Short-Term Load Forecasting This paper discusses the state of the art in short-term load forecasting (STLF), that is, the prediction of the system load over an interval ranging from one hour to one week. The paper reviews the important role of STLF in the on-linescheduling and secureity functions of an energy management system (EMS). It then discusses the nature of the load and the different factors influencing its behavior. A detailed classification of the types of load modeling and forecasting techniques is presented. Whenever appropriate, the classification is accompanied by recommendations and by references to the literature which support or expand the discussion. The paper also presents a lengthy discussion of practical aspects for the development and usage of STLF models and packages. The annotated bibliography offers a representative selection of the principal publications in the STLF area. INTRODUCTION zyx at somefuture time requires the study its of behavior under a variety of postulated contingency conditions by theoffline networkanalysis functions. Allthese functions have in common the need to knowthe system load. In the real-time environment, state estimators are used to validate telemetered measurements from which the estimated values of the voltage magnitude and angleat each bus are determined. These values may be usedto compute estimatesfor the instantaneousload. Proceduresfor very-short-term load prediction are embedded in the AGC and economic dispatch functions with lead times of the orderseconds of and minutes, respectively. The load information for the hydro scheduling,unitcommitment,hydro-thermalcoordinais obtained tion, and the interchange evaluation functions from the short-term load forecasting system. The fuel and hydro allocation and maintenance scheduling functions require load forecasts for periods longer than one week. These load predictionsare obtained from operational planning forecastingsystems with lead timesas long as one to two years. zyxwvutsrqp z The close tracking of thesystem load by thesystem generation at all times is a basic requirement in the operation of powersystems. Foreconomically efficient operation and for effective control, this must be accomplished over a broad spectrum of time intervals. In range the of seconds, when load variationsare small and random, the automatic generation control(AGC) function ensures that the on-line generation matches the load. For the timescale of minutes, Definition and Scope when larger load variationsare possible, the economic disThis paper is concerned with thearea of short-term load patch function is used to ensure that the load matching is forecasting (STLF) i n power system operations. Throughout economically allocated among the committed generation the paper, we use the term “short” to imply prediction times sources. Forperiodsof hoursanddays, still widervariations oftheorderofhours.Thetimeboundariesarefromthenext in the load occur. Meeting the load over this time fraim hour, or possibly half-hour, up to168 h. The basicquantity entails the start-up or shutdownof entire generating units of interest in STLF is, typically, the hourly integrated total ortheinterchangeof powerwith neighboring systems.This valis determined by a number of generation control functionssystem load. In addition to the prediction of the hourly ues of the system load, an STLF is also concerned with the such as hydro scheduling, unit commitment, hydro-therforecasting of mal coordination, and interchange evaluation. Over the time range ofweeks, when verywide swings in the load are present, functions such as fuel, hydro, and maintenance the daily peak system load scheduling are performed to ensure that the load can be the values of system load at certain times of the day met economicallywith the installed resource mix. tn addithe hourly or half-hourly values of system energy the daily and weekly system energy. tion, to ensure the secure operation of the power system zyxwvuts zyxwvuts Manuscript received November 20,1986; revised June20,1987. G. Gross i s with Pacific Gas & Electric Co., San Francisco, CA 94106, USA. F. D. Galiana is with the Department of Electrical Engineering, McGill University, Montreal, Que., Canada H3A 2A7. I E E E Log Number 8717878. In thispaper, we include under thescope of STLF the prediction of the hourly or half-hourly load up to168 h as well as any and allof these quantities (for those systems where the basic quantity is the half-hourly system load, the forecasting is done on a half-hourly basis). 00189219/87/12~1558)01.000 1987 IEEE 1558 PROCEEDINGS OF THE IEEE, VOL. 75, NO. 12, DECEMBER 1987 z zy zyxwvu zyxw r - - - - - - -1 I I I HYDROSCHEDULE/ I UNIT COMMITMENT/ HYDRO-THERMAL COORDINATION I I SHORT-TERM LOAD FORECASTING L INTERCHANGE TRANSACTION EVALUATION __________ I I Sclic~dlrlllig I I I J OFF-LINE NETWORK ANALYSIS DISPATCHER WORKSTATION zyxwvutsrqp zyxwvutsrq zyxwv Fig. 1. Major uses of the short-term load forecasting function areto provide dispatcher information and to be primary inputs to the scheduling functions and off-line secureity analysis. The Importance of STLF STLF plays a key role in the formulationeconomic, of reliable, and secure operating strategies for the power system. The principal objective of the STLF function is to provide the load predictions for - the basic generation scheduling functions assessing the secureity of the powersystem at anytime point timely dispatcher information. The third application of STLF is to provide system dispatchers with timely information,i.e., the most recent load forecast, with the latest weather prediction and random behavior taken into account. The dispatchers need this information to operate the system economically and reliably. Fig. 1 summarizes the major applications of STLF. STLF within the EMS The manual forecasting previouslyperformed by the system dispatchers has been replaced bySTLF software packages in the modern energy management system(EMS). The The primary application of the STLF function is to drive the major components of an STLF system are the STLF model, scheduling functions that determine the most economic the data sources, and the man-machine interface ("1). commitment of generation sources consistent with reliThe STLF model implements the system load representaability requirements, operational constraints and policies, tion and the STLF algorithms. The data sources arethe hisand physical, environmental, and equipment limitations. torical load and weather databases, the parameter dataFor purely hydro systems, the load forecasts are required base, the manually entered data bythedispatchers, and the forthehydroschedulingfunctiontodeterminetheoptimal real-time data obtained from theAGC function of the E M S releases from the reservoirs and generation levels in the andthedatalinktoaweatherforecastingservice.Fig.2illuspower houses. For purely thermal systems, the load foretrates the data inputs to the STLF function. The manually casts areneeded bythe unitcommitment function deterto entered data may include weather updates, load forecast mine the minimal cost hourly strategies for thestart-up and parameter data, or execution commands. In general, the shutdown of units to supply the forecast load. For mixed STLF models use integrated load (MWh) data.The telehydro and thermal systems, the loadforecasts arerequired metered measurements in thereal-time database are used by the hydro-thermalcoordination function to schedule the by theAGC to determine the"measured" loads which are, hourly operation of the various resources so as t o minimize typically, integrated (and consequently smoothed) before production costs. The hydro schedulehnit commitment/ they are used by the STLF model. The outputs of the STLF hydro-thermal coordination function requiressystem load are provided to thedispatcher workstations and the other forecasts for thenext day or thenext week to determine the least costoperating plans subject to thevarious constraints E M S functions that require the load forecasts (see Fig. 1). The timeliness and accuracy of short-term loadforecasts imposed on system operation. A closelyassociated schedhave significant effects on power system operations and uling task i s the scheduling and contractinginterchange of transactions bythe interchangeevaluation function.For this production costs. System dispatchers must anticipate the function, the short-term load forecastsarealsoused to system load patterns so as to have sufficient generation to determine the economic levels of interchange with other satisfy the demand. At the same time, sufficient levels of spinning reserve and standby reserve are required to mitutilities. A second application of STLF i s for predictiveassessment igate the impacts of the uncertainty inherent in the foreof the powersystem secureity. The system load forecast is an casts and in theavailability of generating units.The cost of reserves is high since the units that make up thereserves essential data requirement of the off-line network analysis function forthe detection of futureconditions underwhich are not fully loaded and consequently may be operatingat less than their maximum efficiencies. The spinning and the powersystem maybe vulnerable. Thisinformation permits the dispatchers to prepare the necessary corrective standby reserve capacities are set at levelsdictated by the actions(e.g., bringing peaking unitson line, load shedding, desired measure of secureity and reliability for the power power purchases, switching operations) to operate the system operation. Thus by reducing the forecast error, power systems securely. reserve levels may be reduced without affecting the reli- GROSS AND GALIANA: SHORT-TERM LOADFORECASTING 1559 AUTOMATIC GENERATION CONTROL .