{"Bibliographic":{"Title":"The economic impact of climate : proceedings of two workshops on the structure of economic models. Volume 2","Authors":"","Publication date":"1980","Publisher":""},"Administrative":{"Date created":"08-16-2023","Language":"English","Rights":"CC 0","Size":"0000239023"},"Pages":["QC\n866.2\n.E2\nClimate D Weather\nE2\nv.2\nSystem\nEconomic\nSystems\nBiosphere\nTHE ECONOMIC IMPACT OF CLIMATE\nVOLUME II\nCONVENED BY\nAMOS EDDY\nMAY 1980","A\nQC\n866.5\nE2E2\nV. 2\nTHE ECONOMIC IMPACT OF CLIMATE\n11\nVolume II\nProceedings of Two Workshops\non the Structure of\nEconomic Models\nConvened by\nAmos Eddy\nPrincipal Investigator\nMay 1980\nGEORGETOWN\nCENTER\nSILVER SPRING CENTER\nFEB 51981\nSponsored by NOAA/EDIS/CEAS Contract No. NA 79DA-C00012\nN.O.A.A.\nU. S. Dept. of Commerce\n81 0506","FOREWORD\nThis volume summarizes the third and fourth of a series\nof six workshops to investigate the economic impact of climate.\nThe three chapters deal with energy supply and demand.\nMichael Proctor's contribution illustrates supply prob-\nlems using the electric power utility. He discusses climate\nrelated problems associated with base, intermediate, and peak\nload generation. Examples are given of load variations as a\nfunction of temperature and of time. The setting of rates by\nstate regulatory commissions is also shown to be weather sen-\nsitive.\nSince much of the cost of power generation is associated\nwith peak loads, and since a significant amount of this is\nassociated with residential space heating, we have investigated\nbuilding design models which are climate sensitive.\nEllen Cooter discusses two such models as well as the\nstandard concepts behind their structure. An example is given\nwhich illustrates the manner in which climate-sensitive build-\ning design might affect a regional economy through a heuristic\nuse of input-output analysis.\nElmar Reiter integrates space heating requirements over\ncommunities which range in size from a town to a city. His\nstudy involves the tuning of an adaptive control statistical\nmodel to observations of energy consumption data as a function\nof climate.\nii","Volume I discusses the potential use of standard economic\nmodels in assessing the economic impact of climate.\nVolume III treats water and agriculture in specific re-\ngional contexts. .\nVolume IV is a user-oriented non-technical summary.\niii","WORKSHOP 3.\nNovember 30-December 1, 1979\nAlumni Center, University of Missouri\nColumbia, Missouri\nAttendees:\nUniversity of Oklahoma, Norman, Oklahoma\nEllen Cooter\nBill Cooter\nUniversity of Oklahoma, Norman, Oklahoma\nUniversity of Oklahoma, Norman, Oklahoma\nAmos Eddy\nJack Jalickee\nNOAA/EDIS/CEAS, Washington, D.C.\nUniversity of Missouri, Columbia, Missouri\nStan Johnson\nCharles Lamphear\nUniversity of Nebraska, Lincoln, Nebraska\nNOAA/EDIS/CEAS, Columbia, Missouri\nSharon LeDuc\nJim McQuigg\nCertified Consulting Meteorologist, Columbia, MO\nDonald Murry\nStone & Webster Management Consultants, Inc.,\nWashington, D.C.\n* Michael Proctor\nMissouri Public Service Commission\nClarence Sakamoto\nNOAA/EDIS/CEAS, Columbia, Missouri\nNOAA/EDIS/CEAS, Washington, D.C.\nNorton Strommen\nNOAA/EDIS/CEAS, Columbia, Missouri\nRita Terry\nNOAA/EDIS/CEAS, Columbia, Missouri\nHenry Warren\nUSDA, University of Missouri, Columbia, Missouri\nAbner Womack\nWORKSHOP 4.\nApril 11-12, 1980\nCenter for Environmental Assessment Services\nColumbia, Missouri\nAttendees:\n* Ellen Cooter\nUniversity of Oklahoma, Norman, Oklahoma\nUniversity of Oklahoma, Norman, Oklahoma\nBill Cooter\nUniversity of Oklahoma, Norman, Oklahoma\nAmos Eddy\nEDIS/USDC/NOAA, Washington, D.C.\nKen Hadeen\nUniversity of Missouri, Columbia, Missouri\nStan Johnson\nUniversity of Nebraska, Lincoln, Nebraska\nCharles Lamphear\nNOAA/EDIS/CEAS, Columbia, Missouri\nSharon LeDuc\nJim McQuigg\nCertified Consulting Meteorologist, Columbia, MO\nColorado State University, Ft. Collins, Colorado\nElmar Reiter\nNOAA/EDIS/CEAS, Columbia, Missouri\nClarence Sakamoto\nJerry Sullivan\nNOAA/EDIS/CEAS, Washington, D.C.\nNOAA/EDIS/CEAS, Columbia, Missouri\nRita Terry\nNOAA/EDIS/CEAS, Columbia, Missouri\nHenry Warren\nMichael Weiss\nUSDA, Washington, D.C.\nUSDA, University of Missouri, Columbia, Missouri\nAbner Womack\n*Proceedings contributors.\nThis workshop series is sponsored under a contract by NOAA/EDIS with\nthe University of Oklahoma, Amos Eddy, Professor of Meteorology and\nEnvironmental Design, Principal Investigator.\niv","CONTENTS\nii\nFOREWORD\nCHAPTER\nThe Impact of Weather on Electricity\nI.\nConsumption\n1\nMichael S. Proctor\nEnergy Load Building Models\nII.\nEllen Cooter\n73\nEnergy Consumption Modelling\nIII.\nElmar R. Reiter and Collaborators\n119\nV","The Impact of Weather on Electricity Consumption\nMichael S. Proctor\nI. An Overview of the Literature\n1. Introduction\nAt the outset it should be made clear that electric utility com-\npanies are very much interested in the impact that weather has on\nelectricity consumption for a variety of diversified reasons. In this\nfirst section an attempt is made to classify these reasons and present\na limited bibiliography of models that have been developed to meet the\nvarious requirements. However, the emphasis is on the requirements,\nnot on the models. The various requirements are classified as:\nForecast of the next day's load.\nShort-term (1-5 years) forecast of load.\nLong-term (5-20 years) forecast of load.\nDetermination of normal load.\nBefore these four general classes are considered, the concept of\nload needs to be defined and related to various data sets that are\ntypically available.\nHourly Loads:\nProduction is measured at the plant by the kilowatt-hours per hour\nthat occur in each of the 24 hours of the day. This is usually the\n1","2\nmost disaggregated level of data available. The Edison Electric\nInstitute requires an annual filing of this data by each of its\nmembers. For this filing, the plant use is not included, and the data\nis called Net System Load.\nEnergy:\nEnergy is the sum of the hourly loads that occur over a specified\nperiod of time. Obviously, this data can be obtained from the hourly\nload data by adding up over the appropriate time periods.\nSales:\nSales is a measure of kilowatt-hours occurring over a period of\ntime. However, this is usually measured at the customer's meters, and\nwill not equal the sum of net system load for two reasons: (1) line and\ntransformer losses, and (2) billing cycle differences in time periods.\nFor example, monthly sales are reported on meters which are read in a\ngiven month, even though the actual consumption occurs over the 29-31\ndays previous to the meter reading. One should not expect these num-\nbers to match the monthly sums of net system load even if the latter\ncould be adjusted for losses.\nPeak Load:\nFor a specified period of time, e.g., day, month or year, peak\ndemand is simply the maximum hourly load that occurs for that period.\nPeak demand can be measured for the system, for a customer class, or","3\nfor a specific customer. The system peak demand can be easily deter-\nmined from the Net System Load data. Individual customer peak demand\ncan be measured only if the customer has some form of demand meter.\nThe most common form is an indicator meter that records the largest\nhourly reading that occurred between resettings. Customer class peak\ndemand can only be measured (versus estimated on a sample basis) when\nevery customer in the class is on an hourly meter. Then the\ncustomer's hourly loads are summed to obtain an hourly load profile\nfor the class.\nDaily Load Curve:\nA daily load curve is simply a 24 hour vector of hourly loads.\nLoad Duration Curve:\nA load duration curve is an ordered listing of hourly loads that\nhave occurred over a specified period of time. The order is from\nhighest to lowest.\nEach of the four classes of requirements may involve one or more\nmeasures of load. The measure of interest will determine in what way\nweather is modeled as an explanatory variable.\n2. Forecast of the Next Day's Load\nAn extremely thorough summary paper of the state-of-the-art on next\nday load forecasting techniques was presented by Galiana¹ at an EPRI","4\nworkshop. In that paper he lists the following reasons for the appli-\ncations of these forecasts:\n1. The commitment of equipment and in spinning reserve\ncalculation.\n2. Reliability calculations related to the uncertainty in the\nload forecast.\n3. Economic allocation of generation.\n4. The detection of vulnerable situations well in time for the\ncalculation and possible execution of corrective actions. These\nmay involve procedures such as the start-up of peaking units,\npower purchases, and possibly the systematic preparation of\nemergency procedures such as load shedding or voltage reduction.\n5. For predictions of one or two weeks the scheduling or regular\nmaintenance can be better adjusted according to the forecast to\nmaintain a desired reliability level. Such predictions also play\na role in the scheduling of hydro-thermal generation in an econo-\nmically optimum manner.\nGenerally, these reasons relate to the load dispatching function of\nday-to-day determination of which units will be required to meet\nhourly loads in an economical and reliable fashion. These forecasts\nmust then be of hourly loads.\nGaliana then classifies the models according to three structures\nby\nA1) Those models which include weather effects but do not rely on\nthe latest load behavior for the forecast.\nA2) Those models which rely mainly on the time-of-day and the\nlatest load behavior for the forecast.\nA3) Those models including both weather, time-of-day, and imme-\ndiate past load information.\nThe basic concept in the first class of models is that hourly load\ncan be separated into a base load (weather insensitive) and a weather\nsensitive component. The second set of models operate on the premise","5\nthat the daily load curve has a specific shape to which a function of\ntime is fitted. The third set of models recognize that hourly load\ndepends on past and present weather variables, but recognizes other\ncumulative factors which exist but cannot be explained by weather,\ni.e., cumulative correlation in the residual (unexplained) load.\nA copy of Galiana's annotated bibliography is included in Appendix A\nwith a brief explanation of the annotations.\n3. Short-Term Forecast of Load\nAnother review paper on the state-of-the-art on load forecasting\nwas presented by Taylor2 at an EPRI workshop. His review covers both\nshort-term and long-term forecasts. These terms may be rather con-\nfusing if one takes them literally to refer to periods of time. The\nkey is whether or not the underlying economic structure is included in\nthe modeling process. Taylor notes\nIn general, there are two things to be kept in mind in this\nconnection, namely, the purpose for which a forecast is to be used\nand the extent to which one can rely upon continuity of the\nunderlying structure. In situations, for example, where the pur-\npose is to forecast the peak load over a short horizon and where\nit can be assumed that the underlying structure is reasonably\nstable, then the load series itself, with the possible assist from\nan exogenous forecast of the weather, probably provides the opti-\nmal input for the forecast. Attempting to identify and estimate\nthe underlying structure in this situation is not necessary and\nindeed, would be likely to provide inferior forecasts.\nThis then constitutes the elements of what is called a short-term\nforecast. Such a forecast is unconditional and assumes the underlying\nstructure will continue as in the past. Such forecasts have been done","6\nfor energy, peak demand, daily load curves and load duration curves.\nTypically, forecasts are done on either peak demand or energy and\ndaily load curves, or load duration curves are derived from historical\npatterns that are first put on a per unit basis (either per unit of\npeak demand or per unit of energy) and then are scaled up using the\nforecasted values of peak or energy.\nShort-term forecasts are used primarily for operation planning\nwithin the utility. This would include such functions as:\n1. Maintenance scheduling over a one to five year period.\nFuel budget requirement for various types of fuels, e.g.,\n2.\ncoal, gas and oil.\n3. Purchase power requirements for short-term contracts.\nForecasted revenue requirements in states that allow fore-\n4.\ncasted rate cases.\nThe f'unction for which a forecast is used will determine the type of\nvariable being forecasted. For example, monthly peak loads are\nrequired for maintenance scheduling, while either daily load curves or\nmonthly (weekly) load duration curves are used for fuel budgeting and\npurchase power requirements.\nBasically, short-term load forecasting models fall into one of the\nfollowing three groups:\nB1) Trend models which explain variations from load trends due to\nweather.\nB2) Adaptive forecasting models in which some form of adaptive\nexpectations are brought into the estimation process.\nB3) Time series models which use the ARIMA process to explain the\nbehavior of the load series.\nWhile all of the models can account for variations due to weather,\nuntil recently the typical time series model only used the load data\nseries.","7\nOne other classification occurs on those models that forecast\nenergy. Several utilities will forecast sales by customer class,\ne.g., residential, small commercial and industrial, and large commer-\ncial and industrial. In short-term forecasting, this type of distinc-\ntion is made when a utility has done a survey of its large commercial\nand industrial users and is using this survey information to forecast\ntheir load.\nAppendix B includes a copy of Taylor's bibiliography which covers\nboth short-term and long-term forecasting models.\n4. Long-Term Forecast of Load\nA synonymous term with long-term forecast models is econometric\nmodels of load. Typically these models will include the following\nvariables:\nprice of electricity\nprice of natural gas and/or fuel oil\nreal income or production\npopulation or customer numbers\nemployment\nweather (cooling and heating degree days, etc. )\nEconometric models have been used to forecast peak load, energy and\ndaily load curves. However, the typical econometric model forecasts\nenergy by class of customer. The rationale is that different economic\nand demographic variables impact the various customers. For example,\nreal income of the service territory is usually considered to be a\nrelevant variable in the residential energy forecast, while national\noutput is the appropriate variable for the industrial energy forecast.","8\nLong-term forecasts are used primarily for capacity expansion\nplanning purposes. The issue involved is what type and size of\ngeneration plant should be brought on line to meet future load growth.\nPeaking (oil) units have low investment cost but high running cost,\ncoal units have substantially higher investment cost and lower running\ncost, and nuclear units have the highest investment cost and lowest\nrunning cost. Thus the capacity planner must have a forecast not just\nof peak load and/or energy, but knowledge of the duration of load.\nThis is necessary because a large growth in peak demand that has a\nshort duration is most economically met by a low investment cost unit\neven though that unit might have a high running cost.\nIn order to model duration of load, some utilities have moved away\nfrom econometric modeling to end-use models. Most of these models are\ntypically done at the micro level, e.g., the impact of improved insu-\nlation on commercial office building load profiles. Then the micro\nmodels have to be aggregated to determine the impact on class demand,\nand the control variables (insulation standards) have to be forecast.\nThese end-use models are extremely complicated and the aggregation\nanalysis is difficult. Other approaches will only attempt to model\nthe relative changes occurring in seasonal load, e.g., summer with\nair-conditioning saturation and winter with electric heating\nsaturation. These can relate to either peak or energy, and finally to\nload duration through a per unit analysis which is similar to short-\nterm forecasting. All of the econometric models would fall into this\ngroup, i.e., forecasting energy by seasons.","9\nWhile most long-term forecasting models are typically of the\nsimultaneous equation, structural variety, and hence require addi-\ntional forecasts of all the economic and demographic variables, an\nexception exists that is worth noting. In a recent article,\nUri3 notes that while the time-series models outperform the econo-\nmetric models in terms of forecasting, they are criticized for their\ninability to provide an explanation for poor forecasts when they do\noccur. Uri presented two approaches.\nC1) Box-Jenkin's parameters from a simple ARIMA model on peak\nload were estimated on a quarterly basis and hypothesized to\ndepend on weather, economic and demographic variables. These\nparameters are then forecasted and used in the original ARIMA\nmodel to forecast peak load.\nC2) Structural parameters of a direct econometric model are esti-\nmated and used to calculate the residuals. Then a\nBox-Jenkins model is used to reduce these residuals to white\nnoise, and the combined model is used to forecast.\nThe forecasts of both models were superior to the simple univariate\ntime series approach, and the first model was superior to the second.\nThe reason for pointing out Uri's work is that the movement in load\nforecasting seems to be in the direction of hybrid models that combine\nthe flexibility aspects of time series with the explanatory aspects of\neconometric models.\n5. Summary\nFor all of the forecasting requirements previously mentioned there\nexist models which attempt to take into account the impact of weather\non electricity consumption. The models will run the spectrum from a\nsimple linear relationship between load and degree days to non-linear","10\nrelationships between present and lagged load levels to present and\nlagged levels of temperatures, humidity, cloud cover and wind speed.\nThe form and level of aggregation used depends on what load variable\nis being forecasted, and hence on the purpose to which the forecast is\nto be applied. It is impossible in one paper to detail the variety of\nmodels and approaches taken in modeling the impact of weather on\nelectricity consumption. However, it is important to look at some of\nthe specific problems encountered in this modeling process. Thus, the\nnext section of this paper deals with the experience which the\nResearch and Planning Department of the Missouri Public Service\nCommission has encountered in attempting to normalize electricity\nsales for weather.\nII. Concepts of \"Normal\" Electricity Sales\n1. The Problem\nSales of electricity vary with weather conditions. Hence, for a\ngiven rate structure the revenue collected and the expenses incurred\nby the utility in a given year are random variables whose distribu-\ntions depend on the distribution of weather. This causes some degree\nof uncertainty to exist for the utility on its annual income (return\non investment). .\nIn a rate case proceeding, State Commissions basically hear three\nissues:","11\nWhat operating expenses should be allowed?\nOn how much net investment should the company be allowed to earn a\nreturn?\nWhat rate of return should the company be allowed to earn on net\ninvestment?\nMoreover, if the State Commission determined:\nOperating Expenses = E\nNet Investment\n= I\nRate of Return\n= r\nthen the revenue requirement (R) can be set for the company 4, i.e.,\n,\nR = rI+E .\nOnce the revenue requirement is set, the State Commission must also\ndetermine a rate structure that will allow the company to collect the\nallowed revenues subject to a set of fairly well defined rules. The\nrule of primary interest in this paper is that the annual sales (S)\nover which the revenues can be collected are based on predetermined\ntest years sales adjusted for \"known and measurable changes. \" One of\nthe \"known and measurable changes\" that can be allowed for is\nweather 5\nA formal statement of this problem is that if the State Commission\nadopted a simple single price rate structure, i.e., p = rate set by\nthe State Commission, then the expected value of the revenues collected\nby the utility\nRC = ps\nwould have to equal the expected value of the revenues which the State\nCommission has determined that the utilitiy is allowed to collect, or","12\n-\nRa = rI+E\nwhere S is expected sales and E is expected expenses. 6 In this simple\nrate structure case, the solution is also quite simple, i.e.,\nS\n=\n.\nNotice that if the State Commission can determine S and E (hence p*), ,\nthe actual return on investment (Y) is a random variable defined by\nY(S) = p*S - E(S)\nand this actual return has an expected value equal to the allowed\nreturn (rI), but can be above or below its mean. The variability or\nrisk associated with the return on investment is an additional factor\nthat must be considered in the determination of the \"fair\" rate of\nreturn which the utility is allowed to earn.\nGiven this background in rate making concepts it should be fairly\nobvious why concepts of \"normal\" electricity sales are important. It\nshould also be fairly obvious that only in the case that expenses are\na linear function of sales (which they are not) can that concept of\nnormal be narrowed to the expected value of sales. 7 At the heart of\nthe problem is both the complexity of the response of sales to\nweather, and the complexity of the response of expenses to sales. The","13\ncomplexity of these responses causes difficulty in defining what is\nmeant by normal. Some basic notions are quite clear, e.g., a winter\nthat is exceptionally cold will produce sales that are exceptionally\nhigh, and summers that are exceptionally hot will also produce sales\nthat are exceptionally high. However, these basic notions need to be\ntranslated into explanatory models, and then those models need to be\nused to adjust sales vis-a-vis a well defined concept of normal.\nIn the remainder of this paper various explanatory models will be\nconsidered, but the thrust of the analysis will center on a model that\nis being developed by the Research and Planning Staff of the Missouri\nPublic Service Commission. Having developed the model, the applica-\ntion of that model to \"normalizing\" test year sales and expenses will\nbe considered.\n2. The Response of Sales to Weather\nThe biggest problem in measuring the response of sales to weather\ncomes about because a single test year's observations on sales and\nweather are not sufficient to provide a complete picture of the\nresponse. Thus every model of sales response must incorporate\nvariables that explain year-to-year differences in loads. A second\nproblem comes in the determination of weather variables to be used in\nthe model. Every model will use temperature data in some form. For\nestimating sales response, daily mean temperature is usually used\nits availability. 8 While other measures of weather\nbecause\nof","14\n(humidity, cloud cover, etc.) have been used, it is typical to find\nthat these variables are not modeled for purposes of normalizing\nsales. Assuming that daily mean temperature is the only variable\nmodeled, a third problem is the choice of location at which the\nmeasurement is taken. Many utility service territories include more\nthan one choice of available data. However, the problem of coli-\nnearity between the various choices will usually lead the modeler to\npick a single source. 9\nProximity to the highest density of sales is\nthe usual criteria used in making the choice. A final problem is the\nchoice of the level of aggregation at which the sales are modeled.