(DRAFT)

SENSITIVITY OF BALLAST LIFE CYCLE COST AND PAYBACK ANALYSIS

TO ELECTRICITY PRICE AND ANNUAL LIGHTING HOURS Xiaomin Liu, James E. McMahon, Diane Fisher and Isaac Turiel

Technology and Market Assessment Group

Energy Analysis Program Ernest Orlando Lawrence Berkeley National Laboratory July 26, 1996 1. Introduction In a recent analysis (LBNL 1996), LBNL examined the impacts of energy efficiency levels for fluorescent lamp ballasts. Several measures of the impacts were calculated, including lifecycle costs (LCC), LCC change (the change in LCC between the baseline design and the more efficient design options) and payback periods. These values were calculated using point estimates representing typical values of the input variables. Some sensitivity analyses were performed, using point estimates which bracketed the base case values for the input parameters. This report describes the process of performing thorough sensitivity analyses to account for the full range of actual values for key input variables. LCC change and payback periods are calculated using a probability distribution curve of possible values for the input variables weighted by their likelihood of occurrence and the Monte Carlo simulation technique, instead of relying on point estimates. We examine a specific product class of fluorescent lamp ballasts, the 2-lamp F40T12/ES. The baseline design for this ballast is the energy efficient magnetic ballast, or EEM. The two more efficient design options considered are the cathode cutout (CC) and the electronic rapid start (ERS) ballasts. We examine two input variables, electricity price and annual lighting hours, which contribute signficantly to the economic impacts. This paper shows how variability in these two inputs affects the LCC change and payback periods. The analyses described here were presented at a workshop in Washington, DC on June 20, 1996. At the workshop, several changes in input parameters were suggested (e.g. ballast life and lamp life with CC ballasts) which will impact these analyses when they are revised.
II. Method The lifecycle cost and payback calculations, described in LBNL 1996, are repeated many times using a different input value each time for the parameter being varied, while other input parameters are held constant (See Appendix A for a list of values of input parameters) . Each parameter is varied separately, so that the interaction between parameters is not considered. The
1empirical probability distribution of each parameter is estimated from sample data to fairly

represent the range of conditions among U.S. consumers. The distributions were weighted so that economic benefits and costs of energy efficiency standards could be assessed on a national scale. The simulation calculations were done on a Macintosh desktop computer. The uncertainty model was originally constructed using the program, DEMOS , DEcision Modeling System, and later transferred to its successor , Analytica (Lumina Decision Systems, 1996). The software took 1000 samples from the distribution for one variable at a time while other variables were kept as single point values taken from the conventional engineering and economic analysis. The sampling method used was the Median Latin Hypercube variation of a Monte Carlo simulation. Other sampling schemes (Simple Monte Carlo and Random Latin Hypercube) were also tested but no significant difference in the resulting distribution was observed (see Appendix B for a more detailed description of the sampling methods). III. Sensitivity of LCC and Payback to Electricity Price A. Data To assess the consumer impacts of energy efficiency standards across the country, we have combined two data sets (EIA 1995a, EIA 1995b) to obtain commercial sector electricity prices from EIA financial statistics of 146 major U.S. investor-owned electric utilities and 441 publicly-owned electric utilities. Each utility electricity price is weighted by its commercial sector kWh sales in 1994. The combined data set consists of 587 utilities and accounts for more than 90% of all electricity sales in the commercial sector. A distribution derived from the combined data set should reasonably represent the variability of electricity price in the commercial sector nationwide. Figure 1 illustrates the relative frequency histogram of electricity price and its statistics. The horizontal axis presents the range of electricity price and the height of the bars represents the relative probability of the electricity price. The probability was calculated as the ratio of kWh sales at a specific price to the total kWh sales. Figure 2 presents the same information in a different form, as the cumulative probability distribution of the commercial electricity price. It represents the cumulative probability (y-axis) that electricity sales will happen at less than or equal to a certain price value (x-axis ). Table 1 presents the same information (i.e., percent of electricity sales in commercial sector ). From the cumulative probability distribution one can also easily find the percent (probability) of electricity sales in a specified interval
. For instance , it can be easily estimated that about 90% of electricity sales occur at prices ranging from $0.05/kWh to $0.12/kWh (95 % of sales are at or below $0.12/kWh, less 5 % that are at or below $0 .05/kWh).

