9-i CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTEN TS

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

9.1.1 Analyzed Product Classes, Market Sectors, and Market Segments ........................... 9-3

9.2 SHIPMENTS MODEL METH ODOLOGY .................................................................... 9-4

9.2.1 Conceptual Framework of the Shipments Model ...................................................... 9-4

9.2.1.1 Lighting Demand Module .............................................................................. 9-6

9.2.1.2 Consumer Choice Module ............................................................................. 9-7

9.2.1.3 Price Learning Module .................................................................................. 9-9

9.2.1.4 The Coupled Model ..................................................................................... 9-11

9.2.2 Lamp Specific Modeling and Assumptions ............................................................. 9-11

9.2.2.1 Modeling Lighting Demand for New Construction and Renovations ......... 9-13

9.2.2.2 Modeling the Retirement of Lamps and Lamp- and

- ballast Systems ........... 9-14

9.2.2.3 Incandescent Reflector Lamps: Turnover and Shipments ........................... 9-25

9.2.2.4 General Service Fluorescent Lamps: Turnover, Consumer Choice, and Shipments ..................................................................................................... 9-27

9.2.2.5 General Service Fluorescent Lamps: Market Shares and Stock Shares ...... 9-35

9.3 MODEL CALIBRATION AN D INPUTS ..................................................................... 9-36

9.3.1 Estimation of Historical Shipments and Initial Market Shares ................................ 9-36

9.3.2 Sources of Historical Shipments Data ..................................................................... 9-36

9.3.3 Subdivision of Historical Shipments by Sector, Product Class, and Technology ... 9-38

9.3.4 Consumer Choice Model Calibration ...................................................................... 9-39

9.3.5 Price Learning .......................................................................................................... 9-44

9.3.6 Lamp and Ballast S ystem Assumptions ................................................................... 9-46

9.3.6.1 Ballast Substitution Assumptions ................................................................ 9-47

9.3.6.2 General Service Fluorescent Lamp Characteristics ..................................... 9-49

9.3.6.3 Incandescent Reflector Lamp Characteristics .............................................. 9-53

9.3.6.4 Lamp Usage Assumptions ........................................................................... 9-54

9.3.7 Rare Earth Costs ...................................................................................................... 9-58

9.4 ALTE RNATIVE ANALYSES ...................................................................................... 9-59

9.4.1 Overview .................................................................................................................. 9-59

9.4.2 Light Emitting Diode Impact Determination ........................................................... 9-61

9.4.3 Alternative Incandescent Reflector Lamp Technology ........................................... 9-62

9.5 RESULTS ...................................................................................................................... 9-63

9.5.1 Results of Analyses of Candidate Standards Cases ................................................. 9-63

9.5.2 Results of the Alternative Analyses ......................................................................... 9-679- ii LIST OF TABLES

Table 9.1.1 Candidate Standard Levels Assumed for Each Candidate Standards Case for Each of the Modeled Product Class Groupings ............................................. 9-2

Table 9.1.2 Product Class Groupings Used in the Shipments Model ..................................... 9-3

Table 9.2.1 IRL Options Used in Shipments Model ............................................................... 9-5

Table 9.2.2 GSFL Product Class Groupings and Lamp Options Used in Shipments

Model ................................................................................................................... 9-5

Table 9.2.3 The Parameters and Time Units of the Weibull Distributions Used in the Shipments Analysis ............................................................................................ 9-15

Table 9.2.4 Scaling of Lamp Lifetime with Average Hours of Lamps Use per Start ........... 9-22

Table 9.2.5 Ballast Substitution Matrix ................................................................................ 9-29

Table 9.3.1 Fraction of Lamp Shipments Assumed to be from NEMA Members ............... 9-36

Table 9.3.2 Fraction of Ballast Shipments Assumed to be from NEMA Members ............. 9-37

Table 9.3.3 Input Data for Logit Parameter Calibration ....................................................... 9-40

Table 9.3.4 Logit Parameter Results from Calibration ......................................................... 9-41

Table 9.3.5 Bass Adoption Model Parameters ...................................................................... 9-41

Table 9.3.6 Ballast Acceptance Factors and Lifetime Reduction Factors ............................ 9-43

Table 9.3.7 Lamp Acceptance Factors .................................................................................. 9-43

Table 9.3.8 Data Extracted from Current Industrial Reports (CIRs) for Price Learning Analyses ............................................................................................................. 9-44

Table 9.3.9 Properties of Average Ballasts for Pro duct Class Groupings ............................ 9-46

Table 9.3.10 Ballast Substitution Matrix: Retrofits and Renovations .................................... 9-48

Table 9.3.11 Properties of Representative GSFL Options: Baseline and All CSLs ............... 9-49

Table 9.3.12 GSFL Options for Different Ballast Types ........................................................ 9-50

Table 9.3.13 Properties of Representative GSFL Lamp

- and

- ballast Systems ........................ 9-51

Table 9.3.14 IRLs: Representative Properties for Baseline and CSL 1 Lamps ...................... 9-53

Table 9.3.15 Commercial Sector Annual Hours of Lamp Use and Starts per Day ................ 9-54

Table 9.3.16 Industrial Sector Annual Hours of Lamp Use and Starts per Day ..................... 9-55

Table 9.3.17 Residential Sector Annual Hours of Lamp Use and Starts per Day .................. 9-56

Table 9.4.1 Definition Alternative Analyses ........................................................................ 9-60

Table 9.4.2 Summary of Variable Assumptions for Best Estimate and Alternative Analyses ............................................................................................................. 9-60

T able 9.4.3 IRL Lamp Life Assumptions for Best- Estimate and Alternative Technologies that Meet a CSL 1 Standard ........................................................ 9-63

Table 9.5.1 Best Estimate of Cumulative Shipments of GSFLs and IRLs from 2017 – 2046, for Each of the Candidate Standards Cases ............................................. 9-64

Table 9.5.2 Effects of Candidate Standards Cases on Cumulative Shipments Compared to Base Case for GSFLs and IRLs, Best Estimate ........................... 9-67

Table 9.5.3 Cumulative Shipments of GSFLs and IRLs from 2017 – 2046, for All CSL 1 and Max CSL, Alternative Analyses ...................................................... 9-689- iii LIST OF FIGURES

Figure 9.2.1 Schematic Representation of the Consumer Choice Model ................................ 9-8 Figure 9.2.2 Schematic diagram of the annual ballast turnover in the shipments model, including the effect of the consumer choice model and LED incursion. ........... 9-32 Figure 9.3.1 Generic lighting Bass diffusion curve ................................................................ 9-41 Figure 9.3.2 IRL Learning Curve ........................................................................................... 9-45 Figure 9.3.3 GSFL Learning Curve ........................................................................................ 9-45 Figure 9.3.4 Ballast Learning Curve ...................................................................................... 9-45 Figure 9.3.5 Inflation -Adjusted, Tri-band Phosphor REO Price Index for GSFLs ................ 9-58 Figure 9.4.1 LED Incursion Curve Projections for GSFLs and IRLs, Best Estimate ............ 9-61 Figure 9.4.2 Lumen Capacity of GSFL, IRL, and Combined GSFL and IRL displaced by LED (Total LED), Best Estimate .................................................................. 9-62 Figure 9.5.1 Historical and Projected Shipments of GSFLs by Product Class Grouping,

Best Estimate ..................................................................................................... 9-65 Figure 9.5.2 Historical and Projected Shipments for IRLs, Best Estimate ............................ 9-669-1 CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

The U.S. Department of Energy ( DOE ) developed a consumer

- choice -based model to estimate shipments of general service fluorescent lamps (GSFLs) and incandescent reflector lamps (IRLs). The model projects consumer purchases (hence shipments) based on sector

specific consumer sensitivities to first costs and operating costs of lamps, as revealed by

histo rical data

. To account for non-economic consumer behaviors a technology diffusion model

and a technology acceptance factor are superimposed on the shipments model. The model allows switching across product classes, where there is historical evidence that switching has occurred.

Because of the complexity of the consumer -choice-based shipments analysis, the shipments model was executed as a separate computer model written in the Python language. The inputs and outputs of the shipments model were embedded i n the national impact assessment
(NIA) model, which is coded in a Microsoft Excel ® spreadsheet which are available on regulations.gov, docket number EERE–2011– BT

– STD –0006 at www.regulations.gov/#!docketDetail;D=EERE-2011- BT

- STD -0006.

Shipments projections are a necessary input to calculations of the national energy savings (NES) and net presen t value (NPV) in the NIA , as well as to the manufacturer impact analysis (MIA). F or each product class of lamps DOE projected the change in shipments that would occur

under different candidate standards cases

. Because the model ac counts for product switchi ng across compatible products, exploring the impact of a standard on any given product requires

that the standard levels for all substitutable products be set as well. Accordingly, developing a candidate standards case (CSC) involves setting the assumed candidate standard level (CSL) for all analyzed product class groupings (as defined in section 9.1.1 ), using the CSLs defined in the engineering analysis (chapter 5 of this TSD ).

In this preliminary analysis DOE defined four candidate standards cases to explore the potential range of energy savings, costs, and benefits obtainable from the standards . DOE first

considered two CSCs:

**•** the All CSL 1 CSC, in which the standards were assumed to be set at CSL 1 for all product class groupings, and ‘

**•** the Max CSL CSC, in which the standards were assumed to be set at the maximum CSL for each product class grouping. (I n practice this is CSL 2 for 4 -foot medium bipin ( MBP ) GSFLs and CSL 1 for all other product class groupings. )

DOE also considered a variation on each of these:

**•** the All CSL 1 Except T5=Baseline CSC and

**•** the Max CSL Except T5=Baseline CSC

.

In these variations the T5 standard was kept at the existing standard level (the baseline) to test if this might result in a greater migration to T5s (which generally have higher efficacy than9-2 T8s) a Table 9.1.1 and

, therefore

, in higher overall NES and NPV. shows the assumed s tandard

level s for the modeled product class groupings (defined in the table and discussed in section

9.1.1 ). T he baseline and CSL s are as described in the engineering analysis (chapter 5 of this

TSD ).

Table 9.1.1 C andidate Standard Levels Assumed for Each Candidate Standard s Case

for Each of the Modeled Prod uct Class Groupings

Modeled Product

Class Grouping Base case (No new standards) All CSL1

Standard Max CSL

Standard All CSL 1 Except

T5 = Baseline Max CSL Except

T5 =

Baseline

GSFLs

4

- foot MBP * Baseline CSL1 CSL2 CSL1 CSL2

8

- foot SP ** s limline Baseline CSL1 CSL1 CSL1 CSL1

8

- foot RDC † HO †† Baseline CSL1 CSL1 CSL1 CSL1

4

- foot T5, MiniBP SO ‡ Baseline CSL1 CSL1 Baseline Baseline

4

- foot T5, MiniBP HO Baseline CSL1 CSL1 Baseline Baseline

IRLs

IRL Baseline CSL1 CSL1 CSL1 CSL1

* MBP = medium bi

- pin

, ** SP = single pin

, † RDC = recessed double contact

, †† HO = high output

, and

‡ SO = standard output

.

To evaluate the im pact of the candidate standard s case s on shipments of the two categories of la mps— GS FL s and IRLs— DOE calculated the difference between the standards

case shipments and those of the corresponding base case for each product class grouping. All assumptions for a given standards case are identical to those of its corresponding base case

, except that lamp opti ons that do not meet the standard are excluded in the standards case

. The cumulative impact of each CSC on shipments is determined by summing the annual impacts over

the 2017 through 2046 analysis period.

For each CSC, DOE calculated its best estimate of the impact of the CSC on shipments, broken down by product class grouping. In addition to the best estimate analyses

, DOE ran alternative analyses for three main purposes in this preliminary analysis:

**•** Uncertainty Analysi s : To ga uge the importance of uncertainties in rare earth oxide (REO) prices on GSFL prices and the ir impacts on shipments, NES , and the NPV, DOE ran model scenarios using high and low estimates of REO prices.

**•** Impact Determination

a All lamp efficacy data used in the shipments analysis and the NIA reflect lamp operations at 35 o C, as developed in the engineering analysis (see chapter 5 of this TSD). : To determine the impac ts of the expected growth of s olid

- state lighting (lighting using light emitting diodes (LEDs)) and of lighting controls on shipments, NES, and NPV, DOE ran scenarios both with and without the expected growth included in the best estimate scenario

.9-3 **•** Alternative Technology Option : To te st the potential impact of manufacturers respond ing to an IRL standard by developing higher- wattage, shorter -lived lamps, DOE ran a scenario in which representative products with these properties were added to the

consumer choices.

This chapter reports the effects on shipments of all the CSCs and alternative analyses

. (Chapter 10 of this TSD, which covers the NIA , describes the resulting effect s on NES and

NPV .) Section 0 presents the model m ethodology. Section 9.3 describes model calibration and inputs. Section 9.4 describes the alternative analyses

. Section 9.5 presents the shipments projections for the GS FL and IRL base cases, standards cases , and alternative analyses

.

9.1.1 Analyzed Product Classes, Market Sectors

, and Market Segments

For the purposes of projecting future shipments, DOE modeled the product class groupings and sectors shown in Table 9.1.2

. DOE aggregate d product classes into a smaller set of product class groupings, constrained by the representative products identified in the engineering analysis (chapter 5 of this TSD) and by the lack of sufficient disaggregation of shipments data needed to determine market shares by product class (see, chapter 3 of this TSD ). The properties of the representative products were assumed to reflect the product class grouping as a whole. Specifically , DOE used GSFL lamps with a correlated color temperature ( CCT ) less than 4,500K to be representative of those greater than or equal to 4,500K, and it used standard spectrum IRLs with diameters greater than 2.5 inches operating on less than 125 volts as representative of all covered IRLs.

Table 9.1.2 Product Class Groupings Used in the Shipments Model Product Class Grouping Sector

GSFLs Residential Commercial and Industrial

4

- foot MBP X X

8

- foot SP s limline X

8

- foot RDC HO X

4

- foot T5, MiniBP SO X

4

- foot T5, MiniBP HO X

IRLs Residential Commercial

All IRLs X X

DOE did not directly model shipments of 2-foot U- shaped lamps because of their relatively small market share. Following the procedure adopted in the 2009 GSFL- IRL rulemaking 1

, DOE scaled the results from the 4 -foot MBP product class to approximate the NES

and NPV of the 2-foot U- shaped product class. Specifically, it assumed that U-shaped lamps maintain a market share equivalent to 1/25 th of the 4 -foot MBP market, based on the ratio of the sum of shipments of 4-foot MBP T8s from 2006 – 2011 and the sum of 2-foot T8 U-shaped lamps during the same period reported by the National Electrical Manufacturers Association ( NEMA ) (see chapter 3 of this TSD ).9-4 For all product class groupings DOE aggregated across the commercial and industrial sectors, because of both the similar applications for these product classes and the relatively small

contribution of the industrial sector. Residential usage of GSFLs was considered neglig ible for all lamp types except for 4 -foot MB P lamps.

In addition to modeling the representative products described previously , DOE incorporated T12 lamps into its shipments analysis. While new production of T12 lamps appears unlikely under the 2012 lamp efficiency standards, because of their relatively long lifetimes and their large historical market share, they still constitute a significant fraction of the existing lighting stock. Therefore, the shipments model addresse s replacements for existing s tock of T12 lamps and ballasts with new T5 and T8 lamps and ballasts . Specifically, the model includes three additional T12 product classes: 4-foot MBP T12, 8 -foot SP slimline T12, and 8-foot RDC HO T12 lamps. DOE assume d that no new lamp- and

- ballast syste ms would be shipped during the analysis period for any of these product classes, but DOE d id model new shipments of T12 lamps for the relamping of existing systems, as T12 lamps are available that are exempt from

current standards.

In its projections of I RL shipments , DOE aggregat ed across all IRL product classes (standard - versus modified-spectrum, less than and greater than or equal to 125 V, and less than or equal to and greater than 2.5 inches in diameter). IRL products not directly modeled were

scaled using 120V PAR-38 Standard Spectrum lamps, which constitute an estimated 56 percent of IRL covered products. b

9.2 SHIPMENTS MODEL METH ODOLOGY DOE believes that the national impacts w ould be similar for other product classes not directly analyzed. By aggregating the product classes, DOE assumed that

there w ould be no significant migration of shipments or stock between lamps in different product

classes. As with the modeling of 4 -foot MBP G SFL shipments, DOE aggregated commercial sector IRLs, analyzing residential lamps separately.

This section describes the conceptual framework of the model and the modeling assumptions. Model calibration and inputs are addressed in section 9.3

.

9.2.1 Conceptual Framework of the Shipments Model

The ship ments model estimates the changing market distributions of the covered lamps by product cla ss grouping broken down by efficiency level for input to the NIA analysis. In its shipments and NIA modeling, DOE used the properties of the representative products identified in the engineering analysis (chapter 5 of this TSD ) to represent the lamp option s available to consumers at the different efficiency levels. Table 9.2.1 and Table 9.2.2 s ummarize the wattages and efficacies of representative IRL and GSFL options that meet the indicated efficiency levels

in all product class groupings. Table 9.2.2 also includes lamp option identifiers (IDs) that are

used in section 9.3 to further describe model assumptions about the properties of GSFL lamps

b The 56 percent estimate is based on NEMA shipments from 2006

– 2011 (chapter 3).9-5 and of lamp- and

- ballast systems. As shown, i n some cases
, there are multiple representative lamps options for a given baseline or CSL. (F or a complete listing of IRL properties

, see T able

9.3.14 ) A more complete description of the characteristics of these representative products is presented in section 9.3.6.2 and section 9.3.6.3.

