[studies in computational intelligence] trends in neural computation volume 35 || short term...

Chapter 16

SHORT TERM ELECTRIC LOADFORECASTING: A TUTORIAL

Elias Kyriakides and Marios PolycarpouDepartment of Electrical and Computer EngineeringUniversity of Cyprus, Nicosia 1678, Cyprus

[email protected], [email protected]

Abstract Short term load forecasting is an important tool for every electric utility.A significant number of operating decisions are based on short term loadforecasts. The accuracy of these forecasts leads to significant savingsin operating costs and to an enhanced system reliability. The technicalliterature is abundant with techniques and approaches for performing orimproving short term load forecasting. A number of approaches workwell with certain power systems or certain geographical areas, whilethey fail for some other systems due to the nature of the electric loaddemand: it is complex, highly nonlinear, and dependent on weather,seasonal and social factors. This chapter provides a tutorial introductionto the short term load forecasting problem and a brief summary ofthe various approaches that have been proposed, from conventional tocomputational intelligence methods.

Keywords: computational intelligence, electric load forecasting, expert systems,fuzzy systems, genetic algorithms, neural networks, power system,regression, short term, time series

1. IntroductionThe electric power system is often described as the most complex

system devised by humans. The power system is a dynamic systemcomprising generators, transformers, transmission and distribution lines,linear and nonlinear loads, and protective devices. These componentsneed to operate synergistically in a manner that ensures the stability ofthe system even in cases of disturbances.

E. Kyriakides and M. Polycarpou: Short Term Electric Load Forecasting: A Tutorial, Studies

www.springerlink.com cin Computational Intelligence (SCI) 35, 391–418 (2007 )

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392 E. Kyriakides and M. Polycarpou

One of the most important aspects of the operation of a power sys-tem is the fact that the system response follows closely the load require-ments. An increase or decrease in the system load leads to a respectiveincrease or decrease in power generation. This on-demand power gener-ation creates the need to have available a sufficient amount of generationresources. Hence, a priori knowledge of the load requirements enablesthe electric utility operator to optimally allocate the system resources.

The ability to forecast electricity load requirements is one of the mostimportant aspects of effective management of power systems. The qual-ity of the forecasts directly impacts the economic viability and the relia-bility of every electricity company. Many important operating decisionssuch as scheduling of power generation, scheduling of fuel purchasing,maintenance scheduling, and planning for energy transactions are basedon electric load forecasting.

There are three different types of electric load forecasting dependingon the time horizon and the operating decision that needs to be made:short term, medium term, and long term forecasting. In general, longterm forecasting is needed for power system planning, medium termforecasting is needed for maintenance and fuel supply planning, whileshort term forecasting is needed for the day to day operation of thepower system.

In the deregulated environment, all the involved entities need to per-form load forecasting on a continuous basis. Generation companies,transmission companies, independent system operators (ISOs), and re-gional transmission organizations (RTOs) plan, negotiate, and operatebased on the load forecasts they have at their disposal.

This chapter gives a general description of a power system, motivatesthe discussion on electric load forecasting, and describes both traditionaland computational intelligence based forecasting methods for short termelectric load forecasting.

2. Description of the Electric Power SystemThe power system is a dynamic and complex energy conversion system.

It comprises three stages: generation, transmission, and distribution.The power system transports energy from distant generating stationswhere it is produced, to the load centers through the transmission net-work. The energy is then distributed to the individual loads through anetwork of radial and ring distribution circuits. Distributed generationfrom independent power producers (IPPs) or from small-scale renewableenergy sources may be connected to the network at the transmission orthe distribution stage.

Short Term Electric Load Forecasting 393

Generation

from renewable

energy sources

Industrial

customer Residential customer

with renewable

generation

Commercial

customerResidential

customer

FOSSIL FUEL OR

NUCLEAR POWER PLANT

HYDRO

POWER STATION

WIND POWER

STATION

Tie line to

interconnected system

GENERATION

TRANSMISSION

DISTRIBUTION

Distribution

transformer

Transmission substation

Figure 16.1. A typical configuration of an electric power system.


A typical configuration of a power system is shown in Fig. 16.1. Theconfiguration of the power system may be different from region to regiondepending on the geographical area, the interconnections, the penetra-tion of renewable resources, and the load requirements as to the levelof reliability desired. Nevertheless, power systems have the same ba-sic characteristic: they are three-phase systems operating at constantfrequency and constant voltage (with small deviations due to load fluc-tuations and system faults).