\nThe highest level of disaggregation is hourly load sales. In the\nremainder of this section various models will be considered. These\nmodels vary depending on the choice of level of aggregation.\nModel I: Annual Sales\nThis model is conceptual and is presented only to show some of the\nproblems that are encountered in attempting to model sales. The\nassumption is that the modeler has made the decision to use annual\nsales as the variable to estimate as a function of mean temperature\nand a set of explanatory variables that will explain year-to-year dif-\nferences in load.\nGiven the choice of annual sales, the next decision is what level\nof aggregation to make on daily mean temperature. The basic notions\nabout the relationship of sales to temperature are shown in Figure 1.","15\nLoad\nat Hour\nDaily Mean\nT*\nTemperature\nFIGURE 1\nLOAD RESPONSE TO TEMPERATURE","16\nThis is a hypothetical plot of sales at a specific hour against daily\nmean temperature. The concept conveyed by this diagram is that if\ndaily mean temperature goes above the level T*, then load increases,\nand if temperature falls below the level T*, the load also increases.\nThis basic notion of load response leads the modeler to note that\nsumming up mean temperatures in the same way in which hourly loads are\nsummed is inappropriate. Moreover, the need for at least two tem-\nperature measures is apparent, e.g.,\nTi T T *\nThese measures or aggregates of mean temperature are called degree\n10\ndays, with T1 = heating degree days and T2 = cooling degree days.\nAt this point the modeler recognizes that if heating degree days\noccur in the summer months there will likely be no temperature sen-\nsitive response in load, and vice versa for the winter months. In\naddition, the nonlinearity in the response of load to temperature\ncould be caused by different responses at different times of the year,\ne.g., a high mean temperature in May will result in a different\nresponse than in July. Thus, the modeler is led to disaggregate to\nmonthly sales measures.\nModel II: Monthly Sales\nMonthly sales models are generally estimated independently of one\nanother and are split into three model types. 11","17\nMonthly heating degree days are used for the months of\nHeating:\nNovember, December, January, February and March.\nMonthly cooling degree days are used for the months of\nCooling:\nMay, June, July, August and September.\nTransition: Both heating and cooling degree days are used for the\nmonths of October and April.\nGiven these basic concepts the modeler is likely to formulate a\nmodel of the following form:\nfit(Tit,Vt); i =\n12;\nt\n1,...,N\n=\n,\nwhere:\nSit = sales for month i in year t,\nTit = appropriate degree days for month i in year t, and\nVt = variables that will account for year-to-year growth in\nsales.\nThe functional form of the relationship may be either linear or\nnon-linear, and may be the same for each month or vary from\nmonth-to-month. The minimum number of parameters to be estimated are\nthree for each month, 12 and the modeler is faced with having to make\na decision about how many years of data to include in the regression.\nAt this point notice that a t subscript was put on the function. The\nproblem faced by the modeler is that an assumption\nfit()fi()t1,..,N\nthat the functional form of the response is constant over time must be\nmade in order for the model to be estimated. The rather traditional\nview is that the variable (s) Vt are picking up changes in function\nform that have occurred over time. However, in the basic linear model","18\nSit = Boit + B1it Tit + Eit\nadding a vector of time changing variables simply accounts for shifts\nin the constant term, i.e.,\nOne may also want to account for a time varying parameter on the\nslope, i.e.,\nwhere Ut is a set of variables which are used to account for year-to-\nyear changes in the temperature sensitive response. 13 For this\nexample, the model becomes:\n+ B21Vt + B31TitUt + Eit\nand if Vt and Ut are scalars (which they usually are not) the model\nnow has at least four parameters. The model can be estimated with,\nfor example, twenty years of data, but then one begins to be concerned\nabout such things as price elasticity, the structural impact of the\nArab oil embargo, etc. This means more variables such as price and\ndummy variables, and the process continues, i.e., even more years of\ndata, and hence more variables, and hence more years are required.\nAt this point the modeler can make one of three decisions. First,\nto arbitrarily stop the process and go with a fairly simple model that","19\ndoes not attempt to account for too many changes in parameters. 14\nSecond, to apply parameter reduction techniques that basically assume\na known relationship between the monthly coefficients. Third, to\nscrap the monthly sales model and move to a lower level of aggregation\nin order to pick up more observations. The next two models present\nthe second and third alternatives.\nModel III: Parameter Reduction Techniques\nFor purposes of discussion assume that the monthly sales model is\ngiven by:\nSit = BO1 + B11Tit + B21Vt + Eit\n.\nThen each monthly model requires three parameters. If this model were\nto be estimated in a single regression, the data input matrices would\nlook like\nBO\nS.1\nI\nV.1\nE.1\nS.N : . . = I T.N V.N B2 B1 + E:N\nwhere\nV.t\nVt\n0\n0\nT.t\nT1,t\n0\nSt\nS1,t\n=\n=\n=\n=\n,\n,\n(12x12)\n(12x12)\n(12x12)\n(12x1)\nVt\n0\nT12,t\nS12,t\n0\n1","20\nand\nB1,1\nBO\n80,1\n=\n=\n(12x1)\n(\n(12x1)\n(12x1)\n30,12\nB\n1,12\n2,12\nThis gives a model with 12*N observations and 12*3=36 variables.\nBasically any parameter reduction technique reduces the number of\nparameters to be estimated by assuming a linear relationship\n(constraint) holds among sets of the given parameters. In the example\nstructure one might assume a linear relationship exists between the\nmonthly constant terms and the monthly time varying component of the\nconstant terms, e.g.,\n=\nwhere WO and w2 are 12xk matrices, and * and * are subsets\nof size\n12 from 0 and 2 respectively. Substituting these restrictions\nk\ninto the data matrix gives:\nTHE\nB*\nWO\nS.1\nT.\nV.1W2\nB+\n.\nwo\nB*\nV.NW2\nT.N\nS.12\n2\nwhich is a model with 12xN observations and k+12+k = 12+2k variables.\nWhile the benefits in variance reduction on the estimated parame-\nters is obvious, one has to be concerned about the bias that could be","","22\nimposed on the model by the introduction of the linear constraints.\nSuppose that in Figure 2 the true values of 0 are plotted by month.\nAt first glance there is no obvious way in which this set of twelve\nparameters are linearly related. But suppose the curves connecting\nB0, 1 to B0,4, 30,4 to 80,7, 80,7, to 80,10 and 80,10 to Bo, 1 can be\napproximated by cubic equations. In this case it has been shown\nthat 15 all twelve of the BO values can be written as linear functions\nof 80,1 30,4 80,7 and $0,10 i.e.,\nBO = WO B*\nThe \"art\" of applying this result is in the choice of the size and\nplacement of the knots (B*). One wants to make the number of knots as\nsmall as possible, but too few knots will introduce bias. If the\nnumber and placement of knots is the same for BO and B2, then WO =\nw2 = W.\nA final comment on this model is that the number of parameters on\nB1\nwere not reduced. Recall that heating and cooling degree days are\ndefined differently and this could cause some difficulty in assuming a\nrelationship between the various coefficients. Even if this is not\nthe case, since the primary interest is on the response of sales to\ntemperature, one might be reluctant to take the chance of introducing\nbias on these coefficients. However, there is again a trade-off. If\nthe total number of parameters is reduced further from 20 to say 12,\nthen one might be quite willing to estimate this model with five years","23\nof data (60 observations), while with 20 parameters more data might be\nrequired. The problem is not with the availability of data, but goes\nback to the assumptions which one is wiling to make about the applica-\nbility of the model to the data.\nModel IV: Daily Sales\nThe next level of disaggregation which might be considered by the\nmodeler is to use daily sales data. In figures 3 and 4, the daily\nmegawatt-hours (by day type) are plotted against the corresponding\ndaily mean temperatures. The month of January was chosen because it\nwould represent a strictly winter heating response. There are several\nthings to note in these two plots.\nThe daily load response is negatively correlated with daily mean\ntemperature.\nThe data can be partitioned between weekdays (1-5) and non-\nweekdays (6-8).\nNon-weekdays give fewer observations and seem to have greater\nvariability than weekdays.\nMinimum daily loads are found on non-weekdays and maximum daily\nloads are found on weekdays.\nBoth maximum and minimum daily loads have increased from 1976 to\n1978.\nWith this basic information one might be quite willing to model the\ndaily sales with a simple linear model","24\nJANUARY 1976\n1 = Monday\nDaily\n6 = Saturday\nMegawatt\n2 = Tuesday\n7 = Sunday\n3 = Wednesday\n8 = Holiday\nHours\n4 = Thursday\nA = a 2 and a 5\n5 = Friday\nB = a 2 and a 3\n4000\n3900\n3800\n3\n3700\n4\n3600\n3500\n3400\n2\n3300\n2\n5\nA\n1\n3200\n31\n3\n3100\n4\n1\n3000\nB\n41\n4\n2900\n5\n6\n6\n2800\n5\n5\n2700\n7\n6\n2600\n2500\n6\n2400\n7\n7 6\n2300\n7\n8\n2200\n2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44\nMean\nTemperature\nFIGURE 3\nDAILY WINTER LOAD RESPONSE TO MEAN TEMPERATURE","25\nJANUARY 1978\n6 = Saturday\n1 = Monday\n7 = Sunday\n2 = Tuesday\n8 = Holiday\n3 = Wednesday\nDaily\nA = a 3 and a 5\n4 = Thursday\nMegawatt\n5 = Friday\nHours\n4200\n1\n4\n4100\n4000\n2\n2\n3A\n4\n3900\n1 2\n5\n3\n3800\n1\n3700\n1\n4\n3600\n5\n2\n3500\n6\n6\n2\n3400\n7\n5 3\n3300\n4\n3200\n7\n6\n3100\n7\n3000\n8\n6\n7\n2900\n8\n2800\n2700\n2600\n2500\n2400\n2300\n2200\nMean\n2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40\nTemperature\nFIGURE 4\nDAILY WINTER LOAD RESPONSE TO MEAN TEMPERATURE","26\nTABLE 1\nDAILY WINTER LOAD RESPONSE TO MEAN TEMPERATURE\nJan/78\nJan/76\nMegawatt\nMean\nMegawatt\nMean\nDay\nDay\nDate\nHours\nTemperature\nDate\nHours\nTemperature\nType\nType\n2386\n8\n1\n2992\n11\n8\n35\n1\n3008\n21\n2908\n26\n8\n2\n5\n2\n14\n3453\n29\n6\n3\n2931\n2\n3\n4\n3390\n35\n4\n2746\n12\n3\n7\n4\n3269\n34\n5\n3173\n30\n1\n5\n6\n3356\n34\n6\n5\n3302\n22\n2\n6\n29\n3767\n7\n3022\n2\n3\n7\n8\n3445\n11\n4\n8\n3686\n5\n7\n4210\n8\n3360\n16\n1\n9\n5\n9\n4099\n6\n6\n2745\n31\n2\n10\n10\n3926\n2386\n30\n3\n11\n19\n7\n11\n4\n12\n3701\n22\n2972\n37\n1\n12\n3610\n3043\n13\n21\n2\n13\n37\n5\n6\n14\n3268\n18\n14\n3154\n29\n3\n3004\n18\n3144\n4\n15\n37\n7\n15\n16\n16\n3238\n28\n1\n3922\n11\n5\n4062\n2856\n24\n6\n2\n17\n2\n17\n18\n4014\n18\n2467\n10\n35\n3\n7\n4\n4002\n14\n3065\n32\n19\n1\n19\n28\n5\n20\n3953\n7\n2\n20\n3225\n6\n3061\n37\n21\n3524\n8\n3\n21\n28\n36\n7\n22\n2992\n4\n22\n3009\n3728\n28\n2815\n43\n1\n23\n5\n23\n2488\n24\n3625\n25\n6\n24\n37\n2\n4060\n2471\n28\n3\n25\n11\n7\n25\n4\n26\n4234\n11\n26\n3285\n11\n1\n4000\n11\n3422\n14\n5\n27\n2\n27\n34\n6\n28\n3536\n14\n28\n3100\n3\n2944\n40\n7\n29\n3273\n10\n4\n29\n3843\n20\n2871\n38\n1\n30\n5\n30\n6\n37\n2\n31\n3915\n12\n31\n2501","27\nfor d = days and a = weekdays or non-weekdays. The problem with these\ntwo models is primarily that the non-weekdays (and in some cases the\nweekdays) do not cover the mean temperature range for the month. From\nTable 1, note that the lowest observed mean temperature for non-\nweekdays in January, 1976 is 12°F., occurring on January 4; and the\nhighest observed mean temperature for non-weekdays in January, 1976 is\n37°F. occurring on both January 24 and 31. If one fits the simple\nmodel to this data it is likely to be a poor predictor of load for\ntemperatures occurring outside the data range. Notice that this\nproblem is even more severe for non-weekdays in January, 1978.\nLooking at only the 1976 data, one might be tempted to reformulate\nthe model by restricting the temperature sensitive response to be the\nsame for both weekdays and non-weekdays, i.e., a shift in non-\ntemperature sensitive response:\n+ BTd & E d = 1,...,31\n1 if day type = 1,...,5\notherwise.\nThe major problem with this model is the assumption being made that\nthe error structure is the same for weekdays and non-week days. That\nproblem is more apparent in the January, 1978 plot. In that same plot\nnotice that the highest mean temperature for both is 35°F. occurring\non January 4.\nAt this point the modeler is pretty well convinced that more than\none year's data should be included, and this means that additional","28\nJULY 1976\n1 = Monday\n5 = Friday\nDaily\n2 = Tuesday\n6 = Saturday\nMegawatt\n3 = Wednesday\n7 = Sunday\nHours\n4 = Thursday\n8 = Holiday\nA = a 1 and a 2\n4800\n4700\n4600\n4500\n4400\n2\n3\n3\n5\n4300\nA\n2\n4200\n4100\n1\n4\n4\n4000\n3900\n3\n5\n5\n6\n3800\n1\n3700\n6\n4\n3600\n4\n3500\n3400\n3300\n6\n7\n3200\n3\n3100\n3000\n2\n2900\n2800\n4 5\n2700\n2600\n2500\n7\n2400\n8\n6\n2300\n2200\n2100\n8\n2000\n6\n1900\n7\nMean\n67\n68\n69\n70\n71\n72\n73\n74\n75\n76\n77\n78\n79\n80\n81\n82\n83\n84\n85\n86\n87\n88\nTemperature\nFIGURE 5\nDAILY SUMMER LOAD RESPONSE TO MEAN TEMPERATURE","29\nJULY 1978\n1 = Monday\n5 = Friday\nDaily\n2 = Tuesday\n6 = Saturday\nMegawatt\n3 = Wednesday\n7 = Sunday\nHours\n4 = Thursday\n8 = Holiday\nA = a 1 and a 2\n4800\n4700\n4600\n3\n4500\n4400\n4300\n4200\n3\nA 5\n4100\n3\n1\n6\n4000\n4\n2\n3900\n4\n5\n8\n3800\n4\n3700\n3600\n5\n3500\n1\n3\n7\n3400\n4\n6\n3300\n3200\n5\n6\n3100\n1\n6\n6\n7\n3000\n2900\n2800\n1\n2700\n2\n2600\n7\n2500\n7\n2400\n2300\n7\n2200\n2100\n2000\n1900\nMean\n67\n68\n69\n70\n71\n72\n73\n74\n75\n76\n77\n78\n79\n80\n81\n82\n83\n84\n85\n86\n87\n88\nTemperature\nFIGURE 6\nDAILY SUMMER LOAD RESPONSE TO MEAN TEMPERATURE","30\nvariables are required to account for load growth. The warning is\nthat if growth is not modeled correctly, the resulting estimates of\nparameters on temperature sensitive load will be biased.\nSome additional problems can be noted when summer sales are\nconsidered. Similar plots for July ( summer load) appear in Figures 5\nand 6. In addition to the items noted on the January response, in the\nJuly response\nThere are several observations that do not fit the partitioning\nbetween weekdays and non-weekdays.\nFrom the July 1976 data (Table 2), consider the \"low\" sales that\noccurred on July 7. Notice the consecutively lower mean temperatures\nthat occurred previous to that day. The same type of occurrence\nappears on July 30, however in this case it was simply one or two pre-\nvious days of lower mean temperatures. On July 24, the opposite\noccurs, i.e., a cooler day preceeded by consecutively warmer days.\nKeep in mind that cooler and warmer are relative terms, and all that\nwe have done is try to explain a few observations that seem to be\ninconsistent with the others. These kinds of observations have led\nmany modelers to specify daily summer load as a function not only of\ncurrent mean temperature, but also as a function of previous (lagged)\nmean temperature. While this statement is a perfect lead into a full\ndiscussion of distributed lag models, a simple lag model will be suf-\nficient to illustrate the point.","Temperature\nWeighted\nMean\n87\n85\n83\n86\n88\n84\n79\n78\n76\n70\n78\n76\n77\n78\n79\n82\n84\n83\n79\n83\n80\n74\n78\n79\n71\n71\n80\n82\n81\n77\n76\nTemperature\nMean\n88\n83\n83\n87\n88\n82\n77\n79\n75\n69\n78\n79\n72\n71\n81\n74\n78\n84\n84\n82\n78\n85\n77\n84\n76\n80\n71\n81\n81\n75\n76\nJuly/78\nMegawatt\nDAILY SUMMER LOAD RESPONSE TO MEAN TEMPERATURE\nHours\n3992\n3556\n4044\n3853\n4677\n3124\n4214\n2558\n3919\n3679\n2678\n2807\n2775\n3515\n3476\n3298\n4075\n3857\n4258\n3108\n2303\n3190\n3974\n3704\n3361\n3171\n4211\n4251\n3817\n3299\n3525\nDate\n2\n3\n4\n5\n6\n22\n1\n7\n8\n9\n10\n12\n13\n14\n11\n15\n16\n23\n24\n25\n26\n17\n18\n19\n20\n27\n28\n29\n30\n21\n31\nTABLE 2\nType\nDay\n6\n6\n7\n8\n3\n4\n2\n1\n5\n6\n7\n2\n3\n4\n5\n1\n7\n2\n3\n4\n5\n6\n7\n3\n4\n5\n6\n7\n1\n1\n1\nTemperature\nWeighted\nMean\n68\n70\n76\n79\n82\n84\n84\n83\n82\n83\n78\n68\n73\n84\n82\n84\n84\n77\n83\n78\n82\n80\n71\n71\n71\n71\n71\n81\n81\n81\n85\nTemperature\nMean\n68\n72\n70\n72\n71\n78\n71\n79\n83\n84\n84\n82\n82\n83\n75\n69\n67\n76\n83\n84\n80\n76\n83\n86\n85\n78\n81\n85\n84\n81\n77\nJuly/76\nMegawatt\nHours\n2498\n2052\n2145\n3062\n2890\n2354\n2539\n3925\n4286\n3979\n4127\n4399\n3843\n3242\n4189\n4464\n4066\n3993\n3309\n2851\n1901\n3290\n3509\n3953\n3728\n3373\n4236\n4282\n3605\n4351\n4311\nDate\n2\n3\n4\n5\n6\n7\n8\n9\n10\n12\n13\n14\n24\n1\n15\n16\n25\n26\n27\n28\n29\n30\n11\n17\n18\n19\n20\n22\n23\n21\n31\nType\nDay\n7\n6\n2\n3\n4\n5\n6\n4\n8\n6\n7\n8\n2\n3\n4\n5\n6\n7\n2\n3\n4\n5\n6\n1\n7\n2\n3\n4\n5\n1\n1","32\nJULY 1976\n1 = Monday\n6 = Saturday\nDaily\n2 = Tuesday\n7 = Sunday\nMegawatt\n3 = Wednesday\nof = Holiday\nHours\n4 = Thursday\nA = a 3 and two 5's\n5 = Friday\nB = two 3's\n4700\n4600\n4500\n4400\nB\n5\n4300\n4200\n2\n1 2 2\n4\n4100\n1\n4000\n4\n3900\n1 A\n6\n3800\n6\n3700\n4\n3600\n4\n3500\n3400\n6\n7\n3300\n3200\n3\n7\n3100\n3000\n2\n2900\n2800\n4\n5\n2700\n2600\n2500\n7\n2400\n8\n2300\n6\n2200\n2100\n8\n2000\n6\nWeighted\n1900\n7\nMean\n68\n69\n70\n71\n72\n73\n74\n75\n76\n77\n78\n79\n80\n81\n82\n83\n84\n85\n86\n87\n88\n89\n90\nTemperature\nFIGURE 7\nSUMMER DAILY LOAD RESPONSE TO WEIGHTED MEAN TEMPERATURE","33\nJULY 1978\n1 = Monday\n6 = Saturday\n2 = Tuesday\n7 = Sunday\nDaily\n3 = Wednesday\n8 = Holiday\nMegawatt\n4 = Thursday\nA = a 1 and a 3\nHours\n5 = Friday\nB = a 1 and a 3\nC = a 4 and a 5\n4700\n4600\n3\n4500\n4400\n4300\n4200\nB 5 2\n4100\n4000\nA\n3900\n2\n4\n6\n3800\nC\n8\n3700\n4\n3600\n5\n3500\n1\n3\n7\n3400\n4\n3300\n6\n3200\n5\n6\n3100\n1\n6 7 6\n3000\n2900\n2800\n1\n2700\n2\n2600\n7\n2500\n7\n2400\n2300\n7\n2200\n2100\n2000\nWeighted\n1900\nMean\n68\n69\n70\n71\n72\n73\n74\n75\n76\n77\n78\n79\n80\n81\n82\n83\n84\n85\n86\n87\n88\n89\n90\nTemperature\nFIGURE 8\nSUMMER DAILY LOAD RESPONSE TO WEIGHTED MEAN TEMPERATURE","34\nIn Figures 7 and 8, the same load data is plotted against a two\nday weighted mean temperature, i.e.,\nWTd = (2/3)Td + (1/3)Td-1 .\nThis formulation has been used by the largest electric utility in\nMissouri. Two points should be noted in these diagrams:\nThe apparent reduction in variability of the data.\nThe better fit of the observations into the weekday and non-\nweekday partition.\nWhile the daily sales model is perhaps the best alternative from\nthose considered SO far, one is still faced with the problem of having\nto use several years' data in order to model the complete range of\ndaily mean temperature observations.\nModel V: Daily Load Curves (Hourly Loads)\nThe most disaggregated level of sales is at the hourly load level.\nIn Figures 9-12, winter and summer load curves are presented for 1976\nand 1978. Winter loads in Missouri are characterized by two peaks,\none usually occurring in the morning (9 a.m. - 12 noon), and one\noccurring in the evening (6 p.m. - 10 p.m.) Summer loads in Missouri\nare characterized by a single peak occurring in the late afternoon or\nearly evening (3 p.m. - 6 p.m.). While these facts are interesting,\nwhat the modeler really wants to know is how the load curves shift due\nto changes in temperature. If one is interested in predicting load","35\nMEGAWATT\nLOAD\n179\nMEGAWATT\nHOUR\nLOAD\n126\n1\n2\n122\n3\n122\n123\n4\n5\n125\n6\n137\n7\n149\n167\n8\n9\n179\n10\n179\n178\n11\n12\n174\n13\n173\n14\n169\n15\n166\n16\n163\n17\n167\n18\n177\n19\n179\n20\n175\n21\n172\n158\n22\n23\n151\n24\n136\n122\n1\n24 HOURS\nFIGURE 9\nWINTER LOAD CURVE\nPEAK DAY : JANUARY 1976","36\nMEGAWATT\nLOAD\n205\nMEGAWATT\nHOUR\nLOAD\n1\n140\n2\n135\n3\n137\n4\n137\n5\n139\n6\n144\n7\n165\n8\n187\n9\n193\n10\n193\n11\n198\n12\n192\n13\n192\n14\n193\n15\n190\n16\n186\n17\n193\n18\n205\n19\n201\n20\n195\n21\n191\n22\n182\n23\n169\n24\n153\n135\n1\n24 HOURS\nFIGURE 10\nWINTER LOAD CURVE\nPEAK DAY : JANUARY 1978","37\nMFGAWATT\nLOAD\n240\nMEGAWATT\nHOUR\nLOAD\n1\n119\n2\n112\n3\n105\n4\n102\n5\n99\n6\n104\n7\n107\n8\n131\n9\n153\n10\n168\n11\n184\n12\n204\n13\n213\n14\n227\n15\n229\n16\n237\n17\n240\n18\n232\n19\n232\n20\n216\n21\n212\n22\n207\n23\n187\n24\n169\n99\n1\n24 HOURS\nFIGURE 11\nSUMMER LOAD CURVE\nPEAK DAY : JULY 1976","38\nMEGAWATT\nLOAD\n248\nMEGAWATT\nHOUP\nLOAD\n1\n148\n2\n139\n3\n130\n4\n124\n5\n124\n6\n119\n7\n128\n8\n152\n9\n186\n10\n205\n11\n222\n12\n231\n13\n242\n14\n245\n15\n247\n16\n248\n17\n246\n18\n244\n19\n239\n20\n231\n21\n221\n22\n220\n23\n212\n24\n174\n119\n1\n24 HOURS\nFIGURE 12\nSUMMER LOAD CURVE\nPEAK DAY : JULY 1978","39\nshapes precisely rather than in estimating normal sales, then fairly\nelaborate models involving hourly (or three-hour) temperature readings\nwith lagged values of these temperature readings have been constructed.\nThe use of these models is somewhat limited because they require esti-\nmates of temperature patterns as exogenous inputs to predict hourly\nload.\nThe problem of normalization is somewhat simpler. The objective\nis to determine a \"typical\" load curve that can be associated with\ndaily mean temperature. One of the Missouri based utility companies\nhas been very successful in their modeling of daily load shapes, and\nwhat follows in this section is a brief description of their\nmethodology.\nThe method is based on the assumption that within a given season\nthere is a one-to-one correspondence between daily peak load and the\ndaily load shape. Moreover, with information on the date on which the\npeak occurred and the level of the peak, that day's load shape can be\ndetermined. Seasons are determined empirically as periods of time\nover which load shapes are fairly homogenous. For each season two\nvectors of twenty-four hourly loads are chosen to represent the lowest\nand highest load days that could occur in that season. Suppose those\nvectors are represented by\nY1 = lowest load day\nYn = highest load day","40\nEach of these two days has a peak (maximum) observation, say\ny1 = peak on the lowest load day\nyh = peak on the highest load day.\nThen, any other daily peak that might occur can be written as a convex\ncombination of these two, i.e.,\nyd ^dy1(1-d) yh\n0 d < 1.\nThe initial concept of the model was that given yd, one could easily\nsolve for xd, i.e.,\n= (yh - yd) : (yh-y1)\nand then determine the corresponding daily load shape by taking the\nsame convex combination of the daily load vectors, i.e.,\nYd =d1+(1-d)Y\nHowever, it was determined that while this convex combination did a\n\"good\" job of predicting most hourly loads, the late night and early\nmorning hours did not change at the same rate as the other hours.\nThis led the modeler to devise an empirical relationship between the l\nweights for these hours and Ad.\nThe final and most crucial aspect of the model was to find the\nrelationship between daily peak demand and daily mean temperature,\ni.e.,","41\nyd = f(Td) .\nA non-linear relationship was estimated using the sum of two cumula- -\ntive normal distributions. Perhaps the most amazing fact is that this\nrelationship was initially estimated (several years ago) using a hand\ncalculator. A few years ago, a computer was used to calculate the\nerror sum of squares, using the original set of data, and the original\nestimates were found to minimize the error sum of squares. 16\nThe key to this model is the estimated relationship between daily\npeak demand and daily mean temperature, and as is the case for the\ndaily sales model, the problem is in having to combine several years\nof data. In this case a fairly innovative numerical technique was\nused. Typically, utilities will combine various years of data by\nputting that data on a percentage of peak basis, i.e., by simply\ndividing each year's observations by the peak observation occurring\nin that year. In this case, a similar type of data was constructed\nusing the following formula\n= - (yh - y1) -\nwhere yd is the peak occuring on day d, , y1 is the lowest peak of the\nyear, and yh is the highest peak of the year. Then ud is the percen-\ntage spread of the daily peak observation. While the modeler gave no\nparticular rationale as to why percentage spread might account for\ngrowth, his reason for using it was quite convincing, i.e., it worked.