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Fuzzy approach for short term load forecasting
Electric Power Systems Research 76 (2006) 541–548
Fuzzy approach for short term load forecasting S. Chenthur Pandian a,∗ , K. Duraiswamy a , C. Christober Asir Rajan b , N. Kanagaraj a a
Electrical and Electronics Engg., K.S. Rangasamy College of Technology, Tiruchengode 637209, Tamil Nadu, India b Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Pondicherry, India Received 27 May 2005; received in revised form 27 July 2005; accepted 27 September 2005 Available online 22 November 2005
Abstract The main objective of short term load forecasting (STLF) is to provide load predictions for generation scheduling, economic load dispatch and security assessment at any time. The STLF is needed to supply necessary information for the system management of day-to-day operations and unit commitment. In this paper, the ‘time’ and ‘temperature’ of the day are taken as inputs for the fuzzy logic controller and the ‘forecasted load’ is the output. The input variable ‘time’ has been divided into eight triangular membership functions. The membership functions are Mid Night, Dawn, Morning, Fore Noon, After Noon, Evening, Dusk and Night. Another input variable ‘temperature’ has been divided into four triangular membership functions. They are Below Normal, Normal, Above Normal and High. The ‘forecasted load’ as output has been divided into eight triangular membership functions. They are Very Low, Low, Sub Normal, Moderate Normal, Normal, Above Normal, High and Very High. Case studies have been carried out for the Neyveli Thermal Power Station Unit-II (NTPS-II) in India. The fuzzy forecasted load values are compared with the conventional forecasted values. The forecasted load closely matches the actual one within ±3%. © 2005 Elsevier B.V. All rights reserved. Keywords: Short term load forecasting; Fuzzy logic; Membership functions; Fuzzifier; Defuzzifier
1. Introduction Load forecasting is an essential element of power system operation and planning involving prognosis of the future level of demand to serve as the basis for the supply side and demand side planning. The load requirements are to be predicted in advance so that the power system operates effectively and efficiently. It is done for planning, marketing, risk assessment, billing, dispatch or unit commitment purposes. Short term load forecasting (STLF) is important for the economic and secure operation of power systems. In power systems many uncertainties arises due to aging of machines, unforeseen load, fluctuations, losses in transmission lines, voltage and frequency instability, change of weather conditions. These facts make it difficult to effectively deal with many power systems problems through strict mathematical formulations alone [1]. Therefore, fuzzy set theory based approach, in recent years has emerged as a complement tool to mathematical
∗
Corresponding author. Tel.: +91 4288 274759(O)/085(R). E-mail address: [email protected] (S. Chenthur Pandian).
0378-7796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2005.09.018
approach for solving power system problems [2]. Fuzzy logic is often an effective approach to these uncertainties. Fuzzy logic control is being increasingly applied to solve the power system problems in areas where system complexity, development time, cost and economics are the major issues. The wonderful world of fuzzy logic is a powerful new paradigm, helping us to analyze unknown and complicated systems [3,4]. Load forecasting can help to estimate load flows and to make decisions that can prevent overloading. Timely implementations of such decisions lead to the improvement of network reliability and to the reduced occurrences of equipment failures and blackouts. Economic and reliable operation of an electric utility depends to a significant extent on the accuracy of the load forecast. The load despatcher at main despatch center must anticipate the load pattern well in advance so as to have sufficient generation to meet the customer requirements. Overestimation may cause the startup of too many generating units and lead to an unnecessary increase in the reserve and the operating costs. Underestimation of the load forecasts results in failure to provide the required spinning and standby reserve and stability to the system, which may lead into collapse of the power system network [7,8]. Load forecast errors can yield suboptimal unit commitment decisions. Hence,
542
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
Fig. 1. Typical load curve pattern for a day.
Availability of high resolution and more variety of data, improved computer speed and reduction in cost are all helpful to provide better accuracy in distribution load forecasting. However, we also face the information explosion problem, in which we have so much information that human alone cannot handle the huge amount of data without help from other appropriate technologies. Different technologies such as fuzzy logic, neural networks and distributed database have been developed to manage the large amount of data available and to best utilize the information provided in the data. In general, the better we utilize relevant information, better the results will be. Fig. 2. Triangular membership functions for time (Input 1).
