7

- i CHAPTER 7. ENERGY USE AND END

- USE LOAD CHARACTERIZATION

TABLE OF CONTENTS

7.1 INTRODUCTION ........................................................................................................... 7-1 7.2 LOAD MODEL FOR LIQUI D- IMMERSED TRANSFORMER S ................................ 7-2 7.2.1 Inputs to Hourly Load Model .......................................................................................... 7-3 7.2.1.1 Utility Information ......................................................................................... 7-3 7.2.1.2 Initial Peak Transformer Loading .................................................................. 7-4 7.2.1.3 Hourly Price -Load Model .............................................................................. 7-5 7.2.1.4 Transformer Load Simulation ........................................................................ 7-7 7.3 MODEL FOR DRY

- TYPE TRANSFORMER LOADS ................................................. 7-8 7.3.1 Overview of Monthly Load Model .................................................................................. 7-8 7.3.2 Monthly Load Simulation ................................................................................................ 7-8 7.3.3 Inputs to Monthly Load Model ........................................................................................ 7-9 7.3.3.1 Customer Data ............................................................................................... 7-9 7.3.3.2 Initial Peak Transformer Load ..................................................................... 7-10 7.3.3.3 Transformer Loss Factor .............................................................................. 7-10 7.3.3.4 Coincident Peak Load .................................................................................. 7-11

LIST OF TABLES

Table 7.2.1 Definition of EMM Regions in NEMS ................................................................ 7-4

LIST OF FIGURE S

F igure 7.2.1 Electricity Market Module Regions in NEMS ..................................................... 7-4 Figure 7.2.2 Distribution of Initial Peak Loading Used in the Hourly Load Analysis ............ 7-5 Figure 7.2.3 Binned Load Versus Marginal Price for EMM Region SERC ............................ 7-6 Figure 7.2.4 Average Joint Probability Distribution for C&I Customers, 1998-2000 ............. 7-77

- 1 CHAPTER 7. ENERGY USE AND END

- USE LOAD CHARACTERIZATION

7.1 INTRODUCTION
The U.S. Department of Energy (DOE) characterized energy use and end -use load for distribution transformers. Estimates of energy use enabled evaluation of energy savings associated with operatin g distribution transformers at various efficiency levels . Th e characterization of end

- use load enabled evaluation of the impact of load on electricity demand. DOE’s analysis produced a distribution of results for a range of installation type s, operating conditions, and climate locations intended to represent the diversity of the application and performance of distribution transformers.

D istribution transformers consume energy via both no-load losses and load losses. Noload losses, which are constant over time

, occur whenever a transformer is e nergized by power lines. Load losses vary with the square of the load t he transformer is serv ing

. There are two types of distribution transformers: liquid -immersed and dry. Liquid- immersed transformers are owned primarily by electric utilities . U tilities p ay marginal costs for the power used to generate electricity

, costs that can vary by the hour. DOE therefore developed a statistical simulation model to estimate the hourly load characteristics of liquid

- immersed transformer s and to develop a correlation between hourly loads and system loads. D ry

- type transformers are ow ned by commercial and industrial (C&I) establishments , which are billed for electricity according to a tariff. For dry-type distribution transformers, DOE used empirical estimates of load characteristics to estimate monthly average (root mean square) loads and peak coincident loads. This chapter first describes transformer losses, then presents the details of the load characterization models DOE developed for liquid-immersed and dry- type transformers

. The no-load losses experienced by distribution transformers arise primarily from the switching of the magnetic field in the transformer core material. Tho se losses , which are roughly constant, occur whene ver the transformer is energized ( i.e. , connected to a live power line). L oad losses, also known as resistance or I 2 R losses

, vary in response to the changing load on the transformer . Load losses are proportional to the load squared plus a relatively small temperature correction (<15 percent for loads less than the rated load). DOE uses the following formula, which incorporates both load and no-load losses, to estimat e the energy used by a distribution transformer

.

