IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007 333
Short-Term Bus Load Forecasting of PowerSystems by a New Hybrid Method
Nima Amjady, Member, IEEE
Abstract—In this paper, a new hybrid method is proposed forshort-term bus load forecasting of power systems. The method iscomposed of the forecast-aided state estimator (FASE) and themultilayer perceptron (MLP) neural network. The FASE forecastshourly loads of each bus by means of its previous data. Then theinputs and outputs of the FASE are fed to the MLP neural net-work. In other words, the MLP is trained to extract the mappingfunction between the inputs and outputs of the FASE (as inputfeatures) and real loads as output features. The proposed hybridmethod has been examined on a real power system, a part of Iran’spower network. The obtained results, discussed comprehensively,show that the hybrid method has better prediction accuracythan the other methods, such as MLP, FASE, and the periodicauto-regression (PAR) model.
Index Terms—Bus load forecast, forecast-aided state estimator(FASE), neural network (NN).
I. INTRODUCTION
SHORT-TERM load forecasting (STLF) is a key issue forreliable and economic operation of power systems. STLF
usually consists of prediction of load demand for one hour upto one week ahead [1]. Previously, most efforts in the area ofSTLF have been concentrated on the prediction of the systemtotal load [1]–[3], due to its key role in the fundamental oper-ational functions such as unit commitment, economic dispatch,interchange evaluation, scheduled maintenance, and security as-sessment. Today, however, importance of bus load forecast isalso becoming evident, especially with introduction of advancedoperational procedures, e.g., security constrained unit commit-ment (SCUC), and tendency to deregulation process in manycountries. SCUC incorporates the network constraints in the unitcommitment (UC) problem to obtain a financially viable genera-tion dispatch that is physically feasible [4]. Execution of SCUC,for instance, by independent system operator (ISO) in the elec-tricity markets, requires bus load forecast to perform the powerflow and determination of possible violations of security con-straints, e.g., limits of transmission flows and bus voltages.
Bus load prediction is also required to evaluate security status,i.e., stability margins, of the power system for the future hoursand days. For instance, voltage stability margin (VSM) is de-pendent on the selected load scenario, including load level anddistribution [5]. In [6], a forecast-aided state estimator (FASE)has been used in the continuation power flow to determine load
Manuscript received February 16, 2006; revised June 29, 2006. Paper no.TPWRS-00083-2006.
The author is with the Department of Electrical Engineering, Semnan Uni-versity, Semnan, Iran (e-mail: [email protected]).
Color versions of Figs. 1–4, 6, and 7 are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPWRS.2006.889130
increase direction of the power system in the state space. Then,based on the forecasted load scenario, voltage collapse pointof the power system is estimated. As another application, ad-equacy assessment of power systems in the real composite form(generation and transmission) necessitates bus load forecast [7].This forecast is also required to predict transmission charges andprobable congestions in the power systems. Besides, bus loadforecasting is essential to feed analytical methods utilized fordetermining energy prices in the electricity markets [8].
Due to the above reasons, some researchers in the recent yearspaid attention to this matter. In [9], a hybrid approach utilizinga fuzzy system and artificial neural network has been presentedfor bus load forecasting. Sinha and Mandal proposed a dynamicstate estimator in the form of extended Kalman filter (EKF) withinclusion of second-order terms for bus load forecasting [10].They also incorporate a neural network (NN) in the predictionstep of the state estimator. However, computation time of theirmethod was very large, and so it can not be used for onlineapplications in the real power networks. The authors try to solvethis problem by using a hierarchical model at the filtering stepof their state estimator and presented their approach in [11]. In[12], a linear model has been proposed for bus load predictionin distribution networks. This model relates load measurementswith normalized load curves (state variables) for the individualcustomer groups. In [13], application of periodic time series forbus load forecasting has been presented. Besides, clustering ofdaily load profiles has been evaluated in this paper.
In spite of all performed researches, bus load forecasting stillencounters high prediction errors due to complexity of bus loadtime series in a real power system. For instance, in [13], meanabsolute percentage error (MAPE) of bus load forecast for somebuses is in the range of 10% to 20%. Besides, selection of suit-able input features usually is a key issue for forecast processes(like STLF and price prediction) and has been paid less atten-tion for bus load forecast. By considering importance of busload prediction, especially in the deregulated power systems,it is seen that this matter still demands more attention. In thispaper, a new method is proposed for load forecasting of trans-mission buses. The contribution of this paper can be summa-rized as follows:
1) selection of suitable input features for bus load predictionbased on evaluation of the signal behavior;
2) presentation of a new hybrid method composed of FASEand NN for bus load prediction;
3) design of a new data flow in the proposed method for busload forecasting.