2. Load forecasting exact forecasting of the load is an essential element in power system. The power system should provide a secure supply without many fluctuations in the voltage and frequency. In conventional methods, the models are designed based on the relationship between load power and factors influencing load power. The conventional method has the advantage that we can forecast load power with a simple prediction model. However, since the relationship between load power and factors influencing load power is non-linear, it is difficult to identify its non-linearity by using conventional methods. Several methods based on similarity have been reported for load forecasting. These methods are based on similarity forecast future power load curve by using information of the day being similar to the weather condition of forecast day [9].
Fig. 3. Triangular membership functions for temperature (Input 2).
Load forecasting has always been important for planning and operational decision. Proper load forecasting with less percentage of error has to be made with the help of artificial intelligence techniques. Long term load prediction is normally used for planning the growth of the generation capacity. This long term forecasting is used to decide whether to built new lines and substations or to upgrade the existing systems. Medium-term load forecasts is used to meet the load requirements at the height of the winter or the summer season may require a load forecast to be made a few days to few weeks (or) few months in advance [5]. Short term load forecast is needed to supply necessary information for the system management of day-to-day operations and unit commitment. Out of these three types of forecasting the short term load forecasting being very essential and impor-
Fig. 4. Triangular membership functions for forecasted load (Output).
Table 1 Conventional load and percentage error calculation between fuzzy forecasted and actual load for three different seasons of NTPS-II Time (h)
Medium demand May–September on 02-06-04
Off Peak demand October–December on 09-11-03
Conventional load (MW)
Fuzzy forecasted load (MW)
Actual load (MW)
Error (%)
Conventional load (MW)
Fuzzy forecasted load (MW)
Actual load (MW)
Error (%)
Conventional load (MW)
Fuzzy forecasted load (MW)
Actual load (MW)
Error (%)
1519 1475 1521 1519 1505 1476 1450 1515 1520 1522 1519 1524 1526 1532 1517 1531 1535 1503 1528 1536 1535 1553 1518 1500
1415 1359 1364 1387 1354 1368 1346 1394 1420 1425 1360 1360 1418 1410 1374 1387 1380 1408 1412 1424 1415 1425 1403 1353
1381 1341 1383 1381 1368 1342 1345 1377 1382 1384 1381 1385 1387 1393 1379 1392 1395 1366 1389 1396 1395 1412 1380 1364
2.40 1.32 1.37 0.43 1.02 1.90 0.07 1.22 2.67 2.88 1.52 1.80 2.18 1.20 0.36 0.35 1.07 2.98 1.63 1.96 1.41 0.91 1.64 0.80
1004 980 945 976 999 1018 1003 1080 1060 1108 1115 1122 1123 1112 1115 1117 1122 1095 1126 1120 1125 1124 1120 1101
929 910 867 899 889 906 934 964 953 982 988 995 999 1024 1032 1036 1023 1001 1020 1025 1052 1053 1029 1030
913 891 859 887 908 925 912 982 964 1007 1014 1020 1021 1011 1014 1015 1020 995 1024 1018 1023 1022 1018 1001
1.72 2.08 0.92 1.33 2.09 2.05 2.36 1.83 1.14 2.48 2.56 2.45 2.15 1.27 1.74 2.02 0.29 0.59 0.39 0.6 2.75 2.94 1.06 2.81
967 978 980 957 948 949 968 970 979 974 873 966 983 990 970 969 972 972 975 974 974 969 959 959
892 872 909 892 865 876 885 887 894 897 812 868 869 883 889 897 896 869 872 879 889 888 894 896
879 889 891 870 862 863 880 882 890 885 794 878 894 900 882 881 884 884 886 885 885 881 872 872
1.45 1.91 1.98 2.46 0.34 1.48 0.56 0.56 0.44 1.33 2.21 1.14 2.79 1.88 0.78 1.78 1.33 1.69 1.58 0.66 0.44 0.78 2.46 2.67
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Peak demand January–April on 27-04-04
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Fig. 5. (a) Peak demand fuzzy membership functions for inputs and output and (b) three-dimensional surface views.
tant for the power system day-to-day operations, so it is taken in this paper. The STLF is important for the economic and secure operation of power system. Many operations like real time generation control, security analysis spinning reserve allocation energy interchanges with other utilities and energy transactions planning are done based on STLF [6].
