- Email: [email protected]
Simulation model of household fuel uses
Simulation model of household fuel uses Eric Hirst, William Lin and Jane Cope Energy Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA (Received 19 July 1976)
Two basic types of model are used to evaluate energy use and conservation alternatives. First is the econometric approach, which uses detailed statistical data on energy prices, incomes, energy consumption, and other economic variables. These data are used to estimate coefficients in hypothesized equations that relate energy use to its assumed determinants. These equations can then evaluate the impacts of changes in the independent variables on energy use. For example, an econometric model might relate industrial demand for electricity to prices of electricity. gas, oil, and coal; to GNP; and to the average wage rate. This model can then estimate future levels of industrial demand for electricity, in response to assumed changes in fuel prices and the other independent variables. The second approach is the engineering process model. Here, the laws of thermodynamics are combined with equations from heat transfer, fluid mechanics, and other engineering disciplines to evaluate the energy performance of a particular system. For example, computer models exist that evaluate heating and cooling loads for particular buildings. Input data for these models include the geometry, orientation, and construction of the building; plus detailed weather information (temperatures, solar insolation, wind velocity, wind direction). Outputs from these models include hourly energy flows into and out of the various surfaces of the building; roof, windows, walls and floor. Such models can evaluate changes in building energy requirements due to changes in construction practices (increased insulation, fewer windows, less infiltration). The econometric approach to energy modelling explicitly incorporates behavioural aspects of energy use; these models allow one to predict consumer response to changes in various economic determinants. However, econometric modelling is devoid of information on the technologies of energy use. Such models cannot evaluate the impacts on energy use of new energy-using systems, nor can they evaluate the impacts of government regulations concerning energy efficiencies of equipment, processes, and structures. Engineering models, on the other hand, are explicitly sensitive to design changes and technological advances that affect energy requirements. However, engineering models are silent with respect to behavioural changes induced by either economic or technological changes.
This paper describes a detailed engineeringeconomic model of household fuel uses that is explicitly sensitive to the major demographic, economic, and technological determinants of fuel use. This model was designed to combine the best features of both econometric and engineering process approaches into a single model. The model described here simulates energy use on an annual national basis from 1970 to 2000. The model aims to provide an analytical tool with which to evaluate a variety of energy conservation policies and technological improvements with respect to their impacts on residential energy use and expenditures over time. The model, as presently constructed, deals with energy use at the national level for four fuels (electricity, gas, oil, and other); six end uses (space heating, water heating, refrigeration, cooking, air conditioning, and other); and three housing types (single-family units, apartments, and trailers). Household energy use (for each fuel, end use, housing type, and year) is derived as the product of several determining factors. These factors and their derivations are described here and detailed elsewhere’.
Structure of the model The overall structure 2. The first submodel
of the model is shown in Figure develops the demographic
t Simulation equations
Initial conditions (1970) Boundary conditions (1970-2000)
I
Figure 7 Schematic of residential energy use model. HT, stock of occupied housing units; NHT, new construction of occupied housing units; E, elasticity; Q, fuel use; NEU, energy use for new equipment; NT/, thermal integrity of new structures. Superscripts: i, fuel type (4: electricity, gas, oil, other); j, independent variable (4: prices of electricity, gas, oil; income); k, end-use function (6: space heating, water heating, refrigeration, cooking, air conditioning, other); m, housing type (3: single-family, multifamily, mobile home). Subscripts: o, ownership; U, usage; t, time
Appl.
Math.
Modelling,
1977,
Vol 1, March
177
Simulation
model
of household
fuel uses: Eric Hirst et al.