\nBased on this indisputable empirical fact, 17 the Research and Planning","42\nStaff took a long and serious look at percentage spread as a basis for\ncombining years of data.\n3. The MPSC Staff Models\nThe first question we asked (being well trained deductive\nanalysts) was what does percentage spread measure? That question led\nto several explanations that proved to be untrue. Perhaps the\nfollowing story falls into the same category, however it is the most\nreasonable explanation. Instead of viewing hourly load as a curve or\nset of curves, picture a distribution of load that occurs over a spe-\ncific period of time, say one month. What actually occurs in a given\nmonth is a realization of that probability distribution conditioned on\n(among several determinants) the weather that occurred in that month.\nFor the moment, assume that the probability distribution is known,\ni.e.,\n=ft(x) .\nThe time subscript on the distribution function and on the lower (at)\nand upper (bt) bounds of the distribution indicate that this function\nchanges over time, i.e., the monthly distribution changes from year to\nyear. On the random load variable, X defines the following\ntransformation\n7 = (x - at) (bt-at)","43\nthat is, y is the percentage spread of X. Then y must fall in the\nunit interval and the distribution function becomes\np = gt(y) for Osy1. .\nThe basic assumption that would allow one to combine several years of\ndata using the percentage spread transformation is that the resulting\nprobability function is invariant with respect to time, 18 i.e.,\n8t(y) = g(y) = for all t.\nFor the moment let us assume that the explanation is true. Then\nthe task of estimating normalized sales becomes one of estimating the\nprobability function g(y) and the bounds that apply to X for the time\nperiod in question. To see this consider the definition of normal\nsales to be the expected value of the load distribution times the\nnumber of hours in the same period. Since\nE(x) = at+(bt - at)E(y) -\nit follows that if at, bt and g(y) are known, then normal sales can be\ncalculated. The models presented in this section are aimed at\nobtaining estimates of these factors.\nMPSC Model I: Estimating Maximum and Minimum Hourly Loads\nThe basic problem is to estimate the maximum and minimum hourly\nloads by month for several years of data. The simplest estimate would\ntake the actual maximum and minimum values that occurred. However,","44\nthis simplistic approach ignores the fact that maximums and minimums\nare generated by extreme weather conditions, and it is unlikely that\nthese extremes will be observed in every month and every year. 19 This\nmight lead the modeler to fit data to the observations and then calcu-\nlate the extremes from the model using as inputs the extreme weather\nconditions.\nThe Staff followed this procedure using an annual model that\nrelated maximum daily loads on weekdays and minimum daily loads on\nnon-weekdays to mean temperature. Figure 13 presents what we consider\nto be our worst results. In 1975, the lowest mean temperature was\n14OF. The graph shows that we were interested in estimating values\nfor peak demand as low as -5°F. One of the problems encountered is\nwhen one year's worth of data is used the annual mean temperature\nextremes (line drawn in Figure 13) can be quite unbelievable.\nFigure 13 is presented primarily to indicate the nonlinear nature\nof the response of daily maximum load to mean temperature. The curve\nfitted in Figure 13 is a cubic spline with knots at -50, 150, 600,\n800 and 900. The staff also fit Lagrange interpolation\npolynomials 20 to the same data using the same knot points. Fits were\nmade on ten years (1970-1979) and are presented for both methods in\nFigures 14 and 15. The Lagrandian interpolation polynomial technique\nwas chosen over the cubic spline technique because it seemed to be\nless sensitive to data deficiencies, i.e., the results were more\nbelievable in the annual extreme mean temperature ranges. There were","87\n83\n79\n75\n71\n67\n63\n59\n55\nGraph of Estimated Function over Actual Function\n51\nMaximum Daily Load by Mean Temperature\n47\n43\nDAILY MEAN TEMPERATURE\n39\nDAILY PEAK LOAD ON\nMAXIMUMS 1975\n35\nFIGURE 13\nTMP1\n31\n27\n23\n19\n15\n11\n7\n3\no = 2 observations\n= 3 observations\n-1\no = 1 observation\n-5\nLOAD 1\n240\n224\n208\n192\n176\n160\n144\n128\n112\n96\n80\n64","46\n80\nMW\n79\n300\n78\n77\n280\n76\n75\n260\n240\n220\n200\n180\n160\n140\n120\n55\n65\n75\n85\n-5\n5\n15\n25\n35\n45\nFIGURE 14\nOLS TIME VARYING PARAMETER\nLAGRANGE INTERPOLATION POLYNOMIAL ESTIMATE OF\nDAILY PEAK RESPONSE TO DAILY MEAN TEMPERATURE","78\n78\n77\n77\n76\n76\n75\n75\n74\n74\n73\n73\nMEAN TEMPERATURE ON DAY ON MONTHLY PEAK\n72\n72\nMONTHLY SERIES ON PEAK LOAD\nAND MEAN TEMPERATURE\nMONTHLY PEAK LOAD\n71\n71\nFIGURE 15\n70\n70\n69\n69\n68\n68\n67\n67\n66\n66\n65\n65\n64\n64\n63\n63\n62\n62","48\nstill some problems with the results. Five out of ten of the esti-\nmated curves turned down as the mean temperature approached -50. Two\nof the years, 1975 and 1977, exhibited unusual patterns when compared\nto the other eight years. Moreover, while the other eight curves\nshowed increasing loads from year to year, the 1975 and 1977 curves\ncrossed over the curves for the other eight. At 90°, the 1975 curve\nseems to be too low and the 1977 curve seems to be too high. This\nbehavior could have been caused by the distribution of mean temperature\n(hence load) in those two years.\nAt this point it is important to the rest of this story to indi-\ncate that the Staff was interested in calculating normal energy for\n1980 rather than for any of the historical years. Thus, not only did\nwe need estimates of the historical maximum and minimum monthly loads,\nwe also needed a one year forecast of these monthly maximums and\nminimums. From what we had done to this point, we had estimates of\nthe five knot points over ten years of data, i.e.,\nBiT\nfor i =\n1,...,5\nand t = 70,...,79\n.\nThe natural thing to do is plot these values against time and see if\nsome form of trending could be fit to the estimates that would provide\nforecasted values for these knot points. Once these estimated knot\nvalues were plotted two things were obvious:\nThe 1975 and 1977 estimated knot values were \"out of line\" with\nthe others.","49\nA structural change occurred in 1974 which slowed the growth.\nOn looking at the statistical results two things were obvious:\nIn every year the highest and lowest temperature level knot esti-\nmates had higher variances than the middle three knot estimates.\nThe 1975 knots' estimates had higher variances than the other\nyears.\nThese results led the Staff to use a linear spline, weighted regression\ntrend on each knot value. The linear spline allowed for a change in\nslope of the trend line at 1974, and the weighted regression allowed\nthe model to put more weight on those years with lower standard\ndeviations.\nThe results from this procedure are not presented because the two-\nstep procedure just described can easily be reduced to a one-step\nprocedure. Moreover, the first step model is specified by\nYt = ZtBt + Et\nwhere Yt is a vector of observed daily peak loads for year t, Zt is a\nmatrix of transformed21 daily mean temperature for year t, and Bt is a\nvector of the five knot values for year t. The second step model is\nspecified by\nor","50\nBt = Xta\nThen a one-step procedure would give the model\nY1\nZ1X1\nE1\na +\nYT\nZTXT\n&T\nIn this case the estimates of a could be obtained directly by esti-\nmating the model\nY = Za +\nwhere\n= Y1\nZ ZTXT Z1X1\nE1\n:\nY\nand E =\n,\nYT\nET\nNotice that an error term was not specified on the second step model.\nIf such an error term, say Ut, is specified, then\nE\n=\nET + ZTUT\nWhile E(&)E(t+ Ztut) 0, and an OLS estimate of the one-step\nmodel are unbiased, estimates will not be efficient (minimum\nvariance).22\nNevertheless the method of estimation used for this\ntime varying parameter model was OLS, 23 and the results are presented","51\nTABLE 3\nTIME VARYING PARAMETERS MODEL\nDAILY MAXIMUM LOAD\nYEARS: 1975-1979\nOLS REGRESSION STATISTICS\nKNOT\n't' STAT\nCONSTANT\nESTIMATE\nSTD. ERROR\n7.834\n- 50\n150.218\n19.176\n150\n151.233\n3.314\n45.631\n600\n125.201\n1.358\n92.177\n800\n183.395\n1.834\n99.987\n90°\n6.141\n41.081\n252.297\nSLOPE\n2.409\n- 50\n4.275\n10.299\n150\n8.470\n.927\n9.135\n600\n2.746\n.418\n6.571\n6.168\n800\n3.338\n.541\n90°\n9.365\n1.788\n5.237\nAdjusted R2 =\n.993\nEstimated\n13.495\n=","52\nin Table 3. Notice that for the constant portion of the knots the\nstandard errors of the estimates are fairly small as a percentage of\nthe estimates. Also notice that at the extreme knots (-50 and 900)\nthe standard errors of the estimates are substantially larger than at\nthe other three knots. On the slope portion of the knots, the stan-\ndard errors are also larger at the extremes, and at -50, the size of\nthe standard error as a percentage of the estimate is close to 50%.\nIn Figure 16, the estimated functions for 1975-1979 and for 1980\nare presented. Notice that the crossing problem has been eliminated,\nand the problem of turning down at very cold temperatures has been\nreduced in the 1975 data. Notice that these curves go through the\ndata rather than providing an estimate of the upper bound. Thus, a\ntwo standard deviation upper bound has been drawn on each figure to\ngive an indication of the upper bounds for each month's distribution\nfunction. 24\nIn Table 4, the estimates for the lower bounds are presented, and\nin Figures 18.1 - 18.5 these estimates are plotted against the data\nfor each year. The data is the minimum daily load on non-week days.\nNotice that the knot value at 850 shows negative growth. Also notice\nthat the standard error is extremely large. Since this function (or\nits lower bound) is used to estimate the lower bound of each year's\nprobability distribution, the mean temperatures of interest in the\nsummer are at the low end, and SO this negative coefficient problem is\nnot considered to be significant.","78\n78\n77\n78\n76\n77\n77\n76\n76\n75\n75\n75\n74\n74\n74\n73\n73\n73\n72\nMONTHLY SERIES ON KILOWATT-HOURS\nCOOLING AND HEATING DEGREE DAYS\n72\n72\n71\nHEATING DEGREE DAYS\nCOOLING DEGREE DAYS\nKILOWATT POUR SALES\n71\n71\nFIGURE 16\n70\n70\n70\n69\n69\n69\n68\n68\n68\n67\n67\n67\n66\n66\n66\n65\n65\n65\n64\n64\n64\n63\n63\n63\n62\n62\n62","54\nTABLE 4\nTIME VARYING PARAMETERS MODEL\nDAILY MINIMUM LOAD\nYEARS: 1975-1979\nOLS REGRESSION STATISTICS\nCONSTANT\nESTIMATE\nSTD. ERROR\n't' STAT\n10°\n89.565\n3.703\n24.186\n20°\n84.184\n2.292\n36.726\n550\n63.562\n1.272\n49.953\n750\n68.941\n1.566\n44.017\n850\n99.575\n2.790\n35.689\nSLOPE\n10°\n7.029\n.938\n7.491\n200\n6.272\n.642\n9.768\n550\n2.324\n.393\n5.918\n750\n1.865\n.462\n4.042\n850\n-0.064\n.758\n-0.085\nAdjusted R2 =\n.991\n7.906\nEstimated\n=","55\nThis leads to a discussion of how one uses mean tmeperature infor-\nmation to obtain estimates of the upper and lower bounds of the distri-\nbution function on load. In Table 5, by year and month, are the\nestimates of maximum and minimum loads. In the first column the mean\ntemperature at which the maximum load is expected to occur is\nspecified. Notice that for November through April, the maximum load\nis heating load, while for May through October, the maximum load is\ncooling load. The mean temperatures at which these maximums are\nexpected to occur are determined by estimating the lower bound of mean\ntemperature for each heating maximum month, and the upper bound of\nmean temperature for each cooling maximum month. The number of years\nof mean temperature which should be considered depends on one's view\nof temperature cycles. The ranges in column one are based on\n10° intervals (rounded to 50 end points) where the highest mean tem-\nperatures were observed over the last twenty years. For the minimum\nload, similar ranges in which minimum load occur were developed.\nThese ranges are then applied to the estimated load response functions\nfor each year to obtain mean estimates of monthly maximums and\nminimums. Notice that the minimum loads are the same except for the\nwinter heating months of December through March. Basically, this is\nbecause these loads represent non-temperature sensitive load occurring\non the non-weekdays, and in December through March the mean tem-\nperature is not expected to get high enough (650) to reflect non-\ntemperature sensitive load.","Max\n177\n200\n242\n299\n299\n242\n184\n200\n202\n200\n197\n171\n1979\nMin\n72\n72\n72\n72\n72\n72\n72\n72\n72\n79\n79\n72\nMax\n169\n236\n168\n176\n188\n196\n236\n290\n290\n191\n191\n191\n1978\nMin\n69\n69\n69\n69\n69\n69\n69\n69\n70\n77\n77\n70\nMax\n193\n230\n230\n280\n280\n167\n167\n179\n161\n181\n181\n181\nMONTHLY ESTIMATES OF MAX AND MIN LOAD\n1977\nMin\n67\n67\n67\n67\n67\n67\n67\n67\n68\n74\n74\n68\nMax\n153\n190\n225\n225\n165\n159\n172\n172\n172\n271\n271\n171\n1976\nTABLE 5\nMin\n65\n65\n65\n65\n65\n65\n65\n65\n66\n72\n72\n66\nMax\n146\n187\n219\n262\n262\n219\n162\n163\n163\n163\n162\n151\n1975\nMin\n63\n63\n63\n63\n63\n63\n63\n63\n63\n69\n69\n63\nMin Load\n600 -70°\n600 -70°\n550 -650\n650 -750\n650 -750\n550 -650\n550 -650\n550 -650\n50° -600\n40° -50°\n400 -50°\n-600\nRange\n50°\nMax Load\n30° -40°\n800 -70° -\n850 -750\n90° -80°\n90° -800\n850 -750\n750 -650\n250 -350\n00 -10°\n(-)50 - 50\n0° -10°\n10° -20°\nRange\nMonth\nApr\nMay\nJun\nJul\nAug\nSep\nOct\nNov\nDec\nJan\nFeb\nMar","57\nMPSC Model II: Estimating the Distribution of Load\nGiven the estimates for maximum and minimum monthly load for each\nyear, the transformation\nyj=(xj-atj)\ncan be applied to all the years data, say t = 1975,\n1979. This\ntransformed data can be used in various ways to estimate the probabi-\nlity distribution on load.\nMethod 1: For each month simply find the frequency distribution of\nthe transformed data using all five years of observations. Two basic\nproblems exist with this method. First, it ignores the correlation\nbetween load and mean temperature, or it assumes that the mean tem-\nperatures occurring over the past five years average out to be normal.\nSecond, the delineation of daily load curves cannot be maintained.\nThis delineation is not important in the determination of normal\nsales, but it could be important in the determination of normal\nexpenses. For example, if hydro-electric generation (variable head or\npumped storage) is an important peak shaving source of fuel cost\nsaving, then daily load curves are required to estimate energy\nsupplied from these sources.\nMethod 2: For each month and from all the years, determine which\nyear had the most normal weather for that month. In this case either\nheating or cooling degree days, or simply average mean temperature","58\ncould be used as a measure of normal. Once the \"normal\" year has been\ndetermined for each month, the inverse transformation\n=\nis applied to each observation for the year (T) for which one want to\ndetermine normal sales. The primary problem with this method is that\nif the average monthly mean temperature is determined using the twenty\nyears of data, it is unlikely that any of the five years will be equal\nto normal, though several may be close. Also, even if the year chosen\nis \"normal\" and the resulting estimate of sales is normal, the extremes\nmay not be included, and these extremes can be important determinants\nof cost to the utility. For example, the utility company loads its\nplants to meet demand in order of cost. Combustion turbines burn oil\nand are the most expensive forms of generation. These units are only\nrun on the extreme load days. Thus these estreme days should be\nincluded along with their expected frequency of occurrence.\nMethod 3: From the five years of data, and for each month, each\ntransformed daily load curve is classified by day-type and by mean\ntemperature. Then, daily load curves are chosen from the sets to make\nup a month's worth of curves. If there is more than one daily load\ncurve for a mean temperature, then the daily load curves can be\naveraged or chosen at random. The primary problem here is to devise a\nmethod of choosing day types and mean temperatures that are normal.\nMethod 4: The transformed daily load curves are used to estimate\nthe daily load response to mean temperature. Cubic splines or","59\nLagrange interpolation polynomials can be used to derive fairly reaso-\nnable estimates of daily load as a function of mean temperature. The\nsame problem exists here as in Method 3. To use the estimated func-\ntions to construct a \"normal\" month requires a method for determining\na \"normal\" temperature pattern.\nMPSC Model III: Normal Temperature Distribution\nThe requirements for a normal monthly temperature distribution are\ntwo fold. First, the average of the distribution must equal the\naverage over some pre-specified period. Second, the extremes must be\npresent to reflect the extremes that might occur in load.\nMethod 1: All monthly data from the specified time period are used\nto construct a quantile distribution. The number of quantiles should\nequal the number of days in the month. For example, if twenty years\nof daily mean temperatures is used, and a thirty day month is being\nconsidered, then the lowest twenty observations go into the first\nquantile, the next lowest twenty in the second quantile, and SO forth.\nThe mean of each quantile is calculated and used as one of the tem-\nperatures determining load. Since one must choose load curves for\nweekdays and non-weekdays, the thirty temperatures can be distributed\non a random basis among those two classes. Alternatively, two quan-\ntile distributions can be constructed with the number of weekdays and\nnumber of non-weekdays in the month as the determinant of the number\nof quantiles in each case.","60\nMethod 2: If the sequencing of the daily mean temperatures is\nimportant, then some form of time-series model should be used.\nSequencing can be important as it determines the number of times that\ncertain generating units are taken off-line and started up again.\nHowever, since in actual practice one does not know the weather in\nadvance, these decisions are usually based on weather forecasts\n(three-day). It is not clear in this case that one is not going to be\nunderestimating cost by treating the sequenced mean temperature data\nas both forecasted and actual data. Another important aspect of\nsequencing is when the load models used reflect lagged values of daily\nmean temperature. This problem can be handled in Method 1 by applying\nthe lag to the mean temperature data before estimating the quantile\ndistributions.\n4. Further Research\nAt this point it should be fairly obvious that normalization of\nload for weather and short-run forecasting are basically the same\nactivity. One of the more effective means for short-run forecasting\nis the Box-Jenkins ARIMA, or time series model. 25 Recently these\nmodels have incorporated both intervention techniques and transfer\nfunction capabilities. The flexibility which these additions allow\nmay prove to be the single most important factor in causing an\nincreasing number of load forecasts to be done on a time series model\nbasis.","61\nThe flexibility allowed through intervention techniques is\nillustrated in an appendix of an EPRI study on load forecasting pre-\nsented by G. C. Tiao. 26 In this appendix four models were presented.\nThe first two models used monthly peak data only through September\n1973, and the second two models incorporated two important intervening\nevents:\nthe energy crisis at the end of 1973\nthe economic downturn beginning in the fourth quarter of 1974.\nThe difference in the first two models is that the first model was a\nbasic Box-Jenkins linear growth in the log of monthly peak load\nstructure, while the second model allowed for an asymptotically\ndecreasing rate of growth. Both of these models overforecasted peak\nload from December 1973 on. The third and fourth models allowed for\ndecreasing growth rates and for a level change in December 1973 due to\nthe energy crisis. These two models differed in their treatment of\nthe intervention occurring in November of 1974. The third model\nhypothesized that the growth rate had been altered at that time, while\nthe fourth model hypothesized that the economic downturn was another\nlevel change. Over the period in question, both models performed well\nand produced short-run forecasts that were in close agreement.\nHowever, the asymptotic growth rate in the third model was 2.5%, while\nthe fourth model's limiting growth rate was 4.2% Thus, long-run\nforecasts from the two models were quite different. The choice of\nmodels then depends on whether one views the second intervening event\nto be a permanent or temporary interruption in long-term growth.","62\nAt the present time, the load forecasting unit of Research and\nPlanning at the MPSC has obtained the computer programming packages\nthat will allow us to estimate time series models. Plots of monthly\npeak loads for a Missouri based utility company and mean temperatures\noccurring on the day of monthly peak appear in Figure 19. While the\npattern of mean temperature on day of monthly peak is not exactly the\nsame from year to year, it is extremely close in the summer. A main-\ntained hypothesis is that while the average monthly temperature will\nhave a good deal of variation from year to year, the highs and lows\ntend to consistently occur year after year. This leads the time\nseries modeler to do a univariate analysis of peak load. 27\nConsidering the monthly peak load series it is clear that different\ngrowth in peak load is occurring in the winter than in the summer.\nThis is due to the fact that air conditioning saturation for this uti-\nlity is currently above 85%, while electric heating saturation is\nbelow 15% but growing at a faster rate. Time series modeling of peak\nload can allow for different monthly growth rates as well as interven-\ntions that can account for changes in either levels or growth rates.\nIf one is primarily interested in forecasts of kilowatt-hour\nsales, a different picture emerges. Plots of kilowatt-hour sales and\nboth cooling and heating degree days appear in Figure 20. On the\ncooling degree day series, note the spikes that occurred in 67, 69,\n74, 76 and 77. These match with summer spikes in kilowatt-hour sales\noccurring in the same years. A similar pattern occurs between heating","63\ndegree days and winter spikes. In order to explain these rela-\ntionships in a time series context, transfer functions are used. At\nthis time we do not have any results to report, but hope to have\nseveral models estimated before the end of the year.\nIf the time series modeling proves to be successful, then a simi-\nlar methodology to that used in Section 3 can be applied to obtain\nestimates of daily load curves. A monthly series of \"normal\"\nkilowatt-hour sales can be generated using average monthly cooling and\nheating degree days. Letting\n= load at hour h for month i in year t\nXhit\nPit\n= peak load for month i in year t\n= \"normal\" kilowatt-hour sales for month i in year t\nXit\ndefine\nZhit = (Xhit - Xit) (Pit - Xit)\n.\nThus Zhit is the hourly load adjusted for \"normal\" kilowatt-hour sales\nand peak load. The hypothesis is that the Zhit have been generated by\nthe same probability distribution. A choice of daily load curves for\na given month should satisfy the condition that\nNotice that the inverse transformation for year T is given by\n=\nand\nExh't = Xit + -\n.