2.1. Load characteristics Load means a device or set of devices, which taps energy from the power system networks. Load pattern is not constant for 24 h in a day. It keeps on changing from hour to hour, minute to minute. A typical load curve pattern for 24 h is shown in Fig. 1.
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
Fig. 6. (a) Medium demand fuzzy membership functions for inputs and output and (b) three-dimensional surface views.
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S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
Fig. 7. (a) Off Peak demand fuzzy membership functions for inputs and output and (b) three-dimensional surface views.
It has overnight minimum, Midday peak, Day valley, Evening peak and late high. The load curve changes are due to the customer’s deliberate utility intervention [7,8]. Similarly the week load is also not constant for all 7 days. It changes from weekdays to weekend days. It is also changing on the holidays and special events days [9]. In all these areas, there are many uncertainties. So the implementation of fuzzy logic to forecast the short term will be an opted choice.
3. Short term load forecasting A large variety of statistical and artificial intelligence techniques have been developed for short term load forecasting. Some of the methods are similar day approach, regression methods, time series methods, neural network, fuzzy logic, expert system, support vector machines. Many operations like real time generation control. Security analysis, spinning reserves allocation and energy transactions planning are done based on STLF.
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
4. Fuzzy logic implementation This paper makes use of simplified fuzzy inference in which the consequence of the fuzzy rule is expressed in crisp number. One of the attractive features in fuzzy logic is that the fuzzy rule is capable of easily adding the new memberships function to the existing ones. Fuzzy approach proposed can be used as an aid to forecast the loads with different lead times [3]. A more accurate fuzzy expert system is obtained by dividing the region into intervals [4]. The intervals for the time (Input 1) has been divided into eight triangular membership functions which are as follows: • • • • • • • •
Mid Night (MID NIG), Dawn (DAWN), Morning (MORN), Fore Noon (F.NOON), After Noon (A.NOON), Evening (EVEN), Dusk (DUSK), Night (NIG). The triangular membership function is shown in Fig. 2.
547
The intervals for temperature (Input 2) have been divided into four triangular membership functions which are as follows: • • • •
Below Normal (BEL.NOR), Normal (NOR), Above normal (AB.NOR), High (HIGH).
The triangular membership function is shown below in Fig. 3. The intervals for the forecasted load (output) has been divided into eight triangular membership functions which are as follows: • • • • • • • •
Very Low (V.LOW), Low (LOW), Sub Normal (SUB.NOR), Moderate Normal (MOD.NOR), Normal (NOR), Above Normal (AB.NOR), High (HIGH), Very High (V.HIGH).
The triangular membership function is shown in Fig. 4. Fuzzy logic membership functions and fuzzy rules are designed to provide a simple technique to directly implement
Fig. 8. Comparison of results between the actual load, conventional forecasted load and fuzzy forecasted load for: (a) Peak, (b) Medium and (c) Off Peak demands for NTPS-II.