Power systems consist of multiple generating sources designed to (a)ensure adequate geographical dispersion so as to reduce the transmissiondistance from load centers (and thus reduce power losses on cables sincelosses are proportional to the length of the cables) and (b) to provideenough redundancy in the form of spinning reserves (if a generator fails, anumber of other generators that operate below their maximum capacitycan pick up its share of the load without the need to wait for othergenerators to be committed to the system). The latter is an operatingdecision that depends on short term electric load forecasting: capacitymargins are fixed by the respective regional coordinating councils orregulatory bodies (typically a percentage of the forecasted peak demand)and hence inadequate load forecasting may jeopardize the security of thesystem by reducing the spinning reserve of the system.

Perhaps the most challenging aspect of the operation of power systemsis their ability to meet load requirements instantaneously and at alltimes. This is not the result of a magic trick. And it is certainly nottrue that energy travels from the generating station to the load thatis situated hundreds of kilometers away at the blink of an eye. Whathappens is rather a transaction between the generator and the load.The load requests electric power which is duly supplied to it. However,this extra power requirements cause the generator to slow down, thusreducing the system frequency. Automatic generation control (AGC), afeedback control mechanism, senses the frequency drop and opens thevalve to allow more steam to flow through the turbine and thus increasethe speed to its nominal value. This procedure completes the cycle andmore electric power is supplied at the same frequency.

It is clear from the above example that the generator should have theability to provide the extra load that may be requested at any time.Due to the significant load fluctuations in the various time periods ofeach day, it is imperative for the system operator to be aware of thedemand that will be expected in the next few hours so that appropri-ate planning can be performed. Generators (especially fossil fuel gen-erators) need a considerable time to be synchronized to the networkif they are initially decommitted (in the range of hours). As shown in


Figure 16.2. Electric load demand for the power system in Cyprus on 6 July 2004(measurements used with permission from the Electricity Authority of Cyprus).

Fig. 16.2, significant load variations occur in intervals less than one hour.For further reading on the power system issues discussed in this section,the reader is encouraged to look at Wood and Wollenberg [1] andKundur [2].

3. Load Forecasting TypesForecasting is an important tool that is used in a number of applica-

tions besides electric load forecasting [3]. Examples of such applicationsinclude forecasting of stock prices [4], crude oil spot prices [5], electricityprices in pool-based electric energy markets [6, 7], financial time series[8], as well as forecasting of inflation, gross domestic products and othereconomic and social indices [9, 10].

As discussed previously, there are three types of electric load fore-casting: short term, medium term, and long term forecasts. Electricutilities need to perform all three types of forecasts since each one isimportant for different aspects of the operation, economics, and securityof the power supply.

Short term load forecasting (STLF) covers a period of one hour to oneweek ahead. It is used for the day-day operations of the power system,such as hydro-thermal coordination, scheduling of energy transactions in


deregulated markets, scheduling of start-up times of new units, load flowanalysis, and power system security studies. STLF is an essential com-ponent of Energy Management Systems (EMS) as it provides the inputdata for load flow and contingency analysis [11]. Typically, three maincategories of input variables are used for STLF: seasonal input variables(load variations caused by air conditioning and heating units), weatherforecast variables (temperature, humidity, wind, and cloud cover), andhistorical data (hourly loads for the previous hour, the previous date,and the same day of the previous week). It should be noted that specialattention must be given to distinguish weekdays from weekends and hol-idays as the load pattern varies considerably in each type of day. Thetypical outputs of short term forecasts are the estimated average loadfor every hour in the day, the daily peak load, and the daily or weeklyenergy generation. Fig. 16.3 shows a general input-output configurationof a short term load forecasting system and its major uses.

Medium term load forecasting covers a period of a few weeks up to oneyear. It is used for scheduling maintenance, scheduling of the fuel supply,

Short term load

forecasting model

AUTOMATIC

GENERATION

CONTROL

Off-line data

System

parameters

Weather data

Historical load

dataWeather

forecast

STLF SYSTEM

Dispatcher

workstation

Short termforecast

Manuallysupplied data

MAJOR USES

Scheduling functions

Hydro-thermal coordination

Scheduling of energy transactions

Unit committment

Off-line studies

Load flow analysis

Power system security studies

Real-time

load data

Figure 16.3. An input-output configuration of a STLF system and its major uses[21].


and minor infrastructure adjustments. Ever since the deregulation of theelectricity sector, medium term load forecasting has gained even moresignificance since the market players need to sign annual contracts forenergy transactions. Any significant deviations of the forecasted quan-tities from the actual demand lead to financial penalties. The mediumterm forecasting algorithm needs to take into account seasonal patterns(for example, the average load demand is larger in July than in March),weekly patterns, and economic and demographic factors such as the Con-sumer Price Index and the Average Salary Earning. The medium termload forecast provides estimates of the peak load and the daily energyrequirement [12, 13]. In some respects, short and medium term loadforecasting are complementary, and a certain level of coordination be-tween the two is necessary. Each electric utility needs to ascertain thatthe short term decisions are consistent with the operation objectives thatarise from the medium term forecasting study [14].

