t h e r e s e a r c h b u l l e t i n o f j o r d a n a c...

T h e R e s e a r c h B u l l e t i n o f J o r d a n A C M , V o l u m e I I ( I I ) P a g e | 52

Forecasting Electrical Load using ANN Combined with Multiple Regression Method

Saeed M. Badran Electrical Engineering Department

Faculty of Engineering, Al-Baha University Al-Baha, Kingdom of Saudi Arabia

+966504588910

[email protected]

Ossama B. Abouelatta1 Mechanical Engineering Department

Faculty of Engineering, Al-Baha University Al-Baha, Kingdom of Saudi Arabia

+966532122646

[email protected]

ABSTRACT This paper combined artificial neural network and regression modeling methods to predict electrical load. We propose an approach for specific day, week and/or month load forecasting for electrical companies taking into account the historical load. Therefore, a modified technique, based on artificial neural network (ANN) combined with linear regression, is applied on the KSA electrical network dependent on its historical data to predict the electrical load demand forecasting up to year 2020. This technique was compared with extrapolation of trend curves as a traditional method (Linear regression models). Application results show that the proposed method is feasible and effective. The application of neural networks prediction shows the capability and the efficiently of the proposed techniques to obtain the predicting load demand up to year 2020.

Categories and Subject Descriptors Soft Computing

General Terms Algorithms, Measurement, Performance.

Keywords Electrical load; time series prediction; neural networks; multiple regressions.

1. INTRODUCTION Load forecasting problem is receiving great and growing attention as being an important and primary tool in power system planning and operation. Importance of load forecasting becomes more significant in developing countries with high growth rate such as KSA. Owing to the importance of load forecasting, various models have been proposed for the short-term load forecasting in the last decades, such as regression-based methods [1-4], Box Jenkins model [5], time-series approaches [6, 7], Kalman filters [8], expert system techniques [9], neural network models [10,11, 12-14], fuzzy logic [15, 16], and fuzzy-neural network structures [17]. Recently, applications of hybrid ANNs model with statistical methods or other intelligent approaches have received attentions. Examples of such systems are hybrids with Bayesian inference [18], self-organizing map [19], wavelet transform [20], and particle swarm optimization [21, 22].

A price forecasting system for electric market participants was proposed by Lin et al. [13], to reduce the risk of price volatility. Xiaet al. [23] investigated the modeling and design of a virtual instrument for short, medium and long term load forecasting using ANNs. Thier results demonstrated the effectiveness of the proposed an enhanced radial basis function networkmodel to provide quality information in a price volatile environment. Maia and Gonçalves [24] proposed an approach for next day peak load

forecasting for electrical companies. They remarked that in this methodology it is not necessary to know precisely the temperature of the days since the proposed system is based on an interval for the future temperature instead of a number. A hybrid neural network model based on self-organizing map has been presented by Amin-Naseri and Soroush [19], for daily electrical peak load forecasting.The results proved the superiority and effectiveness of theirproposed hybrid model. The results showed that the suggested clustering approach significantly improves the forecasting results on regression analysis too. Xiaoxing and Caixin et al. [25] proposed a dynamic and intelligent data cleaning model based on data mining theory. The rapid and dynamic performance of the model makes it suitable for real time calculation, and the efficiency and accuracy of the model is proved by test results of electrical load data analysis. Wright and Firth [26] described an exploratory analyses of domestic electricity-profiles recorded at a high time resolution of 1 min on eight houses. The frequency distribution of loads is shown to be highly skewedwith varying.1

