6-i

CHAPTER

6. ENERGY

USE AND END -USE LOAD C HARACTER IZATION
TABLE OF CO NTENTS
6.1 INTRODUCTI ON

..................................................... 6-1 6.1.1 Transformer Losses

.............................................. 6-1 6.1.2 Transformer Loa

ding

............................................. 6-2 6.2 HOURLY L OAD MODEL

.............................................. 6-2 6.2.1 Overview of Hourly Load Model

.................................... 6-2 6.2.2 Hourly Load Simulation Method

.................................... 6-3 6.2.3 Hourly

Load Simulation I

nputs

..................................... 6-5 6.2.3.1 Utility Sample

.......................................... 6-5 6.2.3.2 Customer Type

......................................... 6-10 6.2.3.3 Transformer Initial Peak L oading

.......................... 6-10 6.2.3.4 Load Factor a

nd Inverse Load Factor

........................ 6-11 6.2.3.5 Load Distribution Function

............................... 6-12 6.2.3.6 Hourly Sy

stem Load

..................................... 6-13 6.3 MONTHLY L OAD MODEL

............................................ 6-14 6.3.1 Overview of Monthly L oad Model

................................. 6-14 6.3.2 Monthly L oad Estimation Steps

.................................... 6-14 6.3.3 Monthly

Load Model I nputs

...................................... 6-16 6.3.3.1 Customer D emand an d Usage Data

......................... 6-16 6.3.3.2 Customer Sa

mpling We ights

.............................. 6-16 6.3.3.3 Initial Peak L oad

....................................... 6-17 6.3.3.4 Transformer Loa d Factor

................................. 6-18 6.3.3.5 Root-Mea

n-Square -to-Ave

rage L oad Ratio

................... 6-21 6.3.3.6 Transformer Peak Responsibility F actor

..................... 6-22

LIST OF TABLE S Table 6.2.1 Utility

Sample for Hourly

Load Simulation D ata

....................... 6-6
LIST OF F IGURES Figure 6.2.1 Hi st og ra m o f t he Pe ak Loa di ng Di st ri bu ti on Ge ne ra te d i n t he Ho ur ly

Load Analysis

.................................................. 6-11 Figure 6.2.2 Sc at te rp lo t o f In ve rs e Lo ad Fa ct or ve rs us Pe ak Loa d f ro m H ou rl y ELCAP Data

.................................................. 6-12 Figure 6.3.1 Histogram of Annual Loa d Factors Derived from Monthly CBECS 1995 Bill Data

...................................................... 6-19 Figure 6.3.2 Scatter

plot of Ann

ual L oad Factor vers

us Annual

Peak Demand from Monthly CBECS 1995 Bill Data

................................... 6-20 Figure 6.3.3 Scatterplot of Peak Responsibility Fac tor versus Load Fac

tor

............ 6-236-1

CHAPTER

6. ENERGY

USE AND END -USE LOAD C HARACTER IZATION
6.1 INTRODUC TION The energy

use and end-use load character ization analysis produced ene rgy use estimates and end-use load shapes for distribution transformers. The e nergy use estimates enabled evaluation of energy

savings from the operation of distribution transformer equipment at var ious efficie ncy levels, w hile the e nd-use lo ad shape s allowed evaluat ion of the impact on

electri city monthly and pea k demand f

rom the op eration

of distrib ution tran sformers. The analy sis produced a distribution of results for a variety of building types a

nd uses, covering a rang e of climate l ocations

to repre sent the d

iversity of use, a nd performance , of distri

bution tra nsforme rs. The energy

use by distribution transformers de rives from no-load losses and load losses. No-load losses are constant over time and occur w henever a transformer is ener gized by powe

r lines. L oad losse s vary

with the sq

uare of the load b eing se

rved by the tran sformer . Beca

use liquid-imme

rsed tra nsforme rs are primarily

owned by

utilities, w

hich have marginal elec tricity generation costs that can vary by the hour, the De

partment developed a statistical transformer load simulation model to estimate the hourly chara cteristics of liquid-immersed transformer loads. For dry-type transf ormers, the Department used empirical estimates of load cha racteristics to estimate monthly average root mean square (RMS) loads and peak coincident loads f or distributi on transf

ormers owned by

commerc ial and in

dustrial ( C&I ) establi shments. T his chapter first des cribes tr

ansformer losse s, and the n presen ts the deta

ils of the hourly

and monthl

y end-use load characterization models the Depar tment developed.

6.1.1 Transformer Losses The energy

used by distribution transformers is cha racterized by

two types of losses. The first type are

no-load losses, which arise primarily from the switching of the magnetic field in the transformer core material. No-load losses a re roughly

constant and exist whenever the transformer is energized (i.e., conne cted to live power lines). The second ty pe of losses are load losses, which are also known as resistance or I 2 R losses. Load losses vary with the load on the transformer and at any

point in time

are pro portiona l to the loa

d square d plus a re latively small (<15 percent for loads less than rated load) temperature correction. Considering both load a nd no -l oa d l os se s, th e D ep ar tm en t u se s t he fo ll ow in g f or mu la fo r e st im at in g t he en er gy u se d b y a distribution transformer:
E DT (t) = E

NL + E

LL × [Loa d(t)/(Lr ated × PF)] 2 Eq. 6.1

where: E

DT (t) = the energy used by the distribution transformer at time t , E NL = the no-load losses at rated load, E LL = the load losses at rated load,6-2

Load(t) = the load served by the transformer at time t, Lrated = the rated load of the transformer, and PF = the power factor of the load served by the transformer.
6.1.2 Transform er Loading The key input for e stimating distribution transformer energy use is the transformer load. Because the application of distribution transformers var ies significantly by

type of transf

ormer (liquid-immersed or dry- type) and owne rship (electric utilities own approximately 95 per cent of liquid-imme

rsed tra nsforme rs, commercial/industrial entities use mainly dry -type), the Department performed two separate end-use load analy ses to evaluate distribution transformer efficiency . It designed one a nalysis for liquid-immersed transf ormers that are used mainly by electric uti lities, an d the second a nalysis for dry-type transformers th at are used mai nly by C&I customers. Section s 6.2 and 6 .3 descr ibe these two sepa rate loa d analy ses.