The remaining sections of this paper are organized as follows.A brief review of the problem and its difficulties are presented
334 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007
in Section II. Then, the rationale behind the proposed hybridmethod is explained. In Section III, details of the proposed tech-nique, including its components, are introduced. Moreover, ap-plication of the method for bus load forecast is explained in thissection. Obtained numerical results for a part of Iran’s powernetwork are presented and discussed in Section IV. A brief re-view of this paper is in Section V.
II. PROBLEM DESCRIPTION
In this paper, prediction of hourly load of transmission busesis considered, defined as the sum of energy consumption of allfeeders of the bus (including transmission, subtransmission,and medium voltage feeders) within an hour. For instance,transmission feeders (in Iran’s power network, 400-kV and230-kV feeders) can supply large factories, such as largeiron foundries. Subtransmission feeders (in Iran’s power net-work, 63-kV feeders) may supply different parts of a city ormedium-sized factories. Medium voltage (20 kV in Iran’spower network) feeders of a transmission bus usually supplyinternal consumption of the substation. Active power of eachof these feeders is recorded by means of measuring devices,including CT, PT, and power transducers. Then, the remoteterminal unit (RTU) submits the recorded values to the relateddispatching center, where the SCADA system calculates hourlyenergy consumption from the submitted values by means ofpulse accumulator mechanism [14]. Subsequently, the SCADAstores these hourly values in the real time and then historicaldatabases. The recorded values for the hourly energy con-sumption of each transmission bus are used in this paper forprediction of its values for the next hours. In other words, allexaminations of this paper have been performed with real dataof transmission buses, available in the dispatching centers of thepower system. Although it is possible to see an erroneous valuein the databases of a SCADA system, however, the number ofthese incorrect values is very limited and their deviations areusually small for today’s SCADA systems due to high accuracyof measuring and telecommunication devices and use of baddata detectors [14]. So, bad data cannot significantly affectperformance of a power application software (PAS) functionlike bus load forecast in today’s dispatching centers.
Prediction of bus loads in a real power network can be morecomplex than forecasting of the system total demand. This is dueto the fact that the bus load time series has more outliers (un-usual loads), volatility, nonlinearity, and high-frequency com-ponents than the system total demand. In a real power network,especially in the vast countries, load variations of different busesmay neutralize or attenuate effect of each other on the total de-mand, resulting in less variations and especially less outliers ofthe system load. For instance, different climatic conditions canbe seen in different parts of Iran’s interconnected power net-work. In the hot months of the year, load demand of tropicalregions, located in the southern part of the country, highly in-creases. This results in the large and sudden variations in theload of buses located in this area, especially in the noon andevening hours of the day, due to more use of air conditioningdevices, i.e., electrical cooling devices. As an example, load de-mand of some buses in these areas shows more than 100% in-crease in the noon and evening hours with respect to the early
morning hours. On the other hand, load demand of the cold andtemperate regions in this period of the year has no consider-able increase or even changes in the opposite direction, i.e., de-creases. In temperate regions, few electrical cooling devices areused, and so, the residential load of these regions slightly in-creases. In the cold areas, people not only do not use electricalcooling devices but also remove electrical heaters, and so, loaddemand of these regions has no increase or even decreases. So,the sudden and large variations in the hourly loads of buses in thesouthern part are observed as the softer and more smooth vari-ations of the total load. An opposite situation can be seen in thecold months of the year, when the effect of adverse increase ofcold regions demand (due to consumption of electrical heaters)on the system load is attenuated by the load of mild and tropicalareas.
As another instance, there are some buses in Iran’s powernetwork (like many other power systems) that mainly supplyindustrial loads such as large factories. Peak load of these busesoccurs in the mid-hours (about 9 A.M. to 3 P.M.) of the day,when demand of industrial consumers suddenly increases. Onthe other hand, major component of demand of many buses isresidential load. Demand of these buses adversely increasesin the early hours of night. For a better illustration, load timeseries of three different buses of Iran’s power network in aweek are shown in Figs. 1–3, respectively. Fig. 1 shows loadseries of a 230-kV bus named Kashan. This bus supplies a citywith residential customers as the major load component plussome consumption related to offices. Fig. 2 is related to another230-kV bus named Behrang. This bus mainly supplies a ruralarea, where residential and agricultural consumptions (e.g.,feeding the water pumps) constitute its major load components.Fig. 3 shows load series of a 400-kV bus named Mobarake,which mainly supplies an industrial region. These figures showthree examples of three different load series in a week, athourly values starting at 00:00 h on Saturday until 24:00 onFriday (in the Islamic countries, the weekend is Friday). Theconsidered week is from Nov. 12, 2005 to Nov. 18, 2005. Thesubstations Kashan, Behrang, and Mobarake are geographicallylocated at the center of Iran’s country, which is an strategicarea of the national power system. Indeed, most load centersof Iran’s power system with different load patterns (such asthose mentioned above) are located in this area, which in turnincreases importance of bus load forecast for the substations ofthe area. This part of the country has temperate and relativelydry weather conditions. Whole data of the three substationsused in this paper have been gathered from a dispatching centerof Iran’s transmission network named Central Area OperatingCenter (CAOC) equipped with PN40 SCADA system [14].More details about the selected substations plus their locationon the map of Iran’s power network can be found in [15].
