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IEEE Transactions on Power Systems, Vol. 3, No. 2, M a y 1988
AN EXPERT SYSTEM BASED ALGORITHM FOR SHORT TERM LOAD FORECAST
Saifur Rahman Senior Member
Rahul Bhatnagar Member
Electrical Engineering Department Virginia Tech Blacksburg. VA 24061, USA
ABSTRACT
This paper reviews some of the existing studies on onetotwenty four hour load forecasting algorithms, and presents an expert system based algorithm as an alternative. The logical and syntactical relationships between weather and load, and the prevailing daily load shapes have been examined to develop the rules for this approach. Two separate, but similar, algorithms have been developed to provide onetosix hour and 24 hour ahead forecasts. These forecasts have been compared with observed hourly load data for a Virginia electric utility for all seasons of the year. The one and six hour ahead forecast errors (absolute average) ranged from 0.869% to 1.218%. and from 2.437% to 3.48% respectively. The 24hour ahead forecast errors (absolute average) ranged from 2.429% to 3.300%.
This paper investigates the applicability of expert systems to short term load forecasting. Specifically. it examines whether the analogical thinking that goes into the intuitive forecasting of the electric utility load can be reduced to formal steps of logic and be programmed. Such intuitive analysis is routinely used in conjunction with conventional autoregressivemoving average (ARMA) load forecast to make unit commitment decisions in the electric utility industry. It is expected, then, that an expert system approach to short term load forecasting will benefit from the expert knowledge of the operator, and the inference to be generated from the database of the historical electrical load, weather parameters and other pertinent information. Once an expert system is developed, it will be simple to add new information to the knowledge base, and new rules developed. In this respect, the expert system will be inherently updatable, as opposed to conventional algorithms which are static in the sense that, governing relationships, once determined, stay fixed. The development and rules of a load forecasting program utilizing the proposed expert system approach are discussed in detail. The algorithm utilizes the historical relationship between the load and drybulb temperature for a given season, day type and hours of the day to predict the load in a onetotwentyfour hour time frame for a Virginia electric utility. The load forecasting algorithm discussed in this paper is now online and is being used by the members of the Old Dominion Electric Cooperative in Virginia for use in Load Management decisions.
1.0 INTRODUCTION
Load forecast plays an important role in all aspects of electric utility operations. The forecasting methodology and the requirements of the load forecast, such as accuracy and detail are. of course, dependent on the function of the load forecast. The short term (one to twentyfour hour) load forecast is of importance in the daily operations pf the utility. It is required for unit commitment, energy transfer scheduling and the load dispatch. With the emergence of Load Management, the short term load forecast has a broader role in utility operations  it is also required for the coordination of Load Management programs with conventional system resources. Since the effhctiveness of Load Management programs is sensitive to the system load, this additional function places higher accuracy requirements on the short term forecast. Additionally, the electric utility is no longer the only interested party in the short term load forecast. System peak coincident demand charges and rate structures designed to encourage Load Management programs offer the potential of considerable savings to large industrial customers and electric cooperatives. With advance knowledge of the electric utility load, customers can sohedule Load Management activities to take advantage of the incentives offered in the rate structure. In this context, the development of an accurate, fast and robust short term load forecasting methodology is of importance to both  the electric utility and its customers.
2.0 PROBLEM STATEMENT
The objective of the research reported in this paper was the development of a knowledgebased short term (one t o twentyfour hour) load forecasting algorithm which was robust and accurate and also, had minimal computational and data base requirements. Specifically, the aim was to develop an algorithm which was implementable on a microcomputer. This requirement was imposed in view of the applicability of the short term load forecast to electric cooperatives and other wholesale customers of a utility who may not have any access to mainframe computing that is available to an electric utility. However, all the characteristics cited above, 'for the algorithm, are desirable from any user's viewpoint. In order to present the proper perspective of the work being discussed a brief synopsis of the research on shortterm load forecasting is given in the following. The problem of shortterm (one to twentyfour hour) load forecasting in the electric utility industry has received extensive attention in the last 15 years. These load forecasting methods almost exclusively fall into the category of time series approaches. Some of the earlier work [1,2] have used statistical techniques to correlate the weather information and hourly variations in electric utility load to develop forecasts. Current shortterm load forecasting methods almost exclusively fall into the category of time series approaches These algorithms are primarily based on applying ARMA or ARIMA (autoregressive integrated moving average) models to historical load and weather data 1391 Statistical analvses are then employed to estimate model parameiers For example: Keyhani and Miri [7] have presented a statistical algorithm for online weathersensitive and industrial group bus load forecasting for microprocessor based applications As they have looked into the forecast of bus loads and temperature at the site, the loadtemperature correlation was inherently very strong The reported RMS error for hourly forecasts ranged from 2% to 4 4% of the daily peak load for one step ahead predictions
87 WM 0821 A paper recommended and approved hy t h e I E E E Power System E n g i n e e r i n g Committee o f t h e IEEE Power E n g i n e e r i n g S o c i e t y f o r p r e s e n t a t i o n a t t h e IEEE/PES 1987 W i n t e r Y e e t i n g , New O r l e a n s , Manuscrint L o u i s i a n a , F e h r u a r y 1  6 , 1937. s u b m i t t e d J u l y 21, 1986; made a v a i l a b l e € o r p r i n t i n g November 17, 1986.