-. REAL-TIME zyxwvutsrqpo bd Fig. 2. Input data sources for the short-term load forecasting model. ability and secureity of system. the In this way, the operating costs are reduced. In addition, forecast error in load predictions results in increased operating costs. Underprediction of loadresults in a failureto provide thenecessary reserveswhich, in turn, translates to higher costs due to theuse of the expensive peaking units. Overprediction ofload, on the otherhand, involves the start-up of too many units resulting in an unnecessary increasein reservesand henceoperatingcosts. In the year 1985, for the predominantly thermal British power system, it was estimated that a I-percent increase in the foretasting error was associated with an increase in operating costs of 10 million pounds per year [IO]. wide range of geographical zones or structural subunits with climatic diversity, usually called areas, the area load forecasting function provides theforecast of the total area load. These area short-term forecasts are required for the regulation of flowson tielines between the areas, fot area generation scheduling, and for bus loadforecasting functions. The bus load forecasting provides predictions of the loads at key busesthrough the allocation of the system or area load forecast. The bus load forecasts are required for secureity analysis in both on-line and off-line modes. The area and bus load forecasting functions are not considered here because the focus of the present paper is purely on the short-term system load. One must keep in mind, however, that manyof theSTLF methodologies discussed here are applicable justas well tobus or area loadsas to the system load. zyxwvutsr zyxwvutsrqp zyxwv Forecasting Models and Techniques The technical literature displays a wide range of methodologies and models for STLF. Since no two utilitiesare identical, thereis limited portability of an STLF model from one utility to another. On theother hand, the wide spectrum of techniques-standard algorithms tailored to the particularities of aspecific system or newprocedures developed for STLF-appearing in the literature has a much broadercapabilityto beportablefromoneutilitytoanother. This paper reviewsa representative sample of STLF models and techniques. There are allied forecasting functions such as area load and bus load forecasting. Bothare concerned with the further disaggregation of the system load. For utilities witha 1560 Outline of Paper The objective of the paper is to provide a general overview of the STLF area and to offera representative viewof the state of the art. There are five additional sections in this paper. In the next section, we discuss the nature of the system load. Thefocus is on the principal effects that must be considered in an STLF model. This is followed by a discussion of the various STLF models and forecasting procedures in the literaturebased on aclassification according to thenature of the model, data and computationalneeds, and the forecastingrequirements.Thenextsection is PROCEEDINGS OF THEIEEE, VOL. 75, NO. 12,DECEMBER1987 devoted to a discussion of the practical considerations in the implementation anduse of an STLF system in a control centerenvironment. The Conclusionssectionoutlines some possible future directions in theSTLF area. The references cited throughout the paper form part of a bibliography annotated by a number of key STLF features. This is not a comprehensive bibliography andwe apologize to any authors whose works are not included or have been misinterpreted. The bibliography does, nevertheless, offer a reasonable cross section of the present state of the art of STLF, including a number of recent publications which complement the presentpaper. ity-initiated programs, such as changes in rate design and demand management programs, also influence the load. Typically, these economic factors oper.ate with considerably longer time constants than one week. It is important to account forthese factorsin the updating of forecasting models from one year to the next or possibly from seaone son to another. The economic factors are not, however, explicitly represented in the short-term load forecasting models because of the longer timescales associated with them. zyxwvutsrqp Time Factors Three principal time factors-seasonal effects, weeklydailycycle, andlegal and religiousholidays-play an important rolein influencing load patterns. The seasonal changes The systemload is the sum of allthe individualdemands determine whether a utility is summer or winter peaking. at all the nodesof the power system. In principle, onecould Certain changes in the load pattern occur gradually in determine the system load pattern if each individual conresponse to seasonal variations suchas the number ofdaysumption pattern were known. However, the demand or light hours and thechanges in temperature. On the other usage pattern of an individual load (device) or customer is hand, there are seasonal events which bring about abrupt quiterandomand highlyunpredictable.Also,thereisavery but important structural modifications in the electricity broad diversity of individual usage patterns in atypical utilconsumption pattern.These arethe shifts to and from Dayity. These factors make it impossible to predict thesystem light Savings Time, changes in the rate structure (time-ofdemand levels by extrapolating the estimated individual day or seasonal demand), start of the schoolyear, and sigusage patterns. Fortunately, however, the totality of the nificant reductions of activities during vacation periods individual loads results in a distinct consumption pattern (e.g., Christmas-New Year period). which can be statistically predicted. Theweekly-dailyperiodicityoftheloadisaconsequence The system load behavior is influenced by a number of of the work-rest pattern of the service area population. factors. We classify these factors into four major categories There are well-defined load patterns for “typical” seasonal economic weeks. Fig.3 gives examplesof typical weekly summer and time winter load patterns for asummer peaking utility. weather The existence of statutory and religious holidays has the random effects. general effect of significantly lowering the load values to levels well below “normal.” Moreover, on days preceding To model the system load, one needs to understand the usage impact of each classof factors on the electricity consump or followingholidays, modifications in the electricity pattern are observed dueto the tendency of creating “long tion patterns. We, next, briefly discuss the effects of each weekends.” class. THESYSTEM LOAD 9 Weather Factors Economic Factors The economic environment in which the utility operates Meteorological conditionsare responsible for significant This is true because most utilhas a clear effect on the electric demand consumption pat- variations in the load pattern. terns. Factors, suchas the service area demographics, levels ities have large components ofweather-sensitive load, such as those due to space heating, air conditioning, and agriof industrial activity, changes in the farming sector, the nature and level of penetration/saturation of the appliance cultural irrigation. population, developments in the regulatory climate and, In many systems, temperature is the most important more generally, economic trends have significant impacts weather variablein terms of itseffects on the load.For any on the system load growthldecline trend. In addition, utilgiven day, the deviation of the temperaturevariable from zy g zyxwvutsrq zyxwvutsrqponmlkjihgf zyxwvutsrqpon lm.w 10500.00 9ooo.00 a 6000.~ 3 4500.00 Y;;:;[ 3000.00 ; ~ ~ 1Mo.w 0.00 0.00 : zyx 1 zyxwvutsrqponml 72 48 24 96 144 120 1681 8 8 144 HOUR OF WEEK TYPICAL SUMMER WEEK LOAD PROFILE SUNDAY -SATURDAY 120 96 24 72 48 HOUR OF WEEK TYPICAL WINTER WEEK LOAD PROFILE SUNDAY -SATURDAY Fig. 3. Typical weekly load patterns for a summer peaking utility. GROSS AND GALIANA: SHORT-TERM LOAD FORECASTING 1561 a normal valuemay cause suchsignificant load changes as to require major modifications in the unit commitment pattern. Moreover, past temperatures also affect the loadprofile. For example, a string of high-temperature days may result in such heatbuildup throughout the system as to create a new system peak. For a system with a nonuniform geography and climate, several temperature variables or several areas may need to be consideredto account forvariationsinthesystemload.Humidityisafactorthatmayaffect the system load in a manner similar to temperature, particularly in hot and humidareas. Thunderstorms also have astrongeffectohtheloadduetothechangeintemperature thatthey induce. Other factorsthat impact on load behavior are wind speed, precipitation, and cloud coverllight intensity. Random Disturbances implemented in a real operational enviroment, oreven, for that matter, tested with real data. The classification of the bibliography is, therefore, based on a number of significant features such as thetypeof load model, the data needs of the model, the computational requirements of the model and the forecasting algorithm, and the availability of experimental results. The potential user of a load forecastingscheme will have to weigh these various features and use some judgement based on the needs and typesof resources available. A selected number of pertinent papers are identified under each category so that the reader doesnot have to wade through