\nh","64\nThe second constraint on the choice is that the extremes should be\nincluded. Specifically, a day in which Xhit = Pit should be included\nSO that zhi = 1 is in the data set, and then\nmax xhi = = Xit + (Pit XiT) (max Zhi)\n= Xit + (P1T - X17)(1)\n= Pit\nFinally, to get from peak load and energy forecasts to daily load\nforecasts required the assumption that the probability distributions\ngenerating the load could be characterized by two parameters. This\nhypothesis can be extended to more parameters, e.g., peak load,\nenergy(mean), and minimum load. This would account for more shifts in\nthis distribution, but also would require the modeling of additional\nparameters.","65\nFootnotes\n1. Galiana, F.D., \"Short Term Load Forecasting,' in Proceedings on\nForecasting Methodology for Time-of-Day and Seasonal Electric\nUtility Loads, W EPRI SR-31, Electric Power Research Institute,\nPalo Alto, California, March, 1976.\n2. Taylor, Lester D., \"A Review of Load-Forecasting Methodologies,\nin Proceedings on Forecasting Methodology for Time-of-Day and\nSeasonal Electric Utility Loads, 11 EPRI SR-31, Electric Power\nResearch Institute, Palo Alto, California, March 1976.\n3. Uri, Noel D., \"A Mixed Time-Series/Econometric Approach to\nForecasting Peak System Load,\" Journal of Econometrics, Vol. 9,\n1979, pp. 155-171.\n4. This simple formulation ignores tax calculations which can be\nrepresented by\nT = t (R-E)\nwhere T is annual taxes and t is the tax rate. Revenues then\nbecome\nR =rIET or\nR = r I + E\n(1-t)\nwhere r/(1-t) is called the fixed charge rate and includes returns\nto pay tax expenses.\n5. In Missouri, all gas companies' sales are adjusted for heating\ndegree days as a matter of course in a rate case proceeding.\nHowever, to date, no electric company has been allowed an adjust-\nment due to lack of demonstrated \"measurability\" by either the\ncompany or the staff.\n6. Recall expenses vary with sales, so that if f(S) is the probabi-\nlity distribution of sales, then\nE = SE(S)f(S)dS\n7. The tendency in the past has been to either ignore the fact that\nexpenses vary with sales, or to assume a linear homogeneous (per\nunit) response.\n8. Some models have used daily maximum and minimum temperatures, and\neven hourly temperature readings.\n9. If there is a wide geographic divergence in service territories,\nprincipal component analysis can be used to \"correct\" for the\nmulti-colinearity problem.","66\n10. The standard definition for T* is 65°F.\n11. The months stated for each model type are those that are typi-\ncally used for Missouri. Northern states may have longer heating\nseasons and shorter cooling seasons, and Southern states the\nopposite.\n12. The simplest form of this model is:\nSit = Boi + B1i + B21Vt + Eit\n13. Some usual types of variables used are related to air con-\nditioning and electric heating saturation.\n14. The Research and Planning staff presented rebuttal testimony in a\ncase where the company was using a non-linear estimation proce-\ndure to estimate six parameters for each monthly model using ten\nyears of observations.\n15. The basic paper in which the proof of this result and the\nequations required to develop the W matrix are presented in\n\"Piecewise Regression Using Cubic Splines,\" D. Poirier, Journal\nof the American Statistical Association, 68: 515-524, 1973.\n16. The complete methodology was presented at a recent (June, 1979)\nEPRI conference in a paper entitled \"Synthesis of Hourly Loads,\nby Ed Wulf. The proceedings of this June 1979 conference should\nbe published in the near future.\n17. One must be aware that indisputable empirical facts are only\nvalid as long as they do work. Without a structural explanation\none runs the risk that they might one day fail.\n18. A simple example would be the uniform distribution function\nft(x) = bt - at\nat < x < bt\nFor the transformation X = at + (bt - at)y, the resulting distri-\nbution on y is g(y) = ft(at +(bt - at)y) (dx/dy) = 1 0 32 DEGREES, MUST BE ENTERED IN THE ORDER THE FOUNDATIONS ARE ENTERED,\nFOLLOWED BY THOSE FOR THE MAIN HOUSE)\nNUMBER OF WALLS ENTERED\nHEIGHT LENGTH % BELOW\n'C' IF A\nWALL\nINSULATION\n(FEET) GROUND\nCOMMON WALL\nCODE\nCODE THICKNESS\n(FEET)\nNUMBER OF DOOR TYPES ENTERED\n'C' IF ON A\nDOOR\nFRAME\nNO.OF\nHEIGHT\nWIDTH\nCODE\nCODE\nDOORS\n(INCHES)\n(INCHES)\nCOMMON WALL\nNUMBER OF WINDOW TYPES ENTERED\n'C' IF ON A\nWINDOW AREA (SQ.FT.) ON:\nGLASS\nFRANE\nNORTH SOUTH - EAST - WEST\nCOMMON WALL\nCODE\nCODE\nNUMBER OF CEILINGS ENTERED\nNO. OF\n'C' IF A\nCEILING\nINSULATION\nCODE THICKNESS\nSQ. FEET\nHEATED FLOORS\nCATHEDRAL CEILING\nCODE","112\nSTRUCTURE CODES\nFOUNDATION CODES\n1. FLOOR OF HEATED BASEMENT\n2. CEILING OF UNHEATED BASEMENT\n3. CEILING OF ATTACHED GARAGE (NOT UNDER LIVING SPACE)\n4. CEILING OF GARAGE (UNDER LIVING SPACE)\n5. SLAB AT GROUND LEVEL\n6. CRAWL SPACE\n7. CANTILEVER\nAPPROXIMATE\nUNIT OF\nCOST PER\nBTUs PER\nFUEL TYPE\nMEASURE\nUNIT\nUNIT\nELECTRICITY\n$/KW-HR\n.040\n3413.\nGAS\n$/100 CU.FT.\n.30\n78700.\nLP GAS\n$/GALLON\n.55\n69000.\nCOAL\n$/TON\n30.\n16800000.\nOIL #2\n$/GALLON\n.85\n100000.\nHARD WOODS (OAK, LOCUST, ETC.)\n$/CORD\n85.\n22000000.\nMEDIUM WOODS (ELM, MAPLE, ETC.)\n$/CORD\n75.\n17000000.\nSOFT WOODS (PINE, FIR, COTTONWOOD, ETC.)\n$/CORD\n65.\n12500000.\nEFFICIENCY\nWOODBURNING HEATING ELEMENT CODE\n(PERCENT)\n1. FIREPLACE\n10.\n2. FRANKLIN STOVE\n20.\n3. AIRTIGHT STOVE\n45.\n4. WOOD BURNING FURNACE\n50.\nINSULATION CODES\nEFFECTIVE R VALUE PER INCH\n0. NO INSULATION\n1. BLANKET OF BATT --FIBERGLASS, GLASS WOOL, OR MINERAL WOOL\n3.2\n2. RIGID--POLYSTYRENE (STYROFOAM)\n3.8\n3. RIGID--POLYSTYRENE (BEADBOARD)\n3.4\n4. RIGID--POLYURETHANE\n6.1\n5. LOOSE FILL--FIBERGLASS, GLASS WOOL, OR MINERAL WOOL\n2.8\n6. LOOSE FILL--VERMICULITE\n1.9\n7. LOOSE FILL-CELLULOSE FIBER\n3.5\n8. LOOSE FILL--POLYSTYRENE BEADS OR SHREDS\n2.9\n9. FOAMED IN PLACE--UREA FORMALDEHYDE (RAPCO OR AEROLITE)\n3.8\n99. FOR MULTIPLE TYPES OF INSULATION,\nFOR EACH TYPE NOTE CODE AND THICKNESS","113\nWALL CODES\nEFFECTIVE R VALUE\n1. WOOD, METAL, OR VINYL SIDING+DRYWALL, PLASTER, OR PANELING\n4.5\n2. BRICK OR STONE VENEER+DRYWALL, PLASTER, OR PANELING\n4.1\n3. BRICK OR STONE VENEER+MASONRY BLOCK+DRY, PLAS, OR PANEL\n5.0\n4. FRAME WALL+DRYWALL,PANELING,OR PLASTER ON 1 OR 2 SIDES\n3.3\n1.2\n5. POURED CONCRETE\n1.5\n6. MASONRY BLOCK WALL\n7. MASONRY BLOCK WALL+INSULATION IN CORES\n2.4\n8. CONCRETE BLOCK(CINDER AGG), CONCRETE BLOCK(GRAVEL AGG)\n3.7\n3.7\n9. CONCRETE BLOCK(CINDER AGG) COMMON BRICK\n21.0\n10. ALL WEATHER WOOD FOUNDATION\n2.9\n11. MASONRY, BRICK FACE\n12. POURED CONCRETE, INSULATION PANEL IN THE CONCRETE\n8.0\nEFFECTIVE R VALUE\nGLASS CODES\nf.0\n1. SINGLE GLASS\n2. SINGLE GLASS+PLASTIC OR STORM WINDOW\n2.0\n1.9\n3. DOUBLE GLASS\n4. DOUBLE GLASS+PLASTIC OR STORM WINDOW\n2.3\n2.9\n5. TRIPLE GLASS\n2.0\n6. GLASS BLOCK, 4 INCHES THICK\nADJUSTMENT KULTIPLIER\nWINDOW AND DOOR FRAME CODES\n1.0\n1. WOOD\n0.9\n2. METAL\n1.0\n3. INSULATED METAL\nEFFECTIVE R VALUE\nDOOR CODES\n3.2\n1. SOLID CORE DOOR, NO STORM DOOR\n4.8\n2. SOLID CORE DOOR, WOOD STORM DOOR\n4.3\n3. SOLID CORE DOOR, METAL STORM DOOR\n2.4\n4. HOLLOW CORE DOOR, NO STORM DOOR\n4.0\n5. HOLLOW CORE DOOR, WOOD STORM DOOR\n3.5\n6. HOLLOW CORE DOOR, METAL STORM DOOR\n7. STEEL DOOR WITH POLYSTYRENE CORE, NO STORM DOOR\n2.5\n8. STEEL DOOR WITH POLYSTYRENE CORE, METAL STORM DOOR\n3.6\n9. STEEL DOOR WITH POLYURETHANE CORE, NO STORM DOOR\n5.6\n10. STEEL DOOR WITH POLYURETHANE CORE, METAL STORM DOOR\n6.8\n1.6\n11. GARAGE DOOR\nEFFECTIVE R VALUE\nCEILING CODES\n1.3\n1. DRYWALL OR PLASTER\n2. SHEATHING+FINISH(DRYWALL, PLASTER, ACOU. TILE,ETC.)\n2.4","114\nSAMPLE RUN FOR\nTUCSON, AZ\nHEAT LOSS TABLE\n***\n(ASSUMING TYPICAL INFILTRATION, AND LOOSE DRAPERIES)\nLOCATION: AZ PIMA\nHEATING DEGREE DAYS @ 65 F : 1820\nDESIGN TEMPERATURES:\nSUMMER INSIDE 78.0 WINTER INSIDE 68.0\nOUTSIDE 28.0\nFUEL:\nSUMMER\nELEC\n0.040 $/KW-HR\nEER 10.0 BTU/WT-HR\n(CENTRAL AIR)\nWINTER\nELECTRICITY\nAT\n0.040\n$/KW-HR\nAVERAGE\nTRANSMISSION\nINFILT.\nTOTAL\nSQUARE\nR-VALUES\nHEAT LOSS\nHEAT LOSS\nHEAT LOSS\n% OF\nDESCRIPTION\nFEET\nHR-SQFT-F/BTU\nBTU/HR.\nBTU/HR.\nBTU/HR.\nTOTAL\nWINDOWS\n239\n2.00\n4790\n18104\n22894\n22.0\nDOORS\n1\n48\n3.20\n600\n3628\n4228\n4.1\nWALLS(ABOVE)\n2456\n3.97\n24758\n2415\n27172\n26.2\nCEILINGS+ROOF\n3265\n21.60\n6046\n6046\n5.8\nCRAWL SPACE\n3265\n3.00\n43533\n43533\n41.9\nTOTALS\n9274\n79727\n24147\n103874\n100%\nASSUMING PROPERLY VENTILATED ATTIC (ONE SQUARE FOOT OF OPENING\nPER 300 SQUARE FOOT OF CEILING AREA) --NEEDED FOR MOISTURE CONTROL","115\nESTIMATED ANNUAL HEATING AND COOLING COSTS\n***\nEFFECT OF INFILTRATION, ASSUMING\nSHADED WINDOWS WITH LOOSE DRAPES\nDRAFTY\nTYPICAL\nTIGHT*\nHEATING\n$ 895\n$ 1052\n$ 1288\nNO SETBACK\n$ 540\n$ 456\nWITH SETBACK TO 60.0\n$\n666\nFOR 2. HRS DAY, 12. HRS NIGHT\nCOOLING\n$ 509\nNO SETUP\n$ 578\n$ 536\n$ 423\n$ 443\nWITH SETUP TO 85.0\n$ 474\nFOR 2. HRS DAY, 12. HRS NIGHT\n* TIGHT INFILTRATION ASSUMES STORM DOORS, STORM\nWINDOWS, AND WEATHERSTRIPPING. IF THE WEATHERSTRIPPING AND CAULKING\nIS OVER 5 YEARS OLD IT SHOULD BE INSPECTED AND REPLACED AS NEEDED.\nEFFECT OF WINDOW COVERING, ASSUMING\nTYPICAL INFILTRATION WITH NO SETBACK OR SETUP\nLOOSE\nPULL SHADES\nPULL SHADES\nAND CLOSE\nINSULATED\nBARE FITTING\nOR CLOSE\nWINDOWS DRAPES FITTING DRAPES FITTING DRAPES SHUTTERS\nHEATING\nNOT SHADED\n$ 1006\n$ 1005\n$ 1016\nDRAPES ALWAYS CLOSED\n$ 1077\n$ 1044\ns 1002\ns 1002\n$ 1035\n$ 1011\nDRAPES OPEN DURING DAY\n$ 1077\nSHADED\n$ 1014\n$ 1013\nDRAPES ALWAYS CLOSED\n$ 1088\n$ 1052\n$ 1024\n$ 1013\n$ 1012\nDRAPES OPEN DURING DAY\n$ 1088\n$ 1045\n$ 1021\nCOOLING\nNOT SHADED\n$ 530\n$ 540\n$ 533\n$ 530\nDRAPES ALWAYS CLOSED\n$ 561\n$ 559\n$ 559\n$ 560\n$ 559\nDRAPES OPEN DURING DAY\n$ 561\nSHADED\n$ 527\n$ 527\nDRAPES ALWAYS CLOSED\n$ 556 $ 536\n$ 529\n$ 554\n$ 554\n$ 556 $ 555\n$ 554\nDRAPES OPEN DURING DAY","116\nRECOMMENDATIONS AND THERMOSTAT CHANGES WITH\nAPPROXIMATE SAVINGS IN ANNUAL ENERGY COSTS\n(ASSUMING TYPICAL INFILTRATION, SHADED WINDOWS, AND NO\nSETBACK OR SETUP EXCEPT WHERE INDICATED)\nADDING INSULATION\nWALLS\nPRESENT\nINCREASE\nIMPROVED ANNUAL\nHEIGHT LENGTH %BELOW\nWALL\nINSULATION\nR\nINSULATION\nR\nHEATING\nCODE\nCODE THICKNESS\n(FEET)\n(FEET)\nGROUND\nVALUE\nTHICKNESS TO\nVALUE\nSAVINGS\n2.\n1.\n0.0\n10.0\n37.4\n0.0\n4.1\n3.5\n15.3\n$\n25\n2.\n1.\n0.0\n10.0\n99.8\n0.0\n4.1\n3.5\n15.3 $\n67\n4.\n1.\n0.0\n10.0\n37.4\n0.0\n3.3\n3.5\n14.5 $\n33\n2.\n1.\n0.0\n10.0\n99.8\n0.0\n4.1\n3.5\n15.3\n$\n67\nCEILINGS\nPRESENT INCREASE IMPROVED ANNUAL\nCEILING\nINSULATION\nSQ\nNO. OF HEATED\nR\nINSULATION\nR\nHEATING\nCODE\nCODE THICKNESS\nFEET\nFLOORS\nVALUE\nTHICKNESS TO\nVALUE\nSAVINGS\n2.\n1.\n6.0\n3265.0\n1.\n21.6\n10.0\n34.4\n$\n23\n14.0\n47.2\n$\n34\n18.0\n60.0 $ 41\nIMPROVEMENTS TO WINDOWS AND DOORS IN HEATED AREAS\nANNUAL\nTOTAL\nIMPROVED\nHEATIN\nR VALUE\nIMPROVEMENTS\nR VALUE\nSAVINGS\nWINDOWS\n2.0\nADD STORM WINDOWS\n3.0\n$\n90\nDOORS\n3.2\nADD STORM DOORS\n4.8\n$\n26\nCOST ESTIMATES OF HEATING AND COOLING\nAT VARIOUS INSIDE TEMPERATURES\nHEATING\nTOTAL\nANNUAL\nCOOLING\nANNUAL AIR\nINSIDE\nDEGREE\nHEAT\nHEATING\nDEGREE\nCONDITIONING\nTEMPERATURE\nDAYS\nLOSS\nENERGY COST\nDAYS\nCOSTS\n60\n1094\n83099\n$ 379\n3970\n$ 1476\n62\n1358\n88292\n$ 511\n3505\n$ 1345\n64\n1659\n93485\n$ 666\n3075\n$ 1225\n66\n1988\n98679\n$ 846\n2675\n$ 1110\n68\n2346\n103874\n$ 1052\n2303\n$ 1004\n70\n2733\n109067\n$ 1284\n1960\n$ 900\n72\n3149\n114260\n$ 1534\n1646\n$ 804\n74\n3592\n119455\n$ 1806\n1359\n$ 715\n76\n4062\n124648\n$ 2100\n1099\n$ 626\n78\n4565\n129841\n$ 2414\n872\n$ 547\n80\n5098\n135036\n$ 2746\n675\n$ 472","117\nAPPROXIMATE SAVINGS IN ANNUAL HEATING COST\nWITH DIFFERENT THERMOSTAT SETBACKS\nHOURS SETBACK\nDEGREES\nNIGHT\nDAY\nSETBACK\n4\n6\n8\n10\n4\n6\n8\n10\n4\n$ 112\n157\n201\n240\n$\n8\n25\n47\n74\n94\n6\n$ 159\n226\n288\n346\n$\n8\n27\n55\n8\n$ 203\n289\n370\n445\n$\n8\n27\n57\n103\n10\n$ 245\n350\n449\n538\n$\n8\n27\n57\n106\nAPPROXIMATE SAVINGS IN ANNUAL COOLING COST\nWITH DIFFERENT THERMOSTAT, SETUPS\nHOURS SETUP\nDAY\nDEGREES\nNIGHT\nSETUP\n4\n6\n8\n10\n4\n6\n8\n10\n60\n76\n86\n4\n$\n6\n10\n19\n29\n$ 43\n36\n$ 60\n85\n107\n124\n6\n$\n8\n12\n22\n8\n$ 11\n15\n24\n38\n$ 79\n109\n139\n164\n172\n201\n10\n$ 13\n17\n26\n40\n$ 95\n134\n,\nDIFFERENCES IN SAVINGS BETWEEN DAY AND NIGHT FOR EQUAL SETBACKS ARE DUE\nTO LOWER OUTDOOR NIGHTTIME TEMPERATURES.\nFOR MAXIMUM COMFORT THE RELATIVE HUMIDITY SHOULD BE BETWEEN 35 AND 50 %.\nAS A RULE OF THUMB, FOR EACH VARIATION OF 5 % FROM THIS RANGE A 1 DEGREE\nDIFFERENCE IN THE THERMOSTAT SETTING IS NECESSARY FOR EQUAL COMFORT.","118\nREFERENCES\nASHRAE, 1979. Cooling and Heating Load Calculation Manual. ASHRAE GRP\n158. New York: American Society of Heating, Refrigerating\nand Air Conditioning Engineers, Inc.\nFitch, J.M., 1950. \"Buildings Designed for Climatic Control,\" in\nWeather and the Building Industry, Proceedings Research\nAdvisory Board, BRAB Conference Report 1, National Academy of\nSciences, National Research Council, Washington, D.C., pp.\n91-99.\nKusuda, Tamami, 1976. NBSLD, the Computer Program for Heating and\nCooling Loads in Buildings. Washington, D.C.: U.S.\nDepartment of Commerce, National Bureau of Standards.\nMather, John R., 1974. Climatology: Fundamentals and Applications.\nNew York: McGraw-Hill Book Company.\nOlgyay, Victor, 1963. Design With Climate: Bioclimatic Approach to\nArchitectural Regionalism. Princeton, New Jersey: Princeton\nUniversity Press.\nReiter,\nElmar R., et al., 1978. The Effects of Atmospheric Variability\non Energy Utilization and Conservation. Environmental\nResearch Papers, 14. Fort Collins: Department of Atmospheric\nScience, Colorado State University.\nReiter, Elmar R., et al., 1979. The Effects of Atmospheric Variability\non Energy Utliization and Conservation. Environmental\nResearch Papers, 18. Fort Collins: Department of Atmospheric\nScience, Colorado State University.\nWeinstein, Albert, 1975. \"Technical and Economic Considerations for\nSolar Heating and Cooling of Buildings: A Report by the\nWestinghouse Electric Corporation.\" In Proceedings of the\nWorkshop on Solar Heating and Cooling of Buildings,\nWashington, D.C., June 17-19, 1974. New York: American\nSociety of Heating, Refrigerating and Air-Conditioning\nEngineers, Inc.","1\nENERGY CONSUMPTION MODELLING\nby\nElmar R. Reiter and Collaborators 2\n1.\nWhy Do We Need Models?\nIn an age of affluence and abundance, as depicted in Fig. la, one\ndoes not have to worry much about the pathways by which resources are\nused and, perhaps, even squandered. Investments in resource and pro- -\ncessing capacity development are more or less controlled by market\nforces. Small perturbations in the demand \"box\" will not cause a major\nupset in the market for that commodity, be it energy or food or anything\nelse, as long as the general size proportions of the three boxes in Fig.\nla remain essentially the same.\nProlonged economic growth with subsequent depletion of natural\nresources will spawn an age of restrictions and regulations in which a\nbottleneck or barrier develops in the processing and/or delivery capac-\nity. Such a bottleneck, most likely, is caused in part by factors\nexternal to the market place. Concern for the environment, for in-\nstance, might hamper the development of new energy generating capacity\nnecessary to keep up with increased demand. The imbalance between\nI\nMost of the research described in this paper was supported by the\nU.S. Department of Energy Contract DE-AS02-76EV01340. This paper\nwas presented upon invitation by the National Oceanic and Atmospheric\nAdministration (NOAA) at a workshop held in Columbia, MO, on 11 April\n1980.\n2\nThe research team effort involved Professors G. Johnson (Mechanical\nEngineering), H. Cochrane, J. McKean and J. Webber (Economics), as\nwell as Mrs. A. Starr and Mr. J. Scheaffer (Meteorology), Miss C.\nBurns and Mr. H. Leong (Computer Science).\n119","120\na.) Abundance\nRAW MATERIAL\nDEMAND =\nPRODUCTION\nCONSUMPTION\nCAPACITY\nPROCESSG.\nWeather\nDELIVERY\nNormal\nCAPACITY\nUse\nMaintenance\nb.) Restrictions\nDEMAND >\nCONSUMPTION\nMinimum Needs for\n(10 years)\nDevelopment\nDevelopment\nZero- Growth Demand\nC.) Resource Starvation\nDEMAND >\nCONSUMPTION\nDevelopment\nDevelopment\n(50 years)\nMinimum Needs for Zero Growth Demand\nFig. 1\nSchematic relationship between production capacity (e.g. oil\nor natural gas production in Btu's), processing capacity (e.g. re-\nfining or electricity generating capacity, equivalent to Btu's)\nand consumption (in Btu's). \"Waste\" is loosely defined as resource\nutilization without enhancement in the quality of life (see text).\n\"Weather\" symbolizes a variability in consumption dictated by\nexternal factors. \"Maintenance\" and \"Development\" indicates neces-\nsary investment allocations in (Btu's) to maintain existing, or\nproduce new, production and/or processing facilities.","121\n\"boxes\" 2 and 3 in Fig. 1b will generate a \"seller's market\" with a\ntendency of increased prices which, most likely, will cause more regula-\ntions and restrictions of free development. Such restrictions may\narise, for instance, from a concern for \"unfair\" profit-taking, or from\npriority assessments in the use of limited available resources. We can\neasily envision that, as soon as the processing capacity and demand\nboxes achieve comparable sizes, relatively small perturbations in the\ndemand will lead to noticeable shortages and -- in a free market situa-\ntion to relatively large price fluctuations of the respective com-\nmodity. In the case of energy or food, we have to look at weather and\nclimate as causes for such perturbations.\nThose who are searching for solutions to this dilemma will have to\nstrive for a reproportioning of boxes 2 and 3 in Fig. 1a. Such pro-\nportioning can be achieved in various ways. The most sensible way would\nbe to rapidly enhance the processing capacity. This approach, most\nlikely, will necessitate a (temporary) diversion of resources from the\nconsumer demand box to allow for the necessary capital investment for\nnew development. This will increase pressure on the price of the com-\nmodity in question. For example, new coal-fired generating plants\nembody fossil fuels. Oil and natural gas are consumed in the process of\ncreating the steel, cement and other ingredients that make up a generat-\ning facility.\nIncreased prices tend to diminish, at least temporarily, the demand\nby promoting conservation, partly through elimination of waste. How-\never, conservation alone can lead to only a temporary remission in the\ndisproportion between boxes 2 and 3. A third, but counter-productive\nway of adjusting the mismatch in the volumes of these two boxes is to","122\ncurtail the allocation for re-investment from the demand \"box\". A\ntemporary relaxation of demand pressures, perhaps caused by price-\ninduced conservation, might prompt the adoption of this third course of\naction in favor of the one mentioned first.\nThe third scenario, depicted in Fig. 1c, shows a demand that has\noutstripped the raw-material production or availability. Thus, box 1\nconstitutes the bottleneck by resource starvation in this scenario for\neither technological or political reasons. The possible solutions are\nessentially the same as in the scenario of Fig. 1b, namely the develop-\nment of new or alternate sources, affected by the willingness and capac-\nity to divert disposable resources for investment and conservation. The\nmajor difference between scenarios (b) and (c) lies in the time scales\nof possible cures to the malaise. Whereas we should allow a development\ntime of the order of 10 years for new processing capacity (Fig. 1b), 50\nyears or more might be required to tap altogether new sources. For\ncertain critical commodities, such as energy and food, we may well be\nleft with a \"one-shot decision\", meaning that serious mistakes in long-\nrange decisions may be too costly to be survived by our present form of\nsociety.\n2.\nWhy Weather Sensitive Models?\nIn Fig. 1 we have dealt with the \"demand-consumption\" boxes in a\nrather crude manner, considering mainly their sizes relative to the\nother boxes. We will now apportion this demand box into compartments\nwhose relative sizes are dictated by either individual or collective\ndecisions, depending on the size and structure of the societal segment\nunder consideration (e.g. a family on welfare will apportion its re-\nsources differently than a family of upper-middle class standards, and","123\neven within similar classes there will be differences in apportionment\nbetween societies with strong or weak social security programs. There\nwill be differences of average apportionment between different climatic\nand demographic regions -- rural versus urban --, even within the same\ncountry).\nThe center \"box\" of Fig. 2 depicts, on an arbitrary scale, the\nrelative apportionment of expenses for energy or food by a societal unit\nof manageable size and homogeneity (e.g. a family, a small rural com-\nmunity, or a relatively homogeneous urban sector or neighborhood). As\n\"bare survival\" we could consider one room of a house maintained at 40°F\nduring a winter day (no temperature control during summer), if adequate\nprotective clothing and/or cover were available. A diet of 600 cal/day\nmight suffice for a limited period of time if food curtailment does not\ncoincide with an excessively cold period. Obviously, such low \"surviv-\nal\" values of heat and food do not apply to the very young, old, or\notherwise infirm, but only to healthy specimens of the societal unit.\nCommuting to work on foot or by bicycle (public transportation if avail- -\nable) may be accepted even in excess of 2 h one way, 7 days a week.\nAn American or European family would consider a diet of 1200 cal/\nday/person, and a temperature of approximately 60°F maintained during\nwaking hours in at least one room of the house, and of not less than\n50°F in the bedroom(s) a necessity -- again applying the yardstick of a\nhealthy specimen. Air conditioning could most likely be considered\n\"necessary\" if indoor temperatures exceed 90 to 100°F. Commuting to\nwork 5 days a week is deemed acceptable only up to a radius of approxi-\nmately 1/2 hour by either foot, bicycle or public transportation.\nBeyond this radius either job or home relocation is advocated.","124\nRelative Allocation of Resources\n(Energy)\nWaste\nWaste\nLuxury\nLuxury\nWaste\nLuxury\nComfort\nComfort\nComfort\nNecessity\nNecessity\nNecessity\nSurvival\nSurvival\nSurvival\n\"Normal\"\nEscalating Cost\nAdverse Weather\nFig. 2\nSchematic apportionment of energy use (arbitrary scale, to be\ninterpreted as Btu's per societal unit). For definition of cate-\ngories, especially of \"waste\", see text.","125\nA comfort level will be reached if the living rooms (kitchen,\nfamily or workrooms) can be maintained between 65 and 70°F during waking\nhours of the cold season, and bedrooms at 60° during the night. Working\nand sleeping areas would be air conditioned during the day and night,\nrespectively, when indoor temperatures exceed 80°F. Depending on the\nlevel of activity, the caloric intake might be around 1200 to 3000 cal,\nincluding a sizeable proportion of high-quality fibrous food. Commuting\nto work by car-pool arrangement or public transportation will have job\nopportunity and desirability of neighborhood as primary focal points.\nCommuting distance only plays a secondary role in the choices of home or\njob location. Vacation trips will rely mainly on public transportation.\nAs luxury level we would consider uniformly heated and/or air\nconditioned houses, maintained at 72°F throughout the year, access to\nheated swimming pools, and a wide variety of not locally or seasonally\ngrown foods packaged in small serving units. Commuting to work is\nmainly done in private vehicles with two, or fewer, passengers. Car-\npooling or public transportation are used only if personal schedules are\nnot inconvenienced. Vacation trips rely to a large part on privately\nowned or rented transportation.