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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 Baseline Scenario............................................................................................................. 8-2

8.1.3 Total Owning Cost........................................................................................................... 8-2

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 ........................................................................... 8-3

8.2.2.1 Step 1: Select Parameters A and B ................................................................ 8-5

8.2.2.2 Step 2: Select Designs that Meet a Chosen Candidate Standard Level ......... 8-5

8.2.2.3 Step 3: Select Load and Price Profile ............................................................ 8-6

8.2.2.4 Step 4: Calculate Cost of Losses.................................................................... 8-6

8.2.2.5 Step 5: Project Losses and Costs into the Future........................................... 8-6

8.2.2.6 Step 6: Select Discount Rate.......................................................................... 8-7

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

8.2.2.8 Step 8: Report Results.................................................................................... 8-7

8.2.2.9 Step 9: Repeat Process and Report Results.................................................... 8-7

8.3 INPUTS TO LIFE-CYCLE COST ANALYSIS ............................................................. 8-7

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

8.3.1.1 A and B Parameter Selection for Liquid-Immersed Transformers................ 8-9

8.3.1.2 A and B Parameter Selection for Dry-Type Transformers.......................... 8-11

8.3.2 Database of Transformer Designs.................................................................................. 8-13

8.3.3 Markup and Installation Costs....................................................................................... 8-13

8.3.3.1 Projection of Future Product Prices............................................................. 8-13

8.3.4 Transformer Loading ..................................................................................................... 8-15

8.3.5 Electricity Price Analysis............................................................................................... 8-15

8.3.5.1 Hourly Marginal Electricity Price Model for Liquid-Immersed 

Transformers................................................................................................ 8-16

8.3.5.2 Monthly Marginal Electricity Price Model for Dry-Type Transformers..... 8-19

8.3.6 Trends in Load Growth.................................................................................................. 8-20

8.3.7 Electricity Cost and Price Trends .................................................................................. 8-20

8.3.8 Discount Rate................................................................................................................. 8-21

8.3.9 Effective Date of Standard............................................................................................. 8-26

8.3.10 Transformer Service Life............................................................................................... 8-26

8.3.11 Maintenance Costs......................................................................................................... 8-27

8.3.12 Power Factor.................................................................................................................. 8-27

8.3.13 Default Scenario............................................................................................................. 8-27

8.4 RESULTS OF LIFE-CYCLE COST ANALYSIS ........................................................ 8-27

8.4.2 Results for Design Line 1 .............................................................................................. 8-30

8.4.3 Results for Design Line 2 .............................................................................................. 8-31

8.4.4 Results for Design Line 3 .............................................................................................. 8-31
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8.4.5 Results for Design Line 4 .............................................................................................. 8-32

8.4.6 Results for Design Line 5 .............................................................................................. 8-32

8.4.7 Results for Design Line 6 .............................................................................................. 8-33

8.4.8 Results for Design Line 7 .............................................................................................. 8-33

8.4.9 Results for Design Line 8 .............................................................................................. 8-34

8.4.10 Results for Design Line 9 .............................................................................................. 8-34

8.4.11 Results for Design Line 10 ............................................................................................ 8-35

8.4.12 Results for Design Line 11 ............................................................................................ 8-35

8.4.13 Results for Design Line 12 ............................................................................................ 8-36

8.4.14 Results for Design Line 13A.......................................................................................... 8-36

8.4.15 Results for Design Line 13B.......................................................................................... 8-37

8.5 LIFE-CYCLE COST SENSITIVITY ANALYSIS ....................................................... 8-37

8.5.1 Sensitivity Results for Design Line 1 ............................................................................ 8-38

8.5.2 Sensitivity Results for Design Line 7 ............................................................................ 8-40

8.5.3 Sensitivity Results for Design Line 12 .......................................................................... 8-42

8.6 PAYBACK PERIOD..................................................................................................... 8-44

8.6.1 Definition ....................................................................................................................... 8-44

8.6.2 Inputs to Payback Period ............................................................................................... 8-44

8.6.3 Issues Regarding Baseline Scenario .............................................................................. 8-45

8.6.4 Results of Payback Period Analysis .............................................................................. 8-46

8.6.5 Results for Design Line 1 .............................................................................................. 8-46

8.6.6 Results for Design Line 2 .............................................................................................. 8-47

8.6.7 Results for Design Line 3 .............................................................................................. 8-47

8.6.8 Results for Design Line 4 .............................................................................................. 8-48

8.6.9 Results for Design Line 5 .............................................................................................. 8-48

8.6.10 Results for Design Line 6 .............................................................................................. 8-48

8.6.11 Results for Design Line 7 .............................................................................................. 8-49

8.6.12 Results for Design Line 8 .............................................................................................. 8-49

8.6.13 Results for Design Line 9 .............................................................................................. 8-50

8.6.14 Results for Design Line 10 ............................................................................................ 8-50

8.6.15 Results for Design Line 11 ............................................................................................ 8-51

8.6.16 Results for Design Line 12 ............................................................................................ 8-51

8.6.17 Results for Design Line 13A.......................................................................................... 8-52

8.6.18 Results for Design Line 13B.......................................................................................... 8-52

8.7 REBUTTABLE PRESUMPTION................................................................................. 8-53

LIST OF TABLES

Table 8.3.1 A Parameter Model and Historical Data............................................................ 8-10

Table 8.3.2 A and B Parameter Evaluation Scenarios.......................................................... 8-12

Table 8.3.3 Transmission and Distribution Loss Factors...................................................... 8-17

Table 8.3.4 Generation Capacity Costs................................................................................. 8-17

Table 8.3.5 Capacity Market Auction Results...................................................................... 8-18
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Table 8.3.6 Average Seasonal Marginal Energy and Demand Prices by Census 

Division.............................................................................................................. 8-20

Table 8.3.7 Typical Owners of Various Types of Transformers.......................................... 8-23

Table 8.3.8 Variables Used to Estimate Discount Rates for the C&I Sector........................ 8-24

Table 8.3.9 Real Discount Rates by Transformer Ownership Category............................... 8-25

Table 8.3.10 Transformer Ownership by Design Line ........................................................... 8-26

Table 8.4.1 Candidate Standard Levels Evaluated for Each Design Line ............................ 8-28

Table 8.4.2 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 1 ...... 8-30

Table 8.4.3 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 2 ...... 8-31

Table 8.4.4 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 3 ...... 8-31

Table 8.4.5 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 4 ...... 8-32

Table 8.4.6 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 5 ...... 8-32

Table 8.4.7 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 6 ...... 8-33

Table 8.4.8 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 7 ...... 8-33

Table 8.4.9 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 8 ...... 8-34

Table 8.4.10 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 9 ...... 8-34

Table 8.4.11 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 10 .... 8-35

Table 8.4.12 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 11 .... 8-35

Table 8.4.13 Results of Life-Cycle Cost Analysis: Representative Unit, Design Line 12 .... 8-36

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

13A .................................................................................................................... 8-36

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

13B..................................................................................................................... 8-37

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

Representative Unit, Design Line 1................................................................... 8-39

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

Representative Unit, Design Line 7................................................................... 8-41

Table 8.5.3 Effects of Changed Variables on Life-Cycle Cost Savings (2010$) for 

Representative Unit, Design Line 12................................................................. 8-43

Table 8.6.1 Possible ΔFC and ΔOC Combinations for Payback Period Analysis................ 8-46

Table 8.6.2 Results of Payback Period Analysis: Representative Unit, Design Line 1........ 8-46

Table 8.6.3 Results of Payback Period Analysis: Representative Unit, Design Line 2........ 8-47

Table 8.6.4 Results of Payback Period Analysis: Representative Unit, Design Line 3........ 8-47

Table 8.6.5 Results of Payback Period Analysis: Representative Unit, Design Line 4........ 8-48

Table 8.6.6 Results of Payback Period Analysis: Representative Unit, Design Line 5........ 8-48

Table 8.6.7 Results of Payback Period Analysis: Representative Unit, Design Line 6........ 8-49

Table 8.6.8 Results of Payback Period Analysis: Representative Unit, Design Line 7........ 8-49

