Improvement of Input-Output Correlations of ... - Semantic Scholar

IEEE Intelligent System Applications to Power Sysmtes (ISAP) 2005 1

Improvement of Input-Output Correlations of Electric Power Load Forecasting By Scatter Search Akihiro Mizutani, Tetsuya Yukawa, Kazuyuki Numa and Yasuhito Kuze Tatsuya Iizaka, Toshiyuki Yamagishi, Tetsuro Matsui, and Yoshikazu Fukuyama Member, IEEE

Abstract-- This paper proposes an improving method of inputoutput correlations of forecasting system for electric power load by scatter search. We have developed electric power load forecasting methods using weather information at Nagoya city. For high accuracy of forecasting, input-output correlations of forecasting system must be improved using weather information of other areas. Weighted average weather information at many cities is utilized for realizing high accuracy of load forecasting. The weight rates are optimized for the highest correlation between weighted average weather information and electric power demands by scatter search. The simulation results reveal the effectiveness of the proposed method. Index Terms-- Electric Load Forecasting, Artificial Neural Network, Scatter Search

E

I. INTRODUCTION

lectric load forecasting in power systems is very important task for ensuring reliability and economical operation. Especially, daily peak load forecasting for next day is the basic operation of generation scheduling. Therefore, high forecasting accuracy is required. The electric load forecasting task is usually carried out by statistical methods with some adjustments by operators in central load dispatching centers. However, the development of the forecasting system with high accuracy is expected in order to reduce workloads for the operators. A lot of statistical methods such as linear regression models have been conventionally utilized for the daily peak load forecasting. Recently, a number of artificial neural networks approaches have been proposed and some systems are practically used in central load dispatching centers [1-12]. Chubu Electric Power has actually installed a forecasting system by artificial neural networks [9]. Chubu Electric Power forecasts next day peak load using weather information at only one city. It supplies electric power for the large area, about 250km from the east side to the west side, and about 400km from the north side to the south side. Therefore, large forecasting errors may be occurred when weather conditions of other areas are different

from those of Nagoya area. Therefore, weather information of many areas must be used for improving forecasting accuracy. There are some methods using weather information of many areas for electric load forecasting such as a simple average method and a weighted average method by load demand ratios of each area. However, the best method for the electric load forecasting is not known. This paper proposes an optimizing method of weighting ratios of weather information of several areas using scatter search. The simulation results reveal the effectiveness of the proposed method. II. CHARACTERISTICS OF POWER SUPPLY AREA Chubu Electric Power supplies Electric power for large area, about 250km from the east side to the west side, about 400 km from the north side to the south side. This area includes flat land and mountainous regions. Each weather condition is different from each other. Chubu Electric Power has seven branches in the supply area. Electric load demand ratios of each branch are shown as table 1. TABLE I POWER DEMAND RATIOS OF EACH BRANCH Branch Ratio (%)

Nagoya 29

Shizuoka 16

Gifu 12

Mie 12

Okazaki 18

Nagano branch Nagano

400km Gifu branch Iida brach Nagano branch Gifu Mie branch

Iida

Nagoya Shizuoka

Yokkaichi Tsu

Okazaki

Hamamats

Okazaki branch

Akihiro Mizutani, Tetsuya Yukawa, Kazuyuki Numa and Yasuhito Kuze are with Chubu Electric Power Co., Inc., 1, Toshincho, Higashi-Ku, Nagoyashi, 461-8680, Japan. Toshiyuki Yamagishi, Tetsuro Matsui, Tatsuya Iizaka and Yoshikazu Fukuyama are with Fuji Electric Corporate, Ltd., 1 Fuji-machi, Hino, Tokyo 191-8502, Japan (e-mail: {yamagishi-toshiyuki, matsui-tetsuro, iizaka-tatsuya, fukuyama-yoshikazu}@fujielectric. co.jp).

Nagano 10

250km

Fig.1 Power supply area.