Long term load forecasting typically covers a period of twenty years.This type of forecast is needed for planning purposes such as construct-ing new power stations, increasing the transmission system capacity, andin general for expansion planning of the electric utility. Expansion plan-ning requires a significant time period since it involves feasibility studies,expropriation of land, design and operational analysis, and internationalcompetitions for the supply of equipment. Long term forecasting takesinto account the population growth, industrial expansion, local area de-velopment, the gross domestic product, and past annual energy con-sumption. The output of this type of forecast is the annual peak loaddemand and the annual energy demand for the years ahead [15–17].

4. Why is Short Term Electric Load Forecastingso Important?

Short term electric load forecasting is the cornerstone of the operationof today’s power systems. In the past, experienced system operators wereable to predict the electric load requirements within acceptable ranges(based on their experience with the particular power system). This is notso easy nowadays. The complexity of loads, the system requirements,the stricter power quality requirements, and deregulation have mandatedthe development of advanced load forecasting tools. Short term loadforecasting is so important that no electric utility is able to operate inan economical, secure and reliable manner without it.

STLF provides the input data for load flow studies and contingencyanalysis. These are the studies performed by the utilities to calculate thegenerating requirements of each generator in the system, to determine


the line flows, to determine the bus voltages, and to ensure that thesystem continues to operate reliably even in cases of contingencies (lossof a generator or of a line).

STLF is also useful in other off-line network studies where the util-ity engineers prepare a list of corrective actions for different types ofexpected faults. Such corrective actions may be load shedding, purchas-ing of additional power from neighboring utilities, starting up of peakingunits, switching off interconnections and forming islands, or increasingthe spinning and standby reserves of the system.

The advent of deregulation has highlighted the need for more accurateand faster short term load forecasts. The STLF is not only importantfor system operators (as was the case before deregulation), but it is alsoessential for market operators, transmission owners, and other marketparticipants. The STLF is used to schedule adequate energy transactionsand prepare operational plans and bidding strategies. The adequacy ofsystem resources and the reliability of the network depend on all theabove mentioned actions.

Due to the involvement of an increased number of players in the energymarket, load forecasting has become a significant component of energybrokerage systems [18]. Any forecasting errors would therefore lead toincreased operational costs and reduced revenue. The reason is that un-derprediction of load demand leads to a failure to provide the necessaryreserves and thus, higher costs ensue due to the use of expensive peak-ing units. Respectively, overprediction of load demand wastes resourcessince more reserves are available than needed. Increased reserves causeincreased operating costs [19].

Short term load forecasting is a vital part of the day-day operationsof every utility and every market player. STLF is involved in a num-ber of key elements that ensure the reliability, security, and economicoperation of power systems: (a) actions such as the negotiation of bi-lateral contracts between utilities and regional transmission operators,(b) studies such as economic dispatch, unit commitment, hydro-thermalcoordination, load flow analysis and security studies, and (c) operationssuch as scheduling of committing or decommiting generating units andincreasing or decreasing the power generation.

5. Short Term Load Forecasting MethodsA large number of methods and techniques have been developed to

perform electric load forecasting. The research in this field is as activetoday as it was ten years ago due to mainly two facts: the deregulation ofthe power systems, which caused new challenges in the forecasting prob-lem and the fact that no two utilities are the same, which necessitates


detailed case study analysis of the different geographical, meteorological,load type, and social factors that affect the load demand.

Traditionally, short term load forecasting is performed using methodssuch as time series models, regression-based techniques, and Kalmanfiltering. These methods are sometimes combined with the experienceof the operator to draw conclusions on the proper scheduling of gen-eration. In the last few years, artificial neural network approaches aswell as other computational intelligence methods emerged as potentiallypowerful tools in electric load forecasting.

For ease of presentation, short term load forecasting techniques are di-vided into two major categories: conventional or classical approaches andcomputational intelligence based techniques. The first category includesmethods such as time series models, regression models, and Kalman fil-tering based techniques. Computational intelligence based techniquesinclude expert systems, artificial neural networks, fuzzy inference andfuzzy-neural models, and evolutionary programming. This section offersan overview of the various methods used in short term load forecasting.