\nWaste levels are dictated by deliberate or involuntary inefficien-\ncies (e.g. dual-duct heating and air conditioning systems, over-heated\nor under-cooled house, perhaps with windows open; heated garages;\ninefficient appliances; unnecessary luxury or \"comfort\" of private\ntransportation which, furthermore, often places time and cost factors\ninto wrong proportions). The \"throw-away society\" syndrome extends from\nthe packaging to the consumption of food.\nThis definition of waste will undoubtedly raise the eyebrows of\ntrained economists. At any point in time households must make decisions","126\nregarding expenditures for domestic appliances, for example, and the\nenergy costs of their utilization. When energy prices are low, relative\nto the cost of the appliance, then it would be \"wasteful\" to pay more to\nimprove technical efficiency. However, when energy prices rise, as they\nhave recently, then these inefficient devices appear \"wasteful\" of\nenergy. The term waste is used here in the spirit of the latter situa-\ntion.\nWith this crude definition of \"apportionment\" into compartments\nranging from waste to survival, we will now proceed to assess the impact\nof external cataclysms, such as a severe weather or climate change. A\nweather-related \"catastrophe\" is thought to be of only limited duration\n(up to the length of one season) whereas a climate \"catastrophe\" might\nentail several to many years. We anticipate that adjustments in the\napportionment of available resources will depend strongly on the time\nscale at which the external cataclysmic event operates.\nThe right box in Fig. 2 anticipates involuntary waste of energy to\nincrease dramatically, given extreme weather conditions. Energy use,\nespecially for heating, will increase especially in poorly (wastefully)\ndesigned buildings. Slow or stalled traffic will consume dispropor-\ntionally large amounts of fuel. Similar considerations hold for the\nfood sector. Spoilage (e.g. by excessive heat, cold, or moisture) will\nendanger food at all stages, from production to storage.\nSurvival and necessity requirements will also increase consider-\nably, depending on the severity and duration of the external disruption.\nIn Fig. 2 we have pegged the anticipated increase at the top of the\n\"necessity\" compartment, because it is difficult to conceive of a cata-\nclysmic event, short of a nuclear war, that would reduce societal units","127\nto a mere survival level for any length of time. The increase in\nresource allocation to \"necessity\" and \"waste\" will, most likely, not be\nbalanced by reductions in the comfort and luxury allocations, unless\nsuch reductions are mandated by public appeal or by curtailments in\nenergy delivery. Prolonged curtailments in these allocations will have\neconomic effects of a wide-spread nature. Some of these effects are\npresently being gauged by newly developed economic models that deal with\na regional scale of input parameters.\nOn the left side of Fig. 2 we have indicated anticipated effects of\nnon-cataclysmic events, such as more or less rapid increases in price.\nWhen applied to food and energy, one would anticipate, again, that\n\"necessary\" allocations would receive a relative boost because of de-\ncreased purchasing power, while the luxury and waste allocations would\nsee most of the curtailment.\nUnder the \"double whammy\" of a severe weather disturbance in the\nface of a rapidly eroding purchasing power, even the \"comfort\" alloca-\ntion may be severely affected, to the point of complete cancellation,\nfor an unacceptably large segment of society. Such a scenario\nmight\nseverly and lastingly damage our economic system.\n3.\nMotivation Models\nWithout question it is difficult to determine a dollar or Btu value\nto fill the boxes shown in Fig. 2. It is even more difficult to obtain\nreliable data with which to predict the allocation decisions made by\ndifferent sectors of society. Given that such data could be obtained,\nthe next step would be to use these relationships in conjunction with\neconometric models so as to assess their impacts on local, regional and\nnational economic developments.","128\nFigure 3 illustrates possible factors influencing the motivation\nfor energy conservation, which would have as its ultimate goal a reduc-\ntion in energy use without curtailment of the comfort level. Attempts\nhave been made by H. Cochrane (see Reiter et al., 1980) to assess the\nrelative importance of some of these motivation factors. Figure 4\nillustrates schematically the \"decision tree\" underlying a set of\nquestions that were posed to adopters and nonadopters of retrofitting\nconservation measures. Results of an inquiry conducted in Fort Collins,\nColorado and involving 65 families revealed that most home insulators,\nand those that did not, were aware of energy shortages and believed that\nenergy prices will continue to escalate. Adopters, however, had better\nfaith in cost amortization of retrofitting than nonadopters. Cochrane's\nstudy also points out that the payback period for the investment in\nretrofitting for many of the adopters was disappointingly high. The\nimportance of this finding lies in the conclusion that misinformation on\nthe relative effectiveness of various approaches to conservation\npractices (e.g. caulking, storm windows, weather stripping, added in-\nsulation) not only diminishes the return on investment but leads to a\nwaste of resources.\nThe similarities and differences in the attitudes of adopters and\nnonadopters lead us to the conclusion that public appeal and advertising\ncampaigns should focus on economic issues, stressing the savings that\ncan be realized by conservation measures, rather than on the fact that\nan energy shortage exists and prices are going to rise. Cochrane,\nfurthermore, suggests that general attitudes towards conservation could\nbe enhanced by including the monthly cost of utilities (U) into the\nprocessing of mortgage applications by banks which presently consider","129\nMotivation Factors\nfor Energy Conservation\nI\nClimate\nExternal\nS Weather\nI\nCost Amortization\nEconomic\nS\nCurrent Cost\nIncentives (Tax Credits)\nPublic Appeal\nPsychological\nGeneral Attitude\n* Subject to short-term manipulation\nI Long time scale\nS Short time scale\nFig. 3\nFactors, and their time scales, influencing the motivation\nfor energy conservation.","130\nExogenous\n[Increase\nevent occurs\nPrice of\nNatural Gas]\nHas Individual\n[Is the price of gas going\nthought about\nto continue to go up?\nevent?\nWill there be shortages?]\nIs there any-\n[Is there anything that can\nthing that\nbe done?\ncould be done?\nHave you thought about in-\nsulation as a viable alterna-\ntive to higher fuel prices?]\nWhose\nresponsibility?\nSearch and\nprocess infor-\nmation on event\nWilling to proceed\nWhat do I\n[Do you have the time and\nwant to do?\nresources to implement\nconservation efforts?]\nExamine\nalternative\nalternative\nfeasible\nactions\nNo\nFeasible\nDo not\nalternative\ntake action\nTurn down\nTake action\nthermostat\nPurchase insulation\nInstall storm windows\nThreshold model of decision making (adapted from Kunreuther\nFig. 4.\net al. , 1978).","131\nonly principal, interest, taxes and insurance payments (PITI) versus the\napplicant's income. If PITIU were adopted instead of PITI, a trade-off\nbetween interest on capital investment to reduce utility bills, and\nhigher utility bills, may be critical in the acceptance and rejection of\ncertain applications. PITIU thus would provide for better acceptance of\nconservation measures by the general public. For a sound evaluation of\nsuch a trade-off between interests and utility costs accurate computa-\ntional and modelling procedures for energy consumption have to be avail-\nable.\n4.\nComposite Models\nIn the foregoing discussion we have pointed out several difficul-\nties associated with the assessment of motivation factors influencing\nenergy conservation. These factors will not diminish in their im-\nportance if they are incorporated into an energy consumption model for a\ncommunity system (Fig. 5). In essence, we can identify three categories\nof factors that influence energy consumption: external factors, such as\nclimate and weather; design factors, including use patterns and building\ncodes; and last, but not least, economic factors. Different time scales\nare associated with different factors. Climate, architectural design\nand building codes can be assumed as either constant or slowly varying.\nWeather, on the other hand, will influence energy use on time scales of\nhours to days, perhaps weeks. Some economic factors, such as curtail-\nments and price increases, as well as changes in use patterns and retro-\nfitting designs, operate on intermediate time scales of months to years.\nSeveral feedback mechanisms can be envisioned between various\n\"boxes\" shown in Fig. 5. Under ideal conditions one would presume that\nclimate is a major motivator in architectural design and building codes.","132\nFactors Influencing Energy Use for Heating & Cooling\nClimate\nExternal\nWeather\nArchitect.\nEnergy\nDesign\nConsumption\nDesign\nBuilding Codes\nUse Patterns\nMotivation for\nCurtailments\nConservation\nEconomic\nPrice\nProfit\nRetrofit\nRedesign\nLong Term\nShort Term\nFig. 5\nFactors, and their time scales, influencing the energy use for\nspace conditioning.","133\nThe recent energy shortage, indeed, has helped in aligning these codes\nmore closely to climatic conditions than has been the case with the\ncodes in effect through the early 1970's. Unfortunately, architectural\ndesign still is paying little attention to climatic variables. We\nanticipate that stimulation to do so will come mainly through the eco-\nnomic factors of price and investment amortization considerations.\nWeather and economic factors have been indicated in Fig. 3 as being\nof influence on motivation for conservation. Decisions to conserve\nwithout new investments will mainly affect use and habit patterns (e.g.\nlowering thermostats in winter). If such decisions are widespread in a\ncommunity, energy consumption will be affected in a significant way,\nrendering model calculations of such consumption, which are simply based\non regressions between historic data sets, unreliable and inaccurate.\nDecisions to retrofit and redesign operate on different time\nscales, as symbolized in Fig. 5. Both types of decisions affect energy\nconsumption through the set of design factors as illustrated in that\ndiagram. Most of our data have been collected to date over a relatively\nnarrow range of variability in environmental and economic parameters.\nOver that range the correlations that becomes obvious (e.g. between\nweather and energy use, use patterns and energy consumption motivation\nand retrofitting, etc.) behave either linearly, or at least monotonous-\nly, and our limited understanding of feedback mechanisms is within the\nrange of a stable system behavior. It would be within the framework of\nsuch a stable system that increased energy prices will motivate conser-\nvation attitudes, leading to retrofitting decisions and to changes in\nuse patterns, both resulting in reduced energy use and a stabilization\nof prices. What would happen, however, if the ranges of variability in","134\nsome of these parameters exceeded significantly the amplitudes manifest\nfrom current experience? E.g. a sudden drastic curtailment and/or price\njump will have a drastic effect on energy consumption, that might result\nin a \"runaway\" feedback with economic factors, leading to a crash in a\nvariety of sectors of the national or regional economy, even those which\nare not necessarily heavy energy users. Efforts should be taken to\nidentify critical and potentially unstable feedback loops and to identi-\nfy sets of parameters that might lead to a bifurcation between stable\nand unstable model behavior.\n5.\nWhy Space-Heating Models?\nOur own modelling efforts at Colorado State University have con-\ncerned themselves mainly with aspects of space heating and air condi- -\ntioning. One could think of more profound and wide-flung problems that\nshould or could be modelled, including the various patterns of energy\nuses in industry, commerce and transportation and involving all forms of\nenergy: fossil, nuclear and renewable. There were several compelling\nreasons that motivated our modelling attack on energy consumption for\nspace conditioning:\n(1) In 1972 31% of the energy resources were used in the residen-\ntial and commercial sectors of consumption. Two thirds of this amount\nwere used for space heating on an annual average basis (F.E.A., 1975).\n(2) Data required for model development and model validation can\nbe obtained with relative ease. This is not to say that a considerable\neffort in information network design, data collection, analyses and\ninterpretation will not have to be expended.\n(3) Since a meaningful data base can be established, numerical\nmodelling tools can be developed and tested against the \"real world\"","135\nunder relatively rigorous conditions and with a minimum of assumptions\nthat cannot be substantiated.\n(4) Energy use for space conditioning is subjected in a signifi-\ncant way to the external forcing parameters of weather and climate (Fig.\n5), more so than many industrial uses of energy. Our natural data\nsources, therefore, provide us with a wide range of scenarios for model\ninput. A composite model, such as envisioned in Fig. 5, will have to\ncontend with such natural perturbations.\n(5) Use patterns and decision-making patterns in this sector of\nenergy consumption can be identified within relatively small elements of\nsociety (family, township, etc.). This limitation in scope makes it\nsomewhat easier to collect data for an assessment of the relative im-\nportance of motivation factors involved in energy conservation (Fig. 3).\nBased upon such an assessment more effective ways of motivation man-\nipulation can be designed and tested. Their effectiveness can be gauged\nquantitatively by changes in energy consumption in individual buildings\nas well as in larger communities.\n(6) As home heating and cooling costs take an ever-increasing\nslice out of personal disposable income, the apportionment of energy\nuse, sketched in Fig. 2, becomes a matter of concern and can be treated\nquantitatively with some degree of statistical significance. Consider-\ning a representative cross-section of income levels in typical communi-\nties, one should be able to first calibrate the effects of weather and\neconomic factors, and later predict such effects under a variety of\nextreme factor combinations. The syndrome of \"welfare economics\" should\nreveal itself in such analyses.","136\n(7) The development of numerical and statistical modelling tools,\nhoned by stringent validation procedures, should benefit modelling\nattempts in other sectors of energy consumption as well as in food\nproduction where comprehensive data sources are more difficult to tap.\n(8) Properly constructed models should allow the testing of new\ndesign and construction criteria and of economic decisions in a rather\nquantitative manner.\n(9) Highly accurate and well-tested models for space heating and\ncooling which also allow a reliable assessment of the costs and benefits\nof certain retrofitting conditions are needed if banks and loan com-\npanies should be persuaded to integrate utility costs into an evaluation\nof the credit rating of mortgage applicants.\n6.\nThe Colorado State University Model\n(a) Modelling Philosophy\nFrom the very beginning of our modelling efforts (Reiter et al.\n,\n1976) we were aware of a variety of statistical models which explained\nover 90% of the variability in hourly system demands for electricity\n(e.g. Federal Power Commission, 1970) and gas (e.g. American Gas Associ-\nation, 1969). Such models can claim a high degree of usefulness in\nseparating weather-related energy demand from base loads on various\nenergy systems. Their obvious advantage lies in the fact that usually a\nrelatively easily and inexpensively obtainable amount of input data can\nlead to the desired answers. They suffer, however, from the disadvan-\ntage that the statistical regressions found from these models are\nstrongly location dependent and usually also vary with time.\nThe accuracy of those load-study results depended upon the non-\nvariability of physical structures, use patterns and comfort levels.","137\nIndeed, within the framework of those studies, it was reasonable to\nassume that only the weather changed. However, our investigation is of\nfar broader scope than load studies, in both space and time. Struc-\ntures, space-conditioning equipment, and use and habit patterns may all\nbe expected to vary between geographical regions, and over time within a\nparticular region. Consequently, it is necessary for our investigation\nto account for possible changes in any of these variables mentioned\nabove.\nHistorical data are of questionable value in constructing such a\ngeneral model, because, heretofore, variables in the economic environ-\nment have either changed very little, or they have trended in one direc-\ntion. Examples are real (adjusted for inflation) prices of energy which\nover the past several decades have trended downward, whereas at the same\ntime real incomes have trended upward. Moreover, pronounced trends have\nbeen evident in improved efficiency and decreased cost of space-condi-\ntioning equipment. The combined effects of these changes have profound-\nly increased the weather sensitivity of summer electricity loads\n(McQuigg, 1974; NY Power Pool, 1975, Vol. I. P. 7-52). On the other\nhand, the economy is presently reeling under the impact of dramatic\nincreases in real energy prices, and in the consequential rises in real\nprices of commodities which require relatively large amounts of energy\nfor their production. The suddenness of the change and its political\novertones also induced a \"conservation ethic\" whose effect and duration\ncannot yet be fully measured. Nevertheless, the effect was unmistakable\n(NY Power Pool, 1975, Vol. I, Exhibit 8), even though it differed re-\ngionally in terms of homeowner energy conservation (FEA, 1974).","138\nAs a consequence of limitations such as those discussed above, we\ndecided to base our model on physical features which can be derived from\nbasic heat-transfer relationships. Models of this type have been used\nextensively by architects and engineers (e.g., Kusuda and Powell, 1972;\nKusuda, 1974; Meriwether, 1974; Johnson et al., 1975) concerned with\nspace-conditioning system design. Their validity has been demonstrated\nfor an individual structure in numerous studies (Fox, 1973; Jones and\nHendrix, 1975; Kusuda et al., 1975; Kruger, 1974; Sepsy et al., 1975a,\nb,c; Peavy et al., 1975; Hill et al., 1975), which have shown that heat\nloads calculated from design procedures (e.g., ASHRAE, 1972) can be used\neffectively and that the results are reasonable.\nThe physical model used in this study is an extension of the models\ncited above and has been described in detail by Reiter et al. (1976,\n1978). Here, however, the end result is not the sizing of space-condi-\ntioning equipment, but to compute the energy required for space condi- -\ntioning -- a task with which only a few modelling efforts have been\nconcerned (e.g., Fox, 1973; Petersen, 1974; Johnson et al., 1975). Of\nthese previous attempts to apply a physical model for calculating space-\nconditioning requirements, the study of the Twin Rivers townhouse pro-\nject in East Windsor, New Jersey (Fox, 1973) was perhaps the most am-\nbitious. In view of the many simplifications used in that study, it was\nsurprisingly successful.\nOn the other hand, heretofore heating and cooling systems have\ngenerally been oversized by a factor of two, and load calculations have\nnot had to be of great accuracy. Thus, even though computations of heat\nlosses or gains due to infiltration have not been as satisfactory as\nthose for heat transmission, this should not be judged as a shortcoming","139\nof the procedures used. For example, detailed infiltration calculations\nare quite complex, and simplification procedures which yield conserva-\ntive estimates (such as the air-change method for computing infiltration\nor the use of degree-day data rather than hourly weather observations\nfor calculating heat loads) are customarily introduced to reduce the\nnumber of required calculations. However, for our purpose of predicting\nthe total space-conditioning energy requirement of an entire city,\ncomposed of many diverse structures -- each subject to modifications in\ntheir physical and adaptive characteristics --, it was apparent that the\nmodel must incorporate every feasible procedural refinement.\n(b) The Physical Model.\nThe physical model developed at CSU is based on heat transfer\nequations and on a heuristic, adaptive, self-organizing computation\nlearning approach. The model has been \"trained\" on a number of in-\ndividual buildings which were considered to be typical structures. A\ncommunity's energy use is arrived at from heat loss computations for\nthese typical buildings within the community. To date the program\ncontains 52 such typical buildings, each with up to three age categor-\nies. The age classifications are based upon our assessment of changes\nin building technology and comprise pre-1940, 1940-1970 and post-1970\nstructures. The model was tested extensively in the early validation\nprojects conducted in Greeley, Colorado and Cheyenne, Wyoming. Figure 6\npresents a block and data-flow diagram of this model.\nThe basic elements of the modelling procedure are as follows:\nfirst the physical relationships for heat loss and gain for the subcom-\nponents (i.e. walls, ceilings, windows, etc.) of individual buildings\nare described. These steps are sufficient to calculate the energy con-\nsumption for a building constructed from the subcomponents and operated","140\nREAL SYSTEM\nDIFFERENCE\nENERGY/\nBETWEEN\nCITY BUILDINGS\nCURRENT INPUT\nOUTPUT\nHEAT\nTHERMOSTAT\nCONVERSION\nSETTING\n( ENERGY\nAND INSIDE\nCONSUMPTION )\nTEMPERATURE\nESTIMATION\nESTIMATED\nCURRENT\nDATA\nSMOOTHING\nPAST\nI\nOUTPUT\nPHYSICAL\nFILTERING\nBASE\nPREDICTION\nMODEL\nRECORDS\nSIMULATION\nStructural\nREJECT\n2\nIdentification\nCONTROLLER\nHYPOTHESIS\nSearch new descrip-\ntion of the system\nTESTING\nby optimizing some\n( DECISION\nMODEL\nspecified perfor-\nMAKING )\nCOMPARISON\nmance index,\nACCEPT\nBASED ON\nPRE - SET\nModel Updating\nCRITERIA\n3\nUpdate current model\nwith latest accumu-\nMODEL\nlated information.\nFig. 6\nThe self-organized dynamic forecasting model with adaptive\nfeedback, diagnostics, updating and reevaluation mechanisms.","141\nwithin a given behavioral pattern. The individual buildings which\nrepresent the given building classifications are then lumped together\ninto an \"average building\" for each category in terms of size and ther-\nmal characteristics. Then the energy consumption for each representa-\ntive building type is calculated in response to the meteorological\nparameters. The over-all energy use by the community is computed by\naggregating the individual building classifications and age groups\naccording to their actual distribution encountered in the respective\ncity or its subdivisions. The scheme can be used to calculate the\nenergy demand for a community, city or region. Because of the large\nnumber of buildings within each classification, the statistically\naveraged representation of such a system has been found to be very\naccurate as previously reported. Whereas large errors may be found in\nthe energy consumption estimates for individual buildings, the large\nnumbers of buildings within a certain classification tends to make the\noverall error quite low. If sufficient input information is available\nto characterize a community to the detail needed, the physical model has\nbeen shown to give very good results.