Table 8.6.9 Results of Payback Period Analysis: Representative Unit, Design Line 8........ 8-50

Table 8.6.10 Results of Payback Period Analysis: Representative Unit, Design Line 9........ 8-50

Table 8.6.11 Results of Payback Period Analysis: Representative Unit, Design Line 10...... 8-50

Table 8.6.12 Results of Payback Period Analysis: Representative Unit, Design Line 11...... 8-51

Table 8.6.13 Results of Payback Period Analysis: Representative Unit, Design Line 12...... 8-51

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

13A..................................................................................................................... 8-52

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

13B..................................................................................................................... 8-52
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Table 8.7.1 Average Transformer Efficiency %................................................................... 8-55

Table 8.7.2 Average Transformer Installed Cost ($2010) .................................................... 8-55

Table 8.7.3 First-Year Operating Cost for Rebuttable Presumption Based on DOE Test 

Procedure %....................................................................................................... 8-56

Table 8.7.4 Payback Period for Rebuttable Presumption ..................................................... 8-57

LIST OF FIGURES

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

Cost ...................................................................................................................... 8-4

Figure 8.3.1 Cumulative Distribution of Historical A Parameter and Model A 

Parameter ............................................................................................................. 8-9

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

for Liquid-Immersed Transformers ................................................................... 8-11

Figure 8.3.3 Electricity Price Forecasts from AEO2011........................................................ 8-21

Figure 8.4.2 Design Load Losses versus No-Load Losses in the Base Case and 

Candidate Standard Level 1 for Design Line 1.................................................. 8-29

Figure 8.4.3 Distribution of Life-Cycle Cost Results for Design Line 2, Candidate 

Standard Level 2 ................................................................................................ 8-30

Figure 8.5.1 Average Life-Cycle Cost Savings (2010$) by Scenario for Design Line 1....... 8-40

Figure 8.5.2 Average Life-Cycle Cost Savings (2010$) by Scenario for Design Line 7....... 8-42

Figure 8.5.3 Average Life-Cycle Cost Savings (2010$) by Scenario for Design Line 13..... 8-43

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

Standard Level 2 ................................................................................................ 8-53
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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 DOE’s life-cycle cost (LCC) 

and payback period (PBP) analyses. It describes the method DOE used for analyzing the 

economic impacts of possible standards on customers. The effect of 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 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://www.eere.energy.gov/buildings/appliance_standards/commercial/

distribution_transformers.html). Appendix 8A 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, 7, and 12.

8.1.1 General Approach to Analyses

Recognizing that each 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 transformers that engender economic impacts of varying magnitudes. 

Appendix 8-B provides a detailed explanation of the Monte Carlo simulation process and the use 

of probability distributions in the analyses.

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

transformers, and one for low-voltage and medium-voltage, dry-type transformers. Because most 

owners of 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 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 Baseline Scenario

In developing appliance standards, DOE used the existing standard (10 CFR Part 43) as a 

baseline from which it calculates the impact of any candidate standard level. This approach 

focused on the mix of selection criteria customers are known to use when purchasing 

transformers. 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 

transformers to purchase.1,2

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

and an estimated percent of 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.

8.1.3 Total Owning Cost

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

financial environment faced by each 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 their evaluations. A and B are the equivalent 

first costs of a 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 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 

(2010$). The equation for calculating transformer TOC is:
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TOC = FC + (A × NLL) + (B × LL).

Where:

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

installation cost (2010$);

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 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 (2010$);

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 (2010$/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 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 

are available as an Excel files on the DOE website at 

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

s.html.
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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).
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The calculation of LCC determines the financial impact of the imposition 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 transformers, DOE assumed that 50 percent are purchased based 

on lowest first cost and 50 percent are purchased using the TOC evaluation.3

When deciding on which dry-type 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 

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 Candidate Standard Level

Step 2a: The spreadsheet model selects a candidate standard level (CSL) and its 

associated transformer designs to evaluate. DOE developed as many as seven CSLs 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 CSL, the spreadsheet selects from its database of designs the subset of designs that 

satisfy the selected CSL 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 transformer’s 

first cost. By incorporating this factor, DOE captured the range of typical real-world 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 transformer by as much 
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as 15 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 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 

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 transformer load profile from 

distributions derived from available data. For liquid-immersed 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 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 transformers and in the Demand & Usage worksheet 

of the LCC spreadsheet for dry-type 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 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 

select various scenarios for load growth and future electricity price. The model applies the 
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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
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• 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 Transformer Selection Parameters

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

cost (TOC) characterize the value that transformer purchasers place on reducing no-load 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 transformers, DOE’s default scenario is an evaluation rate of 50

percent. Because few purchasers consider transformer losses as part of the purchase decision for 

low-voltage, dry-type transformers, DOE assumed a default evaluation rate of 2 percent. 

Regarding medium-voltage, dry-type transformers, DOE assumed 10 percent evaluators for 

small-capacity transformers—design lines 9 and 11, and 13A—and 20 percent for large-capacity 

transformers— design lines 10, 12, and 13B. 

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

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

of A for evaluators from public transformer purchase bids available on the Internet.3,4,5,6,7,8,9,10,11

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 liquidimmersed and dry-type transformers.

For each value of A that a 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 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-
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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 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 Transformers

DOE collected A and B parameter values from 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.

12

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
dt_nopr_tsd_chp8_092311 8-10 DRAFT

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.
dt_nopr_tsd_chp8_092311 8-11 DRAFT

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

Transformers

8.3.1.2 A and B Parameter Selection for Dry-Type Transformers

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

those used for liquid-immersed 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 transformers are installed in commercial buildings, 

and 40 percent in industrial buildings.

13 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 

8.3.5.2;

MPDW = the winter marginal demand charge ($/kW) (see section 8.3.5.2);

MPES = the summer marginal energy charge ($/kWh) (see section 8.3.5.2);

MPDS = the summer marginal demand charge ($/kW) (see section 8.3.5.2)

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)
dt_nopr_tsd_chp8_092311 8-12 DRAFT

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.

14

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 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) liquid-immersed, (2) smallcapacity low-voltage dry-type, (3) small-capacity medium-voltage dry-type and (4) largecapacity 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.

Table 8.3.2 A and B Parameter Evaluation Scenarios

Percentage of Evaluators %

Low Medium High
dt_nopr_tsd_chp8_092311 8-13 DRAFT

Liquid-immersed 0 50 100

Low-voltage dry-type 0 2 100

Small-capacity, medium-voltage dry-type 0 10 100

Large-capacity, medium-voltage dry-type 0 20 100

8.3.2 Database of Transformer Designs

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

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

during the engineering analysis (chapter 5) of selling prices, no-load losses, and load losses for 

the range of realistic 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 manufactured transformer into service as an installed piece of electrical 

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

For liquid-immersed transformers, which utilities typically purchase directly from 

manufacturers, 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 transformers, the distribution channel includes intermediaries who add 

their own costs to the manufacturer 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 Product Prices 

To derive a price trend for medium-sized electric motors, DOE obtained historical 

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

spanning the time period 1969-2010 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 integral horsepower motors and generators manufacturing was calculated by 

dividing the PPI series by the Gross Domestic Product Chained Price Index (see 

Error! Reference source not found.).

 

a

 Series ID PCU335311335311; http://www.bls.gov/ppi/
dt_nopr_tsd_chp8_092311 8-14 DRAFT

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 transformers prices in 2016. Thus, prices 

forecast for the LCC and PBP analysis are equal to the 2010 values for each efficiency level in 

each product class.

0

50

100

150

200

250

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 (2010=1)

Deflated Electric Power and Specialty Transformer Manufacturing PPI

Nominal Electric Power and Specialty Transformer Manufacturing PPI
dt_nopr_tsd_chp8_092311 8-15 DRAFT

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 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.

8.3.5 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 transformers, which 

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 (2010=1)

Year

Primary Copper Smelting PPI

Iron and Steel Mills PPI

Delfated Distribuiton Transformers PPI
dt_nopr_tsd_chp8_092311 8-16 DRAFT

are owned predominantly by utilities that pay costs that vary by the hour. DOE used the monthly 

analysis for dry-type 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 

Transformers

To evaluate the electricity costs associated with liquid-immersed 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. DOE developed two 

methods 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).15 The method chosen depends on whether the utility is part of a traditionally regulated 

system, or part of a restructured system that includes functioning capacity markets. 