5.1 Conventional or classical approachesThere is an extensive literature on conventional techniques for the

forecasting of electricity demand. Some of these approaches are estab-lished methods and are used by electric utilities in their day-to-day op-erations. A number of researchers have compiled extensive surveys onload forecasting. Some of these surveys have focused on neural networksfor short term load forecasting [20], some on other techniques for shortterm load forecasting such as time series and regression models [21], whilesome others provided a general look at all types of load forecasting [22].

Time series models Time series techniques model the load demandas a function of historical data. These techniques assume that the datafollow a certain stationary pattern that depends on autocorrelation,trends in the data, and daily, weekly and seasonal variations. Time seriesmodels appear in the literature in different forms such as Box-Jenkins,time series, stochastic models, autoregressive moving average (ARMA),autoregressive integrated moving average (ARIMA), autoregressivemoving average with exogenous variables (ARMAX), autoregressive inte-grated moving average with exogenous variables (ARIMAX), and state-space models.

The basic idea in time series prediction of load demand is to modelthe load as the sum of two terms,

z(t) = yp(t) + y(t), (16.1)


where yp(t) is the contribution to the system load that depends on thetime of day and the normal weather pattern for that day, while y(t) is aresidual term that models the deviation of the weather pattern from theexpected load pattern and random correlation effects [23]. The residualterm may be modeled by,

y(t) =n∑

i=1

aiy(t − i) +nu∑

k=1

mk∑

jk=0

bjkuk(t − jk) +

H∑

h=1

chw(t − h), (16.2)

where uk(t), k = 1, 2, . . ., nu represent the inputs that depend on weatherand w(t) is a zero-mean white random process that represents uncertaineffects on load demand and random load behavior. The goal is to identifythe parameters ai, bjk, ch and the integers n, nu, mk, and H by fitting themodel using historical load and weather data [23].

Amjady uses ARIMA to tune the unknown parameters using past val-ues of the load demand and past values of the inputs, and then uses themodel to forecast the load demand for unknown points of the operatingsystem [24]. Espinoza et al. use a periodic autoregression model to de-velop a set of 24 “seasonal” equations with 48 parameters each [25]. Theset of equations is extended to include exogenous variables that describethe temperature effects and the monthly and weekly seasonal variations.Fan and McDonald [26] and Huang and Shih [27] use ARMA models,while Hagan and Behr [28] use the Box-Jenkins method [29] for shortterm load forecasting.

In general, time series methods give satisfactory results if there is nochange in the variables that affect load demand (such as environmental orsocial variables). If there is an abrupt change in any of these variables,then time series methods are not as accurate. Time series methodsassume that the load demand is a stationary time series and has normaldistribution characteristics. When the historical load data deviate fromthis notion, the time series forecasting accuracy decreases considerably.Further, since there is a need to use a considerable amount of historicaldata and a large number of complex relationships, time series techniquesrequire a significant computational time and may result in numericalinstabilities [30].

Regression models Regression models are widely used for electricload forecasting. The load is represented as a linear combination of vari-ables related to the weather factors, day type, and customer class. Thecoefficients of these variables are estimated using least squares or otherregression techniques. Temperature is the most important informationfor electric load forecasting among weather variables and it is typically


modeled in a nonlinear form. To obtain higher accuracy, a number ofother weather variables are typically introduced in the regression modelsuch as the wind velocity, the humidity and the cloud cover.

Haida and Muto [31] present a regression based daily peak load fore-casting method that is combined with a transformation technique togenerate a model that utilizes both the annual weather-load relation-ship and the latest weather-load characteristic.

Charytoniuk et al. [32] propose a method that is derived from a loadmodel that is described by a multivariate probability density function(pdf) of a number of factors that affect the load demand such as timeof day and temperature. The load forecast can then be determined asa conditional expectation of the load for the given factors. The loadforecast is the local average of observed past loads in a local neighbor-hood of the given factors. Results from a test system were comparedto two artificial neural network models (one for weekdays and one forweekends). The mean errors of the two methods were comparable, withthe regression-based forecasting errors being slightly higher.

Ramanathan et al. [33] developed a number of regression models forforecasting hourly system loads. El-Hawary and Mbamalu [34] describea method to forecast short-term load requirements using an iterativelyreweighted least squares algorithm. Papalexopoulos and Hesterberg [35]and Ruzic et al. [36] describe other regression based techniques for shortterm load forecasting.

Although regression-based methods are widely used by electric util-ities, they suffer from a number of drawbacks. Due to the nonlinearand complex relationship between the load demand and the influencingfactors, it is not simple to develop an accurate model. On site tests ofregression-based methods have shown a deterioration in performance incases where the load deviates due to sudden weather changes and loadevents [11]. One of the main reasons for this drawback is that the modelis linearized in order to estimate its coefficients. However, the load pat-terns are nonlinear and it is not possible to represent the load demandduring distinct time periods using a linearized model.