E T = ∈ NLL + E + ∈ LL � E E max � � 2

Where : ∈ NLL = the no-load loss rate

, E

= the total energy used by a transformer experiencing instantaneous load,
∈ LL = the load loss rate, and E

max = the expected peak load on the transformer

.7

- 2 The characteristics of transformer load s required for DOE’s life

- cycle cost ( LCC ) analysis also depend on the way the user ’s electricity is priced. Because approximately 95 percent of liquid

- immersed transformers are owned by electric utilities, the appropriate electricity price for those transformers is the cost of produc tion , which varies hourly. For those types of transformer s, DOE’s analysis was based on hourly load and price data. The electricity

use of dry- type transformers, which are installed primarily in commercial and industrial buildings, is billed monthly. For those types of transformers , DOE developed an analysis based on monthly, building- level data.

7.2 LOAD MODEL FOR LIQUID

- IMMERSED TRANSFORMER S
This section describes the hourly load model DOE developed in support of its LCC analysis for liquid

- immersed transformers.

The operating cost savings associated with improved transformer efficiency are equal to the energy savings (reduction in losses) times the price of energy. For liquid- immersed transformers, the appropriate pric e is the marginal production cost of electricity. This production
cost , which varies regionally and temporally, correlates strongly with the magnitude of the total electric system load. Because t he load on an individual transformer also correlates some what with system load, there is some correlation between transformer load losses and the price of electricity. To capture those correlations, DOE developed a statistical model based on hourly electric system load data, marginal hourly electric system production prices, a joint probability distribution between transformer and system load levels. The steps in the operation of the hourly load simulation program are described below

.

1. The program selects a transformer owner from a list of utilities that own electricity distribution equipment. 2. The program determines a sample weight for the selected utility, based on total kilowatt -hours sold. 3. The program selects the customer type (residential or C&I) served by the transformer and the appropriate weight for that customer type. The weight is assigned based on the fraction of that utility’s electricity sales to that customer type. 4. The program goes through a loop to calculate the hourly transformer loads and system marginal prices for the selected transforme r . System prices, and their dependence on system load, are determined from historical data. Prices differ by region and season . The transformer load is estimated based on a joint distribution function that predicts the transformer load for a given system load. The individual steps in the loop are as follows.

a. Choose a system load value from the system load distribution function. b. Estimate the system price for that system load

. c. Estimate the transformer load for that system load

. 5. For each simulation , t he progr am provides output to be used in calculating the LCC

. The output includes a transformer identification (ID), the utility ID, customer category , and transformer load losses and operating costs.7

- 3 7.2.1 Inputs to Hourly Load Model
The following sections describe the inputs used in simulating the hourly load for liquidimmersed distribution transformers

.

7.2.1.1 Utility Information
The LCC analysis for liquid

- immersed transformer s uses two types of information related to electric utilities

. The first is drawn from the Energy Information Administration’s ( EIA ’s) Form 861 database. 1 Form 861 provides, through its F orm 2, the annual s ales in megawatt -hours for each utility to the residential, commercial , and industrial sectors. Form 86 1 ’s F orm 4 lists all the utilities that own electricity distribution equipment and the county in which that equipment is located . Based on those data, DO E create d a list of utilities that own transformers and assign ed a weight to each based on the electricity sales of that utility.

The second type of utility information used in the LCC analysis is hourly system loads and prices. DOE developed regional system loads and prices for the set of regions defined in the EIA National Energy Modeling System (NEMS) Electricity Market Module (EMM). 2

Figure 7.2.1 The regions rep r esent both national reliability regions and, where they exist, integrated wholesale electricity markets

, as illustrated in

. Each r egion in turn comprises a number of electric utility control area operators (CAO s), some of which may also be utilit y companies

. DOE obtained hourly load and system lambda data (for regions without wholesale markets) or day- ahead market price data (for market regions) from the Federal Energy Regulatory Commission ( FERC ) Form 714 database. 3 DOE aggregated t he hourly data to produce regional time series for the EMM regions. Appendix 7-B contains the list of entities

, along with their designated CAO and EMM regions, for which DOE obtained the FERC data used to create the hourly time series

.7

- 4 Figure 7.2.1 Electricity Market Module Regions in NEMS

The numbered regions in Figure 7.2.1 are de scribed in Table 7.2.1

.