Table 9.2.1 IRL Options Used in Shipments Model

Lamp Option Nominal Wattage Efficacy (lm/W)

Baseline 1 60 17.8

Baseline 2 60 18.3

CSL 1 55 20

Table 9.2.2 GSFL Product Class Groupings and Lamp Options Used in Shipments

Model

Product Class Grouping CSLLampOption IDLampDiameterNominalWattageEfficacy(lm/W)

4

- foot MBP Baseline L1.0.1 T8 32 89.2

CSL1 L1.1.1 T8 32 90.0

CSL2 L1.2.1 T8 32 95.4

L1.2.2 T8 28 96.0

L1.2.3 T8 25 93.0

8

- foot SP

slimline Baseline L2.0.1 T8 59 98.2

CSL1 L2.2.1 T8 59 99.0

L2.2.2 T8 54 105.6

L2.2.3 T8 50 108.0

8

- foot HO Baseline L3.0.1 T8 86 93.0

CSL1 L3.2.1 T8 86 95.3

T5 SO Baseline L4.0.1 T5 28 104.3

CSL1 L4.2.1 T5 28 109.7

L4.2.2 T5 26 111.5

L4.2.3 T5 25 116.0

T5 HO Baseline L5.0.1 T5 54 92.9

CSL1 L5.2.1 T5 54 97.3

L5.2.2 T5 50 100.0

L5.2.3 T5 47 102.1

Lamp

- and

- ballast interactions were explicitly addressed in the shipments model for two

reasons

. First, the existing ballast limit s the lamp options available to consumers. Second, the ballast to which a lamp is paired affects it s energy use, which in turn affects lamp and ballast shipments in the consumer choice module through its effect on operating costs. Therefore, the shipments model first computes ballast shipments before it calculates GSFL shipments. DOE9-6 estimated the national average energy consumption of GSFLs by modeling GSFLs in each product class grouping as if they were installed on a national average ballast (or one of several

such ballasts in the case of 4

- foot MBP lamps) with properties listed in Table 9.3.9

.

The model has three main interacting elements: (1) a lighting demand module, which estimates the demand for GSFL and IRL lighting for e ach year of the analysis period ; (2 ) a consumer choice module, which assigns shipments to product classes and efficacy levels based on consumer sensitivities to first costs and operation and maintenance costs; and (3 ) a price learning module, which projects future lamp and ballast prices based on historic price trends. To account for product switching, the consumer choice model consults lamp s ubstitution matri c es, which specify the allowable product choices that consumers have available (lamps or lamp

- and

ballast combinations), depending on whether they are renovating lighting systems, installing lighting systems in new construction , or simply replacing lamps. Based on the estimated prices,

the consumer choice model allocates the national lumen demand to the product class groupings

and la mp options for each year of the analysis period , subject to the constraints of the standards

case under consideration

.

9.2.1.1 Lighting Demand Module

A central assumption of the model is that the amount of light needed to fully light a space (lumen capacity dema nd per square foot, measured in units of lumens per square foot ) is

assumed to remain unchanged over the analysis period. That is, sector

- specific lighting demand stays constant in terms of the total lumen capacity per square foot , where lumen capacity is the total maximum (non -dimmed) light output. However, total national lumen demand grows proportionally with floor area (residential, commercial, and industrial) . Therefore, the total lumen demand was adjusted based on the sector- specific floor

- space growth rates extracted from Annual Energy Outlook 2012 (AEO 2012)

. 2

While lumen capacity demand per square foot is expected to remain constant, DOE expects the demand for GSFL and IRL products to be eroded by increased penetration of solid

state lighting ( i.e., lighting that uses LEDs for illumination) into the market. For its best

- estimate (reference) scenario s, DOE assume d th at LED penetration would match the LED incursions

forecast for DOE’s S olid

- State Lighting Program 3 9.4.2 , as described in s ection

.

At the same time that LED lighting is eroding GS FL and IRL lumen capacity demand per square foot, the increasing penetration of lighting controls is expected to erode the lumen -hour

demand per year per square foot, by turning lights off or down when they are not needed or

wanted. While that erosion in conventional lighting demand will mainly affect energy use and

, therefore

, the NIA , controls penetration can have an in direct effect on lamp shipments via its impact on lamp lifetime. DOE’s projection of lighting controls penetration over the analysis period is described in appendix 9 A. The impacts on lamp lifetimes are described in section

9.2.2.2

.9-7 9.2.1.2 Consumer Choice Module

The consumer choice module constitutes the analytical heart of the shipments model. In each year of the analysis period the consumer choice model assigns the market share of new purchases (shipments) to each product class grouping , and to each CSL within each product class grouping, subject to the lamp options (or lam p- and

- ballast options, as appropriate ) that are

available to the consumer. The simplifying assumption of the model is that lamp efficacies exist only at the discrete levels defined by the CSLs in the engineering analysis. First cost and operations and maintenance ( O&M ) costs are the key variables that the model uses to ‘decide’ which option is selected, where consumer sensitivity to first costs and O&M costs are inferred

from historic al data.

For fluorescent lamps the shipments model accounts for the costs and energy savings of both the lamps and their associated ballasts. Ballast shipments are tr acked separately from lamps shipments, b ecause ballasts last longer than lamps, and they affect the choice of replacement lamps, but are generally purchased together with a lamp . (T he model assumes that

, when a ballast is replaced

, the lamp (or lamps) is r eplaced with it .) For both the ballasts and the lamps,

the consumer choice model is used to make the selection. When a ballast is replaced, the

consumer choice module is first run to select the ballast type. T he cost calculation assumes that

the first cost for the ballast includes a lamp of average price for that ballast type, and it accounts for the ballast O&M costs (which include the labor cost of lamp replacement, given the average lamp lifetime for that ballast type). The consumer choice module is then rerun to select which specific lamp type is assigned to the ballast, based only on the lamps’ first costs and O&M costs. Details of the modeling are described in section 9.3.4

.

DOE adopted an existing consumer choice model for this p reliminary a nalysis that also

had been used by DOE to project the penetration of solid- state lighting (SSL) into the U.S. lighting market. 3 The model, also used by others, 4

, 5
Figure 9.1.1 allocates market shares as an aggregate of many individual purchasing decisions. As shown in , the consumer choice module couples an econometric conditional logit model with a technology diffusion mod el , using a Bass diffusion curve, 6

6 which limits the technology adoption rate based on historic al observations. The

Bass diffusion curve capture s barriers to market entry

, like lack of consumer information, that diminish over time with consumer exposure to the growing market . As t hose barriers diminish, the product achieves a market share that is more nearly described by the economic factors captured by the logit model.

While the technology diffusion model captures how product adoption increases over time, there are non

- economic reasons for consumer preferences that persist over time and that are not captured in this model; this analysis uses an acceptance factor to capture these deviations

from ec onomic factors. For example, economic factors do not fully explain consumers’ persistent preference for 4 -foot T8 lamps over 8-foot T8 lamps, which might be explained by aesthetics and greater ease in handling. In this p reliminary a nalysis , the logit calib ration was based on aggregate data from T8 and T5 lamps and was used to represent how consumers respond to price. The acceptance factors were used to calibrate the consumer choice module to how the actual marketshares of the product class groupings considered in the shipments model differed from the logitbased predictions, which had been based on the aggregate T8 and T5 datasets. For example, the9-8 acceptance factor was used to reflect the much larger market share of 4 -foot , rather than 8-foot, T8 lamps. The logit and diffusion model elements are described in more detail in this section ; t he acceptance factor calibration of the consumer choice model is detailed in section 9.3.4

.

Figure 9.2.1 Schematic Representation of the Consumer Choice Model

The Conditional Logit Model. The conditional logit model calculates the probability that a consumer will purchase product j, (P j )—ba sed on a logistic curve probability function of the

form:

P j ( z ) = e z i
∑ e z i

n i=1 Eq. 9.1

Where :

P

j (z) = the p robability a consumer will purchase product j among n possible options, and

z = the ‘logit’, which is defined as follows:9-9 z

j = β FC ∗ FC j + β OM ∗ OM j Eq. 9.2

Where:

β

FC = consumer sensitivity to first cost,

FC j = first cost of product option j

, β OM = consumer sensitivity to operations and maintenance cost, and

OM j = operations and maintenance cost of product option j

.

The regression coefficients (beta values), which represent the consumers’ sensitivity to

first cost ( β FC ) and O&M cost ( β OM ), are determined from a logistic regression that fits historical shipments, first costs ( FC ), and O&M costs ( OM ) to the logistic curve. Sections 9.2.2.3 and

9.2.2.4 describe how first costs and O&M costs are hand l ed for the two categories of lamps and

for ballasts

.

The Bass Technology Diffusion Curve

. The Bass diffusion curve sets the maximum market share the model will allocate to an individual product class grouping, given the technology diffusion rate for lighting products. If the consumer choice module initially allocates

a market s hare that is too large according to the diffusion curve, the excess share is sent back to the consumer choice module to be reallocated with that particular product option eliminated from

the choice matrix.

A Bass adoption curve is a 2- parameter diffusio n curve widely used to describe how new products enter into markets. The two parameters, CE and CI

, represent external and internal influences, respectively, on markets; see Bass 6 and Pacific Northwest National Laboratory ( PNNL ) 16 for more details. If the fraction of the market is zero at time = 0

, the Bass d iffusion

curve is expressed in the following way:

MS ( t ) = 1 − e − ( CE + CI ) t

1 + � CI

CE � e

− ( CE + CI ) t

Eq. 9.3

Where:

MS ( t ) = market share at time t

, t = t ime since the product was introduced to the market (yr)

, CE = the coefficient of external influence

, and

CI = t he coefficient of internal influence.

9.2.1.3 Price Learning Module

As described previously, the consumer choice model uses product prices as inputs. Consistent with current practice, DOE has adopted a ‘ price learning ’ model to project product prices over the analysis period

. 7

, 8 As originally defined, price learning reflects systematic

decreases in manufacturing costs result ing from cumulative production experience. When price9-10 learning analyses are considered o n an industry- wide basis, rather than at the manufacturer level, and when they include learning effect s downstream of production (for example, increased

efficiencies in product distribution), the price learning curve is typically refe rred to as an experience curve, but it takes the same mathematical form. Consequently a broad range of cost and price metrics have been used to quantify learning rates for appliances and equipment (see, for example, Weiss et al., 2010, Table A1). 9

Historical data are used to estimate the learning i mpact by fitting the data to a learning curve of the following form:

p ( X ) = p init ∗ X −b
Eq. 9.4

Where:

p(X) = t he price of a particular product as a fu nction of cumulative production (2011 dollars),

p init = the initial price of the product at the time of market introduction (2011 dollars),

X = cumulative production (total shipments) of the product from the time of its market introduction (number of units), and

b = a positive constant known as the learning rate parameter

.

As described in section 9.3.5 , DOE used historical price and shipments data from the

U.S. Census to determine the cumulative historical production and prices of lamps and ballasts sold into the U.S. market and, thus, to c alibrate the learning rate parameter b

.

Eq. 9.4 can be used to obtain a projection for the price of lamps or fluorescent ballasts in each year, p(y), if the cumulati ve production is written explicitly as a function of time:

X ( y ) = � s ( v ) y−1

v=y init Eq. 9.5

Where:

X(y) = the cumulative production (total shipments) of a product between the year of its

introduction and year y (number of units),

y = the current year,

v = the vintage, or year , in which a product was shipped to market,

y init = the year of the product’s market introduction, and

s ( v ) = the shipments in vintage year v (number of units; see Eq. 9.35

, Eq. 9.38 , and Eq.

9.43 )9-11 Eq. 9.4 and Eq. 9.5 can then be combined to compute a price learning factor:

PLF ( y ) = � X ( y )

X ( 2011 ) � −b

Eq. 9.6

Where:

PLF(y) = the price learning factor in year y, and

all other variables are defined in Eq. 9.4 and Eq. 9.5

.

The price learning factor is then used to calc ulate the price of any lamp option in any

year , given its 2011 price

, as determined in the engineering analysis (see c hapter 5 of this TSD ), using the following equation:

p ( y ) = PLF ( y ) × p ( 2011 ) Eq. 9.7

Where:

p(y) = the price of a particular lamp option in year y , p(2011) = the price of a particular lamp option in 2011, and PLF(y) is as defined in Eq. 9.6

.

9.2.1.4 The Coupled Model

The shipments model uses the price learning rate and cumulative production information described in the previous section to calculate the price of each product in any year of the analysis, given the additions to the cumulative production estimate by the shipments model up to that point. Accordingly, the model proceeds step- wise each year to calculate product shipments

based on prices and O&M costs via the demand and consumer choice modules. It t hen calculates the following year’s product prices based on that year’s shipments.

9.2.2 Lamp Specific Modeling and Assumptions

DOE projected the annual shipments of GSFLs and IRLs by comp uting the lighting demand for new construction and lighting renovation, as well as the lighting demand for replacement of failed lamps in each year, to obtain the total demand for new lighting shipments:9-12 D ( y ) = D NCR ( y ) + D F ( y ) Eq. 9.8

Where:

y = the year of the analysis period c
D(y) = the total lighting capacity demand for new shipments in year y (lm)

, ,

D NCR (y) = the total lighting capacity demand for new construction and lighting

renovations (lm) , and

D F ( y) = the national lumen capacity demand for replacement of failed lamps and lamp

and

- ballast systems (lm)

.

DOE then apportioned this demand among the various technology options via the consumer choice module to determine the shipments of each product class grouping or technology option in each year.

Given values for the retirements and new shipments in year y , as well as the total stock in

year y-1 , the stock of lamps or lamp

- and

- ballast systems in year y can be calculated as:

S ( y ) = S ( y − 1 )

− R ( y ) − F ( y ) + s ( y ) Eq. 9.9

Where:

S ( y ) = the national stock of lamps or lamp

- and

- ballast systems in year y (number of units), R(y) = lamps or lamp

- and

- ballast systems retired for lighting renovations in year y (number of units), F(y) = lamps or lamp

- and

- ballast systems that fail (or are removed for scheduled relamping) and are replaced in year y (number of units)

, and s(y) = the total shipments of new lamps or lamp -and- ballast systems in year y (number of units)

.

Eq. 9.9 requires the stock to be initialized at the beginning of the analysis period. The technique for initializing the stock model is described in s ection 9.1.1 . For the purposes of computing the NES in the NIA (chapter 10 of this TSD), however, it is not necessary to compute the total installed stock of lamps and lamp

- and

- ballast systems in the United State s. The only portion of the stock that is relevant to this calculation is made up of lamps shipped during or after the compliance year of the standard being considered, y rule . For this analysis, DOE refers to that relevant portion of the stock as the operating stock shipped during the analysis period (OSSDAP). The OSSDAP in each year, denoted S ′ ( y )

, can be computed from Eq. 9.9 with the assumption that S ′ ( y rule − 1 ) = 0

.

c The time variable y in this analysis is a discrete variable representing the year of the analysis period. Throughout the remainder of this preliminary analysis, however, quantities that depend on y will be written in the form D(y)

, which is more typically used for functions of a continuous variable, rather than the usual subscript form that is conventionally used for discrete variables D y . This is done for the sake of avoiding confusion with other subscripts

used in the notation.9-13 A complication to this basic picture arises in the case of projecting GSFL shipments. The choice of a fluorescent lamp by a consumer depends on the ballast to which the lamp will be coupled. If a consumer is replacing a lamp on an existing ballast, the lamp must be compatible with the ballast. Therefore, the GSFL part of the shipments model must account for the shipments and stock, throughout the analysis period, of ballasts that can be coupled to the analyzed product clas s groupings . DOE t herefore models GSFL shipments in two steps: first

, a turnover model for ballasts is computed to project ballast shipments and stock using the equations described previously; then , the lamp shipments and stock are derived from the ballast projection by com puting the lamp -replacement probability on the projected stock of ballasts.

With that caveat, the equations described previously are the fundamental equations underlying the shipments and stock modeling in this analysis. The remainder of this section wil l be devoted to computing the various components of these equations for IRLs, GSFLs, and for fluorescent ballasts as a preliminary step to computing the GSFL shipments and stock.

9.2.2.1 Modeling Lighting Demand for New Construction and Renovations

To project the lighting demand for new construction, DOE assumed a constant demand for lighting capacity per square foot of floor space (lm/ft 2 at maximum lamp output), so that overall lighting demand grows at the same sector

- specific annual growth rate as floor space. Thus, the annual lighting demand for new construction (D NC ) in a particular sector is given by:

D NC ( y ) = K ( y 0 )[( 1 + γ ) y−y 0

− ( 1 + γ ) y−y 0 −1 ] Eq. 9.10

Where:

D NC (y) = the total lighting capacity demand for new construction (lm)

, K = the total lighting capacity (lm at maximum output) of the installed stock in the sector being analyzed (lm)

, y o = the initial year of the model, and

γ = the sector

- specific , 25- year (2010-2035 ) average floor space g rowth rate projected by

AEO 2012

.