POP:
changes in fuel prices and incomes, while the second gives the responsiveness of equipment usage (with ownership held constant) to changes in prices and incomes. This submodel computes a total of 144 elasticities (short and long run for 3 fuels x 4 price and income variables x 6 end-uses). The third submodel will, when complete,? calculate unit energy requirements and initial costs for residential heating-ventilating-air conditioning (HVAC) equipment, appliances, and structures. These energy and cost figures will be estimated as functions of engineering design changes to increase energy efficiency. In the present version of the model capital costs do not appear, and energy use values for each type of equipment and structure are exogenously specified. The residential energy use simulator combines outputs from the housing, elasticity, and engineering cost submodels with appropriate initial conditions for 1970 and boundary conditions for the period 1970-2000. Outputs from the simulator include 72 fuel use components (Qfkm) for each year (4 fuels x 6 end uses x 3 housing types).8 Each fuel-use component is determined in the simulation as the product of five factors:
Household formation
HR;
HH: Occupied housing stock
I
I
HT:”
1
New
RR:
construction
I ~ NHT;”
Figure 2 Schematic of housing model. POP, population; HH, households; HR, headship rate, HH;/POP;; G, housing type occupancy rate; HT. occupied housing stock; RR, replacement rate; NHT, new construction of occupied housing units. Superscripts: n, age group; m, housing type. Subscript: i, year
determinants of household fuel use. This housing model (Figure 2) estimates stocks of occupied housing units by type (single-family units, apartments, and trailers) for each year of the simulation. Based on calculations of household formation and retirements from the existing stock of occupied units, new construction requirements are calculated each year to ensure that the stock of occupied housing matches demand. The housing model used here was originally developed for the US Forest Service2. It has since been slightly modified at ORNL. The second component of the energy simulation, the elasticity estimator evaluates the economic determinants of fuel use. This programme (Figure 3) calculates price and income elasticities* of the three major household fuels (electricity, gas, and oil) for each of the six end uses. Each elasticity is decomposed into two elements: an elasticity of equipment ownership (E,) and an elasticity of equipment use (E,). The first gives changes in equipment ownership in response to
Qfk” = Hr.
where HT is the stock of occupied housing units, C, fraction (market share) of households with a particular type of equipment; TI, the thermal integrity of housing units (for space heating and air conditioning only); EU, average annual energy use for the type of equipment, and U is a usage factor (see Figure 1). As an example, consider consumption of electricity for space heating in single-family homes. HT is the stock of occupied single-family homes and C is the fraction of single-family homes that use electricity for heating. TI is the average thermal integrity (scaled to 1970, Tl,,,o = 1.0) of single-family homes that use electricity for heating, EU is the average annual energy requirement (in J/unit) of an electric space heating system, and U is a usage factor (U,,,, = 1.0) that reflects the intensity with which households use their electric heating systems. The stocks of occupied housing units are obtained as outputs from the housing model. The market share and usage terms, C and U , are determined by equations of the form:
c
%&‘!;.
elasticities
C;"" .Tlf”“. EUj”“. Uik
for each end-use E’J’L I,
3
/ I
Estimation of short-run elasticities, lag values for cross-price terms
j= 21 1
c
=
i.j =
estimator. (See Figure 7 for Subscripts: H, household; C. run. d, y, lag values; t, average of H/C use of fuel i in household use of fuel i for end
use k
Appl.
Math.
Modelling,
1977,
II
t Tljkm ,yUjkm I t
+ constantikm
The Y values are the dependent variables (either C or U) and the X values are independent variables (fuel prices and per capita income). The coefficients, E and L, are from the elasticity estimator. The constants are set so that the equations predict correct values of C and U for 1970.
Estimation of short- and long-run, own-price and income elasticities for ownership and usage; lag values for usage ,JT;ik, ,877k, y",
178
Ji
i
4
I Figure 3 Schematic of elasticity definitions of f and superscripts.) commercial; sr, short run; lr, long lifetime of equipment; F’, fraction household sector; f”, fraction of
]n x
+ Ei4k. In X4* + Lik. In c?, E$. iikj # i, j #
&,:E”,,
Eijk,
In Yikm =
Vol 1, March
4
* Elasticity is defined as y, change in the dependent variable, to a 1% change in the independent variable. Y: that is. E =
y due
(Ayiy)/(A.~ix). t Energy submodels are now being developed for gas and electric water heaters, gas and electric ranges, refrigerators and freezers. fMany of these 72 cells are empty, e.g.. oil-fired refrigerators.