2B. Results

Once the variability of electricity price was specified, the life cycle cost and payback calculations were carried out through a set of mathematical equations used in a conventional engineering analysis (LBNL 1996). Figure 3A shows the relationship between change in LCC and the electricity price. The plot illustrates a linear relationship between the input and the output. The crossover point (from Figure 3A) is the electricity price at which the LCC is the same for the baseline and more efficient design. At electricity prices lower than the crossover point, LCC will increase; at electricity prices higher than the crossover point LCC will decrease for the more efficient design compared to the baseline. Figure 3A shows that Cathode Cutout (CC) and Electric Rapid Start (ERS) ballasts tend to reduce LCC (negative LCC change) at prices above $0.038/kWh and $0.064/kWh respectively with respect to the baseline design, Energy Efficient Magnetic (EEM). For CC compared to EEM, at the mean electricity price ($0.0784/kWh), LCC decreases $7, from $180' for EEM to $173 for CC. Lifecycle costs could decrease by up to $21 (at $0.162/kWh), or increase by up to $3 (at $0.016/kWh), based on the current range of electricity prices for U.S. commercial customers. Using the crossover point from Figure 3A applied to the cumulative probability from Figure 3B, for 98% of the sales-weighted electricity prices (those greater than $0.038/kWh) there will be a net reduction in LCC in switching from the EEM to the CC design. For ERS compared to EEM, at the mean electricity price ($0.0784/kWh), LCC is reduced $4 to $176. For the current range of electricity prices, LCC could decrease by up to $25 (at $0.162/kWh), or increase by up to $11 (at $0.016/kWh). For 64% of the commercial electricity sales (at prices greater than $0.064/kWh) there will be a net savings in LCC. Figure 4 and Table 2 show results of a similar analysis of the sensitivity of payback period to the electricity price. The scatter plot shows that there is a non-linear relationship between the electricity price and payback and that the CC design requires less time to obtain a capital return (shorter payback period) than the ERS design. The payback period for the CC ballast, compared to the baseline EEM, ranges from 11 years (at $0.016/kWh) down to about 1.5 years (at $0.162/kWh), with 99% of the ballasts paying back the initial investment in less than 8 years (the mean ballast service life). The payback period for the ERS ballast compared to the baseline ranges from just over 14 years (at $0.016/kWh) to just over 2 years (at $0.162/kWh), with 97% of the ballast paying back in less than 8 years.

1This differs from the value of $174 in LBNL 1996 because the average commercial electricity price there is assumed to be $0.075/kWh. 3IV. Sensitivity of LCC and Payback to Annual Lighting Hours

A. Data The annual lighting hours distribution was developed from Xenergy's XENCAP database (Xenergy, 1995 ). We received an extract from Xenergy ' s lighting equipment database, aggregated to the 3-digit zip code level. This database contains data from audits of over 32,000 buildings across the U.S., and gives information about operating hours and equipment counts for various lighting equipment types in the buildings audited. We used data from audits performed in 1990 through 1995 to approximate current practice. These data were used to obtain a count of four-foot fluorescent lamp ballasts (of which the 2-lamp F4OT12 /ES ballast is an example) found in each of 21 operating hour "bins" (0-8 hrs/wk, 8-16 hrs/wk, etc., corresponding to 0-417 hrs/yr, 417-834 hrs/yr, etc. ). This distribution was weighted by building type using data in the 1992 Commercial Building Energy Consumption Survey (CBECS) (EIA 1994). The absence of a bar for the first lighting hours bin in Figure 5 is an artifact of the sampling process
. As described in Appendix B, in a stochastic simulation each distinct value (or level) of an input distribution is selected based upon the associated probability, which in this case is approximated by the percent of the ballast counts within a specific lighting hour level. The relative frequency of the first lighting hour level is 0.002, and our simulation process picked no values in the first lighting level. Figure 6 presents the cumulative probability distribution of the annual lighting hours. It represents the cumulative probability (y-axis ) that lighting hours will be less than or equal to a certain value (x-axis). Table 3 presents the same information. This cumulative probability distribution can be used to determine the percent of ballasts operating in a specific interval of annual lighting hours. For example, the percent of ballast operating between 2000 and 7000 hours per year is 89% (96% operating at less than 7000 hours/year, minus 7% operating at less than 2000 hours/year). B. Results A scatter plot (Figure 7A) of the sensitivity analysis of LCC change to lighting hours shows a non-linear relationship between the input and the output as well as the points at which the curves cross the zero net saving line (LCC change = 0). Figure 7A shows that when an EEM ballast is replaced with a CC ballast, a net savings in LCC occurs for annual operating hours above approximately 1000 hours /year . A net savings in LCC occurs for operating hours above 2700 hours/year when the EEM ballast is replaced with an ERS ballast. Combining the sensitivity scatter plot (Figure 7A) with the input distribution histogram (Figure 7B ), we can get an estimate of the percent of the ballasts in the commercial sector having a net life-time saving for each of the design options as illustrated in Figure 7B and shown in the chart at the bottom of the same page.