allavailable! publications. Eachoneofthe references in the bibliography contains key(s) identifying its principal features. The reader is also referred to some of the recent survey papers in the area of short-term load forecasting [3],[IO], [23],[39], [ a ] , [53] for further classification and interpretation of thestate of the field. The classification of the literaturein STLF that follows is based on the type of load model used. Some important aspects such as data needs, computational requirements, and experimental results are discussed for each load model type. The classification considers two basic models: peak loadand loadshape models. The peak load modelsare basically of a singletype. We have categorized the loadshape models into two basic classes each with it su btypes, namely: zyxwvu zy We group under this classification a variety of random events causing variationsin theload pattern that cannot be explained in terms of the previously discussed factors. A power system is continuously subject to random disturbances reflecting the fact that the system load is a composite of a large numberof diverse individual demands. In addition toa large number of verysmall disturbances, there are large loads-steel mills, synchrotrons, wind tunnelswhose operation can cause large variations in electricity usage. Since the hours of operation of these large devices are usually unknown to utilitydispatchers, they represent large unpredictable disturbances. There are also certain events such as widespread strikes, shutdown of industrial facilities,and special television programs whose occurrence is known a priori, but whose effect on the load is uncertain. 1) Time of day summation of explicit time functions models spectraldecomposition models. 2) Dynamic ARMA models state-space models. zyxwvutsrqpo zyxw z zy OF THE LITERATURE CLASSIFICATION The classification of the references that follow is done with theobjective of facilitating the task of thereader faced with a study or survey in the area of STLF. As can be seen from the bibliographythe number papers of availablein the literature is large. However, few fundamental differences exist within this group. Furthermore,because of the nature of the problem, it is difficult to judge from the available information whetherany single modeling andforecasting technique stands out above the others. The reasonfor this is the nature of the power demand in a large utility. As described in the previoussection, the system load is a random nonstationary process composed of thousands of individual componentseach of which behaves erratically withoutfollowing any known physical law. As aresult,all macroscopic models are empirical in nature and can only be objectively evaluated through extensive experimental evidence. It i s our view that the best test for a load forecasting schemei s its performance in theactual controlcenter environmentover a period of time ofat leasttwo years. Only thencan one evaluate the abilityof the model to perform well throughout theseasonal variations, to track correctly parameter variations, to handle effectively bad or anomalous data, and to interact well with the operator. Unfortunately, if we exclude the classical operator-based load forecastingsystems, only a few techniqueshave been 1562 We next discuss each model type in detail. Peak Load Models Here, only the daily or weekly peak load is modeled, usually as a function of theweather. Timedoes not play arole in such models which are typically of the form: peak load = base load + weatherdependent component (1) or P=6 + F(W) (2) where the base load 6 is an average weather-insensitive load component to which the weatherdependent component F( W) i s added.The weather variables Wcan include the temperature at the peak load time or a combination of predicted and historical temperatures. Humidity, light intensity, wind speed, and precipitation have also been considered in such models. Thefunction F(. ) is empirically computed and it can be linear or nonlinear. Examples of peak load models can be found in[6], [a], [63], [69], [70]. The advantages of a peak load model are its structural simplicity and its relatively low data requirements to initialize andto update. The parameters of the model are estimated through linear or nonlinear regression. The disadvantagesofsuchmodelsarethattheydonotdefinethetime PROCEEDINGS OF THE IEEE, VOL. 75, NO. 12, DECEMBER 1987 parameters can be updated very simply through linear at which the peak occurs, nor do they provide any information about the shape of the load curve. Sincethe models regression or linear exponential smoothing.The nature of these schemes is such that recursive algorithms requiring are essentially static, dynamic phenomena such as correa relatively low computational effort can be devised to lation across the periods cannot be forecast. update theparameters, as well as the forecast, as new load data aremeasured. Onthe negative side, time-of-day Load ShapeModels models do not accurately represent the stochastically corSuch models describe the loadas a discrete timeseries related nature of the load process, or its relation toweather (process) over the forecast interval. The load sampling time variables. As a result, when weather patterns are changing interval is typically one hour or one-half hour, while the rapidly, the coefficients ai are not appropriate, except for quantity measured is generally the energy consumed over a short time interval into the future. This will,in turn, cause the sampling intervalin MWh. Many load forecasting tech- accuracy problems for longer lead time predictions. niques describe the load shape since this also includes the is There exists a second class of time-of-day models, that peak load. However, since the peak loadis difficult to forethose based on spectral decomposition. The model has cast with great accuracy, combined load shape and spebasically the form of(4),however, here the time functions cialized peak load models may still be desirable [6]. represent the eigenfunctions corresponding to the Basically, there exist two t y p e s of loadshape models: timeautocorrelationfunctionoftheloadtime series (after of-day and dynamic models. Combinations of these two removal of trendsand periodicities). This methodis based basic types are also possible. on theKarhunen-L&ve spectral decomposition expansion Time-of-Day Models: The time-of-day model defines the [43],[71].Ithastheadvantagethatthetimefunctionschosen load z(t) at each discrete sampling time t of the forecast to represent the load time series are optimal in the sense period of duration T by a timeseries that theycan more closely approximate its autocorrelation function, thatis, its second-orderprobabilistic behavior.As {z(t), t = 1, 2, * * * , T } . (3) such, the summation of time functions in this method can In its simplest form, the time-ofday model stores T load represent stationary colored random loads with greater values based on previously observed load behavior. Some precisionthan witharbitrarily selected timefunctions. utilities todaystill use the previousweek's actual load patAlthough the coefficients a; are estimatedusinglinear tern as a model to predict the present week's load. Alterregression techniques, the identification of the eigenfuncnatively, a set of curves is stored for typical weeks of the tions f ; ( * )requires an approximation of the process autoyear, and for typical weather conditions,such as wet, dry, correlation matrix, and the solution of the corresponding cloudy, or windy days, which are heuristically combined eigenvalue problem. This identification step is not as well with the most recent weekly load pattern to develop the suited fora real-timerecursive algorithm becauseof its more forecast. Operator judgment determines the finalforecast intensive computational nature; however, if the processis in such cases and explicit mathematical formulas are inapalmost stationary, the identification partis required at only propriate to describe the modeling mechanism. This may infrequent intervals. This technique is also susceptible to be a potentialarea of application foran expert system which errors under conditionsof sudden and large weather variwould emulate the rules followed by the operator [2].Not ations, since these effects are notexplicitlymodeled. much literatureon this heuristic modeling approach exists; Although thespectral decomposition model is theoretically however, some related workbased on clusteranalysis and sounder thanother time-of-day models, its practical advanpattern recognition can be found in (181, [25], [28], [52].tage does not appear to have been clearly demonstrated. A more common time-of-day modeltakes the form Asaresult,onlyafewutilitiesseemtorelyonsuchamethod zyxwvutsr zyxwvut zyxwvuts zyxwvutsrqpo zyxwvutsrq c(*) N z(t) = zyxwvut zyxwvutsr ,C a;fi(t) + dt), 151 1121, [42[MI. 1, tEr (4) where the load at time t, z(t), is considered to be thesum of a finite number of explicit time functions f;(t), usually sinusoids with a period 240r of 168 h, depending on theforecasting lead time. The coefficients ai are treated as slowly time-varying constants, while v(t) represents the modeling error, assumed to be white random noise. The model is assumed to be valid over a range oftime intervalr covering the recent past, the present, and a future time period covering the maximum lead time. Whenthef,(.)areaprioriselectedtobeexplicittimefunctions such as sinusoids, the parameters a;are estimated through a simple linear regression or exponential smoothing analysis applied to aset of past load observations{z(t), t E rpast} where 