DOE developed two sets of capacity costs to be applied to the two types of losses.

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

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

These terms are defined as follows.

CCNLL = (1 + CM)(βCGFG + CTFT),

and

CCLL = (1 + CM)(βCGFG + CTFT)∆P.

Where:

CM = the reserve capacity margin;

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

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

FG = the fixed charge rate used to calculate the annual revenue needed to support an 

investment in generation capacity;

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

FT = the fixed charge rate for transmission investments; and

∆P = the reduction in system peak load.

DOE calculated the various inputs of this equation as follows.
dt_nopr_tsd_chp8_092311 8-17 DRAFT

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

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

industry standard of 15 percent.

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

electricity that is dissipated from the electrical system during generation and transmission. It is 

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.

3 The 

regional transmission and distribution loss factors are given in Table 8.3.3.

Table 8.3.3 Transmission and Distribution Loss Factors

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

β 1.070 1.065 1.072 1.068 1.088 1.080 1.080 1.068 1.068 1.081 1.093 1.093 1.093

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

building new generating capacity, as provided by NEMS.15 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.

Table 8.3.4 Generation Capacity Costs

EMM 

Region

EMM 

Region 

Load Loss Generation No-load Loss Generation

Technology $/kW-year Technology $/kW-year

1 ECAR Combined Cycle 158.71 Advanced Coal 560.39

2 ERCOT Combined Cycle 158.71 Advanced Coal 560.39

3 MAAC Half & Half 359.55 Advanced Coal 560.39

4 MAIN Half & Half 359.55 Advanced Coal 560.39

5 MAPP Half & Half 359.55 Advanced Coal 560.39

6 NY Combined Cycle 158.71 Combined Cycle 158.71

7 NE Combined Cycle 158.71 Combined Cycle 158.71

8 FL Combined Cycle 158.71 Advanced Coal 560.39

9 SERC Half & Half 359.55 Advanced Coal 560.39

10 SPP Half & Half 359.55 Advanced Coal 560.39

11 NPP Combined Cycle 158.71 Advanced Coal 560.39

12 RA Combined Cycle 158.71 Advanced Coal 560.39

13 CA Combined Cycle 158.71 Advanced Coal 560.39

Generation Fixed Charge Rate (FG): This fixed charge rate is used to calculate the 

annual revenue required to pay for investment in generation capacity. DOE used a value of 0.15.3

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

new transmission capacity is provided by NEMS.

15
dt_nopr_tsd_chp8_092311 8-18 DRAFT

Transmission Fixed Charge Rate (FT): This rate is used to convert a lump-sum 

investment into an annual revenue requirement. DOE used a value of 0.12.15

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. 

DOE preformed similar calculations for regions that have functioning capacity markets. 

For those regions DOE assumed that the value of generation capacity for load losses can be 

inferred from the capacity market results:

CCLL = (1 + CM)(CAP + CTFT)∆P.

Capacity Market Rate (CAP): For systems having functioning capacity markets, DOE 

collected forward results for capacity market auctions from the website of each region’s 

independent system operator (ISO).

16,17,18 Those values are shown in Table 8.3.5.

Table 8.3.5 Capacity Market Auction Results

EMM Region ISO

Market Auction Results

Percent of Region Served % CAP $/KW-year

1 ECAR PJM 30 63.66

3 MAAC PJM 100 64.45

4 MAIN PJM 20 63.66

6 NY NYISO 100 162.18

7 NE NEISO 100 54.00

9 SERC PJM 5 63.66

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;
dt_nopr_tsd_chp8_092311 8-19 DRAFT

∈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.

19 DOE used the most recent data 

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

Hourly Transformer Load (e

2

(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.

8.3.5.2 Monthly Marginal Electricity Price Model for Dry-Type Transformers

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

prices from an analysis of marginal energy prices from tariffs for commercial buildings.20, 21

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 imposes mandatory time-ofuse (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

 

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

CBECS sample.

Those monthly data were processed using Coughlin et al.’s tariff bill calculation tools20 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. 
dt_nopr_tsd_chp8_092311 8-20 DRAFT

DOE’s tariff data were updated most recently in 2004. To convert to 2010 dollars, DOE 

used two datasets: (1) the report, Average Regulated Retail Price of Electricity22 for 2004–2007, 

and (2) the Edison Electric Institute (EEI) Typical Bills and Average Rate reports for 200723

through 2010.24,25Based 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.13 The EEI data cover only 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 

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 

2010$/kWh

Marginal Demand Price 

2010$/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 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 no growth trend for both 

liquid-immersed3 and dry-type 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 AEO2011.

26 The default price trend scenario that 

DOE used in the LCC analysis is the trend in the AEO2011 reference case. LCC spreadsheet 

users have the choice of using electricity price trends from the AEO 2011 low-growth scenario, 
dt_nopr_tsd_chp8_092311 8-21 DRAFT

reference scenario, or high-growth scenario.

Figure 8.3.5 shows the trends for the three AEO2011 price projections. Because 

AEO2011 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. 

Figure 8.3.5 Electricity Price Forecasts from AEO2011

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 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.27 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.28

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 

80%

85%

90%

95%

100%

105%

2005 2010 2015 2020 2025 2030 2035

Real Price Relative to 2008

Year

Reference Case High Growth Low Growth
dt_nopr_tsd_chp8_092311 8-22 DRAFT

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

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.29 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.30

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 
dt_nopr_tsd_chp8_092311 8-23 DRAFT

took the sample from the list of companies included on the Damodaran Online website.31 DOE 

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 Electric utilities, both publicly and investor owned

5, 6, 7 Electric utilities, commercial property owners, commercial and 

industrial

8, 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.32 DOE estimated the State and local 

discount rates from the interest rates on State and local bonds between 1971 and 2010.

33

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.
dt_nopr_tsd_chp8_092311 8-24 DRAFT

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

Utilities, InvestorOwned

(SIC 49)

2005 0.86 3.47 3.89 0.50 61 39

2006 0.92 3.44 4.55 0.25 61 39

2007 0.88 3.74 3.80 0.25 60 40

2008 0.79 4.21 2.19 1.00 50 50

2009 0.76 4.15 3.20 1.50 51 49

2010 0.75 6.74 3.23 1.00 53 47

*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).
dt_nopr_tsd_chp8_092311 8-25 DRAFT

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.27 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.
dt_nopr_tsd_chp8_092311 8-26 DRAFT

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.

34 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 2010$.

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),

35 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.
dt_nopr_tsd_chp8_092311 8-27 DRAFT

8.3.11 Maintenance Costs

Maintenance costs are those 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 candidate standard 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: AEO2011reference.

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 
dt_nopr_tsd_chp8_092311 8-28 DRAFT

preliminary analysis. The lowest candidate standard level (CSL) 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 CSLs 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 Candidate Standard Levels Evaluated for Each Design Line 

CSL 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

1

Base + % 0.08 0.09 0.06 0.08 0.06 0.23 0.23 0.2 0.17 0.09 0.14 0.09 0.13 0.08

Efficiency % 99.16 99 99.48 99.16 99.48 98.23 98.23 98.8 98.99 99.31 98.81 99.21 98.76 99.23

2

Base + % 0.14 0.16 0.09 0.14 0.09 0.47 0.47 0.42 0.3 0.18 0.27 0.18 0.22 0.16

Efficiency % 99.22 99.07 99.51 99.22 99.51 98.47 98.47 99.02 99.12 99.4 98.94 99.3 98.85 99.31

3

Base + % 0.17 0.20 0.12 0.17 0.12 0.60 0.60 0.54 0.46 0.28 0.39 0.27 0.29 0.23

Efficiency % 99.25 99.11 99.54 99.25 99.54 98.6 98.6 99.14 99.28 99.5 99.06 99.39 98.92 99.38

4

Base + % 0.23 0.27 0.15 0.23 0.15 0.80 0.80 0.65 0.56 0.31 0.46 0.34 0.47 0.28

Efficiency % 99.31 99.18 99.57 99.31 99.57 98.8 98.8 99.25 99.38 99.53 99.13 99.46 99.1 99.43