6.2 HOURLY LOAD MODEL This sect ion descr ibes the hourly

load mode l the Depa

rtment de veloped t o estimate transformer loads for use in analy zing potential efficiency

standards for liquid-immersed transformers. 6.2.1 Overview of Hourly Load Model The Department estimated hourly loads on individual liquid-immersed transformers using a statistical load simulation model. The statistical load simulation model takes several inputs and performs a statistical simulation for the hourly load on a set of sample transformers. There a re five main inputs to the

statistica l load simul ation mode l:
1. an estima

te of the annual pe ak load;
2. a relati onship bet

ween pe ak load a

nd load fa

ctor; 3. a relationship between the load factor and the loa d distribution function;
4. the hourly sy

stem load; and
5. the correlation between hourly system load and an individual transfor mer load.
The Department performed the hourly load simulation with a data-processing progra m that generated load inputs for the life-c ycle cost (L

CC) spreadsheet. It estimated the a nnual peak load on the transformer from the rated size of the transfor mer and a distribution of peak loads that ranged from 50 percent to 130 per cent of rated load, with a mean of 85 perc ent of the rated peaka

If transf ormers are s ized for moderat e loa d growt h on av erage (f

or exa mple, one per cent annua l gr owth over 30 years), t hen the average peak loading should be somewhat below the rating st ated on the nameplate. The Department modeled t

he i nit ial peak l oading of l iqui d-i mmerse d transf ormers in t

he hour ly load mode l wi th asmooth dis tri buti on wit h a mi nimu m peak l oading of 50 per cent of na meplat e, a medianof 85 per cent of na meplat e, an d a maxi mum 130 perc ent of na mep late. T he me dian v alue se lected by the D epa rtmen t prov ides so me ro om fo r load grow th, while utili zing the abil ity of

the transf

ormer to tolerate temporary loads greater than nameplate in t

he later years of the trans former' s li feti me. The Department a ssumed a f airl y wide r ange of i nit ial peak loadin gs for liqui d-immers ed transformers and an average ini tial peak l oading of 85 percent

b PJM coordina tes the movement of el ectr ici ty in a ll or par ts of Del aware , Maryl and, New Jers ey, Ohio, Pennsyl vania, Virgini a, West Virgi nia, and the Dis tri ct of Col umbia.
6-3 load of the transformer. a The Department derived a scaling relationship between peak load and load factor from available hourly load monitoring data. It deter mined a load distribution function with the estimated load factor and simulated the transformer load c onsistent with the load distribution function. The Department obtained the hourly system loads from the U.S. Fe deral Energy Regulatory

Commission (FERC) and market data from the Inde pendent System Opera

tors for the California, New England, and PJM I nterconnection b for the ye ar 1999. It determined the correlation between transformer load a nd system load from distributions of corre lation coefficients for commercial and re sidential customers that it derived from available hourly load monitoring data. The economically

important characteristics of transformer loads de pend primarily on the load factor, the relationship between peak load a nd transformer capacity, and the correlation between transformer load and sy stem load.
6.2.2 Hourly Load Simulation Method The Department developed an hourly transformer load simulation model to capture the vary ing dy namics a nd economics of tr

ansformer loads . The loa d simulation progr

am takes utility inputs tha t include the hourl y sy stem loads , hourly

prices, or sy stem lambd

as (lambd a is roug hly the marginal operating cost of g eneration), and then simulates a distribution of customer loads. The prog ram provides summa

ry data on c ustomer lo ads, cost s, and pri ces as ou tput. Simulation of customer or building loads is a common method for estimating building energy use when specific monitoring data are not a vailable. A statistical simulation takes informat ion on the mathemati cal and s tatistica l chara cteristi cs of buil ding loa

ds and pe rforms a Monte Carlo simulation to produce sets of building loads that have the same mathematical and statistical characteristics as measured building data . A Monte Carlo simulation is a computer calcula tion with a

built-in r andom pro cess tha

t estimate s the prob ability of diffe rent re sults. With regard to the economics of ene rgy use by transfor

mers, the most important mathematical charac teristic s of the bu

ilding lo ads are

their size relative to the tra nsforme r capac ity, their variation, and their correlation with system loads and prices.6-4

The Department determined the values used for c ustomer load variability, and c ustomer load correlation with syste m loads, by analy

zing available hourly

building load data. In more detail, the specif

ic steps in the oper ation of the hourly

load simula

tion prog ram are as follow s: 1. The program selects a utility from a database of utilities that publicly report system load and system lambda data

. 2. The program determines a sample we ight for the utility, based on total kilowatt-hours (kWh) sold.
3. The program selects the capa city for the tra

nsformer, based on the design line.
4. The program selects the transforme r peak load relative to the transformer ca pacity, and the corresponding weight from a transformer peak load distribution.
5. The prog

ram sele cts the tr

ansformer load f

actor ba sed on the

peak loa d versus i nverse load factor distribution. It calculates the characteristics of the load factor distribution from End-Use Load a

nd Consumer Assessment Program (EL CAP) data. 1
6. The prog

ram sele cts the c

ustomer ty

pe serve d by

the tran sformer

and the a ppropria te weight for that customer ty pe. It selects the rela

tive customer weight from the fraction of electricity sa

les to the customer type f or the particular utility.
7. From the transformer inverse load fac tor estimate, the program calculates the load distribution function. The load distribution function in the program is an exponential function with the selected inverse load factor.
8. Based on the cust

omer ty pe serve d, the pro gram se lects the (rank or der) correlati on with system load, based on cor relation coefficient distributions calculated from hourly load data.
9. The program then calculates the hour ly sy stem load rank orders for each hour of the year by sorting the hour

ly sy stem load values for the y ear and assigning a ra

nk to each.
10. The prog

ram calc ulates the hourly transformer-lo ad rank o

rders by adding the appr opriate random variation to the system ra nk order to produce transformer rank or ders with the selected rank-order corre lation. The program normalizes the rank orders of the transformer load so they

are evenly

distributed between 1 and 8760, inclusive.
11. The program calculates the hourly transformer load from the simulated hourly transformer rank order. This calculation uses the cumulative transforme r load-probability func

tion, which is an integral of the load-distribution function.6-5

12. The program then calculates the c oefficients of a Fourier repr esentation of the transformer load shap e for ea

ch day typ e (i.e., weekda

y, weekend , and pea

k day ). It makes the

same calculation for the load-square-weig hted price curves, which are a f unction of day ty

pe, hour, and the month of the ye ar. 13. The program provides output for use in the LCC spreadsheet in the form of tab-separated values. These data contain a customer load identifica tion (ID), transformer

characteristic, the utility ID, s ummary statistics on price and load, and load a

nd price shape co efficie

nts.