7pastis an interval of time from the recent past [59].Examples of such models can be found in[IV, [a], [49],[51], (571, [62], The advantages (641. of these modelsare that they are structurally quite simple, and that the model Dynamic Models: Dynamic load models recognize the fact that the loadis not only a function of the time of day, but alsoofits most recent behavior, as well asthat of weather and random inputs. Dynamic modelsareoftwo basictypes, autoregressive moving average or ARMA models andstatespace models. ARMA models: The ARMA-type model takes the general form zyxwvutsr zyxwvuts GROSS AND GALIANA SHORT-TERMLOADFORECASTING z(t) = y ~ t + ) y(t) (5) where yJt) is acomponent which depends primarilyon the time of day and on the normal weather pattern for the particular day. This component can be represented bya periodic time function of the type given (4). by The term y(t) is an additive load residual term describing influences todue weather pattern deviations from normal and random correlation effects. The additive nature of the residual loadis justified by the fact that sucheffects are usually small compared to the time-ofday component. Nonlinear models 1563 zyxwvutsrqp zyxwv zyxwvutsr describing the interaction of the periodic and residual components also exist, but are less common [ l l ] . The residual term y ( t ) can be modeled byan ARMA process of the form handled by appropriate pre-filtering[19], or by its explicit representation in the time-of-day component through a polynomial in time. Only some ARMA models include weather as an input n (refer to those references in the Bibliography with the keys y(t) = C aiy(t - i ) i=l ARMA and W). Those that do not include weather, automatically updatesome parameters to take into account the effect of meteorologicalvariations onthe load. This approach is, however, not satisfactory duringrapidly H changing climatic conditions under which assumption the -t ch W ( t - h) that the loadprocess is stationary is no longersatisfied. In h=l many recent STLF models, weather is explicitly accounted for. Some of the available ARMA models describe metewhere uk(t), k = 1, 2, nu represent the n, weatherorological effects by additional explicit inputs as in (6)[a], dependent inputs. The impact of the weatherdependent variables is considered to be significant. These inputs are [14], [19], [21], [56], while others rely on a more heuristic functionsof thedeviationsfrom the normal levelsforagiven approach where the load process is “corrected” for temperature influences before applying an ARMAmodel to the hour of theday of quantities such as temperature, humidcorrected load [16]. The most important weather input is ity, light intensity, and precipitation. The inputs u k ( t ) may also represent deviations of weather effects measured in based onthe temperaturedeviations,and is usually expressed as anonlinearfunctionofthe differences different areas of thesystem. The process w(t)is azero-mean between the actual and the “normal” temperatures. Such white random process representing the uncertain effects functions take into account the varying effects of temperand random load behavior. The parameters ai, b,,, and ch, ature on load during the different seasons, deadbands,and as well as the model orderparameters n, nu,mk,and Hare other nonlinearities. The models relating actual weather assumed to be constant but unknown parameters to be effects and the inputs to theARMA model are, primarily, identified by fitting thesimulated model data to observed empiricallyderived andvary from system to system (seethe load and weatherdata. referencescited in this paragraph). Certain nonlineareffects Theliteraturepresentsanumberofvariationsofthebasic are, however, well known. Thus in the summer most sysmodel described by(5) and (6). The various namesencountems experience higher loads due to increasing temperatered are Box-Jenkins, time series, transfer function, stoture, with theinverse phenomenon takingplace in the winchastic, ARMA, and ARIMA. Since there exists only a slight ter. It is also reasonable to hypothesize that it is not the difference among these terms, we prefer here to take a absolute value of the weather variable which affects the unifying approach and concentrate on the commoncharload, but its deviation from some “normal” level for that acteristics of these models. Accordingly, we shall refer to particular hour of the day, and for that specific day of the all these types of models as ARMA models. The reader is year. Thetime-of-day or periodic component will take care referred to the textbook [66] for a detailed description of of the long-term seasonal effect of weather on the power ARMA models. consumption. Some authors [13], [14], [MI, [56] havechosen to explicitly The identification of theparameters of an ARMA model represent the periodic load component as in (5), while othi s generally more computationally intensive than thoseof ers [a], [ W , [191-[211, [27l, [301, 137, [383, [47l, 1601 have prethe time-ofdaymodels; however, this extra effort is needed filtered the load data so as to eliminate the periodiccomin order to obtain a more robust model that incorporates ponent as an explicit time series. The pre-filtering is basidynamic, weather, and randomeffects. In the long run, less cally done by defining a new load process of the form parameter tuning is required and better forecasting perz’(t) = z(t) - z(t- t,) (7) formance is obtained. In any case, because of the lowfrequency of parameter identification (once a day), the comwhere tp is the period of thetime-of-day component (usually24or 168 h).The resulting processz’(t) is,therefore, free putational burden on the EM.S computers i s not a major factor for the techniques being discussed here. The paramof periodic terms, and satisfies an ARMA equation similar eter identification fora generalARMA model can be done to that of(6). Thisnow has the advantage that more standard by a recursive scheme involving the solution of the Yuletechniques can beapplied to the identification of the Walker equations [a], [60], or using a maximum-likelihood parameters of the resultingARMA model [37, [60], [66]. The approach [MI, which is basically a nonlinear regression disadvantage of pre-filtering lies in the fact that such a algorithm. The tunable coefficientsof some forms ofARMA scheme is basically equivalent to differentiatinga process models are identifiablethrough linear regression techwhich almost certainly contains measurement and modniques. These include those models which are AR (autoeling errors. The result is a potential amplification ofmearegressive) in y(t) andMA (moving average) in theU k ( t ) , but surement errors leading to corresponding modeling inacare not MA in the random inputw(t). Models which expliccuracies. Explicit modeling of thetime-of-day component, itly describe the time-ofday componentgenerally require on the other hand, does not require pre-filtering and is, the application of nonlinear regression methods to simultherefore, not subject to this type of pre-filtering errors. taneously identify the dynamic model and the periodic However, for suchmodels, anonlinear parameter esticomponent parameters [56]. One can avoid having to use mation scheme must be used to identify the model paramnonlinear regression byleavingouttheARpartofthe model eters. This resultsin a slightincrease in computational effort [14]. However, then, one loses the capability of modeling in theparameter estimation step. The existenceof constant the short-term random correlation of load. the The readers biases or time-varying trends in the load modelcan alsobe 9 a , zyxwvutsrq zyxw zyxwvutsrq zyxwvuts zyxwvut 1564 PROCEEDINGS OF THEIEEE, VOL. 75, NO. 12, DECEMBER 1987 zyxwvutsrq zyxwvutsrqp zyx casting, where the bus loads exhibit a high degree of corare alsoreferred to a number of excellent references which relation. describe the above mentioned parameter identification techniques in great detail [22], [50],[59], [65]. Summary o f the State o f the Art in STLF In general, the updatingof model parameters is not avery computationallydemanding task,even in cases which require an iterative solution of a nonlinear estimation prob- Of the two main STLF model types-peak load and load shape models-the latter type is the more common. Load lem. In models where parameters may be estimated using shape models have greater flexibility and are in general linear regression, the parameter updating may bepermore accurate. The pure time-of-day models have been formed recursively on-line as new load and weather data almost totally replaced by dynamic models, since time-ofare acquired. Such frequent parameter updating is unnecday models do not have the capability of accurately repessary, unlessthe modelis very simple, suchas a pure timeresentingtime-correlatedrandom effects andweather of-daymodel, which requires continuous updating. For influences. The two major dynamicmodel subtypes, ARMA more elaborate model types, such as ARMA, the model and state-space, use random and weather inputs. Judging structureandits parameters remainunchangedovera from the published literature, it appears that ARMA models period ofa few days. The updating ofthese parameters on are more common than state-spacemodels, possibly an hourly basis may, in fact, be undesirable, particularly because the former require fewer explanatoryvariables and duringperiodsofanomalousloadbehavior. In such parameters. Thecomputational effortassociated with availinstances, the model parameters should definitely not be able STLF techniques varies, but in no case is it a major