Table 7.2.1 Definition of EMM Regions in NEMS

Index Abbreviation Definition 1 ECAR East Central Area Reliability Coordination Agreement 2 ERCOT Electric Reliability Council of Texas 3 MAAC Mid

- Atlantic Area Council 4 MAIN Mid

- America Interconnected Network 5 MAPP Mid

- Continent Area Power Pool 6 NY New York 7 NE New England 8 FL Florida Reliability Coordinating Council 9 SERC Southeastern Electric Reliability Council 10 SPP Southwest Power Pool 11 NPP Northwest Power Pool 12 RA Rocky Mountai n Power Area 13 CA California

7.2.1.2 Initial Peak Transformer Loading

DOE used a distribution of values for initial peak loading to characterize the annual peak load served by each transformer in its simulation. The initial peak loading is the ratio of the7

- 5 transformer’s peak load in the first year of operation to the transformer’s rated load

, before accounting for any new load growth that occurs later

. 4 DOE selected a distribution of initial peak loadings that had a median of 85 percent, a minimum of 50 percent, and a maximum of 130 percent. Standard engineering practice for sizing distribution transformers selects a transformer based on the expected annual peak of the load being served, with some provision for load growth. Given the provision for future growth, initial peak loading usually is less than 100 percent. In practi ce, h owever , there usually is some error in estimating the peak load that will be served, and engineers generally use a discrete set of transformer ratings that are imperfectly matched with the expected peak load. Distribution transformers generally are manufactured in discrete kilovolt- ampere (kVA) ratings and, on average, the next

- larger kVA rating is 50 percent larger than the next

- lower kVA rating (measured relative to the smaller size). Therefore, the initial peak loading can be as high as 130 percent, because for short periods a transformer can be loaded to more than 130 percent of nameplate capacity. 5 Figure 7.2.2 illustrates the distribution of initial peak loading that DOE used.

Figure 7.2.2 Distribution of Initial Peak Loading Used in the Hourly Load Analysis

7.2.1.3 Hourly Price -Load Model
The price -load model relates the marginal cost of meeting the next load increment to the current system load. The marginal cost is interpreted as the time -varying marginal price of electricity for a system. The Department estimated the relationship between system loads and system marginal prices for each region based on hourly data collected by FERC Form 714 3 and, where appropriate, day- ahead market da ta from independent system operators. FERC data provide hourly system load and lambda values, where the system lambda is defined approximately as the operating cost of the generating unit on the dispatch margin. For regions that have integrated wholesale e lectricity markets , DOE used the d ay

- ahead market data that include the hourly system load and the market- clearing price. D OE used data for 2008, the most recent year for which data from all sources were available. 0.00 0.02 0.04 0.06 0.08 0.10 0.12

50% 60% 70% 80% 90% 100% 110% 120% 130%Peak Load Probability

Transformer Peak Loading7

- 6 The c orrelation between hourly system price s and loads is illustrated in Figure 7.2.3

. This figure shows a scatter plot of price v ersus load for the SERC region. The data pairs (price and load values in each hour) are sorted into bins based on load level . Those bins are represented by different colors in the figure.

Figure 7.2.3 Binned Load V ersus Marginal Price for EMM Region SERC

DOE estimated the marginal system price within each bin as follows.

p j = p̅ j + δ j

Where:

j = the bin index, p̅

j = the average value of the prices in bin j and, δ

j = a random increment within bin j

.

In general, both the average price and the range of hourly prices increases with system load. To capture the increase in price volatility as a function of system load, DOE added a random increment δ to the average marginal price p̅ for each load bin j

. To estimate t he increment δ j , DOE us ed a probability distribution function (PDF) calculated independently for each bin j . The PDF for the increment is assumed to be triangular and centered at zero , with the distribution parameters for each bin determined by the data. The approach is described in more detail in Appendix 7-A. 0 50 100 150 200 250

0 20000 40000 60000 80000 100000 120000 140000 160000Lambda $/MWh

Load MWh7

- 7 Within the LCC spreadsheet , system loads are represented using a load distribution function. This function is calculated by counting the number of times the load level falls inside each load bin. The bin sizes are variable and depend on region; the number of bins is constant and equal to fifteen

.