4For the CC ballast compared to the EEM, the LCC change ranges from a net increase of

about $1.60 (at 834 hrs/yr) to a net reduction of about $8 (at 8760 hrs/yr). A net reduction in LCC will result for 98.5% of the ballasts, that is those operating more than 1000 hrs/yr. For the ERS ballast compared to the EEM, the LCC change ranges from a net increase of just above $8 (at 834 hrs/yr) to a net decrease of approximately $6 (at 8760 hrs/yr). A net reduction in LCC results for 76% of the ballasts, namely those operating more than 2700 hrs/yr. . The exact same procedures were implemented for the sensitivity of the payback period to annual lighting hours. Figure 8 and Table 4 present the results

. For the CC ballast compared to the EEM, the payback period ranges from just over 14 years (at 834 hrs/yr) to under 2 years (at 8760 hrs/yr). The payback is less than 8 years for 96% of the ballasts, those operating at less than about 1500 hrs/yr. For the ERS ballast compared to the EEM, the payback period ranges from approximately 16 years (at 834 hrs/yr) to just over 2 years (at 8760 hrs/yr). The payback period is less than 8 years for 76% of the ballasts , that is those operating for less than about 2500 hrs/yr.. V. Summary of Results This sensitivity analysis shows how the calculated LCC change and payback period for switching from EEM ballasts to more efficient CC or ERS ballasts is affected by variability in two important input parameters, electricity price and annual lighting hours. We find that for the range of commercial electricity prices found in the U.S., substituting CC ballasts for the baseline EEM ballasts would result in a change of LCC ranging from an increase of $3 to a decrease of $21, with 98 % of the sales-weighted commercial electricity prices resulting in a reduction in LCC. The payback period for the EEM to CC switch ranges from approximately 11 years to about 1.5 years. Switching from EEM to ERS ballasts results in a LCC change ranging from an increase of about $12 to a decrease of $25 for the range of electricity prices, with 64% of sales-weighted electricity prices resulting in a reduced LCC. The payback period for this switch ranges from just over 14 years to just over 2 years. For the range of annual operating hours examined , substituting CC ballasts for EEM ballasts results in an LCC change ranging from an increase of approximately $ 1.60 to a decrease of $8, with 98.5% of ballast operating hours leading to a reduction in LCC. The payback period for the EEM to CC switch ranges from about 14.5 years down to approximately 1.5 years. Switching from EEM to ERS results in an LCC change ranging from an increase of $8 to a decrease of $6, with 76% of ballast operating hours leading to a reduction in LCC. The payback period for changing EEM ballasts to ERS ranges from just over 16 years down to just over 2 years.