In order to partially alleviate this drawback, it is often necessary toemploy sophisticated statistical techniques to enable the forecaster tocapture the load deviations due to sudden weather changes and specialevents. Finally, as with time series methods, regression-based methodsmay suffer from numerical instability.

Kalman filtering based techniques Kalman filtering [37–39] isbased on a particular method of characterizing dynamical systems calledstate-space representation or state-space model. The Kalman filter is an


algorithm for adaptively estimating the state of the model. The prob-lem formulation of the Kalman filtering approach includes the presenceof additive stochastic terms influencing the state and output variables.In the case of load forecasting, the input-output behavior of the systemis represented by a state-space model with the Kalman filter used toestimate the unknown state of the model.

A number of algorithms in the literature use the Kalman filter to per-form short term load forecasting. Sargunaraj et al. [40] use the Kalmanfilter to predict the average hourly loads that are used to adjust the val-ues of the peak load estimates. Park et al. [41] developed a state spacemodel for the nominal load, whose parameters are identified throughKalman filtering. It is assumed that the noise vectors are independentzero-mean Gaussian sequences. The effect of weekend days is representedthrough a “type load” model which is added to the nominal load esti-mated through Kalman filtering; the “type load” is determined throughexponential smoothing. To account for the modeling error, a “residualload” is also calculated. Trudnowski et al. [42] describe a method toperform very short term load forecasting using slow and fast Kalmanestimators. The authors separate the total load demand into a deter-ministic component (dependent on factors such as time of day, day ofweek, and weather factors) and a stochastic component that is mainlydependent on random variations of customer requirements and intercon-nection loading. One of the key difficulties in the use of Kalman filteringbased techniques for load forecasting is to identify the state-space modelparameters.

5.2 Computational intelligence based techniquesIn an attempt to improve the performance of conventional load fore-

casting techniques in predicting load patterns, researchers have focusedmuch of their attention to computational intelligence based techniques.The search for increased accuracy in load forecasts is mainly driven bythe transformation of the power industry into a competitive market andthe fact that for every small decrease in forecasting error, the operatingsavings are considerable. It is estimated that a 1% decrease in forecast-ing error for a 10 GW electric utility can save up to $1.6 million annually[43]. Some computational intelligence based techniques have proved tobe promising, while others still require a significant amount of researchin order to reach the stage of being used as a forecasting tool by utilities.

Artificial neural networks Artificial neural networks are based onmodels of biological neurons. They attempt to capture some of thekey properties on which the remarkable computation power of the brain


is based. These properties include massive parallelism among a largenumber of simple units, learning capabilities, robustness in the presenceof noise, and fault tolerance with respect to the overall network operatingreasonably well even if some of the units (neurons) are not performing asexpected. There has been significant research on the connection betweenartificial neural networks and biological neural models with the objectiveto better understand the functionality of the brain. There has also beena lot of work on the use of artificial neural networks in applications suchas approximation and modeling, pattern recognition and classification,signal and image processing, and feedback control. In most of theseapplications, the use of artificial neural networks is carried out withoutparticular emphasis on its biological counterpart.

Artificial neural networks have been extensively used for time seriesprediction and forecasting [44–47]. The main idea behind the use ofneural networks for forecasting is the assumption that there exists anonlinear function that relates past values and some external variablesto future values of the time series. In other words, future values of a timeseries are assumed to be an unknown function of the past values as wellas some external variables that influence the time series. Neural networkmodels are used to approximate this unknown function. The training ofthe neural network is performed by using past historical data that maybe available. In general, the input-output function being approximatedby the neural network is multivariable (multiple inputs and multipleoutputs), where the inputs represent the past historical data and theexternal variables influencing the time series and the outputs are futurevariables that we are trying to predict. There are three steps that need tobe considered in using neural network models for time series prediction:(i) designing the neural network model; e.g, selecting the type of neuralnetwork that will be employed, the number of nodes and the numberof adjustable parameters or weights, (ii) training the neural network –this includes selecting the training algorithm, the training data that willbe used and also the pre-processing of the data, (iii) testing the trainednetwork on a data set that has not been used during the training stage –this is typically referred to as neural network validation.