\n(c) Detailed Data Requirements\nInformation required to execute the model includes inputs from two\nsources. One of these inputs comprises factors which are essentially\nphysical and fixed, in that they represent items over which we have no\ncontrol or which cannot be changed with ease. The other source repre-\nsents factors which are controllable or predictable to the extent that\nthe contemporary habit patterns of the general public can be influenced\nas a consequence of governmental action, or in response to changes in\nthe cost and/or availability of energy, or because of extreme environ-\nmental conditions. The first of these sources comprises the data banks","142\nof meteorological and structural information. The second source is the\nadaptive reaction of building occupants to external influences, as\nmeasured in terms of thermostatic settings, infiltration-rate adjust-\nments and retrofitting.\nThe meteorological data base consists of insolation or percent of\ncloudiness (amounts, types, thicknesses and altitudes), wind speed and\nambient air and ground temperature. The ambient temperature is the\nprimary driving function of the model and, except for buildings with\nextensive basements, we need to consider only variations in outside air\ntemperature. In the case of structures with large, deep basements, such\nas are represented by virtually all high-rise and some large low-rise\nbuildings, it is necessary that for the subterranean portion we substi-\ntute a representative ground temperature as the ambient temperature to\nwhich the model responds. Wind speed is used in the infiltration cal -\nculations, and insolation or cloudiness in the solar heat-gain calcula-\ntions.\nAccording to the purpose for which the model is being run, the\nmeteorological data base may contain either current or historical, or\nperhaps contrived or forecast weather conditions. However, except for\nunusual circumstances, weather conditions vary geographically and diur-\nnally to such a degree across all except the smallest communities that\nthe meteorological data inputs to the model for a particular date cannot\nbe satisfied by a single number for each parameter. Hence, establish-\nment of a meteorological data base in the detail required for accurate\nenergy-consumption calculations proved to be a sizable data-collection\nand analysis task.","143\nThe generation of an urban heat island, and the simultaneous reduc-\ntion in wind speed can affect local energy demand by as much as 20%.\nIt\nwas necessary, therefore, to monitor in detail the local distribution of\nmeteorological parameters with the aid of station networks specially\ninstalled in Greeley, Colorado, Cheyenne, Wyoming, and Minneapolis,\nMinnesota. Nevertheless, considerable amount of data massaging was\nrequired to interpolate for missing data. The mean heat-island intensi-\nty (urban-rural temperature difference) in Minneapolis was about 2°C\nduring the abnormally cold monitoring period in early 1979. Extreme\nheat island intensities of 7°C were observed on occasion, but were\nprobably still underestimated. The effects of anthropogenic heat on the\nformation of the urban heat island could be demonstrated quite clearly\n(Fig. 7).\nUnder light-wind conditions cold-air drainage lends some importance\neven to relatively minor topographic details (Fig. 8) conditions as\ninput to an energy consumption model.\nNo less, and perhaps even more formidable than the development of a\nmeteorological data base is the development of a census of the buildings\nthat make up the population region to be studied, by types, usages,\nages, numbers, sizes, construction characteristics and materials,\nshading/sheltering from sun/wind, energy sources, heating and cooling\nsystems, internal heat loads and locations. The importance of this task\narises not only in connection with recognition of the need for specific\nbuilding-type models, or of the fact that identical buildings may be\nlocated only a short distance apart and yet be exposed to markedly\ndifferent weather conditions. The census is required also for purposes\nof determining \"characteristic mixes\" as to the numbers of, and dimen-\nsional as well as thermal variations among, the buildings within the","144\n10.0\nO\n-10.5\n-10,0\n-9.5\n-9.0\n-8.5\n-9.0\nAnalysis of the mean temperature field (heat island) in the\nFig. 7\nminneapolis area for all data from January 1, 1979 through\nMarch 31, 1979. The circles represent temperature monitor\nlocations.","145\n-23\n-24\n-21\n21\n-22\n-22\n-22\n-24\n-23\n-23\n-24\nheat island for 200-400 CST, January calm conditions 25, 1979.\nMinneapolis time period skies were clear, and the top of\nFig. 8\nDuring this at all surface monitors. Winds at meters per\nwere the 152 observed meter tower (Station 34) averaged 2.0\nsecond from the northeast.","146\ncity for each thermally equivalent structural type, use and vintage\nclassification.\nThe acquisition of building census data for Minneapolis was a\ndifficult task. Only 13% of the total number of heated structures had\nany use pattern information that could be extracted from the assessor's\ncomputerized files. Use information could be supplemented for approxi-\nmately 4500 buildings, by addresses, from the Yellow Pages telephone\ndirectory. 1200 structures, occupied by interruptible customers, were\nremoved from our census files, including 20 downtown buildings linked to\na central heating system not supplied by the utility company that pro-\nvided our data. Our final census file contained 105,722 buildings that\ncould be grouped into distinct categories (Table 1). The city was\ndivided into 127 census tracts. Missing size or structural data were\nsubstituted by using the average values for such parameters obtained for\nthe remainder of the buildings of the same type within the respective\ncensus tract.\nIn Greeley, the input information was obtained by a survey of each\nstructure within the community. As we moved our modelling efforts from\ncommunities to cities, and eventually to regions, the volume of detailed\ninformation became prohibitive. To circumvent this problem, a statisti-\ncal sampling technique was developed and tested in Cheyenne, Wyoming.\nThe results were presented by Reiter et al. (1978). It was found that\nthese results were not quite as good as those obtained for Greeley,\nColorado. We think that the primary difference in quality was due to\nthe level of detail in the available input data on the individual build-\nings within the community. Not nearly as much work had gone into creat-\ning the Cheyenne data base as had gone into the Greeley data base, and","147\nTABLE 1\nSummary of building data and gas consumption by\nbuilding type for Minneapolis, Greeley and Cheyenne.\nM = Minneapolis (Jan. 1978)\nG Greeley (Dec. 1975)\nC Cheyenne (Jan. 1977)\nAverage Size\n% of Total\n% of Gas\n(Sq. Ft. )\nBuilding Count\nConsumed\nBuilding Type\nM\nG\nC\nM\nG\nC\nM\nG\nC\nSingle Family\npre-1940\n1397\n1157\n1196\n70.1\n22.0\n19.1\n18.63\n-\n-\n1940-1970\n1190\n1252\n1097\n21.0\n39.0\n50.0\n20.25\n-\npost-1970\n1277\n1666\n1506\n.8\n14.6\n8.9\n6.93\n-\n42.71\n45.81\n44.21\nDuplex\n2104\n1616\n2549\n1.3\n1.2\n1.9\n.92\n.88\n2.45\nTriplex\n2654\n3219\n1789\n.02\n.06\n.23\n.02\n.06\n.15\nFourplex\n18077\n1825\n5262\n.01\n.10\n.10\n.03\n.17\n.24\nSixplex\n1900\n7530\n.02\n>.01\n.02\n.02\n-\nMobile Home\n730\n821\n11.4\n11.5\n3.67\n4.83\n-\n-\nApartments\n15818\n5552\n7262\n1.0\n3.3\n1.2\n3.98\n5.67\n3.86\nTotal\nResidential\n1514.\n1391.\n1239.\n94.3\n91.7\n93.0\n47.7\n56.3\n55.8\nBusiness\nSales\n12236\n5847\n5346\n2.4\n3.5\n1.6\n17.69\n16.93\n8.14\nBusiness\nService\n16681\n3431\n5237\n.05\n.21\n.14\n.44\n.50\n.65\nLaundry\n5106\n4336\n.13\n.08\n.45\n.28\nBank\n78492\n10346\n13296\n.04\n.15\n.04\n.80\n.89\n43\nChurch\n14175\n7264\n5624\n.18\n.39\n.48\n.78\n2.45\n2.11\nNursing Home\n10569\n11137\n33970\n.03\n.17\n.02\n.22\n1.27\n.43\nSchool (Elem.\n& High)\n68083\n28043\n49707\n.12\n.26\n.22\n2.25\n1.95\n3.98\nSchool\n(Colleges)\n17577\n9836 18725\n.03\n.11\n.09\n.30\n.65\n1.05\nGovernment\nBuildings\n119642 15291 12191\n.11\n.15\n.43\n4.05\n1.64\n2.70\nCafes &\nRestaurants\n8500\n3469\n4830\n.50\n.38\n.25\n2.62\n.94\n95\nLibrary\n13466\n8000 15638\n.01\n.01\n.02\n.06\n.03\n.19\nBowling,\nPool Halls\n13746\n7855 14933\n.01\n.03\n.03\n.07\n.14\n36\nFire Dept.\n6273\n4595\n.02\n.02\n.08\n.10\nGrocery\n12552\n12310 13309\n.02\n.11\n.09\n.17\n.90\n.98\nOffice\n47821\n6992\n6705\n.82\n.20\n1.00\n10.64\n.95\n6.64\nCommunity\nBuilding\n36136\n8902\n6205\n.03\n.04\n.05\n.25\n.23\n.13\nBars\n2226\n4976\n.08\n.03\n.17\n.16\nTheaters\n11059\n7644\n16348\n.01\n.02\n.02\n.07\n.09\n.47\nPrivate\nBuildings\n15734\n10276\n7223\n.07\n.10\n.04\n.68\n.63\n32\nDepartment\nStores\n78461\n22000\n21362\n.06\n.01\n.03\n2.61\n10\n.53\nMalls\n5325\n.45\n1.20\nMotels,\nHotels\n47900\n13620\n6414\n.02\n.14\n.55\n.30\n1.13\n1.74\nBakery\n18904\n2097\n1344\n.02\n.02\n.01\n.19\n.04\n.01\nIce Cream\nStore\n1097\n1678\n-\n.02\n.03\n.02\n.03\n-\n-\nGreenhouse\n7240\n2485\n.02\n.03\n.19\n.04\n-\n-\nHospital\n8386\n69555\n34023\n.04\n.03\n.09\n.20\n1.08\n2.34\nUniv. North-\nern Colo.\n44268\n.34\n2.65\n-\n-\n-\n-\n-\nMuseum\n4002\n.01\n.02\n-\n-\nSauna\n7284\n.01\n.01\n-\n-\n-\n-\n-\n-\nTotal Com-\nmercial &\nPubl\n24015\n9353\n9283\n4.6\n7.1\n5.4\n44.4\n37.3\n34.8\nAuto Repairs\n5875\n4598\n7876\n.18\n.19\n.08\n65\n.68\n53\nAuto Sales\n3008\n5698\n7868\n.04\n.18\n.06\n.08\n.77\n.40\nMachine Shop\n11471\n3760\n29090\n.01\n.01\n.02\n.06\n.07\n.52\nWarehouse\n26338\n14745\n8124\n.13\n.24\n.65\n1.93\n2.44\n5.29\nGas Station\n1963\n2185\n1588\n.09\n.43\n44\n.12\n.72\n.58\nClothes Prod.\n24000\n.01\n.10\n-\nDistributing\nCo.\n7000\n13500\n18520\n<.01\n.01\n.01\n.01\n.13\n.07\nBottling Co.\n15200\n.01\n.13\n-\nTransportation\nStation\n49600\n6000\n10608\n<.01\n.01\n.02\n.05\n.03\n24\nSteel & Metal\nCo.\n3200\n3660\n01\n01\n.01\n.02\nGrain Storage\n9600\n40740\n<.01\n.01\n.01\n.34\nGeneral\nStorage\n28726\n3683\n1713\n.06\n.04\n.07\n.95\n09\n.09\nGarage\n21199\n7610\n6568\n14\n.08\n.14\n1.63\n.50\n93\nStockyard\n7500\n.01\n.03\nManufacturing\nCo.\n9993\n18125\n17121\n36\n01\n07\n2.15\n.29\n.75\nIndustrial\nLaundry\n12737\n2880\n2014\n.04\n01\n02\n27\n.01\n04\nCreamery\n10000\n.05\n-\n-\n.01\nAsphalt\n1426\n3000\n1435\n.01\n.01\n.02\n.01\n.02\n02\nRefinery\n2533\n-\n<.01\n>.01\nGenerating\nPlant\n7000\n-\n<.01\n<.01\n-\nTotal\nIndustrial\n12976\n6851\n6527\n1.1\n1.3\n1.6\n7.9\n6.4\n9.5","148\nconsequently the modelling results were also not as good. Even using\nstatistical sampling schemes, the amount of work in data collection was\nstill significant for a community the size of Cheyenne, Wyoming. Again,\nif the model were to be used for larger communities or perhaps even\nentire regions, some other approach to data collection will be required.\nA comparison of building census data from Minneapolis with similar\ndata from Greeley and Cheyenne showed relatively larger percentages of\nresidential structures, but relatively higher energy use for space\nheating by commercial buildings in Minneapolis than in the other two\ncities (Table 1).\nEnergy consumption computed on a daily basis from our model can now\nbe compared with the actually observed daily energy consumption. Using\nGroup Method of Data Handling (GMDH) model validation procedures to be\ndescribed later, our model either accepts or rejects its computational\nresults, based upon present accuracy criteria. In the latter case\nimprovements, mainly in the building modules, are sought until satis-\nfactory performance of the model on a \"learning\" set of data as well as\non a independent \"test\" set is achieved. This procedure is illustrated\nschematically in Fig. 9.\nObviously, a model cannot be devleoped for each building in a\nregion to be studied. Nevertheless, thanks largely to a remarkable\ndegree of thermal similarity among the vast majority of U.S. residen-\ntial, commercial and industrial high- or low-rise buildings constructed\nwithin fairly distinct time periods, it is our premise that buildings\ncan be grouped into thermally equivalent classifications and aggregated.\nIn order that our model may take advantage of the fact that the\ncompositing of similar structures is permissible because of the extent","149\nBUILDING\nCENSUS\nOBSERVED\nENERGY\nCONSUMPTION\nTEMPERATURE\nWIND SPEED\nSOLAR RADIATION\nDATA\nBASE\nTYPICAL BUILDING MODULES\nAND THEIR CHARACTERISTIC\nHEAT LOSS\nPHYSICAL\nMODEL\nGMDH\nIF ERRONEOUS\nCHANGE CHARACTERISTIC\nCOMPARISON\nFILES\nIF ACCEPTIBLE\nVALID\nMODEL\nFig. 9\nFlow diagram of our physical model with input, adjustments\nand output.","150\nto which buildings in the U.S. were \"mass produced\", hence that the\ntotal number of modules and the associated calculations may be kept to a\ntractable magnitude, it is necessary to preprocess the building census\nbefore this data bank becomes an input to the model. As implied above,\npreprocessing entails the assignment of appropriate weighting factors so\nas to characterize the aggregated difference between the actual build-\nings comprising a particular structural type, use and age classifica-\ntion, and that structure for which the associated model was defined and\nvalidated. It involves a consideration of numbers and sizes, and of\nvariations in their space-conditioning systems, internal heat loads and\nconstruction characteristics The model sums the resulting energy\nconsumptions calculated for each of the several modules employed to\narrive at an overall space-conditioning energy budget for a region\nwithin a city, or for the whole city under investigation.\nIn Minneapolis a further complication arose from the fact that\ndaily natural gas sendout data were not available for the city proper,\nbut for a much larger area for which, on the other hand, no detailed\nbuilding census could be obtained. The average ratio between monthly\ngas consumption within the city limits and in the wider area (both sets\nof values were available for the Minnesota Gas Company) was used as\nweighting factors to arrive at daily sendout information for the city of\nMinneapolis.\n(d) The Adaptive Part of the Model\nThe model provides also for the selection of thermostatic settings,\nfor the introduction of multipliers to characterize infiltration rates,\nand for the variation of the physical (thermal) characteristics of\nstructures for known or assumed building uses and occupant habit pat-\nterns. At present, these inputs are entered manually; but the program","151\nis designed for their introduction by the adaptive model when the\ninterfacing of the physical and adaptive models has been completed.\nIt is well known that energy usage in identical structures can vary\nby a factor of two or more, depending upon considerations related to the\nfunctions of the buildings. For example, if one such structure is a\nhome for the aged, a second is an office building and a third is a\ndepartment store, it should be expected that under normal circumstances\nthe department store would experience the greatest infiltration rate and\nthe home the least, with door openings of the office building restricted\nlargely to employee arrival, departure and luncheon periods. Analogous-\nly, the office building will probably evince the greatest lighting and\noccupancy contributions to internal heat generation, and the home for\nthe aged the least. On the other hand, thermostatic settings will\nundoubtedly be highest in the home, so as to maintain the degree of\nwarmth required for the comfort of elderly occupants; but the greater\nsedentary nature of office-building activities is customarily associated\nwith higher thermostatic settings than are typical of a department store\nor industrial plant. That is, building use tends to be a good indicator\nof thermostatic settings, whereas occupant habit patterns primarily\ninfluence infiltration. Examples of the latter include: windows being\nleft open in the second floor of a duplex, owing to poor heating-system\ndesign, while the building is being heated so as to maintain the desired\nlevel of comfort in the ground-floor appartments; or a large number of\ndoor openings as is to be expected of families with several small\nchildren or pets; or the substitution of revolving doors for swinging\ndoors in commercial buildings, etc.","152\nThe adaptive model will also provide physical (thermal) change\ninformation to the physical model. For instance, as energy costs in-\ncrease and as tax rebates, deductive allowances, low-interest loans or\noutright grants are instituted, utility customers will retrofit to\nconserve energy. The first changes will be the simple ones that the\noccupant can implement. Examples include the installation of weather\nstripping, storm windows, storm doors, caulking cracks, etc. In some\ncases the occupant may even be able to increase attic insulation levels\nand/or subfloor (crawl-space) insulation. As energy costs continue to\nrise, the addition of wall insulation and thermopane windows eventually\nwill become cost effective. Similar trends will be found in new con-\nstruction. Tighter structures will be built with higher overall levels\nof insulation, better windows and doors, etc. Ultimately, new construc-\ntion techniques and new materials will be developed and utilized. The\ninput by the adaptive model of changes such as these into the physical\nmodel, whether across the board or for specific types, uses and/or ages\nof buildings -- and regardless how arrived at, i.e., whether actual or\npostulated retrofitting actions -- will prompt the physical model to\ngenerate revised calculations of the energy required for space condi-\ntioning by the structures affected within the region to which the model\npertains.\nIn summary, then, the adaptive portion of the model receives energy\nconsumption information from the physical model, and affords the policy\nmaker with a capability to introduce a variety of alternative socio-\neconomic scenarios into the physical model in order that their relative\nimpacts on space-conditioning energy consumption may be explored.","153\n(e) Computational Aspects of the CSU Model\nSince our model, so far, has been used mainly as a research tool to\ntest the effects of various intermeshing factors, as described above, on\nenergy consumption and energy conservation, we have not yet felt com-\npelled to document every step and procedure in the form of a \"user's\nhandbook\". Our concern has been twofold: (1) to develop modelling\nconcepts which will accept physical (engineering), environmental and\nsocio-economic factors as quantitative input and (2) to develop and test\nnew methods of data handling, especially where large volumes of data are\nconcerned for which correlation patterns are not a priori established\nand stationarity of the data sets is not assured.\nThe heat-load computations for individual buildings are relatively\nsimple and straightforward. They are described to some detail by Reiter\net al. (1976, 1978).\nThe GMDH has been applied to heat-load and meteorological data by\nH. Leong and is extensively described by Reiter et al. (1978, 1980).\nThe method is based on mathematical developments by Ivakhnenko (1971),\nand Ivakhnenko et al. (1974).\nConsider a non-linear system with a single output Y(t) and S number\nof inputs X(t), i=1,2,...,S. This system could be represented by the\nfollowing equation\nY(t) = f[X1(t),\nX(t)]\n(1)\nThe problem is to determine the unknown structure f(X, X2....,XS) from\nthe available past data.\nAssuming the data to be a stationary random sequence, the\nKolmogorov-Gabor polynomial for stationary stochastic process is used to","154\ndetermine the structure of f(X, X5). The polynomial takes the\nform of\nY\n=\n+\n(2)\n+\nijk\nIf the number of variables is S, the first-order polynomial will contain\n(S+1) terms, the second-order will have (S+1) (S+2)/2! terms, the third-\norder (S+1)(S+2)(S+3)/3! terms, etc. However, to determine the large\nnumber of coefficients in Eq. 2, a large amount of data and computation\nof high-dimensional matrices is required. For example, consider a\nfourth-order polynomial with four arguments X1, X2, X3 and X4. The\ncomplete polynomial including terms of all powers and all covariations\nof arguments has 70 terms.\nThe complete polynomial is:\nY 3X3 45x22 =\n+ B7x x11X4 + +\n+ B12X2X3 + B13*2*4 + B14X3X4 +\n+ + +\n+\n+ + +\n+ + + +\n+ + + +\n+ + +\n+ + +\n+","155\n+\n+ +\n+\n+ + +\n+ + + +\n+ + + +\n+\n+\n+\n+\n+\n(3)\nTo determine the coefficients by solving Gaussian normal equations, it\nwould be necessary to invert matrices with dimension of 70 X 70 com-\nponents, a very expensive task. To overcome this difficulty, Ivakhnenko\nproposed to break down the complete polynomial into several layers of\npartial polynomials each of which contains two or more of the input\nvariables such that the complete polynomial could be reconstructed by\nback substitution from all the layers considered. The advantage of the\nIvakhnenko proposal lies in the fact that by breaking down the complete\npolynomial into partial polynomials having fewer input variables results\nin equations with much smaller matrices, and thus the ill-conditioned\nmatrix of the complete polynomial is replaced with smaller, well-condi-\ntioned matrices. In addition, solving the coefficients of the partial\npolynomials requires many fewer data points than if the complete poly-\nnomial is used directly.\nApplying Ivakhnenko's proposal to our previous example of a second-\ndegree polynomial with four variables X1, X2, X3 and X4, the partial\npolynomials for the combination of variables (X1, X2) and (X3, X4) are:","156\n(4)\n+ c4x 2 + c5x3x4\n(5)\nand the complete polynomial is constructed from 1 and Y2 as:\ny=d1dyd3y\n+\n+ d4y22 d 55Y1Y2\n+\n(6)\nIn this case it is sufficient to solve three systems of equations\neach with a 6 X 6 matrix, instead of solving one system with a 70 X 70\nmatrix.\nThere are six ways in which two of the four variables X1, X2, X3\nand X4 can be combined in a partial polynomial, and thus six partial\npolynomials would be constructed in the first layer. By passing the six\npartial polynomials to the next layer we would have 15 ways in which the\nsix partial polynomials from the first layer could be combined, and the\nnumber of partial polynomials would keep increasing from one layer to\nthe next.\nThe GMDH algorithm is performed in such a manner that only\nvariables and partial polynomials that satisfy certain chosen heuristic\ndecisions or thresholds are passed from one layer to the next in order\nto obtain an optimum complete descriptive polynomial. The structure of\nthe GMDH algorithm resembles the structure of a multilayered Percep-\ntron*, where separating \"useful\" and \"harmful\" information by thresholds\nat each level of the solution is possible.\nThe concept of the Perceptron is discussed by Frank Rosenblatt in his\nbook Principles of Neurodynamics, where the Perceptron concept is used\nas a model for the brain. The perceptron is defined as a signal trans-\nmission network, in which signals are passed from one stage of the net-\nwork to the next only if the input signal exceeds a given threshold.","157\nIn summary, the GMDH algorithm used in this study is performed as\nfollows: to obtain an optimum complete descriptive polynomial for a\nprocess with one output and S input variables, the GMDH algorithm breaks\ndown the expected complete descriptive polynomial into sets of partial\ndescriptive polynomials at several layers, with each partial polynomial\ncarrying only a few of the total number of independant variables. Then\nfrom the available data the coefficients of each partial polynomial are\nestimated using the least squares method. A sum of squares error cri-\nterion is used to judge which polynomials will be passed from one layer\nto the next, where the sum of squares error for each partial polynomial\nis computed between the observations and the estimated polynomial.