In addition, DOE assumes that a fixed percentage of the lamp stock in each year is removed from service for renovations or lighting retrofits. The number of lighting units (IRLs or

fluorescent lamp

- and

- ballast systems) r emoved for renovations in year y is then:

R ( y ) = S ( y − 1 ) f
ren Eq. 9.11

Where:

R(y) = stock removed for renovation in year y (number of units),

S ( y − 1) = total installed stock (number of units) in year y-1 (computed in the following sections for IRLs and for fluorescent ballasts), and9-14 f

ren = fraction of the stock retired for renovations in each year.

This is added to the new-construction demand to yield the total lighting demand for new

construction and renovation:

D NCR ( y ) = D NC ( y ) + R ( y ) Λ Eq. 9.12

Where:

D NCR ( y ) = total lighting capacity demand for new construction or renovation in year y (lm) , and

Λ = maximum lumen output of the lamp or lamp

- and

- ballast system being considered (lm /unit).

DOE takes the fraction f

ren to be 3% of the total commercial and industrial stock and 1% of the total residential stock, following the assumptions used in the 2011 fluorescent b allast rulemaking. 10

Table 9.1.2 Shipments projections for GSFLs and IRLs are computed independently for the

sectoral breakdowns indicated in

.

9.2.2.2 Modeling the Retirement of Lamps and Lamp-and-ballast Systems

DOE determined the lighting demand for replacement shipments in a given year by computing the number of shipments from previous years that would be ex pected to retire in that

year. DOE based its model for the retirement of lamps and ballasts on the Weibull distribution

. T he probability that a particular unit survives to a time t after its initial installation is:

w S ( t ) = �

exp �− � t − d

λT � k �

, t > d

1

, t ≤ d Eq. 9.13

Where:

w

S ( t ) = the probability that a unit survives to time t after its initial installation,

t = the time since installation, in units of either hours or years, which is always nonnegative,

T = a characteristic lifetime for the lamp or ballast, in the same units as t

, d = a delay parameter specifying the minimum lifetime of the unit , in the same units as t

, k = a parameter controlling the shape of the distribution, and

λ = a parameter controlling the characteristic retirement age.

The specific parameters and time units that DOE used to specify the survival probability of different lamps and ballasts are summarized in Table 9.2.3

. Their derivations are described

later in th is section.9-15 Table 9.2.3 The Parameters and Time Units of the We ibull Distributions Used in the Shipments Analysis

Product Time

Units Delay
parameter
d Weibull shape
parameter k Weibull

scale
parameter λ Characteristic

Lifetime T

IRL Hours 0 4.26 1.02 Lamp life hours ( Table 9.3.14 )

GSFL Hours 0 5.50 1.10 Lamp life hours ( Table 9.3.13 )

Fluorescent ballast

– Residential Sector Years 2.00 2.50 1.02 15.0

Fluorescent ballast

– Commercial Sector Years 1.50 5.00 1.04 12.6

Fluorescent ballast

– Industrial Sector Years 0 5.00 0.92 10.3

It is more computationally useful in many cases to utilize the probability that a lamp retires during some well

- defined time interval —during the tenth year of its life, say, or the 5,000 th hour of its operation. In this discussion, the probability that a unit retires between time t-1

and time t is written as:

w R ( t ) = w S ( t − 1 )

− w S ( t ) Eq. 9.14

Where:

w R ( t ) = the probability that a unit retires between time t- 1 and time t

,

w

S ( t ) = the survival probability defined in Eq. 9.13 , and

t = the time since installation as defined following Eq. 9.13

.

IRL Retirement

. As described previously , the Weibull retirement distribution for IRLs depends on the characteristic lifetime, T, of the IRL. To determine T for the purposes of the shipments modeling, the rated lifetime for each lamp option given in the engineering analysis (chapter 5 of this TSD ) is adjusted to account for the impact of dimmers on lamp life. Operating an incandescent lamp dimmed ( i.e., at reduced wattage) increases lamp lifetime, often by a significant factor.

To account for this, DOE made use of the dimmer

- related correction factors discussed in appendix 6A of this TSD. DOE assumes that operating a lamp on a dimmer will lead to a 20% reduction in energy consumption on average; this corresponds to a factor of 3.94 increase in lamp lifetime for individual incandescent lamps. DOE assumed that 29% of residential IRLs and 5% of commercial IRLs operate on dimmers and that these fractions are constant with time. d

d Growth in controls penetration for IRLs in the model is assumed to be purely in switch

- based controls, not in dimmers, and growth is assumed to occur only in the commercial sector.9-16 These fractions imply that the national average lamp lifetimes in each sector increase by 8 5% and 15%, respectively. Therefore, in the shipments analysis, DOE adjusts upward by these

amounts the estimated lifetime from the e ngineering a nalysis for IRLs.

DOE use d the Weibu ll retirement distribution to compute an IRL survival function that is defined as a function of the total hours of lamp use (see Table 9.2.3 ). Thus, computing the lamp failures in each year required transforming the survival function from a function of the hour h to a function of the year a of a particular lamp’s lifetime. DOE did this by convolving the Weibull

retirement distribution

, Eq. 9.14

, with the same sector -specific hours- of -use distribution, f(u)

, that was used in cal culating the life

- cycle cost ( LCC ) (chapter 8 of this TSD) e

P R ( a ) = � w

R ( h ) f ( h / a ) h max

h=0 :

Eq. 9.15

Where:

P

R ( a ) = probability of lamp retirement in year a of lamp’s life,

w R ( h ) = the Weibull retirement function, as defined in Eq. 9.14

,

a = the lamp’s age (yr)

, h = the total time that the lamp has been operated (hr)

, h

max = the maximum expected lifetime of a lamp (hr) , and f(h/a) = hours of use distribution f(u) evaluated at the value u=h/a

.

To parameterize the Weibull distribution in Eq. 9.15 , DOE uses the parameters determined from laboratory testing of incandescent lamp failure rates

. 11 Table 9.2.3 These parameters are listed in

.

From the probability function

, Eq. 9.15

, one can calculate the average lamp lifetime measured in years, L, with all parameters defined as in Eq. 9.15 :

L = � aP

R ( a ) ∞

a=0 Eq. 9.16

It is also possible to use th at probability function to compute the expected lamp failures in year y , given a time series of historical shipments spanning the maximum exp ected age reached by any lamp, a max :

e In princ iple this distribution should be adjusted to account for the increasing penetration over the analysis period of

switch

- based controls, like timers and occupancy sensors, in the commercial sector. However, the impact of this effect is relatively small (typ ically around 15% on average across all shipments if controls reduce usage by 30%) and will have a negligible impact given the very short lifetimes of commercial IRLs, so DOE neglects this effect in its shipments analysis. However, the impact on energy con sumption of switch

- based controls is accounted for in the

NIA.9-17 F IRL ( y ) = � P

R ( y − v ) y−1

v=y−a max s IRL ( v )

Eq. 9.17

Where:

F

IRL ( y ) = f ailures of IRLs in year y (number of units),

y = current year,

v = vintage, or year, of shipments,

a max = maximum expected lamp lifetime (yr ),

P

R ( y − v ) = probability of lamp failure in year a=y

- v of a lamp’s lifetime, and

s IR L ( v ) = shipments that occurred in a particular vintage (number of units).

DOE uses the equations just defined , along with historical shipments data, to compute the lamp failures that require replacement in each year. The lighting capacity demand that must be met to replace these failed lamps is then:

D F

, IRL ( y ) = F IRL ( y ) ΛC L Eq. 9.18

Where:

D F

, IRL ( y ) = l ighting capacity demand to replace failed lamps in year y (lm)

, F

IRL ( y ) = lamp failures in year y (number of units),

Λ = maximum lumen output of the lamp being considered (lm /unit), and

C

L = a lifetime correction factor.

The lifetime correction factor C L = max ( L , 1 ) , where L is the lamp lifetime in years ( Eq.

9.16 ), is necessary to account for lamps with average lifetimes shorter than one year, which will yield multiple shipments per fixture per year , which will not be operated simultaneously. The total lighting demand is then D IRL =D NC R,IRL + D F,IRL (where D NCR,IRL is the demand for IRLs in new construction and renovations)

. In practice, DOE computes the demand independently for

each of the three lamp options considered in the e ngineering analysis for IRLs (Baseline 1, Baseline 2, and CSL 1).

Fluorescent Ballast Retirement

. To compute the demand associated with the replacement of retired ballasts, DOE follows the ballast retirement model used in the 2011

f luorescent b allast rulemakin g 10 . The probability of a ballast’s retirement from the stock during

year a B of its lifetime is described by a Weibull distribution:9-18 P BR ( a B ) = w R ( a B ) Eq. 9.19

Where:

P

BR ( a B ) = the probability that a ballast retires from the stock in the a B th year since its installation,

w R ( a B ) = the Weibull retirement distribution given in Eq. 9.14

, and

a B = the ballast’s age (yr)

.

The probability that a ballast survives to be a B years old is also described by the appropriate

Weibull function:

P BS ( a B ) = w S ( a B ) Eq. 9.20

Where:

P

BS ( a B ) = the probability that a ballast survives for a B years after installation,

w S (a B ) = the Weibull survival distribution given in Eq. 9.13

, and

a B = the ballast’s age (yr)

.

For ballasts, DOE used a retirement and survival probability defined as a function of ballast age, rather than hours of use as for lamps, for consistency with the 2011 fluorescent

b allast rulemaking analysis. In that analysis, DOE used the sector

- specific model parameters given in Table 9.2.3 , which are the same model parameters used for the present analysis. To model the commercial and industrial sectors jointly in this analysis, DOE used a weighted average of the parameters for the commercial and industrial sector when modeling each product class, a ccording to the relative distribution of each class among the two sectors, as given in Table

4.1 of DOE’s 2010 Lighting Market Characterization (LMC)

. 12

The retirement model for ballasts was developed in the ballast rulemaking from studies

that measured the actual lifetimes of fluorescent ballasts in the field. Thus, DOE assumed that it

includes the effect both of ballasts that fail and of ballasts that are retir ed for renovations. The

num ber of ballasts that are removed from the stock due to failures and renovations in each year is given by:

F B ( y ) + R B ( y ) = � P

BR ( y − v ) y

v=y−a B

, max s B ( v )

Eq. 9.21

Where:

F

B ( y ) = b allast failures in year y from the product class being considered (number of units),

R B (y) = b allasts retiring in year y from the product class being considered (number of units),9-19 y = the model year,

v = the vintage, or year, of shipment,

a B

, max = the maximum expected ballast age (yr ),

s B ( v ) = shipments in vintage year v (number of units) , and

P

BR ( y − v ) = probability of ballast retirement in or before year y − v of the ballast life,

as defined in Eq. 9.19

.

Because renovations are already accounted for as a fixed fraction of the total stock in the computation of D NCR above, this portion of the demand must be subtracted from the total demand for replacing retired ballasts to yield the total demand for replacing failed ballast s:

D F

, B ( y ) = ( F B ( y ) + R B ( y ) ) Λ B ( y ) − S B ( y − 1 ) f
ren Λ B ( y − 1 ) Eq. 9.22

Where:

D F ,B (y) = the lighting demand to replace failed ballasts in year y from the product class being considered (lm)

, Λ B ( y ) = the average lumen output of installed ballasts (lm /unit ) (This depends on the distribution of installed lamps among the various efficiency levels and technology options, computed in s ection 9.2.2.5

. ),

S B ( y − 1) = stock of ballasts in the product category being considered in year y-1 (number of units) ( Eq. 9.38 ), and f

ren = fraction of the stock retired for renovations in each year.

GSFL Retirement

. As is the case with IRLs, the GSFL survival function depends on the

GSFL Weibull retirement fu nction, Eq. 9.14 , which in turn depends on the characteristic lamp lifetime, T . In the case of IRLs, lamp lifetimes were corrected for the effect of lighting controls, before being used by the Weibull function in the shipments model. In the case of GSFLs, the effect of lighting controls is different and more complicated. Increased use of lighting capacity under lighting controls in the commercial and industrial sectors has the effect of shifting lighting systems to programmed start ballasts more rapidly, because fluorescent lighting control systems generally include these ballasts. GSFLs operating on programmed start ballasts tend to last longer than those operating on instant start ballasts. Other effects of lighting controls include increased lamp lifetime due to decreased operating hours as well as decreased lamp lifetimes due to increased switching. DOE assumes the net effect of these two approximately cancel out and considers only the lamp lifetime increase caused by the programmed start ballast itself. This requires no adjustment of GSFL lifetimes obtained from the engineering analysis (chapter 5 of

this TSD ) for the shipments modeling, given that t he model explicitly addresses the shift to

program med

- start ballasts caused by controls, and the model then selects the lamp lifetime appropriate to the ballast it is coupled with (see Table 9.3.13 ).

DOE believes that a certain fraction of GSFLs in the commercial and industrial sector are subject to scheduled group relamping, in which all lamps within a space are replaced simultaneously when they h ave reached a predetermined fraction of their rated lifetime (in hours). DOE assumed that group relampings occur, on average, when lamps reach 85% of their9-20 rated lifetime. To account for this effect, DOE computed the characteristic lamp lifetime by adjusting the GSFL life hours in chapter 5 of this TSD

, according to the following equation.

T = T Rated (1

− 0. 15 f GR ) Eq. 9.23

Where:

T

Rated = the rated lamp lifetime, in hours , and f

GR = the fraction of lamps that are subject to group relamping.

DOE used the group relamping fractions reported in the 2011 ballast rulemaking 10 f or this preliminary analysis. To simplify the model, DOE also assumed that, for each ballast type, all lamps coupled to that ballast have the same rated lifetime, T Rated , and that this is given by the lifetime of the baseline lamp option, which was t aken to be representative of all lamps in the product class grouping.

DOE uses the ballast shipments and stock projections as the basis to compute the shipments and stock of GSFLs. To do this, DOE developed a relamping schedule

, P relamp ( a B )

, which represents the probability that a ballast has a new lamp installed when it is a B years old (provided that it survives to that age). DOE assumes that old lamps are disposed of upon ballast retirement so that all new ballasts are coupled with new lam ps when they are installed. This implies that P relamp ( 0 ) = 1 : that is , there is a 100% probability in the model that a ballast has a new lamp installed when it is first installed.

For a B >0 , the probability of ballast relamping depends on the pro bability of lamp failure

in the h B th hour of the ballast’s operation. The relamping probability also depends on the annual hours of lamp use, u, and on the average number of hours, η

, that the lamp is operated each time it is started, as GSFLs that are switched on and off more frequ ently have degraded lifetimes. For a set of discrete usage patterns across a given sector, the lamp failure probability in each year of

the ballast life is:

P relamp ( a B ) = � � P
relamp ′ �a B u q �η
q �f
q

q , a B > 0

1

, a B = 0 Eq. 9.24

Where:

P

relamp ( a B ) = the probability that a ballast is relamped when it is a B years old

, q = an index specifying a particul ar lighting application with a particular usage pattern,

u q = the average annual hours of lamp use for application q (hr)

, η q = the average hours of use per lamp start for application q (hr)

, f

q = the fraction of all lighting demand associated with application q ,

a B = the number of years since the ballast’s installation (yr) , and9-21 P

relamp ′ ( a B u q | η q ) = the conditional probability that a ballast is relamped in hour
h

B = a B u q of its operation, given an average of η q hours of use per start.

DOE used the distribution of usage hours from the LCC analysis (c hapter 8 of this TSD)

to determine u q and f q . For each application q, DOE also specified an average hours of use per

start, η q , based on industry estimates. The values used in this analysis are given in Table 9.3.15

, Table 9.3.16 , and Table 9.3.17

.

The probability of relamping as a function of the ballast’s operating hours, given its usage pattern, can be computed by summing over the probability that the ballast undergoes its

n th relamping, for all values of n :

P relamp

′ ( h B | η ) = � P
relamp

, n ( h B | η )

n Eq. 9.25

Where:

P

relamp

, n ( h B | η ) = the conditional probability that the ballast has its n th relamping in

hour h b of its operation, given that it is burned for η hours per start,

h B = the number of hours that the ballast has been operated (hr)

, and all other parameters are defined as in Eq. 9.24

.

The sum in Eq. 9.25 is formally an infinite sum, but in practice it is sufficient to compute the first few terms of the sum over a domain limited to the maximum expected ballast lifetime in hours.

The sum can be truncated ; adding extra terms ha s a negligible impact on the probability computed over that domain.

The probability of the n th relamping can be defined recursively from the probability of an individual lamp’s retirement as a function of each individual lamp’s operating hours and the average number of hours per start, P LR ( h L | η )

. The probability of the first relamping on a ballast is just equal to this distribution evaluated at h L = h B :

P relamp

, 1 ( h B | η ) = P LR ( h B | η )
Eq. 9.26

Where:

P

LR ( h B | η ) = the probability that a lamp retirement occurs in hour h L = h B of the lam p’s

lifetime (specified below)

.

The probability of the n th relamping can then be computed recursively for n > 1 using the following equation:9-22 P relamp

, n ( h B | η ) = � P

LR ( h B ′ | η ) P relamp

, n−1 ( h B − h B ′ | η ) h B

h B

′ =0 Eq. 9.27

Where:

all parameters are defined as in the previous equations.