7.2.1.4 Transformer Load Simulation

DOE estimated the loads on individual liquid

- immersed transformers for both residential and non- residential customers b y creating hourly proxy transformer loads. The important quantities for the LCC analysis are the number of hours the transformer is subject to a given load level and the correlation between transformer loads and system loads. The first is important for determining the total load losses, and the second for accurately estimating the economic value of load losses. To estimate the coincident between peak transformer load and system load

, DOE constructed a joint probability distribution function (JPDF) based on a dataset c onsisting of several hundred hourly whole-building loads. For this analysis, a proxy system load was constructed by summing all the available building loads. DOE then estimated t he J PDF by defining a set of bins for both the proxy system load and individua l load time series, and counting the number of values that fell into each bin. The system load bins used in the JPDF are the same as the load bins used in the hourly price -load model. DOE created a separate JPDF for residential and for C&I customers

. Figure 7.2.4 shows a color plot of the JPDF for C&I
customers . The figure shows the system load bins on the horizontal axis and the transformer load bins on the ver tical axis, with different colors representing the probability that, in a given hour, the system load and transformer loads will fall into the given bin. The figure shows that, for low system loads, transformer loads are distributed broadly , whereas for hi gher system loads transformer loads are more tightly correlated with system load.

Figure 7.2.4 Average Joint Probability Distribution for C&I Customers , 1998-2000 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Transformer Load Bins

Proxy Sytem Load Bins 0.015

- 0.020

0.010

- 0.015

0.005

- 0.010

0.000

- 0.005 Probability7

- 8 7.3 MODEL FOR DRY

- TYPE TRANSFORMER LOA DS

This section describes the modeling approach DOE used to estimate the loading for drytype distribution transformers. Given that this type of equipment is owned primarily by C&I entities , which are billed monthly for electricity, DOE developed appropriate methods to estimate the impacts of higher transformer efficiency on monthly energy losses and demand.

7.3.1 Overview of Monthly Load Model

DOE defined a customer sample for dry -type distribution transformers based on buildinglevel data drawn from the EIA’s Commercial Buildings Energy Consumption Surveys ( CBECS ) for 1992, 1995, and 2003. In its analysis, DOE assumed that each building ha s a transformer, and used building monthly electricity consumption and demand data as inputs to a statistical model that estimates the transformer

- level data. DOE determined the e conomic value of no-load and load losses by the marginal price of electricity for each building, as determined by the electricity tariff. In this analysis, DOE used a previous, detailed study of commercial building energy prices

, 6 which showed that every building’s electricity costs can be represented as a marginal price for energy and a marginal price for demand. Both p rices vary by region and season.

Transformer losses contain a constant component (the no-load or core losses) and a component that depends on the square of the load on the transformer (the load or coil losses). The economic value of transformer losses is a function of the load on the transformer and the timing of th at load with respect to variable energy costs and building peak demand. To the extent that there is a correlation between transformer losses and variable energy costs, the cost of the electrici ty supplying the transformer losses will be different from the average cost of electricity. The LCC analysis for dry

- type transformers uses a statistical model of the monthly transformer loss factors, along with a correlation between individual transformer and whole-building loads, to estimate changes in monthly electricity consumption and peak demand and the corresponding electricity cost savings for C&I customers.

7.3.2 Monthly Load Simulation
The monthly load simulation model embedded in the LCC spreadsheet proceeds as follows.

1. A customer (building) is selected from the sample in the spreadsheet; if the building ’s annual peak load is smaller than the rated capacity of the transformer design under consideration, the building is dropped from the sample. 2. An initial peak loading is assigned to the transformer. 3. The program begins a loop on the monthly electricity consumption and demand data for the building. For each month, the program:

a. calculates the load factor (LF), which is equal to the ratio of the average load to the peak load for that month; b. estimates the transformer loss factor (LSF) as a function of the LF ; and

c. estimates the transformer coincident peak load (CPL) as a function of the LF.7

- 9 4. The monthly load data are passed to the controlling loop and used in the LCC analysis to calculate the operating cost savings from reduced load losses.

7.3.3 Inputs to Monthly Load Model
The following sections describe the inputs to DOE’s monthly load model, which include customer data, initial peak transformer load, transfor mer loss factor, and coincident p eak
t ransformer l oad

.