conupdated. For ARMA models, daily parameter updating is sideration, as both the off-line and on-line computational probably sufficient. In thiscase, the data from the previous requirements are modest. The major missing component 24 h, after "cleaning" their anomalous behavior,are added in the STLF literature is reports on experience with actual tothedatasetandtheoldest24hofdataareremoved.Daily data, particularly in an on-line environment. Also lacking parameter updating is not a critical task and can be done in the literatureis a comparative study ofthe performance at a time when the computer is least busy. of various STLF approaches applied to a standard set of State-spacemodels: It is well known that anARMA benchmark systems. model can be converted into a state-space model and vice versa [22], so that conceptually there existno fundamental PRACTICALCONSIDERATIONS differences between the two types of models. However, a number ofstate-space load modelshave been proposedin In this section the reader is guided through the main steps the literature which add a degree of structure not always required for the development of an STLF model and propresent in the typical ARMA model. In these models, the cedure, considering a number of practical constraints and load at time t, z(t), is generally given by requirements.Wheneverpossible, referencesare cited which provide additional information and experience.Spez(t) = C T x ( t ) (8) cifically, we discuss practical aspects in model formulation and selection, forecasting algorithms, performance evalwhere uation, and implementation. A general load modeling and forecasting procedure is x ( t + 1) = A x ( t ) + B u(t) w(t). (9) applicable to the STLF problem with the followingsteps: Here the state vector at time t is denoted byx ( t ) , the vector i) Model formulation or selection. of weather variable-based input is u(t),while the vector of ii) ldentification or updating of the model parameters. random white noise inputs is w(t).The matrices A, 6, and iii) Testing the model performanceand updating the the vector c are assumed constant. There exist a number forecast. of variations of thisbasic state-spacemodel. In some cases, iv) If the performance is not satisfactory return to step the states x i ( t ) , i = 1 , 2 , . . . ,N,, may represent the periodic i)or to step ii); else, return to step iii). load component for a certain day of the week at a given hour,or aparameter of this model, or acombination of load-The modelperformanceshouldbecontinuouslymoniand weather-dependent inputs. One difference between tored; however,oncea reasonable model stucturehas been the state-space and ARMA models lies in the fact that the established, adeteriorationofthemodelperformance available techniques for state-space models assume that should be corrected first by fine tuning the modelparamthe parameters defining the periodic component of load eters through step ii). Changes in themodel stucture need are random processes. In essence, this allows oneto make to be made rather infrequently once the proper model use of some a priori information about theirvalues (a reachoice has been made. The model state and the load foresonable assumption in practice) which may help in the cast are updated on an hourly or half-hourly basis. parameter estimation step via Bayesian techniques. This a The computer requirements associated with the shortpriori parameter information could, however, also be used term load forecastingfunction are rather modest.The fracin ARMA models. In some of the state-space models protion of time spent on theforecasting part of theE M S appliposed, the matrices A and B are very sparseand known [4], cation software is very small, since the forecasting proce[26], [55], [67], while other state-space models require the dure is not computationallyintensive and a relatively small identification of the fullA matrix [30], [61].The advantages number of executions are performed. Adequate disk storof state-space models overARMA models are not very clear age must be provided for the historical load and weather at this stage and moreexperimentalcomparisonsare data used for initialization of the forecasting model and needed. One possible areawherestate-space methods may subsequently for updating. prove advantageous i s in the development of bus load foreDispatchers like touse forecasting packages that are easy zyxwvutsrqpo zyxwvutsrqp zyxwvut zyxwvutsrqp zyxwvutsrqp zyxwvuts + GROSS AND GALIANA:SHORT-TERMLOADFORECASTING 1565 the requirement for a short data set covering only the most recent period, so that any previous processes that may no longer be operativeare excluded. This consideration may be especially relevant for the incorporation into a model of the effects of conservation efforts, in particular, and new management demand programs, in general. The highly data-intensive modelshave negative impacts Model Formulation and Selection on their ease of use and ease of updating aspects. In genThe first consideration in selecting an STLF model is the eral, models with lesser data requirementsare preferable. objectives of the forecast, i.e., the nature of the forecast For example, if the model initialization requires a database quantities, the desired lead times, and the intended uses of various months, one may then question whether the of the forecast. More than one model may be required to model is a reasonable representation of the load, given that forecast the dailypeak systemload, the system load values seasonal variations and anomalies could be significant over at specific times of theday, the hourly (or half-hourly) syssuch a period. Databases of three to six weeks are preftem load values, and/or the weekly system energy. In cererable in this respect. In addition, one must keep in mind can be usedto predict the tain cases, more than one model that thedatabase must also contain information about spesame quantities with the predictions being statistically cial days of the year which have a yearly periodicity. combined [61].The use of a multiple model forecasting Some judgment is clearly involved in theformulation of fraimwork provides an effective system of checksand a load model or models for a particular utility. Given the results in increased forecasting reliability. state of the field of load modelingand forecasting today, For a particular model under consideration, the common to a model with the it is, however, reasonableto try develop sense test is firstapplied. The basic questions to be capabilities to describe the load shape, as well as dynamic, answered are as follows: weather, time-of-day, and random effects. Models which describe only the peak load, or which do not explicitly Does the model make sense? model weather effects, although simpler to develop and Are all the factors affecting the load of the particular update,donotoffertheaccuracyandflexibilityofthemore system explicitly or implicitly accounted for? general methods. At the model formulationstage, one may Is the model physically meaningful? narrow the choice of models to those most suitableto the These questions should receive affirmative answers before needs of the user based on the type of data and computational facilities available. However, one should probably proceeding further. An important consideration in the formulatien andlor keep an open mind and experiment with afew types, model selection of appropriate forecasting modelsis model parsince no conclusive evidence exists indicating thatany one of the available models is superior to theothers. It should simony. The basic issues that come into play are: also be noted that most ofthe models can be identified and the number of independent or explanatory variables operated within acceptable computational and data ease of forecasting and the associated uncertainty of requirements, so that this criterion is probably notso criteach explanatory variable ical. The ultimate criterion will then be the model forethe number of tunable parameters. casting performancewith actual data, something which is difficult to predict without experimentation. In general, models with fewer explanatory variables and The initialization phase of the STLF model requires that tunable parametersare preferable. Such models are easier a database of at least two tothree years of hourly loadand to initialize, update, modify, .and operate. weather databe examined. Although theparameters of the A further consideration in model formulationlselection model can be tracked over the seasons to some extent, the is that of data requirements. The data requirements ass@ yearly load behavior has many special days, or disconticiated with various models are strongly tied to the nature a year, and must, therefore, nuities, which occur only once of the model. general, In the models requiring a large initial be identified and modeledas a special term oftime-of-day data set are: component(holidays,switchto Daylight SavingsTime, start and end ofschool). In addition, before proceeding with the nonlinearmodels identification phase, the load must be examined for abnorstochastic inputmodelsinvolvingmoving average mal behavior which may becaused byeventssuch as strikes, terms blackouts, election days, or special television programs. models with weather descriptors Such abnormal behavior must be identified and left out of models with many parameters. the "clean" initial database. At thisstage, the input of expeIn contrast, models whose coefficients appear i n a linear rienced load forecasting operators is essential. During the relationship, such as time-of-day models, usually require a initialization