In Fig. 1, daily cycles as well as weekend effects are vis-ible. Moreover, intra-day effects, such as morning peak (smallerpeak), early night peak (larger peak), and mid-night valley, canbe seen. In spite of high-frequency components, e.g., in the fasttransition from the early night hours to the valley hours, the se-ries has regular pattern. Fig. 2 shows less seasonal behavior andmore irregularities than Fig. 1, due to more volatility of the agri-cultural load than the residential load. In Fig. 3, daily peak load
AMJADY: SHORT-TERM BUS LOAD FORECASTING OF POWER SYSTEMS BY A NEW HYBRID METHOD 335
Fig. 1. Load series of Kashan 230-kV bus within a week.
Fig. 2. Load series of Behrang 230-kV bus within a week.
Fig. 3. Load series of Mobarake 400-kV bus within a week.
of the 400-kV bus Mobarake for the working days, i.e., Saturdayto Wednesday, occurs in the mid-hours of the day. Consumptionof this bus in the other hours is mainly related to some resi-dential load supplied by this substation. On Thursday, the daybefore the weekend, a smaller and narrower peak is seen dueto some industries working for the first half of the day. On theweekend, no industrial peak load is seen and the small increase
Fig. 4. Load series of Iran’s power system within a week.
in the consumption, occurring in the early hours of the night, isdue to the residential load. Again, high-frequency componentsof the bus load time series can be seen from Fig. 3, e.g., in therapid variation from the early morning hours to the mid-hours ofthe working days. Moreover, load pattern of the Mobarake hassomewhat more irregularities than the Kashan. Load behaviorof various types of buses, such as Figs. 1–3, combine with eachother, resulting in the softer changes of the system load within aday. For a better illustration, load curve of Iran’s power system,in the same interval, is shown in Fig. 4. As seen, less volatilityand outliers plus more seasonality and regular patterns are exis-tent in the system load than the three previously shown bus loads(especially, Figs. 2 and 3). It is noted that Iran is a developingcountry, and so, its major load component is still the residentialload. Thus, the system load pattern is relatively similar to Fig. 1.
In a real power network, there are many bus load patterns,usually including rapid variations and outliers. So, the expertoperators of the dispatching centers usually have less experi-ence about the bus loads than the single series of the systemload. Moreover, the unbundling between generation, transmis-sion, distribution, and supply induced by the market liberaliza-tion has led to less knowledge of network managers about busloads [13]. Thus, the prediction methods based on the experi-ence, such as expert systems, fuzzy methods (for instance, fuzzyneural networks and fuzzy time series), and modified ARIMAtechnique [1], [9], [16] are less applicable for the bus load fore-casting than the system load forecasting. Recently, some re-searchers tried to decompose target signal through Fourier se-ries and wavelet transform [8], [17]. However, bus load time se-ries usually has multiple seasonalities and high-frequency com-ponents, as shown in Figs. 1–3. Thus, many terms appear inthe output of the decomposition techniques, which complicatesthese techniques and requires much computational burden. Inthis paper, a new hybrid method composed of FASE and NN ispresented for bus load forecasting. FASE is based on the ana-lytical evaluation and NN learns numerical examples of the pasthistory without requiring experience of the expert operators andhigh computational burden. Besides, a new data flow is con-sidered in the proposed method to modify the accuracy of thepredictions.
336 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007
III. PROPOSED HYBRID METHOD
FASE is a linear predictor and somewhat similar to EKF [18].However, bus load time series has a hard nonlinear behavior,and so, a linear predictor cannot provide accurate predictionsover the whole forecast horizon. Thus, a forecast tool with ca-pability of modeling nonlinear behaviors is also required. NNsare good candidates for this purpose. Here, MLP neural networkis used due to its flexibility as a nonlinear predictor and ease ofimplementation [8]. However, tracking a nonstationary signalwith rapid variations, e.g., the bus load time series, for NNs isusually very hard, and large deviations may be seen in the esti-mation of the NN. On the other hand, if the MLP has an initialforecast following the trend of the target signal, then it can learnbehavior of the signal much easier. In this case, the MLP mustlearn the difference between the two trajectories instead of theglobal values of the target trajectory. However, the initial trajec-tory must have a close correlation with the target one; otherwise,it has no use and can even be misleading for the MLP. In [6], ithas been shown that FASE is a good candidate to provide suchan initial estimation for bus load prediction, and so, it is consid-ered here with some modifications.