DOE modeled the lamp retirement probability in the above equations as a Weibull distribution whose characteristic lifetime parameter depends on the usage pattern:

P LR ( h L | η ) = w R ( h L ; T ( η ) ) Eq. 9.28

Where:

P

LR ( h L | η ) = the probability of a lamp’s retirement in year h L of its operation (given that its ballast survives that long),

w R ( h L ; T ( η ) ) = the Weibull retirement function ( Eq. 9.14 ), where the dependence on the

characteristic lifetime T has been made explicit,

h L = the number of hours that the lamp h as been operated (hr)

, and

T ( η ) = the characteristic lifetime parameter of the Weibull distribution, which depends

on η

, as described below

.

DOE determined the parameters of this distribution from the lamp failure curves published in chapter 6 of the Lighting Handbook 13

Table 9.2.3 , obtaining the values of k and λ given in

. DOE also determined the scaling of lamp lifetime with η from the same published

curves. T he characteristic lifetime T ( η ) is given by scaling the rated lamp lifetime by a scaling factor that depends on η . Assuming that the rated lamp lifetime reported by manufacturers corresponds to η =3 hours per start, the scaling of lamp lifetime to different values of η is

tabulated in Table 9.2.4 . Combining the previously defined equations, it is possible to compute the relamping schedule P relamp ( l B ) from Eq. 9.24

.

Table 9.2.4 Scaling of Lamp Lifetime with Average Hours of Lamps Use per Start Average burn hours per lamp s tart Lamp mean

lifetime as a percentage of the

nominal lifetime

0.1 24

0.2 38

0.3 45

0.4 50

0.5 54

0.6 58

0.7 619-23 0.8 64

1 70

2 89

3 101

4 110

5 116

6 121

7 125

8 129

10 134

20 149

30 156

40 159

60 161

100 162

The equations above, with some minor modifications, can also be used to derive the average lamp lifetime, measured in years, after accounting for the various usage patterns present in the stock and assuming that the ballast survives throughout the lamp’s life:

L L = � a

B P 1 st relamp ( a B ) ∞

a B =0 Eq. 9.29

Where:

L L = the average lifetime of a GSFL, in years, given that its ballast does not fail during the lamp’s life, and

P

1 st relamp ( a B ) = the probability that a ballast undergoes its first relamping in year a B of
its life, which can be computed from Eq. 9.24 , with the substitution of P relamp

, 1 ( Eq. 9.26 ) for P relamp ′

.

Fluorescent Lamp and Ballast Joint Survival Probabilit y. The relamping schedule depends on the probability P LR that a given lamp is retired, provided that its ballast survives. For some applications in th is p reliminary a nalysis it will be necessary to know the total probability that a lamp survives to a given age, without either being retired on its own or because its ballast is being replaced. This probability depends on the ballast lifetime model and on the probability that a lamp is installed on a ballast of a particular age. It is derived below.

The probability that a particular lamp is installed on a ballast that is in year a B of its life

is:9-24 P LIB ( a B ) = 1

N LIB P relamp ( a B ) P BS ( a B )

Eq. 9.30

Where:

P

LIB ( a B ) = the probability that a lamp is installed on a ballast when the balla s t is a B years old,

P

relamp ( a B ) = the probability that a ballast is relamped in year a B of its life, provided that it survives that long,

P

BS ( a B ) = the probability that the ballast survives to age a B ( Eq. 9.20 ),

a B = the age of the ballast (y r), and

N

LIB = a normalization factor that ensures that this quantity sums to unity.

The probability that a lamp’s ballast is retired in year a L of the lamp’s life is then:

P BRL ( a L ) = 1

N BRL � � P

BR ( a B ) P LIB ( a B − a L ′ ) L B

, max

a B =a L ′ L B

, max

a L

′ =0 Eq. 9.31

Where:

P

BRL ( a L ) = the probability that a lamp’s ballast is retired in year a L of the lamp’s life,

P

BR ( a L ) = the probability that a ballast retires in year a B of its life ( Eq. 9.19 ),

a L = the age of the lamp (yr)

, L B

, max = the maximum ballast lifetime (yr)

, and

N

BRL = a normalization factor that ensures that this quantity sums to unity.

A ll other variables are as in Eq. 9.30

.

The previous distribution can be combined with the lamp retirement and survival probability distributions to give the approximate f

P LBR ( a L ) = 1

N LBR �P

BRL ( a L ) P LS ( a L ) + P LR ( a L ) �1 − � P

BRL ( a L ′ ) a L

a L

′ =0 �� probability that a lamp or its ballast are retired in year a L of the lamp’s lifetime:

Eq. 9.32

Where:

P

LBR ( a L ) = the probability that a lamp or its ballast is retired in year a L of the lamp’s lifetime,

f Eq. 9.32 is only approximately correct

, because it does not account for the growth of the ballast stock over the

summation period. However, as this computation only feeds into the calculation of the stock fractions represented by different technologies, this approximation is sufficient

, given that these fractions do not change rapidly during the analysis period.9-25 P

LS ( a L ) = the probability that a lamp survives to age a L , P

LR ( a L ) = the probability that a lamp is retired in year a L of its life,

N

LBR = is an appropriate normalization parameter, and all other parameters are as in Eq. 9.31

.

The average lamp lifetime and the probability that a lamp and its ballast both survive to lamp age

a L are then simply given by summing over the retirement probability:

L LB = � a

L P LBR ( a L ) ∞

a L =0 Eq. 9.33

P LBS ( a L ) = 1 − � P

LBR ( a L ′ ) a L

a L

′ =0 Eq. 9.34

Where:

L LB = the average lifetime of a GSFL, in years, accounting for the probability that either the lamp or its ballast retires.

P

LBS ( a L ) = the probability that a lamp and its b allast both survive to the end of year a L of the lamp’s life, and all other parameters are as in Eq. 9.32

.

Th e latter equation is the probability distribution that is used in s ection 9.2.2.5 in apportioni ng the lamp stock among the various efficiency levels.

9.2.2.3 I ncandescent R eflector L amps: Turnover and Shipments

Because the three different lamp options considered for IRLs have significantly different lifetimes, it was necessary to explicitly model the shipments for each IRL lamp option separately. Additionally , because of the different usage patterns in each sector, DOE modeled lamps separately in the residential and c omme rcial sectors.

DOE computes the total lighting demand for each lamp option separately within each sector, according to Eq. 9.8

, Eq. 9.12 , and Eq. 9.18

. DOE then reallocates this demand among the

three lamp options using the consumer choic e model, yielding a projection for the shipments of

each lamp option in each year:

s IRL

, l ( y ) = � D k ( y ) Λ k −1 σ kl ( y )

k Eq. 9.35

Where:

s IRL

, l ( y ) = projected shipments for IRL option l in year y (number of units),9-26 D k = the total lighting demand for lamp option k , which is the sum of the demand for replacements and new construction (lm)

, Λ k = maximum lumen output of lamp option k (lm /unit), and

σ kl (y)= the substitution matrix in year y.

The substitution matrix

, σ kl , specifies the fraction of consumers who switch between the lamp options, according to the consumer choice model:

σ kl ( y ) = Λ i C L

, l
Λ

j C L

, k P kl ( z ) A kl ( y )

Eq. 9.36

Where:

Λ k = maximum lumen output of lamp being replaced k (lm /unit),

Λ l = maximum lumen output of replacement lamp l (lm /unit ),

C L, k = lifetime correction factor for lamp k

, C L, l = lifetime correction factor for lamp l

, P kl = probability of purchasing lamp option l from among the available lamp options, given that option k is being replaced, and

A kl (y) = availability matrix.

The availability matrix A kl (y) specifies the products that are available to a consumer who is replacing a failed lamp of lamp option k : it is zero when lamp option l is not a direct substitute

for k, or when lamp option l has been eliminated by a proposed standard in the standards case; it is equal to unity otherwise. In the case of IRLs, all lamp options being considered are directly interchangeable, so A kl (y) =1 for all l except those that would be eliminated by a proposed standard. The choice probability P kl (z) is the probability of purchasing lamp option l from among

the available lamp options, given that lamp k is being replaced, according to the consumer choice

model described in section 9.3

.

As also described in section 9.3

, the logit z depends linearly on the first costs and the annual O&M costs of the available lamps. It is thus an implicit function of time

, because the product price varies in ea ch year according to the learning model, starting from the prices determined for the year 2011 in the engineering analysis. The lamp first costs FC l are given by

th e learning -corrected lamp price, computed from Eq. 9.4 and Eq. 9.5 , plus sales tax and the labor cost for installation determined in the LCC analysis. The O&M costs for IRLs have two components: energy costs and the relative relamping costs, averaged annually, for lamps with

different lifetimes:

OM l ( y ) = p E ( y ) × W l × u � + � 1

L l − 1

max ({ L k }) � FC l

Eq. 9.37

Where:

OM l = the O&M costs of lamp option l ($ /yr ),9-27 FC l = the first cost of lamp option l ($)

, p E ( y ) = the sector

- specific price of electricity , in year y , as forecast in the AEO 2012

reference scenario g

W

l = the national- average wattage of lamp option l (W)

, ($/kWh),

u� = average annual hours of use in the sector being considered (hr)

, L l = the average li fetim e of lamp option l (yr)

, and

max ( { L k } ) = the maximum lifetime of all lamp options (yr)

.

For years beyond the end of the AEO projection, which was in 2035, DOE extrapolated

p E ( y ) from the trend in the period from 2025 to 2035, through 2060, and held prices constant

thereafter. While for the shipments analysis electricity prices are relevant only through the end of the shipments analysis period in 2046, a longer analysis period is required for the NIA, as described in chapter 10 of this TSD

. As d iscussed in section 9.2.2.3 , DOE considers that some

fraction of IRLs is installed on dimmers

. Since the use of dimmers will affect operating wattages

of IRLs , DOE adjusts the rated wattage of each IRL option downward by a factor of 6% and 1% in the residential and commercial sectors, respectively, to account for typical dimming rates and the fractions of lamps that are installed on dimmers in each sector.

DOE us es the model above to project the shipments of each IR L option in each year of the analysis. The input parameters, and their calibration, are discussed in s ection 9.3.4 . Given the projections of failures, renovations, and new shipments in each year, and a calculation of the total operating stock in the initial year of the analysis period, Eq. 9.9 then yields the total operating stock of IRLs in the United States in each subsequent year. DOE also uses that equation to compute the OSSDAP (as described in the text following Eq. 9.9 ) as an input for computing the NES in the NIA (chapter 10 of this TSD ).

9.2.2.4 G eneral Service Fluorescent Lamps: Turnover, Consumer Choice, and

Shipments

As discussed previously , DOE takes a two -stage approach to projecting GSFL shipments,

first by projecting the shipments and stock of fluorescent ballasts, then using this projection as a basis to project lamp shipments. This approach introduces a few complications to the consumer choice model used to compute lamp turnover. For example, if the consumer is purchasing a new lamp

- and

- ballast system, for a lighting renovation or new construction, the choice will depend on

the first cost and O&M cost of the lamp

- and

- ballast system, with the O&M cost also including the pr ice of replacement lamps; but , if the consumer is purchasing only a replacement lamp, the lamp price will be included in the first cost. An a dditional complication also arises because the

g Some model scenarios for the NIA in c hapter 10 of this TSD use the High

- or Low

- Economic

- Growth AEO forecasts for electricity price. In principle, the shipments analysis should also use these forecasts in such cases,

because the different electricity prices will impact the consumer choice model. However, DOE performed a sensitivity analysis using the different AEO forecasts in the shipments model and found negligible impact on the projected shipments. DOE

, therefore

, chose to use only the reference AEO scenario in the shipments analysis, regardless of the electricity price forecast selected for the NIA.9-28 GSFL category includes multiple product class groupings, so the consumer choice model must apportion lighting demand among these product class groupings in addition to the different efficiency levels ( i.e., lamp options) within each product class grouping. To address these issues, DOE treats the choice of lamp and lamp

- and

- ballast system as independent choice events in the

consumer choice model. As the different GSFL product class groupings are not interoperable on the same ballast, DOE assumes in the shipments analysis that a consumer’s choice of a product

class grouping o ccurs when choosing a ballast, while the choice of an efficiency level occurs when choosing a lamp to couple to a new or existing ballast.

Each product class grouping in the model is then represented by one or a few notional ballast types that have properties consistent with the national average for each type. T he 4 -foot MBP T8 grouping is represented by two commercial ballast types (programmed and instant start) and one residential type, and the 4-foot MBP T12 grouping is represented by one commerci al and one residential ballast. All other groupings are represented by a single ballast type. The ballast types are listed in the first column of Table 9.2.5

.

Ballast Shipments

. DOE use s a ballast turnover model that is broadly similar in its operation to the turnover model for IRLs developed in s ection 9.2.2.3 , but there are differences

in the details. DOE determined the total demand for new ballast shipments according to Eq. 9.8

, Eq. 9.12 , and Eq. 9.22 . DOE then apportions this demand among the available product class groupings in two ways. DOE assumes that , when ballasts are replaced due to equipment failure, they are replaced with a ballas t of the same type . In the case of new construction and renovations, how ever, DOE allocates the shipments to different ballast types , using the consumer

choice module. The total shipments of ballasts in ballast type j are then given by:

s B

, j ( y ) = D F

, j ( y )

Λ B

, j ( y ) + � D NCR

, i ( y ) σ ij ( y )

Λ B

, i ( y )

i Eq. 9.38

Where:

s B

, j ( y ) = the shipments of ballasts of type j , in year y (number of units),

D F

, j ( y ) = t he lighting capacity demand for replacements of failed ballasts of typ e j in

year y ( lm)

, D NCR

, i ( y ) = the lighting capacity demand for ballasts of type i in new construction and renovations in year y (lm)

, Λ B

, i ( y ) = the average light output of a ballast of type i in year y (lm /unit)

, and

σ

ij ( y ) = the substitution matrix for ballast s of types i and j

.

The substitution matrix for ballasts, σ ij , is similar to the one defined for IRLs in Eq. 9.36 , but no lifetime correction factors are required:

σ ij ( y ) = Λ B

, i
Λ B

, j P ij ( z ) A ij ( y )

Eq. 9.399-29 Where:

P ij = the probability of purchasing a ballast of type j given that ballast type i is being replaced,

z = the logit variable, defined in s ection 9.2.1 , and

A ij (y) = the availability matrix of ballast types

.

The availability matrix in the ballast turnover model defines whether or not ballast type j

can be considered a substitute for ballast type i . This matrix is fixed throughout the analysis period, and, unlike in the case of lamps, it does not change between the base case and the standards cases, as the candidate standard levels analyzed here will not eliminate any product

classes. Table 9.2.5 summarizes the substituti ons that are available in the ballast choice model.

Notably, as shown in Table 9.2.5

, the consumer choice model does not allow for consumer switching between instant start and programmed start ballasts for the 4 -foot MBP lamps. DOE believes that these different ballast types are generally used in different applications; therefore , these ballast types are not considered interchangeable in the consumer

choice model. To model any switching between instant and programmed start ballast, DOE notes that the latter category is typically used in conjunction wit h automatic lighting controls. Therefore, in each year of the shipments projection, DOE exogenously reallocates a fraction of

the instant start ballast shipments to the programmed

- start category, so that the market share of programmed start ballasts within the 4 -foot MBP product class is equal to the fraction of

commercial floor space implementing controls in that year (see appendix 9A)

.

Table 9.2.5 Ballast Substitution Matrix Description of retiring ballast type Available substitute ballast type s
4

- foot MBP T12 (Commercial Sector) 4

- foot MBP T8 Instant Start (Commercial Sector);

T5 SO

4

- foot MBP T8 Instant Start (Commercial Sector) 4

- foot MBP T8 Instant Start (Commercial Sector) * ; T5 SO

4

- foot MBP T8 Programmed Start (Commercial Se ctor) 4

- foot MBP T8 Programmed Start (Commercial Sector); T5 SO

4

- foot MBP T12 (Residential Sector) 4

- foot MBP T8 Instant Start (Residential Sector)

4

- foot MBP T8 Instant Start (Residential Sector) 4

- foot MBP T8 Instant Start (Residential Sector)

8

- foot SP slimline T12 8

- foot SP s limline T8; 4

- foot MBP T8 Instant Start (Commercial Sector); T5 SO; T5 HO

8

- foot SP s limline T8 8

- foot SP s limline T8; 4

- foot MBP T8 Instant Start (Commercial Sector); T5 SO; T5 HO

8

- foot T12 HO 8

- foot RDC T8 HO; T5 HO

8

- foot T8 HO 8

- foot RDC T8 HO; T5 HO

T5 SO T5 SO

T5 HO T5 HO

* A fraction of these i nstant start ballasts are later reallocated to the p rogrammed s tart category to account for the incursion of lighting controls , as discussed in this section

.9-30 The purchase probability P ij in Eq. 9.39 is determined by the consumer choice model from the logit z , defined in s ection 9.2.1 , which depends on the first cost and O&M costs of each lamp

- and

- ballast system. The first cost for a lamp

- and

- ballast system of ballast type j, for a consumer who is replacing a system of bal last type i, is given by a combination of ballast price, the average lamp price in the previous year, and any costs associated with substitution:

FC ij ( y ) = p B

, j ( y ) + n � lamp

, j � MS

l

, j ( y − 1 ) p L

, l ( y − 1 )

l Eq. 9.40

Where:

FC ij (y) = the total first cost for a consumer switching from product class grouping i to product class grouping j in year y (2011 $)

, p B

, j ( y ) = the purchase price of a ballast in product class grouping j in year y (2011$),
including corrections for learning, as computed using Eq. 9.4 and Eq. 9.5

, n� lamp

, j = the average number of lamps installed on a ballast in product class grouping j

, l = an index specifying a particular lamp option within product class grouping j

, MS l,j (y

- 1) = the market share of lamp option l in product class grouping j in year y -1, determined by the consumer choice model as described in section 9.3 , and

p L

, l ( y − 1) = the purchase price of lamp option l in year y -1 (2011$), including corrections for learning and any rare -earth price scenario corrections, as defined in appendix 9B

.

