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decomposition and neural networks has been reported in the literature [9]. This method uses wavelet to decompose load into a low frequency component and three high frequency components. It opens the door for analyzing complex load features at different frequencies. However, since the high frequency load components are mistreated as noise, the high frequency load features are not appropriately captured. In order to gain the benefits of precise load and energy forecasting, TOP will be issuing new edition of Load & Energy Forecast Report every six months. This work aims at developing more accurate methods for issuing that report.

is 24 hours (for more details see attachment 1). Based on Fourier Synthesis theorem, a periodic signal can be described by a Fourier decomposition as a Fourier series, i. e. as a sum of sinusoidal and cosinusoidal oscillations. By reversing this procedure a periodic signal can be generated by superimposing sinusoidal and cosinusoidal waves. A great thing about using Fourier series on periodic functions is that the first few terms often are a pretty good approximation to the whole function, not just the region around a special point. Therefore, because of periodic variation of load requirement in DEWA system, we used Fourier series to analyze load requirement behaviors. We performed a parametric curve fitting on hourly load requirement using MATLAB, then explored and analyzed data sets & fits visually and numerically. We found that the goodness of fits always is more than 99.6% (see attachment 2 for some fitted curves). It means Fourier function can accurately describe the behavior of hourly load requirement in DEWA system during winter as well as summer. The Fourier function that can describe load requirement in DEWA system during all seasons is as bellow:

2 Problem Formulation In this work the following data were used to analyze and investigate load requirements in power system system and evaluate the proposed method and prove its validity. 1. Actual hourly load requirement MW values for 2006 (24 samples for each day). These data were used in order to analyze load curve and to calculate energy using proposed method. Calculated energies using proposed method were compared with actual energies taken from historian to confirm the validity of proposed method. 2. Actual values of energy requirement MWhr for 2006 (one value for each day). These actual energies were compared with calculated energy using proposed method to prove the validity of the proposed method. 3. Forecasted load requirement MW values for 2007 (24 samples for each day). These values were taken from “Load and Energy Forecast Report for the Year 2007 Update, February 2007”. These data were used in forecasting energy using proposed method. 4. Forecasted values of energy requirement (MWhr) for 2007 (One value for each day). These data were taken from “Load and Energy Forecast Report for the Year 2007 Update, February 2007”. The forecasted energies using the proposed method were compared with the forecasted one taken from that report (using existing method).

Load(t) = a0 + a1* cos(t * w) + b1* sin(t * w) + ... a2 * cos(2 * t * w) + b2 * sin(2 * t * w) + a3 * cos(3 * t * w) + b3 * sin(3 * t * w) + ... a4 * cos(4 * t * w) + b4 * sin(4 * t * w) + a5 * cos(5 * t * w) + b5 * sin(5 * t * w) + ... a6 * cos(6 * t * w) + b6 * sin(6 * t * w) + a7 * cos(7 * t * w) + b7 * sin(7 * t * w) + ... a8 * cos(8 * t * w) + b8 * sin(8 * t * w)

The parameters of this equation depend on factors influence the load behavior such as weather, type of day and etc. (we will try to find the relationship between these parameters and parameters of above equation in next reports). The interesting thing about above function is that this function can calculate load requirement not only hourly but also at each custom time including hour, minute and second. To prove this, we calculated energy using above equation and compared these calculated energy with the actual energy collected from historian system for 2006. Table 1 shows the difference between calculated energy using the above equation and actual energy taken from historian. Attachment 3 presents the difference between these two values for each day of individual months of year 2006. It is clearer that difference between the total calculated energy and total actual energy for year 2006 is less than 0.3%. In the other words, the

3 Proposed Method Actual hourly load requirement (MW) for year 2006 were collected from historian system and thoroughly analyzed. It was found that load requirement in DEWA system has a periodic variation and its cycle

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accuracy of proposed method for calculation

(and forecasting) energy is more than 99.7%.

Table1- comparison between calculated energy using proposed method and actual energy for year 2006.

Month

Calculated Energy MWhr

Actual Energy MWhr

Error %

January-06

1113717

1118153

0.39672567

February-06

1132756

1135199

0.21520456

March-06

1318038

1320665

0.19891494

April-06

1580459

1583178

0.17174316

May-06

2058354

2074568

0.78156026

June-06

2291755

2305496

0.59603088

July-06

2489980

2502185

0.48775782

August-06

2600036

2601158

0.04311965

September-06

2387259

2386731

-0.0221173

October-06

2190092

2191439

0.06146363

November-06

1745236

1745473

0.01360307

December-06

1306560

1310482

0.29931244

Total 2006

22214242

22274728

0.27154367

calculated energy using proposed method in January, February and March 2007 has 0.374%, 3.13% and 2.32% error respectively but calculated energy using existing method has –1.61%, -13.62% and 3.09% error respectively. So, because of better accuracy of proposed method, using of this method for daily, monthly and annual energy forecasting is recommended. The criteria to select similar days are based on ISO New Eng- land’ operation procedures [3], and the selected day is required to have the same weekday index and similar weather to that of tomorrow. In this selection process, Tuesday, Wednesday, and Thursday are not differentiated following the rationale presented in Section II-A. To avoid seasonal variations, the selected day is also

4. Application of Proposed Method for Energy Forecasting Forecasted load requirement MW values (24 samples for each day) for 2007 were taken from “Load and Energy Forecast Report for the Year 2007 Update, February 2007”. We applied the proposed method to these data to forecast energy for 2007. Table 2 presents the forecasted energy using the proposed method and forecasted energy using the existing method. Although both proposed and existing method have used the same load requirement for forecasting energy, but their results are different. From table 2 it can be shown that

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required to have its day-of-a-year index within a

neighbourhood of that of tomorrow.

