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Peak load estimation of pole-transformer using load regression equation and assumption of cooling load for customer
Electrical Power and Energy Systems 24 (2002) 743±749
www.elsevier.com/locate/ijepes
Peak load estimation of pole-transformer using load regression equation and assumption of cooling load for customer Sang-Yun Yun a,*, Jae-Chul Kim a, Chang-Ho Park b a
Power System Laboratory, Department of Electrical Engineering, Soongsil University, 1-1 Sangdo 5-Dong, Dongjak-Ku, Seoul 156-743, South Korea b Korea Electric Power Research Institute, 103-16, Munji-Dong, Yuseong-Ku, Taejoen 103-16, South Korea Received 28 November 2000; revised 5 July 2001; accepted 20 September 2001
Abstract This paper summarizes the results of the research for load management of pole-transformers done in 1997±1999 in Korea. The purpose of the research is to enhance the peak load estimation of pole-transformers. For this purpose, we concentrate on two parts. One is to modify the load regression equation for load management of pole-transformers. The other is to estimate the cooling load possessions of customers and reduce estimation errors of the peak load for pole-transformers in the summer season. To do this, we propose indices of cooling load estimation using the increment of electric energy from spring to summer. Case studies for sample pole-transformers show that the proposed peak load estimation method could reduce estimating error of the peak load in the summer season, compared with the conventional method in Korea. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Load management of pole-transformer; Load regression equation; Peak load estimation; Cooling loads
1. Introduction As the social framework has shifted to the information and industrialization-centered society, the electrical power demands steadily increase. Among other things augmented is a concern about load management of distribution transformers that directly supply electrical power to customers. Utilities have implemented a variety of load management methods [1,2]. These methods have merits of showing direct and clear results for the speci®c topology and operation philosophy of each utility because a distribution transformer is the equipment that directly re¯ects the load pattern of customers. In Korea, pole-transformers far exceed other kinds of distribution transformers, and load management is performed mostly on the pole-transformers. To optimize the load management, each pole-transformer should be managed. However, it is impossible to manage individually pole-transformers because their number is about 1.3 million, and their types and capacities are various. For this reason, the load management has been traditionally performed through the peak load estimation using the load regression equation. The parameters of the load regression equation are electric energy (kWh) and peak load current (A). The * Corresponding author. Tel.: 182-2-817-7966; fax: 182-2-817-0780. E-mail addresses: [email protected] (S.-Y. Yun), [email protected] (J.-C. Kim), [email protected] (C.-H. Park).
coef®cients of the load regression equation can be estimated by surveying the electric demand of customers through load data acquisition for sample pole-transformers. These attempts were made in 1975 and 1986. Compared with the electric demand in 1986 when the latest load regression coef®cients were adjusted, the current electric demand has increased tremendously. Therefore, to re¯ect such electric demand increase, it necessitates adjusting the load regression equation coef®cients. This paper summarizes the results of the research for load management of pole-transformers done in 1997±1999 in Korea [3]. The object of this research is to enhance the peak load estimation for pole-transformer through the readjustment of load regression coef®cients that is suitable for distribution circumstances and customers' load demand recently. For this purpose, we installed the load data acquisition devices to the 144 sample pole-transformers. The modi®ed load regression model is selected as the most suitable one from among the various types. The peak load estimation using the load regression equation will have inherent errors. In the summer season when the load generally peaks in a year, the error is very important. To reduce the error in peak load estimation in the summer season, we propose the indices indicating the cooling load possession of customer (CLPC). By compensating the peak load estimation using the proposed indices, the accuracy of peak load estimation in the summer season could be enhanced.