Due to their nonlinear approximation capabilities and the availabilityof convenient methods for training, artificial neural networks is amongthe most commonly used methods for electricity load forecasting, espe-cially during the last ten years. Chen et al. [48] present an artificialneural network model for predicting the hourly electric loads up to oneweek ahead of time. They use both past load as well as the temperatureas input variables. Peng et al. [49] use an adaptive linear combiner called“Adaline” for one-week ahead prediction. Papalexopoulos et al. [11]


employ a large network with several inputs for predicting the electricityload at the Pacific Gas & Electric Co., with special emphasis on han-dling holidays. Dash et al. [50] use a neural network with a learningalgorithm that is based on an adaptive Kalman filter. In their work,Bakirtzis et al. [51] present a neural network model for forecasting 1-7days ahead of time. Special emphasis is given to handling holidays andreducing the prediction error in the days following the holidays. Chowand Leung [52] employ a neural network based on a nonlinear autoregres-sive formulation, which takes into account several weather parameters asinputs to the neural network approximator. Ranaweera et al. [53] pro-vide a method for calculating the mean value of the load forecast and theconfidence levels for the given predicted load. AlFuhaid et al. [54] use acascaded neural network learning algorithm for predicting load demandsfor the next 24 hours. Kiartzis et al. [55] describe their experience indeveloping a forecasting system based on neural network models, whileYoo and Pimmel [56] develop a self-supervised adaptive neural networkfor load forecasting.

Senjyu et al. [57] propose a neural network methodology for one-hour-ahead prediction based on a simplified network structure, which corre-sponds to a correction term to a selected similar day data. It is wellknown that the weather plays a key role in electric load demand. How-ever, since forecasting is made ahead of time, the weather is not exactlyknown. In their work, Taylor and Buizza [58] investigate the use ofweather ensemble predictions in order to enhance the load forecastingaccuracy. Abdel-Aal [59] attempts to improve load forecasting perfor-mance using network committees, which is a technique from the neuralnetwork literature. An extensive review and evaluation of neural net-work methodologies for short-term load forecasting is provided in [20].

Expert systems Expert systems are a set of programs, rules andprocedures that attempt to emulate the decisions that would have beentaken by a human expert operator at a given situation. An expert systemis a computational model that comprises four main parts: a knowledgebase, a data base, an inference mechanism, and a user interface. Theknowledge base is typically a set of rules that are derived from the ex-perience of human experts. These rules are formulated in the form,

IF < statement > THEN < decision >.

The data base is a collection of facts obtained again from the humanexperts and information obtained through the inference mechanism ofthe system. Optimally, this data base increases with time as the inter-action between the users and the system intensifies. The inference mech-anism is the part of the expert system that “thinks”. The expert system


makes logical decisions by using a control strategy while using infor-mation from the data base and knowledge from the knowledge base.The most common control strategies are the forward chaining and thebackward chaining [60].

The advantages of expert systems are that they can make decisionswhen the human experts are not available, they can retain knowledgeafter a human expert retires, reducing the work burden on human ex-perts, and that they can make fast decision in cases of emergency. Often,expert systems are a component of an overall hybrid model to improvethe system performance. For example, they are often combined withneural networks to make the overall system adaptive i.e., to allow it tolearn from new experiences. Another frequently encountered combina-tion is expert systems with fuzzy logic.

Rahman and Bhatnagar [61] proposed an expert system based algo-rithm for short term load forecasting. The proposed algorithm preparesfour sets of forecasts (one for each season) which are based on histor-ical relationships between weather and load in each season. Since theboundaries between seasons are not clear cut, the expert system runs aseparate forecast for each season, and the most accurate of the two ispresented to the user. Other variables that are taken into considerationto perform the forecast are the day of the week and the temperature.The data base of the expert system comprises the year, month, data,hour, day type, temperature, and load data.

Rahman and Hazim [62] developed a short term load forecasting al-gorithm that combines knowledge based expert systems and statisticaltechniques. The proposed algorithm uses a limited set of historical datathat resembles the target day. This data set is then adjusted to lo-cation specific conditions to make the method site-independent. Suchadjustments include the annual load growth, load offset on specific days,or the effects of extreme weather. The initial estimates of the targetload used in the next step of the algorithm are the inputs to the pair-wise comparison algorithm [63] and then regression is used to fine-tunethe initial estimates of the load demand. The algorithm was used toperform short term load forecasting for four different electric utilitiesin the United States. The daily average errors for weekdays rangedfrom 1.22% to 2.70% and lied in approximately the same range as othertechniques cited in the paper. Weekend forecast errors, however, weretypically higher than their weekday counterparts. The authors analyzethe knowledge acquisition and rule development process in constructingthe expert system in a subsequent paper [64].

Jabbour et al. [65] and Ho et al. [66] describe short term load forecast-ing expert systems developed for a specific utility and a power systemrespectively.