5REFERENCES :

Burmaster , David E. and Paul D. Anderson , 1994. Principles of Good Practice for the Use of Monte Carlo Techniques in Human Health and Ecological Risk Assessments
. Risk Analysis, Vol. 14, No. 4 EIA 1994. Commercial Buildings Characteristics 1992: Commercial Buildings Energy Consumption Survey. Energy Information Administration, United States Department of Energy. DOE/EIA-0246(92). EIA, 1995a. Financial Statistics of Major U.S. Investor-Owned Electric Utilities 1994. DOE/EIA-0437(94)/1, Energy Information Administration U.S. Department of Energy, Washington DC. EIA, 1995b. Financial Statistics of Major U.S. Publicly Owned Electric Utilities 1994. DOE/EIA-0437(94)12, Energy Information Administration, U.S. Department of Energy, Washington DC. Iman, R.L. and W.J. Conover , 1980. Small Sample Sensitivity Analysis Techniques for Computer Models, with an Application to Risk Assessment. Communications in Statistics, A17:1749. Lawrence Berkeley National Laboratory, 1996. Draft Report on Potential Impact of Possible Energy Efficiency Levels for Fluorescent Lamp Ballasts. LBNL, Berkeley, CA, 94720. Lumina Decision Systems, 1996. Analytica User Guide. Lumina Decision Systems, Los Altos, CA 94022. Morgan, M. Granger and Max Henrion, 1990. Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press. Ripley, Brian D, 1987. Stochastic Simulation. John Wiley & Sons. Smith, Roy L, 1994. Use of Monte Carlo Simulation for Human Exposure Assessment at a Superfund Site. Risk Analysis , Vol. 14, No. 4. Xenergy, 1995. Extract from XENCAP database, received by LBNL from Xenergy, Cambridge Massachusetts, January 1995.

6

## Figure U.S. Comm ercia l Sector Electricity Prices

0.04

0.03

0.011 ------------------------- - ---------------------------------

.» ................»..» - 4-

i 0 0 I

0.05 Statistics

0.15 Max 0.1616 Mean 0.0784 Median 0.0719 Min 0.0162 Std. Dev. 0.0226

$/kWh

0.2 

### Electricity Price ($/k h)

## Figure 2 Cu mulative P r obability of Commercial Electricity Price

..................................... ........ »...}........ . ........ ..... ........ ..

}- ....... ........ .......

. . ....... ..... ........ .. ........ . ... ...... ..... ......... ^.. ......

.....» .. ....... ..... ......... .}.._.__....p. . ....... ...... ....... ..

b 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2



### Electricity Price ($/kWh) ----»--•.».»..... ----------- 8...»...... d----------- - ----------- T t7 ;------------ P ---------- ------------

---------- ----- -------- - - }- - ------- -- ........ ........ ..

....................... .. .......... :......... . . }-



## Table 1 Cu mulative P rob ab ility Table

of Electricity Price Electricity Price Less an ($/kWh)

0.02 

## 0.'04 0.06 

## 0.08 0.10 0.12 0.14 0.16 Percent of

Sales 1% 2% 

## 27% 64%® 80% - 94% 99% 99% 0.18 1 100% 

# 1

### Figure 3 A .'.L LCC C j a Tw o --_- " 1174O T1 2ES



## Net Net C Depend um - a,mct^cit Ice ...E ® EEM . .....:..............................:.............. ......_......

$0.064/kWh

0.05 ctrl ku 0.15

W 

### kWh) 0.2

Figure For , N et S avin g s O ccur Above - 8` IfkWh

For Net Savings O ccur Above w. 6/ h

I $0.064/kWh 0.04T°

U 0
0 -----•------ ------... ..._ ............................Y............................

.. ...................... .......... .............

............................ . . !. . ............................. ........... ---------------------...

I AN w



### P ercent H avin g ,-: ".

`- CC ®EE 

# ERS 

# ®EE - 0.03

$0.038/kWh

0.01 y -.1



### Electricity Price ($/kWh)



## Net Sa 0.15 0.2



# 36% WM^ 64- /

## Figure 4 Sensitivity of PAYBACK To Electricity Price Two Lamp T1 S 1 6T -- -*--* --- * ------ * ................................... ............_..............s_ .-........--------..-...-

_..._..._... ------------------•....-••-• ------..........----..----•

............................. ............................. ............................ ...........................