Shizuoka branch

Iida 2

2 III. PAST LOAD FORECASTING STUDY OF CHUBU ELECTRIC POWER [9] A. Past study Chubu Electric Power has forecasted a daily peak load by regression models and forecasting methods using actual load of some similar days of target day. Therefore, there are limitations to improve forecasting accuracy by these methods because there are non-liner relations between electric load and weather conditions. The neural network is a non-liner model, and it can learn the relations between electric load and weather conditions easily. Therefore, Chubu Electric power investigated loadforecasting methods by the neural networks, and developed the actual forecasting system. The system forecasts daily peak load more accurately than the conventional methods. The developed system has been practically used in the central load-dispatching center. B. Actually used forecasting method The neural networks of the forecasting system are composed of three layers feed forward networks. Target load is next day daily peak load. Input data of neural networks are the past actual peak loads, daily maximum temperatures, minimum temperatures, minimum humidity, and flag data of weekday and weekend. These input data are shown in table 2. The neural networks are developed for each season because the relations between electric load and weather conditions of each season are different. Season types are decided shown as below. These are decided by the relations between load demands and weather conditions, and the time of peak load. (1) Spring season is between April 1st and June 30th. (2) Summer season is between July 1st and September 15th. (3) Autumn season is between September 16th and August 31st. (4) Winter season is between November 1st and March 1st. Learning of the neural networks is performed every week using the past actual data. C. Construction of Forecasting System The forecasting system consists of a load forecasting engineering work station (EWS) and a load dispatching control system as shown in fig. 2. The load forecasting EWS performs learning of neural networks and forecasts daily peak load. Input data of the forecasting system are obtained from the load dispatching control system throw the LAN. IV. PROPOSED AVERAGE METHOD OF WEATHER INFORMATION AT MANY AREAS A. Average method of weather information at many areas The conventional system forecasts peak load using weather information at only Nagoya city. Therefore, large forecasting error may be occurred when weather conditions of other areas are different from those of Nagoya area. There are two methods using weather information at many areas as follows: (1) All data are input to forecasting models directly. (2) Weather information is averaged out.

TABLE II INPUT DATA OF NEURAL NETWORKS Spring Summer Autumn Electric Daily peak i-1, i-7 load Load Weather Max. Temp. i ～ i～ i～ Min. Temp. i-2 i-7 i-2 Min. humidity Weather Flag Saturday i ～ i-2 Holiday *: “i” means target day.

Winter

i～ i-2 i

LAN

Load forecasting EWS

Load dispatching control system

Fig.2 An electric load forecasting system

The first method is not used usually because network size becomes larger and learning time becomes longer than the second method. The second method is used conventionally. There are some average methods such as a simple average method, a weighted average method by load demand ratios of each area [10,11], and a weighted average method by intuitive ratios of experienced operators [12]. The best average method is not studied yet. B. Objective function and constraints There is a quadric relation between load demands and weather conditions. Especially, daily maximum temperature is the most important factor for electric peak load forecasting. Generally, input data with higher input-output correlations realize more accurate forecast. Weighted ratios are used for generating input data. Therefore, The best weighted ratios with the highest correlation can realized the most accurate forecast. In this paper, daily maximum temperatures at eight cities are examined. Seven cities of them are located in each branch. Another one is Yokkaichi city, which is located near Nagoya city. An objective function is correlation r2 between the weight ed average daily maximum temperatures and an approximate quadric function of peak loads. The objective function and constraints are shown as follows: Objective Function:

max .(r 2 ) Constraints:

(1)

3

wn ≥ 0% wn ≤ 100% 8

∑w n =1

n

Start

(2)

= 100%

where, r2: a coefficient of correlation wn: weighted ratios C. Scatter search [13] Scatter search is an non-liner optimizing method proposed by F. Glover in 1977. It is a multi searching optimizing algorithm like genetic algorithm (GA), and it can apply to continuous problems. The algorithm of scatter search is shown as follows: Step1: Generate a starting set of solution Generate a set of P distinct solutions randomly. These solutions are improved by a local search. Sets of b best solutions are added to the reference set. Step2: Create new solutions Choose any two sets of solutions from the reference set, and create new solutions at inside and outside of these solutions. For example, new x3 solution is created from solutions of x1 and x2 by the following equation: (3) x3 = x1 + rand ⋅ ( x1 − x 2 ) Step3: improve solutions Sets of solutions created in setp2 are improved by a local search. Step4: Update reference set Evaluate all solutions and update reference set using sets of b best solutions at step3 and previous reference set. Step5: Stop Stop when reaching a specified iteration limit, or go to step2. D. The proposed optimizing method A flow chart of the proposed method is shown in fig. 3. Weighted ratios are generated randomly at step 1. New weighted ratios are created at step 2. The solutions are improved by a local search at step 3. At step 4, firstly, all solutions are evaluated using the following sub steps. 1) Average maximum temperatures are calculated. 2) Eight daily maximum temperatures of each city are averaged out to one temperature by weighted ratios. The quadratic function is approximated using weighted average temperatures and peak loads. 3) The coefficient of correlation between the average temperatures and the quadratic function (objective function value) is calculated. Then, reference set is updated. V. SIMULATION RESULTS The proposed method and three conventional methods are compared in order to reveal effectiveness of the proposed method. Raw daily maximum temperatures at Nagoya city are used in case 1 instead of the weighted average temperatures. Case 1 is the same method of conventional forecasting system

Generation of weighted ratios randaml y

Step 1

Create new weighted ratios

Step 2

Improve weighted ratios

Step 3

Update reference set (1) Evaluate weighted ratios - Calculation of average maximum temperature - Approximation of quadratic function - Calculation of correlation (2) Update reference set

No

Reach a specified iteration limit?