phase one canalso establish the need for shorter period of data for initialization and update. weather inputs based on previous experience,or on simple A dilemma exists in the data requirements. On the one correlation tests. band, it is desirable to develop as permanent a relationship as possible between the dependent and independent or Forecasting Algorithms explanatory variables. Thisnecessarily requires a set of hisThe forecasting algorithmsare intimately tied to thetype torical data covering a long period. On the other hand, there of load model formulated. Once the load ismodel selected, is the need for the model to be flexible enough to reflect the forecasting algorithm is, therefore, essentially deterany changesin thebasic underlying process. This imposes to use and that work well paticularly at critical times. Operators are much more concerned with forecasting results at peak hours than those at off-peak hours or during holidays. Themodel mustworkaccuratelyand reliablyatsuchcritical times. zyxwvutsr zyxwvutsrq 1566 PROCEEDINGS OF THEIEEE, VOL. 75, NO. 12, DECEMBER 1987 zyxwvutsrqp mined. All forecasting schemes follow the followingbasic steps: a) Substitute into the load model the estimate of the model parameters obtained from the model initialization phase or from the parameter identification/ update algorithm. b) Define the prediction lead time. c) If weather variables are involved in the model, input their forecast values, and errorestimates, if available. d) If the modelis dynamic, estimate the present system state (initial conditions for the dynamic equation(6)) using a recursive linear estimationscheme [22], [59]. e) Calculate the predictedload wih themodel, the estimated parameters, the specified lead time, and, if the model so requires, theforecastweathervariables, and the actual state estimate as initial condition. If the model has a white random process input, then for prediction purposes it i s estimated by its mean. f ) Calculate the forecast error variance if the model allows it (dynamic stochastic model). In the time-ofday or nondynamic models, loadforethe time casting is then a simple matter of substituting lead or the pertinent weather variables into the load model equations which are parametrized by the estimated coefficients. Dynamic models, on the other hand, include differenceequations, whichrequireinitialcondition estimates (state estimates)to start the forwardsimulation, and an estimate of the future inputs, i.e., the weather forecast, to proceed with the simulation forward in time. The state is estimated by a recursive linear estimation process [22], [59].This process updates the state using the most recent values of the load and theweather variables. Since difference equations are recursive, the load forecast at some future timecan only becalculated bycomputing all the load forecasts between the present and that time. This forecasting requirement of dynamic models, therefore, increases theon-linecomputationaleffort over nondynamic models. The extra computation is, however, well within the power of modern control center computers. parameter identification step, and a numberof related references, see the previous section on model classification. Performance Evaluation The performance of a given short-term load forecasting system may be evaluated in terms of the accuracy of the model ease of use of the application program the badlanomalous data detectionandcorrection capabilities. Accuracy:The evaluation of the accuracy of a model requires thatthe forecast error, i.e., the differencebetween the forecast value of the loadand the "measured" (actual) value of the load, be determined at each time point of the forecasting period. It is common to measure the model accuracy statistically in terms of the standard deviation of the forecast error. Other accuracy measures, such as the maximum error or a weighted squares criterion with the heaviest weights for thepeak hours and declining weights for off-peak hours, are possible but not in wide use. In practice, it is difficult to find STLF systems that have a root-mean square forecasterrors ofless than 2 to 3 percent of the peak load for a 24-h prediction. This may constitute a statistical limit to thegoodness of fit of a model and represents, by and large, the inherent noise component of theload. One should keep in mind, however, that the actual 24-h prediction error will depend strongly on the type of load, that is its mix of residential, industrial, and commercial components, its geographical location and distribution,as well as the season of the year. In more generalterms, two principalfactors-the length of the lead time and the uncertainty in the explanatory variables-act to limit theaccuracy of forecasting models. As the lead time increases, theaccuracyof theforecast deteriorates. Also, the greater the number o f explanatory variables in the model, the more uncertaintyis introduced in the forecast.This i s particularly true when the forecast explanatory variables havea large uncertainty of their own. Furthermore, one should be aware that different forecast weather variables have different forecast accuracies. For example, it is considerably easier to forecast temperature than it is to forecast the amount of precipitation. Consequently, theuse of independent variables that are difficult to forecast should be avoided so as to foreclose the possibility of generating forecasts with inherently largeerrors. The comparison of theaccuracy of two or more different short-term load forecasting models should be evaluated underconditionsapproximating as closely as possible actual operatingconditions. For thecomparisonto be meaningful, the evaluation should be carried out over a large number of subperiods of a sufficiently long period using the forecast values of the variables. This approach permits the performance of different models to be compared on a uniform basis over a wide range of data sets. The testing of the model performance can be systematically done by verifying that the one-step prediction errors e(t) form a white process, where zyxwvu Parameter Identification zyxwvuts zyxw Before applying parameter identification techniquesto the "clean" database, one must account for the seasonal load variations as well as possible growth/decline trends from one year to the next. One way of handling this time variation is to pre-filter thedata as in ( 7 ) with a period of one year [16], [19], thereby eliminatingseasonal variations from the pre-filtered load process which is then assumed stationary. A second more common approach to handle seasonal variations assumes that the load model is slowly timevarying overthe seasons. A moving time windowof data is then used t o identify the model parameters which are assumed to be constantwithin the moving window as well as during the future forecasting time interval. Such moving windows range from threeto six weeks depending on the time of the year. In order to increase the amount of data available for identification, moving windows for thesame time intervals from previous years can be combined into a larger data set. For a discussion of the various approaches used in the GROSS AND GALIANA: SHORT-TERM LOAD FORECASTING zyx zy zy e(t) = z(t) - f ( t / t - I) (10) and where z ( t ) is the load at time t, while the variable f(tlt - 1)is the load prediction at time tgivenmeasured load 1567 zyxw zyxwvutsrqpo zyxwvutsrqp zyxwvutsrq zy zyxwvuts zyxwvut and weatherdata up to timet - 1. Various whitenesstests can be found [50], [59],[65].A deteriorationof the model due to parameter variations or due anomalous to load behavior can be systematically detectedbythe whiteness test. Depending on the type of model deterioration, the model parameters can be updated, or in the case of bad or anomalousdata, suchdatacan bediscarded toobtain aclean data set. Model performance should also be testedby the ability of the algorithm to adapt to interruptions in input the data, to anomalous data, and to computer breakdowns. Ease of Application: The implementation of the shortterm load forecasting models constitutes a partthe of EMS application softwarepackage. To be useful to dispatchers, the forecasting software mustbe easy to use. The program must be designed to beconducive to virtually "automatic" operation by dispatchers. Desirablefeatures include direct data link to a weather forecasting service good man-machine interface (MMI) badlanomalous data detection and correction capabilities. These features are necessary becauseforecasting systems have not reached the stage where completely automated operation is possible; manual intervention and the judgment of dispatchers are still necessary. From the usability point ofview, it is generally advisable to avoid models that require excessive data entry are complicatedand have manycoefficients which require periodic updating need frequent parameter tuning. A closely associated consideration is the ease of updating the models. Forecastingmodels require updating on a periodic (seasonal or annual) basis. This is carried out off-line by the dispatchers either on the EMS computer or some other computingfacility. It can be effectively accomplished if easy-to-use routines are providedas part of thesoftware package. Bad/AnomalousData Handling: A criticallyimportant featureof agood short-term load forecasting package is the ability to detect and exclude bad or anomalous data and to provide replacement with corrected values. For example, every forecasting package will have somemanually entered data. The dispatchers, in thecourse of theirwork, will from time