6.2.3 Hourly Load Simulation Inputs The inputs

used in the

hourly load simula

tion are describ ed in the f

ollowing sections

. 6.2.3.1 Utility Sample The utility sample is the subset of electric utilities in the Nation whose economic and load data are represented in the hourly load analysis. I

n the hourly load ana

lysis for liquid-immersed transformer designs, the Department be gan with hourly system load and ec onomic data from the Nation's electric utilities. The Department compiled the full list of the Nation’s ele ctric utilities by combining a

ll utilities that report retail data using DOE's Energ y I nformation Administration (EIA)’s For

m 861, 2 with utilities that reported data in FERC Form 1, 3 and utilities that are listed in the FERC Form 714 4 respondent list. The Department included a utility in its hourly load simulation sample if the utility reported distribution transformer da ta in FERC Form 1 for the ye ar 2000, and if suf

ficient i nformati on was av ailable t o chara cterize t he utility 's load a nd hourly marginal elec tricity

costs, ei ther from FERC For

m 714 data

or from the relev ant electricity market. Table 6.2.1 shows the list of 80 utilities that satisfy all of these data requirements.6-6

Table 6.2.1 Utility Sample for Hourly Load Simulation Data EIA Code* NERC Region** Name 296 SPP Alfalfa Electric Coop I nc. 733 ECAR Appalachian Power Co. 963 MAAC Atlantic City Electric Co. 1167 MAAC Baltimore Gas & Electric Co. 1179 NPCC Bangor Hy dro-Electric Co. 1796 NPCC Blackstone Valley Electric Co. 1998 NPCC Boston Edison Co. 2886 NPCC Cambridge Electric L ight Co. 3292 NPCC Central Vermont Pub Serv Corp. 3266 NPCC Central Maine Power Co. 3597 MAAC Citizens Electric Co. 4062 ECAR Columbus Southern Power Co. 4110 MAIN Commonwealth Edison Co. 4089 NPCC Commonwealth Electric Co. 4148 NPCC Concord Electric Co. 4184 NPCC Connecticut Valley Ele c. Co. Inc. 4176 NPCC Connecticut Light & Power Co. 4254 ECAR Consumers Energy Co. 5027 MAAC Delmarva Power & Light Co. 5109 ECAR Detroit Edison Co. 5416 SERC Duke Energy Corp. 5487 ECAR Duquesne Light Co. * The EIA C ode is the unique identi ficati on number assigned by EIA to com panies and entiti es operating in t he electric pow er indu stry. ** The North Ameri can Elect ric Rel iabil ity

Council (

NERC ) regi ons, i n the order theyappear in t

his u til ity

sample, are: So uthwe st Po wer P ool (S PP ), Eas t Centr al Are a Re liability Co ord ination A greem ent (E CA R), M id-Atlan tic Area Council (MA AC), No rtheast Power Coordinating Council (NPCC ), Mid-America Interconnected Network, Inc. (MAIN ), Southeastern Elect ric Reliabil ity Council (SERC ), Mid-Continent Area Power Po ol (MAP P), W estern Elect ric ity Coordi nating Counc il (WECC), Elect ric Reli abil ity Counc il of Texas , In c. ( ERCOT ), and Flor ida Rel iab il it

y Coor din ating Counci l ( FRCC). FERC pro vi des loa d and lam bda da ta in fi les org ani zed by NERC region.6-7

Table 6.2.1 Utility Sample for Hourly Load Simulation Data (continued ) EIA Code* NERC Region** Name 5389 NPCC Eastern Edison Co. 5659 ECAR Edison Sault Electric Co. 5860 SPP Empire District Electric Co. 13478 SPP Entergy New Orleans Inc

. 814 SPP Entergy Arkansas Inc. 7806 SPP Entergy Gulf States Inc. 11241 SPP Entergy Louisiana I

nc. 12685 SPP Entergy Mississippi Inc. 6077 NPCC Exeter & Hampton Electric Co. 6342 SPP First Electric Coop Corp. 6374 NPCC Fitchburg Gas & Elec. L ight Co. 26510 NPCC Granite State Electric C.o 7601 NPCC Green Mountain Power Corp. 9162 MAPP IES Utilities Inc. 9324 ECAR Indiana Michiga n Power Co. 9392 MAPP Interstate Power Co. 9726 MAAC Jersey Central Power & Light Co. 22053 ECAR Kentucky Power Co. 10331 ECAR Kingsport Power Co. 11118 SERC Lockhart Power Co. * The EIA C ode is the unique identi ficati on number assigned by EIA to com panies and entiti es operating in t he electric pow er indu stry. ** The North Ameri can Elect ric Rel iabil ity

Council (

NERC ) regi ons, i n the order they appear in t

his u til ity

sample, are: So uthwe st Po wer P ool (S PP ), Eas t Centr al Are a Re liability Co ord ination A greem ent (E CA R), M id-Atlan tic Area Council (MAAC ), Northe ast Power Coordin atin g Council (NPCC), M id-Ameri ca Int erconnect ed Network, I nc. (MA IN), Southeastern Electri c Reliabilit y Council (SERC), M id-Continent Area Power Pool (M APP ), Western Elect ric ity Coordi nating Counc il (WECC), Elect ric Reli abil ity Counc il of Texas , In c. ( ERCOT ), and Flor ida Reliabilit

y Coordinating Council (FRCC). FER C provides load and lamb da data in fil es organized by NER C region.

Table 6.2.1 Utility Sample for Hourly Load Simulation Data (continued )6-8

EIA Code* NERC Region** Name 11804 NPCC Massachusetts Electric Co. 12390 MAAC Metropolitan Edison Co. 12341 MAPP MidAmerican Energy Co. 12796 ECAR Monongahela Power Co. 13214 NPCC Narragansett Electric Co. 13407 WECC Nevada Power Co. 13441 NPCC New Hampshire Elec Coop I nc. 13549 NPCC Newport Electric Corp. 13781 MAPP Northern States Power Co. 13780 MAPP Northern States Power Co. 14006 ECAR Ohio Power Co. 14063 SPP Oklahoma Gas & Electric Co. 14328 WECC Pacific Gas & Electric Co. 14940 MAAC PECO Energy Co. 14711 MAAC Pennsylvania Electric Co. 15270 MAAC Potomac Electric Power Co. 15263 ECAR Potomac Edison Co. 15466 WECC Public Service Co. of Colorado 15473 WECC Public Ser vice Co. o f NM 15472 NPCC Public Service Co. of NH * The EIA C ode is the unique identi ficati on number assigned by EIA to com panies and entiti es operating in t he electric pow er indu stry. ** The North Ameri can Elect ric Rel iabil ity

Council (

NERC ) regi ons, i n the order they appear in t

his u til ity

sample, are: So uthwe st Po wer P ool (S PP ), Eas t Centr al Are a Re liability Co ord ination A greem ent (E CA R), M id-Atlan tic Area Council (MAAC ), Northe ast Power Coordin atin g Council (NPCC), M id-Ameri ca Int erconnect ed Network, I nc. (MA IN), Southeastern Electri c Reliabilit y Council (SERC), M id-Continent Area Power Pool (M APP ), Western Elect ric ity Coordi nating Counc il (WECC), Elect ric Reli abil ity Counc il of Texas , In c. ( ERCOT ), and Flor ida Reliabilit

y Coordinating Council (FRCC). FER C provides load and lamb da data in fil es organized by NER C region.