08858950/88/05OO0392$01 .OO 01988 IEEE
3 93
Vemuri, et al. [E] have presented an autoregressivemoving average (ARMA) based model which is claimed to be superior to Box and Jenkins based methods in terms of less human interventiori. improved model identification and better results. They have presented results for one day. The RMS value of the houily forecast errors ranged from 3 6646 to 5 28%. The hourly load during that day ranged from 189 to 349 MW. AbuHussien. et al. 19) have presented an adaptive model based on hourly loads and weather information. They have used the hourly load of an individual bus, which is strongly dependent on weather variables, to test the accuracy of their algorithm Maximum error has been observed to be 4 % of the average hourly load with a standard deviation of 1.4%. Irisarri. et al [IO] have presented results of a study on a model for shortterm integral system load forecasting. They have implemented an online algorithm using the Generalized Least Squares approach to provide unbiased estimates of the model's parameters. They have presented one to twentyfour hour forecasts for the integral system load and their average absolute errors have ranged from 2 21% to 4.77%. There is another group of papers 111141which have approached the load forecasting problem from the Load Management viewpoint. McRae, et al. [IO] and Gellings and Taylor 1111apply regression based techniques in the forerasting algorithm. The other approach has been the application of end u s e models for load forecasting [12I31 In these models the authors attempt to synthesize the load using the response of various end use appliances to varying weather conditions. There is yet another approach where the authors have applied a pattern recognition approach [15] to hourly load forecasting They have presented results for a small town load forecast with a peak load of 123 MW They claim that the proposed method is intended for small area power systems. because in a large area the diversity of loads distort the weather sensitive pattern of load. This is probably the reason why this approach, seeniingly innovative, has not received much attention in the industry
A close look at these papers would indicate that these models require a large number (sometimes, up to several hundred) of complex mathematical relationships resulting in a heavy computational burden: and there is always the possibility of nunierical instability due to improper modeling of the stochastic component of load. Typical error bands for these approaches have already been discussed. Iri addition. the database reqitirements are usually large: sometimes the algorithms requiring historical data for up l o five years
This section provides an indepth discussion of the load forecasting methodology for a onetosix hour forecast for Spring season. The purpose is to provide an example of the development process and methodology in setting up the load forecasting rules. It is obvious, of course, that the four seasons provide broad boundaries requiring different sets of rules. However. there are similarities in the algorithms for different seasons and tliis considerably simplifies the task. Four sets of forecasts are prepared, one for each season These are based on historical relationships between weather and load in winter, spring, summer and autumn During the period of season change two forecasts are run  one for the current season and the other for the upcoming one. The performance of these forecasts are monitored and the better one is put online for viewing. The other one continues to run in the background. The alyorithm for a 24 hour forecast, also for Spring season. is discussed in Section 3 4.
3.1 Variable Identification
Correlation analyses between the historical load and the following weather parameters  drybulb and wetbulb temperatures, relative humidity. wind direction and wind speed indicated that: 1) The strongest correlations existed between the load and the diybulb temperature. 2) All other correlations were "weak",
3) There were stronq correlations between load. drybulb temperature aiid relative humidity during some of the Summer months; and 4) In Winter, the correlations were negative and in Summer, they were
positive Thus. the weather parameter of interest for Spring was indicated to he the diybulh temperature and it was chosen for the load forecasting p ror e s s Examination of tlie load shapes for different seasons indicated a seasonal influciice Thus, in Winter, the load shape invariably has two peahs  one in the morning and the othrr in the evening The Summer load shape, on the other hand, has a single broad peak in the late allernoon During Spring and Fall, "transitional load shapes" were obseivrd, which were dependent on the prevailing weather conditions and "seasonal depth" (The term "seasonal depth" implies the length of the cui rent season that has already passed ) Thus, for example, a very cool day in late Spring will not exhibit the Winter load shape that would he seen oii a similar day in early Spring Hence, seasonal boundaiies are indicated as another factor affecting the load forecasting process. Further, witliin a season. the development of the load shape durinq a twentyfour hour time frame will be dependent on the day of the week And, in turn, the typical dayoftheweek load shape for a Teason will be modified by tlie prevailing weather conditions. A roiripreheiisive discussion on the 24hour load forecasting algorithm is provided in section 3 4 Sunimarizing, the variables of interest in the load forecasting process will he
a)
It was, therefore. our objective to investigate alternate algorithms which might yield improved accuracies and have lower computational and online data base requirements 111 this paper, we demonstrate that this would he possible through the use of knowledge based algorithms. The analogical problem solvirig approach inherent in the algorithm allows:
1. a very selective use of the data, thus reducing the online data base
requirements,
2
the use of very recent data. thus making the algoritlini sensitive to changing weather conditions and patterns of power usage, and
3. taking advantage of the expertise of system operalois who, through t t i e i r expe r i e nce , have developed i nt u it ive ire Ia t i on s h i ps bet wee n electrical load and weather parameters. timeofday. dayoftheweek, season and time lag of response.
The season under consideration This will indicate the broad 'loyic" to be followed when relating weather parameters to the load A s an example, the negative correlation observed for Winter iiidicates that as temperature rises, load decreases.