\nObserve that the available data are divided into training and testing\nsets where the training data are used to estimate the coefficients of\nthe polynomials, and the testing data are used to compute the sum of\nsquares errors; this is done so that overfitting the data is eliminated.\nThis process is repeated from one layer to the next until a specified\naccuracy criterion is reached or until a specified number of layers is\nreached. Details of the exact algorithm are shown schematically in Fig.\n10. For a more extensive discussion of the GMDH algorithm see Reiter et\nal. (1978).\nThe results of employing such an approach for the prediction of\nenergy consumption for space conditioning, using our pilot model, demon-\nstrated high accuracy for both Greeley, Colorado and Cheyenne, Wyoming\n(as reported in Reiter et al., 1976 and Reiter et al., 1978). However,\nit is anticipated that a community, being a complex system of growth and\ndevelopment, is nonstationary and no matter how well our current model\npredicts the energy consumption of a community, its habit patterns vary","DESCRIPTION\nOPTIMUM\nSYSTEM\nPD2 (ORDER)\nMECHANISM\nADJUSTING\n8g BIVARIATE POLYNOMIAL ORDER\n2 ARE THE RESIDUALS RANDOMLY\nOn ACCURACY THRESHOLD\n8c= COUPLING THRESHOLD\n(MIN (MSE) ' 6 ACCURACY)\nI IS MIN (MSE) SATURATED ?\nDISTRIBUTED? (RUN-TEST)\nOF SIFTING THRESHOLD\nIT GENERATES A BIVARIATE POLYNOMIAL G.\nCOMPLETE DESCRIPTION\nPARTIAL DESCRIPTION GENERATOR\nSUCH THAT xo\" &0 G (X,X,)\nRECONSTRUCTION\nFEED BACK\nSTAGE III\nOR\nADJUSTING\nTHRE SHOLD\nVALUES\nYS2\nBIS3\ns,\n-2,\nXo\nX,\nX2\nA\nB\nPD2\nXa\nSTAGE 11c\nREPEAT\nCHECKING\na A\nMSE\nLAST LAYER\nTESTING\nSTAGE 11b\nS-\nREPEAT\nW5,\nXo W\nXs W,\nW\nx8\n80°\n8g\nPD,\nPD2\nPD2\nPD2\nSELECTING\nLAYER 3\nSTAGE 110\nCOUPLE\n0c\nIXI.\n12,52\nREPEAT\nCHECKING\n0.0.\nMSE\nThe GMDH block diagram.\nTESTING\nSTAGE 11c\nREPEAT\n8.2\n1x, 121 s,\nLAYER 2\n8.\nPD2\nPD\nPD2\nPD2\nPY2\nSTAGE lla STAGE 11b\nXIN ) BE A (Nx1) OBSERVED th INPUT VECTOR\nIs2-2\nREPEAT\n-Xo\nTRAINING\nY3\nXO\nA (Nx1) OBSERVED OUTPUT VECTOR\nSELECTING\nCOUPLE\nREPEAT\n8c\nCHECKING\nCRITERION\nSTAGE 11c\nBY MEAN\nA\nMSE\nSQUARE\n06\nERROR\nTESTING\nY.\nOF LEAST SQUARES\n8.1,\n&gys.\n&gy\nBY THE PRINCIPLE\n&d\n8.\nCORRELATION CRITERION\nLAYER I\n8g\nPD2\nPD2\nPD2\nPD2\nFig. 10\nSTAGE STAGE lla STAGE llb\nX13\nU\nXs.-2\nXo\nX2\nX\nX.\nX3\nDo\nTRAINING\nVAKHNENKO'S\nSELECTING\nCOUPLE\nEITHER BY\nA\nVARIANCE\nAs\nx\nX 2\nOR\n1\nDENOTE\nINPUT\nDATA\nDo\nD2\nx,\nX3\nXs\n:","159\nslowly with time. We have tried to deal with this nonstationary\nsituation by developing an adaptive identification framework which was\nfirst introduced in Reiter et al., 1978. Although this variation in\nhabit pattern is not predictable ahead of time, the identification\nframework should be able to measure the goodness-of-fit between the\nactually evolving and the predicted pattern of the community under\ninvestigation. This framework should also be capable of updating the\ncurrent model to cope with the evolution of a community.\nH. Leong (Reiter et al., 1979, 1980) presented a systematic proce-\ndure by which one can test the statistical performance of the identified\nmodel. These statistical techniques consist of three hypothesis tests\nusing distribution-free statistics which employ the observational and\nestimated data from the past data base. Such tests may not be able to\npinpoint definitely the specific event which caused the behavior of the\nsystem to change, but they do logically establish when the system re-\nsponse is off-sided from the previously identified reference level or\npattern. Depending upon the degree of the discrepancy which has been\ndetected, appropriate action is undertaken in accordance with the adap-\ntive framework.\nOne of our criteria to check the degree of change between the real\nsystem and our model is based on the residual, that is, the difference\nbetween the observed and the calculated energy use from the current\nmodel. By using statistical testing we can determine whether or not the\nresiduals are due purely to random variations or whether a pattern still\nexists within these residual values. If the latter is the case the\nobservational data are reprocessed through the GMDH alogrithm to arrive","160\nat an improved model which will provide a better estimate of the energy\nconsumption for the community. In terms of our actual modelling pro-\ncedures, the physical model is then separated into two components: (1)\nthe physical module component which is the set of mathematical equations\nderived from the building modules, and (2) the time series component\nwhich is the set of mathematical descriptions derived from the statis-\ntics of the residual time series. Obviously, should the physical module\ncomponent perfectly represent the real system, the residual time series\ncomponent would have a white noise response. On the other hand, should\nphysical changes occur in the community which are not represented in the\nphysical module component, the time series component will describe both\nthe fluctuations of random factors as well as the trend of these changes\noccurring in the real system. The time series component can be updated\nor reidentified to incorporate these changes into the physical model as\nmore energy consumption and weather data become available.\nIn our opinion, the refined model, which is a combination of physi-\ncal, heuristic, and statistical models, is capable of deriving highly\naccurate weather sensitive energy demand estimations for any geographi-\ncal area, whether it is an extensive region of the U.S. or simply a\nsmall suburban community.\nOne of our main modelling goals has been the development of a space\nconditioning energy demand model which would provide reliable and highly\naccurate estimations of the real system. On the other hand, the\nstochastic components inherent in a community make it virtually certain\nthat any two daily energy consumption values will differ even when they\nhave identical weather conditions. In order to infer when the departure\nof the model from the real system should be considered acceptable or","161\nwhen the model must be updated, we have posed three criteria and have\nincorporated the corresponding statistical hypothesis testing procedures\ninto our calculations in order to check the performance of the model.\nThe three criteria are formulated under the following situations which\ndepend upon the availability of information.\n1) If a relatively long period of time has elapsed since the last\nmodel validation (e.g. one year) or if a sequence of abnormal indica-\ntions has been detected (e.g. 10 out of 100 estimated points failed to\nbe included in the performance confidence region), we will evaluate that\nperiod to check if model parameters have significantly changed from the\nlast evaluation period. To accomplish this the basic patterns of inter-\nest such as the range of response, the shape of the pdf (probability\ndistribution function) etc., which appear in the systems input and\noutput samples are compared.\n2)\nAfter the record of actual energy consumption has arrived, the\nmagnitude of the deviations between the observed and the estimated\nconsumption values are computed. The deviations are then determined to\nbe either due purely to random variations or are caused by some unknown\nabnormality in the system. The performance index of the current model\nshall not be worse than that computed from the \"reference model\" de-\nscribed below.\n3) Even before we have received the observed energy consumption\ndata, a prediction is made based on a new input weather data sample via\nthe current physical model. In this we assume that the community has\nnot changed since the last evaluation. As a primary check for such new\nestimations, we shall be able to show whether the predicted values fall\nwithin the range of expected variation of a given confidence level.","162\nThere are many different ways by which we could have chosen to\ncheck these criteria. The choice depends upon the investigator's pref-\nerence as well as how much information is available for verification\npurposes. One of the premises of an adaptive identification system (as\ndiscussed by Reiter et al., 1978) is that the system itself, as well as\nits input and output variables, are subject to change without warning as\ntime progresses. This means that the statistical distribution functions\nof the variables usually cannot be specified exactly but must be esti-\nmated empirically from the accumulated data. Hence, all the test pro-\ncedures designed for our model performance checking are nonparametric or\ndistribution-free, which means that the tests do not use a specified\ndistribution. In accordance with the size of the data set, three dif-\nferent tests will be applied, namely, (1) the Kolmogorov-Smirnov Test,\n(2) the \"Runs\" Test, and (3) the Reliability Test. The number of data\npoints required for each succeeding test is smaller than for the pre-\nceding test. These tests have been described in detail by Reiter et al.\n(1979) and are illustrated schematically in Fig. 11.\n(f) The Statistical Reference Model\nAs stated before, it is necessary to construct an independent\nestimate of the energy consumption of a community, parallel with the\nestimation derived from our physical model. For this purpose a statis-\ntical reference description has been devised which will provide a per-\nformance confidence region to facilitate the adaptive identification\nframework in keeping track of any changes in the system. The purpose of\nthe statistical reference description is threefold: 1) It aids in de-\ntecting whether the prediction from the physical model is within a\nreasonable fluctuation range, or if in fact the response of the system","163\nSystem Input\nA\nand Feedback\nReference Model\nPhysical Model\nRough (Average) Estimate\nPhysical Time Series\n+\nand\nModule Component\nReference Interval\nObserved\nB\nOutput\nTest\nReliability\nC\nReject\nAccept\nTest\nCompute Residual\nAction I\nError\nYes\nin\nwith Obs. Output\nCorrection\nObs. Input\nof Input\nNo\nNo Accuracy\nYes\nCheck\nGo to\nExtreme Event Model\nA\nAction 2\nIssue\nGo to\nSpecial Handling\nWarning\nNo\nA\nand\nChange\nIssue Warning\nAction 3\nGo to\nMany\nNo\nGo to\nUpdate\nC\nA\nWarnings\nModel\nParameters\nYes\nObserved Input\nNo\nTest 2\nEnough\nNo\nChange of\ndata\nA\nState\nYes\nYes\nTest 3\nAction 4\nSystem\nNo\nRe-identify\n(Change of\nSystem\nGMDH Model\nYes\nB\nAction 5\nGo to\nPostulate and\nA\nReconstruct System\nObserved Output\nSYSTEMS OVERVIEW\nFig. 11\nSchematic flow diagram of performance checking in the adaptive\nidentification framework.","164\nis\ndiverging from the normal course; 2) it helps in preventing the\nidentification framework from being too sensitive to small irregular\nchanges and as a result might modify the physical model unrealistically;\nand 3) in many cases the statistical reference model approaches the\naccuracy of the physical model in estimating daily energy requirements\nwithout calling for as detailed a data base.\nThis statistical reference model uses the same heuristic algorithm\nas was employed in the physical model for the identification of the\ncoefficients of the heat transfer equations involved in modelling in-\ndividual buildings within a certain typical structure category. How-\never, instead of requiring actual building information, the statistical\nreference model attempts to use the meteorological input information and\nthe actual response of a community in terms of energy consumption to\nidentify a single high-order equation which describes the response of\nthe entire community. This model was initially developed for estimating\nthe performance confidence intervals which show acceptability regions of\nthe model output and which indicate when the real community is changing\nin complexion over time in contrast to the earlier identified physical\nmodel assumptions.\nIt was also found that the reference model could be used as a\nstand-alone model to identify individual communities without a need for\na prohibitively large amount of historical data and particularly without\nthe detailed information required about individual structures within a\ncommunity or a subset thereof, from which the community data base might\nbe synthesized. The statistical reference model can be used as a first-\ncut model for new communities in anticipation of more detailed informa-\ntion to be gathered in order to support the physical model. In fact, it","165\nhas been found through our studies within the Minneapolis-St. Paul\nregion that the identified statistical reference model is almost as\naccurate as the physical model.\nThe limitations of the statistical reference model are the same as\nfor any regression-type model. Even though our model is rather sophis-\nticated it is still based on coefficients -- in contrast to the physical\nmodel -- and does not entail explicitly the physics of the processes\ninvolved in a need for energy consumption for space heating. It is,\ntherefore, not possible to \"ask\" this model decision-making questions as\none can do with the physical model. That is, we can not assess how\nvarious energy conservation policies might affect the energy consumption\nwithin a city. For questions of this type, or questions relating to the\neffects of behavioral changes, structural changes, etc., the physical\nmodel is required because that model incorporates actual physical heat-\nloss processes. However, the statistical reference model can play an\nextremely important role in assessing the energy use of communities with\na small amount of data. It can also be used in conjunction with the\nphysical model to provide levels of acceptability of the output from the\nphysical model associated with the computed response to environmental or\nsystems changes.\nThe following conditions must be satisfied in the selection of our\nstatistical reference description: 1) It must be relatively simple and\nfast in identifying parameters for comparison with the physical model;\n2) only the daily input-output observational data may be utilized in its\nconstruction and thus it would not use detailed building information;\nand 3) it must be able to be incorporated readily with our statistical\ntesting procedures.","166\nAs a consequence of the considerations discussed above, a straight-\nforward statistical reference description is formulated by means of K\ndiscrete states. The K states are defined as follows: Let us assume\nthat an empirical cumulative distribution function (cdf) of the daily\nenergy consumption from N data points over a period [t1, t2] is computed\nand denoted as FN(Y). For a given integer, K > 0, the FN(Y) can be\nsubdivided into K portions such that each portion defines an equal\nprobability, 1/K (Fig. 12). The daily energy consumption response or\n,th\nthe observed output data of the community are said to be in the\nstate of output if the value falls in the kth portion, for k = 1, 2,\n, K. All the data points contained in the kth portion can be thought\nof as a sample drawn from an unknown conditional population of the kth\nstate of output, F(YK). All the concurrent daily weather records or\nobserved input data corresponding to the kth state of output are de-\nscribed as the sample drawn from an unknown joint conditional population\nof the kth state of input, F(Xk).*\nHaving developed the K states of input and output samples, various\nstatistics may be derived to characterize the relationship between or\nwithin the input and output states. ** For the present, we apply the\nGMDH algorithm to identify the mapping relationship between the input\nEven though the output states are partitioned into K portions exclu-\nsively, the K input state samples are almost never exclusive sets such\nthat the data points may belong to more than one input state popula-\ntion, or in other words any two adjacent input state populations have\noverlapping pdf tails.\nsimple but useful kth state statistic is the range of each variate\nin the state sample. For example, let a kth state energy consumption\nrange be defined as (YL, Yu) and its corresponding input variate\nrange for temperature be (30, 40) for the first year's data. As new\npredictions are made, we group all the observations of the energy con-\nsumption values which fall within (Y L' YU) to form a kth state of this\nnew period. If it turns out that the range of temperature of the kth\nstate has shifted to (40, 60), we are fairly certain that a change\nin consumption patterns has occurred.","167\nA Typical Partitioning of K-States\nBased on Cheyenne Data, 1975-76\nK=10\nK=9\nK=8\nK=7\nK=6\nK=5\nK=4\nK=3\nK=2\nK=1\n00\n12.00\n16.00\n20.00\n24.00\n28.00\n32.00\n36.00\n40.00\nNATURAL GAS (MCF) & 10'\nFig. 12\nThe 10 K-states partitioned from the empirical probability\ndistribution function of energy consumption in Cheyenne,\nWyoming based on the period 11/2/75-3/31/76.","168\nand the output on the basis of the sample means of different states, and\nconsequently this GMDH description is adopted as our statistical refer-\nence description. The GMDH algorithm is used for this description\nbecause it is especially effective when there is no prior knowledge of\nthe structure of the mapping function and when there are not many avail-\nable data points. For more detail see Reiter et al. (1978).\nTo summarize, both models are useful and can be run as stand-alone\ncomputer model systems. The physical model can be used if sufficient\ndata are available. The statistical reference model can also be used if\nonly climatological and actual consumption figures are available and\npredictions can be made based on these inputs. The two models can be\ncombined to form a hybrid statistical-physical model. The statistical\nreference description could be used to model the existing energy con-\nsumption pattern based upon past history, whereas the physical model\nwould be used to model new or projected buildings and developments to\npredict how growth will alter the pattern of energy consumption. This\nhybrid model should be most useful for large cities or metropolitan\nregions. Its concept has not been tried to date, however.\nOver the next year, both models will be subject to modifications to\ninclude cooling as well as space heating. The cooling modifications\nwhich will be necessary for the reference model are straightforward and\nwill be accomplished easily because it is only necessary to obtain the\nproper meteorological and energy consumption data and to identify the\nappropriate model equations. For the physical model, it is necessary to\ninclude the physics of building space cooling which is not nearly as\neasily handled as the space heating situation. Basically, the framework\nof each model will remain the same. We do anticipate that additional","169\ninput information, such as humidity levels, will be required in order to\nobtain reasonable energy consumption estimates.\n7. Modelling Results\nThe energy consumption by the city of Minneapolis, Minnesota, was\nmodelled successfully for two winter seasons. A physical model and a\nstatistical reference (regression) model were tuned during the evalua-\ntion period, 11/1/77 to 2/28/78, and then applied to the period of in-\ndependent data (prediction period), 1/1/79 to 3/31/79. Statistical\ntests accept the null hypothesis that the residual time series (observed\nminus computed energy consumptions) are random. The performance in-\ndices, expressed as mean daily absolute errors, were 6.26% and 5.54% for\nthe physical and statistical reference models, respectively, over the\ntime period 12/1/77 to 2/28/78. Applications of these two models to the\nperiod 1/1/79 to 3/31/79 yielded daily absolute errors of 5.39% and\n5.94%.\nFigures 13 and 14 show typical model outputs for Minneapolis in\nterms of observed energy use, physical and statistical model results,\nconfidence limits, residual time series and input weather data.\nEnergy use in the city of Cheyenne, Wyoming, was reexamined using\nnewly acquired energy consumption data for 1975-76. Since meteorologi-\ncal data were available for that season only from the airport station of\nthe National Weather Service, urban distributions of meteorological\nelements derived from our special network operation during the 1976-77\nwinter had to be used to generate local meteorological model input data\nfor 1975-76. Applications of the adaptive identification framework\nrejected the null hypothesis that the sequence of unexplained energy\nconsumption values were random, when the model developed for the 1975-76","170\nMINNEAPOLIS 77-78\nPRE-ADJUSTED\nall\n0.9 PERFORMANCE INTERVAL\nOBSERVED\nRESIDUAL\nDEC 77\nJAN 78\nFEB 78\n1\n7\n14\n21\n28\n4\n11\n18\n25\n1\n8\n15\n22\nMINNEAPOLIS 77-78\nTEMPERATURE\n00\nINSOLATION\nWIND\n1\n7\n14\n21\n28\n4\n11\n18\n25\n1\n8\n15\n22\n29\nDEC77\nJAN78\nFEB 78\nFig. 13\nEnergy consumption estimates for Minneapolis by the physical\nmodel during the 1977-78 heating season in thousands of cubic\nfeet of natural gas. 90% performance intervals were added\nfrom the statistical model. The residual curve represents\nthe observed minus the preadjusted consumption values. The\nlower portion of the diagram shows average daily weather data.","171\nMINNE APOLIS 78-79\n0,9 PERFORMANCE INTERVAL\nOBSERVED\nADJUSTED\nFINAL ERROR\n00\n0\n1\n7\n14\n21\n28\n4\n11\n18\n25\n11\n4\n18\n25\nJAN 79\nFEB 79\nMAR 79\n00\nMINNEAPOLIS 78-79\nTEMPERATURE\nWIND\nINSOLATION\n0\n1\n7\n14\n21\n28\n4\n11\n18\n25\n4\n11\n18\n25\nJAN 79\nFEB 79\nMAR 79\nEnergy consumption estimates for Minneapolis by the statisti-\nFig. 14\ncal reference model, adjusted by the time series description,\nfor the 1977-78 heating season, in thousands of cubic feet of\nnatural gas. 90% performance intervals are indicated. The\nmiddle curve gives the final error which is the observed\nminus the adjusted consumption. The lower portion of the\ndiagram shows average daily weather data.","172\nseason was applied to 1976-77 (Fig. 15). Reexamination of our input\ndata revealed that during 1976-77 the use of processing gas by an inter-\nruptible customer was subtracted from the total daily gas consumption in\nCheyenne, using wrong line pressure values. A redesign of the physical\nmodel for Cheyenne yielded the conclusion that building modules tested\nfor Greeley were interchangeable with those representing Cheyenne (Fig.\n16).\nPreliminary model applications to the 1978-79 winter season in\nGreeley, Colorado, provide firm indications that the energy use patterns\nof this community have changed significantly during the past two years,\nmainly due to the addition of new structures. For a final model run to\ncheck for the effectiveness of energy conservation measures we have to\nawait a forthcoming, updated building census.\nA comparison between the energy uses in these three communities\nrevealed that the per capita energy use as a function of average daily\ntemperature is significantly less in Minneapolis than in Greeley and\nCheyenne, due to more conservative building practices that have prevail-\ned for many years in the colder northern climate (Fig. 17).\nApplication of the physical model to census block areas permits a\ndetailed evaluation of the geographic distribution of energy demand\nwithin a city. In Minneapolis the city region has been subdivided into\n127 such areas. A predominant energy use for space heating in the\ndowntown core areas became apparent (Fig. 18). Application of model\noutputs to the planning of alternative energy systems can be advocated.