The market share from the prior year, y- 1, is assumed to define the average lamp price that consumers encounter when choosing between product classes.

The O&M costs associated with a ballast of type j in the choice model are given by the mean fuel costs associated with powering the lamp

- and

- ballast system, as well as the first costs of the new lamps required to relamp the ballast over its lifetime:

OM j ( y ) = p E ( y ) u �

1000 � MS

l

, j ( y − 1 ) SIP l

, j

l + n � lamp

, j n

� relamp

, j � MS

l

, j ( y − 1 )

l p L

, l ( y − 1 )

Eq. 9.41

Where:

OM j (y) = the operation and maintenance costs in product class grouping j perceived by a consumer in year y (2011 $/yr),

p E ( y ) = the price of electricity in year y (2011$/kWh),

S

IP l, j = the average system input power of lamp -and- ballast systems in product class grouping j that have lamp option l installed (defined in Eq. 9.52 ) (W ),

u� = the average annual hours of use in the sector being considered (hrs)

,9-31 n� relamp

, j = the average number of relampings that occur over a ballast lifetime in product

class grouping j , and

all ot her variables are as defined in Eq. 9.40

.

As discussed following Eq. 9.35 , DOE used the sector- specific AEO 2012 forecasts for electricity prices, extrapolated to years beyond 2035. For ballast types that were analyzed in the commercial and industrial sectors joint ly, DOE used a weighted average of those sectors’ price forecasts, based on the fraction of each ballast type found in the stock estimates from DOE’s

2010 Lighting Market Characterization (LMC)

. 12 These fractions are summarized in Table

9.3.13

.

The average number of ballast relampings is given by combining the relamping schedule (discussed in section 9.2.2.2 ) with the ballast survival probability:

n � relamp

, j = � P
relamp ( a B ) P BS ( a B ) a B

, max

a B =0 Eq. 9.42

Where:

n� relamp

, j = the average number of relampings that occur on a given ballast of type j

,

a B = the ballast age (yr)

,

a B

, max = the maximum expected ballast age (yr)

, P

relamp ( a B ) = the relamping schedule, or probability of ballast relamping in year a B of
the ballast’s life, as defined in Eq. 9.24 , and

P

BS ( a B ) = the ballast survival probability, defined in Eq. 9.20

.

DOE uses th is model to project the shipments of fluorescent ballasts in each year of the analysis via Eq. 9.38 . The input parameters, and their calibration, are discussed in s ection 9.3.4

. Given the projections of failures, renovations, and new shipments in each year, and a calculation of the total operating stock in the initial year of the analysis period, Eq. 9.9 yields the total operating stock of ballasts in the United States in each subsequent year. The steps in the ballast shipments turnover model are summarized as a schematic diagram in Figure 9.2.1 , which shows failed ballasts and ballasts removed for renovation leaving the stock, the allocation of demand for new construction and renovation in the consumer choice module, the compilation of the annual shipments projection, and the reallocation of some shipments to LEDs. DOE also uses that equation to compute the OSSDAP (as described in the text following Eq. 9.9 ) as an input for computing the NES in the NIA (chapter 10 of this TSD ).9-32 Figure 9.2.2 Schematic diagram of the annual ballast turnover in the shipments model, including the effect of the consumer choice model and LED

incursion.

G eneral Service Fluorescent Lamp Shipments

. After computing the shipments and stock of fluorescent ballasts, DOE projects the shipments and stock of GSFLs by combining the ballast projection with the relamping schedule defined in Eq. 9.24 . The total operating stock of GSFLs

in the United States is simple to compute from the total operating stock of ballasts:

S GSFL

, j ( y ) = S B

, j ( y ) n � lamp

, j Eq. 9.43

Where:

S GSFL

, j = the total operating stock of GSFLs coupled to ballasts of type j in year y (number of units),

S B

, j = the total operating stock of ballasts of type j in year y (number of units), and

n� lamp

, j = the average number of lamps coupled to a ballast of type j

.

In the context of computing the NES, however, the relevant quantity is not the total stock

but the OSSDAP (described in the text following Eq. 9.9 ). This can be computed by adding the9-33 stock of lamps installed on new ballasts since the rulemaking compliance year y rule to the stock of lamps shipped during or after y rule installed on old ballasts that were installed prior to y rule :

S GSFL

, j ′ ( y ) = S LONB

, j ′ ( y ) + S LOOB

, j ′ ( y )
Eq. 9.44

Where:

S GSFL

, j

′ ( y ) = the OSSDAP of all GSFLs installed on ballast type j (number of units),

S LONB

, j

′ ( y ) = the OSSDAP of lamps on new ballasts— i.e., ballasts installed in y rule or
later —of type j (number of units), and

S LOOB

, j

′ ( y ) = the OSSDAP of lamps on old ballasts— i.e., ballasts installed prior to y rule that have had their lamps replaced since y rule

— of type j (number of units)

.

The two terms on the right hand side of Eq. 9.44 can be computed from the projection of ballast shipments, the probability distribution of ballast retirement over the ballast lifetime, and the probability distrib ution of lamp replacement on an existing ballast over the ballast lifetime. For ballasts installed during or after the compliance ye ar, the operating stock of lamps is:

S LONB

, j ′ ( y ) = � s

B

, j ( v ) P BS ( y − v ) y

v=y rule Eq. 9.45

Where:

S LONB

, j

′ ( y ) = the OSSDAP of lamps on new ballasts (LONB) of type j (number of units),

v = the vintage, or year, of ballast shipment,

y = the model year,

y rule = the compliance year of the proposed new standards,

s B

, j ( v ) = the shipments of ballasts of type j in vintage year v (number of units), defined

in Eq. 9.38

, and

P

BS ( y − v ) = the probability of ballast survival to year y - v of the ballast lifetime,

defined in Eq. 9.20

.9-34 For lamps shipped in or after y rule that are coupled to ballasts installed prior to y rule , the

OSSDAP is:

S LOOB

, j ′ ( y ) = � s

B

, j ( v ) P
surv ( y − v ) C relamp ( y | y rule , v ) y rule −1

v=y 0 Eq. 9.46

Where:

S LOOB

, j

′ ( y ) = the OSSDAP of lamps on old ballasts (LOOB)

— i.e., ballasts installed prior

to y rule that have had their lamps replaced since y rule

— of type j (number of units),

C

relamp ( y | y rule , v ) = the cumulative probability that a ballast has been relamped at least once since the year y rule , given that it was initially installed in the vintage year v , and

all other variables are as defined in Eq. 9.45

.

The cumulative relamping probability is computed by integrating over the differential relamping probability:

C relamp ( y | y rule , v ) = max �1

, � P
relamp ( y ′ − v ) y

y ′ =y rule �

Eq. 9.47

Where:

P

relamp ( y ′ − v ) = the relamping schedule, i.e., the probability that a ballast shipped in
vintage year v is relamped in year y′ ( Eq . 9.24 ), and

all other variables are defined as in Eq. 9.46

.

The projected annual shipments of GSFLs, necessary to compute the equipment costs portion of the NPV, can also be computed from the relamping probability, when combined with the ballast shipment s projection:

s GSFL

, j ( y ) = � s

B

, j ( v ) P relamp ( y − v )

v Eq. 9.48

Where:

s GSFL

, j ( y ) = the shipments of GSFLs installed on ballasts of type j in year y (number of
units),

s B

, j ( y ) = the shipments of ballasts of type j in year y , defined in Eq. 9.38 (number of
units), and

a ll other variables are defined as in Eq. 9.43

, Eq. 9.44 , and Eq. 9.45

.9-35 9.2.2.5 G eneral Service Fluorescent Lamps: Market Shares and Stock Shares

To compute the projected equipment costs and energy consumption for GSFLs, it is necessary to apportion the projected shipments among the various lamp options available for each product class grouping. DOE computes the market share using the consumer choice model developed in s ection 9.2.1.2 . Consumers are assumed to be choosing from among the various lamp options that can be coupled to their installed ballasts, as given in Table 9.3.12

.

The market share of shipments allocated to lamp option l of lamps installed on ballast

type j is given by:

MS l

, j ( y ) = P l

, j ( z ( y ) )
Eq. 9.49

Where:

MS l,j (y) = the market share of lamp option l among lamps installed on ballast type j during year y , y = the model year,

P

l

, j ( z ) = the consumer choice probability of selecting lamp option l , as defined in

s ection 9.2.1.2 , and

z = the logit variable of the consumer choice model.

The lo git z depends on the first cost and the average annual O&M cost of each lamp option. For a GSFL, the first cost is simply the sum of the purchase price (including sales tax) and the lamp installation cost. The average annual O&M cost for each lamp option i s simply the electricity cost associated with operating the lamp on a ballast with the average ballast factor for the product class for the sector -specific average annual operating hours. The average annual operating -hour values in each sector are computed as a weighted average of the annual hours of use in each of the building applications documented in section 9.3.6.2

.

The market share projection for each lamp option can be converted to shares of the OSSDAP by summing over the market shares in prior years:

φ l

, j ( y ) = ∑ MS l

, j ( y ′ ) s GSFL

, j ( y ′ ) P LBS ( y − y ′ ) y ′

y ′ =y rule ∑ s GSFL

, j ( y ′ ) P LBS ( y − y ′ ) y

y ′ =y rule Eq. 9.50

Where:

φ l

, j ( y ) = the fraction of the OSSDAP of GSFLs installed on ballasts of type j that is represented by lamp option l

,

s GSFL

, j ( y ) = the shipments of GSFLs in stalled on ballast s of type j in year y (number of

uni ts)

,9-36 P

LBS ( y − y ′ ) = the probability that a lamp and its ballast both survive for y − y′ years after the lamp’s installation, as defined in Eq. 9. 34 , and a ll other variables are as

in Eq. 9.49

.

9.3 MODEL CALIBRATION AND INPUTS

9.3.1 Estimation of Historical Shipments and Initial Market Shares

Because the lamp shipments modeled in any given year depend on sums of shipments of IRLs and GSFL ballasts in prior years (see Eq. 9.28, Eq. 9.14, and Eq. 9.12 for IRLs and Eq. 9.31, Eq. 9.18, and Eq. 9.17 for ballasts) , DOE needed historical data to initiate the shipments model. Although the GSFL shipments model does not require a sum of GSFL shipmen ts ( because it is derived from the ballast shipments), DOE used historical GSFL shipments data as a calibration tool by ensuring that the projected GSFL shipments were qualitatively consistent with

historical data.

To accurately compute the initial shipm ents and stock projections from historical data, it is necessary to have data spanning a sufficiently long time period such that products shipped at the beginning of the historical period have a negligible surviving fraction in today’s stock. DOE

estimates that, for IRLs, 10 years is a sufficiently long historical period to meet this criterion; for fluorescent ballasts a historical period of at least 30 years is required. This section describes the sources of the historical shipments data; their disaggregat ion into different sectors, product classes, and technology options; and their use in initializing the shipments and stock model.

9.3.2 Sources of H istorical S hipments D ata

DOE obtained historical data on GSFL and IRL shipments from NEMA for the years 2006-2011. When combined with NEMA data provided for the 2009 lamps rulemaking, these data yield a continuous time series of shipments of GSFLs and IRLs by NEMA members over the period from 2000 to 2011. As mentioned previously , a historical period of at least ten years’ duration is required for an accurate initialization of the IRL shipments model, so this data set is sufficient for that purpose. Where possible, the provided data were subdivided by NEMA into product categories that are very similar to the product c lasses considered in this rulemaking analysis. The details of any further disaggregation or rearrangement of these data by DOE are given in section 9.3.1.2. To account for shipments to the U.S. market by non

- NEMA members, DOE assumed that NEMA shipments accounted for a fixed fraction of the total U.S. shipments over the historical period, using the same fractions that were utilized in the 2009 lamps rulemaking. These fractions are summarized in Table 9.3.1

.

Table 9.3.1 Fraction of Lamp S hipme nts Assumed to be from NEMA Members Lamp Type Fraction of shipments from NEMA members

GSFL 90

IRL

– Halogen 85

IRL

– Traditional Incandescent 709-37 DOE also obtained data from NEMA on shipments of fluorescent ballasts for the years 2006-2011, divided into subcategories that are very similar to the product classes considered in this rulemaking, with an additional subdivision into T12 and T8 ballasts where appropriate. (As discussed in section 9.1.1, DOE analyzed T8 and T12 lamps and ballasts separately in the shipments analysis and the NIA.) To estimate fluorescent ballast shipments from earlier years,

DOE made use of data from the U .S. Census Bureau’s Current Industrial Reports 14

Table 9.3.2 ( CIR), which also were originally obtained from NEMA, spanning the years 1995 (the first year in which T8 shipments were reported separately from T12) to 2005 (the final year in which data were reported). To account for shipments to the U.S. market by non- NEMA me mbers, DOE again assumed that NEMA shipments accounted for a fixed fraction of the total U.S. shipments over this period, using the same fractions that were utilized in the 2011 fluorescent ballasts rulemaking. These fractions are summarized in

.

Table 9.3.2 Fraction of Ballast Shipments Assumed to be from NEMA Members Ballast Type Fraction of shipments from

NEMA members

4

- f oot MBP T12

– Commercial 70

4

- f oot MBP T8

– Commercial 90

4

- f oot MBP T12 and T8

– Residential 50

8

- f oot S P s limline T12 70

8

- f oot S P s limline T8 90

8

- f oot RDC HO T12 60

8

- f oot RDC HO T8 90

4

- f oot Mini BPT5 SO 90

4

- f oot MiniBP T5 HO 90

4

- f oot MBP T8

– Commercial 90

As mentioned previously, a historical time series spanning 30 years is required for an accurate initialization of the fluorescent ballast shipments model. To obtain historical shipments of T12 ballasts for years prior to 1995, DOE made use of data from the Lighting Mar ket Sourcebook for the U.S

. 15 and the Census Bureau’s CIR

, 11 which span the period from 1977 to 2005 for 4-foot and 8-foot T12 ballasts. To estimate the shipments of T8 ballasts prior to 1995, DOE noted that T8s were a very small fraction of the market at t hat time, having only been

introduced to the market in 1990. Therefore, DOE assumed a linear increase in historical T8 shipments from zero in 1989 to the CIR values in 1995. Because T5 lamps were introduced to

the U .S. market after 1995, no modeling of their shipments in prior years was required.

As discussed in section 9.1.1 , DOE included T12 lamps and ballasts in its model, even though they were largely eliminated by new standards with co mpliance dates in 2012, because T12 products remain a large fraction of the existing stock, making it necessary to model their retirement and replacement. As historical shipments data were only available through 2011,

how ever, and as explicitly modeling T12 shipments in 2012 would require a significantly more complicated model, DOE simply extrapolated the disaggregated historical shipments data to 2012 for GSFLs and fluorescent ballasts, based on 2009-2011 trends. Modeling of GSFL and9-38 fluorescent ballast shipments was performed beginning in 2013. For IRLs no such extrapolation was necessary, and modeling began in 2012.

9.3.3 Sub division of Historical Shipments by S ector, Product Class, and T echnology

As mentioned previously, th e historical shipments data from NEMA and the CIR are subdivided into categories that closely resemble the product class groupings considered in this analysis. In a few cases, however, it was necessary to combine or further subdivide some of these categories to more accurately match the product class groupings or technology options being modeled. It was also necessary to subdivide the shipments in some cases into estimated shipments to the r esidential and the c ommercial and industrial sectors.

As mentioned in s ection 9.1.1 , DOE models shipments of IRLs and 4- foot MBP GSFLs separately in the r esidential sector and the commercial (for IRL) or combined c ommercial and

industrial (for GSFL) s ectors. To subdivide the historical shipments data for these products appropriately, DOE estimated the residential fraction of each product’s shipments from the estimates of lamp stocks i n the 2010 LMC and from the mea n lamp lifetimes in each sector:

f Res = S Res

L Res
S Res

L Res + S CI

L CI Eq. 9.51

Where:

f

Res = the fraction of lamp shipments in the residential sector

, S

Res = the stock of lamps in the residential sector, as reported in Table 4.1 of the LMC (number of units),

S CI = the stock of lamps in the commercial (IRL) or commercial and industrial (GSFL)

sectors , f ro m the same table (number of units),

L

Res = the average lamp lifetime in the residential sector (yr)

, i.e., the average failure age derived from the lamp failure distribution in Eq. 9.15 or Eq. 9.32 using the appropriate hours-of- use distribution and ballast lifetime for the residential sector,

and

L CI = the lamp lifetime in the commercial (IRL) or commercial and industrial (GSFL)

sector s (yr) , computed as above, except with the use of the appropriate hours-ofuse distribution and ballast lifetimes for the c ommercial and industrial sectors.