3.0 KNOWLEDGEBASED LOAD FORECASTING
Any knowledge based system (referred to as an expert system) essentially emulates the acquired knowledge arid thought piocesses of an expert in arriving at decisions and/or solutions concerning a problem The objective in our research was to develop a load forecasting system that emulated the knowledge, experience and analogical thinking of experienced system operators Specifically. the aim was to identify variables and rules that are used by system operators in estirnating or forecasting the systern load and the criteria for einploying different rules in different situations The successful formulation of such a system would then provide a viable load forecasting methodology.
b) The seasonal load shape or the "load shape impact" This provides the basis for the load forecast in terms of a seasonal load shape. c) The dayoftheweek impact This factor "finetunes" the seasonal load sliape for the dayoftheweek under consideration. d) The drybulb temperature and the change in this temperature, AT. This factor will determine how the prevailing weather conditions will affect the load There is an additional factor that arises due to the therinal mass of builtiirigs, there is a time lag of response between weather variations and the load change
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3.2 Relating Variables and the System Load
The order of the variables listed above, also indicates the nesting of their impacts, starting from the most general and overall impacts to the smallest fluctuations. This subsection discusses the broad relationships between those variables and the system load. The next subsection will then discuss the quantification and implementation of those relationships for a onetosix hour forecast. The seasonal impact, which dictates the board "logic" or relationship between the weather and the load, will change with each season. Since the load behavior is assumed to represent this, the seasonal impact will also determine the memory depth of the data base. As the memory depth is increased, the data base extends across monthly and more importantly, seasonal boundaries. It is already assumed that seasonal boundaries cause a change in the load shape. Further, the effect of identical weather conditions will be different for different seasons. Although, as the forecast proceeds, it is not possible to avoid crossing seasonal boundaries, it is in the best interest of forecast accuracy to minimize crossing such boundaries in the memory depth. This conclusion combined with test results indicated a memory depth and hence data base length of 4 weeks. In order to cover weekends and holidays we have added an extra week in the data base. Thus the available data base is five weeks long. Once the load shape representing the forecast period has been isolated using the memory depth of the data base, the dayoftheweek impact is then best isolated by utilizing data only from the dayoftheweek on which the forecast is being made. This further limits the number of data points that can be used from the history for the load forecast. Since the memory depth is four weeks, only four data points exist for a given hour of a given dayoftheweek. The dayoftheweek variable is also advantageous in forecasting for holidays. If the seven days of the week are coded from 17 starting with Monday, then a Saturday is day type 6. If it is hypothesized that a holiday load shape is similar 16 that of a Saturday, then the forecasting for a holiday is straightforward. This eliminates the need to model holidays separately. As a next step, it should be noted that weather changes will alter the load shape for a particular day type. The implication is that if, for example, one Tuesday in Spring is cool and another is warmer, the latter Tuesday, while exhilarating the load shape characteristics of a Tuesday in Spring, will also reflect the warmer weather in terms of load magnitudes and load changes. In this context, the seasonal impact again comes into play. For a season such as Winter, it has been noted that temperature rises lead to load decreases. In a transitory season such as Spring, the relationship will depend on the temperature. If, as test results indicated, temperatures are below 6OoF, the negative correlation of winter needs to be applied. On the other hand, temperatures above 82OF required the positive correlation of summer: and the band 6OoF82"F was a 'deadband" where the predominant effect was the load shape impact. The above interplay of weather and load shape impacts indicated that for a onestep predictor: 1) The actual load value of the hour just elapsed would reflect the prevailing weather conditions: 2) The historical change in the load (AMW) for a given day type and season would represent a typical load shape impact: and 3.3.1 Data Base The data base consists of the hourly drybulb temperature and load for a five week period immediately preceeding the current day. Each record of the data base contains the year, month, date, hour, day type, drybulb temperature and load data. In addition, it also contains all the above data (load data only for hours' elapsed) for the current day and the next day. [The weather data for these two days is forecasted data.] To reduce storage requirements, the data base is scrolled up every 24 hours. At that time the oldest day is dropped and the newest day is added.
It will be noted that the data base is of five weeks duration instead of four. As discussed in a subsequent section, this is necessary for holiday load forecasting.
4) The computational burden is minimized. The relevant information in the chosen data points is utilized through rules and simple models.
5) Forecasting for holidays is simplified.
6)
The effect of weather fronts is incorporated not only in the application of rules, but also in the choice of the last actual load value as the "base" load value on which the forecast is based. MW. even with a correction for the weather conditions, the forecast error will still be "wellbehaved". Finally, the timelag in the load response to weather changes is incorporated using the following procedures:
7) Since the forecast variable, AMW. is usually of the order of m I 6 O O
I) The drybulb temperature for the previous hour is chosen as the
"base" temperature from which the temperature change, AT, is calculated. For example, if the forecast is for hour I, the drybulb temperature used for forecasting is the temperature at hour (11). This provides for a onehour lag. 2) A second forecast is made using the temperature at hour (12) and the temperature change, AT, between hours (12) and (11). This provides for a 2hour lag. Since the forecast is based on the load value at (11). a larger timelag was not required. The two forecasts are combined using a simple average. (Test results indicated this rule.)
3.3 Sixhour Forecasting Algorithm
This subsection discusses the algorithm and rules for the onetosix hour forecast for Spring. The forecasting algorithm utilizes a sixstep predictor. Thus, the six hour forecast is based on six consecutive onehour predictions. For each step, the forecast variable is the change in load, AMW, from hour (11) to the forecast hour (I). The forecasted AMW is then added to the load (actual or forecasted) for hour (11). The forecasting of AMW is a two step process, as discussed earlier, to account for the timelag in the load response to the change in weather conditions. In the first step, the weather variables, drybulb temperature and the forecasted change in temperature from hour (11) to hour (I) are related to the change in load, AMW. between hours (11) and I. In the second step, the weather variables for hours (12) and (11) are related to the same AMW. The two hourly load changes forecasted, AMW, and AMW, , are combined as a simple average. The forecasting of AMW is described below. For clarity of discussion, only the calculation of AMW, is described. The calculation of AMW, will proceed in exactly the same manner, except for the change in the weather variables noted above.