To introduce the proposed approach for bus load prediction, atfirst, its input features are presented. Generally for a forecastingprocess in the power system, e.g., STLF and price forecast, acombination of exogenous variables or cross-regression part andhistory of the signal or auto-regression part has been used [19].An important group of exogenous variables for bus load fore-cast consists of weather parameters and especially temperature.For system load forecast, some research works and industrialsoftware packages consider temperature and sometimes a fewother parameters (such as moisture) of one or a few load cen-ters of the system [1], [14], [16], [20]. However, in this paper,these exogenous variables have not been used for bus load fore-cast due to the following reasons. Major component of load de-mand of some buses in the power system, such as Mobarake inFig. 3, is industrial load, not sensitive to weather parameters.Besides and more importantly, there are usually a large numberof transmission buses in a real power network, and climate con-ditions of all of them are not recorded in the SCADA systemsor even in the meteorological substations. For instance, thereare more than 500 transmission buses in Iran’s power network.However, only temperature of three large cities, representativeof three different climate conditions (warm, mild, and cold),are recorded, including many deficient measurements [1]. Aftertraining and in the real forecast conditions, where the predictionof the weather parameters are required [8], [13], lack of reliabledata becomes more serious. Poor prediction of the climate con-ditions can lead to the large errors in the STLF. Even for thesystem load forecast, recently some researchers do not use theweather parameters, due to unavailability of reliable predictionof these parameters [21], [22].
To model the multiple seasonalities characteristic of the busload time series, an implicit modeling has been considered here,since the NNs and especially MLP tend to this kind of modelingand can better learn it. To model the effect of a seasonal patternin the prediction of an hourly load, load of the same hour inthe previous period(s) (and sometimes a few hours around it)
are considered as the input features. For instance, to considerthe effect of daily, weekly, and monthly seasonalities, load ofthe same hour in the previous day(s), week(s), and month(s),respectively, can be taken as the input features. Besides, for dailyseasonality, in addition to (load of 24 h ago),and can be also considered and similarly for the otherperiods. In addition to the seasonal patterns, short-run trend ofthe load time series is another effective factor for the STLF.To model the trend of the load signal, consumption of someprevious hours are considered, owning a high correlation withthe next hourly load. With consideration of all the above factors,the following set of input features has been considered for busload prediction:
(1)
In (1), the first four terms consist of information about the trendof the signal. The next six features contain information aboutthe daily seasonality (up to two days ago), while the later nineterms are related to weekly seasonality (one to three weeks ago).Farther days and weeks have less correlation with the targethour and so are not considered here. Besides, seasonalities withlonger periods like monthly and annual periodicities are less ef-fective for short-term bus load forecast, especially in a devel-oping country like Iran where load pattern of many buses rapidlyvaries. So, they are ignored here. By means of the selected inputfeatures, the hybrid method can discriminate different types ofdays, e.g., weekday, Thursday, weekend, holiday, working daybefore or after a holiday, working day between a holiday and aweekend, each one owning a specific load pattern. For instance,by information of the trend, the hybrid method can distinguishpublic holidays containing a sudden decrease of load demand(especially for the industrial regions), except probably for a fewinitial hours. For Thursdays (the day before the weekend), inaddition to the trend information, daily and weekly seasonalitycan be also effective. In other words, the hybrid method can rec-ognize Thursday as a day with two previous weekdays and asimilar load profile (half day high, half day low) in the previousweeks. Due to these reasons and to avoid decreasing number ofeffective training samples (which degrades the training phase),for each bus, only one hybrid method is considered.
More input features from the trend or different seasonalitiesmay contain more information content than the selected set.However, for more input features, both the NN and FASE re-quire more training samples, and so, a longer training periodmust be considered. Load pattern of transmission buses usu-ally varies with time (for instance, by commissioning of newindustries or variation of weather conditions). So, farther timeperiods may have poor correlation with the next hours and bemisleading for the hybrid method. Besides, in the NN applica-tions, if a large number of inputs are used, the number of inputnodes as well as interconnecting weights will increase, and theconvergence rate of the training mechanism will be extremelyreduced and may even diverge. Moreover, unrelated input fea-tures can be misleading for the construction of the I/O mapping
AMJADY: SHORT-TERM BUS LOAD FORECASTING OF POWER SYSTEMS BY A NEW HYBRID METHOD 337
function. So, in this paper, a minimum set of input features withan acceptable discrimination capability and information contentis used for bus load forecast. The selected input variables plusoutput feature, i.e., bus load of the next hour, constitute formatof training samples of the FASE.