The second kind of prediction is known as medium-term forecasting. There are several methods of medium-term load forecasting such as time-series approaches [27, 28], neural network models [29, 30], and Fourier series approach [31]. Almeshaiei and Soltan [2], presented a pragmatic methodology that can be used as a guide to construct electric power load forecasting models. Some results are reported to guide forecasting future needs of this network. An adaptive fuzzy combination model based on the self-organizing map, the support vector regression and the fuzzy inference method was presented by Che et al. [15].Their result confirmed the validity of the developed model. Abbas and Arif [32] proposed a seven support vector machines model, based on a genetic algorithm for optimization, for daily peak load demand long range forecasting. A better result is found as compare to best result found in the competition.A new technique is proposed by Abu-Shikhah and Elkarmi [33] that uses hourly loads of successive years to predict hourly loads and peakload for the next selected time span. The proposed method can be implemented to the hourly loads of any power system. Pedregaland Trapero [34] developed a general multi-rate methodology in order to forecast optimally load demand series sampled at an hourly rate for a mid-term horizon. The results showed that this method produces a notable reduction on the prediction error and its variability. The development of a dynamic artificial neural network model for medium term electrical load forecasting has been presented by Ghiassi et al. [29].They

1 On leave from Production Engineering and Mechanical Design

Department, Faculty of Engineering, Mansoura University, 35516 Mansoura, Egypt. email: [email protected]


compared results with those of multiple linear regressions, ARIMA and a traditional neural network model.

The third kind of prediction is known as long-term forecasting. The major methods for long-term load forecasting are time-series approach [35], intelligent methods [36], neuro-fuzzy approach [37], dynamic simulation theory [38], hierarchical neural model [39], and support vector machines [40]. The optimal involvement in derivatives electricity markets of a power producer to hedge against the pool price volatility has been addressed by Azevedo et al. [21]. Their results demonstrated the effectiveness of the methodology handling this type of problems.A mathematical method is proposed by Filik et al. [3], for modeling and forecasting electric energy demand in which it enables the possibility of making short-, medium-, and long-term hourly load forecasting within a single framework. A new method for annual peak load forecasting in electrical power systems has been presented by AlRashidi and EL-Naggar [41]. The performance of the proposed method is examined and evaluated. Qader and Qamber [42] applied Monte Carlo method to electric power network of the Kingdom of Bahrain over a period of five years taking into consideration the maximum electrical loads. The results showed similarity between the forecasted data and simulation results. Abou El-Ela et al. [43] introduced what so called a proposed optimization technique, for predicting the peak load demand and planning of transmission line systems. The application on a selected network showed the capability and the efficiently of the proposed techniques to obtain the predicting peak load demand and the optimal planning of transmission lines of the selected network up to year 2017. In order to improve the results accuracy, artificial neural network (ANN) technique for long-term peak load forecasting was modified and proposed by Abou El-Ela et al. [44] as an alternative technique in long-term load forecasting.

The objective of this study is aimed to develop a generalized method for precise load forecasting within the horizons of short-, medium-, and long-terms, all in hourly accuracy.

2. ELECTRIC LOAD FORECASTING Load forecasting problem is receiving great and growing attention as being an important and primary tool in power system planning and operation. Importance of load forecasting becomes more significant in developing countries such as KSA. The accuracy of load forecasting is crucial due to its direct influence on generation planning, and for its economic impacts.

In the modern system operation, the advance technology of computer has been extensively applied in the field of power system planning, monitoring and control. Nowadays, most operation of electric utility utilizes the energy management system (EMS). The traditional way for power engineers to perform the system analysis is to use mathematical model. This model is usually difficult especially when dealing with large systems. Handling these problems with mathematical model is therefore not realistic.

Due to the ability of ANN model to perform pattern recognition, prediction and optimization in a fast and efficient manner, it has become one of the main topics of interest for many researchers to investigate its application in many fields including power system. Some examples of utilizing ANN in power system applications are: Load forecasting, fault classification, power system assessment, real time harmonic evaluation, power factor

correction, load scheduling, design of transmission lines, and power system planning.

Load forecast has been an attractive research topic for many decades and in many countries all over the world, especially in fast developing countries with higher load growth rate. Load forecast can be generally classified into four categories based on the forecasting time, Table 1.

Table 1. Classification of Load forecast based on the

forecasting time

Load

forecasting Period Importance

Long-term One year to ten Years

To calculate and to allocate the required future capacity. To plan for new power stations to face customer requirements. Plays an essential role to determine future budget.