3) The change in the hourly load (AMW) is dependent not only on the
day type and season, but also the prevailing weather conditions. Therefore, the forecast variable is not the complete actual hourly load value, but instead the change to be expected in the load from the current hour to the next hour, i e., AMW The forecasted AMW will, of course, be dependent on the historical AMW. calculated from the data base, for a particular hour and day type, as well as the change in the weather conditions There are several important ramifications of the above approach: I) The data base requirements are minimal 2) The computations are based on a very selected number of data points, three to be precise (as is explained in the next subsection).
3.3.2 Data Selection The forecast AMW is based on three sets of data points in history which best represent the prevailing conditions on the current day. The choice of three days is an empirical rule. Two days were found to be insufficient. For four days, the increased computational requirements along with the danger of picking up very dissimilar days didnot offer any marginal benefit.
3) The selection of data points is such as to incorporate the most
recent and relevant information.
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These three sets of data points consist of the drybulb temperatures for hours I, (11) and (12) for the current day, previous day and four similar days in the past. It should be noted here that temperature for hour I on the current day will be a forecasted quantity. The selection of data points from the same day type ensures factoring the load shape impact (of the day type) into the load forecast. The previous day is selected to reflect the prevailing weather conditions. However, the weekdays and weekends are treated as distinct groups for the choice of the previous day. For example, a Friday is considered the previous day for a Monday. Also, a weekday holiday is treated as a Saturday. Thus for the Memorial day (which falls on the last Monday of May) we shall look at the previous Saturday and four additional Saturdays in the past. (This rule explains the need to maintain a five week database.) The sign of DTFACT, which is calculated as a positive value is determined as follows: 1. If T, is greater than 82.0¡ãF, indicating summer conditions and AT, > ATa then the sign of DTFACT is positive, because these conditions would tend to magnify an increase in AMW, or reduce a decrease in AMW,. Else, the sign of DTFACT is negative.
2. If T, < 82.0"F and ATc > ATa , then the sign of DTFACT is negative, because summer conditions have not been reached and therefore higher ATc will lead to reducing the magnitude of a load increase or magnify a load reduction. [Note that in Spring, temperatures in the high 60's to mid 70's are not unusual and the temperature  load correlation will be negative in these temperature ranges.] Else, the sign is positive. 3.3.6 Forecasted AMW The forcasted AMW for hour I will consist of AMW, adjusted for variations of T, and ATc from Ta and ATa respectively. The rules for this step are enumerated below. They were based on observed load behavior in the history and test results.
1. If the forecast hour I is between 11 p.m.
3.3.3 Data Reduction
Out of the five drybulb temperature readings for the hour I in history we choose three which are closest to the current day's forecasted temperature at hour I. The average of these readings is called T , the "base temperature" for hour 1. We also calculate the average temperatures for hours (11) and (12) for these same three days in history. It is expected that, AMW between hours I and (11) in history was related to temperature changes between hours I and (11) and between (11) and (12). Hence we claim that if we know these two temperature differentials for the current day and the prevailing load, we shall be able to relate the historical AMW to the current day's AMW. The three AMW's between hours I and (11) in history are weighted according to the closeness of the AT between these two hours, and ATc between the same two hours on the current day. In other words, if AT, and AT, are close then the corresponding AMW gets a higher weight than otherwise.
 5 a.m., then
AMW, = AMW,
It was observed that during these hours the greatest impact was that of the timeofday and the load shape, not the weather variables.
2. For the hours 6 a.m.
 10 p.m., the following rules apply
AMW,
(a) For 6 8 O F < T, I 82'F i.e., in deadband. and
< 100MW. then
=
3.3.4 Temperature Threshold
It is recognized that the effect of the AT rise (or fall) from different temperature levels will be different. Thus the effect of temperature difference between T, and T, on AMW is modeled as a combination of linear and exponential effects and quantified as a base factor variable, BFACT. In simple terms, BFACT is a function of the ratio between the average temperature for the hour for the three selected days and the current day. Test results indicated that in the range I T,  T, 1 10¡ãF. BFACT could be modeled as a linear variable. Any residual variation above 10¡ãF would give rise to a saturation effect represented by an exponential function.
AMW,
AMW,
It was observed that, the load profile during the Spring afternoon hours was nearly flat with small variations. These variations were independent of normal temperature changes. ( b ) For68"F I Tc I 82"FandAMWa > IOOMW, then AMW, = BFACTx AMW,
3. If T , 2 82¡ãF and peak temperatures on two consecutive days are
3.3.5 Adjusting for AT,
greater than 8OoF, then the load is expected to have a positive correlation with temperature, i.e., a Summer load shape. This is accounted for in the additional rules for the calculation of BFACT. AMW, = BFACTx AMW,
The magnitude of the change in temperture from hour (11) to hour I, which reflects the rate at which the drybulb temperature is changing is also assumed to affect the forecast for AMW. This is based on the observation that a change in temperature of, say, 5.0"F will cause a greater change in AMW than an increase of only 2.0"F. However, the effect of the variation of ATc from ATa can be expected to be a "second order" effect, with saturation characteristics. Specifically, it is modelled as a "second order", saturating effect with a deadband. The deadband was empirically chosen as 1¡ãF for the variable: d(AT) =
+ DTFACT
If the peak temperature will exceed 82¡ãF only on the current day, then BFACT is calculated accordingly and
AMW, = AMW, x BFACT. 4. If T , S 68"F, then a negative correlation is used in the calculation of the sign of BFACT, as discussed earlier, and AMW, = BFACTx AMW,
+ DTFACT.