Consider the general form of the nonlinear prediction model[10], [11], [18]
(2)
(3)
where and are the state and measurement vectors,respectively, at time instant (hour) . The state vector con-sists of hourly energy consumption of the considered transmis-sion buses. represents the vector of control actions. and
describe the state transition process and measurement equa-tion, respectively. and are white Gaussian noise vectors withzero mean and covariance matrices and , respectively [6],[10], [11]. For the nonlinear model (2) and (3), the EKF algo-rithm provides the linear minimum variance estimate of the statevector , as follows:
(4)
(5)
where and are predicted and filtered state vectorat time instant , respectively. and indicate the statetransition matrix and Kalman gain at time instant , respectively[10], [11], [18]. Here, the filtering step, i.e., (5), is not appli-cable, due to the following reasons. For bus load forecasting,the proposed candidates for the measurement vector or arevoltage magnitudes, active and reactive power flows and injec-tions, or a combination of these factors [6], [10], [11]. However,for the future hours, the values of these factors are unknownand prediction of them may be even more complex than theprediction of the bus loads. Besides, the SCADA systems usu-ally save these quantities (especially the voltage magnitudes) astrend without defining the hourly value of them. Moreover, themeasurement function does not have a simple form like loadflow equations. Without the measurement vector , the filteringstep reduces to
(6)
and so, for the prediction step, we will have
(7)
The unknown matrix and vector can be obtainedfrom the regression process [1], [6]. However, (7) can be modi-fied to enhance the prediction accuracy. The state transition ma-trix in (7) relates load of all transmission buses in the previoustime instant to those of the next one. Load demand of transmis-sion buses usually has poor correlation with each other [10],[11], since these buses usually supply different areas and indus-tries with long distances among them. Thus, the off-diagonalelements of the state transition matrix can be much smallerthan the diagonal elements. On the other hand, load of each bushas strong correlation with its previous values, indicated in (1).
Fig. 5. Data flow of the proposed hybrid method.
So, a better state transition model can be obtained by decoupling(7) for different buses and replacing with the input fea-tures of (1) for each bus. Thus, the prediction step becomes asfollows:
(8)
where and indicate load of bus at time instant andits input features according to (1), respectively. is the numberof buses. After training (by means of the regression), the ad-justable parameters of the FASE model, i.e., and , can beobtained for each bus, and then, the FASE can forecast the fu-ture hourly bus loads. These parameters are also dependent onthe time. In other words, they can be updated (i.e., the trainingprocess can be repeated) once every hour, day, week, month,etc., dependent on the variation rate of the bus load pattern. Ifthe load pattern of a bus rapidly varies, such as a newly commis-sioned bus, the training process of the FASE for that bus mustbe performed more frequently. However, for a bus with a stableload pattern, output of the training process, i.e., and , canbe kept constant for a long time. This adaptable training processis an advantage of the proposed FASE model.
Inputs of the FASE according to (1) and its output, i.e., pre-diction of the bus load for the future hour, are considered as theinput features of the NN, the second part of the hybrid method.Structure and data flow of the proposed hybrid method areshown in Fig. 5. As seen, the FASE part is trained to constructa mapping function from the input features based on (1) to theoutput variable, i.e., bus load of the next hour. The NN part istrained with the input features of (1) plus the information con-tent provided by the FASE. It is noted that the NN is a nonlinearforecast tool and is basically different from the FASE linearmodel. From the linear algebra viewpoint, outputs of the FASEand NN are linearly independent. So, the information contentof the FASE can be so useful for the NN as an initial forecast.As seen from Fig. 5, the NN has one output feature dedicatedto forecast of bus load for the next hour, like FASE. However,prediction accuracy of the final forecast provided by the NN,which is also output of the hybrid method, is better than theinitial forecast of the FASE. The NN part of the hybrid methodhas MLP structure and Levenberg–Marquardt learning algo-rithm, which is one of the most efficient training mechanismsfor the estimation tasks. The Levenberg–Marquardt algorithm
338 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007
trains an neural network 10 to 100 times faster than the usualgradient descent back propagation method [23]. This algorithmis an approximation of Newton’s method, and it computesthe approximate Hessian matrix. Mathematical details of thisalgorithm can be found in [23] and [24].