0142-0615/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0142-061 5(01)00076-X
744
S.-Y. Yun et al. / Electrical Power and Energy Systems 24 (2002) 743±749
2. Present state of load management for poletransformer in Korea The capacities of pole-transformers in Korea range from 10 to 100 kVA [3]. For the load management, the types of customers are divided into commercial, residential, and farming and ®shing. Those customers have limits in their contract powers according to their types. Commercial, farming and ®shing customers are limited to 10 kW, but residential customers are not limited. Also, customers receiving power from pole-transformers are called `lamp-use load'. Load management of pole-transformers in Korea aims to estimate the peak load of each transformer in the next summer and winter season, and to prevent the transformer from being overloaded. Through this estimation, utilities are able to determine the replacement time and the new capacities of pole-transformers. The load management is done in ®ve steps. Step 1. We need to estimate the peak load current for each pole-transformer at present, 12 and 24 months ago. This estimation can result from a regression equation between the monthly electric energy (kWh) and peak load current (A) of each pole-transformer. A linear regression model has been used so far in Korea. Thus, the peak load current of the ith pole-transformer is Iti AXti 1 B:
1
here, Iti denotes the peak load current (A) of the ith pole-transformer at the tth month. A and B are regression coef®cients and Xti represents the monthly electric energy (kWh) of the ith pole-transformer at the tth month. Table 1 shows the conventional regression coef®cients of poletransformers in the summer season. Step 2. The average peak load current (A) of customers for the ith pole-transformer at present, 12 and 24 months ago is computed as ICUti
Iti ; Nti
2
where ICUti is the average peak load current of customers for the ith pole-transformer at the tth month, and Nti denotes the total number of customers for the ith pole-transformer at the tth month. Table 1 Load regression coef®cients for pole-transformers in summer season Area
Electric energy (kWh)
A
B
Commercial
under 2000 2001±10,000 over 10,000
0.0680 0.0438 0.0197
0 48.0 287.0
Residential
under 1000 1001±7500 over 7500
0.1010 0.0422 0.0166
0 59.0 260.0
Farming and ®shing
under 500 over 500
0.1199 0.0339
0 43.0
Step 3. The result of step 2 is used for calculating the increasing rate of load current for the ith pole-transformer, Ri : ! ! 1 ICU2i 2 ICU4i 21 1 21 3 Ri 1 1 3 ICU0i 3 ICU2i in Eq. (3), ICU4i ; ICU2i and ICU0i represent the average peak load current of customers for the ith pole-transformer at present, 12 and 24 months ago, respectively. Step 4. The peak load current in the next summer or winter season can be computed as I6i I4i £ Ri :
4
here, I6i represents the estimation value of the peak load current after 12 months from the present month. Monthly electric energy demands (kWh) for the summer and winter season mean the ones for August and January, respectively. Thus, in the case of the peak load current estimation for the next summer, I4i and I6i are the peak load currents for August this year and the next year. As shown in Eq. (4), the number of customers up to this year is only taken into account, without considering the number of customers related to the next year. This is because we estimate the peak load of the next summer at this summer. Step 5. The peak load (kVA) of pole-transformers for the next summer or winter season, kW6i ; can be calculated as kW6i Vi £ I6i £ 1023
5
in Eq. (5), Vi is the secondary voltage (V) of the ith poletransformer. From this result, we forecast an overload for the ith pole-transformer in the next summer or winter season, and determine a replacement of the ith poletransformer. From the above steps, it is important to estimate the peak load at step 1 using the load regression equation. If step 1 had many errors, the overall estimation process would be wrong. 3. Modi®cation of load regression equation for poletransformer load management The regression coef®cients in Table 1 were estimated in 1986 for which the power demand was low. To re¯ect increases of the power demand, the regression coef®cients need to be readjusted. Therefore, we utilize the load data acquisition devices for pole-transformers. The measurement devices are able to record voltages, currents, power demands and temperatures automatically. The measurement devices are installed at 144 points in six distribution branch of®ces in Seoul. This is because Seoul is the largest city in Korea where all customers with the highest and lowest power demand exist. Of the 144 devices installed, 72 units are installed in residential areas while the remainders are installed in commercial areas. The farming and ®shing areas were excluded from this research.
S.-Y. Yun et al. / Electrical Power and Energy Systems 24 (2002) 743±749
Data used for this research are categorized into two parts. One contains the status information of pole-transformers, which was measured by load data acquisition devices. The other part contains data of customers belonging to sample pole-transformers. We obtained these data from the database of KEPCO (Korea Electric Power corporation). The latter includes monthly electric energy (kWh), contract power (kW) and types of customers. The load data acquisition was performed for 12 months from September 1997 to August 1998. Using the data measured, we attempt to adjust the load regression equation explained in Eq. (1). A comparison measurement that is used to select the load regression equation is the good-of-®tness of data and is expresses as 2 P Iti 2 IREti r 2 P 6 2 P 2 ; Iti 2 IREti 1 IREti 2 Iti where r 2 0 # r 2 # 1 is the good-of-®tness between the actual and estimation values. Also, Iti ; IREti and IREti denote the estimated current by the selected regression equation, the mean of actual current and the actual current by measurement, respectively. Four types (linear, quadratic, logarithmic and exponential regression models) of equations are compared, and the equation with the largest r 2 value is selected for the load regression equation in the customers' area. Fig. 1 shows a selection procedure of the load regression equation. The comparison of good-of-®tness for the load regression equation is shown in Table 2. Through the calculation of standard deviation s; over ^3s data are excluded from the calculation of load regression coef®cients. From this result, we decided that the quadratic model ®ts the load regression equation. A typical formulation of the quadratic regression model is I ti AXti2 1 BXti 1 C:
7
here, A, B and C are regression coef®cients. We could not consider load saturation in the conventional model in Eq. (1), the linear regression equation. However, we considered a
Fig. 1. Selection procedure of a modi®ed load regression equation.