Table 6.2.1 Utility Sample for Hourly Load Simulation Data (continued )6-9

EIA Code* NERC Region** Name 15477 MAAC Public Service Electric & Gas Co. 8901 ERCOT Reliant Energy HL& P 17535 MAPP South Beloit Water Gas & Elec. Co. 17539 SERC South Carolina Electric & Gas Co. 17609 WECC Southern California Edison Co. 17633 ECAR Southern Indiana Gas & Elec. Co. 17718 SPP Southwestern Public Service Co. 18454 FRCC Tampa Electric Co. 24211 WECC Tucson Electric Power Co. 19497 NPCC United Illuminating Co. 19840 WECC Valley Elec tric Assn. Inc. 19876 SERC Virginia Electric & Power Co. 20387 ECAR West Penn Power Co. 20455 NPCC Western Massachusetts Elec. Co. 20521 ECAR Wheeling Power Co. 20856 MAPP Wisconsin Power & Light Co. 20847 MAIN Wisconsin Electric Power Co. 20860 MAIN Wisconsin Public Service Corp. * The EIA C ode is the unique identi ficati on number assigned by EIA to com panies and entiti es operating in t he electric pow er indu stry. ** The North Ameri can Elect ric Rel iabil ity

Council (

NERC ) regi ons, i n the order they appear in t

his u til ity

sample, are: So uthwe st Po wer P ool (S PP ), Eas t Centr al Are a Re liability Co ord ination A greem ent (E CA R), M id-Atlan tic Area Council (MAAC ), Northe ast Power Coordin atin g Council (NPCC), M id-Ameri ca Int erconnect ed Network, I nc. (MA IN), Southeastern Electri c Reliabilit y Council (SERC), M id-Continent Area Power Pool (M APP ), Western Elect ric ity Coordi nating Counc il (WECC), Elect ric Reli abil ity Counc il of Texas , In c. ( ERCOT ), and Flor ida Reliabilit

y Coordinating Council (FRCC). FER C provides load and lamb da data in fil es organized by NER C region.
The hourly load model uses da ta from each utility a s a basis for the hourly simulation and valuation of transformer loads in that utility. The Department statistically simulated a se t of transformer loads for each utility that were correlated with the utility ’s hourly sy stem load. The Department also calculated average hourly price profiles using hourly

system lambdas (or mar

ket prices) . It w eighte d the pric es by the squar e of the s tatistica

lly s imulated t

ransfor mer load to calculate average

prices (since load losses are proportional to the square of the load on the transformer).6-10

6.2.3.2 Custom er Type The Dep art men t u sed th e da ta o n el ect ric it y sal es b y cus to mer cla ss es r epo rte d i n EIA Form 861 to characterize the differe nt types of customer loads a s residential, commercial, or industrial. The customer type f or a transformer is the class of customers whose loads a re served by the transfor

mer. The data simulation model for hourly loa ds is a Monte Carlo simulation. This means the Department sampled transformer and customer c haracteristics from probability distributions using a random number gener ator. The results of the simulation are output with weights that are proportional to the probability of the c omputed result. In the hourly load simulation, the Department selected the customer ty pe for the transformer after it had se lected the sample utility. It simulated an equal number of sample tr ansformers for each customer ty pe and each utility. The Department then assigned a we ight to each sample transformer in the simulation that represented the population of transformers re presented by

that sample. The assignment of customer -ty pe weig hts assume d that the

population of tran sformers for ea ch customer ty

pe is roughly pr

oportional to the electricity sa les to that customer type.
6.2.3.3 Transform er Initial Peak Loa ding The Department used a distribution of initial peak loading values to char acterize the annual peak load served by each transformer in its simulation. The transformer initial peak loading is the ratio of the transformer peak loa d in the first year

of operation to the rated load of the transformer. The Department selected a distribution of initial peak loadings with a median of 85 percent, a minimum of 50 percent, and a maximum of 130 percent. Standard e ngineering practice for sizing distribution transformers selects a transf ormer based on the expected annual peak of the load being served, with some provision made f or load growth. Because of the provision for load growth , initial pe ak loadin g will usu ally be less than 100 pe

rcent. H owever , in pr ac ti ce , t he re is al so so me er ro r i n e st im at in g t he an nu al pe ak lo ad th at wi ll be se rv ed by a transformer, a

nd engi neers g eneral ly u se a discrete set of trans former r atings t hat are imperfe ctly matched with the expected pe ak load. D istribution transf ormers g eneral ly a

re manuf acture d in discrete kilovolt-ampere (kVA) ratings a nd, on average, the next large r kVA rating is 50 percent larger than the previous kVA rating (measured relative to the smaller size). An initial peak loading as high a s 130 perc ent can o ccur be cause tr ansformers can

be loade d for shor

t periods to le ve ls of mo re th an 13 0 p er ce nt of na me pl at e c ap ac it y. 5 Figure 6.2.1 illustrates the distribution of initial peak loading the Department used.6-11

Figure 6.2.1 Histogra m of the P eak Loading D istributio n Gener ated in the

Hourly Load Analysis

6.2.3.4 Load Factor and Inverse Load Factor The load factor is the ratio of the average load to the peak load. Inve rse load factor is the ratio of t he peak load to the

average load. T

he trans former l oad simula tion provi des hourl

y simulated loads using a distribution of load factors that depends on the initial peak load. Consistent with data on electrical customer loads, transformers serving larger annual peak loads tend to serve loads with larger load fac tors. The load factor of customer and transfor mer loads has a wide range of va riation, but correlates with the averag e size of the load and the annual peak load. The initial annual peak load on a transformer is the product of the transforme r initial peak loading, the transformer capacity , and the power factor, assumed to be 1 watt (W)/kVA. The Depa rtment analy

zed hourly

load data from EL CAP and confirmed i ts results with confidential utility data to develop an a ggregate distribution that models the inverse load factor as a functi on of ann

ual peak load. The

Department fit a p ower-la w regr ession to the relati onship between inverse load factor and pe ak load. The power-law reg ression produced the following equation for inve rse load factor as a func tion of pe ak load: InvLoadFact = 1 + 9.59 × (Peak Load) -0.418 Eq. 6.2 Figure 6.2.2 shows a scatterplot of the inverse load factor versus peak load relationship. The figure plots both the ELCAP data a nd the regression function used to relate inverse load6-12 Figure 6.2.2 Scatterplot of Inverse Load Factor versus Pe ak Load

from Hourly ELCAP Data factor and initial peak loading for the hourlyload model that the Department used for liquidimmersed transformers. Also shown is the plot of

the reg ression e quation us ed to mode l inverse load factor as a function of peak load for the hourly load model.