Simulation
The price elasticities are multiplied by the natural logarithm of the product of fuel price, average equipment energy use, and average structural thermal integrity (for space heating and air conditioning). Thus it is hypothesized that consumers respond not to fuel prices alone but to annual operating costs. This formulation provides a strong link between technological changes (in EU and/or TI) and economic changes (fuel prices). For example, if EU for gas waterheating is reduced because of increased jacket insulation, the above equations will predict increases in gas water-heater ownership (at the expense of electric and oil water-heater ownership) and in gas-heated hot water usage (e.g., people will take longer showers), because the cost of operating a gas water heater has been reduced. Thus part of the gaS savings one would predict from increased technical efficiency is lost because of fuel switching (which saves other fuels) and behavioural changes in usage patterns. The EU terms for each type of equipment are calculated on the basis of the NEU (new equipment energy use values) input to the model, average life times, and existing stocks. Thus the EL’ values represent the average energy use of all equipment of that type in use during year t (including new units sold that year and units remaining from the previous year). The TI terms (which only apply to space heating and air conditioning) are derived in a similar manner. However, TI for the housing stock can change in two ways in the model: for new housing units and for existing housing units (retrofit). The simulator keeps track of new housing construction, removals of past housing stocks, and the appropriate TI values for each fuel, end use, and housing type. Household use of ‘other’ fuels (coal, coke, LP gas, and wood) is specified as a residual based on 1970 saturations and fuel use estimates for these fuels. Equipment saturations for the combination of ‘other and none’ are assumed to decay exponentially over time3x4. This simplified specification of other fuel use is unlikely to cause significant forecasting errors, because these fuels only account for a small and declining fraction of total residential fuel use-IO% in 1960; 60/o in 1970 and 5% in 1974. The initial conditions required to run the simulator include values for equipment saturation by fuel, end use, and housing type for 1970 and the corresponding 1969-70 ratios. The 1970 values were determined by performing cross-classifications with the 1970 public use sample tape3. The 1969/1970 ratios were obtained from the 1960. 1970 and 1973 saturations by fuel and end use3v4. Initial values of EU for 1970 were obtained from Dole5, and scaled up to match control totals for residential uses of electricity, gas. oil, and other fuels from Hirst er ul.’ The values of U for 1970 were defined to be 1.0. The ratios of 196911970 usage factors for each fuel were obtained by comparing the 1969 and 1970 residential fuel uses and assumed equipment saturations. Boundary conditions from 1970 to 2000 required to run the model include population, headship rates, fuel prices, incomes. new equipment energy use (by fuel. end use, and housing type). thermal integrity for new structures (by fuel and housing type), and thermal
model
of household
fuel uses: Eric Hirst et al.
integrity for buildings constructed during or earlier than a specified year to, the standards to be implemented in year t, > to (by fuel and housing type). Changing the boundary conditions allows the user to simulate energy use over this 30-year period under various conditions. This can be used to test the energy and energy-expenditure impacts of changes in demographic, economic, technological, and regulatory conditions.
Validating the model It is necessary to evaluate the model’s ability to predict actual energy use (aggregate, by fuel, by end use) for the period 1960-74. This evaluation is performed twice: first with the model starting in 1960 and second with it starting in 1970. Figure 4 compares the actual residential fuel use (electricity, gas, oil, total) with outputs from the model for each year, from 1960 until 1974. The 1960 simulation is excellent at predicting the trends for all three fuels up to 1970. But it under estimates electricity use and over estimates natural gas use for 1970-74; these errors are probably due to the natural gas shortages that first appeared around 1970. Predictions made with the 1970 simulation are more accurate than those with the 1960 simulation, presumably because the initial conditions used for the 1970 run implicitly recognize the recent changes in the availability of natural gas. The 1960 simulation’s end-use distributions for 1970 and 1973 are compared with estimates’,5 in Table 1. (The 1970 simulation’s 1973 end-use distribution exactly matches the actual distribution.) The model slightly over estimates the energy use for space- and water-heating, and under estimates electricity uses for refrigeration and other energy consumers. The refrigerator under prediction was caused by a growth in the average electricity consumption of refrigerators during the 1960s. This growth was due to the use of larger units and widespread adoption of the automatic defrost option. Under prediction of other electricity uses stems from fact that the model does not distinguish between electric dishwashers, clothes washers and dryers. televisions and other small appliances.