5

Base + % 0.34 0.40 0.19 0.34 0.19 0.93 0.93 0.72 0.68 0.38 0.65 0.41 0.66 0.34

Efficiency % 99.42 99.31 99.61 99.42 99.61 98.93 98.93 99.32 99.5 99.6 99.32 99.53 99.29 99.49

6

Base + % 0.42 0.50 0.27 0.42 0.27 1.17 1.17 0.84 0.77 0.45 0.83 0.47 0.85 0.43

Efficiency % 99.5 99.41 99.69 99.5 99.69 99.17 99.17 99.44 99.59 99.67 99.5 99.59 99.48 99.58

7

Base + % 0.42 0.55 0.31 0.52 0.27 1.44 1.44 0.98 0.77 0.45 0.83 0.53 0.85 0.43

Efficiency % 99.5 99.46 99.73 99.6 99.69 99.44 99.44 99.58 99.59 99.67 99.5 99.65 99.48 99.58

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 CSL 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 

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. 
dt_nopr_tsd_chp8_092311 8-29 DRAFT

Figure 8.4.2 Design Load Losses versus No-Load Losses in the 

Base Case and Candidate Standard 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 CSL. The LCC spreadsheet tool can generate graphical representations such as Figure 

8.4.3 for each design line and candidate standard level.

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

900.00

1,000.00

0 20 40 60 80 100 120 140 160 180

Load Losses (watts)

No Load Losses (watts)

Load Losses (LL) vs No-Load Losses (NL)

Available Designs

Selected Designs, Base

Selected Designs, Standard
dt_nopr_tsd_chp8_092311 8-30 DRAFT

Figure 8.4.3 Distribution of Life-Cycle Cost Results for Design 

Line 2, Candidate Standard Level 2

The 14 tables that follow summarize the results from DOE’s LCC analysis. For each 

evaluated design line and each CSL, DOE presents the percent efficiency; the percent of 

evaluated transformer purchases that would experience negative, zero, and positive LCC savings 

when subject to the CSL; and the mean LCC savings. 

8.4.2 Results for Design Line 1 

Table 8.4.2 summarizes the 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 99.17 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

shipping costs, distributor markup, and sales tax, was $2,149; the installation cost was $1,381. 

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 99.16% 99.22% 99.25% 99.31% 99.42% 99.50% 99.50%

Transformers with Net Increase in 

LCC (%) 41.18% 0.69% 0.59% 3.93% 11.20% 38.08% 38.08%

Transformers with No Impact on 

LCC (%) 17.94% 15.54% 15.54% 11.66% 8.44% 0.08% 0.08%

Transformers with Net LCC 

Savings (%) 40.88% 83.77% 83.87% 84.41% 80.36% 61.84% 61.84%

Mean LCC Savings ($) 116 918 920 902 797 369 369

Median LCC Savings ($) 0 976 977 946 761 251 251
dt_nopr_tsd_chp8_092311 8-31 DRAFT

8.4.3 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 98.96 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $1,365; the installation cost was $1,608.

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 99.00% 99.07% 99.11% 99.18% 99.31% 99.41% 99.46%

Transformers with Net Increase in 

LCC (%) 14.98% 5.50% 6.44% 10.35% 29.64% 48.46% 66.73%

Transformers with No Impact on 

LCC (%) 11.87% 11.34% 10.41% 6.88% 2.13% 0.18% 0.00%

Transformers with Net LCC 

Savings (%) 73.15% 83.16% 83.15% 82.77% 68.23% 51.36% 33.27%

Mean LCC Savings ($) 467 574 562 528 215 11 -214

Median LCC Savings ($) 525 621 607 575 230 18 -219

8.4.4 Results for Design Line 3 

Table 8.4.4 summarizes the 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 99.51 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $9,519; the installation cost was $4,343.

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 99.48% 99.51% 99.54% 99.57% 99.61% 99.69% 99.73%

Transformers with Net Increase in 

LCC (%) 4.44% 4.87% 1.66% 1.15% 1.64% 9.54% 27.12%

Transformers with No Impact on 

LCC (%) 48.48% 43.30% 28.70% 27.83% 24.68% 10.16% 0.00%

Transformers with Net LCC 

Savings (%) 47.08% 51.83% 69.64% 71.02% 73.68% 80.30% 72.88%

Mean LCC Savings ($) 2192 2739 5371 5733 6748 8485 7110

Median LCC Savings ($) 0 513 5704 6239 7157 7734 5278
dt_nopr_tsd_chp8_092311 8-32 DRAFT

8.4.5 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 99.23 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $5,902; the installation cost was $3,964.

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 99.16% 99.22% 99.25% 99.31% 99.42% 99.50% 99.60%

Transformers with Net Increase in 

LCC (%) 6.02% 0.03% 0.03% 0.03% 0.44% 18.86% 42.53%

Transformers with No Impact on 

LCC (%) 35.55% 35.55% 35.55% 35.55% 33.48% 8.67% 0.00%

Transformers with Net LCC 

Savings (%) 58.43% 64.42% 64.42% 64.42% 66.08% 72.47% 57.47%

Mean LCC Savings ($) 1429 2953.9 2953.9 2954.3 3023.3 2874 1187

Median LCC Savings ($) 275 3499.7 3499.7 3501.3 3570.5 2793 772

8.4.6 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 99.45 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $26,553; the installation cost was $11,199.

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 99.48% 99.51% 99.54% 99.57% 99.61% 99.69% 99.69%

Transformers with Net Increase in 

LCC (%) 27.61% 24.66% 15.91% 14.50% 10.42% 17.97% 17.97%

Transformers with No Impact on 

LCC (%) 9.87% 3.70% 1.93% 1.30% 0.00% 0.00% 0.00%

Transformers with Net LCC 

Savings (%) 62.52% 71.64% 82.16% 84.20% 89.58% 82.03% 82.03%

Mean LCC Savings ($) 4937 7786 10734 11282 15347 15754 15754

Median LCC Savings ($) 4662 7359 8991 9588 14095 13993 13993
dt_nopr_tsd_chp8_092311 8-33 DRAFT

8.4.7 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-kilovolt (kV) 

basic impulse insulation level (BIL). The average efficiency of the baseline units selected during 

the LCC analysis was 98.33. The customer equipment cost before installation, which includes the 

manufacturer selling price, distributor markup, contractor markup, and sales tax, was $1,006; the 

installation cost was $900.

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

Candidate Standard 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 (%) 0.00% 36.61% 25.24% 37.54% 32.43% 53.32% 97.68%

Transformers with No Impact on 

LCC (%) 0.00% 61.96% 74.53% 62.46% 67.57% 46.68% 2.32%

Transformers with Net LCC Savings 

(%) 100.00% 1.43% 0.23% 0.00% 0.00% 0.00% 0.00%

Mean LCC Savings ($) 0 29 59 76 122 9 -952

Median LCC Savings ($) 0 18 48 60 102 -24 -1005

8.4.8 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 basic BIL. 

The average efficiency of the baseline units selected during the LCC analysis was 98.41 percent. 

The customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $2,557; the installation cost was 

$1,604.

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

Candidate Standard 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 (%) 0.0% 0.5% 18.5% 10.9% 10.1% 69.8% 69.8%

Transformers with No Impact on 

LCC (%) 21.5% 72.8% 80.0% 89.1% 90.0% 30.2% 30.2%

Transformers with Net LCC Savings 

(%) 78.5% 26.7% 1.5% 0.0% 0.0% 0.0% 0.0%

Mean LCC Savings ($) 323 826 849 1093 1328 -511 -511

Median LCC Savings ($) 0 685 657 883 1103 -745 -745
dt_nopr_tsd_chp8_092311 8-34 DRAFT

8.4.9 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 98.67 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $6,144; the installation cost was 

$2,734.

