

13A 300 31,786 32,654 34,425 37,994 40,670 43,227 54,983

13B 2000 79,667 81,065 89,004 101,526 113,266 126,627 126,627

Table 8.7.4 Average Transformer Installed Cost for Fractional Efficiency Levels

(2011$)

Design Line Rated Capacity 

kVA Efficiency % Efficiency Level Installed Cost 2011$

1 50 99.11 0.4 4,278

2 25 98.95 0.5 3,159

3 500 99.49 1.1 13,088

Table 8.7.4 and 8.7.5 show the rebuttable payback period as a function of design line and 

standard level. The data indicate the rebuttable presumption is for design lines 6, 8, 9, and 10. 

For design lines 9 and 10 the rebuttable presumption payback is satisfied for efficiency level 1 

only. 
8-64

Table 8.7.5 Payback Period for Rebuttable Presumption (years)

Design 

Line

Rated 

Capacity 

kVA

Efficiency Level

1 2 3 4 5 6 7

1 50 17.7 12.5 12.5 14.9 14.2 20.0

2 25 20.7 16.5 17.1 18.3 31.3 34.2 36.3

3 500 9.0 9.0 8.0 7.6 7.5 10.0 16.9 

4 150 8.1 5.5 5.5 5.5 5.8 9.8 17.5

5 1500 13.1 8.4 8.7 8.5 10.0 19.9

6 25 12.6 13.7 15.7 13.0 12.5 14.5 25.7

7 75 3.8 3.8 3.5 4.0 5.6 6.1 14.1

8 300 5.5 6.5 8.7 10.0 9.3 9.3 19.4

9 300 1.8 4.2 7.6 7.3 7.9 14.1 

10 1500 1.3 5.5 10.6 16.4 16.4 19.9

11 300 10.0 13.1 13.1 12.7 13.4 18.3

12 1500 5.9 7.3 11.5 11.5 11.9 14.5 19.7

13A 300 12.7 12.5 17.8 21.4 18.3 27.9

13B 2000 5.7 10.4 14.5 18.3 18.7 18.7

* Values less than 3 indicate a rebuttable presumption that the standard level is economically justified.

Table 8.7.6 Payback Period for Rebuttable Presumption for Fractional Efficiency 

Levels

Design Line Rated Capacity 

kVA Efficiency % Efficiency Level Payback years

1 50 99.11 0.4 17.5

2 25 98.95 0.5 22.5

3 500 99.49 1.1 9.1
8-65

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