Medium-term

One week to few months

Fuel allocation and maintenance schedules.

Short-term One hour to a week

Accurate for power system operation. To evaluate economic dispatch, hydro-thermal co-ordination, unit commitment, transaction. To analysis system security among other mandatory function.

Very short-term

One minute to an hour

Energy management systems (EMS).

3. ARTIFICIAL NEURAL NETWORKS An Artificial Neural Network (ANN) is a computational model that attempts to account for the parallel nature of the human brain. Specifically, it is a network of highly interconnecting processing elements (neurons) operating inparallel, Fig. 1. An ANN can be used to solve problems involving complex relationships between variables. The particular type of ANN used in this study is a supervised one, wherein the observation (target) is specified, and the ANN is trained to minimize the error between the ANN output and the target, resulting in an optimal solution (assuming the global minimum is reached.) This is accomplished by adjusting the connections between the elements, which involves an adjustment to the weights (w1

1,1…w11,z). In theory, this adjustment

process can be viewed as a form of ‘learning’. Thus, the ANN is considered to be a form of artificial intelligence. ANNs were selected for this study owing to their ability to model non-linear relationships. The relationship between the input and output parameters in this study is highly non-linear.

Figure 1. A 2-layer ANN with multiple inputs and single

hidden and output neurons.

Inputs Hidden Layer Output Layer

. .

. .

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1) A

2=f

2(w

2p a

1+b

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∑∑∑∑ ∑∑∑∑ f1

f2


4. NETWORK DESIGN Forecasting of electricity demand has become one of the major research fields in electrical engineering. The supply industry requires forecasts with lead times that range from the short term (a few minutes, hours, or days ahead) to the long term (up to 20 years ahead). Load forecasting is however a difficult task because of complexity of load series that have high non-linearity relation among variables and load exhibits several levels of seasonality. In addition, there are many important exogenous variables that must be considered, especially weather-related variables. One of the promising tools to achieve a good load forecasting is the ANN which achieved great success in dealing with non-linear problems such as load forecasting problem.

4.1 Data Analysis The power system has a complicated behavior and the load is influenced by many factors. The energy consumption served by the utility can be generally categorized into industrial, commercial and residential loads. The demand of commercial and industrial activities basically relies on the level of production, which is somewhat steady and relatively easy to be estimated.

There are many factors that affect load changes. They can be generally classified as calendar, weather and random factors. Examples of calendar factors are the day type (working day or weekend day), season and so on. Fig. 2 shows hourly load variations from 1 January 2006 to 31 December 2006 (one year) of Jeddah city in KSA. Fig. 2(a) shows the hourly electric load variation whereas Fig. 2(b) shows the same data after applying moving average filter to clear the presentation of data. It can be observed that the load during summer is higher than that in other seasons. Seasonal variation is mainly due to temperature variance.

A detailed (zoomed) 1-D plot of one day period of years from 2002 to 2006 is shown in Fig. 3. It must be noted that for a lower complexity model, it is better to take the starting hour of the day as 8:00 AM, which typically corresponds to the minimum demand hour. Comparing Fig. 3(a) and (b), one can see that the daily load shown in Fig. 3(b) is more useful in terms of providing a simpler model. This strategy was already applied in presenting the mesh plot of Fig. 4.

Load is generally higher during weekdays because there are more social activities. In KSA as any Islamic country, weekend is Friday and many of private sector and governmental institutions consider Thursday and Friday as weekends. As a result, the weekly load curve will be completely different between Islamic countries and European countries. Fig. 5(a) plots hourly load data for one week of years from 2002 to 2006 in Jeddah, KSA. Fig. 5(b) plots hourly load data for one week of years from 1988 to 2006 in Jeddah, KSA.