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S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
experience and intuition into a computer program [1,2]. The membership functions and fuzzy rules in the fuzzy logic formulation provide an intuitive and straightforward manner to include heuristics into the load forecasting. In the fuzzy logic approach, the preference calculation is based on the entire profile of the membership functions rather than base on point values [3,4]. This approach is much closer to people’s decision-making process in real life. 5. Case study Case study has been carried out for Neyveli Thermal Power Station Unit-II (NTPS-II) in India. The values are taken for specific days, the conventional and fuzzy forecasted load values and actual load values and the percentage of error values are shown in Table 1. Simulation of results has been carried out in ‘MATLAB’ simulation package. The fuzzy membership functions for the inputs and output, three-dimensional surfaces views for these three Peak demand, Medium demand and Off Peak demand are shown in Figs. 5–7(a and b), respectively. 6. Results The fuzzy rule approach is designed to closely describe the input–output relationship of the actual problem by using linguistic terms. The membership functions and fuzzy rules in the fuzzy logic formulation provide an intuitive and straightforward manner to include heuristics into the load forecasting. The results are compared between the conventional load, actual load and fuzzy forecasted load. The values are shown in Table 1 and the compared results are shown in Fig. 8(a–c) for Peak, Medium and Off Peak demand seasons, respectively. From these figures it is observed that the fuzzy-based STLF is having much lower forecasted value than the conventional method. Hence, the fuzzy logic approach is more effective and economical, it is very close to the actual load. 7. Conclusion It is concluded that if the loads turn out to be lower than forecasted values, then the power generated will be costlier one and uneconomical and on the other hand if the loads are greater than anticipated, then the security constraints such as spinning reserve margins, frequency and the reliability of the system are in danger. In this case, the percentage error is less than ±3%. The comparison of the forecasted load has been carried out between the conventional method and fuzzy method. The comparison has been carried out for Peak Demand, Medium Demand and Off
Peak Demand. For all these cases, the fuzzy based load forecasting is much closer to the actual load. Hence it is concluded that for STLF, the fuzzy logic provides a better solution. References [1] R.C. Bansal, Bibliography on the fuzzy set theory applications in power systems, 1994–2001, IEEE Trans. Power Syst. 18 (November (4)) (2003) 1291–1299. [2] S. Chenthur Pandian, K. Duraiswamy, Networking for power system economics by implementing fuzzy logic, in: National Conference at A. Kalasalingam College of Engineering, Krishnankoil, India, 19th & 20th December, 2003. [3] T.J. Ross, Fuzzy Logic with Engineering Application, McGraw-Hill Inc., New York, 1995. [4] G.J. Klir, Bo Yuan, Fuzzy Sets and Fuzzy Logic, Prentice Hall of India Private Limited, New Delhi, 2000. [5] G.-C. Liao, T.-P. Tsao, Application of Fuzzy Neural Networks and Artificial Intelligence for Load Forecasting, vol. 70, Elsevier—Electric Power System Research, 2004, pp. 237–244. [6] X. Wang, N. Hatziargyriou, L.H. Tsoukalas, A new methodology for nodal load forecasting in deregulated power systems, IEEE Power Eng. Rev. (May) (2002) 48–51. [7] S. Chenthur Pandian, K. Duraiswamy, A.A. Sadagopan, Implementation of fuzzy logic for short term load forecasting, in: International Conference by JNNCE, Shimoga India & MIT, Cambridge USA on 20th to 23rd December, 2004. [8] S. Chenthur Pandian, K. Duraiswamy, Fuzzy logic approach for the load forecasting, in: International Conference by Pentagram Research Centre, Hyderabad, India, 6–9th January, 2005. [9] H. Mori, H. Kobayashi, Optimal fuzzy inference for short-term load forecasting, IEEE Trans. Power Syst. 11 (February (1)) (1996) 390– 396. Dr. S. Chenthur Pandian has received his M.E. degree in power system from Punjab University, Chandigarh. He has received his Ph.D. degree from Periyar University, Salem, India. He is with the department of EEE, in K.S. Rangasamy College of Technology, Tiruchengode, Tamil Nadu, India. His research areas are power system optimization, power system operation and control, power electronics and intelligent techniques application to power system. Dr. K. Duraiswamy is the Dean of K.S. Rangasamy College of Technology, Tiruchengode, Tamil Nadu, India. He has received his Ph.D. degree from Anna University, Chennai. He has published many technical papers in international and national Journals. His areas of interests are power generation scheduling, state estimations, optimization technique, computer networks, soft computing techniques. He has guided many Ph.D. scholars. Dr. C. Christober Asir Rajan has received his Ph.D. degree from Anna University, Chennai, India. He is with the department of EEE in Pondicherry Engineering College, Pondicherry, India. His fields of interests are power system operation and control, soft computing techniques, neural network and fuzzy applications for power systems. N. Kanagaraj is a research scholar in National Institute of Technology, Trichy, Tamil Nadu, India. He is with the department of EEE in KSRCT, Tiruchengode, Tamil Nadu, India. His research area is fuzzy logic, neural network and its application.