745
Table 2 Comparison of good-of-®tness r2 for each load regression equation Area
Season
Regression equation, Model
r2
Residential
Summer
Linear Quadratic Logarithmic Exponential Linear Quadratic Logarithmic Exponential
0.805 0.806 0.693 0.798 0.688 0.714 0.708 0.685
Linear Quadratic Logarithmic Exponential Linear Quadratic Logarithmic Exponential
0.716 0.719 0.611 0.622 0.738 0.740 0.679 0.646
Winter
Commercial
Summer
Winter
load saturation problem by using the quadratic regression equation in Eq. (7). Fig. 2 shows the quadratic regression models selected for the summer and winter seasons for residential and commercial areas. The formulations in Fig. 2 are the selected quadratic regression equations. 4. Accuracy enhancement of peak load estimation in summer season Though we chose the ®ttest load regression model, it still has an error when compared with the actual value in Fig. 2. The accuracy of peak load estimation for summer season is more important than in the other seasons because the magnitude of the peak load in summer has the largest value. The large current increases the oil-temperature of pole-transformers in the summer season, and this eventually causes a failure [4,5]. The failures of pole-transformers in Korea occur mostly in the summer season [6]. For this reason, we propose an error reduction method of peak load estimation in the summer season. We analyzed why customers using similar electric energy in the summer season differ greatly in the peak load. The load of each pole-transformer can be calculated by the sum of the load of each customer. Therefore, it would not be dif®cult to estimate the peak load if we exactly knew the customers' load pattern. However, the load capacity and load pattern of each customer is very uncertain and it is dif®cult to forecast the load change. The main causes that have an effect on customers' load pattern are economy, time, weather, and irregular demand. Among the causes, we thought that the cooling load (air conditioners) has the greatest effect on the customers' peak load in summer [7]. To analyze the power demand pattern of customers, we classify them into two categories. One group of customers changes its monthly electric energy pattern greatly in the
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S.-Y. Yun et al. / Electrical Power and Energy Systems 24 (2002) 743±749
Fig. 2. Quadratic load regression models of residential and commercial area pole-transformers in summer and winter season. (a) Residential area (summer), (b) Residential area (winter), (c) Commercial area (summer), (d) Commercial area (winter).
summer season compared with other seasons, while the other group does not. Fig. 3 demonstrates the change of monthly electric energy of residential customers from January 1996 to December 1996. The horizontal axis denotes months and the ordinate axis represents monthly electric energy consumptions (kWh). The symbols in the ®gure denote the customers. Fig. 3 demonstrates that the deviation in the monthly electric energy between summer and the other seasons varies according to customers. This electric energy deviation in the summer season is attributed to the cooling load. We compared the daily load patterns of two sample poletransformers for the same day of April and August in 1998. The peak load current in Fig. 4(a) far more increases in
Fig. 3. Change of monthly electric energy of each customer.
Fig. 4. Comparison of daily load pattern of a sample pole-transformer in spring and summer. (a) Large difference pattern, (b) Small difference pattern.
S.-Y. Yun et al. / Electrical Power and Energy Systems 24 (2002) 743±749
summer than in spring. However, Fig. 4(b) demonstrates that the peak load currents in spring and summer are similar. From these patterns, it can be said that the cooling loads of customers increases the peak load current of pole-transformers in Fig. 4(a). This is because the cooling load is simultaneously loaded by temperature [8±10]. The concept of the proposed method is as follows. If a certain customer's monthly electric energy in summer (August) is largely increased compared to that in spring (April), it could be assumed that such a customer possesses a cooling load. For the proposed concept of the cooling load in each customer, we propose the CLPC index. The CLPC of the jth customer is formulated into a membership function [11] and is illustrated as l 1 2 y l21 Xj 2 a CLPCj 8 l l ; 1 2 y l21 Xj 2 a 1y l21 b 2 Xj where Xj is an increment of electric energy (kWh) for the jth customer from spring (April) to summer (August) and a and b are the lower and upper limits of increment kWh for the customer, respectively. y represents an in¯ection point and is assumed as 0.5. Also l is a transition rate. For the estimation of the peak load current for each poletransformer, it is necessary to calculate its average. To do this, we propose an average cooling load possession of poletransformers (ACLP). The ACLP of the ith pole-transformer can be calculated as Nj X
ACLP i
j1
CLPCj Nj
;
9
where Nj represents the total number of customers for the ith sample pole-transformer. The peak load estimation equation is ®nally formulated as IPLi Iti 1 f ACLPi £ S:
10
here, IPLi denotes the ultimate estimation value of peak load current (A) of the ith sample pole-transformer in summer by the proposed peak load estimation method, and Iti is the estimation value of the peak load current (A) for the ith pole-transformer by the modi®ed regression equation (quadratic equation). Also, f ACLPi represents the regressive equation between ACLP of the ith pole-transformer and standard deviations (s ) of the peak load current for each ACLP value. It means that the deviation of the peak load current due to the cooling load is represented by the regressive equation using the value of each ACLP and the standard deviations of the peak load current for each ACLP of sample pole-transformers. S in Eq. (10) denotes the actual current value for standard deviation u ^ 1su: Therefore, f ACLP i £ S is the compensation value of the peak load current estimated by the load regression equation.