4.2 Data Preparations Successful operation of load forecasters using ANN requires an appropriate training data set and training algorithm. The training data set should cover all ranges of the input patterns sufficiently to provide the network knowledge to recognize and generalize the relations among the variables in the problem. In this work, ahistorical data from the city of JeddahinKSA from 1/1/1988 to 31/12/2006 were used.

(a) Hourly load over.

(b) Hourly load over one year after applying moving average filter.

Figure 2. Hourly load over one year (2006).

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(a) The day assumed to start mid-night.

(b) The day assumed to start 8:00 AM. Figure 3. Hourly load data in 1-D time plot for one day of

years from 2002 to 2006.

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4.3 Network Creation and Training Load forecasting is important for energy suppliers, financial institutions, and other participants in electric energy generation, transmission, distribution, and markets. The three load forecasting types, which are short-, medium-, and long-term, are very important for power planning and operation.

In neural network methodology, learning, which extracts information from the input data, is a crucial step that is badly affected through the selection of initial weights and the stopping criteria of learning. If a well-designed neural network is poorly trained, the weight values will not be close to their optimum and the performance of the neural network will suffer. In general, initial weight is implemented with a random number generator that provides a random value. To stop the training process, we could either limit the number of iterations or set an acceptable error level for the training phase.

The training and validation procedures for specific network architectures were repeated in order to handle uncertainties of the initial weights and stopping criteria. In the preliminary investigation it was found that about 300 trials were enough to find the best result. The performance efficiencies of each trial were recorded and compared.

5. APPLICATION AND RESULTS This work provides a unified approach that enables the “hourly” resolution property for all of the mentioned forecast ranges. The proposed method consists of a nested combination of two methods

for modeling and forecasting electric loads. The two methods are: neural network and linear regression models. The procedure of work could be summarized as follows:

1. A neural network was applied using electric load data from year 2002 to year 2006 to predict hourly loadfor one day, one week, one month and one year. Figure 6 show the output of neural network training regression.

2. A linear regression models were derived for all cases (one day, one week, one month and one year). An example for the estimated maximum, minimum and average values are shown in Fig. 7.

3. Then, the electric load was calculated as the predicted neural network (Step 1) shifted by the predicted average value calculated using (Step 2). Figure 8 shows a graphical user interface used to predict electric load.

There is no guarantee that coefficients which are close to optimal values will be found during the learning phase even though the number of iterations is capped at a predefined value. Therefore, the performances of the proposed models are measured with four efficiency terms. Each term is estimated from the predicted values of the model and the measured discharges (targets). The accuracy of the proposed method is tested using hourly actual load values

(a) The day assumed to start mid-night.

(b) The day assumed to start 8:00 AM. Figure 4. 2-D representation of hourly consecutively load

data of years from 1998 to 2006 for one day.

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(a) 1-D representationof hourly consecutively load data for one week of years from 2002 to 2006.

(b) 2-D representationof hourly consecutively load data for one week of years from 1998 to 2006.

Figure 5. Weekly cycle of load changing characteristics.

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for the years 1988–2006. The forecasting results are obtained for the proposed model variations and different years in terms of mean absolute percentage Error (MAPE),root mean square error (RMSE), normalized root mean square error (NRMSE) and

correlation coefficient (R), whose definitions are given in (1), (2), (3) and (4), respectively. Overall, the model responses are more precise if MAPE, RMSE, NRMSE and R are found to be close to 0, 0, 0 and 1, respectively.

�� = ��∑ �� (1)

�� = ��∑ (�� − ��)�� (2)

�� = ��∑ (�� )�� !(" #$)� �%(" #$) (3)

� = &∑ (��' )�� ∑ (�� )��∑ (��' )�� (4)

where: N = Number of observations

Lf= Forecasted load (MW)

La= Actual load (MW)

Each model will be checked by four types of error to guarantee the maximum accuracy and to ensure that the forecasted load is near as possible to the actual load. This will add more complications to the problem but in the same time it adds more guarantee for the forecasting accuracy. Since the numerical values of the load entity increases every year, in order to make a fair comparison in terms of the squared error, we also present a ‘‘normalized RMSE”, which corresponds to the RMSE value normalized by the average year load value for each year. Table 1 lists MAPE, RMSE, normalized RMSE and R for hourly loads of years between 1988 and 2006 in case of linear regression models, whereas, Table 2 lists MAPE, RMSE, normalized RMSE and R for hourly loads of years between 1988 and 2006 in case of Neural networkmodels.