Fuzzy approach for short term load forecasting S. Chenthur Pandian a,∗ , K. Duraiswamy a , C. Christober Asir Rajan b , N. Kanagaraj a a
Electrical and Electronics Engg., K.S. Rangasamy College of Technology, Tiruchengode 637209, Tamil Nadu, India b Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Pondicherry, India Received 27 May 2005; received in revised form 27 July 2005; accepted 27 September 2005 Available online 22 November 2005
Abstract The main objective of short term load forecasting (STLF) is to provide load predictions for generation scheduling, economic load dispatch and security assessment at any time. The STLF is needed to supply necessary information for the system management of day-to-day operations and unit commitment. In this paper, the ‘time’ and ‘temperature’ of the day are taken as inputs for the fuzzy logic controller and the ‘forecasted load’ is the output. The input variable ‘time’ has been divided into eight triangular membership functions. The membership functions are Mid Night, Dawn, Morning, Fore Noon, After Noon, Evening, Dusk and Night. Another input variable ‘temperature’ has been divided into four triangular membership functions. They are Below Normal, Normal, Above Normal and High. The ‘forecasted load’ as output has been divided into eight triangular membership functions. They are Very Low, Low, Sub Normal, Moderate Normal, Normal, Above Normal, High and Very High. Case studies have been carried out for the Neyveli Thermal Power Station Unit-II (NTPS-II) in India. The fuzzy forecasted load values are compared with the conventional forecasted values. The forecasted load closely matches the actual one within ±3%. © 2005 Elsevier B.V. All rights reserved. Keywords: Short term load forecasting; Fuzzy logic; Membership functions; Fuzzifier; Defuzzifier
1. Introduction Load forecasting is an essential element of power system operation and planning involving prognosis of the future level of demand to serve as the basis for the supply side and demand side planning. The load requirements are to be predicted in advance so that the power system operates effectively and efficiently. It is done for planning, marketing, risk assessment, billing, dispatch or unit commitment purposes. Short term load forecasting (STLF) is important for the economic and secure operation of power systems. In power systems many uncertainties arises due to aging of machines, unforeseen load, fluctuations, losses in transmission lines, voltage and frequency instability, change of weather conditions. These facts make it difficult to effectively deal with many power systems problems through strict mathematical formulations alone [1]. Therefore, fuzzy set theory based approach, in recent years has emerged as a complement tool to mathematical
∗
Corresponding author. Tel.: +91 4288 274759(O)/085(R). E-mail address: [email protected] (S. Chenthur Pandian).
0378-7796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2005.09.018
approach for solving power system problems [2]. Fuzzy logic is often an effective approach to these uncertainties. Fuzzy logic control is being increasingly applied to solve the power system problems in areas where system complexity, development time, cost and economics are the major issues. The wonderful world of fuzzy logic is a powerful new paradigm, helping us to analyze unknown and complicated systems [3,4]. Load forecasting can help to estimate load flows and to make decisions that can prevent overloading. Timely implementations of such decisions lead to the improvement of network reliability and to the reduced occurrences of equipment failures and blackouts. Economic and reliable operation of an electric utility depends to a significant extent on the accuracy of the load forecast. The load despatcher at main despatch center must anticipate the load pattern well in advance so as to have sufficient generation to meet the customer requirements. Overestimation may cause the startup of too many generating units and lead to an unnecessary increase in the reserve and the operating costs. Underestimation of the load forecasts results in failure to provide the required spinning and standby reserve and stability to the system, which may lead into collapse of the power system network [7,8]. Load forecast errors can yield suboptimal unit commitment decisions. Hence,
542
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
Fig. 1. Typical load curve pattern for a day.
Availability of high resolution and more variety of data, improved computer speed and reduction in cost are all helpful to provide better accuracy in distribution load forecasting. However, we also face the information explosion problem, in which we have so much information that human alone cannot handle the huge amount of data without help from other appropriate technologies. Different technologies such as fuzzy logic, neural networks and distributed database have been developed to manage the large amount of data available and to best utilize the information provided in the data. In general, the better we utilize relevant information, better the results will be. Fig. 2. Triangular membership functions for time (Input 1).