7.3.3.1 Customer Data
The customer sample for the dry- type transformer LCC analysis was drawn from the 1992 and 1995 CBECS. 7,8 Th o se survey years were used because they include data on monthly building-level electricity consumption and demand. All 1992 and 1995 samples that provided a complete year of monthly data were combined into a single sample. Weights for the full sample were determined by scaling the original building weights to match the floorspace for the corresponding building cate gories given in the most recent CBECS (from 2008). The building categories used to define the weights were based on building activity, census division, and building size.

DOE had no comparable sample to provide monthly data for industrial customers. To represent the fraction of transformers that are installed in industrial buildings, DOE assumed that (1) industrial buildings share the load characteristics of the large buildings defined in CBECS, and (2) industrial buildings utilize transformers in a way that is comparable to similarly sized warehouse-type buildings. In the previous final rule for distribution transformers

, 9 DOE assumed that m onthly demand and usage for large industrial and commercial customers are similar. It verified this assumption by comparing load factor distributions of C&I customers for a utility in the southeastern United S tates . DOE found that the differences among cus tomer classes were much smaller than those within each class

. 9

DOE used f loorspace data from the EIA’s 2006 Manufacturing Energy Consumption Survey 10 to estimate the total floorspace of industrial buildings that would contain transformers covered by this rulemaking. This floorspace was added to the CBECS-based f loorspace for large commercial buildings to determine total weights for each building in the customer sample.

Buildings having annual peak loads less than the transformer capacity specified in the design under consideration we re screened out of the sample. The customer sample contains a
range of building sizes having a wide range of annual peak loads. Although larger buildings undoubtedly contain multiple transformers, DOE currently has no quantitative information on how the number of transformers in a building scales with either the building floorspace or the building annual peak load. Thus, to account for the effect of multiple transformers i n a single building, DOE used a simple approach whereby it multiplied the building sample weight by the number of floors in the building.7

- 10 7.3.3.2 Initial Peak Transformer Load
Initial peak load is the annual peak load on the transformer in the first year of operation divided by its rated capacity . The Institute of Electrical and E lectronics Engineers (IEEE) has a Draft Guide for Distribution Transformer Loss Evaluation 11 that defines a similar measure of peak transformer loading called an “ equivalent annual peak load, ” which accounts for changes in peak load throughout the life of a transformer. IEEE’s Draft Guide , which refers to the initial peak loading as “ initial transformer loading ,” uses values of 0.9 and 0.95 in its example calculations. Rather than applying the IEEE’s equivalent annual peak load, DOE accounted for annual changes in peak load in the LCC calculation by applying an annual rate of change in transformer load. DOE characterized a range of initial peak loa ds by defining a distribution of initial peak loads.

Distribution transformers generally are manufactured in discrete kVA ratings that represent their power- handling capacity. On average, each higher kVA rating is 50 percent larger than the previous kVA rating (measured relative to the smaller rating). Transformers can be loaded above their kVA rating (or nameplate capacity) for short periods. However, transformers are often sized conservatively to avoid the possibility of an overload, especially for low-voltage, dry- type transformers. DOE received stakeholder comments that medium -voltage, dry- type transformers are loaded more heavily than are low -voltage, dry- type transformers

. 12 DOE therefore selected higher initial peak loading for medium-voltage, dry- type transformers than for low-voltage dry-types. I f electrical engineers accurately size dry

- type transformers conservatively with a 10- percent safety margin relative to the nameplate capacity , initial peak load ranges from 60 percent to 90 percent . The high end of the range is the maximum initial peak load that allows for a 10

- percent margin of safety. The low end of the range reflects the th reshold peak load at which the next- smaller kVA rating will provide 90 percent peak loading. In response to stakeholder comments, DOE adjusted this assumption for medium-voltage, dry- type transformers

, select ing initial peak loadings that were 10 percent higher than for the low-voltage, dry- type transformer s. Thus the distribution of initial peak load for low -voltage, dry- type transformers has a constant probability between 60 percent and 90 percent of nameplate capacity ; the distribution for medium-volt age , dry- type transformers has a constant probability between 70 percent and 100 percent of nameplate capacity

. DOE believes that, in selecting an appropriate kVA rating for an application, engineers choosing dry-type transformers are conservative and do no t take advantage of the fact that transformers can be safely overloaded for short periods. The National Electric Code 13

7.3.3.3 Transformer Loss Factor encourages conservative transformer sizing by requiring a transformer that is serving a secondary circuit of less than 600 volts to be rated at not less than 80 percent of the total amperage of the secondary circuit protection ( table 450.3(A) of the code).