The data on GSFL and fluorescent ballast shipments from NEMA and the CIR were nearly all subdivided into categories corresponding directly to the analyzed product class groupings, with additional subdivisions into T12 and T8 technologies, where appropriate. The exceptions were 8 -foot recessed double contact ( RDC ) high output ( HO ) lamps and ballasts, for which no subdivision into T12 and T8 technologies was available, and 4-foot MiniBP T5 standard output ( SO ) ballasts, for which no shipments were available from the CIR. To9-39 disaggregate the data for 8 -foot RDC HO lamps and ballasts into T12 and T8 subcategories,

DOE assume d that the fractions of T12 and T8 lamps in this product class were the same as the

fractions in the 8-foot SP s limline product class. Similarly, to infer shipments of 4 -foot MiniBP T5 SO ballasts prior to 2006, DOE assumed that the ratio of SO to HO T5 ba llasts was fixed at its 2006 value in the period 2002-2005 and that there were zero shipments of 4-foot MiniBP T5

ballasts in any year before 2002.

As mentioned in section 9.2.2.3, DOE model ed the shipments independently for each of the three IRL technology options (the two baseline lamps and the one CSL1 lamp), because their lifetimes were significantly different. It was

, therefore

, necessary to disaggregate the historical shipments data for IRLs into estimated shipments for each of the technology option s. DOE is aware that many shipments prior to 2012 did not correspond to any of these three technology options, as compliance with the 2009 GSFL

- IRL lamps rulemaking was challenging for some significant types of IRL technology. Because these older technolog ies had lifetimes close to the

Baseline 2 lamp lifetime, however, it sufficed to categorize under Baseline2 all historical shipments outside the CSL1 technology.

To disaggregate the historical IRL shipments, DOE used the consumer choice model to

compute the expected market shares of the Baseline1, Baseline2, and CSL1 technology options

in the commercial and residential sectors in 201 1, denoting the CSL1 f raction

, MS CSL 1 ( 2011 )

. By researching historical manufacturer literature, DOE found that the techno logy options corresponding to CSL1 were only introduced to the U .S. market in or around 2007, so DOE assumed that the market share of CSL1 lamps, MS CSL 1 ( y )

, increased linearly in each year from zero in 2006 up to the 2012 value. The shipments of CSL1 l amps in each year were then given by s CSL 1 ( y ) = MS CSL 1 ( y ) s Tot ( y ) , where s Tot ( y ) represents the total annual shipments in each

sector. As mentioned previously, the remainder of the historical shipments was allocated to the Baseline2 category for the purposes of initializing the shipments model.

9.3.4 Consumer Choice Model Calibration

As introduced in s ection 9.2.1.2

, DOE used a logit model, described by Eq. 9.1 and Eq.

9.2 , as the main driver of the consumer choice model used to predict product market share. The logit has two parameters, β FC

and β OM , which characterize consumer sensitivity to first cost and

O&M cost

, respectively. Because commercial and industrial customers are expected to respond

similar l y to lighting costs but d ifferently from residential customers, DOE calculated two sets of logit parameters, one for the commercial and industrial sector and the other for the residential

sector . The logi t parameters for the residential sector were scaled from the results of the

commercial and industrial sector analysis , as describe d below.

Following the procedure adopted by D OE ’s Solid State Lighting Program in its report on
the Energy Savings Potential of Solid-State Lighting in General Illumination Applications

, 3 the shipments model calculates the logit parameters for the commercial and industrial sector using data on fluorescent lamps and ballasts, because GSFL usage is dominantly c ommercial and industrial. The results of the analysis were then used in the consumer choice model to reflect9-40 decision

- making in that sector. The following describes how the logit parameters were obtained

for the commercial and industrial sector.

Calculat ion of the logit parameters requires both market share data ( shipment s) and first cost and O&M cost data for products with different costs. DOE used 2011 aggregate data for T8 and T5 SO lamps and ballasts for this purpose, because they are two product type s that can provide similar lighting service s and are direct competitors in the market for new construction,

retrofit , and renovation. The cost data included lamp and ballast systems costs and O& M costs to reflect the full cost of ownership. Specifically, DOE used data on the baseline 2- lamp 4 -foot MBP T8 system with a programmed start ballast and the baseline 2

- lamp 4 -foot T5 SO system

with a programmed start ballast, documented in the engineerin g analysis ( c hapter 5 of this TSD ).

Table 9.3.3 lists the cost and market share input data used in the calibration. First costs include the price of the lamps and ballast, installation

, and sales tax h . As a proxy for the annual O&M cost, DOE used the electricity cost for the first year of system operation , which is calculated from system wattage, annual run hours, and the cost of electricity in 2011. All costs were normalized by dividing by the lumen output of the system.

Table 9.3.3 Input Data for Logit Parameter Calibration Lighting System First Cost ($/thousand lum ens ) O&M Cost ($/thousand lum ens ) Market Share

T8 MBP 12.12 5.07 79%

T5 SO 14.07 4.60 21%

Using the input data from Table 9.3.3 in Eq. 9.1 and Eq. 9.2 results i n the system of equations below, which can be solved for β FC

and β OM

. i

0

. 79 = e 12

. 12 ∗ β fc +5

. 07 ∗ β om

e 12

. 12 ∗ β fc +5

. 07 ∗ β om + e 14

. 07 ∗ β fc +4

. 6 ∗ β om

0

. 21 = e 14

. 07 ∗ β fc +4

. 6 ∗ β om

e 12

. 12 ∗ β fc +5

. 07 ∗ β om + e 14

. 07 ∗ β fc +4

. 6 ∗ β om

The results of the calibration are listed i n Table 9.3.4

.

h DOE looked into the effects of utility rebates on first costs seen by consumers by studying a comprehensive data set of nationwide rebate programs compiled by the Consortium for Energy Efficiency for 2011. These data do not indicate any substantive difference in rebate amounts between high efficiency T8 lamps or lamp and ballast systems and T5 lamps or lamp and balla st systems. Therefore, no adjustments to first costs were made to account for rebates.

i In practice this system of equations is difficult to solve analytically. To solve numerically, DOE used Microsoft Excel’s Solver tool to minimize the sum of squared re siduals between the probabilities predicted by the logit model using the input prices and the market shares listed in Table 9.3.3

.9-41 Table 9.3.4 Logit Parameter Results from Calibration

Sector β FC β OM Commercial/Industrial

- 1.22

- 2.13

Residential

- 0.67

- 1.07

For the residential sector , the SSL report used data for medium screw- based lamps to calibrate the logit parameters. Given that reliable residential sector price data were unavailable for this analysis, DOE scaled the commercial and industrial logit parameters to obtain the residential logit parameters shown in Table 9.3.4

, consistent with the results of the SSL analysis. j

As discussed in section 9.2.1.2 DOE used a diffusion curve published by PNNL 16

Table 9.3.5 for its shipments model. The adoption curve parameters are shown in and the curve is plotted in Figure 9.3.1

.

Table 9.3.5 Bass Adoption Model Parameters

CE 0.005

CI 0.25

Figure 9.3.1 Generic lighting Bass diffusion curve

j The analysis performed for the SSL report made use of proprietary data not available for the analysis presented in

this TSD

.9-42 To calibrate the consumer choice model, DOE used acceptance factors and ballast lifetime reduction factors to capture differences among the observed market shares of product class groupings and lamp options, as compared to what would be predicted by pric e factors in the logit model alone. A cceptance factor s limit the total market share that can be assigned to a product and are nominally set to 1 for products with a wide acceptance among consumers. Acceptance factors for ballast s that accept 8 -foot lamps and reduced wattage 4-foot MBP T8 lamps were affected by calibration. Ballast lifetime reduction factors, also nominally set to 1,

reduce a ballast’s lifetime to account for reasons other than failure for ballast replacement, such

as new standards eliminati ng some lamp options (e.g., T12s) or a preference of 4-foot lamps over 8-foot lamps. Ballast lifetime reduction factors for ballast types that accept 8 -foot lamps and

T12s lamps were affected by calibration.

Acceptance factors for ballast s affect the outcome of the consumer choice module wh en allocating new lighting demand ( i.e., new construction, retrofit, and renovation) among product class groupings . Consumers show a preference for 4 -foot lamps over 8-foot lamps, as evidenced by shipment data. Therefore, during calibration

, acceptance factors were reduced for 8 -foot

slimline and 8

- foot RDC HO ballast types until the shipments predicted by the consumer choice module in the first year of the analysis period were consistent with the 2011 shipment data

pro vided by NEMA for these ballasts. After calibration the acceptance factors were assumed to apply over the entire analysis period.

Acceptance factors for lamps affect the outcome of the consumer choice module when allocating market share among different l amp options ( i.e., 32W, 28 W, and 25W lamps) when choosing a new lamp. During calibration, market shares were decreased for some 4 -foot MBP T8s until the market shares predicted by the consumer choice module were consistent with

observed market shares . B ecause market share data are not available disaggregated down to the lamp option level, market shares were estimated based on the share of on line listings of each lamp option offered by four retailers k . As for ballasts, the calibration involved adjusting t he acceptance factors until the predicted market shares agr e ed with those estimates. After calibration the acceptance factors were assumed to apply over the entire analysis period.

In the final calibration, b allast lifetime reduction factor s w ere reduced for T12 ballasts

and ballast type s that accept 8 -foot lamps until shipments in the analysis period were consistent with historical shipment trends. Again

, after calibration, these parameters were not changed.

Ballast type acceptance and lifetime r eduction factors are listed in Table 9.3.6

, and lamp option acceptance factors are listed in Table 9.3.7

.

k DOE based these market shares on 309 product listings obtained from four lamp retailers.9-43 Table 9.3.6 Ballast Acceptance Factors and Lifetime Reduction Factors

Ballast Type Acceptance

Factor Lifetime

Reduction

Factor

4

- foot MBP T12 Com/Ind 1 0.7

4

- foot MBP T8 IS Com/Ind 1 1

4

- foot MBP T8 PS Com/Ind 1 1

4

- foot MBP T12 Res 1 0.5

4

- foot MBP T8 Res 1 1

8

- foot Single Pin T12 1 1

8

- foot Single Pin T8 0.5 0.7

8

- foot RDC HO T12 1 0.9

8

- foot RDC HO T8 0.3 0.7

4

- foot T5 SO 1 1

4

- foot T5 HO 1 1

Table 9.3.7 Lamp Acceptance Factors

Product Class Grouping CSL Wattage Efficacy (lm/W) Acceptance

Factor

4-foot MBP (T8) Baseline 32 89.2 1

CSL1 32 90 1

CSL2 32 95.4 0.7

28 96 0.5

25 93 0.7

8-foot S P s limline (T8) Baseline 59 98.2 1

CSL1 59 99 1

54 105.5 1

50 108 1

8-foot HO T8 (T8) Baseline 86 93 1

CSL1 86 95.3 1

T5 SO Baseline 28 104.3 1

CSL1 28 109.7 1

26 111.5 1

25 116 1

T5 HO Baseline 54 92.9 1

CSL1 54 97.3 1

50 100 1

47 102.1 19-44 9.3.5 Price Learning

As indicated in section 9.2.1.3

, DOE uses a price learning model to project future prices

in its shipments analysis. Accordingly, the initial lamp prices determined in the pricing analysis (chapter 7 of this TSD ) are adjust ed for the observed learning rate at later times in the analysis period. DOE developed price learning rates for the two categories of lamps and for GSFL

ballasts based on historical shipments data from the U.S. Census CIRs. DOE extracted the historical pro duct data indicated in Table 9.3.8 from the CIRs to calculate price learning rates for GSFLs, IRLs, and ballasts. Table 9.3.8 indicates which product categories listed in the CIRs were used to represent the two categories of lamps and the ballasts tracked in the shipments

model.

Table 9.3.8 Data Extracted from Current Industrial Reports (CIRs) for Price Learning Analyses

Dates CIR product category Product addressed in rulemaking

1958 to 1994 fluorescent, hot c athode (GSFL) GSFL

1960 to 1994 PAR IRL

1986 to 2005 e lectronic ballasts ballasts

The CIRs report annual data on shipments (units shipped) and the total nominal dollar value of those shipments. DOE interpolated reported shipments to estimate missing year values and extrapolated to estimate shipments back to the first unit shipped. Those data were then used

to calculate the annual cumulative production ( Eq. 9.5 ) used in the price learning analysis. The dollar values reported in the CIRs represent the net selling value of units shipped free-on-board (FOB) from the factory l

. These were converted to pe r-unit sales values and adjusted for inflation using the U.S. Office of Budget and Management Gross Domestic Product chained price index 17
Eq. 9.4 . The data on price and cumulative shipments were then fitted to the learning curve ( ) to calculate the learning rates used in the shipments model. The results of these fits are shown in Figure 9.3.3

, Figure 9.3.4 , and Figure 9.3.4 for IRL, GSFL, and ballasts, respectively. The equations in the figures indicate the fits to Eq. 9.4 for each of the product groups. The rate

paramet ers (exponents) were then used in Eq. 9.6 to determine the product group specific price learning factors, which in turn were used by the model, in Eq. 9.7 , to calculate the prices in any given year.

l Free

- on

- board values reflect discounts and allowances, are exclusive of excise taxes

, but includ e freight charges. This approximates the cost of production to the manufacturer plus a single mark

- up to the first customer, most likely

a distribut or . Ideally, consumer prices would have been used for this analysis, rather than the manufacturer selling prices given in the CIR, but the CIR data were considered the bes t option for two reasons. (1) Given the assumption of constant markups, the learning rates deducted from the manufacturer selling prices will be the same as for the retailer selling prices. (2) The multi

- decade CIR data constituted the most comprehensive and consistent data source available that covered the longest time period.9-45 Figure 9.3.2 IRL Learning Curve

Figure 9.3.3 GSFL Learning Curve

Figure 9.3.4 Ballast Learning Curve9-46 9.3.6 Lamp and Ballast System Assumption s

As discussed in chapters 5 and 6 of this TSD , computing the power usage associated with a particular GSFL requires assumptions about the ballast to which it is coupled. In the previous chapters, DOE analyzed GSFLs coupl ed to particular representative ballasts to determine representative energy consumption values. In those chapters there were several representative ballasts in each product class, with different ballast factors and different numbers of lamps per

ballast. I n the case of the NIA ( chapter 10), however, the relevant power consumption value is

not the representative value for individual products, but rather the national- average value. Moreover, when implementing the consumer choice module of the shipments model, DOE is modeling average consumer behavior, which can be captured by considering GSFLs coupled to a single average ballast.

Thus, in the current chapter and in chapter 10 of this TSD, DOE considers coupling lamps to a single composite model ballast in ea ch product class. DOE based these composite ballasts on the representative ballasts used in chapters 7 and 8 of this TSD , with some properties, such as ballast factor and number of lamps per ballast, replaced with national- average values where appropriate. The composite ballast properties were computed from the average of available models found in a database of fluorescent ballasts gathered in support of the Federal Energy Management Program (FEMP) 18

Table 9.3.9 . The average ballast properties , thus, may not correspond to the properties of any specific ballast on the market (for example, the national average number of lamps per ballast will not necessarily be an integer), but they will allow accurate modeling of average consumer behavior and tot al nat ional energy consumption. The composite ballast properties are presented in

.

Table 9.3.9 Properties of Average Ballasts for Product Class Groupings

Ballast Type Ballast Factor Lamp s per Ballast

4

- foot MBP T12 Com/Ind 0.88 2.6

4

- foot MBP T8 IS Com/Ind 0.95 2.4

4

- foot MBP T8 PS Com/Ind 0.95 2.1

4

- foot MBP T12 Res 0.88 2

4

- foot MBP T8 Res 0.88 2

8

- foot Single Pin T12 0.87 2

8

- foot Single Pin T8 0.87 2

8

- foot RDC HO T12 0.81 2

8

- foot RDC HO T8 0.81 2

4

- foot T5 SO 1 2

4

- foot T5 HO 1 2
Source: Ballast factors and number of lamps are averages computed from data in the Federal Energy Management Program’s lamp and ballast database. 18

The average system input power of a lamp

- and

- ballast system in a particular product

class grouping using a particular GSFL technology option within that product is then given by the following formula:9-47 SI P l

, i = W l BF i n� lamp

, i Eq. 9.52

Where:

SIP l,i = t he average system input power of a lamp

- and

- ballast system using lamp option l in product class grouping i (W)

, W

l = the rated wattage of lamp option l (W)

, BF i = the ballast factor of the composite ballast used in modeling product class grouping

i , and

n� lamp

, i = the average number of lamps per ballast in product class group ing i

.

The following section s document the values used to model properties of IRL s , GSFL

ballasts , and GSFLs, respectively

.