6.2.3.5 Load Distribution Function The load distribution function determines the probability tha t a customer load (transformer load) will be a particular va lue during some hour of the y ear. The Department ensured that the simulated transformer load has a spec ified load factor by selecting a consistent load distr ibution fu nction. A consiste nt load fu nction is one that c an be mat hematica lly shown to result in l oads with t

he give n load fa ctor. I n the simula

tion, the D epartme

nt calcu lated hou rly loads using the selected load distribution function. The Department approximated the load distribution function with a one-parameter exponential fit that depended on the load factor. Specifically, the Department used a load selecte d from a f

unction of

the norma

lized load: Load/Lmax , where Lmaxis the annual maximum load. The following three equations define the load distribution function:

LoadProb = BLoad × ( exp(-ALoa d × Load/L max)) when Load/ Lmax < x 0 Eq. 6.3 LoadProb = CLoad × ( exp(-DLoad × ( Load/Lmax - x 0 ))) when Load/Lm ax > x 0, Eq. 6.46-13 LoadProb = 1/8760 wh en Load/L max = 1 Eq. 6.5 The function is continuous, and ALoad , BLoad , CLoad , and DLoad are constants. The variable x 0 is a parameter that defines when the load proba bility function (

LoadProb ) begins decreasing rapidly

to the value of 1/8760. The Department selected the appr oximate value of x 0 by examining the load distribution functions from ava ilable hourly load data. Lmaxis the maximum or pe ak annua

l load. The

constant s are de

termined by t he follow ing con ditions:
1. The integral from 0 to 1 of LoadProb with respect to Load/Lmax is 1;
2. The inve

rse load factor is set to a p articula

r, give n value;
3. The load probability function is continuous; and
4. Load Prob(1 ) = 1/8760.
The load distribution function is, therefore, a probability function of Load/Lmax that depends on the parameters of inverse load f actor and the constant parameter x 0 . For each transformer in the hourly

simulation model, once the Department selected the inverse load fa ctor, the values of ALoad , BLoad , CLoad , and DLoad were calculated given the f our conditions that the probability function satisfies. The D epartment selected the value of the turning -point parameter x 0 as 0.95, b ased on examination o f load dis tribution f unctions f rom the EL

CAP hourly load data. On a logarithmic scale, the empirica l load distribution functions showed a point at which the y w ould desc end rapi dly

toward the value o f 1/8760 a t Load/Lmax = 1.
6.2.3.6 Hourly System Load The hourly sy

stem load is the hourly load in the control ar ea or electricity

market where the transformer is located. Electricity hourly

load and cost data come from FERC and electricity market web sites. The source of data for reg ulated utilities was FERC Form 714, 4 which pr ovides da ta on hour

ly system loads, data on hourly system lambdas, and fore casts of peak demand for transmission control areas. In a

control area, there is usually “one electric utility c

harged with operating the control area” and other utilities “which are bound tog ether through pooling contracts, holding company oper

ations or other contractual arrang ements” (see: http://www.ferc.gov/docs-filing/eforms/form-714/instructions.asp) . Each utility with a planning area that has an annual peak dema nd greater than 200 mega watts must file Form 714. The sys tem lambda

file in F orm 714 is d

erived f rom the e conomic d

ispatch f unction a ssociate d with automatic generation control. I t is the incremental fuel cost for a set of on-line and loaded thermal generating units “when e ach unit is loaded and operating at the same incr emental fuel cost ($/MWh) with the sum of the unit loadings (MW) equal to the system de mand plus the net of6-14

interchange with other control are as.” The Department used the sy stem lambda as the marginal fuel cost of electricity

for regulated utilities. For utilities that sell into regional electricity markets, DOE obtained the hourly system load and e lectric ity c ost data f rom the I ndepend ent Sy stem Oper

ator of that marke

t. These d ata include both the actual syste m load and the hourly mar ket price. For electricity

markets, the system load is the “Actual System L oad” as published by the operator of that market. The Department used the actual market sy stem load as the system load for utilities in areas where there are electricity mar

kets. The Department assumed that the marginal wholes ale ele ctricity economic s of a utili

ty a re char acterize d by

the econ omics show

n in the loca l control a

rea or e lectric ity market. T his assump tion mean s that some geog raphica lly small-sc ale var

iations in e lectric ity e conomics may not be ca ptured in the anal ysi s.

6.3 MONTHLY LOA D MODEL This sect ion descr ibes the mo del the De

partmen t develop ed to estimate month ly transformer loads for use in analy zing potential efficiency

standards for dry-type distribution transformers, w

hich are owned ma

inly by C &I e ntities.
6.3.1 Overview of Monthly Load Model For dry-type transf

ormers, the Department developed a monthly load model that estimates the impacts of tran sformer loads and

resultan t transformer loss es on the m onthly electri city usage , demand, and elec

tricity bills of cu stomers. Transformer loss es have a constant loss component (the

no-load or core l osses) a nd a loss component that depends on the square of the load on the transfor mer (the load or coil losses). The economic value of transformer losses is a func tion of the load on the transformer and the timing of the load w

ith respe ct to var

iable energy

costs and peak de mand. To the extent the

re is a correl ation bet

ween tra nsforme r losses a nd varia ble ener gy costs, the n the cost of the el ectrici

ty supply ing the t ransfor mer losse s will be di ffere nt from the

average cost of

electri city . The L CC analysis for dry

-type transf

ormers estimated the economic impact of losses by estimating changes in monthly peak demand and the corresponding demand charg es for C&I customers. 6.3.2 Monthly Loa d Estimat ion Steps The Depa rtment use d monthly

load estimates to c alculate the L CC saving s due to efficiency standards for dry-type distribution transformers. Commercial and industrial customers are usua lly b illed for

electri city

accord ing to mon

thly demand, u sage, and fixed c harge s. There

is a great variety

of electricity

tariff structures, including time-of-use ra tes and real-time prices, that are use d for billi

ng elec tricity to C&I customers. For sim

plicity in estimat

ing the m onthly bills for C&I customers, the D epartment used only the commercial tariffs that have monthly demand,6-15

usage , and/or f

ixed char ges in the tariff

formula ( this proc ess is des cribed i n more de tail in section 8 .3.5.2). Load

estimate s of monthly

customer usage and dema

nd are in puts to the

bill calcula tor in the L

CC analy sis. To estimate the impact of transformer losses on C&I electricity bills, the Depa rtment modeled the relationship between monthly transformer load characteristics and c ustomer demand and usage. The model used by the Department estimates the load factor, coincident pea k load, and RMS load on the transformer, relative to the total customer load. The Depa rtment derived distributi ons of loa

d parame ters from hourly

load data from EL CAP and confirmed t he resul ts with proprietary utility

data. It used these same loa d-parameter distributi ons as inpu ts to estimat

e the monthly transformer e nergy and coincident peak demand losses. When used as inputs into a monthly electri city

bill calc ulator, monthly

transformer energy

demand a

nd energ y incremen

ts provided the estima

te of month

ly b ill impacts

for tran sformer

owners. The Department took the following steps in calculating the monthly load:
1. The Departmen t obtained a statist ical sampl e of monthl y demand and usage data for C &I buildings from the EIA’s 1995 Commercial Building Energy Consumption Survey (CBECS) 6 and other data sources.
2. The Department estimated an annual peak tra nsformer load from a transformer pea k loading distribution, derived from an estimate of the impacts of conserva tive transformer sizing pr actice that tend s to over- size distrib ution tran sformers. 3. The Department estimated the load factor (i.e., the ratio of the average load to the a nnual peak loa d) of the load on the

transformer fr

om load fa

ctor distr ibutions fo

und in CBE CS.
4. The Department derived distributions for the ratio of the RMS load to the average load as a function of the transformer load factor, thr ough an analysis of hourly building load data