~~~~~
1960
1965
t=
----
1970
1975
FIgwe 4 Comparisons of residential energy use data from 1960-74 with outputs from model. (---y, simulation from 1960-75; (---), simulation from 1970-75; 0, total; A, electricity; 0, gas; 0. oil
Appl.
Math.
Modelling,
1977,
Vol 1, March
175
Simulation
model
Table 1 Comparison end-use distributions
of household
fuel uses: Eric Hirst et al.
of actual and predicted
1970, (%) Simulation* Actual Space heating Water heating Refrigeration Cooking Air conditioning Other Total * Simulation
household
1973, (%) Simulation’ Actual
56 14 8 5 4 13 100
58 17 6 5 4 10 100
results from 1960-90
energy
57 17 6 5 5 10 100
55 14 8 5 6 12 100
baseline run.
The results presented here suggest that the residential energy use simulation provides excellent predictions of actual fuel use by fuel and end use from 1960 to 1974. This lends confidence to our use of the mode1’.6 to simulate future residential fuel use trends and patterns.
Conclusions The mode1 developed here provides detailed forecasts of national annual energy use in the household sector for four fuels, six end uses, and three housing types. To calculate each of these fuel use components, the model computes stocks of occupied housing units (and new construction) by type, equipment market-shares by fuel for each end use, average thermal integrity of occupied housing stocks, average unit energy requirements by type of equipment, and usage factors that reflect household behaviour. Thus, the model is sensitive to the major demographic. economic. and technological determinants of household fuel use. Comparisons of
the model’s outputs with historical data for 1960-74 and with other forecasts to 2000 suggest that the mode1 performs well. Although the present mode1 will probably be useful in the evaluation of energy and expenditure impacts of a variety of conservation policies and programmes, it has several limitations. Additional work is currently in progress at ORNL to overcome these 1imitations7.
Acknowledgement The work reported here is sponsored by the Federal Energy Administration and the Energy Research and Development Administration under Union Carbide Corporation’s contract with the Energy Research and Development Administration.
References Hirst, E., Lin. W. and Cope, J. ‘An engineering-economic model of residential energy use’, ORNL/TM-5470, Oak Ridge National Laboratory, 1976 Marcin. T. C. Agricu. Handbook No. 428. US Department of Agriculture, 1972; also Marcin, T. C. Tech. Rep. NC-f I, US Department of Agriculture, 1974 Bureau of the Census, 1970 Census of housing, detailed housing characrrristics. United States Summary. HC( 1)-B], 1972; also 1960 and 1950 Censuses of Housing, US Department of Commerce. Bureau of the Census, Annual Housing Suraq: 1973, General Housing Characteristics for the Unired States and Regions. H-150-73A, US Department of Commerce, 1975 Dole, S. H. Rand Corp., Report R-1641-NSF, 1975 Hirst. E. ‘Residential energy conservation strategies’, ORNLYCON-2. Oak Ridge National Laboratory. 1976 Hirst. E. er ul. ‘An improved engineeringPeconomlc model of residential energy use’, ORNL.CON-8. Oak Ridge National Laboratory. 1977.