9.3.6.1 Ballast Substitution Assumption s

Table 9.3.10 indicates which ballasts the shipments model considers allowable substitutes for existing ballasts replaced during retrofits or renovations. An X in an intersecting column and row indicate that the ballast in the column header may be replaced by the ballast in the row

header. In developing this matrix, DOE considered ballast options to be potential substitutes if they are used for similar applications. DOE also assumed that consumers do not sw itch from newer back to older technologies (e.g., there is no switching from T5s to T8s). Note that no T12 ballasts were allowed to substitute for any existing ballasts, even for existing T12 ballasts,

because DOE assumes that they do not comply with the 2011 fluorescent lamp ballast rulemaking 10

.9-48 Table 9.3.10 Ballast Substitution Matrix: Retrofits and Re novations Original Ballast TypeBallast Type4-footMBP T124-foot MBP T8Instant Start4-foot MBP T8Programmed start4-foot MBP T12(Residential)4-foot MBP T8(Residential)8-foot Single Pin SPslimline T128-foot Single Pin SPslimline T88-foot RDC HighOutput T128-foot RDC HighOutput T8Two Lamp PST5 SOTwo Lamp PS T5 HOB1.0IB1.IB1.PB1.0RB1.RB2.0B2.IB3.0B3.IB4.PB5.P

B1.0I

B1.I X X X X

B1.P X

B1.0R

B1.R X X

B2.0

B2.I X X

B3.0

B3.I X X

B4.P X X X X X X

B5.P X X X X X9-49 9.3.6.2 G eneral Service Fluorescent Lamp Characteristics

This section documents the model inputs for general service fluorescent lamps in the following tables:

**•** Table 9.3.11. Properties of Representative GSF L Option s: Baseline and All CSLs

,

**•** Table 9.3.12. GSF L Option s for Different Ballast Types ( Table 9.3.12 ), and

**•** Table 9.3.13. Properties of Representative GSFL Lamp

- and

- ballast Systems

.

Table 9.3.11 Properties of Representative GSF L Option s: Baseline and All CSLs

Product Class Grouping CSLLamp OptionIDLamp DiameterNominalWattageANSI RatedWattageEfficacy (rated)Initial LumensMean LumensLamp Price

4

- foot MBP Baseline L1.0.1 T8 32 32.5 89.2 2900 2725 $4.85

CSL1 L1.1.1 T8 32 32.5 90.0 2925 2770 $5.23

CSL2 L1.2.1 T8 32 32.5 95.4 3100 2941 $7.95

L1.2.2 T8 28 28.4 96.0 2725 2560 $6.95

L1.2.3 T8 25 26.6 93.0 2475 2350 $9.30

8

- foot SP

slimline Baseline L2.0.1 T8 59 60.1 98.2 5900 5430 $13.27

CSL1 L2.2.1 T8 59 60.1 99.0 5950 5650 $15.31

L2.2.2 T8 54 54.0 105.6 5700 5360 $16.78

L2.2.3 T8 50 50.0 108.0 5400 5075 $20.56

8

- foot HO Baseline L3.0.1 T8 86 8 4 .0 93.0 8000 7600 $12.58

CSL1 L3.2.1 T8 86 8 4 .0 95.3 8200 7800 $15.15

T5 SO Baseline L4.0.1 T5 28 27.8 104.3 2900 2697 $5.90

CSL1 L4.2.1 T5 28 27.8 109.7 3050 2898 $6.90

L4.2.2 T5 26 26.0 111.5 2900 2660 $7.38

L4.2.3 T5 25 25.0 116.0 2900 2750 $8.12

T5 HO Baseline L5.0.1 T5 54 53.8 92.9 5000 4850 $7.62

CSL1 L5.2.1 T5 54 53.8 97.3 5237 4871 $9.06

L5.2.2 T5 50 50.0 100.0 5000 4650 $11.69

L5.2.3 T5 47 47.0 102.1 4800 4410 $13.50
Source: Engineering a nalysis (chapter 5 of this TSD ). Prices are given in 2011$ for the beginning of the analysis period (2012).9-50 Table 9.3.12 identifies which lamps are assumed to pair to which ballasts. Ballast types

are indicated in the column header. Lamp Options ID are indicted in the row headers. See T able

9.3.11 for lamp option specifications.

Table 9.3.12 GSF L Option s for Different Ballast Types Ballast types4-foot MBP T124-foot MBP T8 InstantStart4-foot MBP T8Programmed start4-footMBP T12(Residential)4-foot MBP T8(Residential)8-foot Single Pin SPslimline T128-foot Single Pin SPslimline T88-foot RDC HighOutput T128-foot RDC HighOutput T8Two Lamp PS T5 SOTwo Lamp PS T5 HOB1.0IB1.IB1.PB1.0RB1.RB2.0B2.IB3.0B3.IB4.PB5.P

L1.0.1 X X X

L1.1.1 X X X

L1.2.1 X X X

L1.2.2 X X X

L1.2.3 X X X

L2.0.1 X

L2.2.1 X

L2.2.2 X

L2.2.3 X

L3.0.1 X

L3.2.1 X

L4.0.1 X

L4.2.1 X

L4.2.2 X

L4.2.3 X

L5.0.1 X

L5.2.1 X

L5.2.2 X

L5.2.3 X
Source: Engineering a nalysis (chapter 5 of this TSD ).9-51 Table 9.3.13 Properties of Representative GSFL Lamp -and-ballast SystemsBallasttype4-footMBP T12(Commercial andIndustrial)4-footMBP T8Instant Start(Commercial andIndustrial)4-footMBP T8Programmed start(Commercial andIndustrial)4-footMBP T12(Residential)4-footMBP T8(Residential)8-footSingle Pin SPslimline T128-footSingle Pin SPslimline T88-footRDC HighOutput T128-footRDC HighOutput T8Two Lamp PS T5SOTwo Lamp PS T5HO

Product Class Grouping 4ftMBP 4ftMBP 4ftMBP 4ftMBP 4ftMBP 8ftSP 8ftSP 8ftRDC 8ftRDC 4ftT5SO 4ftT5HO

Start Method IS IS PS IS IS IS IS IS IS PS PS Lamp Diameter T12 T8 T8 T12 T8 T12 T8 T12 T8 T5 T5

Sector Com Com Com Res Res Com Com Com Com Com Com Baseline System

Mean Lumens * 5262 6213 5436 4048 4796 10276 9448 13195 12312 5394 9700 Avg

. System

Mean Lumens

, 2013 ** 5262 613 4 5 399 4048 4786 10276 94 04 13195 12450 551 3 9 499 Group relamping

fraction † 0.25 0.25 0.25 0.00 0.00 0.3 7 0.3 7 0.31 0.31 0.25 0.25 Lamp Life Hours 18938 24000 40000 18938 24000 11108 24000 11070 18000 30 000 24000 Lamp Life

Years †† 5. 4 6. 7 1 0.8 17.6 18.1 3. 3 6. 5 3. 3 5. 1 6.9 6. 7

Ballast Price $0.00 $18.69 $19.28 $0.00 $9.61 $0.00 $21.00 $0.00 $16.75 $28.84 $ 30.18

Ballast

Installation Cost $0.00 $27.99 $26.41 $0.00 $32.55 $0.00 $54.96 $0.00 $58.79 $25.88 $2 5.88 Lamp

Installation Cost $0.00 $6.73 $6.68 $0.00 $0.00 $0.00 $4.72 $0.00 $6.31 $6.67 $6.67

Fixture

Disconnect Cost $0.00 $2.71 $2.71 $0.00 $2.71 $0.00 $2.71 $0.00 $2.71 $2.71 $2.719-52 Avg

. Lamp Price,

2013 ** $0.00 $6.19 $5.75 $0.00 $5.76 $0.00 $14.90 $0.00 $12.77 $6.60 $9.0 7 Lamp disposal

cost $0.00 $0. 24 $0. 24 $0.00 $0.00 $ 0.48 $ 0.48 $ 0.48 $ 0.48 $0. 24 $0. 24 Avg

. First Cost,

2013 ** $0.00 $70.98 $67.16 $0.00 $56.38 $0.00 $113.32 $0.00 $110.10 $77.29 $8 5.38 Avg

. Lamp

Lifetime ††† 5.66 4.20 2.27 2.00 2.00 6.97 3.50 6.99 4.56 3.37 3.50 Avg

. System Wattage, 2013 ** 77.8 70.9 62.4 59.8 55.2 130.5 98. 5 178.2 13 6.1 53.4 104. 0 Avg. Annual Energy Costs,

2013 ** $37.76 $ 34.43 $3 0.27 $3.92 $3.61 $63.35 $47. 81 $86.51 $6 6.06 $25.9 0 $50.5 0 Avg. Annual O&M, 2013 $37.76 $ 35.39 $3 0.39 $3.92 $3.61 $63.35 $49. 83 $86.51 $ 68.85 $26.6 9 $51.6 7

Bass

Introduction

Year ‡ 1950 1989 1989 1950 1989 1950 1989 1950 1989 2001 2001

Industrial

Fraction ‡‡ 0.06 0.08 0.08 0.00 0.00 0.09 0.11 0.09 0.11 0.08 0.08 Source: Engineering a nalysis (chapter 5 of this TSD ) and LCC (chapter 8 of this TSD ) unless otherwise noted (with 2 and 4 lamp ballasts aggregated into weighted averages based on number of lamps per ballast )

. Prices are given in 2011$ for the beginning of the analysis period (2012)

. * System lumens were calculated assuming lamps are installed on a ballast with DOE calculated average ballast factor and average lamps per ballast , see Table

9.3.9

** These values are computed by the consumer choice model for lamps, based on inputs from the engineering analysis. They are then used as inputs to the

consumer choice model for ballasts in 20 13. New inputs are computed for subsequent years from the output of the previous year, as described in section 9.2.2

. † Source: 2011 fluorescent lamp ballast rulema king TSD

. 10

†† Compute d from Eq. 9.27

††† Computed from Eq. 9.31

‡ Introduction year for T12s is arbitrary since T12 are not a choice in the consumer choice module. T8 introduction year from Elliot et al

. 2004. 16 T5 introduction year from 2011 fluorescent lamp ballast rulemaking TSD. 10

‡‡ Co mputed from LMC stock fractions of commercial and industrial stock.9-53 9.3.6.3 Incandescent Reflector Lamp Characteristics

Table 9.3.14 shows the IRL lamp characteristics assumed by the shipments model

.

Table 9.3.14 IRLs: Representative Properties for Baseline and CSL 1 Lamps

Source: Engineering a nalysis unless otherwise noted. Prices are given in 2011$ for the beginning of the analysis period (2012)

. * Wattage and lamp life hours are adjusted to account for lamps on dimmers (see section 9.2.2.2 ).

** Average, dimmer

- corrected lamp life in years calculated from Eq. 9.15

. *** Computed using Eq. 9.37

† Baseline 1 introduction year set to ensure 100% market penetration by 2011 , as this is a mature technology

. Baseline 2 and CSL 1 from gelighting.com. 19

†† Extrapolated from the 2012 market shares produced by the consumer choice module, as described in section 9.3.3

.Residential Baseline 1Residential Baseline 2Residential CSL1Commercial Baseline 1Commercial Baseline 2Commercial CSL 1

Rated Wattage * 60 60 55 60 60 55

Dimmer Fraction 0.29 0.29 0.29 0.05 0.05 0.05 Dimming Energy

Reduction 0.2 0.2 0.2 0.2 0.2 0.2

Dimming Lifetime

Correction Factor 3.94 3.94 3.94 3.94 3.94 3.94

Wattage * 56.5 56.5 51.8 59.4 59.4 54.5 Efficacy (lm/w) 17.8 18.3 20 17.8 18.3 20 Rated Lamp Life

Hours 1500 3000 4400 1500 3000 4400

Lamp Life Hours * 2779 5558 8151 1721 3441 5047 Lamp Life Years ** 3.7 7.3 10.7 0.4 0.8 1.1

Initial Lumens 1070 1100 1100 1070 1100 1100 Lamp Installation

Cost $ - $ - $ - $1.12 $1.12 $1.12

Lamp Price $10.25 $10.12 $17.50 $10.25 $10.12 $17.50 Lamp First Cost $10.25 $10.12 $17.50 $11.37 $11.24 $18.62

Annual O&M*** 7.00 5.59 4.72 46.55 31.64 24.72

Bass Introduction

Year † 1980 1991 2007 1980 1991 2006

2011 M ar k e t
Share †† 0.94 0.05 0.01 0.94 0.03 0.039-54 9.3.6.4 Lamp Usage Assumptions

Table 9.3.15

, Table 9.3.16 , and Table 9.3.17 document, for the two categories of lamps in

each of the three sectors , the model assumptions for lamp usage (hours per year), starts per day, and the probability that the space in which a la mp is installed is of a given type

.

Table 9.3.15 Commercial Sector Annual Hours of Lamp Use and Starts per Day

Building Use Type GSFL Probability

* GSFL

Hrs * IRL Probability

* IRL

Hrs * Starts Per Day **

Education 8.3% 4028 8.3% 4526 5

Food Service 6.4% 4064 6.4% 4380 2

Food Store 4.8% 4138 4.8% 4490 2

Health Care

- Inpatient 0.2% 4028 0.2% 4453 5

Health Care

- Outpatient 2.6% 4028 2.6% 4490 2 Lodging 3.0% 4028 3.0% 4453 5
Offices (Non

- medical) 17.6% 4028 17.6% 4490 4 Public Assembly 5.9% 4064 5.9% 4417 4

Public Order and Safety 1.5% 4028 1.5% 4526 2 Religious Worship 7.9% 4028 7.9% 4417 2

Retail

- Mall & Non

- Mall 14.0% 4174 14.0% 4563 2

Services 13.3% 4028 13.3% 4526 2 Warehouse and Storage 12.8% 4028 12.8% 4526 4

Other 1.7% 4028 1.7% 4563 4

Total 100% 100%
Average 4058 4496 3.10

* Source: Energy use analysis (chapter 6 of this TSD ). ** Source: Expert opinion.9-55 Table 9.3.16 Industrial Sector Annual Hours of Lamp Use and Starts per Day Building Use Type GSFL Probability* GSFL

Hrs* Starts

Per Day** Apparel 0.9% 4582 2 Beverage and Tobacco

Products 1.0% 4582 2

Chemicals 8.1% 4582 2 Computer and Electronic

Products 2.3% 4582 2

Electrical Eq. Appliances & Components 1.0% 4618 2

Fabricated Metal Products 10.2% 4618 2

Food 6.0% 4545 2

Furniture and Related

Products 2.5% 4545 2

Leather and Allied Products 0.2% 4582 2 Machinery 5.2% 4545 2

Nonmetallic Mineral

Products 5.1% 4582 2

Paper 1.8% 4545 2

Petroleum and Coal Products 1.8% 4545 2

Plastics and Rubber Products 3.0% 4618 2 Primary Metals 2.8% 4618 2 Printing and Related Support 3.2% 4618 2

Textile Mills 0.8% 4582 2

Textile Product Mills 0.6% 4508 2 Transportation Equipment 4.9% 4582 2

Wood Products 6.4% 4435 2

Miscellaneous 32.2% 4618 2

Total 100% Average 4585 2

* Source: Energy use analysis (chapter 6 of this TSD ). ** Source: Expert opinion

.9-56 Table 9.3.17 Residential Sector Annual Hours of Lamp Use and Starts per Day Building

Type Room Type GSFL Probability GSFL

Hrs IRL Probability IRL

Hrs Starts Per Day *Single Family Detached Basement(s) 4.191% 584 0.55% 584 1
Bathroom(s) 3.143% 584 3.88% 584 7
Bedroom(s) 1.936% 584 3.58% 584 3
Closet(s) 2.884% 511 0.63% 511 1 Dining Room(s) 0.409% 694 1.51% 694 2
Exterior(s) 1.078% 949 21.94% 949 5 Garage(s) 20.357% 548 0.00% 548 2
Hall(s) 1.118% 548 6.20% 548 5
Kitchen(s) 15.807% 840 10.64% 840 7 Laundry/Utility Room(s) 3.912% 548 0.52% 548 2

Living/Family Room(s) 2.245% 730 8.31% 730 4

Office(s) 1.357% 694 2.51% 694 3

Other/Unknown 4.790% 365 2.95% 365 2Single Family Attached Basement(s) 0.672% 621 0.09% 621 1
Bathroom(s) 0.344% 584 0.41% 584 7
Bedroom(s) 0.213% 584 0.38% 584 3
Closet(s) 0.249% 511 0.05% 511 1 Dining Room(s) 0.048% 694 0.17% 694 2
Exterior(s) 0.072% 986 1.41% 986 5 Garage(s) 0.953% 548 0.00% 548 2
Hall(s) 0.125% 548 0.67% 548 5
Kitchen(s) 1.996% 840 1.29% 840 7 Laundry/Utility Room(s) 0.262% 511 0.03% 511 2

Living/Family Room(s) 0.240% 730 0.86% 730 4

Office(s) 0.096% 657 0.17% 657 3

Other/Unknown 0.640% 365 0.38% 365 2Multifamily Basement(s) 0.689% 511 0.08% 511 1
Bathroom(s) 1.881% 584 1.97% 584 7
Bedroom(s) 1.082% 584 1.70% 584 3
Closet(s) 1.463% 475 0.27% 475 1 Dining Room(s) 0.209% 694 0.66% 694 2
Exterior(s) 0.271% 986 4.67% 986 5 Garage(s) 3.136% 548 0.00% 548 29-57 Hall(s) 0.541% 548 2.55% 548 5
Kitchen(s) 11.903% 840 6.80% 840 7 Laundry/Utility Room(s) 0.689% 475 0.08% 475 2

Living/Family Room(s) 1.512% 730 4.75% 730 4

Office(s) 0.492% 657 0.77% 657 3

Other/Unknown 0.885% 329 0.46% 329 2Mobile Home Basement(s) 0.128% 694 0.01% 694 1
Bathroom(s) 0.485% 584 0.46% 584 7
Bedroom(s) 0.301% 584 0.43% 584 3
Closet(s) 0.271% 511 0.05% 511 1 Dining Room(s) 0.057% 694 0.16% 694 2
Exterior(s) 0.132% 949 2.06% 949 5 Garage(s) 0.697% 584 0.00% 584 2
Hall(s) 0.064% 548 0.27% 548 5
Kitchen(s) 2.206% 840 1.14% 840 7 Laundry/Utility Room(s) 0.638% 548 0.06% 548 2

Living/Family Room(s) 0.383% 767 1.08% 767 4

Office(s) 0.036% 657 0.05% 657 3

Other/Unknown 0.711% 329 0.34% 329 2

Total 100% 100%
Average 648 761 4.03

Probabilities and hours of use were calculated as part of the life cycle cost analysis (chapter 6 of this TSD).