IV. NUMERICAL RESULTS
The proposed hybrid method has been examined on threetransmission buses Kashan, Behrang, and Mobarake, and ob-tained numerical results are shown in Tables I–III, respectively.In this examination, four weeks of year 2005, including Feb-ruary 12 to 18, May 14 to 20, August 13 to 19, and November12 to 18, representative of four seasons of the year, have beenconsidered, respectively. This is an usual way for presentation oftypical results of a forecast method for the whole year [17], [25],[26]. Weekly mean error (WME) and weekly peak error (WPE)of the proposed hybrid method (FASE and NN), single FASE,single NN, and periodic autoregression (PAR) are representedin the tables. The three other methods were previously consid-ered by the other researchers for bus load prediction [6], [10],[11], [13]. In each cell of these tables, the first number indicatesWME and the second one is WPE. The last row of each table isthe average of the four weeks. WME and WPE are well-knownstatistical indexes for evaluation of forecast methods, defined asfollows:
(9)
(10)
where and are actual and forecasted bus load ofhour , respectively. The mean and max operators are executedfor 168 h or one week. For the sake of a fair comparison, sim-ilar conditions have been considered for all methods. Bus loadsusually are nonstationary signals with rapidly varying patterns.Time series of the electricity prices usually have the similarcharacteristic, and a usual training period for the price forecastmethods consists of 48 days ago [17], [25]. This training periodis also considered here for the four prediction methods. Thus,each forecast method totally has training sam-ples. Besides, all considered methods have the same input fea-tures of (1). For load forecast of each bus in each week, tunableparameters of all methods are updated once every day. In thisexamination, each bus load forecast process is executed for onestep ahead or one hour ahead prediction. In other words, for pre-diction of each hourly load, all its previous values are assumedto be known. It is noted that today’s SCADA systems (used inthe dispatching centers of the transmission networks) by regularpolling of the RTU devices can easily compute energy consump-tion of each substation once every hour or a fraction of hour [14].Thus, assumption of availability of bus load data up to the lasthour is a completely practical assumption, which also has beenused in [8] and [13]. In the one hour ahead prediction, each fore-cast stage for each bus has only one test sample.
As seen from the WME values, prediction of the PAR isslightly better than both the FASE and NN due to considerationof a separate time series for each hour of the day in the PAR
TABLE IWME AND WPE OF FOUR WEEKS FOR BUS KASHAN
TABLE IIWME AND WPE OF FOUR WEEKS FOR BUS BEHRANG
TABLE IIIWME AND WPE OF FOUR WEEKS FOR BUS MOBARAKE
model [13]. The proposed hybrid method presents a better solu-tion than all the other methods. Besides, for more volatile loadpatterns where the forecast error of all methods increases (i.e.,the load series of Behrang and Mobarake), difference betweenaccuracy of the proposed technique with the other methods in-creases. Another important point, which can be seen from theobtained results, is that the FASE and NN can cover weak pointsof each other for bus load prediction, resulting in more fore-cast capability of the proposed method. For instance, FASE isa better solution for Kashan and Mobarake, while NN has lessforecast error for Behrang. Besides, it is observed that predic-tion accuracy of the proposed hybrid method has a meaningfulrelation with the error of its components. When the FASE parthas a high forecast error, it can introduce little improvement forthe NN part or even be misleading for it (e.g., the May weekfor Behrang). On the other hand, if the FASE part has a highprediction accuracy while the forecast of the NN part is poor,the hybrid method may have no significant improvement withrespect to the FASE or even be poorer than it (e.g., the May andAugust weeks for bus Kashan). Indeed, the most increase in theprediction accuracy of the hybrid method in comparison withits components occurs between these two extreme cases whenthe FASE and NN parts have relatively close forecast errors, in-cluding most test cases.
Although WME is a useful indicator, it cannot describe thestability of the predictions. To cover this deficiency, an indexof uncertainty, i.e., WPE, is also considered here, and its re-sults are also shown in Tables I–III. It can be seen that averageWPE of the proposed method is also less than the other exam-ined methods. The hybrid method has more stable results andless sharp errors in comparison with its components. As seenfrom Tables I–III, the largest WME and WPE of the proposed
AMJADY: SHORT-TERM BUS LOAD FORECASTING OF POWER SYSTEMS BY A NEW HYBRID METHOD 339
Fig. 6. Actual load curve (dark), load forecast of the proposed method (grey),and its error (grey, at the bottom) for bus Mobarake in November week.
method is related to bus Mobarake in the November week. InFig. 6, actual load curve (dark), load forecast of the proposedmethod (grey), and its error (grey, at the bottom) for this testcase are shown. It can be seen that even for the worst test case,the method follows the trend of the load curve and its accuracyis reasonable. Only some deviations are seen in a few sharp vari-ations and outliers of the bus load series. Indeed, the forecast ofthe proposed method resembles a low-pass approximation of thetarget signal.
The previous examination was repeated with the iterative pre-dictions for the next 24 h, instead of one hour. In the new exami-nation, when bus load of a hour is forecasted, it is used asfor the load prediction of the next hour, and this cycle is repeateduntil the bus loads of the next 24 h are predicted. In other words,bus load data are updated once every day. So, in this case, WMEis indeed the average of seven daily mean errors. In the one dayahead prediction, for each forecast stage of each bus, there are24 test samples, in which their output features are sequentiallypredicted. In a practical power system, dispatchers require bothkinds of bus load forecast (one hour ahead and one day ahead).Due to space limitation, detailed results of this examination arenot presented. However, as a brief comparison with the previousone, WME and WPE values of all forecast methods generally in-crease in this examination, since a part of input features, e.g., thetrend variables, in many predictions become forecasted valuesinstead of real ones. Forecast error of these features are prop-agated in the iterative predictions, resulting in the larger errorsfor the farther hours. Increase of average WME of the proposedmethod for Kashan, Behrang, and Mobarake in the new exami-nation was 0.21%, 0.96%, and 1.16%, respectively. Increase ofaverage WPE of the method was 0.73%, 3.73%, and 4.54%, re-spectively. As seen, prediction error of Behrang and Mobarakehas much more increase than Kashan. This is due to the factthat by increasing forecast horizon, prediction of more volatileload patterns has more chance to miss a sudden change or de-viate from the load curve in an unexpected variation. For theday ahead load forecasting, the proposed method approximatelysaved its difference with the other methods and was overall thebest method.