\nEnergy requirements for space heating can easily be computed on an\nhourly basis. Results for Minneapolis and Cheyenne are shown in Figs.","173\nPRE - ADJUSTED\nCHEYENNE 76-77\nOBSERVED\nADJUSTED\nEST. TIME SERIES\n00\nRESIDUAL\nFINAL ERROR\n0\n0\nJAN 77\nFEB 77\nMAR 77\n25\n1\n12\n18\n8\n15\n22\n29\n5\n12\n19\n26\n5\nEnergy consumption prediction of the statistical reference\nFig. 15\nmodel during the 1976-77 heating season, in thousands of\ncubic feet of natural gas, for Cheyenne, Wyoming. Both the\npreadjusted (without the time series description) and the ad-\njusted (which includes the time series description) model out-\nputs are presented. Note that this model is identified from\nthe 1975-76 - evaluation period data only. The middle curve\nshows the predicted time series which is used to adjust the\nmodel results. The residual curve is the observed minus the\npreadjusted consumption. The final error curve is the ob-\nserved minus the adjusted consumption.","174\nCHEYENNE 76-77\nADJUSTED\n0.9 PERFORMANCE INTERVAL\n0\n'ON\n0\nOBSERVED\nPREDICTED TIME SERIES\nRESIDUAL\n00\nFINAL ERROR\nJAN77\nFEB 77\nMAR77\n5\n19\n26\n4\n8\n15\n22\n29\n12\n11\n18\n25\nCHEYENNE 76-77\nTEMPERATURE\nWIND\nSOLAR\nJAN 77\nFEB 77\nMAR 77\n1\n8\n15\n22\n29\n5\n12\n19\n26\n5\n12\n18\n25\nFig. 16\nRevised energy consumption estimates for Cheyenne, Wyoming,\nmade with the statistical reference model for the 1976-77\nheating season, in thousands of cubic feet of natural gas.\nThe computed results include adjustments for the estimated\ntime series. 90% performance intervals are indicated. The\nresidual curve is the observed minus the preadjusted consump-\ntion. The final error is the observed minus the adjusted\nconsumption. The lower portion of the diagram contains\naverage daily weather data.","175\n-10\nMinn. 78\nMinn 79\n0\n+10\n+20\nChey. 76\n+30\nChey 77\nGre. 75\nGre. 79\n+40\nGre. 76\n+50\n20\n25\n30\n35\n40\n45\nBTU/PERSON (x10,000)\nLeast squares analysis of average daily energy consumption\nFig. 17\nper person versus average daily temperature in Greeley, Colo-\nrado, Cheyenne, Wyoming and Minneapolis, Minnesota.","176\n(a)\n(b)\nFACE\n(c)\n(d)\nenergy commercial-plus-public Three-dimensional consumption block for diagram space heating of comparative for residential daily average\nFig. 18\n(d) in Minneapolis, Minnesota (b), industrial for the 1978-79 (c), and heating all buildings (a),\nseason.","177\n19 and 20. Unfortunately, we do not have available actual hourly\nsendout data from the utility company to be able to check the veracity\nof this presentation.\nPreliminary model development for the cooling season, applied to\nseveral buildings in Ft. Collins (Fig. 21), indicated midday wet bulb\ntemperature to be a more important parameter than dry bulb temperature.\nSurprisingly, solar radiation was rejected as significant input to the\nmodel. However, operating schedules for building occupancy proved to be\na parameter of consequence. Inefficiencies of a dual-duct air condi-\ntioning system could be pointed out.\nWith the aid of our model we can calculate energy consumption not\nonly by census section of a city, but also by user type (see Table 1).\nSuch a breakdown provides a natural fusion point with regional economic\nmodels.\nA regional input-output (I-0) model has been developed for Greeley,\nColorado, to arrive at local economic multipliers and to study certain\ndevelopment scenarios. Special attention was given in this model to\nenergy requirements for space heating under expanding economic activity\nand under varying meteorological conditions.\nData were collected by questionnaires which served as focal points\nfor interviews and could be left for further consideration with the\ninterviewed firm. Information was solicited on the nature of the firm's\nproduct lines, the number of employees, the level of capacity utiliza-\ntion, cash flow and non-cash flow outlay patterns, and sales distribu-\ntion. Sales and outlay patterns were disaggregated by economic sector\nand regionalized according to location within and outside Greeley city\nlimits.","178\nHourly model-estimated energy consumption for single family\nFig. 19\ndwellings in Cheyenne, Wyoming as a function of time of day\nand date. Day 1 is November 1, 1975 and day 152 is March 31,\n1976. Hour 1 refers to 1 a.m. and hour 12 is noon.\nDAY\n24\nSimilar to Fig. 19, except for Minneapolis from January 1,\nFig. 20\n1979 to March 31, 1979.","179\nBUILDING 2\nGMDH MODEL\nMEASURED\na\n00000\n9-0\n00\nTEMP\n00\n00\nINSOLATION\n08\nWIND\nx\non\nDOB\n()\nSEPT. 78\nAUG. 78\n29\n25\n15\n22\n11\n18\n1\n8\nComparison of energy consumption predicted by the statistical\nFig. 21\nreference model and the observed energy consumption for Build-\ning 2 from 8/11/78 to 9/23/78. Lower graph shows average day-\ntime (10 A.M. to 3 P.M.) wet bulb temperature, insolation and\naverage daily (24 hour) wind speed for this same period.","180\nSince space heating requirements are known for various types of\nbuildings in Greeley from our physical energy demand modelling results,\nthese requirements could be obtained for 1978 by economic sector as\ncubic feet of natural gas per dollar of output per month and for average\ntemperatures (Table 2). Hotels and motels showed the largest natural\ngas use for space heating per dollar of output, followed by transporta-\ntion (including warehousing) and local government. Business multipliers\n(i.e. the production in each sector of the economy generated by an\nincrease of 1 dollar in the final demand on each sector) are largest for\nthe local government (2.93) and for the university (2.88). They are at\n1.53 for natural gas and 1.48 for electricity (Table 3).\nMultipliers for space heating energy use as a function of tempera-\nture were developed for each economic sector in Greeley (Table 4).\nThese multipliers relate the effect of increased demands by increased\ndollar output in one sector to the reverberating effects in other\nsectors. For instance, the direct space heating requirements in schools\nare 0.81 cu. ft. of gas per month for each dollar of output at a tem-\nperature of 14.1°F (Table 2). If the final demand for output for the\nschool expanded by one dollar, there would be a total direct plus in-\ndirect monthly gas requirement of 1.84 cu. ft. developed throughout the\neconomy (Table 4). The indirect impact (1.84-0.81 = 1.03) in this case\nexceeds the direct requirement because of the important interdependen-\ncies between schools and other sectors of the economy. Applying only\nthe direct energy requirement to assumed increases in deliveries to\nfinal demand can obviously result in an understatement of space-heating\nenergy use. Similar multiplyers can, and should be applied to projec-\ntions of future energy needs for space heating. If this is done, the","181\n.01434\n.35543\n.07610\n.27632\n1.34082\n.09357\n.01642\n02185\n.26998\n07820\n.29437\n.15609\n3.27580\n.15498\n.17047\n.24822\n61110\n46795\n.65667\n.56786\n40.8°\nMonthly consumption Cu. Ft. Natural Gas per $ of Sales\n.01505\n.37121\n.08004\n.28852\n1.37853\n.09770\n01716\n02283\n28186\n08095\n.30394\n.16055\n3.30249\n.16183\n.17387\n.25729\n61620\n48036\n.68210\n.59961\n34.0°\n.01526\n37439\n08103\n.29103\n1.38038\n.09854\n01737\n02311\n28423\n08134\n30522\n16090\n3.28292\n.16324\n17308\n25863\n61213\n47766\n68666\n60822\n29.7°\nPhysical Input Resource Vectors\n.02059\n49969\n10895\n.38869\n1.81146\n.13154\n02316\n.03082\n37948\n10758\n40298\n.21131\n4.22657\n.21786\n.22436\n34246\n78735\n61969\n.91193\n82188\n17.3°\nTable 2\n02135\n51729\n11300\n40223\n1.86854\n13622\n02389\n03180\n39287\n11160\n41609\n21799\n4.33571\n.22560\n.23068\n35395\n80762\n63770\n.94306\n85354\n14.1°\nPrinting and Publishing\nWater and Sanitation\nManufacturing N.E.C.\nLocal Government\nFood Processing\nHealth Services\nServices N.E.C.\nTransportation\nCommunication\n13. Hotels-Motels\nConstruction\nSector\n7. Electricity\nNatural Gas\nRestaurants\n20. Households\nWholesale\nSchools\nCollege\nRetail\n14. FIRE\n10.\n11.\n12.\n15.\n16.\n17.\n18.\n19.\n1.\n2.\n3.\n4.\n5.\n6.\n8.\n9.","182\nTable 3\nBusiness Multipliers for the Greeley Economy *\nSector\nMultiplier\n1.\nFood Processing\n1.421\n2.\nPrinting and Publishing\n2.195\n3.\nManufacturing N.E.C.\n2.049\n4.\nConstruction\n2.074\n5.\nTransportation\n2.814\n6.\nCommunication\n2.355\n7.\nElectricity\n1.476\n8.\nNatural Gas\n1.529\n9.\nWater and Sanitation\n1.871\n10.\nWholesale\n1.305\n11.\nRetail\n1.362\n12.\nRestaurants\n2.160\n13.\nHotel-Motel\n2.395\n14.\nFIRE\n1.452\n15.\nHealth Services\n1.829\n16.\nServices N.E.C.\n1.843\n17.\nSchools\n2.788\n18.\nColleges\n2.879\n19.\nLocal Government\n2.932\n20.\nHouseholds\n2.213\n*\nChange in dollars of total transactions in Greeley per dollar of change\nin exports by the sector indicated.","Additional cubic feet of gas per month required by the total Greeley economy for a $1 increase in\n0.18\n40.8°\n0.80\n0.49\n0.63\n2.03\n0.63\n0.22\n0.25\n0.56\n0.22\n0.42\n0.47\n3.73\n0.33\n0.49\n0.57\n1.33\n1.23\n1.52\n0.93\nDirect Plus Indirect Gas Requirement\n0.19\n0.84\n0.52\n0.66\n2.11\n0.66\n0.23\n0.26\n0.58\n0.23\n0.44\n0.49\n3.78\n0.34\n0.51\n0.59\n1.36\n1.28\n1.58\n0.97\n34.0°\nSpecific Industry Growth Economic Natural Gas Multipliers*\n0.19\n0.67\n2.11\n29.7°\n0.85\n0.52\n0.66\n0.23\n0.26\n0.59\n0.23\n0.44\n0.49\n3.77\n0.35\n0.51\n0.60\n1.37\n1.29\n1.59\n0.98\n17.3°\n0.25\n1.13\n0.70\n0.89\n2.80\n0.89\n0.30\n0.35\n0.78\n0.30\n0.59\n0.66\n4.88\n0.46\n0.68\n0.80\n1.80\n1.71\n2.11\n1.32\nTable 4\n14.1°\n0.26\n1.16\n0.72\n0.92\n2.87\n0.91\n0.31\n0.36\n0.81\n0.31\n0.60\n0.67\n5.00\n0.48\n0.70\n0.82\n1.84\n1.75\n2.17\n1.34\nsales to export by the sector indicated.\nPrinting and Publishing\nWater and Sanitation\nManufacturing N.E.C.\n19. Local Government\nFood Processing\n15. Health Services\n16. Services N.E.C.\n5. Transportation\nCommunication\n13. Hotels-Motels\nConstruction\nSector\n7. Electricity\nNatural Gas\n12. Restaurants\n20. Households\n10. Wholesale\n17. Schools\n18. College\n11. Retail\n14. FIRE\n1.\n2.\n3.\n4.\n6.\n8.\n9.\n*","184\ndemand for energy is anticipated to rise at an ever increasing rate\n(Table 5). Scarcity, rising prices and factor substitution will, most\nlikely, become severely limiting factors. With annual growth rates for\nspace heating energy demand projected to rise from 6% in the 1980's to\n10% by the year 2000, it is clear that even a 30% reduction in heating\nenergy by conservation will buy only three added years.\nBy computing employment multipliers, the I-0 model is capable of\nassessing which economic sectors will be hardest hit by energy curtail-\nments and by switching to more expensive alternate fuels. Employment\nmultipliers in Greeley are highest for the education, hotels-motels,\nlocal government and transportation sectors, meaning that in these\nsectors the most employment is stimulated per dollar of exports (Table\n6). Unfortunately, these sectors are also among the largest space\nheating energy users in the city and therefore are expected to suffer\nconsiderably from energy shortages and price increases. The model\nprovided estimates of the sensitivity to temperature changes of natural\ngas use in various sectors of the Greeley economy. Households, food\nprocessing, manufacturing, utilities, financial services and local\ngovernment all show above-average sensitivity and therefore are main\ncontributors to peak-load problems in energy generation and transmission\n(Table 7). Notably for the manufacturing sector a rapid growth has been\nprojected for the next few years. This growth might compound some of\nthese peak-load problems.\nA final model application concerns itself with an estimate of the\nrelative sensitivity of employment in various economic sectors to short-\nfalls of natural gas required directly or indirectly in these sectors\n(Table 8). Vulnerability was computed to be highest in the sectors","185\nTable 5\nProjected Extreme Weather Space Heating Gas Use in Greeley, 1978-2003.\n*\nGas Consumption\nGas Consumption\nat 40.8°F\nYear\nat 14.1°F\n(1,000 cu. ft.\n(1,000 cu. ft.\nper month)\nper month)\n463,841\n1978\n677,939\n624,479\n1983\n911,900\n856,495\n1988\n1,249,673\n1,223,823\n1993\n1,784,169\n1,839,445\n1998\n2,679,766\n2,937,699\n2003\n4,277,926\nAssuming continued economic growth and no substitution or technological\n*\nchange in the use of natural gas for space heating.","186\nTable 6\nEmployment Multipliers in the Greeley Economy\nDirect\nIndirect\nRequirement 1\nRequirement 2\n3\nSector\nMultiplier\n1.\nFood Processing\n6\n6\n12\n2.\nPrinting and Publishing\n37\n13\n50\n3.\nManufacturing N.E.C.\n32\n13\n45\n4.\nConstruction\n13\n15\n28\n5.\nTransportation\n50\n20\n70\n6.\nCommunication\n22\n19\n41\n7.\nElectricity\n12\n8\n20\n8.\nNatural Gas\n9\n9\n18\n9.\nWater and Sanitation\n6\n14\n20\n10.\nWholesale\n7\n4\n11\n11.\nRetail\n17\n5\n22\n12.\nRestaurants\n52\n13\n65\n13.\nHotels-Motels -\n62\n17\n79\n14.\nFIRE\n11\n6\n17\n15.\nHealth Services\n29\n10\n39\n16.\nServices N.E. C.\n39\n11\n50\n17.\nSchools\n89\n19\n108\n18.\nCollege\n82\n19\n101\n19.\nLocal Government\n42\n47\n89\n20.\nHouseholds\n1\n20\n21\n21\nFederal-State Government\n1\n-\n-\n1\nDirect employment by the sector indicated per million dollars of\nsales.\n2\nEmployment induced throughout the Greeley economy due to a one million\ndollar increase in sales to final demand by the sector indicated.\n3\nDirect employment plus employment induced throughout the Greeley\neconomy for a one million dollar increase in sales to final demand by\nthe sector indicated.","187\nTable 7\nSensitivity of Sector Space Heating Energy\nRequirements to Temperature\nPercentage Increase in Natural Gas\nUse When Average Monthly Temperature\nFalls from 40.8F to 14.1F\nSector\n49\n1.\nFood Processing\n46\n2.\nPrinting and Publishing\n48\nManufacturing N.E.C.\n3.\n46\n4.\nConstruction\n39\n5.\nTransportation\n46\n6.\nCommunication\n46\n7.\nElectricity\n46\n8.\nNatural Gas\n46\n9.\nWater and Sanitation\n43\n10.\nWholesale\n41\n11.\nRetail\n40\n12.\nRestaurants\n32\n13.\nHotels-Motels\n46\n14.\nFIRE\n35\n15.\nHealth Services\n43\n16.\nServices N.E.C.\n32\n17. Schools\n36\n18\nColleges\n44\n19.\nLocal Government\n50\n20.\nHouseholds\n41\n21\nFederal-State Government","188\nTable 8\nGreeley Employment Vulnerability to Gas Shortages\n(full time equivalent workers)\nDirect Plus Indirect Employment Loss\nPer Direct 1,000,000 Cu. Ft. Loss of\nSector\nNatural Gas\n14.1°\n40.8°\n1.\nFood Processing\n557\n830\n2.\nPrinting and Publishing\n96\n140\n3.\nManufacturing N.E.C.\n384\n570\n4.\nConstruction\n59\n85\n5.\nTransportation\n48\n52\n6.\nCommunication\n296\n431\n7.\nElectricity\n833\n211\n8.\nNatural Gas\n563\n819\n9.\nWater and Sanitation\n51\n74\n10.\nWholesale\n81\n115\n11.\nRetail\n50\n71\n12.\nRestaurants\n295\n412\n13.\nHotels-Motels\n18\n24\n14.\nFIRE\n72\n105\n15.\nHealth Services\n163\n220\n16.\nServices N.E.C.\n135\n192\n17.\nSchools\n133\n176\n18\nColleges\n158\n215\n19.\nLocal Government\n91\n131\n20.\nHouseholds\n21\n32","189\nencompassing electric services, natural gas services, food processing\nand manufacturing.\nThe manufacturing sector is singled out as having extremely high\nprojected growth, its energy demand being strongly sensitive to tempera-\nture variations, and also having a high impact on employment (Table 9).\nThe present and projected trend in Greeley away from trade and services\ntowards manufacturing forebodes an adverse effect on the region's eco-\nnomic stability in view of an uncertain energy future. Health services,\nanother industry of rapid growth, are foreseen to suffer less from\nproblems generated by energy shortages.\n8. Outlook and Plans\nIn the foregoing sections we have described a highly sophisticated\nand accurate approach to compute on an hourly or daily basis the energy\nconsumption for space heating by individual buildings, urban sectors,\nand whole cities.\nPreliminary attempts have been made of developing a similar model\nfor the energy use in summer air conditioning. Several commercial\nbuildings in the Ft. Collins, Colorado, area have been monitored for\ntheir daily energy use for space cooling. Fig. 21 reveals a surpris-\ningly small response of these buildings with central air conditioning\nsystems to environmental weather fluctuations. Especially insensitive\nwas a dual-duct system installed in 1966/67 (Table 10). In this system\nheated and refrigerated air is mixed to the desired comfort level in\nindividual rooms. It appears that such systems operate at high, if not\nfull, capacity irrespective of outside weather.\nThere are other systems, not yet monitored by us in detail, which\nwe suspect to be more sensitive to environmental conditions, notably\nsystems in residential buildings.","Projected 5\nGrowth\nL-M\nL-M\nL-M\nL-M\nL-M\nVH\nupon the relative size of the gas input multiplier. The larger the multiplier the greater the\nL\nM\nM\nH\nM\nL\nL\nM\nL\nL\nM\nM\nM\nM\nBased upon the percentage of sales made within Greeley. The forward linkage indicates both a sen- -\nsitivity to local business conditions and also the dependence of the Greeley economy on the sector\ndustry. An indicator of how gas shortages will affect total employment when gas is restricted for\nRatio of projected employment for the year 2003 divided by projected employment for the year 1983.\nBased upon all adjusted employment multiplier on sales and the ratio of sales to gas input by in-\nRatio of gas required for space heating at 14.1F to that required at 40. 8F Source: Table 7.\n4\nTemp. Variation\nSensitivity to\nH\nH\nH\nH\nM\nH\nH\nH\nH\nH\nM\nM\nL\nH\nL\nH\nL\nL\nH\nH\nRelative Vulnerability of Sectors to Gas Shortages\nVulnerability\nchance of supply interruption or price rise for inputs. Source: Table 4.\n3\nEmployment\nVH\nVH\nVH\nM\nH\nL\nL\nH\nL\nM\nL\nM\nL\nM\nM\nM\nM\nM\nM\nL\nLoss of 2\nCustomers\nL\nH\nM\nH\nH\nH\nH\nH\nH\nL\nH\nM\nM\nH\nL\nH\nH\nM\nH\nH\nTable 9\nL = Low, M = Medium, H = High, VH = Very High.\n1\nInput Cost Rise\nor Shortages\nM-H\nL\nM\nL\nL\nL\nL\nL\nL\nL\nL\nL\nH\nL\nL\nL\nM\nM\nM\nM\nindicated for inputs to other sectors.\nPrinting and Publishing\nWater and Sanitation\nManufacturing N.E.C.\nLocal Government\nFood Processing\nHealth Services\nServices N.E.C.\nTransportation\nCommunication\nHotels-Motels\nConstruction\na given sector.\nElectricity\nNatural Gas\nRestaurants\nHouseholds\nWholesale\nSector\nColleges\nSchools\nRetail\nFIRE\nBased\nKEY:\n10.\n11.\n12.\n13.\n14.\n15.\n16.\n17.\n19.\n20.\n18\n1.\n2.\n3.\n4.\n5.\n6.\n7.\n8.\n9.\n1\n2\n3\n4\n5","191\nTable 10\nComparative energy consumption statistics for Building 1 through 4 for a\n30-day period.\nEnergy Consumption\nBuilding\nBtu/Day\nBtu/Sq. Ft./Day\n15.0 X 10 6\n1\n350\n6\n2\n18.5 X 10\n250\n6\n3\n25.5 X 10\n1100\n4","192\nThus we are faced with the complication that modelling of energy\nconsumption in individual buildings will have to take into account\ncertain criteria of systems design. To model the consumption of energy\nby larger communities, we will have to find the characteristic \"mix\" of\nefficiency factors of various air conditioning systems in use.\nEven with our ongoing modelling efforts we can point out a number\nof \"sins\" against energy conservation that are being committed by poor\narchitectural design -- insensitive to climatic conditions -- and by\ninefficiencies in ventilation and air conditioning systems. Efforts\nshould be made to educate the public, but also the building profession,\nthat energy conservation by improved design criteria employed in in-\ndividual structures, but also by more judicious land-use planning in-\ncorporating climatological factors, pays for itself in the long run.\nThe detailed model which we have developed helps to pinpoint energy\nuse for space heating to a much greater detail and accuracy than gross\nsend-out data from utility companies can provide. Therefore, the ef-\nfects of certain energy-conservation measures (e.g. retrofitting with\ninsulation, reduced thermostat settings, etc.) can be tested to a con-\nsiderable degree of reliability, good enough to serve as a basis for\nstrict cost effectiveness assessment. The requirement of a detailed\nbuilding census, even when derived by various \"short cut\" methods that\nwe have developed, makes the model cumbersome to employ on a state-wide\nor regional basis. We, therefore, have started to develop a \"hybrid\"\nmodelling approach which attempts to match historical weather data with\nenergy consumption over a wide region (e.g. over Colorado and Wyoming)\nwithout detailed knowledge of a building census. Such a match is an-\nticipated to meet with some difficulties because a region such as the","193\nstate of Colorado may be under the simultaneous influence of several\nwidely differing weather regimes. We are hopeful, however, that sta-\ntistical techniques developed and employed during our past efforts will,\nagain, provide us with reasonable weighting functions for individual\nsub-regions. A \"physical\" model can then be used to account for changes\nin the energy consumption by new construction and altered habit and use\npatterns in individual sub-regions. We hope that such a modelling\napproach will meet the requirements of detailed energy audits voiced by\nvarious legislative bodies and public utility commissions.\nWe have mentioned earlier that urban climate has a feedback link\nwith anthropogenic heat release. The physical model developed by us\nenables us to estimate anthropogenic heat production from the space-\nheating energy consumption over relatively small area elements (e.g.\ncensus blocks) of a city. We thus should be able to isolate the con-\ntribution from anthropogenic heat release to the urban heat-island\neffect. If other effects, such as those of surface characteristics,\nalbedo, radiation fluxes and atmospheric diffusivity also could be\nestimated independently, one might be able to develop quantitative urban\nclimate models. Such models could properly take into account topo-\ngraphy, open green areas with lakes, etc., and might provide a tool for\noptimum city planning. Environmental impact assessments of new con-\nstruction and new industrial and commercial activities could receive\nsignificant help from such model development.\nWe have mentioned in the introductory chapters several conceptual\nsimilarities in the weather-dependent aspects of energy use in space\nheating and in various branches of industry, such as agriculture.\nEspecially in the semi-arid west energy use by agriculture is strongly","194\nweather dependent where irrigation pumping is required. Farther to the\neast crop-drying becomes a weather-dependent factor of agricultural\nenergy use. Most of the modelling approaches which we have developed\ncan be transferred directly to agricultural data bases.","195\nReferences\nAmerican Gas Association, 1969: Load characteristics research manual.\nA.G.A., New York, NY.\nAmerican Society of Heating, Refrigerating and Air-Conditioning\nEngineers, 1972: Handbook of fundamentals. 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Johnson, H.H. Leong, B.C. Macdonald, W.L.\n,\nSomervell, Jr., A.M. Starr, and K.O. Timbre, 1978: The effects of\natmospheric variability on energy utilization and conservation.\nEnvironmental Research Paper No. 14, Colorado State University,\nFort Collins, CO, 75 pp.\nC.C. Burns, H.C. Cochrane, G.R. Johnson, H.H. Leong, J.R. McKeen,\n,\nJ.D. Shaeffer, and A.M. Starr, 1980: The effects of atmospheric\nvariability on energy utilization and conservation. Environmental\nResearch Paper No. 24 (in press).\nSepsy, C.F., R.S. Blancett and M.F. McBride, 1975a: Heat transfer\nmodels and energy needs for residential homes. EPRI 137, Report\nNo. 3, EPRI, Palo Alto, CA.\n.L. Moentenich and M.F. McBride, 1975b: A study of attic tem-\n,\nperatures and heat loss in residential homes. EPRI 137, Report\nNo. 1, EPRI Palo Alto, CA.","197\nJ.M. Salvadore and M.F. McBride, 1975c:\nThermal response and\n,\nmodeling of heating and cooling equipment for residential homes.\nEPRI 137, Report No. 2, EPRI, Palo Alto, CA."]}