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SIMULA T/ON 1DDA Y is a tutorial series of papers begun in 1971. They appear in most issues of S/MULA T/ON and in separately bound annual volumes. They cover the fundamental “do’s and don’ts” of simulation dnd applications in the numberless new fields in which simulation is proving its power and usefulness. SCS PROCEEDINGS are semiannual cloth-bound books devoted to particular areas of simulation and modeling. Subjects explored in past issues included: Mathematical Models of Public Systems, Systems and Simulation in the Service of Society. The Mathematics of Large Scale Simulation-and more drc soon to Lome!
Two basic types of model are used to evaluate energy use and conservation alternatives. First is the econometric approach, which uses detailed statistical data on energy prices, incomes, energy consumption, and other economic variables. These data are used to estimate coefficients in hypothesized equations that relate energy use to its assumed determinants. These equations can then evaluate the impacts of changes in the independent variables on energy use. For example, an econometric model might relate industrial demand for electricity to prices of electricity. gas, oil, and coal; to GNP; and to the average wage rate. This model can then estimate future levels of industrial demand for electricity, in response to assumed changes in fuel prices and the other independent variables. The second approach is the engineering process model. Here, the laws of thermodynamics are combined with equations from heat transfer, fluid mechanics, and other engineering disciplines to evaluate the energy performance of a particular system. For example, computer models exist that evaluate heating and cooling loads for particular buildings. Input data for these models include the geometry, orientation, and construction of the building; plus detailed weather information (temperatures, solar insolation, wind velocity, wind direction). Outputs from these models include hourly energy flows into and out of the various surfaces of the building; roof, windows, walls and floor. Such models can evaluate changes in building energy requirements due to changes in construction practices (increased insulation, fewer windows, less infiltration). The econometric approach to energy modelling explicitly incorporates behavioural aspects of energy use; these models allow one to predict consumer response to changes in various economic determinants. However, econometric modelling is devoid of information on the technologies of energy use. Such models cannot evaluate the impacts on energy use of new energy-using systems, nor can they evaluate the impacts of government regulations concerning energy efficiencies of equipment, processes, and structures. Engineering models, on the other hand, are explicitly sensitive to design changes and technological advances that affect energy requirements. However, engineering models are silent with respect to behavioural changes induced by either economic or technological changes.
This paper describes a detailed engineeringeconomic model of household fuel uses that is explicitly sensitive to the major demographic, economic, and technological determinants of fuel use. This model was designed to combine the best features of both econometric and engineering process approaches into a single model. The model described here simulates energy use on an annual national basis from 1970 to 2000. The model aims to provide an analytical tool with which to evaluate a variety of energy conservation policies and technological improvements with respect to their impacts on residential energy use and expenditures over time. The model, as presently constructed, deals with energy use at the national level for four fuels (electricity, gas, oil, and other); six end uses (space heating, water heating, refrigeration, cooking, air conditioning, and other); and three housing types (single-family units, apartments, and trailers). Household energy use (for each fuel, end use, housing type, and year) is derived as the product of several determining factors. These factors and their derivations are described here and detailed elsewhere’.
Structure of the model The overall structure 2. The first submodel
of the model is shown in Figure develops the demographic
t Simulation equations
Initial conditions (1970) Boundary conditions (1970-2000)
I
Figure 7 Schematic of residential energy use model. HT, stock of occupied housing units; NHT, new construction of occupied housing units; E, elasticity; Q, fuel use; NEU, energy use for new equipment; NT/, thermal integrity of new structures. Superscripts: i, fuel type (4: electricity, gas, oil, other); j, independent variable (4: prices of electricity, gas, oil; income); k, end-use function (6: space heating, water heating, refrigeration, cooking, air conditioning, other); m, housing type (3: single-family, multifamily, mobile home). Subscripts: o, ownership; U, usage; t, time
Appl.
Math.
Modelling,
1977,
Vol 1, March
177
Simulation
model
of household
fuel uses: Eric Hirst et al.