. 5. The Department estimated monthly peak transformer load and monthly RMS transformer load by scaling

annual peak transformer values. The sc aling resulted in estimates of monthly values of transfor mer peak and RMS load that were proportional to customer mo nt hl y de ma nd an d e ne rg y us ag e d at a, re sp ec ti ve ly.
6. Using an analy sis of available hourly building load data, the Department estimated a transformer peak responsibility factor (PRF) distribution that is a function of load factor.
7. The Depa

rtment ap plied the average PRF to mon

thly transformer pe aks to est

imate monthly transformer de

mand.
8. The Department’s model calculated increme ntal monthly customer usag e and demand from no-load and load loss coefficients, transformer RMS load, and tra nsformer coincide nt peak lo ad in the L

CC spread sheet.6-16

6.3.3 Monthly Load Model Inputs The monthly load model inputs are:

C customer

demand a

nd usag e data

C customer

sampling weight s

C initial peak load

C transformer load factor

C root-mea

n-squar e-load- to-aver

age-l oad rati o

C transformer peak responsibility factor
6.3.3.1 Customer Demand and Usage Data
Cust omer d emand and us age are t he mon thly peak load a nd ele ctric al ener gy consumption, in units of kilowatts (kW) and kWh, respectively. Usag e is sometimes also called energy , or consumption. The Department used these data to calculate the base monthly customer electricity bills that may

be affected by

changes in transformer eff iciency. Commerc ial and industrial customers may have many distribution transformers on their pr emises. An individual transformer will make an incremental impact on the customer electricity bill by

making incremental changes in the customer de mand and usage.
For commercial c

ustomers, the Depa

rtment obt

ained a s tatistica

lly r eprese ntative sa mple of monthly customer demand a nd usage from data collected in the 1995 CBE CS. The Department did not have at its disposal a sample of monthly demand and usage data for industrial customers. It a

pplied the CBECS commercial c

ustomer monthly

data to e stimate th e monthly billsfor i ndust rial customersby

adju sting the c ustom er we ight s to compen sate for t he la rge r size and the c orresponding la

rger l oad factors of ind

ustrial c ustomers. The Dep artme nt ass umed t hat mo nthl y demand an d usage for la rger in dust rial a nd lar ge commercial customers are similar. I t verified this assumption by comparing load factor distributions for C&I customers for a utility in the southeastern U.S. The Department found that the differences between customer classes were much smaller than the variability within each class, a lthough t he aver age loa d factor for gr oups of ind

ustrial c ustomers w

ith peak l oads less than 500 kW can be 0–30 percent less than the load factor f or commercial customers with the same annual peak load. The Department explored the potential impact of this assumption on the analysis by

examining the sensitivity of the L CC results to changes in the average transformer loadi ng. 6.3.3.2 Customer Sampling Weights The customer sampl ing wei ght is a n umber tha

t is propor

tional to the probab ility

that a particular customer sample will be selected during a national LCC calculation. I t should be pr op or ti on al to th e p ro ba bi li ty t ha t a tr an sf or me r o f a pa rt ic ul ar de si gn li ne ma y be ow ne d b y a6-17

customer with load characteristics similar to the customer sample data. The Department adjusted the sample

weight s for com

mercial customers provide d by

CBECS to pr

oduce sa mple weig

hts for equivalent industrial customers and to ensure that customers with loads too small for a particu lar tran sformer

design were not i

ncluded. The Depa

rtment ad justed the CBECS wei ghts by a power o f the cu stom er load to pro duce a d istr ibut ion o f cust omers that h as the same av erage load as in dustrial c ustomers. The Depa

rtment as signed a

zero weig

ht to those

customers whose av er ag e d em an d w as le ss th an th e t ra ns fo rm er ca pa ci ty. To produce a distribution of monthly demand a nd usage data to represent industrial customers, the De

partmen t examined t

he EI A’s For m 861 data

2 from 1995 to calculate the average size ratio between industrial and c ommercial customers for 1995. The Department found that, on average, industrial customers had loads 26.2 times larg er than those of commercial customers in 1995. T

hen, for the CBECS d

istribution of customers, for those bu ildings w ith monthly usage a

nd demand data, the Department constructed a ne w set of weights that had the sam e to tal sum , bu t an ave rag e lo ad 2 6.2 ti mes lar ger th an t he C BEC S d is tri but io n. It const ructed the ne w dist ribut ion b y multip lying the CBECS weight by a power o f the av erage load of the CBECS cu stomer. T he Depa rtment chose the power to pr ovide the desired chang e in average customer size.
Since the Department estima

ted that 6 0 perce

nt of dry -ty pe trans formers

go into commercial buildings, while 40 percent go into industrial buildings, it used a 60/40 we ighted average of the C&I

building weights for the total building weight, whe n the average building demand is larger than the transformer capacity . If the avera

ge building demand is less than the transformer capacity, then the CBECS data for that building have no weight or inf luence on the LCC calculation. This is because dry -type transf

ormers are ty

pically used for c

ustomer componen

t loads for partic

ular cir cuits or e quipment. These c ircuits ha ve deman d that is le ss than the total building demand, and the transformers for the c ircuits are sized to meet this smaller demand. The approach DOE took was based on the fa ct that, when the transformer is larger than the entire customer demand, the customer will own the transformer . In addition, the Department belie ves th at the load c haract erist ics of indu stri al cus tomer s are si mila r to th ose of large commercial customers.
6.3.3.3 Initial Peak Load Initial peak load is the annual, per- unit peak load on the transformer during the first year of operation. The initial peak load is estimated as a percenta ge of the rated peak load of the tran sformer . The I

nstitute of

Electric al and Ele ctronic s Engine ers, I nc. (I EEE)’s Draft Guide for Distribution Transformer Loss Evaluation 7 defines a similar but distinct measure of peak transformer loading called an “E quivalent Annual Peak Load” that a ccounts for changes in peak load over the life o f the tra

nsforme r. IEEE’s Draft Guide refers to the initial peak loading as “In itial Tra nsforme r Loa ding” a nd uses va