I AT,

ATc I
5. Finally, the load forecast is given by:
Forecasted Load = Load at hour (11)
[The term "second order" is used here to reflect the double difference inherent in the variable d(AT)] 1. If d(AT) S 1.0, then no adjustment is made for the variation of ATc 2. If d(AT) > 1.0, then the adjustment is computed from the following model: d(AT) = I ATa  ATJ
U
+ AMW,
In the following section a summary of rules for the 24hour ahead Spring forecast is presented.
3.4 24Hour Forecasting Algorithm
This algorithm is designed to provide a 24hour ahead forecast for every hour of the day. In other words, this algorithm issues 24 independent forecasts each 24steps long. Hence, the rules and algorithm for the 24hour forecast are different from that of the onetosix hour forecast, although the database remains the same. The reason for switching to a 24step predictor lay in test results which indicated an increasing deterioration of forecast accuracy using the Istep predictor for forecasts greater than six hours.
= d(AT)
U
2.0 I d(AT) 1 4 . 0 d(AT) > 4.0 x [I exp(
t
= 4
DTFACT = (BFACT)" x abs [AMW,]
+
I)]
3%
The primary difference between the two algorithms is that the 24hour forecast algorithm operates on the actual MW values to account for the prevailing weather conditions, whereas the onetosix hour forecast algorithm operates on the expected change in the load, i.e., A MW, to account for weather influences. For the 24hour forecast, the benefit of the previous hour's load reflecting current weather conditions is not available and hence the necessity to operate on the full MW load value. However, the basic premise of the algorithm remains essentially the same as for the onetosix hour forecast, specifically,
(a) *BFACT (Base Factor) corrects for the difference in the historical and forecasted base temperatures at hour 1. It is calculated from the following equation BFACT = 1 1  a1 xBaseForecastx(1 a = . T C

(1) The load shape impact is preserved through 'the judicious
selection of data points from the base: (2) The impact of weather conditions dictated the rules for forecasting the load shape modification; and
T, = Average temp. of the hour I for selected days.
(b) DTFACT is used to correct for the rate of change of the temperature. The magnitude of DTFACT is calculateed as follows:
( 3 ) The "inertia" in the load response dictated a twopass forecast.
The next three subsections discuss the rules for each of the above three components of the 24hour forecast algorithm for Spring.
DTFACT = P C T ~ B a s e F o r e c a s t x a ~ x ( 1 eT)
p =y
2.0 i y i 4.0
y = lATc
 ATal
3.4.1 Selection of Data Points and the Base Forecast
Considerations of the seasonal impact on the load shape had limited the database length to four weeks for a nonholiday (section 3.2). Hence the database length for the 24hour forecast is also limited to four weeks. This has the advantage of allowing the same database to be used for the onetosix hour forecast as well. Then, on the assumption that loads on similar day types with similar weather conditions will be the same, a base forecast is made for hour I as follows. Similar days are chosen based on day type and peak temperature for the day. Base Forecast = [ where
(Note: 0 = y only when y lies between 2.0 and 4.0, otherwise f3 will be clamped either at 2.0 o r 4.0.) PCT = ratio of base forecast that can be attributed to a change in AT
= lMWaw
 Base ForecastllBase Forecast
3.4.2.1 Utilization of BFACT
The rule for determining the load response to temperature will determine the sign of BFACT once the magnitude has been obtained from the equation given above. These rules are given below: If the peak temperature on the current day is above 8S0F and the peak temperature on the previous was above 80¡ãF then a positive correlation exists between temperature and load. Then, (i) if a
]=1
t Wj x MWj]/ g Wj
]=1
Wj
MW. = actual load (MW) at hour Ion selected day j = w i g h t i n g factor for day j.
< 1.0, BFACT has a  ive sign
(ii) if a > 1.0 BFACT has a
+ ive sign
Tk = drybulb temperature at hour I on three selected days. Tc = drybulb temperature at hour I on the current day. T, = drybulb temperature at hour I on the selected day j. (note: Ti is a subset of Tk)
The base forecast is thus made on the assumption that if the base drybulb temperature on a day in the history is close 16 Tc,then the load on that day in history should get a higher weighting. The base forecast obtained above then needs to be modified according to actual weather conditions.
3.4.2.2 Utilization of DTFACT
The sign of DTFACT is determined by the magnitude of AT. with respect to ATc. Let d(AT) = IAT,
 ATcJ
Then the rules for determining the sign of DTFACT are as follows: (a) If the peak temperature on the forecast day is less than or equal to 85OF, then a negative correlation is assumed to exist between AT and the load. The sign of DTFACT will be: (i) positive if d(AT) is negative. (ii) negative if d(AT) is positive. (b) If the peak temperature is greater than 85OF then a positive correlation will hold and the sign of DTFACT will be: (i) positive if d(AT) is positive (ii) negative if d(AT) is negative. The modified forecast for hour I is then given by: LOAD FORECAST = BASE FORECAST
3.4.2 Rules for Modifying the Base Forecast
Rules developed for modifying the base forecast to account for prevailing weather conditions on the current day have to reflect the observed response of the load to changing weather conditions for a particular season. For example, in winter there is a negative correlation between temperature and load and a positive correlation in summer. In a "transitory" season such as Spring. both types of responses will be observed. depending on the temperature. Therefore, for Spring, temperature thresholds are established to differentiate between the two behaviors. Based on available data and test results, the threshold was indicated to be a peak temperature of 85OF. provided the peak temperature on the previous day had exceeded 8OOF. This implied that if there were two consecutive "hot' days, then there would be a positive correlation between the temperature and load. Otherwise. the load shape impact will prevail. The modification of the base forecast itself is quantified through two factors, called BFACT and DTFACT for clarity and simplicity.