POP:
changes in fuel prices and incomes, while the second gives the responsiveness of equipment usage (with ownership held constant) to changes in prices and incomes. This submodel computes a total of 144 elasticities (short and long run for 3 fuels x 4 price and income variables x 6 end-uses). The third submodel will, when complete,? calculate unit energy requirements and initial costs for residential heating-ventilating-air conditioning (HVAC) equipment, appliances, and structures. These energy and cost figures will be estimated as functions of engineering design changes to increase energy efficiency. In the present version of the model capital costs do not appear, and energy use values for each type of equipment and structure are exogenously specified. The residential energy use simulator combines outputs from the housing, elasticity, and engineering cost submodels with appropriate initial conditions for 1970 and boundary conditions for the period 1970-2000. Outputs from the simulator include 72 fuel use components (Qfkm) for each year (4 fuels x 6 end uses x 3 housing types).8 Each fuel-use component is determined in the simulation as the product of five factors:
Household formation
HR;
HH: Occupied housing stock
I
I
HT:”
1
New
RR:
construction
I ~ NHT;”
Figure 2 Schematic of housing model. POP, population; HH, households; HR, headship rate, HH;/POP;; G, housing type occupancy rate; HT. occupied housing stock; RR, replacement rate; NHT, new construction of occupied housing units. Superscripts: n, age group; m, housing type. Subscript: i, year
determinants of household fuel use. This housing model (Figure 2) estimates stocks of occupied housing units by type (single-family units, apartments, and trailers) for each year of the simulation. Based on calculations of household formation and retirements from the existing stock of occupied units, new construction requirements are calculated each year to ensure that the stock of occupied housing matches demand. The housing model used here was originally developed for the US Forest Service2. It has since been slightly modified at ORNL. The second component of the energy simulation, the elasticity estimator evaluates the economic determinants of fuel use. This programme (Figure 3) calculates price and income elasticities* of the three major household fuels (electricity, gas, and oil) for each of the six end uses. Each elasticity is decomposed into two elements: an elasticity of equipment ownership (E,) and an elasticity of equipment use (E,). The first gives changes in equipment ownership in response to
Qfk” = Hr.
where HT is the stock of occupied housing units, C, fraction (market share) of households with a particular type of equipment; TI, the thermal integrity of housing units (for space heating and air conditioning only); EU, average annual energy use for the type of equipment, and U is a usage factor (see Figure 1). As an example, consider consumption of electricity for space heating in single-family homes. HT is the stock of occupied single-family homes and C is the fraction of single-family homes that use electricity for heating. TI is the average thermal integrity (scaled to 1970, Tl,,,o = 1.0) of single-family homes that use electricity for heating, EU is the average annual energy requirement (in J/unit) of an electric space heating system, and U is a usage factor (U,,,, = 1.0) that reflects the intensity with which households use their electric heating systems. The stocks of occupied housing units are obtained as outputs from the housing model. The market share and usage terms, C and U , are determined by equations of the form:
c
%&‘!;.
elasticities
C;"" .Tlf”“. EUj”“. Uik
for each end-use E’J’L I,
3
/ I
Estimation of short-run elasticities, lag values for cross-price terms
j= 21 1
c
=
i.j =
estimator. (See Figure 7 for Subscripts: H, household; C. run. d, y, lag values; t, average of H/C use of fuel i in household use of fuel i for end
use k
Appl.
Math.
Modelling,
1977,
II
t Tljkm ,yUjkm I t
+ constantikm
The Y values are the dependent variables (either C or U) and the X values are independent variables (fuel prices and per capita income). The coefficients, E and L, are from the elasticity estimator. The constants are set so that the equations predict correct values of C and U for 1970.
Estimation of short- and long-run, own-price and income elasticities for ownership and usage; lag values for usage ,JT;ik, ,877k, y",
178
Ji
i
4
I Figure 3 Schematic of elasticity definitions of f and superscripts.) commercial; sr, short run; lr, long lifetime of equipment; F’, fraction household sector; f”, fraction of
]n x
+ Ei4k. In X4* + Lik. In c?, E$. iikj # i, j #
&,:E”,,
Eijk,
In Yikm =
Vol 1, March
4
* Elasticity is defined as y, change in the dependent variable, to a 1% change in the independent variable. Y: that is. E =
y due
(Ayiy)/(A.~ix). t Energy submodels are now being developed for gas and electric water heaters, gas and electric ranges, refrigerators and freezers. fMany of these 72 cells are empty, e.g.. oil-fired refrigerators.