lues of 0. 9 and 0.95 in its exampl e calcu lations.6-18

Rather than use the equivalent annual peak load method, the De partment accounted for annual c hange s in peak l oad by

apply ing an a nnual ra te of cha nge in tr ansformer load i

n the L CC calculation to account for y ear-to-y ear changes in transforme r load. The Department characterized a range

of possible initial peak loads by defining a distribution of initial peak loads. Distribution transformers generally are manufactured in discrete kVA r atings representing their power handling capacity . On average, the eac h kVA rating is 50 percent larg er then the previous kVA rating (measured re lative to the smaller rating). Transformers c an be loaded above their kVA rating (or "namepla te capacity ") for short periods of time. However, tra nsformers are often sized conservatively to avoid the possibility of an overload, espe cially for low-voltage, dry-ty pe transformers. The Department rec eived stakeholder comments that medium-voltage, dry-ty pe trans formers

are loa ded more heavily than low- voltage , dry

-ty pe trans formers , 8 and thus the Department selected higher initial peak loa ding for medium-voltage, dry -type transf

ormers compared to low-voltage dry -types. The initial peak loa d on a transformer ranges f rom 60 percen t to 90 per

cent if e lectric al engi

neers a ccurat ely size dry -ty pe trans formers

conservatively with a 10 percent safety

margin relative to the nameplate capa city. The hig

h end of the range, i.e., 90 p ercent

initial pe ak loadin

g, is the maximum initia

l peak loa d with a 10

percen t safety margin. The low end of the rang e of 60 percent initial peak loading ref lects the threshold peak load whe re a sma ller kVA rating can be se lected w

ith 90 per cent pea k loading . In r

esponse t o stakeholder comments, the Department adjusted this assumption for medium-voltage, dr y-ty pe transformers and selected initial peak loadings 10 pe rcent higher than the low-voltage , dry-ty pe transformer case. The Depar tment therefore selected a distribution for the initial peak load that has a constant probability be tween 60 percent and 90 percent of na meplate capacity

for lowvoltage, dry-type transf

ormers and a constant probability between 70 percent and 100 perce nt of namepla te for me dium-volta

ge, dr y- typ e transf

ormers. The Department believes that, in selecting an a ppropriate kVA rating for an applica tion, engineers choosing dry

-type transf

ormers are conservative and do not take a dvantage of the fact that transformers can be safely overloaded for short periods of time. The National Electric Code 9 encou rages co nserv ative trans forme r siz ing beh avior by requir ing a tr ansfo rmer t hat is servi ng a secon dary circu it of l ess th an 600 V to be rated a t not less t han 80 percen t of th e tota l ampe rage of the secondary

circuit protection (Table 450.3(A) of the Code).

6.3.3.4 Transformer Load Factor The transformer load factor is the ratio of the a verage load to the annual peak loa d. To estimate the load factor on the transformer, the De partment examined the load factors of the loads in the CBECS 1995 monthly building demand and usage data and derived distributions consistent with these data. Figure 6.3.1 shows an aggregate histogra m of the load factors from these data, for those buildings with both demand and usage data.6-19

Figure 6.3.1 Histogram of Annual Load Factors Derived from Monthly CBECS

1995 Bill Data

From Fig ure 6.3. 1, the De

partmen t estimate d that the

minimum loa

d factor is approxima

tely 0.01 and t

he maximum lo ad fact

or is appr oximately 0.85, with

only a few da ta points outside this range. The Department modeled the distribution of transformer load factors as a triangular probability

distribution with the values of 0.01 and 0.85 as the minimum and maximum of the distribution, respectively. The Depar tment set the maximum probability point of the triangular distribution at 0.32 so that the mean load factor of the triangular distribution matched the mean load factor of the CBECS data.
Availabl e data in

dicate that, on ave

rage, for build

ings, loa d factors increa se with increasing peak load. This relationship is due to diversity effects, where the fluctuations of many smaller loads tend to average out over time, such tha t the relative fluctuations in the sum of many individual loads is smaller than the relative fluctuations in the sum of a few individual loads. The variation of the load factor with the annual peak de mand is illustrated in Figure 6.3.2 for the CBECS 1995 building s that hav e both mont hly usage and dema

nd data. T

he rela tionship between load factor and peak load illustrated he re is insensitive to whether monthly or a nnual data are used. The Department used the f ollowing equation to model the relationship between annual peak load and mean load factor:6-20

Figure 6.3.2 Scatter

plot of Annual Lo ad Fact or versu s Annual Pe ak Dema nd from Monthly CBECS 1995 Bill Data

LF = 0.0504Ln(x) + 0.1212 Eq. 6.6
where:
Ln = the natur al loga rithm, x = the annual peak load, and LF = the load factor. Figure 6.3.2 also shows the logarithmic fit to the load fa ctor/annual demand relationship for the CBECS data.

Application of this analysis to the estimation of transfor mer load factors assumes that the statistical behavior of transformer loads is similar to the statistical behavior of whole building loads.6-21

6.3.3.5 Root-M ean-Square-to-Ave rage Load R atio The root-mean-square-to-aver age load ratio is the ratio of the RMS load on the transformer to the average load on the transformer. Distribution transformer load losses are pr op or ti on al to th e s qu ar e o f t he RM S l oa d o n t he tr an sf or me r. Fo r l oa ds wi th la rg e v ar ia bi li ty, the RMS and the average load on the transfor mer may be sig

nificantly differ

ent. The Department analyzed hourly

load data to characterize the ratio of the RMS load to the avera ge load on the trans forme r. Thi s chara cteri zati on in clude d an es tima te of t he vari abili ty in the RMS- to-av erage load ratio, and the dependence of this ratio on the load fa ctor of the load being served by the transformer. The Depa rtment analy

zed both old

er, publi c data f

rom an ELCAP study

of hourly electrical loads in the Northwest in 1987 and 1988, 10 and more recent (proprietary ) hourly load data from the Southeast from 1998, 1999, and 2000. I t found consistent behavior between ELCAP commercial building loads and both industrial and commer cial loads from the more recent southeastern data. The Depa rtment found the differences between theaverage RMS-toaverage load ra

tios from t

he data s ets to be le ss than 10 p ercent

. The Depa rtment fo und that the RMS-to-a

verag e load ra

tio depen ded on the

load factor. I

t fit the relationship between load factor and (RMS/Avg -1) to an exponential trend line with an R-square of 0.8. This relationship can be expressed by the following equation: (RMS/Avg - 1) = 1.4 × e -7*LF Eq. 6.7 where: RMS/Avg = the ratio of the RMS load to the average load, and LF = the annual load factor.
In its treatme nt of RMS-to -avera

ge load ratios, the Depar

tment assu

med that:
1. The statistical behavior of a set of whole-building loads of a given average loa

d is similar to th e stat isti cal beh avior of a set of ind ivid ual tr ansfo rmer l oads w ith t he sam e average load;
2. The RMS loa

d analy zed from hourly

data is the

same as the RMS load a

naly zed from d

ata of higher time resolution (in reality , RMS values from higher-time-resolution data may be higher than RMS values from hourly data); and
3. The load losses on the transformer vary as the square of the load being serve d by the transformer.6-22