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

Candidate Standard 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

(%) 3.87% 1.30% 1.93% 5.15% 4.05% 4.06% 56.08%

Transformers with Net LCC Benefit 

(%) 86.71% 91.63% 94.83% 94.85% 95.95% 95.94% 43.92%

Transformers with No Change in 

LCC (%) 9.42% 7.07% 3.24% 0.00% 0.00% 0.00% 0.00%

Mean LCC Savings ($) 1401 3554 4253 4999 5826 5844 -186

Median LCC Savings ($) 1172 3487 4162 4537 5510 5531 -632

8.4.10 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 98.86 percent. 

The customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $10,717; the installation cost was 

$3,157.

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 98.99% 99.12% 99.28% 99.38% 99.50% 99.59% 99.59%

Transformers with Net LCC Cost 

(%) 0.48% 2.18% 10.97% 7.72% 18.57% 60.50% 60.50%

Transformers with Net LCC Benefit 

(%) 88.25% 96.29% 89.03% 92.28% 81.43% 39.50% 39.50%

Transformers with No Change in 

LCC (%) 11.27% 1.53% 0.00% 0.00% 0.00% 0.00% 0.00%

Mean LCC Savings ($) 2761 3863 3700 5085 3998 -673 -673

Median LCC Savings ($) 2746 3807 3298 4708 3488 -1285 -1285
dt_nopr_tsd_chp8_092311 8-35 DRAFT

8.4.11 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 99.28

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $37,303; the installation 

cost was $6,328.

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 99.31% 99.40% 99.50% 99.53% 99.60% 99.67% 99.67%

Transformers with Net LCC Cost 

(%) 11.05% 24.79% 31.68% 27.38% 35.45% 69.49% 69.49%

Transformers with Net LCC Benefit 

(%) 82.63% 75.18% 68.32% 72.62% 64.55% 30.51% 30.51%

Transformers with No Change in 

LCC (%) 6.32% 0.03% 0.00% 0.00% 0.00% 0.00% 0.00%

Mean LCC Savings ($) 2778 4329 4849 6311 5574 -5311 -5311

Median LCC Savings ($) 2142 3372 3787 4986 3842 -7440 -7440

8.4.12 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 98.70

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $16,358; the installation 

cost was $3,755.

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 98.81% 98.94% 99.06% 99.13% 99.32% 99.50% 99.50%

Transformers with Net LCC Cost 

(%) 27.05% 46.40% 16.55% 14.00% 22.24% 57.84% 57.84%

Transformers with Net LCC Benefit 

(%) 70.46% 53.60% 83.45% 86.00% 77.76% 42.16% 42.16%

Transformers with No Change in 

LCC (%) 2.49% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Mean LCC Savings ($) 810 497 2709 3121 3120 -309 -309

Median LCC Savings ($) 606 177 2477 2857 2673 -1003 -1003
dt_nopr_tsd_chp8_092311 8-36 DRAFT

8.4.13 Results for Design Line 12

Table 8.4.13 summarizes results of the LCC analysis for the representative unit from 

design line 12, a 1500-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 99.14

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $44,886; the installation 

cost was $6,773.

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

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 99.21% 99.30% 99.39% 99.46% 99.53% 99.59% 99.65%

Transformers with Net LCC Cost 

(%) 15.02% 13.00% 24.56% 24.33% 25.64% 33.51% 64.68%

Transformers with Net LCC Benefit 

(%) 79.00% 85.75% 75.44% 75.67% 74.36% 66.49% 35.32%

Transformers with No Change in 

LCC (%) 5.98% 1.25% 0.00% 0.00% 0.00% 0.00% 0.00%

Mean LCC Savings ($) 5322 8865 8644 8076 9726 8504 -4210

Median LCC Savings ($) 4216 7422 6868 6644 7815 6146 -6987

8.4.14 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 98.66

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $23,567; the installation 

cost was $4,562.

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

13A

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 98.76% 98.85% 98.92% 99.10% 99.29% 99.48% 99.48%

Transformers with Net LCC Cost 

(%) 27.55% 28.94% 41.10% 30.88% 33.17% 87.49% 87.49%

Transformers with Net LCC Benefit 

(%) 70.74% 71.01% 58.90% 69.12% 66.83% 12.51% 12.51%

Transformers with No Change in 

LCC (%) 1.71% 0.05% 0.00% 0.00% 0.00% 0.00% 0.00%

Mean LCC Savings ($) 855 1107 749 1701 2060 -6331 -6331

Median LCC Savings ($) 654 860 470 1439 1600 -7068 -7068
dt_nopr_tsd_chp8_092311 8-37 DRAFT

8.4.15 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 99.18

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $60,907; the installation 

cost was $8,485.

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

13B 

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency (%) 99.23% 99.31% 99.38% 99.43% 99.49% 99.58% 99.58%

Transformers with Net LCC Cost 

(%) 20.61% 12.20% 19.90% 39.80% 26.67% 39.77% 39.77%

Transformers with Net LCC Benefit 

(%) 73.56% 87.69% 80.10% 60.20% 73.33% 60.23% 60.23%

Transformers with No Change in 

LCC (%) 5.83% 0.11% 0.00% 0.00% 0.00% 0.00% 0.00%

Mean LCC Savings ($) 4351 8668 8878 4642 9271 6033 6033

Median LCC Savings ($) 3397 7455 7495 2917 7794 4359 4359

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 

five 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); and

5. equipment price (see chapter 6); and

6. electricity price trends (see section 8.3.7).
dt_nopr_tsd_chp8_092311 8-38 DRAFT

This analysis examines how sensitive the LCC results are to changes in key DOE 

assumptions. For this NOPR, 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. Each of the six variables has three values—low, medium, and high—that are 

described in the previous sections discussing each individual input variable. 

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 50 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 small-capacity, medium-voltage, dry-type 

transformers represents a scenario in which 10 percent of purchases are evaluated. The medium 

value for large-capacity, medium-voltage, dry-type transformers represents a scenario in which

20 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 decreases the medium scenario load by 15 percent; the 

high scenario increases it by 15 percent. For load growth, the annual low, medium, and high 

scenarios are 0 percent, 1 percent, and 2 percent, respectively. Electricity price trends use the 

AEO2011 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 during the LCC 

analysis was 99.17 percent. The customer equipment cost before installation, which includes the 

manufacturer selling price, shipping costs, distributor markup, and sales tax, was $2,149; the 

installation cost was $1,381. 

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 CSLs 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. 
dt_nopr_tsd_chp8_092311 8-39 DRAFT

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

Representative Unit, Design Line 1 

Scenario

Candidate Standard Level

1 2 3 4 5 6

Efficiency % 99.16% 99.22% 99.25% 99.31% 99.42% 99.50%

Baseline 144 913 915 916 851 459

Low A & B Distribution -73 996 996 982 899 450

High A & B Distribution 205 880 883 861 745 328

Low Loading 39 934 937 864 645 115

High Loading 206 900 901 946 974 664

Low Electricity Price 87 828 830 802 683 251

High Electricity Price 147 1011 1013 1005 920 505

No Load Growth 116 918 920 902 797 369

High Load Growth 175 906 908 931 913 561

Low Equipment Price 24 917 921 929 888 592

High Equipment Price -135 790 792 713 504 -148

Low Electricity Price Trend 102 874 876 854 740 307

High Electricity Price Trend 130 963 965 951 854 431
dt_nopr_tsd_chp8_092311 8-40 DRAFT

Figure 8.5.1 Average Life-Cycle Cost Savings (2010$) 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 

during the LCC analysis was 98.41 percent. The customer equipment cost before installation, 

which includes the manufacturer selling price, distributor markup, contractor markup, and sales 

tax, was $2,557; the installation cost was $1,604.

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. The changes tend to increase with the efficiency of the CSL. For design line 

7, the change in percentage of transformers purchased using evaluation of parameters A and B; 

low equipment prices; and, at higher efficiency levels, high electricity cost result in significantly 

larger changes in the LCC savings than do the other variables for all CSLs examined. The 

purchase behavior described by evaluation of parameters A and B strongly affects how much 

energy is used when there is no standard, and thus affects potential savings. The low savings 

from the case of high A and B evaluation result from the fact that DOE assumes that all 

purchasers place an economic value on losses and will purchase a transformer based on those 

values instead of lowest first cost. 