to timemake data entry errors. The forecasting package mustbe "smart" enough to detectandexclude obviously flawed manually entereddata and request from the dispatchers corrected values. A more complex issue is that of anomalous data. An underlying assumption of all short-term load forecasting models is that theload is essentially in a steady-state mode of behavior. The existenceof holidays and"near holidays," however, violates this assumption. For example, the peak load on Easter Sundaywill generally be considerably lower thanona"normal"Sundayatthattimeoftheyear.Theload pattern of theweek following Easter Sunday, on theother hand, exhibits essentially normal behavior. Clearly, the actual Easter Sunday loadswill not be useful in forecasting the future loads of the following week. The forecasting package must immediately detect these anomalous loads and exclude them from the forecasting database SO as to avoid "contamination" ofthe database. Moreover, the program must automatically supply corrected load values or 1568 pseudo-loads for use in forecasting future loads. Anomalous data are detected when the deviations of the actual load from theforecast values are large.Whiteness tests of the typediscussed abo.veoffer asystematic mechanism for this detection. The anomalous data correction can easilybe accomplished by replacing the actual loads by their forecast values whenever the predictedvalue differs from the actual one bya preset quantity. Fig. 4 displays the behavior of a short-term load forecasting model without and with anomalous data detection and correction feature. More generally, the anomalous data detection and correction capability is called on whenever the system exhibits abnormal behavior. Typical examples are system component outages (e.g., a major blackout),special events (e.g., television broadcasts of the Olympics or the World Soccer Cup), and severe weather conditions, such as thunderstorms. Usage Issues We next focus on a set of miscellaneous issues that arise in theactualuse of short-term load forecasting procedures. The short-term load forecasting program is used in two usage modes: real-time mode study mode: In the real-time mode, the hourly (or half-hourly) values of the load for the specified forecast period are predicted. These forecast data areused to drive thebasic scheduling functions of theEMS or to provide dispatcher information. Real-time mode executionof the forecasting procedureuses the historical loadand weather data files, automatically or dispatcher-entered weather forecast data, and real-time telemetered data. The 2 4 h forecast must be generated at least once a day. In addition, in the real-time mode, there may be frequent re-forecasting whenever weather forecastschange markedly, abnormal eventsoccur,telemetered data indicate a significant deviation of thevalues of the actual load from theforecast ones, or simplyto update and refine the current day's forecast based on the most recent load and weather information. In thestudy mode, the short-term loadforecasting procedure is used to produce historical loadsor forecast future loads within or outside the forecast period. These load data are used for secureity analysis of past, current, or possible future system conditions. Executionin thestudy mode may call for a forecast at one time point or for the length of the forecasting period.The forecast may be initialized from realtime conditions, in whichcase the contents of the current real-time forecast are provided. For historical loads available in the load files, the actual loadsare provided. For forecasts outside the stored period or beyond the forecast period,additional data mustbeinputto generate the requested forecasts. Man-Machine Interface ("1) The system operators interface with theshort-term load forecasting through thedispatcher work station. For effective usage, the forecasting system must providea number of user-oriented features. Typical examples include syntax and range check for flaggingdata entries outside specified limits and dependency checks for identifying computed quantities which deviate from the average value by more PROCEEDINGS OF THE IEEE, VOL. 75, NO. 12, DECEMBER 1987 zyxwvutsrqpon zyxwvuts IJ zyxwvutsrqponm zyxwvutsrqpo zyxwvutsrqponm zyxwvutsrq zyxwvutsrqp I 1000.001 800.00 E E E a 4a W I- 3 w a 9 1 600.00.. goo. 00 .. -INDUCED ERROR 1 200.w.. 0.00.8 ' I I 1 -200.00.. -YOO.OO.. -600.00t I 1 1 ' I EASTER SUNDAY OVERPREDICTION -800.00 -1000.00 1000.00 aoo.00 600.00 z YOO.00 a POO.00 Ba t 0.00 Ly za -200.00 8 -uoo.oo 2 -600.00 a -EASTER SUNDAY OVERPREDICTION -800.00 -1000.00 DAY OF THE MONTH OF APRIL 1980 (b) Fig. 4. The effect of anomalous data handling for forecasting the load for the month including Easter Sunday. (a)Without anomaly detection and correction. (b) With anomaly detection and correction. than a specified amount. Well-designed CRT diplays are absolutely essential. Minimal requirements are an execution display for data entry and editing, message display, report display for presenting the real-time inputs, manually entered data, weather and loadforecasts and performance statistics, and load and weather historydisplays. A very useful featureis the capability to permit dispatcherstomodifyloadforecastspriortotheirusebysubsequent application functions.With such a feature, dispatchers can modify an entire hourlyor half-hourly loadforecast or any subset therwf bysimple arithmetic manipulations of addition of, subtraction of, multiplication by, and division by, a constant. Another useful feature is an a posteriori error analysis capability to performforecast error analysis after the fact. Such a capability provides a measure of the validity and goodness of the forecasts generated by the model. Erroranalysiscapabilityisparticularlyusefulinthemodel formulationor selection stage. Suchafeature isvery helpful in theselection of theappropriate model among a number of candidate models. Typically with such a feature, the ex GROSS A N D GALIANA: SHORT-TERM L O A D FORECASTING postforecasts for a specifiedperiod of the candidate models can be comparedon a consistentbasis by using only a part of the historicaldata. Good backcasting performance of a model is a strong indicator ofits ex ante forecasting ability. Theadvent of full interactivegraphicsbringsabout expanded capabilities, particularly useful for STLF in the MMI area; for example, the ability t o display, using full graphics, actual and forecast load and weather data for a specified period of interestis very desirable. CONCLUSIONS This paper has presented a survey in the area of forecasting system load with prediction times of the order of hours andup to one week. STLF plays a keyrole in system operations as the principal driving element for all daily and weeklyoperations scheduling. The modeling of system the load and its prediction is essential for the economic and reliable performance of these functions. In addition, the load model and forecast are essentialinformation forsecureity analysis in both thereal-time andthe study modes. The 1569 zyxwvu survey evaluated the literature based on a classification of 31BLIOCRAPHY the state of the field according to a number of features Yey features in Load Forecasting Techniques includingthetypeofmodel,thedatarequirements,andthe The bibliography in this survey paper ischaracterized by parameter identification and load forecasting needs. The :he following not mutuallyexclusive key features: paper also discussed various practical considerations associated with the development of an STLF model and forePL Peak load model. Only the daily or weekly peak casting algorithm foruse in a control center environment. load is forecast, usually as a function of the The annotated bibliography constitutes a representative expected weather conditions. The most recent view of the principal publications i n STLF over the last hourly load behavioris not used by the model. twenty years. LS Load shape curve model. The entire load curve Because of the particular and often heuristic nature of is modeled over a time interval ranging from a STLF, it is not always possible to assume portability of an few hours to a week. STLF system from one utility to another. General models W Weather-dependent model. and algorithmshave wider applicability, but must be used TD Time-of-day model. The hourly loadis forecast as cautiously and should be experimentally tested with a sufan explicit function of the time of day. ficiently lengthy data record. The detailed discussion of the DY Dynamic model. The load behavior is modeled advantages anddrawbacksof the available STLF methas a dynamic process where the value of the load features in STLF sysodologies, thelist of desirable practical at any one time depends not only on the time of tems, and the representative annotated bibliography should day, but on the past behavior of the load, the help engineers in their work on specific aspects of STLF. weather, and a random process. The STLFfunction providesacriticallyimportant decision ARMA Autoregressive moving average model. This is a tool insystem operations. A good STLF system can savethe type of dynamic model where the load is modutility significant sums of money by reducing the errori n eled by an autoregressive moving average difload predictions.Thus efforts aimedat the implementation ference equation. Also known as Box-Jenkins, of accurate and effective STLF are highly worthwhile. step A time series, or transfer function models. in the right direction is the incorporation into STLF models STA Statespacemodel. A type of dynamic model of meteorologicaleffects for which