2. Load forecasting exact forecasting of the load is an essential element in power system. The power system should provide a secure supply without many fluctuations in the voltage and frequency. In conventional methods, the models are designed based on the relationship between load power and factors influencing load power. The conventional method has the advantage that we can forecast load power with a simple prediction model. However, since the relationship between load power and factors influencing load power is non-linear, it is difficult to identify its non-linearity by using conventional methods. Several methods based on similarity have been reported for load forecasting. These methods are based on similarity forecast future power load curve by using information of the day being similar to the weather condition of forecast day [9].
Fig. 3. Triangular membership functions for temperature (Input 2).
Load forecasting has always been important for planning and operational decision. Proper load forecasting with less percentage of error has to be made with the help of artificial intelligence techniques. Long term load prediction is normally used for planning the growth of the generation capacity. This long term forecasting is used to decide whether to built new lines and substations or to upgrade the existing systems. Medium-term load forecasts is used to meet the load requirements at the height of the winter or the summer season may require a load forecast to be made a few days to few weeks (or) few months in advance [5]. Short term load forecast is needed to supply necessary information for the system management of day-to-day operations and unit commitment. Out of these three types of forecasting the short term load forecasting being very essential and impor-
Fig. 4. Triangular membership functions for forecasted load (Output).
Table 1 Conventional load and percentage error calculation between fuzzy forecasted and actual load for three different seasons of NTPS-II Time (h)
Medium demand May–September on 02-06-04
Off Peak demand October–December on 09-11-03
Conventional load (MW)
Fuzzy forecasted load (MW)
Actual load (MW)
Error (%)
Conventional load (MW)
Fuzzy forecasted load (MW)
Actual load (MW)
Error (%)
Conventional load (MW)
Fuzzy forecasted load (MW)
Actual load (MW)
Error (%)
1519 1475 1521 1519 1505 1476 1450 1515 1520 1522 1519 1524 1526 1532 1517 1531 1535 1503 1528 1536 1535 1553 1518 1500
1415 1359 1364 1387 1354 1368 1346 1394 1420 1425 1360 1360 1418 1410 1374 1387 1380 1408 1412 1424 1415 1425 1403 1353
1381 1341 1383 1381 1368 1342 1345 1377 1382 1384 1381 1385 1387 1393 1379 1392 1395 1366 1389 1396 1395 1412 1380 1364
2.40 1.32 1.37 0.43 1.02 1.90 0.07 1.22 2.67 2.88 1.52 1.80 2.18 1.20 0.36 0.35 1.07 2.98 1.63 1.96 1.41 0.91 1.64 0.80
1004 980 945 976 999 1018 1003 1080 1060 1108 1115 1122 1123 1112 1115 1117 1122 1095 1126 1120 1125 1124 1120 1101
929 910 867 899 889 906 934 964 953 982 988 995 999 1024 1032 1036 1023 1001 1020 1025 1052 1053 1029 1030
913 891 859 887 908 925 912 982 964 1007 1014 1020 1021 1011 1014 1015 1020 995 1024 1018 1023 1022 1018 1001
1.72 2.08 0.92 1.33 2.09 2.05 2.36 1.83 1.14 2.48 2.56 2.45 2.15 1.27 1.74 2.02 0.29 0.59 0.39 0.6 2.75 2.94 1.06 2.81
967 978 980 957 948 949 968 970 979 974 873 966 983 990 970 969 972 972 975 974 974 969 959 959
892 872 909 892 865 876 885 887 894 897 812 868 869 883 889 897 896 869 872 879 889 888 894 896
879 889 891 870 862 863 880 882 890 885 794 878 894 900 882 881 884 884 886 885 885 881 872 872
1.45 1.91 1.98 2.46 0.34 1.48 0.56 0.56 0.44 1.33 2.21 1.14 2.79 1.88 0.78 1.78 1.33 1.69 1.58 0.66 0.44 0.78 2.46 2.67
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Peak demand January–April on 27-04-04
543
544
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
Fig. 5. (a) Peak demand fuzzy membership functions for inputs and output and (b) three-dimensional surface views.
tant for the power system day-to-day operations, so it is taken in this paper. The STLF is important for the economic and secure operation of power system. Many operations like real time generation control, security analysis spinning reserve allocation energy interchanges with other utilities and energy transactions planning are done based on STLF [6].