-200

0

200

400

600

800

1000

1200

99.16% 99.22% 99.25% 99.31% 99.42% 99.50% 99.50%

Life-Cycle Cost Savings ($2010)

Transformer Efficiency

Baseline

Low A & B Distribution 

High A & B Distribution 

Low Loading 

High Loading 

Low Electricity Price

High Electricity Price 

No Load Growth

High Load Growth

Low Equipment Price

High Equipment Price

Low Electricity Price Trend

High Electricity Price Trend
dt_nopr_tsd_chp8_092311 8-41 DRAFT

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

Representative Unit, Design Line 7

Scenario

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency % 98.23% 98.47% 98.60% 98.80% 98.93% 99.17% 99.44%

Baseline 323 756 826 849 1093 1328 -511

Low A & B Distribution 359 839 915 948 1,173 1,422 -418

High A & B Distribution 0 1 6 -53 395 473 -1,362

Low Loading 325 746 800 693 1,136 1,193 -871

High Loading 322 762 839 927 1,072 1,396 -332

Low Electricity Price 286 671 733 736 874 1,064 -787

High Electricity Price 360 841 918 963 1,313 1,593 -236

Medium Load Growth 322 762 840 935 1,070 1,403 -315

High Load Growth 321 769 856 1,032 1,044 1,486 -94

Low Equipment Price 19 210 471 554 854 1,157 -254

High Equipment Price 233 562 852 819 890 1,032 -1,491

Low Electricity Price Trend 296 694 757 750 941 1,124 -750

High Electricity Price Trend 345 809 884 933 1,222 1,501 -310
dt_nopr_tsd_chp8_092311 8-42 DRAFT

Figure 8.5.2 Average Life-Cycle Cost Savings (2010$) by 

Scenario for Design Line 7

8.5.3 Sensitivity Results for Design Line 12

The representative unit from design line 13 is a 1500-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 99.14 percent. The customer equipment cost before installation, 

which includes the manufacturer selling price, distributor markup, contractor markup, and sales 

tax, was $44,886; the installation cost was $6,773.

Table 8.5.3 and Figure 8.5.3 illustrate the LCC sensitivity to changes in the six userselectable variables for design line 13. For all the variables, each sensitivity run causes some 

change in the LCC results. The changes tend to increase with the efficiency of the CSL. For 

design line 13, the change in percentage of transformer loading results in the most significant 

increase in LCC savings for all CSLs examined. The reason that transformer loading is important 

is that it is directly related to 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

98.23% 98.47% 98.60% 98.80% 98.93% 99.17% 99.44%

Life-Cycle Cost Savings ($2010)

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
dt_nopr_tsd_chp8_092311 8-43 DRAFT

Table 8.5.3 Effects of Changed Variables on Life-Cycle Cost Savings (2010$) for 

Representative Unit, Design Line 12

Scenario

Candidate Standard Level

1 2 3 4 5 6 7

Efficiency % 99.21% 99.30% 99.39% 99.46% 99.53% 99.59% 99.65%

Baseline 5,322 8,865 8,644 8,076 9,726 8,504 -4,210

Low A & B Distribution 5,443 9,112 8,912 8,349 9,999 8,778 -3,935

High A & B Distribution 4,011 6,302 5,852 5,273 6,917 5,693 -7,025

Low Loading 2,318 4,205 2,198 4,278 4,213 1,353 -12,989

High Loading 6,706 11,007 11,603 9,817 12,261 11,791 -177

Low Electricity Price 4,722 7,795 7,160 5,405 6,573 5,070 -7,900

High Electricity Price 5,921 9,935 10,128 10,747 12,878 11,939 -521

Medium Load Growth 6,770 11,107 11,744 9,901 12,379 11,947 16

High Load Growth 8,400 13,629 15,233 11,956 15,365 15,820 4,771

Low Equipment Price 5,314 7,836 9,986 10,448 13,600 13,681 5,090

High Equipment Price 4,725 5,731 4,311 810 1,214 -1,862 -20,753

Low Electricity Price Trend 4,654 7,728 7,067 5,860 7,029 5,475 -7,553

High Electricity Price Trend 5,886 9,825 9,974 9,943 11,999 11,058 -1,393

Figure 8.5.3 Average Life-Cycle Cost Savings (2010$) by 

Scenario for Design Line 13

-25,000

-20,000

-15,000

-10,000

-5,000

0

5,000

10,000

15,000

20,000

99.21% 99.30% 99.39% 99.46% 99.53% 99.59% 99.65%

Life-Cycle Cost Savings ($2010)

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
dt_nopr_tsd_chp8_092311 8-44 DRAFT

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 CSL 

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) (2010$), 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 candidate standard 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 

payback, the electricity price DOE uses is only for the year the standard takes effect, assumed 

here to be 2016.
dt_nopr_tsd_chp8_092311 8-45 DRAFT

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 candidate 

standard levels (CSLs) 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 CSL. 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

CSL 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.
dt_nopr_tsd_chp8_092311 8-46 DRAFT

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 candidate 

standard levels, the mean PBP and the percentage of the 10,000 Monte Carlo simulations to 

which the PBP calculation applies. For every CSL 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

8.6.5 Results for Design Line 1 

As the efficiency of the CSLs 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.

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 99.14 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $2,259; the installation cost was $2,162.

Table 8.6.2 Results of Payback Period Analysis: Representative Unit, Design Line 1 

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 30.7 8.8 8.8 11.6 16.3 26.2 26.2

Median Payback (Years) 19.6 8.4 8.4 10.0 13.5 20.3 20.3

Transformers having Well Defined 

Payback (%) 70.93% 84.45% 84.46% 87.69% 90.36% 96.31% 96.31%

Transformers having Undefined 

Payback (%) 29.07% 15.55% 15.54% 12.31% 9.64% 3.69% 3.69%

Mean Incremental First Cost ($) 2,253 2,313 2,314 2,360 2,449 2,591 2,591

 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.
dt_nopr_tsd_chp8_092311 8-47 DRAFT

Mean Operating Cost Savings ($) 178 138 137 132 122 116 116

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 98.96 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $1,365; the installation cost was $1,608.

Table 8.6.3 Results of Payback Period Analysis: Representative Unit, Design Line 2 

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 17.4 12.6 13.3 16.6 25.9 31.3 35.6

Median Payback (Years) 9.7 9.7 10.1 11.7 19.2 23.5 27.6

Transformers having Well Defined 

Payback (%) 86.19% 88.33% 88.95% 92.68% 95.78% 98.65% 99.63%

Transformers having Undefined 

Payback (%) 13.81% 11.67% 11.05% 7.32% 4.22% 1.35% 0.37%

Mean Incremental First Cost ($) 1,768 1,795 1,804 1,845 2,017 2,051 1,946

Mean Operating Cost Savings ($) 87 80 80 78 72 68 65

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 99.51 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $9,519; the installation cost was $4,343.

Table 8.6.4 Results of Payback Period Analysis: Representative Unit, Design Line 3 

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 6.6 7.6 6.2 5.9 6.5 13.0 23.6

Median Payback (Years) 4.2 4.3 4.9 4.9 5.2 8.3 14.4

Transformers having Well Defined 

Payback (%) 48.83% 54.49% 71.08% 72.09% 75.28% 89.38% 98.22%

Transformers having Undefined 

Payback (%) 51.17% 45.51% 28.92% 27.91% 24.72% 10.62% 1.78%

Mean Incremental First Cost ($) 4,395 4,434 4,538 4,554 4,612 4,994 5,608

Mean Operating Cost Savings ($) 1,208 1,177 1,041 1,023 966 805 703
dt_nopr_tsd_chp8_092311 8-48 DRAFT

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 99.23 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $5,902; the installation cost was $3,964.

Table 8.6.5 Results of Payback Period Analysis: Representative Unit, Design Line 4

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 12.9 6.5 6.5 6.5 6.9 19.7 32.9

Median Payback (Years) 11.7 6.2 6.2 6.2 6.3 11.3 20.9

Transformers having Well Defined 

Payback (%) 64.45% 64.45% 64.45% 64.45% 66.50% 88.58% 99.91%

Transformers having Undefined 

Payback (%) 35.55% 35.55% 35.55% 35.55% 33.50% 11.42% 0.09%

Mean Incremental First Cost ($) 4,160 4,222 4,222 4,222 4,232 4,570 4,664

Mean Operating Cost Savings ($) 492 419 419 419 415 365 305

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 99.45 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, and sales tax, was $26,553; the installation cost was $11,199.