Simulation
The price elasticities are multiplied by the natural logarithm of the product of fuel price, average equipment energy use, and average structural thermal integrity (for space heating and air conditioning). Thus it is hypothesized that consumers respond not to fuel prices alone but to annual operating costs. This formulation provides a strong link between technological changes (in EU and/or TI) and economic changes (fuel prices). For example, if EU for gas waterheating is reduced because of increased jacket insulation, the above equations will predict increases in gas water-heater ownership (at the expense of electric and oil water-heater ownership) and in gas-heated hot water usage (e.g., people will take longer showers), because the cost of operating a gas water heater has been reduced. Thus part of the gaS savings one would predict from increased technical efficiency is lost because of fuel switching (which saves other fuels) and behavioural changes in usage patterns. The EU terms for each type of equipment are calculated on the basis of the NEU (new equipment energy use values) input to the model, average life times, and existing stocks. Thus the EL’ values represent the average energy use of all equipment of that type in use during year t (including new units sold that year and units remaining from the previous year). The TI terms (which only apply to space heating and air conditioning) are derived in a similar manner. However, TI for the housing stock can change in two ways in the model: for new housing units and for existing housing units (retrofit). The simulator keeps track of new housing construction, removals of past housing stocks, and the appropriate TI values for each fuel, end use, and housing type. Household use of ‘other’ fuels (coal, coke, LP gas, and wood) is specified as a residual based on 1970 saturations and fuel use estimates for these fuels. Equipment saturations for the combination of ‘other and none’ are assumed to decay exponentially over time3x4. This simplified specification of other fuel use is unlikely to cause significant forecasting errors, because these fuels only account for a small and declining fraction of total residential fuel use-IO% in 1960; 60/o in 1970 and 5% in 1974. The initial conditions required to run the simulator include values for equipment saturation by fuel, end use, and housing type for 1970 and the corresponding 1969-70 ratios. The 1970 values were determined by performing cross-classifications with the 1970 public use sample tape3. The 1969/1970 ratios were obtained from the 1960. 1970 and 1973 saturations by fuel and end use3v4. Initial values of EU for 1970 were obtained from Dole5, and scaled up to match control totals for residential uses of electricity, gas. oil, and other fuels from Hirst er ul.’ The values of U for 1970 were defined to be 1.0. The ratios of 196911970 usage factors for each fuel were obtained by comparing the 1969 and 1970 residential fuel uses and assumed equipment saturations. Boundary conditions from 1970 to 2000 required to run the model include population, headship rates, fuel prices, incomes. new equipment energy use (by fuel. end use, and housing type). thermal integrity for new structures (by fuel and housing type), and thermal
model
of household
fuel uses: Eric Hirst et al.
integrity for buildings constructed during or earlier than a specified year to, the standards to be implemented in year t, > to (by fuel and housing type). Changing the boundary conditions allows the user to simulate energy use over this 30-year period under various conditions. This can be used to test the energy and energy-expenditure impacts of changes in demographic, economic, technological, and regulatory conditions.