2.1. Load characteristics Load means a device or set of devices, which taps energy from the power system networks. Load pattern is not constant for 24 h in a day. It keeps on changing from hour to hour, minute to minute. A typical load curve pattern for 24 h is shown in Fig. 1.
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
Fig. 6. (a) Medium demand fuzzy membership functions for inputs and output and (b) three-dimensional surface views.
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S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
Fig. 7. (a) Off Peak demand fuzzy membership functions for inputs and output and (b) three-dimensional surface views.
It has overnight minimum, Midday peak, Day valley, Evening peak and late high. The load curve changes are due to the customer’s deliberate utility intervention [7,8]. Similarly the week load is also not constant for all 7 days. It changes from weekdays to weekend days. It is also changing on the holidays and special events days [9]. In all these areas, there are many uncertainties. So the implementation of fuzzy logic to forecast the short term will be an opted choice.
3. Short term load forecasting A large variety of statistical and artificial intelligence techniques have been developed for short term load forecasting. Some of the methods are similar day approach, regression methods, time series methods, neural network, fuzzy logic, expert system, support vector machines. Many operations like real time generation control. Security analysis, spinning reserves allocation and energy transactions planning are done based on STLF.
S. Chenthur Pandian et al. / Electric Power Systems Research 76 (2006) 541–548
4. Fuzzy logic implementation This paper makes use of simplified fuzzy inference in which the consequence of the fuzzy rule is expressed in crisp number. One of the attractive features in fuzzy logic is that the fuzzy rule is capable of easily adding the new memberships function to the existing ones. Fuzzy approach proposed can be used as an aid to forecast the loads with different lead times [3]. A more accurate fuzzy expert system is obtained by dividing the region into intervals [4]. The intervals for the time (Input 1) has been divided into eight triangular membership functions which are as follows: • • • • • • • •
Mid Night (MID NIG), Dawn (DAWN), Morning (MORN), Fore Noon (F.NOON), After Noon (A.NOON), Evening (EVEN), Dusk (DUSK), Night (NIG). The triangular membership function is shown in Fig. 2.
547
The intervals for temperature (Input 2) have been divided into four triangular membership functions which are as follows: • • • •
Below Normal (BEL.NOR), Normal (NOR), Above normal (AB.NOR), High (HIGH).
The triangular membership function is shown below in Fig. 3. The intervals for the forecasted load (output) has been divided into eight triangular membership functions which are as follows: • • • • • • • •
Very Low (V.LOW), Low (LOW), Sub Normal (SUB.NOR), Moderate Normal (MOD.NOR), Normal (NOR), Above Normal (AB.NOR), High (HIGH), Very High (V.HIGH).
The triangular membership function is shown in Fig. 4. Fuzzy logic membership functions and fuzzy rules are designed to provide a simple technique to directly implement
Fig. 8. Comparison of results between the actual load, conventional forecasted load and fuzzy forecasted load for: (a) Peak, (b) Medium and (c) Off Peak demands for NTPS-II.