Table 8.6.6 Results of Payback Period Analysis: Representative Unit, Design Line 5 

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 16.9 15.7 13.1 13.2 12.7 17.7 17.7

Median Payback (Years) 8.8 12.4 14.2 14.5 13.8 16.2 16.2

Transformers having Well Defined 

Payback (%) 75.90% 86.47% 92.98% 94.63% 99.22% 100.00% 100.00%

Transformers having Undefined 

Payback (%) 24.10% 13.53% 7.02% 5.37% 0.78% 0.00% 0.00%

Mean Incremental First Cost ($) 11,235 12,214 13,480 13,768 14,531 11,274 11,274

Mean Operating Cost Savings ($) 4,318 4,097 3,880 3,829 3,496 2,761 2,761

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 

impulse insulation level (BIL). The average efficiency of the baseline units selected during the 
dt_nopr_tsd_chp8_092311 8-49 DRAFT

LCC analysis was 98.33. The customer equipment cost before installation, which includes the 

manufacturer selling price, distributor markup, contractor markup, and sales tax, was $1,006; the 

installation cost was $900.

Table 8.6.7 Results of Payback Period Analysis: Representative Unit, Design Line 6

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) NA 17.4 14.5 17.6 16.0 19.8 41.7

Median Payback (Years) NA 15.4 13.4 16.3 15.6 19.2 40.0

Transformers having Well Defined 

Payback (%) 0.00% 97.75% 99.73% 99.97% 100.00% 100.00% 100.00%

Transformers having Undefined 

Payback (%) 100.00% 2.25% 0.27% 0.03% 0.00% 0.00% 0.00%

Mean Incremental First Cost ($) 0 111 138 417 508 781 1,871

Mean Operating Cost Savings ($) 0 8 11 27 34 43 50

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 98.41 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $2,557; the installation cost was 

$1,604.

Table 8.6.8 Results of Payback Period Analysis: Representative Unit, Design Line 7

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 0.1 0.6 1.1 11.1 9.5 9.8 25.7

Median Payback (Years) 0.0 0.0 0.0 5.6 8.1 9.0 23.4

Transformers having Well Defined 

Payback (%) 22% 62% 73% 97% 100% 100% 100%

Transformers having Undefined 

Payback (%) 78% 38% 27% 3% 0% 0% 0%

Mean Incremental First Cost ($) -10 -20 -7 325 711 1,097 3,337

Mean Operating Cost Savings ($) 17 40 44 63 97 131 153

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 98.67 percent. The 

customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $6,144; the installation cost was 

$2,734.
dt_nopr_tsd_chp8_092311 8-50 DRAFT

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

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 7.0 4.2 4.4 8.0 7.3 7.3 20.9

Median Payback (Years) 6.5 4.0 4.0 7.6 7.0 7.0 19.7

Transformers having Well Defined 

Payback (%) 90.58% 92.93% 96.65% 100.00% 100.00% 100.00% 100.00%

Transformers having Undefined 

Payback (%) 9.42% 7.07% 3.35% 0.00% 0.00% 0.00% 0.00%

Mean Incremental First Cost ($) 649 912 1,118 3,196 3,281 3,291 10,522

Mean Operating Cost Savings ($) 110 241 289 442 491 492 557

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 98.86 percent. 

The customer equipment cost before installation, which includes the manufacturer selling price, 

distributor markup, contractor markup, and sales tax, was $10,717; the installation cost was 

$3,157.

Table 8.6.10 Results of Payback Period Analysis: Representative Unit, Design Line 9 

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 1.9 3.8 10.6 9.5 13.0 22.2 22.2

Median Payback (Years) 1.8 3.1 9.3 8.9 12.2 20.6 20.6

Transformers having Well Defined 

Payback (%) 88.67% 98.40% 99.87% 100.00% 100.00% 100.00% 100.00%

Transformers having Undefined 

Payback (%) 11.33% 1.60% 0.13% 0.00% 0.00% 0.00% 0.00%

Mean Incremental First Cost ($) 290 753 3,386 4,391 6,859 12,111 12,111

Mean Operating Cost Savings ($) 164 249 382 511 585 617 617

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 99.28 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $37,303; the installation 

cost was $6,328.

Table 8.6.11 Results of Payback Period Analysis: Representative Unit, Design Line 10 

Candidate Standard Level
dt_nopr_tsd_chp8_092311 8-51 DRAFT

1 2 3 4 5 6 7

Mean Payback (Years) 8.2 14.9 16.6 14.8 16.5 25.2 25.2

Median Payback (Years) 5.2 11.1 14.5 14.1 15.5 23.1 23.1

Transformers having Well Defined 

Payback (%) 92.30% 98.93% 99.91% 100.00% 100.00% 100.00% 100.00%

Transformers having Undefined 

Payback (%) 7.70% 1.07% 0.09% 0.00% 0.00% 0.00% 0.00%

Mean Incremental First Cost ($) 1,119 5,611 14,638 16,183 20,807 35,727 35,727

Mean Operating Cost Savings ($) 210 536 1,051 1,213 1,423 1,641 1,641

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 98.70 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $16,358; the installation 

cost was $3,755.

Table 8.6.12 Results of Payback Period Analysis: Representative Unit, Design Line 11 

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 15.8 21.1 12.8 12.2 14.0 20.9 20.9

Median Payback (Years) 11.4 17.0 12.0 11.9 13.5 20.0 20.0

Transformers having Well Defined 

Payback (%) 95.25% 99.07% 100.00% 100.00% 100.00% 100.00% 100.00%

Transformers having Undefined 

Payback (%) 4.75% 0.93% 0.00% 0.00% 0.00% 0.00% 0.00%

Mean Incremental First Cost ($) 1,250 3,275 4,494 4,926 7,213 12,644 12,644

Mean Operating Cost Savings ($) 111 203 389 434 557 665 665

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 99.14 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $44,886; the installation 

cost was $6,773.

Table 8.6.13 Results of Payback Period Analysis: Representative Unit, Design Line 12 

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 9.9 9.9 14.7 14.3 14.4 16.1 23.8

Median Payback (Years) 6.3 6.7 10.6 13.5 13.7 15.0 21.7
dt_nopr_tsd_chp8_092311 8-52 DRAFT

Transformers having Well Defined 

Payback (%) 91.10% 97.59% 98.83% 100.00% 100.00% 100.00% 100.00%

Transformers having Undefined 

Payback (%) 8.90% 2.41% 1.17% 0.00% 0.00% 0.00% 0.00%

Mean Incremental First Cost ($) 2,603 4,629 10,060 18,184 22,242 27,410 43,835

Mean Operating Cost Savings ($) 427 728 1,009 1,416 1,725 1,938 2,138

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 98.66 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $23,567; the installation 

cost was $4,562.

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

13A

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 14.9 15.8 19.3 15.7 16.1 30.9 30.9

Median Payback (Years) 10.5 12.6 15.9 15.4 15.7 29.3 29.3

Transformers having Well Defined 

Payback (%) 94.62% 99.24% 99.81% 100.00% 100.00% 100.00% 100.00%

Transformers having Undefined 

Payback (%) 5.38% 0.76% 0.19% 0.00% 0.00% 0.00% 0.00%

Mean Incremental First Cost ($) 1,139 2,023 3,373 6,307 8,549 19,052 19,052

Mean Operating Cost Savings ($) 107 169 222 432 572 686 686

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 99.18 

percent. The customer equipment cost before installation, which includes the manufacturer 

selling price, distributor markup, contractor markup, and sales tax, was $60,907; the installation 

cost was $8,485.