* Source: Expert opinion.9-58 9.3.7 Rare Earth Costs

As described in section 9.1 , DOE considered the impact of possible changes in REO prices in its GSFL shipments modeling. REOs are used in fluorescent lamp phosphors at higher

concentrations in more- efficient models. REO s saw large price increase s in the third quarter of 2010 and into 2011, which have now largely corrected themselves, as shown by the GS FL tri

band phosphor price index shown in Figure 9.3.5 and described in appendix 9B. This volatility has resulted in significant uncertainty about the potential long- term impact on GSFL prices.

Figure 9.3.5 Inflation

- Adjusted, Tri

- band Phosphor REO Price Index for GSFLs

Given the large uncertainty caused by such price volatility, DOE modeled GSFL lamp prices assuming three different price estimates: a best

, a high

, and a low estimate, as reflected in the model scenarios (section 9.3 ). Given the lack of any clear consistent price trend, in any given scenario, the REO real price was assumed to remain constant over the analysis period.9-59 The best

- estimate analys is assumes current (October 2012) REO prices, resulting in the following manufacturer materials costs for the indicated lamp type s:

**•** 4-foot T8, c REO

, Ref = $ 0. 47 /GSFL,

**•** 4-foo t T5

, c REO

, Ref = $ 0. 30 /GSFL, and

**•** 8-foot T8, c REO

, Ref = $ 0. 95 /GSFL.

9.4 ALTERNATIVE ANALYSES

9.4.1 Overview

In additi on to determining best estimates of the impact s of the four candidate standards

cases described in the introduction to this chapter ( section 9.1 ) , DOE conducted alternative analyses to gauge the importance of various assumptions on the shipments and NIA. Alternative analys e s that affect the NIA only are described in chapter 10 of thi s TSD . This section describes the analyses that affect both shipments, and, therefore, also the NIA. As summarized in Table

9.4.1 , these analys e s are (a) an analys is of shipments uncertainty resulting from uncertainties in REO prices, (b) a determination of the impacts on GS FL and IRL shipments resulting from the incursion of LEDs and lighting controls into the GSFL and IRL markets, and (c) an analysis of the impact that could result from manufacturers meeting an IRL CSL 1 standard by using higherwattage, shorter- lamp -life lamps, as described in chapter 5. This section describes the se scenarios. The results of the scenarios are presented in section 9.5

.

Table 9.4.1 summarizes the configuration in the shipments model of the scenario

variables used to generate the analyses. As shown, an individual scenario tests the effect of modifying only one scenario v ariable. The effect is determined by comparing the results of the

alternative scenario model runs to the standard best- estimate scenario model runs, which hold all

variables at their reference values.9-60 Table 9.4.1 Definition Alternative Analyses

Scenario Variables

Analysis Type Scenario Rare

Earth

Price LED Controls Adoption Short

IRL Life

Standard Best Estimate Ref Ref Ref Ref

Uncertainty Analyses REO High High Ref Ref Ref

REO Low Low Ref Ref Ref

Impact Determination Controls Ref Ref Fixed Ref

LED Ref No LED Ref Ref

Alternative Technology Effect IRL Short Life Ref Ref Ref Short life

Table 9.4.2 summarizes the variable assumptions used in the best estimate and alternative standards analyses. As indicated in the table, Appendix 9A describes the analysis used to generate DOE’s best estimate of the future penetration of lighting controls. Further information

on the best- estimate and alternative assumptions about REO price s is contained in appendix 9B. The impact of the LED incursion and shortened IRL lamp life assumptions are described in

section 9.4.2 and section 9.4.3 , r espectively.

Table 9.4.2 Summary of Variable Assumptions for Best Estimate and Alternative Analyses Shipments

Scenarios

Variables Best Estimate Alternative 1 Alternative 2

Rare earth oxide prices (appendix 9 B ) Ref : Prices in October 2012 High : 2011 peak price Low : 2006 – 2009 average price

Lighting controls penetration (appendix 9 A) Ref : Commercial in

- growth determined by today’s building codes (a ppendix

9 A). Residential constant at today’s level. 2 Fixed : Constant controls penetration at today’s level

LED market

incursion (section 9.4.2 ) Ref : Increasing according to Figure 9.4.1 No LED : No additional

LED incursion

Alternative technology (chapter 5 and

section 9.4.3 ) Ref: Lamp life for CSL 1

IRLs assumed to be 55- watt, 4400 hour lamp life Short life . Two 60

- W

models assumed to meet CSL 1, one with a lamp life of 1046 hours, the other with a lamp life of 2564 hours9-61 9.4.2 L ight Emitting Diode Impact Determination

As discussed in Section 9.2.2.1 , DOE assumes in its reference scenario that LED lighting technology will pe netrate GSFL/IRL markets. To simplify the shipment s model, DOE does not include LEDs as a choice in the consumer choice model, but rather models LEDs as an exogenous effect on the GSFL and IRL markets. The lumen demand satisfied by LEDs in each year is det ermined by a logistic curve, discussed in this section and in section 9.2.1.1 , with the remaining lighting demand allocated to covered products by the consumer choice module as

discussed in section 0

.

The logistic curve that characterizes LED incursion, assumed to be a Bass adoption curve ( Eq. 9.3 ), is based on the analysis in the SSL report 1 . The SSL report projects the percentage of lumen demand (lm-hr/year) fulfilled by LEDs between 2010 and 2030 for a variety of lamp categories, in cluding linear fluorescent and reflector lamps, in each sector. DOE used the SSL forecasts for LED incursion into the residential and commercial GSFL market in this analysis.

The commercial forecast was assumed to cover both the commercial and industrial s ectors for simplicity, since the forecast for LED incursion into the industrial GSFL market was nearly identical to the commercial forecast. The SSL report used a single curve for all sectors for IRLs,

which DOE used in this analysis. These curves were the n extrapolated out to the end of the analysis period.

Figure 9.4.1 shows the growth in the percentage of the GSFL and IRL markets that DOE expects to be serviced by LEDs over the shipments analysis period. Because of the large expected impact of LED incursio n into the GSFL and IRL markets, DOE is considering conducting an analysis that reflects uncertainties in these incursion rates. DOE seeks input on

these uncertainties.

Figure 9.4.1 LED Incursion Curve Projections for GSFL s and IRL s, Best Estimate9-62 DOE used the incursion curves shown in Figure 9.4.1 to project GSFL and IRL lumen capacity (teralumens) displaced by LEDs over the analysis period. Figu re 9.4.2 shows DOE’s

best estimate of the IRL and GSFL lumen capacity displaced by LEDs (light blue and dark blue, respectively ) and the lumen capacity expected to remain as IRL and GSFL ( light green and dark green, respectively ). As revealed by Figure 9.4.1 and 9.4.2 together, while the LED incursion is expected to result in a large reduction in the use of both categories of lamps, the total impact on GSFLs is expected to be much larger, because of the much larger size of their market.

Figure 9.4.2 Lumen Capacity of GSFL, IRL, and Combined GSFL and IRL displaced by LED (Total LED)

, Best Estimate

9.4.3 Alternative Incandescent Reflector Lamp Technology

Chapter 5 described the possibility that manufacturers respond to an amended IRL standard set at CSL 1 by producing shorter- lifetime lamps. DOE identified two representative

short- lived lamp options that would meet a CSL 1 standard. Their lifetimes and O&M costs , as used in the shipments analysis and the N IA, are documented in Table 9.4.3 , along with the properties of the longer- lived reference lamp used in DOE’s best

- estimate scenario. Because the

Alternative1 and Alternative2 short- lifetime lamps were very similar to the Baseline1 and Baseline2 lamp options, DOE assumed that their prices and wattages were the same, respectively, as those baseline lamps. The alternative IRL technology analysis includes all of9-63 these lamp options ( listed in Table 9.4.3 ) in the consumer choice mod el, with the reference models being available only after the 2017 compliance year

.

Table 9.4.3 IRL Lamp Life Assumptions for Best

- Estimate and Alternative Technologies that Meet a CSL 1 Standard

Lamp Technology Assumption Initial Light Output (lumens) Efficacy (lm/w) Rated Lamp

Life (hours) Lamp

Life (hours) Lamp

Life (years) Annual

O&M**

Reference technology,*

reference lamp life 1100 20.0 4400 8151 10.7 $3.98

Alternative 1, short lamp

life 1124 17.8 1046 1938 2.5 $7.41

Alternative 2, short lamp

life 1124 18.3 2564 4750 6.2 $5.02

* The reference technology is the lamp option that DOE determined to be most representative of lamps able to meet CSL 1 in the engineering analysis, see Table 9.3.14. **Calculated using Eq. 9.37

.

9.5 RESULTS

This section presents the results of the analyses of the CSCs and the alternative analyses.

9.5.1 Results of Analyses of Candidate Standards Cases

Table 9.5.1 presents DOE’s best estimates of cumulative shipments of GSFLs and IRLs over the 30-year shipments analysis period (2017 – 2046) for the four CSCs considered in the analysis (see Table 9.1.1 , for definitions of the CSCs). As described in section 9.1 , DOE initially considered two CSCs: one ( CSL 1 ) in which the standards were assumed to be set at CSL 1 f or product class groupings, and the other ( Max CSL ) in which the standards were assumed to be set at the maximum CSL for each product class grouping (which in practice is CSL 2 for 4-foo t

MBP and CSL 1 for all other product class groupings). DOE also considered a variation on each

of these— the All CSL 1 Except T5=Baseline CSC and the Max CSL Except T5=Baseline CSC

— in which the standard for T5s is kept at its current level ( i.e ., at the baseline)

.

The T5 = Baseline CSCs were included to test if this might result in a greater overall energy and cost savings due to more rapid migration to T5s (which generally have higher9-64 efficacy than T8s)

. m

Table 9.5.1 The assumption is that

, if a standard increases the price of 4 -foot MBP T8 lamps relative to 4

- fo ot MiniBP T5 lamps, consumers should adopt the more efficacious T5s more rapidly, because the marginal cost of switching is reduced. It is not immediately obvious whether this will lead to greater savings from the increased migration to T5s or reduced savi ngs from the lower efficacy of the T5s in the standards case. While shows that maintaining the T5 standard at the baseline level has essentially no imp act on the overall shipments of GSFLs, the results of the NIA project that NES and NPV are lower than would be achieved by setting the T5 standard at CSL 1 (see chapter 10). For this reason, in the subsequent discussion of results, only the All CSL 1 and t he Max CSL CSCs are included.

Table 9.5.1 Best Estimate of Cumulative Shipments of GSFLs and IRLs from 2017 – 2046, for Each of the Candidate Standards Cases

Cumulative Shipments (Millions of Lamps Shipped)

Analysis

Type Scenario Base

Case All

CSL 1 All CSL 1 Except

T5=Baseline Max

CSL Max CSL Except

T5=Baseline

Standard Best

Estimate GSFL 7049 7048 6827 7040 6827

IRL* 564 388 388 388 388

* All CSCs produce the same result for IRLs because all CSCs reflect an IRL standard set at CSL 1, the only CSL considered for this category of lamps.

Figure 9.5.1 shows DOE’s best estimate of the historical and projected shipments of GSFLs, broken down by product class grouping. The modeling projects a systematic migration of the market toward the adoption of standard output T5s over the 30-year analysis period, with

and without new standards. That shift occurs fastest for the Max CSL CSC

, because the higher

standard on 4-foo t MBP GSFLs drives the market toward T5s more rapidly . The projections also

ref lect the expected large incursion of LEDs into the GSFL market (see section 9.4.2 ), which causes a marked drop in shipments for all product class groupings except for standard output

T5s

.

m See footnote a.9-65 Figure 9.5.1 Histori cal and Projected Shipments of GSFL s by Product Class Grouping

, Best Estimate n

n In some cases

, the change in shipments between the candidate standards case and base case is so small it is indistinguishable on the figure. In that case

, the hig her standard level overwrites the lower.9-66 Figure 9.5.2 shows DOE’s best estimate of the historical and projected shipments of

IRL s, broken down into residential, commercial , and total shipments. Again, both the base case

and the CSC show a sharp decline in shipments due to the expected market incursion of LEDs, which is expected to occur faster, earlier, and to a greater extent in the IRL market than the GSFL market (see Figure 9.4.1 ). The noticeable dip in shipments after the 2017 compliance year for CSL1 occurs because the CSL1 lamp option has a much longer lifetime than the baseline options, so fewer replacement lamps are shipped for a period until the stock turnover regains equilibrium.

Figure 9.5.2 Historical and Projected Shipments for IRLs

, Best Estimate o

Table 9.5.2 shows DOE’s best estimates of cumulat ive shipments for each of the modeled product class groupings for the All CSL 1 and Max CSL CSCs. In each case the table also shows the percentage change in shipments of the CSC relative to the base case.

o In some cases

, the change in shipments between the candidate standards case and base case is so small it is indistinguishable on the figure. In that case

, the higher standard level overwrites the lower.9-67 Table 9.5.2 Effects of Candidate Standard s Cases on Cumulativ e Shipments Compared to Base Case for GSFLs and IRL s, Best Estimate

Product Class

Groupings Base Case All CSL 1 Max CSL*

Cumulative Shipments

millions Cumulative Shipments

millions Change in Shipments

Relative to

Base Case Cumulative Shipments

millions Change in Shipments

Relative

to Base

Case

4

- foot MBP 5,082 4,989

- 2% 4,814

- 6%

8

- foot SP slimline 46 46 1% 46 1%

8

- foot RDC HO 20 22 12% 22 12%

4

- foot T5, MiniBP

SO 826 925 12% 1,097 33%

4

- foot T5, MiniBP

HO 867 861 -1% 863 0%

2-foot U- shaped 208 204 -2% 197 -5%

Total GSFL** 7,049 7,048 0% 7,040 0%

IRL Residential 498 329 -34% 329 -34%

IRL Commercial 66 60

- 10% 60

- 10%

Total IRL** 564 388

- 31% 388

- 31%

* The maximum CSL is CSL 2 for 4

- foot MBP GSFLs and CSL 1 for all other GSFLs.

The maximum CSL for all IRLs is CSL 1. ** May not add due to rounding.

9.5.2 Results of the Alternative Analyses

Table 9.5.3 summarizes the cumulative shipments results for all of the alternative analyses for the CSL 1 and Max CSL CSCs. These analyses include scenario comparisons run to

estimate

**•** the uncertainty introduced into the GSFL shipments analysis because of the uncertainty in REO prices,

**•** the impact of LEDs,

**•** the impact of controls penetration, and

**•** the impact should manufacturers respond to an IRL standard at CSL 1 by making compliant, but shorter-lived, lamps.

Table 9.5.3 summarizes the results of the alternative analyses and compares them to the

best

- estimate analyses. As shown, the uncertainty in the cumulative GSFL shipments introduced by vol atile REO prices is small given the assumed bounds on the uncertainty in REO prices. p

p It is wo rth noting in this context that the analysis assumes constant lumen capacity demand per square foot, i.e.

, that consumers will not respond to increased lamp prices by using less light, although the analysis does capture

shifts that can occur because differ ent lamp options have different amounts of triband phosphor per unit lumen

output. By9-68 contrast, the assumed LED incursion has a very large impact on the projected shipments for both product categories, nearly halving shipments of GSFLs and reducing IRL shipments more than

fivefold compared to a projection that neglects LED incursion . The reference controls

penetration assumption decreases the estimated GSFL shipments only slightly (about 2%) over a projection with fixed controls penetration, because of the controls’ indirect effect on lamp

lifetime. Because the penetration of dimmers , for all sectors, was assumed to be fixed at the

current level s , and because the impact of growth in switching

- based contro ls on IRL life was

assumed to be negligible , there is no detectable effect on IRL shipments. However, t he

introduction of short- lived IRL s into the market in the alternative standards case could increase IRL shipments by almost 65 percent over a standards case with no such short- lived lamps

.

Table 9.5.3 Cumulative Shipments of GSFLs and IRLs from 2017 – 2046, for All CSL 1 and Max CSL, Alternative Analyses

Standard Uncertainty Analysis Impact

Determination Alternative

IRL Technology

Best

Estimate REO High REO

Low No LED Fixed

Controls IRL Short Life

GSFL Base Case 7049 7024 70 43 1254 9 7201 NA

CSL 1 7048 7022 7043 12 546 7195 NA

Max CSL 7040 7016 7035 12 531 7179 NA

IRL Base Case 564 NA NA 3229 564 564

CSL 1 388 NA NA 2375 388 6389-69 REFERENCES

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