+ BFACT + DTFACT
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3.4.3 Inertia of Load Response
The "inertia" of the load in responding to changing weather conditions is a well known phenomenon. For example, i f the peak temperatures on two consecutive days are 90¡ãF. then the load magnitudes on the second day will be higher than those on the first day. As another example, if peak temperatures on two consecutive days are 78"F, and 88OF, the load on the second day does not only reflect a temperature of 88'F because of the "cooler" day which preceded i t This type of timelag can be termed as an "inertia" in the response of the load to prevailing weather conditions. In developing an algorithm for the 24hour forecast it was necessary to account for the above behavior of the load. It becomes easier to model that behavior if stated in the following manner. the load on a given day behaves in part according to the weather conditions for that day, and in part according to the weather conditions existing during the past 2448 hours.
If the "inertial" behavior of the load is characterized by the above statement, then it can be accounted for by using a second forecast for each hour I, during the 24hour time frame of interest, using the weather data for the past 2448 hours. This second forecast can then be combined with the forecast issued using the forecasted temperatures.
The onetosix hour forecast error gradually deteriorates because the error of a succeeding hour contains the error of the previous hour The 24hour forecast, however, does not suffer from the same problem This forecast is made as a onestep process, always looking 24 hours ahead In our sample, the 24hour forecast appears to be as good if not better than the 6hour forecast TABLE 1 Summary of Forecast Errors in Percentage Lead Time 1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 24 hours Winter Fall
1039 1609 2 150 2 630 3 063 3 480 2 755
I
1218 1.874 2.386 2 746 3 031 3 317 2 459
0 879 0 869
1399 1924 2 390 2 808 3 219 3 300
1269 1.658 1964 2 224 2 437 2 429
In order to provide a more detailed analysis of the forecast errors
we present the hourly profile of the 24hour ahead load forecast in
The second forecast forms the second pass of the 24hour forecast algorithm. During the second pass (a) a "composite" 24hour temperature profile is obtained by averaging the hourly drybulb temperatures of the previous two days
Table 2. The data in this table represents the absolute average of the daily percentage errors (with respect to the daily peak) for all days, taken one month at a time. For example, the first entry (2.094) under the column "Winter" represents the absolute average error (in percentage) for 1 a.m. on all 28 days in February. It is noted here that the error vafues between the hours of 2 and 5 are considerably less than they are for the rest of the day This is because the utility load is quite stable and easily predictable for this Deriod
(b) the "composite" profile is then used to calculate a second
load forecast for each hour of the 24 hours of interest The final load forecast is obtained by Load Forecast = FCSTI = FCST2 U1, U2
=
TABLE 2.Hou ' Profile c the 24ho Hour 1 2
3
Forecasl .rror Summer 1712 1305 0 678 0 887 1260 1623 1866 2 274 2 497 2 859 3 889 4 064 4 148 4 680 5 498 4 782 4 636 4 794 5 434 4 527 4 303 3 811 4 060 3 610
Winter 2 094 1013 1321 1417 1529 1542 2 603 3 226 2 188 2 235 2 783
3 440
1134
0 495 0 408 0 510 0 892
Spring
i f Percentage Fall 
=
U1 x FCSTI + U2 X FCST2 Load forecast based on the current day's forecasted temperatures. Load forecast based on the "composite" temperature profile. ratios to apportion the load forecast.
1369
0 427
0 534
0 591 0 856
4 5
6
7
8
The ratios U1 and U2. as determined from test results, are 0.8 and 0 2 respectively. The combined forecast calculated above is then the final load forecast. In the following section the results obtained using this algorithm are presented
4.0 RESULTS
In order to test the accuracy of the expert system based algorithm we have compared the hourly load forecasts for several months during the year with actual data. The sample presented in Table 1 is obtained from using the 1983 hourly load data for Virginia Power Company. The temperature information is from the National Climatic Center weather tapes of Washington, D C . . Richmond and Norfolk. Our initial screening of several weather sites in and aiound Virginia Power service area showed that these three stations best capture the prevailing weather conditions there. Results from testing the algorithm for four representative months in four seasons are presented in Table 1. These months are February, May, July and October for Winter, Spring, Summer and Fall respectively. The numbers represent the absolute average of the errors with respect to the daily peak for all days of the month For example, the 1 039% error for winter represents the absolute average of all (24 x 28 = 672) onehour ahead forecasts In February.
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 
3 595 3 283 3 524 3 191 3 944 3 647 3 202 3 256 3 235 3 213 3 229 3 402
1689 1957 2 199 2 368 2 516 2 535 2 582 2 888 3 297 2 849 3 316 3 224 3 384 3 436 3 741 4 295 3 347 2 932 3 019
1606 2 342 2 126 2 462 2 032 1847 3 083 2 680 3 013 3 190 3 632 4 910 4 973 4 015 3 731 2 515 2 318 2 104 1942
1 ? execution time of a 24hour ahead forecast for a day is between one and two seconds on an IBM3084 mainframe. The same prograrn takes between 20 to 30 seconds to execute on an AT&T 382 microcomputer The time variation on any computer is due to the number o f conditions that need to be checked and flags set during the execution of the program.