Table2- comparison between forecasted energy using proposed method and forecasted energy using existing method for year 2007.

Difference Difference Calculated % (between Actual Energy between New Energy MWhr Existing MWhr Method and (Existing and new (Historian) Actual Method) Method) Energy%

Difference between Existing Method and Actual Energy%

Month

Calculated Energy MWhr (New Method)

January-07

1291427

1317110

1.94995103

1296287

-0.374917

1.606357

February-07

1318818

1452996

9.23457463

1278786

3.130469

13.623077

March-07

1540701

1528601

-0.7915735

1577293

-2.319924

-3.087061

April-07

1850702

1897500

2.46629776

1910628

-3.136456

-0.687104

May-07

2387623

2618446

8.81526677

2450580

-2.569065

6.850052

June-07

2649040

2521496

-5.058267

2729305

-2.940859

-7.613990

July-07

2870354

2935172

2.20832033

2877976

-0.264839

1.987369

August-07

2994434

3066640

2.35456395

3051347

-1.86517

0.501188

September-07

2739779

2751100

0.41150812

2777685

-1.36466

-0.957091

October-07

2516757

2595781

3.04432462

2387020

-5.435103

-8.7456745

November-07

2042674

2038302

-0.2144923

December-07

1495215

1332593

-12.203426

Total 2007

25697524

26055737

1.37479512

described by proposed Fourier function during all seasons. This function can presently calculate load requirement at each custom time including hour, minute and second. Finally, application of the proposed method for energy forecasting was tested and because of its high accuracy, it was used for calculating energy requirement for 2007. The use of periodic method

4 Conclusion This work described a more accurate method for calculating and forecasting energy in DEWA system. Firstly, it was found that load requirement in power system has a periodic variation and its cycle is 24 hours. Secondly, it was shown that although load patterns differ greatly during winter and summer, but load profiles can always be

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for load forecasting will be tested in next reports. The results obtained in this work confirm the applicability as well as the efficiency of neural networks in short-term load forecasting. The neural network was able to determine the nonlinear relationship that exists between the historical load

ISBN: 978-960-474-283-7

data supplied to it during the training phase and on that basis, and make a prediction of what the load would be in the next one hour. It must, however, be ensured that the network is not over-trained as this will lead to a loss of its generalizing capability.

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Figure1: Samples of Fitted Curves Performed on Load Requirements Using of Proposed Fourier Equation

Figure 2: Plots of the ‘Target’ and ‘Forecast’ Load in MW Values against the Hour of the Day

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[13] M.A.Abido. Optimal power flow using particle swarm optimization. Electrical Power and Energy Systems, 2002,(24):563-571 [14] Kennedy J, Eberhart R. Particle Swarm Optimization. In Proceedings of IEEE International Conference on Neural Networks, 1995(4): 1942~1948

References: [1] Christiannse W.R. Short-term load forecasting using general exponential smoothing, IEEE Trans. Power Apparatus and Systems, 90(2)(1971) [2] Liang Ruey-Hsun, Cheng Ching-Chi. Shortterm load forecasting by a neuro-fuzzy based approach, International Journal of Electrical Power and Energy Systems, Volume: 24, Issue: 2, February, 2002, pp. 103-111 [3] Jiang Chuanwen, Li Tao. Forecasting method study on chaotic load series with high embedded dimension. Energy Conversion & Management, 46(5), 2005, 667-676. [4] Spyros Tzafestas, Elpida Tzafestas. Computational intelligence techniques for shortterm electric load forecasting, Journal of Intelligent and Robotic Systems,31(2001),7-68 [5] Mori H, Urano S. Short-term load forecasting with chaos time series analysis, Proceedings of the International Conference on Intelligent Systems Applications to Power Systems, ISAP '96., 28 Jan.-2 Feb. 1996, Page(s): 133 -137. [6] Moghram I, Rahman S. Analysis and evaluation of five short-term load forecasting techniques. IEEE Trans Power Syst, 4:1484–1491 (1989). [7] Xie Kaigui, Li Chunyan, Yu Jihui．Genetic algorithm based combination forecasting model for short term load．Power System Technology, v 25, n 8, Aug. 2001, p 20-3. [8] Park J. H, Park Y. M, and Lee K Y. Composite modeling for adaptive short-term load forecasting, IEEE Trans. on Power Systems, Vol. PWRS-6, No. 2, pp. 450–457( 1991) [9] Xie Kaigui, Li Chunyan, Zhou Jiaqi．Research of the combination forecasting model for load based on artificial neural network. Proceedings of the Chinese Society of Electrical Engineering, v 22, n 7, July, 2002, p 85-89 [10] Shi Y, Eberhart R. A modified particle swarm optimizer. In: IEEE World Congress on Computational Intelligence, 1998: 69-73 [11] Shigenori Naka, Takamu Genji, Toshiki Yura, Yoshikazu Fukuyama. A Hybrid Particle Swarm Optimization for Distribution State Estimation. IEEE Transactions on Power Systems, 2003(18): 60~68 [12] Jiang Chuanwen, Etorre Bompard. A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimization. Mathematics and Computers in Simulation, 68(1), 2005, 57-65.

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MEHRAN RASHIDI

A New Method Based on Signal Processing for Energy Forecasting in Power Systems

MEHRAN RASHIDI

A New Method Based on Signal Processing for Energy Forecasting in Power Systems