................... . . .... .. .. .......................... ........................................................ ...........e ®........^ ...................... ...........................

, ---------- ....................................... .. . . ........................... ..

Key 0 1 + 2 0.05 .......... ................ .........

0.1 0.15 Electricity Price (/kWh) (CC E (E - E



### Table 2 

## PAYBACK BY PER

ELE OF U.S. CO

SALES 0.2

## Figure 5 B allast Annual. L ighti ng Hou rs in U.S.- Commercial Stock Four Foot La mp ---- ................ ................ ...... -............ .!_.'.............. --..--..

.. 

## . .,
Max 8760 Mean 3791 Median 3754 Min 834 std. Dev. 1479

04 

## 0 20Cr6 1^ 0 6 Ci0 8 00

Lighting Hours hours/ rs

10K

### Figure 6 Cumulative Probability of Annual Lighting Hours Four Foot Lamp

- -----------

0.7 0.6 0.5 0.4 

### -------------------------------------------------------- --- ---------------------

---------- -------------------------------- ---- -------------- ----------- ----------- ------------------

------------------------ ------------------- -- --------------------- ----------- ------------- - ----------



### ------------------------

----------------- ---- ----------------

----------- ---- z ---- 

# --------

--------------------------------------------

----------------------- ---------------------------------------------------------------- - -----------------------

2000 4000 6000 8000 10K 

### Lighting Hours (Hours /year)



## Table 3 Cu mulative Probability Table

of Annual Lighting H ours Lighting Hours Less Than (Hours/year) Percent of Ballasts in Commercial Stock 1000 

## 1.5% 2000 7% 3000 30 % 

## 4000 57 % 

## 5000 80 % 

## 6000 92% 7000 

## 96% : ..8000 

## 98% 8760 100%

## Figure 7A TOTAL LCC CHANGE: Two Lamp F'40T12 S

Net Savings or Net Costs D epend on Ligh ting Hours

0 0 10



### 6 6 4 2 0 -2 -41 -61 --------------------- 

## --------------------- -------------------

--

## ----------- ----- -- ------

## ------------------- --

------ 

## ---- - 

## ---- --- 

## ----- ------------ -------- -- 

## --__...... -....... ... 

## ---------------------- »----------•-------- _ ._ _.».._. _ ...__-»----•------ -- ---- _------- •-------

2700 hrs --------------------- d

-------- ----•-------------- ----------- ---------- - -- -------------------- --

------------------------ a --------------- 

### _-----»--.------- -- 

### -ti ...... ,»^.----, »»...... ».......

... . ---- 

### ------ -- - »».. ..---- .. ---

. Ens - EE11-- ---------------------

--- - - - - --- - --•a-- --._M-_.-.*. _,^. ¢ -- - -----

- - - -- - 

### .._- -- -------- - --- .. . .. . --- ------------------ 

### ----- ------------- 1000 hrs

. - ------ - - -----

CC - EEM 13 93 --_--------------------------------- - -------- -»------ ------ - -- -»a---®- .et --a
-- ^ ----------- -

2000 4000 6000 8000 10K 

### Lighting H ours 

### (Hours/year)
figure 7B For CC - EE M, Net Savings Occur Above 1000 Hours/Year

For ERS - EEM , Net Savings Occur Above 2700 Hours/Year 0.14T ----»_.._.»; 0.12

0.02 

### ------------ 1000 hrs -

-

Lighting Hours ours/year Percent H aving:

CC - EEM: ERS - EEM: Net

24% avings

76%t 

### , Figure 8 itivity 

## of PAYBACK To Lighting Hours Two Lamp F4 12 S

.cn to

1 -»«__^».«-----«a. ...«_._...«--°•--- a -•--._ ..»«»..«....P»_«__----«-----•- - «-------- ««. 16 »---- _«_«_.._-_°.-._.._._ 12 -._._««__.«μ «......«.««.-______.. ._«.« ............. 10

.6

2 {_{p 8«.«.__•---.»«» «@:..._.««..«... ««.... «««...... . __......... «-.«..._ .............. -- --------- - --- - -----