An important part of the STLF problem is load forecastof public holidays. System load pattern for public holidays
TABLE IVDME AND DPE OF TWO PUBLIC HOLIDAYS FOR BUS KASHAN
TABLE VDME AND DPE OF TWO PUBLIC HOLIDAYS FOR BUS BEHRANG
TABLE VIDME AND DPE OF TWO PUBLIC HOLIDAYS FOR BUS MOBARAKE
is somewhat different from that of working days [1], [22]. Asimilar phenomenon is seen in the bus load patterns. Besides, apublic holiday may have different effects on the load profile ofdifferent buses. For instance, an industrial load profile may bemore affected than a residential one. The four considered weeksof the previous examination do not include any public holiday,since that examination was focused on the evaluation of the pro-posed method for weekdays and weekends. In Tables IV–VI,obtained results (one hour ahead forecast horizon) for twopublic holidays of Iran, i.e., PH1 (Thursday, February 10,2005) and PH2 (Tuesday, April 26, 2005), are shown. PH1 is anational festivity, while PH2 is related to an Islamic ceremony.In these tables, DME (the first number) indicates daily meanerror, and DPE (the second number) stands for daily peak error.DME and DPE are calculated similar to WME of (9) and WPEof (10), respectively; however, instead of 168 h, 24 h (one dayahead) should be considered. For a better illustration of theeffect of public holidays, PH1 and PH2 can be compared withtheir close weeks of the previous examination (see Tables I–III)that are February and May weeks, respectively. As seen, theprediction error of all examined methods increases for publicholidays with respect to normal weeks. This is due to the factthat load profile of a public holiday has a sudden change withrespect to the previous days or the same day in the previousweeks. Besides, it can be observed that increase of error for PH2is slightly more than PH1, since PH1 is a Thursday or a halfholiday, while PH2 is Tuesday or a working day. It is noted thatthese expressions are overall conclusions, and some exceptionsmay be seen due to stochasticity of bus load forecasting.
From Tables IV–VI, it can be seen that the proposed methodhas a better prediction accuracy for public holidays than theother methods, except a slightly better performance of PAR forKashan and NN for Behrang. In Fig. 7, actual load curve, loadforecast of the proposed method, and its error for the worst testcase of Tables IV–VI, i.e., PH2 for Mobarake, are shown. If PH2is divided into three equal parts, the method’s forecast fits well
340 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007
Fig. 7. Actual load curve (dark), load forecast of the proposed method (grey),and its error (grey, at the bottom) for bus Mobarake in PH2.
to the actual load curve in the first and third parts. However, thesecond part consists of large prediction errors. The industrialload pattern of Mobarake has a sudden rise for the middle hoursof a working day, like Tuesday, which is not seen in the loadcurve of PH2. So, the method’s forecast incorrectly increasesfor these hours due to the similar bus load behavior observed inthe previous days and especially the same day in the previousweeks. Indeed, only the trend information aids the method tofollow the load curve in this part.
The whole training time of the proposed hybrid method, in-cluding both the FASE and NN parts, in all test cases was lessthan 280 s (4 min and 40 s) on a Pentium IV 3.2 GHz, with 1 GBRAM, indicating a small computation burden. Besides, there area few dispatching centers in a real power network, each one con-trolling a number of substations. For instance, in Iran’s powernetwork, there are 16 dispatching centers. Finally, today dis-patching centers usually are equipped with advanced SCADAservers, PAS servers, and workstations with more processingcapability than a Pentium PC. So, the mentioned computationburden is reasonable for real power networks. The single NNas the forecast method in all previous examinations had threelayers with 19 nodes (number of input features) in the first orinput layer, six nodes in the second or hidden layer, and one nodein the third or output layer. The NN part of the hybrid methodhad 20 nodes in the first layer, including the input features andoutput of the FASE part.
