Applied Mathematical Sciences, Vol. 7, 2013, no. 80, 4003 - 4014 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.33149

Electricity Load Forecasting in UTP Using Moving Averages and Exponential Smoothing Techniques Samsul Ariffin Abdul Karim1,* and Saiful Azli Alwi2 1

Department of Fundamental and Applied Sciences Universiti Teknologi PETRONAS, Bandar Seri Iskandar 31750 Tronoh, Perak Darul Ridzuan, Malaysia 1,* [email protected] 2

Electrical and Electronics Engineering Department Universiti Teknologi PETRONAS, Bandar Seri Iskandar 31750 Tronoh, Perak Darul Ridzuan, Malaysia Copyright © 2013 Samsul Ariffin Abdul Karim and Saiful Azli Alwi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract This paper study the used of moving averages (MA) and Exponential smoothing techniques (EST) for load forecasting. The case study was in Universiti Teknologi PETRONAS (UTP), Malaysia. The study was divided by two types of load forecasting namely Semester On (SOn) and Semester Off (SOf). Later, MA and ESMT being used to forecast the usage load for both SOn and SOf. The results indicated that ESMT gives better forecasting compared to MA in terms of less measurements of error e.g. Mean Absolute Percentage Error (MAPE). Keywords: Moving averages, exponential smoothing, load forecast, usage load, error

1

Introduction

Prediction of future events and conditions is called forecasts, and the act of making such prediction is called forecasting. It is essential to have accurate models to forecast future load demand. Load demand forecasting is typically categorized into long term and short term prediction respectively. There exist many research articles in forecasting ( [1] - [12]) and the references cited therein.

   

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Short term load forecast is normally carried out for an interval ranging from possibly half an hour or one hour to one week ahead. To supply the load demand over this particular duration of time involves the start up and shutdown of entire generating units, which will be determined by a number of generation control functions such as hydro scheduling, hydro thermal coordination, unit commitment and interchange evaluation. These load information is obtained from STLF system and it is vital to the operational of dispatch centre in order to dispatch load economically. It is main goal for any utilities company to operate as low as possible of operating cost. One way to achieve this is to minimize the forecast error. It was estimated that an increase of operating cost associated with a 1% increase of forecast error was 10 million pounds per year. Thus, the accuracy of the load forecasting is really important and crucial to minimize the costing. Short term load forecast (STLF) plays an important role in economic operation and also for the reliability of powers systems. Therefore, with an accurate prediction model, it is also purposed to determine the performance of electricity forecasting model by using moving average and exponential smoothing techniques. Next will be the data gathering from GDC UTP. The data will be transformed to model and will be simulated using MATLAB software. The data usually will predict based on one week prediction. Further analysis will be carried out to obtain the most accurate forecast model. Our man objective is to obtain the best model possible method in order to forecast the electricity consumption in UTP based on data obtained from GDC. MATLAB software and Microsoft Excel will be used to generate all the numerical results.

2

Forecasting Methods

In this section, two (2) forecasting methods will be discussed in detail. Those methods are moving average (MA) and Exponential Smoothing (EST) techniques. Moving averaging techniques provide a simple method for smoothing past demand history. These decomposition components are the basic underlying foundation of almost all time series methods. There exist various extensions to the basic moving average model such as ARMA, ARIMA etc. [8]. The principle behind moving averaging is that demand observations (weekly/monthly periods) that are close to one another are also likely to be similar in value. Moving Averages (MA) A simple N-day moving average is given as follows: 1 N −1 (1) y (n ) = ∑ x(n − k ) N k =0 Eq. (1) is a causal FIR filters that have been widely being used in digital signal processing.

   

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Single Exponential Smoothing (Exponential Moving Averages - EMA) The most practical extension to the moving average method is using weighted moving average to forecast future demand. The simple moving average uses a mean (or average) of the past k observations to create a future one-period-ahead forecast. It implies that there are equal weights for all the k data points. The future demand forecasts are denoted as Ft. When a new actual demand period is observed, Yt becomes available, allowing to measure the forecast error, which is Yt – Ft. The single exponential smoothing (SES) method essentially takes the forecast for the previous demand period and adjusts it using forecast error. Then it makes the next forecast period [9]. Ft+1 = Ft + α(Yt – Ft) (2) where α is a constant between 0 and 1. Each new forecast is simply the old forecast plus an adjustment for the error that occurred from the last forecast. An α close to 1 will have an adjustment value is substantial, making the forecast more sensitive to swings in past historical demand based on the previous period’s error. The closer the α value is to 1, the more reactive future forecast will be, based on past demand. When the value of α is close to 0, the forecast will include very little adjustment, making it less sensitive to past swings in demand. In this case, the future forecasts will be much smoothed, not reflecting any prior swings in demand. These forecasts will always trail any trend or changes in past demand, since this method can adjust the next forecast based only on some percentage of change and the most recent error observed from the prior demand period. In order to adjust for this deficiency associated with sample method, there needs to be a process that allows the past error to be used to correct the next forecast in the opposite direction. This has to be a self-correcting that uses the same principles as an automatic pilot in an airplane, adjusting the error until it is corrected, or we have equilibrium. With this approach, the forecasting equation can be rewritten as follows: Ft+1 = αYt + (1 - α) Ft and Ft = αYt + α(1-α)Yt-1 + (1-α)2 Ft-1