Step 4

Step 5

Yes End

Fig.3A flow chart of the proposed method.

used in Chubu electric power. The simple average method is used in case 2. The weighted average daily maximum temperatures are calculated from temperatures at eight cities. In case 3, weighted ratios are the same as ratios of electric load demands of each branch. Ratios of Tsu city and Yokkaichi city are divided from the ratio of Mie branch load demand because both cities are located in the same branch. Ratio of Hamamatsu city is the same ratio of load demand of Okazaki branch because weather information of Okazaki city can’t be obtained, and Hamamatsu city is located near Okazaki city. The proposed method is used in case 4. Weighted ratios are optimized by scatter search. Simulation data are weekday data since 2000 until 2003. The proposed method optimizes weighted ratios for maximizing the objective function. Simulation results are shown in table 3. Correlation r2 calculated by the proposed method is the highest among all of methods. Fig. 4 shows relations of peak loads and daily maximum temperatures of case 1. Fig. 5 shows relation of peak loads and daily maximum temperatures of case 4. According to the correlation r2 shown in table 3, data of case 1 should be dispersed more widely than those of case 4. For example, data A and data B in fig.4 are far from other data, while data A and data B in fig. 5 are closer than those in fig. 4. Large forecasting errors must be occurred when these data are used. Actually, forecasting error of A day is 4.47 % and the error of B day is 7.46% by the conventional forecasting system. These errors are larger than the average error 2.38% in 2002. Data A of case 4 is shifted –3.6 degrees Celsius from data A of case 1 because the average weighted temperature is used in case 4. Similarly, data B of case 4 is shifted –3.2 degrees Celsius from data B of case 1. These data of case 4 get close

4 T ABLE III 30000

S IMULATION R ESULTS

Ratio (%)

Correlation (r2)

No. Nagoya

Proposed

1

2

3

4

100

12.5

28.8

38

Shizuoka

0

12.5

16.2

18

Tsu

0

12.5

6.0

16

Gifu

0

12.5

12.2

0

Nagano

0

12.5

10.3

21

Iida

0

12.5

2.0

0

Hamamatsu

0

12.5

18.4

7

Yokkaichi

0

12.5

6.0

0

2000

0.822

0.843

0.844

0.851

2001

0.850

0.880

0.881

0.889

2002

0.820

0.846

0.851

0.858

2003

0.894

0.903

0.919

0.925

Average

0.847

0.868

0.874

0.881

27000 Peak Load[MW]

Case

Conventional

24000

A

21000 18000

B

15000 0

5

10

15

20

25

30

35

40

Maximum Temperature[℃]

Fig.4 Simulation results of Case 1. 30000 27000 Peak Load[MW]

Method

24000

A

21000 18000

B

to other data. Namely, accurate forecast is expected by the proposed method.

15000 0

5

10

15

20

25

30

35

40

Weight Average Maximum Temperature[℃]

VI. CONCLUSIONS This paper proposes an optimizing method of weighted average ratios of weather information at many areas by scatter search in order to forecast daily electric peak load accurately. Simulation results reveal that correlation between peak loads and weighted average temperatures calculated by the proposed method is higher than three conventional methods. Verification of the proposed method using actual forecasting system is one of our future works. VII. REFERENCES [1] [2] [3] [4] [5] [6]

[7] [8]

D. C. Park, M. A. El-Sharkawi, R. J. Marks, L. E. Atlas and M. J. Damborg, "Electric Load Forecasting using an Artificial Neural Network", IEEE trans. on Power Systems, Vol. 6, No. 2, May 1991. K. Y. Lee, Y. T. Cha, and J. H. Park, "Short-term Load Forecasting using an Artificial Neural Network", IEEE Trans. on Power Systems, Vol. 7, No. 1, February 1992. T. M. Peng, N. F. Huble, and G. G. Karady, "Advancement in the Application of Neural Networks for Short-term Load Forecasting", IEEE Trans. on Power Systems, Vol. 7, No. 1,February 1992. C. N. Lu, H. T. Wu, and B. Vemuri, "Neural Network Based Short Term Load Forecasting", IEEE Trans. on Power Systems, Vol. 8, No. 1, February 1993. A. D. Papalexopoulos, S. Hao, and T. M. Peng, "An Implementation of a Neural Network Based Load Forecasting Model for the EMS", IEEE Trans. on Power Systems, Vol. 9, No. 4, November 1994. A. Khotanzad, R. Afkhami-Rohani, T. L. Lu, A. Abaye, M. Davis, and D. J. Maratukulam, "ANNSTLF - A Neural-network-based Electric Load Forecasting System", IEEE Trans. on Neural Networks, Vol. 8, No. 4, July 1997. W. Charytoniuk, M. Chen, "Very Short-term Load Forecasting using Artificial Neural Networks", IEEE Trans. on Power Systems, Vol. 15, No. 1, February 2000. T. Matsumoto, S. Kitamura, Y. Ueki, T. Matsui, "Short-term Load Forecasting by Artificial Neural Networks Using Individual and Collective Data of Preceding Years", Proc. of ANNPS '93, 1993.