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experience and intuition into a computer program [1,2]. The membership functions and fuzzy rules in the fuzzy logic formulation provide an intuitive and straightforward manner to include heuristics into the load forecasting. In the fuzzy logic approach, the preference calculation is based on the entire profile of the membership functions rather than base on point values [3,4]. This approach is much closer to people’s decision-making process in real life. 5. Case study Case study has been carried out for Neyveli Thermal Power Station Unit-II (NTPS-II) in India. The values are taken for specific days, the conventional and fuzzy forecasted load values and actual load values and the percentage of error values are shown in Table 1. Simulation of results has been carried out in ‘MATLAB’ simulation package. The fuzzy membership functions for the inputs and output, three-dimensional surfaces views for these three Peak demand, Medium demand and Off Peak demand are shown in Figs. 5–7(a and b), respectively. 6. Results The fuzzy rule approach is designed to closely describe the input–output relationship of the actual problem by using linguistic terms. The membership functions and fuzzy rules in the fuzzy logic formulation provide an intuitive and straightforward manner to include heuristics into the load forecasting. The results are compared between the conventional load, actual load and fuzzy forecasted load. The values are shown in Table 1 and the compared results are shown in Fig. 8(a–c) for Peak, Medium and Off Peak demand seasons, respectively. From these figures it is observed that the fuzzy-based STLF is having much lower forecasted value than the conventional method. Hence, the fuzzy logic approach is more effective and economical, it is very close to the actual load. 7. Conclusion It is concluded that if the loads turn out to be lower than forecasted values, then the power generated will be costlier one and uneconomical and on the other hand if the loads are greater than anticipated, then the security constraints such as spinning reserve margins, frequency and the reliability of the system are in danger. In this case, the percentage error is less than ±3%. The comparison of the forecasted load has been carried out between the conventional method and fuzzy method. The comparison has been carried out for Peak Demand, Medium Demand and Off
Peak Demand. For all these cases, the fuzzy based load forecasting is much closer to the actual load. Hence it is concluded that for STLF, the fuzzy logic provides a better solution. References [1] R.C. Bansal, Bibliography on the fuzzy set theory applications in power systems, 1994–2001, IEEE Trans. Power Syst. 18 (November (4)) (2003) 1291–1299. [2] S. Chenthur Pandian, K. Duraiswamy, Networking for power system economics by implementing fuzzy logic, in: National Conference at A. Kalasalingam College of Engineering, Krishnankoil, India, 19th & 20th December, 2003. [3] T.J. Ross, Fuzzy Logic with Engineering Application, McGraw-Hill Inc., New York, 1995. [4] G.J. Klir, Bo Yuan, Fuzzy Sets and Fuzzy Logic, Prentice Hall of India Private Limited, New Delhi, 2000. [5] G.-C. Liao, T.-P. Tsao, Application of Fuzzy Neural Networks and Artificial Intelligence for Load Forecasting, vol. 70, Elsevier—Electric Power System Research, 2004, pp. 237–244. [6] X. Wang, N. Hatziargyriou, L.H. Tsoukalas, A new methodology for nodal load forecasting in deregulated power systems, IEEE Power Eng. Rev. (May) (2002) 48–51. [7] S. Chenthur Pandian, K. Duraiswamy, A.A. Sadagopan, Implementation of fuzzy logic for short term load forecasting, in: International Conference by JNNCE, Shimoga India & MIT, Cambridge USA on 20th to 23rd December, 2004. [8] S. Chenthur Pandian, K. Duraiswamy, Fuzzy logic approach for the load forecasting, in: International Conference by Pentagram Research Centre, Hyderabad, India, 6–9th January, 2005. [9] H. Mori, H. Kobayashi, Optimal fuzzy inference for short-term load forecasting, IEEE Trans. Power Syst. 11 (February (1)) (1996) 390– 396. Dr. S. Chenthur Pandian has received his M.E. degree in power system from Punjab University, Chandigarh. He has received his Ph.D. degree from Periyar University, Salem, India. He is with the department of EEE, in K.S. Rangasamy College of Technology, Tiruchengode, Tamil Nadu, India. His research areas are power system optimization, power system operation and control, power electronics and intelligent techniques application to power system. Dr. K. Duraiswamy is the Dean of K.S. Rangasamy College of Technology, Tiruchengode, Tamil Nadu, India. He has received his Ph.D. degree from Anna University, Chennai. He has published many technical papers in international and national Journals. His areas of interests are power generation scheduling, state estimations, optimization technique, computer networks, soft computing techniques. He has guided many Ph.D. scholars. Dr. C. Christober Asir Rajan has received his Ph.D. degree from Anna University, Chennai, India. He is with the department of EEE in Pondicherry Engineering College, Pondicherry, India. His fields of interests are power system operation and control, soft computing techniques, neural network and fuzzy applications for power systems. N. Kanagaraj is a research scholar in National Institute of Technology, Trichy, Tamil Nadu, India. He is with the department of EEE in KSRCT, Tiruchengode, Tamil Nadu, India. His research area is fuzzy logic, neural network and its application.