(3)

In other words, Ft+1 is actually a moving average of all past demand periods, which is can be described by substituting the value of α as 0.2, 0.4, 0.6, 0.8, or any positive number between 0 and 1 [9]. The simplest way to study the EMA is by using output response equation given below: y (n ) = αx(n ) + (1 − α ) y (n − 1) (4) where α = 2 /( M + 1) and α ∈ (0,1) . M is a positive integer chosen by the user/trader (also known as length of the EMA). For example, if α = 0.1, then M = 19. To calculate the frequency response of EMA, the z-transform will be use. Eq. (4) can be re-written in z-transform as follows:

   

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Samsul Ariffin Abdul Karim and Saiful Azli Alwi Y ( z ) = αX ( z ) + (1 − α )z −1Y ( z )

(5)

where z = re iω . Let the transfer function H ( z ) = Y ( z ) / X ( z ) , then we obtained H (z ) =

α

1 − (1 − α )z −1

(6)

Finally, Eq. (3) can be further iterates and resulting in Eq. (7) below: ∞

y (n ) = ∑ α (1 − α ) x(n − k ) k

(7)

k =0

This is causal IIR with h(k ) = α (1 − α ) and α = 2 /( M + 1) [Don, 15]. k

UTP Load Data Gathering

Time Series Technique (MA and EST)

Simulation in Matlab

Validation and Error Measurement (MAPE)

Result with Proposed Model Figure 1 Procedure for UTP load forecasting model

3. Results and Discussion The data have been collected in GDC, UTP. The data have been divided into two parts namely (1) Semester ON and (2) Semester OFF. Thus, our main results will be divided into two parts: Semester On and Semester Off.

   

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Electricity load forecasting in UTP

For short term load forecasting case study in UTP, we used year duration of data of 2010. The data then were divided into two parts which are taken during Semester ON and Semester OFF. This is because, the usage of electricity in UTP when the semester is ON are higher than the usage of electricity when semester OFF. Therefore, we apply those methods into Semester ON and Semester OFF separately. After that, the load forecasting in UTP for the year 2011 will be done by using exponential smoothing technique (EST). The value of α, plays important rules here. Figure 2 show the original load for Semester ON 2010. Figure 3 shows the forecasting using simple moving average (SMA). Figure 4 show the forecasting using exponential smoothing technique with α = 0.3. Based on Table 2.3.1 and the fact that the forecasting data must be closed as possible with the original data together with little adjustment to the original data and fall within the acceptable range of error i.e., in our case we utilized Mean Absolute Percentage Error (MAPE). We concluded that exponential smoothing technique gives the better results when α = 0.3 with MAPE around 12.9994%.

Figure 2 Loads for Semester ON 2010

   

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Figure 3 Simple Moving Average for Sem ON 2010 : 3-sample leading and 30-sample lagging moving average.

Figure 4 Forecast Load for Semester ON 2010 Exponential Smoothing Techniques with with α = 0.3

   

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Electricity load forecasting in UTP

Table 2.3.1 Forecast Error (MAPE) Semester ON 2010 with various α.

Alpha (α) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mean Absolute Percentage Error (MAPE) (%) 0 3.3998 6.8728 12.9994 14.0540 17.5482 20.5752 22.5821 22.868 31.4652 35.8388

Semester OFF 2010 Figure 5 shows the original load forecasting for Semester OFF on year 2010. For load forecasting when the Semester OFF, after we try various type of simple moving average, it was noticed that 3-sample leading and 7-sample lagging moving average, gives better indication for the future forecasting. Figure 6 shows these examples. For exponential smoothing techniques, after several times of simulation with various value of α , it was indicated that exponential smoothing with α = 0.3 gives better results. The MAPE is around 14.4330%. This fact can be seen clearly from Figure 7 and MAPE value.

   

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Figure 5 Load for Semester OFF 2010

Figure 6 Simple Moving Average for Sem OFF 2010

   

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Electricity load forecasting in UTP

Figure 7 Forecast Load for Semester OFF 2010 using Exponential Smoothing Techniques with α = 0.3.