Results presented in Tables 1 and 2 are based on true temperature information because a l l data is historical. In reality, however. the temperature information will be forecasted and this forecast error will be built into the load forecast. In figure 1 we present some results for the online load forecast for the Virginia Power system load. Here we show the one and sixhour ahead hourly load forecasts for Tuesday, July 8, 1986. On that day the system experienced the highest peak load in its history. The peak was unofficially recorded at 10 330MW at 6 P M For that 24hour period lhe absolute average errors for the one and sixhour ahead forecasts were 54 58MW and 203 9GMW respectively These numbers translate to 0.53"/0 and 1.97% errors with respect to the day's peak load.
, *
398
3.
SIXHOUR FORECAST
TUESDAY 7/8/1966
D. J. Aigner, 'New Directions In Load Forecasting with Emphasis on TimeofUse Analysis', Paper No. IO, Proc. of the 1979 EPRl Load Forecasting Symposium.
4. F. Meslier, "New Advances in Short Term Load Forecasting Using BoxJenkins Approach'. /E€€ 1978 PES Winter Meeting, New York. Paper No. A 78 0515. 5. B. Krogh. et al.. 'Design and Implementation of an Online Forecasting Algorithm', IEEE Transactions on Power Apparatus and Systems, vol. PAS101, Sept. 1982, pp. 32843289. Dale W. Ross, el al., "ShortTerm Load Prediction for Economic Dispatch of Generation", Proc. Power lndustry Computer Applications Conference, 1979, pp. 198204. A. Keyhani and S. M. Miri, 'OnLine WeatherSensitive and Industrial Group Bus Load Forecasting for Microprocessor Based Applications", /E€€ Transactions on Power Apparatus and Systems, vol. PAS102, 1983. pp. 38683876.
6.
7.
8. S. Vemuri, et al.. "Online Algorithms for Forecasting Hourly Loads of an Electric Utility'. ibid., vol, PAS100, 1981, pp. 37753784.
9.
M.S. AbouHussien, et al., "An Accurate Model for ShortTerm Load
Forecasting", ibid., vol. PAS100. 1981. pp. 41584165.
10. G. D. Irisarri. et ai., 'OnLine Load Forecasting for Energy Control Centre Application", ibid., vol. PAS101. January 1982. pp. 7178. Figure 1 . Comparison of a c t u a l & f o r e c a s t e d l o a d s
11. M. R. McRae, et al.. "Integrating Load Management Programs into Utility Operations and Planning with a Load Reduction Forecasting System", ibid., vol. PAS104. No. 6. 1985. pp. 13211325.
12. C. W. Gellings and R. W. Taylor, "Electric Load Curve Synthesis A Computer Simulation of an Electric Utility Load Shape", ibid.. vol. PAS100. NO. 1, 1981. pp. 6065. 13. T. M. Calloway and C. W. Brice, 'Physically Based Model of Demand with Applications to Load Management Assessment and Load Forecasting", ibid., vol. PAS101, No. 12, 1982, pp. 46254631. 14. J.H. Broehl. "An EndUse Approach to Demand Forecasting", ibid., vol. PAS100, June 1981. pp. 27142718. 15. A. S. Dehdashti. et al., 'Forecasting of Hourly Load by Pattern Recognition  A Deterministic Approach", ibid.. vol. PAS101, Sept. 1982, pp. 32903294.
Figure I brings to light an interesting dilemma the load forecaster faces when the forecast is used for load management. On this day, based on the load forecast, the members of the Old Dominion Electric Cooperative initiated load control in the afternoon. Consequently the actual load was lower than forecasted, resulting in a forecast error of two to three hundred megawatts. It can, therefore be argued that. had there been no load control the forecast errors would have been smaller. Probably the expert system can be made smarter by letting it guess how much load control may be initiated in response to a peak load forecast, and incorporate that information in the forecast database.
5.0 CONCLUSIONS
An expert system based load forecasting algorithm has been developed and tested with electric utility historical data. The algorithm has been developed based on the logical and syntactical relationships between weather and load, and prevailing daily load shapes. It is robust and accurate and has yielded results that are equally good. if not better, when compared to the regression based forecasting techniques. The data and computational requirements of the algorithm are also minimal. Therefore, the expert system approach t o the load forecasting problem has yielded a viable algorithm which has the desired performance, and is implementable on a microcomputer.
Saifur Rahman (S75. M78, SM83) graduated from the Bangladesh University of Engineering and Technology in 1973 with a B. Sc. degree in Electrical Engineering. He obtained his M.S. degree in Electrical Sciences from the State Univeristy of New York at Stony Brook in 1975. His Ph.D. degree (1978) is in Electrical Engineering from the Virginia Polytechnic Institute and State University. Saifur Rahman has taught in the Department of Electrical Engineering, the Bangladesh University of Engineering and Technology, the Texas A8M University and the Virginia Polytechnic Institute and State University where he is an Associate Professor. His industrial experience includes work at the Brookhaven National Laboratory, New York and the Carolina Power and Light Company. He is a member of the IEEE Power Engineering, industry Applications, and Computer Societies. He serves on the System Planning and Demand bide Management subcommittees of the IEEE Power Engineering Society. His areas of interest are demand side management. power system planning, alternative energy systems and expert systems. He has authored more than 70 technical papers and reports in these areas. Rahul Bhatnagar was born in Muzaffarnagar. India. He graduated from the Birla Institute of Technology and Science, India in 1979 with a BE. (Hons.) in Electrical and Electronic Engineering. He obtained his M.S. and Ph.D. degrees in Electrical Engineering from the Virginia Polytechnic Institute and State University in 1982 and 1985 respectively. He currently holds a visiting position on the faculty of the Department of Electrical Engineering at V.P.I. 8 S.U. His current areas of interest are expert systems and microcomputer applications in power systems planning and operations. Rahul Bhatnagar is a member of the IEEE Power Engineering Society.