Table 1. MAPE, RMSE, normalized RMSE and R for hourly

loads of years between 1988 and 2006 in case of linear

regression models

Year MAPE RMSE ××××109 NRMSE R

1988 14.320 3.611 1.272 0.880 1989 14.350 3.333 1.174 0.880 1990 14.009 2.922 1.029 0.882 1991 14.030 2.341 0.824 0.883 1992 13.920 1.803 0.635 0.887 1993 13.387 1.241 0.437 0.895 1994 13.379 0.921 0.324 0.900 1995 13.036 0.772 0.272 0.905 1996 12.587 0.866 0.305 0.910 1997 12.411 1.083 0.381 0.916 1998 12.120 1.222 0.430 0.922 1999 12.127 1.426 0.502 0.921 2000 12.616 1.495 0.526 0.915 2001 11.979 1.620 0.570 0.918 2002 12.143 1.846 0.650 0.913 2003 12.153 2.039 0.718 0.911 2004 12.085 1.970 0.694 0.912 2005 11.578 1.579 0.556 0.911 2006 11.842 1.554 0.547 0.916

Figure 6. Neural network training regression plot.

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Figure 8. Graphical user interface of Electric load

forecaster.

Figure 7. Maximum, average and minimum electric load

from year 1988 to year 2006 during one working day.

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Table 2. MAPE, RMSE, normalized RMSE and R for

dailyloads of years between 1988 and 2006 in case of NN

models

Year MAPE RMSE ××××103 NRMSE R

1988 2.438 0.876 0.058 0.935 1989 3.376 1.722 0.110 0.954 1990 3.108 1.409 0.092 0.935 1991 3.278 1.582 0.103 0.937 1992 3.143 1.464 0.099 0.939 1993 3.333 1.588 0.103 0.946 1994 5.059 3.699 0.238 0.933 1995 4.131 2.480 0.161 0.951 1996 4.151 2.560 0.166 0.930 1997 4.918 3.549 0.237 0.926 1998 3.887 2.193 0.141 0.931 1999 5.268 4.054 0.266 0.882 2000 4.937 3.514 0.226 0.913 2001 4.576 3.019 0.197 0.934 2002 4.570 3.099 0.203 0.936 2003 5.885 5.040 0.334 0.953 2004 5.372 4.186 0.272 0.935 2005 7.578 8.573 0.665 0.963 2006 8.036 9.675 0.768 0.953

Comparing the average MAPE, RMSE, normalized RMSE and R for daily loads of years between 1988 and 2006, it was found that these values are less in case of neural network than those resulting from linear regression method, Table 3.

Table 3. Average MAPE, RMSE, normalized RMSE and R for

dailyloads of years between 1988 and 2006

Year MAPE RMSE NRMSE R

Linear regression 12.846 1.771×109 0.624 0.904

Neural network 4.581 3.383×103 0.234 0.936

6. CONCLUSION One of the primary tasks of an electric utility is to accurately predict load requirements at all times. Results obtained from load forecasting process are used in planning and operation. Neural Network can learn to approximate any function just by using example data that is representative of the desired task. They are model free estimators, which are capable of solving complex problem based on the presentation of a large number of training data. Neural Networks estimate a function without mathematical description of how the outputs functionally depend on the inputs. They represent a good approach that is potentially robust and fault tolerant. In this work, an electric forecasting method based on neural network integrated with simple linear regression model was implemented using MATLAB. The system performs better results than some other systems. The accuracy can further be improved if we take more than one factor (calendar, temperature, humidity and random factors) as input, which is large enough to incorporate all the effects which can be quantified.

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