For a distribution transformer, the l oss factor (LSF) is the ratio of the annual average load losses to the peak value of load losses. The LSF is equal to the average of the square of the transformer load divided by the square of the peak transformer load.7

- 11 The characteristics of transformer load DOE needed for C&I building owners are the energy and demand savings associated with load losses. The energy savings depend on the LSF, which is proportional to the average value of the squared load. To estimate the load loss factor for each building, DOE used an expression that relates LSF to load factor ( LF ):

LSF = α*LF + (1

- α)*LF 2

where α is a parameter with α < 0.5. The LF , which is available from the CBECS data, is equal to the rati o of the average hourly load to the peak load. DOE estimated a probability distribution for the parameter α based on hourly building load data from the End -Use Load and Consumer Assessment Program ( ELCAP ) 6

7.3.3.4 Coincident Peak Load survey and additional confidential data from stakeholders.

Coincident peak load ( CPL ) captures the coincidence between a transformer’s load and the building’s peak load. For a building that has a single transformer

, the coincidence would be perfect , and the CPL would equal one. In practice , the degree of coincidence depends on how transformers are installed in the building. To model the diversity within transfo rmer loads and total building load s , DOE constructed a statistical model that predicts the CPL as a function of a building’s load factor. T he statistical model is based on data for monthly LFs and LSFs calculated using hou rly building load data from the ELCAP dataset 6 and other data. The modeling approach is discussed in more detail in Appendix 7-A.7

- 12 REFRENCES

1. U.S. Department of Energy- Energy Information Administration Form EIA

- 861: Annual Electric Power Industry Database . (2008).at <http://www.eia.doe.gov/cneaf/electricity/page/eia861.html>

2. Energy Information Administration - Office of Integrated Analysis and Forecasting The National Energy Modeling System . (U.S. Department of Energy: Washington DC, 2009).at <http://www.eia.doe.gov/oiaf/aeo/overview/>

3. U.S. Department of Energy- Federal Energy Regulatory Commission Form No. 714 - Ann ual Electric Control and Planning Area Report . (U.S. Department of Energy- Federal Energy Regulatory Commission: 2008).at <http://www.ferc.gov/docs- filing/forms/form

714/overview.asp>

4. M. E. de Oliveira, A. Padilha-Feltrin & F. J. Candian Investigation of the Relationship between Load and Loss Factors for a Brazilian Electric Utility. (2006). DOI :10.1109/TDCLA.2006.311390

5. U.S. Department of the Interior - Bureau of Reclamation Permissible Loading of OilImmersed Transformers and Regulators. (1991).

6. Pratt, R., Williamson, M., Richman, E. & Miller, N. Commercial Equipment Loads: End

- Use Load and Consumer Assessment Program (ELCAP) . (1990).

7. U.S. Department of Energy- Energy Information Administration 1992 Commercial Buildings Energy Consumption Survey (CBECS) . (1992).at <http://www.eia.doe.gov/emeu/cbecs/92microdat.html>

8. U.S. Department of Energy- Energy Information Administration 1995 Commercial Building Energy Consumption and Expenditures (CBECS) . (1995).

9. U.S. Department of Energy- Office of Building Technologies Chapter 6. Energy Use and End

- Use Load Characterization. Distribution Transformers Energy Conservation Standard Technical Support Document (2007).

10. Institute of Electrical and Electronics Engineers Inc. Draft Guide for Distrib ution Transformer Loss Evaluation . (2001).

11. P.J. Hopkinson HVOLT Consultants Inc. ANOPR for Distribution Transformers, EERM/STD -00-550, SNOPR and ANOPR Comments, comment No. 65, p. 3. (2004).

12. National Fire Protection Association National Fuel Gas Code - 2002 Edition . (National Fire Protection Association: 1 Batterymarch Park, P.O. Box 9101, Quincy MA, 2002).