'
6.0 ACKNOWLEDGEMENTS
The authors wish to acknowledge the sponsorship of the Virginia Center for Coal and Energy Research, and the Old Dominion Electric Cooperative for this research effort.
REFERENCES
1. P. C. Gupta and K. Yamada, 'Adaptive Short Term Load Forecasting of Hourly Load Using Weather Information'. /E€€ Transaction on
Power Apparatus and Systems, vol. PAS91, 1972. pp. 20852094. 2.
K. Srinivasan and R. Pronovost. 'Short Term Load Forecasting Using Multiple Correlation Models", ibid. vol. PAS94, 1975. pp.
18541858.
399
Discussion
A. C. Tsoi (The University of New South Wales, Campbell, ACT, Australia): The authors are to be congratulated for introducing some novel ideas in this paper. The idea of using a rulebased expert system for load forecasting is especially interesting.
1) One of the key problems in using a rulebased expert system is the extraction of a knowledge base from experts. In the electricity industry, this can be rather difficult, as often, the experts find it difficult to articulate their experience and knowledge. The authors appear to have circumvented this step by arguing from the behavior of the load and from largely ¡°heuristic¡± means, see e.g., Section 3.3.6. Could the authors comment on how a human expert would view these rules? Are these rules apparent when the human expert is faced with the load curve and attempts to forecast the load, say, an hour ahead, or six hours ahead? 2) It is interesting to note that five week deep database used by the authors correspond with our own experience [l]. In fact, we find that for a relatively smooth seasonal variation of the load, e.g., late winter, it is beneficial to use five weeks of past data. However, for relatively sharp variation of the seasonal component, e.g., in midwinter preferably, it is better to use shorter historical data, e.g., one to two weeks. Did the authors find the same experience? If so, would it be possible to vary the historical database depth according to the seasonal variations? 3) It should be mentioned that we have attempted a crude form of expertsystembased forecasting in [2]. This has actually been used in practice for a number of years. It is found to be operating rather satisfactorily. 4) It is interesting to note that the authors attempt to forecast the controlled load in Fig. I . In our own experience, it is almost impossible to forecast to accuracy the controlled load, as the load depends very much on the amount of load shed or restored. We find one way to test the performance of a load forecasting method is to use it to forecast the uncontrolled load. (For a method to reconstruct the uncontrolled load from the controlled load and the load shed record, please see, e.g., [3]). This would give a better evaluation of the performance of the method. Do the authors find the same experience? 5) The methods introduced in this paper appear to apply to a local public utility. Could the authors indicate what should be changed if another person wishes to use the method at another public utility?
[2] A. C. Tsoi and B. Simmonds, ¡°A simple load management guideline,¡± Electric Energy Conference Proc., Inst. of Engineers, Australia, 1517 Oct., 1985, Newcastle, Aust. pp. 118124. [3] M. U. Kobe and A. C. Tsoi, ¡°Modelling of domestic hot water heater load from online operating records, and some applications,¡± Proc. IEE, vol. 133, 1986, pp. 336345.
Manuscript received February 27, 1987.
S. Rahman and R. Bhatnagar: We appreciate Professor Tsoi¡¯s comments
on our paper. W e shall answer his questions in the order they appear. 1) These rules are generally obtained by analyzing the observed relationship between load, weather conditions, day type (i.e., weekday, weekend, or holiday), time of day, and season. W e relied on the field data, our experience in this subject, and interviews with electric utility system operators. Thus these relationships will be apparent to the human expert in a qualitative manner. However, some analysis will be necessary to quantify them. 2) Yes, we have implicitly varied the depth of the data base. When we are in the season changeover period, there are significant variations in temperature from one week to another. Since we weight the change in load (AMW) based on the temperature spread, any day for which temperature is very different from the current day gets a very small weight. Consequently the day which falls outside the seasonal boundary has very little significance on the current day¡¯s load forecast. 3) It is interesting to note that the discusser has also tried ¡°a crude form of expertsystembased forecasting¡± and it works. This further validates our contention that there is merit to this approach. 4) In discussing Fig. 1 we said that, since there was load control our forecast error was higher than expected. In other words, if there was no control, the actual load seen by the system would have been higher and it would then be closer to our forecasted value. W e did not attempt to forecast the controlled load. As the discussion points out, that will be a very difficult thing to do without knowing what amount of load control will be initiated by the operator under that situation. 5) The methodology presented in this paper is portable. If one wants to apply this to another utility, two to three years¡¯ hourly load and weather data have to be analyzed, and the system operators and the utility load forecasters have to be interviewed to obtain some heuristic relationships. These will provide the knowledge base that has to be queried to develop the rules for the forecast Manuscript received March 19, 1987
References
Kobe, .¡®Load forecasting in a power system [11 A , Tsoi and M , from a supply authority point of view,¡± Electric Power System Research,voi. 6 , 19831 pp. 147159.