Fig.5 Simulation results of Case 4. [9] [10] [11]

[12]

[13]

(proposed method)

Y. Ueki, T. Matsui, H. Endo, T. Iizaka, T. Kato, R. Araya, "Peak Load Forecasting Using Neural Networks and Fuzzy Inference", Proc. of IASTED '96, 1996. O. Ishioka, et al., "Development of Electric Load Forecasting using Neural Networks", The Trans. of Institute of the Electrical Engineering in Japan, Vol.120-B, No.12, pp.1550-1557, 2000 (in Japanese). T.Kakkonda, T.Ishihara, E.Tsukada, T.Matsui, T.Iizaka and Y.Fukuyama, “Electric Load Forecasting by Neural Networks Considering Various Load Type”, Proc. of ISAP, No.56, 2003 Kugimiya, Suzuki, Matsui, Iizaka, Fukuyama, Kobayashi, ” Development of Electric Load Forecasting System wth Explainability for Reasons of Forecasting Results”, The Paper of Joint Techical Meeting on Power Engineering and Power Systems Engineering, IEE Japan, PE03-62, PSE-03-73, (2003) (in Japanese) F.Glover,”Heuristics for Integer Programming Using Surrogate Constraints”,Decision Sciences,Vol.8,pp.156-166, (1977)

VIII. BIOGRAPHIES AKIHIRO MIZUTANI graduated from Handa Technical High School, Aichi, Japan in 1985. He has been working at Chubu Electric Power Co., Inc., Japan from 1985. His research interests include load forecasting and control of power system. TETSUYA YUKAWA received B.S. degree in electrical engineering in 1991 from Tokyo Institute of Technology, Tokyo, Japan. He has been working at Chubu Electric Power Co., Inc., Japan from 1991. His research interests include power system operations. He is a member of IEE of Japan. KAZUYUKI NUMA graduated from Nakatsu Technical High School, Oita, Japan in 1983. He has been working at Chubu Electric Power Co., Inc., Japan from 1983. His research interests include development of Short-term Load Forecasting System for Central Load Dispatching Center using intelligent systems such as neural network, and fuzzy inference techniques. YASUHITO KUZE received B.S. and M.S. degrees in electrical engineering in 1986 and 1988, respectively, from Toyohashi University of Technology, Aichi, Japan. He has been working at Chubu Electric Power Co.,

5 Inc., Japan from 1988. His research interests include development of conrol systems such as SCADA and EMS. He is a member of IEE of Japan.

fuzzy inference techniques to power and industrial systems. He is a member of IEE of Japan.

TATSUYA IIZAKA received B.S. and M.S. degrees in electrical engineering in 1992 and 1994, respectively, from Saitama university, Saitama, Japan. He has been working at Fuji Electric Co. Japan from 1994. His research interests include application of intelligent systems such as neural network, and fuzzy inference techniques to power systems. He is a member of IEE of Japan.

YOSHIKAZU FUKUYAMA (M'90) received B.S., M.S., and PhD degrees in electrical engineering in 1985, 1987, and 1997, respectively, from Waseda university, Tokyo, Japan. He has been working at Fuji Electric Co. Japan from 1987. He was a visiting scientist at Cornell University from 1993 to 1994. His research interests include application of intelligent systems such as expert system, neural network, and modern heuristic techniques to power and energy systems and power system analysis including voltage stability and load flow. He is also interested in applications of meta-heuristic techniques to practical and general optimization problems. He is a member of IEEE and IEE of Japan.

TOSHIYUKI YAMAGISHI received B.S. and M.S. degrees in electrical engineering in 1993 and 1995, respectively, from Nihon university, Tokyo, Japan. He has been working at Fuji Electric Co. Japan from 1995. His research interests include application of intelligent systems such as neural network to power systems. TETSURO MATSUI received B.S. degree in information engineering in 1988, from Yokohama national university, Kanagawa, Japan. He has been working at Fuji Electric Co. Japan from 1988. His research interests include application of intelligent systems such as expert system, neural network, and