Validating the model It is necessary to evaluate the model’s ability to predict actual energy use (aggregate, by fuel, by end use) for the period 1960-74. This evaluation is performed twice: first with the model starting in 1960 and second with it starting in 1970. Figure 4 compares the actual residential fuel use (electricity, gas, oil, total) with outputs from the model for each year, from 1960 until 1974. The 1960 simulation is excellent at predicting the trends for all three fuels up to 1970. But it under estimates electricity use and over estimates natural gas use for 1970-74; these errors are probably due to the natural gas shortages that first appeared around 1970. Predictions made with the 1970 simulation are more accurate than those with the 1960 simulation, presumably because the initial conditions used for the 1970 run implicitly recognize the recent changes in the availability of natural gas. The 1960 simulation’s end-use distributions for 1970 and 1973 are compared with estimates’,5 in Table 1. (The 1970 simulation’s 1973 end-use distribution exactly matches the actual distribution.) The model slightly over estimates the energy use for space- and water-heating, and under estimates electricity uses for refrigeration and other energy consumers. The refrigerator under prediction was caused by a growth in the average electricity consumption of refrigerators during the 1960s. This growth was due to the use of larger units and widespread adoption of the automatic defrost option. Under prediction of other electricity uses stems from fact that the model does not distinguish between electric dishwashers, clothes washers and dryers. televisions and other small appliances.
~~~~~
1960
1965
t=
----
1970
1975
FIgwe 4 Comparisons of residential energy use data from 1960-74 with outputs from model. (---y, simulation from 1960-75; (---), simulation from 1970-75; 0, total; A, electricity; 0, gas; 0. oil
Appl.
Math.
Modelling,
1977,
Vol 1, March
175
Simulation
model
Table 1 Comparison end-use distributions
of household
fuel uses: Eric Hirst et al.
of actual and predicted
1970, (%) Simulation* Actual Space heating Water heating Refrigeration Cooking Air conditioning Other Total * Simulation
household
1973, (%) Simulation’ Actual
56 14 8 5 4 13 100
58 17 6 5 4 10 100
results from 1960-90
energy
57 17 6 5 5 10 100
55 14 8 5 6 12 100
baseline run.
The results presented here suggest that the residential energy use simulation provides excellent predictions of actual fuel use by fuel and end use from 1960 to 1974. This lends confidence to our use of the mode1’.6 to simulate future residential fuel use trends and patterns.
Conclusions The mode1 developed here provides detailed forecasts of national annual energy use in the household sector for four fuels, six end uses, and three housing types. To calculate each of these fuel use components, the model computes stocks of occupied housing units (and new construction) by type, equipment market-shares by fuel for each end use, average thermal integrity of occupied housing stocks, average unit energy requirements by type of equipment, and usage factors that reflect household behaviour. Thus, the model is sensitive to the major demographic. economic. and technological determinants of household fuel use. Comparisons of
the model’s outputs with historical data for 1960-74 and with other forecasts to 2000 suggest that the mode1 performs well. Although the present mode1 will probably be useful in the evaluation of energy and expenditure impacts of a variety of conservation policies and programmes, it has several limitations. Additional work is currently in progress at ORNL to overcome these 1imitations7.
Acknowledgement The work reported here is sponsored by the Federal Energy Administration and the Energy Research and Development Administration under Union Carbide Corporation’s contract with the Energy Research and Development Administration.
References Hirst, E., Lin. W. and Cope, J. ‘An engineering-economic model of residential energy use’, ORNL/TM-5470, Oak Ridge National Laboratory, 1976 Marcin. T. C. Agricu. Handbook No. 428. US Department of Agriculture, 1972; also Marcin, T. C. Tech. Rep. NC-f I, US Department of Agriculture, 1974 Bureau of the Census, 1970 Census of housing, detailed housing characrrristics. United States Summary. HC( 1)-B], 1972; also 1960 and 1950 Censuses of Housing, US Department of Commerce. Bureau of the Census, Annual Housing Suraq: 1973, General Housing Characteristics for the Unired States and Regions. H-150-73A, US Department of Commerce, 1975 Dole, S. H. Rand Corp., Report R-1641-NSF, 1975 Hirst. E. ‘Residential energy conservation strategies’, ORNLYCON-2. Oak Ridge National Laboratory. 1976 Hirst. E. er ul. ‘An improved engineeringPeconomlc model of residential energy use’, ORNL.CON-8. Oak Ridge National Laboratory. 1977.
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