Fuzzy inference and fuzzy-neural models A relatively new re-search venture is the combination of fuzzy logic techniques and artificialneural networks to develop forecasting algorithms that merge some of thesuperior properties of each methodology. Artificial neural networks arenot typically able to handle significant uncertainty or to use “commonsense knowledge” and perform accurate forecasts in abnormal situations.In contrast, fuzzy logic techniques have the ability to manage success-fully sudden changes in load demand.

The combination of fuzzy logic and artificial neural networks creates ahybrid system that is able to combine the advantages of each techniqueand diminish their disadvantages. The main advantages of the hybridsystem are the ability to respond accurately to unexpected changes inthe input variables, the ability to learn from experience, and the abilityto synthesize new relationships between the load demand and the inputvariables.

The fuzzy-neural forecasters are typically combined in four differentways [67]:

(a) the neural network performs the forecasting and the fuzzy logicsystem is used to determine the final output [68]

(b) the data are preprocessed using fuzzy logic to remove uncertaintiesand subsequently a neural network is used to calculate the loadestimates [69]

(c) integrated fuzzy-neural systems where the hidden nodes of theneural network correspond to individual fuzzy rules which areadaptively modified during the training process [70]

(d) separate neural and fuzzy systems that perform a forecast of differ-ent components of the load; these components are then combinedat the output to calculate the total load demand.

Srinivasan et al. [71] developed a parallel neural network-fuzzy expertsystem to perform short term electric load forecasting. The authorstrain Kohonen networks that act as pattern matchers identifying theload curves for different days. The networks predict the load pattern fora month and then the fuzzy system manipulates the neural outputs sothat the variables and membership functions that relate weather dataand special events to load changes are taken into consideration when thefinal output is computed.

Kim et al. [72] propose a hybrid model that forecasts the load demandfor special days. The authors define as special days the public holidays,consecutive holidays, and days preceding and following holidays. Five


different artificial neural network models are developed, one for eachtype of special day. The neural networks are trained using historicaldata from days of similar type and the forecasted load curve for eachday is obtained. Subsequently, two fuzzy inference models are used toforecast the maximum and minimum loads of the special days. Theresults of both parts of the hybrid system are then combined to forecastthe hourly loads for the special days. The average percent relative errorfor this method was shown to be 1.78% while the maximum error was9.31% for special days for a period of one year. The authors comparetheir results with two other methods for the same period. As comparedto the method that was used by the electric utility at the time, therewas a significant improvement in the accuracy of the forecasts.

A number of other papers in the literature describe different ap-proaches towards the forecasting of load demand from one hour to oneweek ahead [73–81].

Evolutionary programming and genetic algorithms A numberof load forecasting techniques available in the literature use genetic meth-ods combined with one or more other methods such as regression orneural network approaches. Two examples of genetic methods are evolu-tionary programming and genetic algorithms. Both methods are inspiredfrom biological processes such as natural selection and survival of thefittest. The main difference between genetic methods and traditionaloptimization techniques is that genetic methods search from a popula-tion of solutions instead from a single point. In each iteration the poorsolutions “die out” and the “better” solutions are recombined with othersolutions (or mutated by changing them slightly) so that new solutionsare generated shifting the population towards the region of the optimalsolution [82, 83].

The main advantages of genetic methods are their global convergence,the parallel search capabilities, and their robustness. These methods donot get stuck in local minima and can perform well even with noisydata. However, these benefits come at the cost of slow convergence,thus significant computation periods are needed.

One of the applications of evolutionary programming in short termload forecasting is in connection with time series models [84]. The prob-lem that is typically faced with this type of models is that the traditionalgradient search may stall at local minima and therefore an incorrectmodel is obtained. The authors of this paper use the autoregressivemoving average with exogenous variables (ARMAX) model to representthe relationship between the load and the temperature (considered tobe the only influencing factor). Then, the evolutionary algorithm is


implemented to force the elements of the population of possible solu-tions to compete with each other and create offspring that approach theoptimal solution. The competition for survival is stochastic: the mem-bers of the population (parents and offspring) compete with randomlyselected individuals based on a “win” criterion. The members of thepopulation are then ranked according to their score and the first half ofthe population become the parents of the next generation. The processstops once the fitness values of the new generation are not improved sig-nificantly. This method has been used to forecast the load demand for apower system. The results have shown an improvement in the forecasterror as compared to the traditional gradient search method.

Evolutionary programming techniques have also been used with fuzzyneural networks [85] and fuzzy autoregressive moving average withexogenous input variables (FARMAX) models [86].