In all previous examinations, the proposed method has beencompared with the other forecast methods. Now the eligibilityof the selected input features is examined. For this purpose, twoother sets of input features are considered. The first one, pro-posed for the system load forecasting in [1], consists of 169 pasthourly loads from to and one temperature vari-able for the whole system (totally, 170 input features). Thesecond one, proposed in [13] for bus load prediction, includes 48past hourly loads from to , six dummy variablesindicating day of week, 11 dummy variables indicating monthof year, and three temperature variables constructed from a ref-erence temperature (totally, 68 input variables). In Iran’s powernetwork, the temperature of three large cities (Tehran, Ahvaz,and Tabriz), indicating the main load centers of the system, arerecorded. The temperature variable of the first set is the
TABLE VIIMME OF DIFFERENT SETS OF INPUT FEATURES FOR BUS KASHAN
TABLE VIIIMME OF DIFFERENT SETS OF INPUT FEATURES FOR BUS BEHRANG
TABLE IXMME OF DIFFERENT SETS OF INPUT FEATURES FOR BUS MOBARAKE
weighted average (based on their consumptions) of these threetemperatures [1]. The reference temperature of the second setshould be a local temperature at a reference location as recom-mended in [13]. Tehran is the closest city to the three selectedbuses, and so, its temperature is selected as the reference tem-perature for the second set.
Obtained results from the proposed hybrid method for theselected input features of (1) and the two other sets are shownin Tables VII–IX. In these tables, monthly mean error (MME)of the method for four months February, May, August, andNovember of 2005 is shown. To compute MME values, themean operator is executed for all hours of the month. In thisexamination, one hour ahead load forecasting has been con-sidered so that the obtained results can be also compared withthe previous test (see Tables I–III). As seen, the proposed setof input features overall has a better performance than theother sets. Although the two other sets have more informationcontent than the proposed set, however, learning of these largesets of inputs for the hybrid method (especially the NN part)is very hard. Indeed, the method must derive effect of eachfeature on the output, and by increasing the number of inputs,this task becomes more complicated, especially for complexload patterns like Mobarake. MME of the two other sets forthis bus increases faster than the proposed set. Besides, eachof these two sets considers a long sequence of lagged hourlyloads, including both correlated and uncorrelated ones. Finally,it is seen that use of the temperature variables cannot decreasethe forecast error of bus load prediction and may even increaseit. In addition to the previous reasons described in Section III,it is noted that Iran is a vast country. So, neither the weightedaverage temperature of the system nor a local temperature ofa reference location with considerable distance (here, about450 km) from the related loads can correctly present the actualtemperatures. In addition to the forecast error, computation
AMJADY: SHORT-TERM BUS LOAD FORECASTING OF POWER SYSTEMS BY A NEW HYBRID METHOD 341
burden of the two other sets highly increases in comparisonwith the proposed one, and in some cases, the whole trainingtime for these sets reaches to about one hour.
In spite of this examination, it cannot be claimed that the se-lected input features are the optimum set for bus load prediction,even for the considered test case. For instance, the set with 170features is the better choice for Kashan, due to the fact that thisset is suitable for the system load forecasting [1], and load be-havior of Kashan is similar to the system. Indeed, bus loads havevarious patterns and dependencies, and so, a single set cannot beoptimum for all of them. However, this examination shows thatby appropriately selecting the input features, a bus load forecastprocess with reasonable accuracy and computation burden canbe constructed, which is so valuable for both dispatchers and in-dependent system operators.
In addition to the above tests, we performed other examina-tions on the structure of the hybrid method. The FASE part wasreplaced by the PAR, due to its better performance. However,on the whole, no considerable improvement was observed. Wealso changed the order of FASE and NN parts so that the FASEwas fed by the NN. However, the overall performance of thehybrid method was degraded, since the NN has more flexibilityto use the initial forecasts. As a consequence, hybrid forecastmethods present more learning capability suitable for predictingcomplex signals (e.g., bus load time series) involving ill-condi-tioned characteristics like nonstationarity, volatility, and high-frequency changes. However, care must be taken in design ofthese hybrid methods, as their performance is highly dependenton their building blocks and data flow among them. This is achallenging task, which demands more research.
V. CONCLUSION
In this paper, the problem of bus load prediction has been de-scribed. It has been shown that this problem may be more com-plex than the system load forecasting. So, a hybrid predictionmethod, including FASE and NN parts, has been proposed tosolve it. The proposed method was examined on three buses ofIran’s power network (owning three different load patterns), andthe obtained results were compared with those of the other fore-cast methods for both normal days and public holidays. Besides,the effect of different sets of input features was investigated,showing that a minimum set of correlated inputs may provide aforecast alternative with reasonable accuracy and computationalburden.
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Nims Amjady (M’97) was born in Tehran, Iran, on February 24, 1971. He re-ceived the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from SharifUniversity of Technology, Tehran, in 1992, 1994, and 1997, respectively.
At present, he is an Associate Professor with the Electrical Engineering De-partment, Semnan University, Semnan, Iran. He is also a Consultant with the Na-tional Dispatching Department of Iran. His research interests include securityassessment of power systems, reliability of power networks, load forecasting,and artificial intelligence and its applications to the problems of power systems.