In this part of the analy

sis, the Department made no assumptions about the load factor of the load being served by

the transformer, but only estimated the relationship between load factor, average load, and RMS load.
6.3.3.6 Transformer Peak Responsibility Factor The transformer PRF is the square of the ratio of the tr ansformer load at the time of the customer peak load to the transformer peak load. T he PRF of a load depends on how well the load is correlated with the sy stem load; it also depends on the load factor (L F). A load with an LF close to one is likely

to also have a PRF close to one. The Department estimated the distribution of PRF as a function of LF from a vailable hourly load da

ta. The Department used a distribution for PRF values that varies with LF. Fig ure 6.3.3 shows a scatterplot of PRF versus LF for hourly

commercial data from the EL CAP study. The Department a lso examined more recent C&I hour

ly load data and f

ound the results of the ELCAP data analy sis to be consistent with the more recent hourly load data from the Southeast from 1998, 1999, and 2000. The Department fit the mean value of the PRF as a f unction of LF to the following c urve, which is also illustrated as the solid center line in Figure 6.3.3:
PRF mid = (1 + e C

PRF ) /(1+ e C

PRF /LF ) Eq. 6.8
where:
PRF

mid = the mean PFR, C PRF = a calibrated constant equal to 0.6, and LF = the annual load factor. The Department fit the maxima and minima of the scatterplot distribution as a function of LF u sing the

following

equation s: PRF max = Min(1, 6 × PRF mid ) Eq. 6.9
PRF min = Max(0, PRF mid - (1.2 - PRF

mid )) Eq. 6.10
where:

PRF

max and PRF

min = th e m ax im um an d m in im um PF Rs , r es pe ct iv el y, Min = the function that r eturns th e minimum of

two arg uments, and Max = the function that r eturns th e maximum of

two arg uments. The upper and lower solid lines on Figure 6.3.3 a lso show the maximum and minimum bo un ds on th e E LC AP da ta sc at te rp lo t, re sp ec ti ve ly.6-23

Figure 6.3.3 Scatterplot of Peak Responsibility Factor versus Load Factor

In its treatment of PRF, the Depar tment assumed that building loads and transformer loads with the same load factor and annual peak a mplitude have statistically similar behavior for the p eak r espo nsibi lity

fact or, a nd tha t indu stria

l and comme rcia l load s of the sam e ave

rag e size and load factor have statistically similar behavior for the peak responsibility factor. The Depa rtment fo und the af

orement ioned ass umptions to b e consist

ent with ho

urly ELCAP and proprietary

utility data ana lyze d by the Depa rtment.6-24 REFEREN CES

1. Pratt, R. G., M. A. Williamson, E. E. Richman, and N. E. Miller. Commercial Equipment Load s: End -Use L oad an d Con sumer Asses sment Progr am (ELC AP). July, 1990. Pac ific Northwest Laboratory . Richland, WA. Report No. DOE/BP-13795-24. Prepared for the Bonneville Power Administration.
2. U.S. Department of Energy - Energy Information Administration. Form EIA-861: Annual Electric Utility Data. 2001. (La st acce ssed July , 2005.) T his mater ial is ava ilable in Docket #86. Contact Ms. Brenda Edwards-Jones, U.S. Department of E nergy , Building Technologies Program, Mailstop EE-2J, 1000 I ndependence Avenue, SW, Washington, DC, 20585-0121, telephone (202) 586-2945 for more information. <http://ww

w.eia.d oe.gov /cneaf /electr icity /page/ eia861.h tml>
3. U.S. Department of Energy - Federal Energy

Regulatory

Commission. Form No. 1 - Electric Utility Annual Report. 2002. (La st acce ssed Fe bruary 11, 2005.)

This mate

rial is available in Docket #86. Contact Ms. Brenda Edwar ds-Jones, U.S. Department of Energy , Building Technologies Progra m, Mailstop EE-2J, 1000 Independence Avenue, SW, Washington, DC, 20585-0121, telephone (202) 586-2945 for more information. <http://www.ferc.gov/docs-filing/efor ms/form-1/form1_blank.pdf>
4. U.S. Department of Energy - Federal Energy

Regulatory

Commission. Form No. 714 - Annual Electric Control and Planning Area Report. 2002. (Last accesse d February 18, 2005.) Th

is materi al is ava

ilable in D ocket #86 . Contact M s. Bren da Edwar ds-Jones, U.S. Department of Energy , Building Technologies Progra m, Mailstop EE-2J, 1000 Independence

Avenue, SW, Washington, DC, 20585-0121, telephone (202) 586-2945 for more information. <http://www.ferc.gov/docs-filing /eforms/form-714/data.asp>
5. U.S. Department of the Inter ior - Bureau of Reclamation. Permissib le Loading of OilImmersed Transformers and Regulators. 1991. Facilities Branch, Denver Of fice, Denver, CO. (L ast acc essed Ma

rch 25, 2 005.) <h

ttp://www. usbr.g ov/power /data/fi st_pub.htm

l>
6. U.S. Department of Energy -Energy Information Administration. Information on the Commercial Building Sector. 1995. (La st acce ssed June, 2 005.) Thi s materia l is availa ble in Do ck et #8 6. Co nt ac t M s. Br en da Ed wa rd s- Jo ne s, U. S. De pa rt me nt of En er gy, Buil ding Tech nolog ies Pr ogr am, Ma ilsto p EE- 2J, 100 0 I

ndep ende nce A venue, SW, Washington, DC, 20585-0121, telephone (202) 586-2945 for more information. <http://ww

w.eia.d oe.gov /emeu/cb ecs/>
7. Institute of Electrical and Elec tronics Engineers I

nc. Draft Guide for Distribution Transformer Loss Evaluation. October, 2001. 345 East 47th Street, New York, NY. Report No. IEEE PC57.12.33/D8.6-25

8. Hopkinson, P. J. HVOLT Consultants Inc. ANOPR for Distribution Transformers, EERM/STD-00-550, SNOPR and ANOPR Comments, comment No. 65, p. 3. Personal communication. November 8, 2004.
9. National Fire Protection Association. National Fuel Gas Code -2002 Edition. 2002. 1 Battery march Park, P.O. Box 9101, Quincy MA

. 10. Taylor, Z . T. and R. G. Pratt. Description of Electric Energy Use in Commercial Buildings i

n the Pac ific Northwe

st. 1989. Bonneville Power Administration. Portland, OR. Report No. DOE/BP-13795-22. .