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

13B 

Candidate Standard Level

1 2 3 4 5 6 7

Mean Payback (Years) 11.6 10.3 13.1 17.9 14.9 17.3 17.3

Median Payback (Years) 7.0 9.0 11.6 16.1 14.5 16.8 16.8

Transformers having Well Defined 

Payback (%) 88.90% 99.68% 99.90% 99.93% 100.00% 100.00% 100.00%
dt_nopr_tsd_chp8_092311 8-53 DRAFT

Transformers having Undefined 

Payback (%) 11.10% 0.32% 0.10% 0.07% 0.00% 0.00% 0.00%

Mean Incremental First Cost ($) 2,776 7,515 13,333 21,788 26,857 38,839 38,839

Mean Operating Cost Savings ($) 385 873 1,198 1,427 1,950 2,421 2,421

Error! Reference source not found. illustrates the full PBP results from the Monte 

Carlo simulation as a histogram for one example design line and CSL. The LCC spreadsheet tool 

can be used to generate similar histograms for all design lines and each CSL.

Figure 8.6.1 Distribution of Payback Period Results for Design 

Line 2, Candidate Standard Level 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.
dt_nopr_tsd_chp8_092311 8-54 DRAFT

• 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 

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 8.7.3 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 CSL 1 through CSL 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 CSL. 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, 0.059 $/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 8.7.3 shows the first-year operating cost for the transformer, which is 

the annual losses calculated based on the test procedure assumptions times the average marginal 

cost of electricity. 
dt_nopr_tsd_chp8_092311 8-55 DRAFT

Table 8.7.1 Average Transformer Efficiency %

Design 

Line

Rated 

Capacity 

kVA

Candidate Standard Level

Base 1 2 3 4 5 6 7

1 50 99.08% 99.16% 99.22% 99.25% 99.31% 99.42% 99.50% 99.50%

2 25 98.91% 99.00% 99.07% 99.11% 99.18% 99.31% 99.41% 99.46%

3 500 99.42% 99.48% 99.51% 99.54% 99.57% 99.61% 99.69% 99.73%

4 150 99.08% 99.16% 99.22% 99.25% 99.31% 99.42% 99.50% 99.60%

5 1500 99.42% 99.48% 99.51% 99.54% 99.57% 99.61% 99.69% 99.69%

6 25 98.00% 98.23% 98.47% 98.60% 98.80% 98.93% 99.17% 99.44%

7 75 98.00% 98.23% 98.47% 98.60% 98.80% 98.93% 99.17% 99.44%

8 300 98.60% 98.80% 99.02% 99.14% 99.25% 99.32% 99.44% 99.58%

9 300 98.82% 98.99% 99.12% 99.28% 99.38% 99.50% 99.59% 99.59%

10 1500 99.22% 99.31% 99.40% 99.50% 99.53% 99.60% 99.67% 99.67%

11 300 98.67% 98.81% 98.94% 99.06% 99.13% 99.32% 99.50% 99.50%

12 1500 99.12% 99.21% 99.30% 99.39% 99.46% 99.53% 99.59% 99.65%

13A 300 98.63% 98.76% 98.85% 98.92% 99.10% 99.29% 99.48% 99.48%

13B 2000 99.15% 99.23% 99.31% 99.38% 99.43% 99.49% 99.58% 99.58%

Table 8.7.2 Average Transformer Installed Cost ($2010)

Design 

Line

Rated 

Capacity 

kVA

Candidate Standard Level

Base 1 2 3 4 5 6 7

1 50 $4,420 $2,472 $4,909 $4,909 $5,056 $5,403 $5,982 $5,982

2 25 $2,973 $3,312 $3,370 $3,393 $3,477 $3,931 $4,230 $4,539

3 500 $13,863 $14,352 $14,544 $15,207 $15,298 $15,654 $17,845 $21,703

4 150 $9,867 $10,634 $10,889 $10,889 $10,889 $10,918 $12,270 $15,409

5 1500 $34,372 $38,177 $40,101 $41,463 $41,935 $45,597 $66,539 $66,539

6 25 $1,906 $1,906 $2,018 $2,044 $2,323 $2,414 $2,687 $3,777

7 75 $4,161 $4,151 $4,141 $4,154 $4,485 $4,871 $5,258 $7,498

8 300 $8,879 $9,527 $9,791 $9,996 $12,074 $12,159 $12,170 $19,400

9 300 $13,874 $14,165 $14,627 $17,260 $18,265 $20,733 $25,986 $25,986

10 1500 $43,640 $44,767 $49,248 $58,272 $59,826 $64,447 $79,362 $79,362

11 300 $20,113 $21,363 $23,388 $24,606 $25,039 $27,326 $32,757 $32,757

12 1500 $51,660 $54,262 $56,288 $61,719 $69,844 $73,902 $79,069 $95,494

13A 300 $28,129 $29,268 $30,153 $31,503 $34,436 $36,678 $47,181 $47,181

13B 2000 $69,392 $72,168 $76,907 $82,724 $91,180 $96,249 $108,231 $108,231
dt_nopr_tsd_chp8_092311 8-56 DRAFT

Table 8.7.3 First-Year Operating Cost for Rebuttable Presumption Based on DOE 

Test Procedure ($2010)

Design 

Line

Rated 

Capacity 

kVA

Candidate Standard Level

Base 1 2 3 4 5 6 7

1 50 $288 $256 $233 $233 $218 $186 $161 $161

2 25 $175 $152 $144 $142 $136 $111 $100 $92

3 500 $1,624 $1,519 $1,494 $1,346 $1,323 $1,241 $998 $832

4 150 $767 $676 $605 $605 $605 $599 $492 $396

5 1500 $4,940 $4,620 $4,413 $4,194 $4,137 $3,765 $2,967 $2,967

6 25 $152 $152 $142 $138 $126 $115 $99 $85

7 75 $343 $327 $302 $296 $260 $251 $195 $146

8 300 $993 $844 $706 $649 $488 $446 $443 $322

9 300 $1,212 $1,050 $930 $725 $620 $501 $424 $424

10 1500 $3,638 $3,381 $2,870 $2,324 $2,160 $1,840 $1,493 $1,493

11 300 $1,354 $1,185 $1,065 $942 $889 $693 $513 $513

12 1500 $4,388 $3,738 $3,315 $2,902 $2,690 $2,254 $1,920 $1,600

13A 300 $1,374 $1,221 $1,145 $1,076 $929 $725 $532 $532

13B 2000 $5,322 $4,795 $4,291 $3,840 $3,535 $3,390 $2,676 $2,676

Table 8.7.4 shows the rebuttable payback period as a function of design line and standard 

level. The data indicate the rebuttable presumption is for design lines 7 and 9. For design line 7 

the rebuttable presumption payback is satisfied for all CSLs up to CSL 3; while for design line 9

it is satisfied for candidate standard level 1 only. 
dt_nopr_tsd_chp8_092311 8-57 DRAFT

Table 8.7.4 Payback Period for Rebuttable Presumption

Design 

Line

Rated 

Capacity 

kVA

Candidate Standard Level

1 2 3 4 5 6 7

1 50 16.4 9.6 9.5 10.1 11.6 17.3 17.3

2 25 18.8 16.1 15.7 15.2 18.0 20.6 23.2

3 500 6.9 8.0 6.1 5.8 5.7 9.9 18.0

4 150 12.9 6.6 6.6 6.6 6.7 13.7 23.1

5 1500 13.5 14.0 11.7 11.5 10.7 18.3 18.3

6 25 NA** 14.8 11.3 17.6 14.7 16.4 32.3

7 75 0.1* 0.5 0.9 7.4 10.7 8.7 20.2

8 300 5.3 3.5 3.7 7.1 6.7 6.6 17.7

9 300 2.0 3.3 8.4 8.3 10.9 17.9 17.9

10 1500 7.2 10.4 13.2 12.4 13.4 19.9 19.9

11 300 10.7 15.2 12.1 11.5 12.1 17.1 17.1

12 1500 6.4 6.5 10.1 12.3 12.0 13.1 18.9

13A 300 10.8 11.8 14.7 15.4 14.4 25.9 25.9

13B 2000 9.2 9.2 10.8 14.7 15.3 16.0 16.0

* Values less than 3 indicate a rebuttable presumption that the standard level is economically justified.

** Not applicable
dt_nopr_tsd_chp8_092311 8-58 DRAFT

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