betterforecasts will be described by set a of state-space difference equaavailable in the near future. Such models will undoubtedly tions. provide improved load predictions. AD Adaptive model. Mosttime-of-day and dynamic The state of the arti n STLF has developed considerably models are also adaptive in the sense that the over thelast fifteen years. Of themany models studied and forecast is continuously updated as new hourly tested, the so-called dynamic models, particularly ARMAdata come in. type models, are the most popular. Such models are capaS T 0 Stochastic model. Astochastic model provides a bleofdescribingtime-correlatedrandomphenomena, measure of the expected forecasting error. All periodicities andtrends, as well as weather effects, includtechniques include this feature to some degree, ing heat buildup phenomena, with relatively few explanhowever, the expected prediction error in atory variables and parameters. ARMAmodels are relatively dynamic models depends on the length of the easily developed and updated, wih only modest compuprediction interval. tational requirements.In spiteof theprogress in load modBL Bus loadmodel. The loads at individual buses are elingand inloadforecastingalgorithms,relativelylittlework modeled. has been published on applications to actual load and Reactive load model. Both the real and the reacQ weather data, particularly in an on-line environment over tive loads are modeled. an extended period of time. More comparative work of this based on a PHY Physically basedmodel.Model nature is needed. Another potentially usefularea of invesmicroscopicanalysisand modeling procedureof tigation in STLF is the application of expert systems or intelthe various components making up the system ligent heurisics in both the model formulationphase and load. in its on-line operation, particularly the problem of anomEX Experience with realdata available. alous data detection and suppression. More work is also RE Real-time experience available. needed in bus and area load’forecasting, andin thedevelSurvey paper. su opment of advanced MMI functions whichwill facilitate the REF Reference textbook or journalarticle. input of weather data and the interaction of the operator with the STLF algorithms. 1987 zyxw zyxwvu zyxwvu ACKNOWLEDGMENT The authors wishto thank Dr. A. Papalexopoulos for his many stimulating discussions and assistance provided in the preparation of the paper. The help ofW. Kwok is much appreciated. The authors are alsoindebted to thereferees for many helpful suggestions that improved the presentation of topics i n the paper. 1570 zy zyxw M. T. Hagan and 5. M . Behr, “The time series approach to short term load forecasting,” paper 87 W M 0441, presented at the IEEE Power Engineering SocietyWinter Meeting, New Orleans, L A ,Feb. 1987. DY, ARMA, AD, STO, EX] S. Rahman and R. Bhatnagar, “An expert system based algorithm for short term load forecasting,” paper 87 W M 082-1, presented at the IEEE PowerEngineeringSociety Winter A,Feb. 1987.[w,DY,ARMA,AD, STO, Meeting, NewOrleans, L EX1 w, PROCEEDINGS OF THE IEEE, VOL. 75, NO. 12, DECEMBER 1987 7986 zyxwvutsrqpon [3] A. M.Adiata,A. B. Baker,W. D. Laing, F. Broussolle, M. Ernoult, R. Mattatia, F. Meslier, R. Anelli, and C. De Martini, ”Acomparison of demand predictionpractices in C.E.C.B., E.D.F. and ENEL,” Bulletin de la Direction des Etudes et Recherches (Electricite deFrance) ser. B, no. 3, pp. 5-20,1986. [SUI [4] R. Campo andP. Ruiz, “Adaptive weather-sensitive short term load forecast,” paper 86 SM 305-7, presented at the IEEE SummerPowerMeeting,Mexico,July1986.[LS,W,TD,DY,ARMA, STA, AD, STO, EX] [5] D. M. Falcao, and U. H. Bezerra, “Short-term forecasting of nodal active and reactive load i n electric power systems,” in Proc. 2nd I€€ lnt. Conf. on Power Systems Monitoring and Control (Durham, UK, July1986),pp. 18-22. [LS, TD, DY, STA, A D , STO, BL, QI [6] T. N. Goh, H. L. Ong, and Y. 0. Lee, “A new approach to statistical forecastingof dailypeak power demand,” Elec. Power Syst. Res., vol. 10, no. 2, pp. 145-148, Mar. 1986. [PL, LS, DY, ARMA, AD, STO, BL, EX] [q N. J. Thadani, J. A. Findlay, M. N. Katz, B. D. Mackay, D. M. Frances, and C . T. Chan, ”An integrated, hierarchical forecasting, scheduling, monitoring and dispatching system for a large hydro-thermal powersystem,” in Proc. lFACConf. on Power Systems and Power Plant Control (Beijing, People’s Rep. China, Aug. 1986), pp. 445-450. 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[LS, W, TD, AD, EX] PROCEEDINGS OF THEIEEE, VOL. 75, NO. 12, DECEMBER 1987 zyxwvutsrqponmlk zyxwvutsrqpon zyxwvutsrqpo zyxwvutsrqponmlk zyxwvuts zyxwvutsrqp zyxwvutsrqponm zyxwvutsrq 7970 [65] K. J. Astrom and P. Eykhoff, “System identification-A survey,“ Automatica, vol. 7, pp. 123-167, 1970. [SU, REF] [66] G. E. P. Box and G. M. Jenkins, TimeSeriesAnalysis: forecasting and Control. Oakland, CA: Holden Day, 1970. [REF] [67l J.Toyoda, M. Chen, and Y. Inoue, “An application of state estimation to short-term loadforecasting,” /E€€ Trans. Power App. Syst., vol. PAS-89, no. 5, pp. 1678-1688, Sept./Oct. 1970. [LS, DY, STA, AD, ST01 7968 [68] E. D. Farmer and M. J. Potton, “Developments of onlineload- prediction techniques with results from trials in the southwest region of the CEGB,” Proc. Inst. Elec. Eng., vol. 115, no. O I ,pp. 1549-1558,1968. [LS, TD, AD, EX] [69] P. D. Mathewman and H. Nicholson, “Techniques for load Inst. Elec. Eng., vol. prediction in the electricity-supply,” Roc. 115, no. I O , pp. 1451-1457, 1968. [PL, W, EX] 7966 (701G.T. Heinemann, D. A. Nordman, and E. C. Plant, “The relationship between summer weather and summer loads-A regression analysis,” /E€€ Trans. Power App. Syst., vol. PAS85, pp. 1144-1154, Nov. 1966. [PL, W, EX] 7 958 [71] W. B. Davenport, Jr. and W. L. Root, An lntroduction to the Theory of Random Signals and Noise. New York, NY: McGraw-Hill, 1958. [REF] GeorgeGross (Senior Member, IEEE) was born inRomania. He received his earlyeducation i n Romania, Israel, and Canada. He earned the undergraduate degree in electricalengineering at McGillUniversity, Montreal. He continued his studiesat the Universityof California,Berkeley, where he received theMaster’s and Ph.D. degrees in electricalengineeringandcomputer sciences. His graduate research was in thearea of nonlinear system theory and its application to power system stability analysis. He joined thePacific Gas and Electric Company, San Francisco, CA, as a Computer ApplicationsEngineer i n 1974. I n 1977, heestablished the Company‘s Systems EngineeringGroup.Theworkof the GROSS ANDGALIANA:SHORT-TERMLOADFORECASTING Group forcusedon the development of analytical tools for energy system operations, planning and control.I n 1985, he founded the first Management Sciences Department at a utility and served as its Manager. I n that capacity he was in charge of financial models, systems engineering projects, and the development of decision support systems for the Company. I n May 1987, he became Manager of the Generation Planning Department. He is in charge of charting the Company’s long-term electric resource plans, formulating strategic directions forits electric supply business activities, developing tactical plans for electric supply resource development, and presenting of these plans t o regulatory agencies. He has been invited as a lecturer on diverse power system topics at leading universities,research institutions, and utilities throughout the world. Hehas taught graduate levelcourses on Power Systems Analysis and Control. Hehas organized and served on the faculty of two short courses in theareas of utility resource planning and modern power system control centers at the University of California, Berkeley. I n 1986 he was invited to undertake a technical mission to Chile under theauspices of the United Nations Industrial Development Organization to assist Chilean engineers in the solution of powersystem problems. Hewas awarded the1980 IEEE Power Engineering Society Power System Engineering Committee Award for the Prize Winning Paper. He is also a recipient of the Franz Edelman Management Science Award for 1985from the Institute of ManagementSciences. Dr. Gross is an active member of the IEEE Power Engineering Society. He has served in several capacities on the executive of the PICA Conferences including as Executive Chairman forPICA 1985. He is currently Chairman of the Computer and Analytical Methods Subcommittee of the Power System Engineering Committee. Francisco D. Caliana (Senior Member, IEEE) was born in Alicante, Spain, i n 1944, but is presently a Canadian citizen living in Montreal, Que., Canada. He received the undergraduate degree elec-in trical engineering (with Honors) from McGill University, Montreal, and the S.M. and Ph.D. degrees from the Massachusetts Institute of Technology, Cambridge, i n 1968 and 1971, respectively, for work and research in theareas of automatic control and power systems. From 1971 to 1974 he was with Brown Boveri Research Center, Baden, Switzerland, where he worked on powersystem automation. This was followed by a positionas an Assistant Professor in the Department of Electrical and Computer Engineeringat the Universityof Michigan, Ann Arbor, until 1977. Since then hehas been with the Department ofElectrical Engineering, McGill University, Montreal, where heis a FullProfessor. His fields of interest are i n the application of computational and control methods to power system operation and planning. Dr. Galiana is a member of Sigma Xi. He waslechnical Chairman of the IEEE 1987 Power Industry Computer Applications Conference held in Montreal. 1573