4000 2.000 Key Lighting ours a 1 (CC - EE + 2 (ERS - E 6000 8000 (Hours/year) 10K



## Table 4 PAYBACK BY PERCENT OF U.S. BALLASTS COMMERCIAL STOCK (BASE D ON D ISTRIBUTI ON OF ANNUAL LIGHTING HO URS )



## PAY TH 

## BA AN CK LESS (Years) 

## CC - EEM ERS - EEM

2 8% 0% 4 64% 17% 6 91% 58% 8 96% 76%. 10 98% 91% 12 99% 96%Appendix A Lifecycle Cost and Payback Period Inputs The following input parameters were used to calculate the total lifecycle cost for each option, the change in LCC between the design options and the baseline, and the payback period for each option. The values shown below for operating hours and electricity price are the values at which each of these parameters was held constant while the other was varied
. Electricity price was varied over the range shown in Figure 1. Annual operating hours were varied over the range shown in Figure 5. Table A.I. Input Parameters for LCC analysis Parameter Value Annual lighting hours 4230 Baseline ballast consumer price ($) $12.44 Design 1 (CC) ballast consumer price ($) $18.86 Design 2 (ERS) ballast consumer price ($) $28.94 Discount rate 0.08 Electricity price ($/kWh) $0.075 Labor rate, electrician's helper $29.35 Labor rate, electrician $42.10 Lamp price (both lamps, $) $3.28 Lifetime of ballast (hours) 33000 Normalized fixture watts, baseline option 72.7 Normalized fixture watts , design option 1 (CC) 65.6 Normalized fixture watts , design option 2 (ERS) 61.9 Relamp life (hours) 19000 Time to change ballast (minutes) 30 Time to change lamp (minutes) 23.5

A-1Appendix B Monte Carlo Simulations Simulation can be defined as the repetitive analysis of a mathematical model. The Monte Carlo simulation refers to a class of simulation techniques for decision-making in which probability distributions are used to obtain input parameters when the model is being evaluated (Ripley, 1987; Smith, 1994; Burmaster and Anderson, 1994). The distributions are used to generate random outcomes for each parameter that is considered to be important and has a probabilistic value. A distribution can either be approximated by a theoretical one such as a normal or exponential distribution curve, or represented by an empirical probability table in which the probabilities of occurrence of various distinct values (levels) are estimated by their relative frequencies in sampled data or weighting factors from the existing data sources. These random outcomes are then used in calculations of the decision criterion (or measure of merit), which in this analysis are life cycle cost and payback period. Since other parameters are entered as fixed values in all calculations, the variability in the outputs (LCC and Payback) calculated by Monte Carlo simulation is due entirely to the variation in the parameter under study. The core of the Monte Carlo simulation is that the outcomes of the parameter under study must be randomly selected from the distribution representing it. Two sampling methods widely used in computer simulations are the Simple Monte Carlo and the Latin Hypercube (Morgan and Henrion, 1990). The Simple Monte Carlo sampling first draws a cumulative probability curve from a specified distribution (theoretical distribution or empirical probability table). Then a random generator is used to produce a set of independent, uniformly distributed numbers, R,, (i.e., between 0 and 1).Through the rule of a reserve function, a set of the input values Xn corresponding to the cumulative probability curve can be obtained for a given sample size n (Lumina Decision System, 1996). However, in a parametric sensitivity study, the ultimate goal of the simulation is not the randomness but the resulting equidistribution (or equiprobable) properties of the sets of values in the parameter space (Morgan and Hendon, 1990). To improve this equidistribution a technique, called Latin Hypercube Sampling (LHS), which uses a stratified sampling approach, was originated (Iman and Conover, 1980). It divides each input distribution into n (sample size) equiprobable intervals. A single value is sampled at random from within each of these intervals, based upon the probability distribution. This produces a sample of n values for each input distribution which are more uniformly spread out than for strict random sampling. In a variation of LHS, Median Latin Hypercube, the median of each of the n intervals is chosen instead of a random value so that a more uniform sampling is produced.