The other type of genetic method, genetic algorithms, has also foundits way into the research towards deriving short term load forecastingtechniques [87, 88]. Maifeld and Sheble [89] present a load forecasterthat uses a genetic algorithm to optimize the weights of an artificialneural network. The authors use elitism, reproduction, crossover, andmutation to improve the quality of their population (the members ofwhich are the weights in binary form). Load forecasts compared toother methods show an improvement in the average and maximum error.However, in some cases the solution was stuck in local minima resultingin significant forecast errors. To alleviate this problem, the authors usedanother technique to restart the process and obtain improved solutions.However, the technique leads to an increased computational intensity.The increased computational period is one of the shortcomings of geneticmethods. For the interested reader, Leung et al. [90] explain the tuningof the structure and of the parameters of a neural network through agenetic algorithm.

Support vector machines Support Vector Machines (SVM) is a newlearning methodology which has attracted significant attention in com-putational intelligence and machine learning research [91–93]. Duringthe last few years, there has been a lot of work on the use of SVMfor data classification. More recently, SVM have also been applied todata regression, which is often referred to as Support Vector Regres-sion (SVR). The basic idea behind SVR is to use a nonlinear mappingin order to transform the original data into a high-dimensional fea-ture space, and then to do linear regression in this higher dimensionalspace. In other words, linear regression in a high dimensional fea-ture space corresponds to nonlinear regression in the low dimensional


input space. Once this transformation is achieved, optimization tech-niques are used for solving a quadratic programming problem, whichyields the optimal approximation parameters.

One of the applications of SVR is the problem of time series predic-tion and forecasting [94, 95]. So far there have been just a few attemptsto utilize SVR for short-term load forecasting. Chen et al. [96] ap-plied a support vector regression technique to a specific load forecastingproblem for predicting the daily maximum load for the next 31 days.This problem was the theme of a forecasting competition organizedby EUNITE network (EUropean Network on Intelligent TEchnologiesfor Smart Adaptive Systems), and in fact the algorithm described bythis reference was the winning entry. The competition organizers pro-vided the following data: (i) electricity load demand, recorded every halfhour from 1997 to 1998; (ii) average daily temperatures from 1995 to1998; and (iii) the date of holidays from 1997 to 1999. The competitorswere required to predict the maximum daily values of electricity load forJanuary 1999. The SVR methodology used several experimental studiesto enhance the predictive performance of the algorithm, and paid par-ticular attention to the historical data segments that were selected fortraining [96]. More recently, Espinoza et al. [97] used Least SquaresSupport Vector Machines (LS-SVM) [93] for load forecasting. In thisstudy, the authors use the Nystrom approximation and the primal-dualformulation of LS-SVM. The resulting algorithm is used to predict theelectricity load 24-hours ahead, based on data coming from a local lowvoltage sub-station in Belgium.

6. ConclusionsShort term load forecasting is an important component of the oper-

ating decisions and the market operations of every electric utility in theworld. For electric utilities that are operating in a deregulated environ-ment, short term load forecasting is even more critical as it is a guidingforce for their bilateral contracts and the pricing of electric energy. Theload demand is a nonlinear combination of a number of variables thatare dependent on weather, social, or seasonal variations; thus, the aimto accurately predict the short term load demand is not a trivial task.

The non triviality of the forecasting problem has lead to a consider-able amount of methods for predicting the load demand. These meth-ods can be classified into conventional and computational intelligencetechniques. Conventional methods include time series, regression, andKalman filtering based techniques. Computational intelligence meth-ods include artificial neural networks, expert systems, fuzzy inference,


evolutionary programming, and genetic algorithm techniques. A numberof methods are hybrid: they combine two or more techniques to improvethe load forecast by combining the good aspects and downplaying thedisadvantages of each technique.

Even to date, it is not clear which method is the best. Certain meth-ods work well in some cases while they are inferior in some other cases.The accuracy and speed of the forecast depends on the level of detail usedin modeling, the selection of the appropriate influencing factors (such associal trends and weather variables), and the level of testing that themethods undergo. A lot of techniques are developed having in mind acertain geographical area, or a certain power system. Although the ideasused in the development of each forecaster can be applied to mostly allpower systems, most of the methods do not perform well when they aregeneralized due to the weight placed on different influencing factors.

Short term load forecasting is an active research field that is ex-pected to continue to thrive in the coming years. Computational in-telligence methods are expected to be the driving force for the researchperformed in this field, due to the ability of these methods to general-ize and to model nonlinear phenomena. Perhaps, the one factor thatcan distinguish a good short term load forecasting method is the wideand extensive testing that the developed forecast tools will be subjectedto. The appropriate tuning of the parameters and the inclusion of allinfluencing factors in the prediction process along with the extensivetesting may hold the key to better, more accurate, and faster short termload forecasts.

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