Table 2.3.2 Forecast Error (MAPE) Semester OFF 2010 with various α. Alpha (α) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mean Absolute Percentage Error (MAPE) (%) 0 1.1402 7.6311 14.4330 16.3926 24.4939 33.5172 42.9938 52.4392 61.3656 70.2559

   

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Comparison with Actual Load Data 6000 Load Deman (kw)

5000 4000 3000 2000 1000 0

Day Actual

Moving Average

Exponential Smoothing

Figure 8 Load Forecasts for Semester ON 6000

Load Deman (kw)

5000 4000 3000 2000 1000 0

Day

Figure 9 Load Forecasts for Semester OFF Actual

Moving Average

   

Exponential Smoothing

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Electricity load forecasting in UTP

The load forecasting methods (MA and EST) could be use to forecast the load in UTP for the next 5 years. Meaning that, the proposed models are useful for UTP to minimize the usage of the electricity load either for semester on or semester off. Even though the model that being used is a simple one, but from the results, its gives us better indication and some information to the load usage in UTP. Based on the results, EST gives better results as compared with MA approach. Thus, to forecast short term load or (STLF), EST method is suitable. In fact, it is interesting to integrated EST and ARIMA with wavelet based method to forecast the load (either in UTP or generally in Malaysia) ([12, 13]). Finally, more results including numerical comparison between MA, EST and ARIMA to model the load forecasts in UTP can be found in [14].

4. Conclusion and Recommendation Exponential smoothing is a statistical method of forecasting, rarely being used for load forecasting due to poor results compared to the fitting techniques (linear regression, fuzzy, neural networks etc.). However, if the time series is stationary and the consumption is similar to the recent past, without any important variance in time, it might be useful to use a simpler technique for the load forecast than a sophisticated method that could easily introduce some errors in the validation processes. Future work will be initiated to study appropriate time series for the load forecast of each day types. The method can be adjusted and probably the accuracy of the forecast will significantly improve (in term of less error etc.) by using other fitting techniques such as cubic spline or wavelets together with the exponential smoothing. This will be subject for our future works. Acknowledgment. The authors would like to acknowledge Universiti Teknologi PETRONAS (UTP) for the financial support received in the form of a research grant: Short Term Internal Research Funding (STIRF) No. 76/10.11 and No. 35/2012 also for the facilities provided such as computer and MATLAB software.

References 1. W. R. Christiaanse, Member IEEE, “Short-Term Load Forecasting Using General Exponential Smoothing” IEEE Transactions on Power Apparatus and Systems, Vol. Pas-90, No. 2, pp. 900-911, 1971. 2. Saifur Rahman and Rahul Bhatnagar, “An Expert System Based Algorithm for Short Term Load Forecast”, IEEE Transactions on Power Systems, Vol. 3, No. 2, pp. 392399, 1988. 3. Ibrahim Moghram and Saifur Rahrnan, “Analysis and Evaluation of Five ShortTerm Load Forecasting Techniques”, IEEE Transactions on Power Systems, Vol. 4, No. 4, pp. 1484-1491, 1989.

   

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4. Martin T. Hagan and Suzanne M. Behr, “The Time Series Approach to Short-Term Load Forecasting”, IEEE Transactions on Power Systems, Vol. PWRS-2, No. 3, pp. 785-791, 1987. 5. Nima Amjady, “Short-Term Hourly Load Forecasting Using Time-Series Modeling with Peak Load Estimation Capability”, IEEE Transactions on Power Systems, VOL. 16, NO. 3, pp. 498-505, 2001. 6. C.W. Gellings, PE., “Demand forecasting for electric utilities”, The Fairmont Press, Inc 1991. 7. Heiko Han, Silja Meyer-Nieberg, Stefan Pickl, “Electric Load Forecasting Methods: Tools for Decision Making”, European Journal of Operational Research 199 pp. 902-907, 2009. 8. G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, “Time Series Analysis: Forecasting & Control”, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1994. 9. Don K. Mak, “Mathematical Techniques in Financial Market Trading”, World Scientific, 3rd Ed, 2006. 10. Rafal Weron and Adam Misiorek, “Forecasting Spot Electricity Prices with Time Series Models”, International Conference “The European Electricity Market EEM05”, Proceedings Volume, pp. 133-141, 2005. 11. John O. McClain, “Dynamics of Exponential Smoothing With Trends and Seasonal Terms”, Vol. 20, No. 9, pp. 1300, The Institute of Management Science,1974. 12. Karim, S.A.A. , B.A. Karim, M.T. Ismail, M.K Hasan, and J. Sulaiman, Applications of Wavelet Method in Stock Exchange Problem. Journal of Applied Sciences, 11 (8), 1331-1335, 2011. 13. Al-Wadi, S., Ismail, M.T. and Karim, S.A.A. Discovering Structural Break in Amman Stocks Market. Journal of Applied Sciences, 11 (7), 1273-1278, 2011. 14. Alwi, S.A. A Comparative Study of Load Forecasting Using Moving Average, Exponential Smoothing and ARIMA Model. BEng. (Hons) Thesis, Department Electrical and Electronic Engineering, Universiti Teknologi PETRONAS, Malaysia, pp. 81, 2012. 15. Don, K.M. The Science of Financial Market Trading. World Scientific Publishing Co. Pte. Ltd., Danvers, MA01923, USA, 2003.

Received: March 15, 2013