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The proposed method is simulated using residential area data for 16 sample pole-transformers. To determine CLPC, it is necessary to determine the value of a , b and l in Eq. (8). According to Refs. [12,13], we deemed the average time of use of the cooling load in residential areas and average rated capacity as 4.93 h and 1.75 kW, respectively, and set b value at about 280 kWh ù 4:93 £ 1:75 £ 30: Also, we ®xed a value at 0 and adjusted l to induce a coef®cient suitable for the load environment in residential areas. To obtain comparison data useful for selecting l value, on March 2000, we surveyed whether a total of 44 customers for two sample residential transformers possessed cooling loads. Table 3 shows the result. For the assumed l value, the CLPC for each customer was calculated, and to select a l closest to the sum of CLPC, we underwent trial and errors and determined l as about 3. The l value determined is deemed to be suitable for general residential customers. The determination of these coef®cients (a , b and l ) can vary subject to the load environment for each country. The regressive equation of ACLP and standard deviations of the peak load current for each ACLP of sample poletransformers in residential areas is formulated as f ACLPi 1:646 1 1:758 £ ln ACLPi :
11
The logarithmic regression model as in Eq. (11) is selected for the ®ttest regression model. This model is obtained from data acquired from measuring 72 sample pole-transformers for residential areas in September 1997±August 1998. The real current value S [A] for u ^ 1su is about 150 for the 72 sample pole-transformers. We compared the conventional method of peak load estimation with the proposed method. To verify the effectiveness of the proposed method, the error between actual and estimation values, e i ; is calculated as I 2I ESi REi %; 12 ei £ 100 IREi where IREi and IESi are the actual and estimated value of the peak current for the ith pole-transformer in the summer season (August), respectively. For the conventional method, IESi is equal to Iti that is determined by the linear regression equation as Eq. (1). If we estimate the peak load using the improved load regression equation, quadratic equation, IESi Table 3 Comparison of CLPC calculation and survey result of customers P. Tr. ID No.
9721B8741 9721C8421
Item Number of customers
Number of customers that possessed cooling load (surveying result)
Sum of CLPC (calculation result)
24 20
10 6
10.15 6.09
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S.-Y. Yun et al. / Electrical Power and Energy Systems 24 (2002) 743±749
Table 4 Results of peak load estimation for sample pole-transformers of residential areas in summer season P. Tr. No.
Actual peak current
1 332 2 351 3 381 4 399 5 442 6 459 7 469 8 493 9 515 10 534 11 563 12 576 13 662 14 666 15 711 16 722 Average error (ei )
Linear regression equation (conventional method in Korea)
Quadratic regression equation (modi®ed load regression equation)
Proposed error reduction method of peak load in summer season
IESi (Iti in Eq. (1))
ei
IESi (Iti in Eq. (7))
ei
IESi (IPLi in Eq. (10))
ei
537 547 530 541 607 630 524 542 646 674 526 614 615 628 646 648
61.9 56 39.3 35.7 37.5 37.4 11.9 10.1 25.5 26.3 6.4 6.6 7.1 5.7 9.1 10.2 24.1 (%)
430 444 420 435 528 559 411 437 580 617 414 537 537 555 579 582
29.6 26.7 10.4 9.2 19.4 21.8 12.1 11.2 12.7 15.5 26.3 6.75 18.7 16.5 18.4 19.3 17.2 (%)
330 337 390 378 383 555 466 441 488 596 550 564 665 697 732 723
0.5 3.9 2.3 5.1 13.2 20.9 0.6 10.5 5.1 11.7 2.1 1.9 0.5 4.7 3 0.2 5.3 (%)
will be the same as Iti in Eq. (7). Also, if we use the proposed error reduction method for estimating the summer peak load, IESi will be the same as IPLi in Eq. (10). Table 4 compares the calculation results by each method done in August 1999 for 16 sample pole-transformers. The average error is 24.1% with the existing method used while when using the quadratic equation for estimating the peak load, it is 17.2%, thus being able to reduce about 7% error compared to the existing method. When using the proposed error reduction method in estimating the summer peak load, the average error is calculated as 5.4%. This can reduce the error by about 19% compared to the existing method. It further has an effect on reducing the error by about 12% compared to that which estimates the peak load using the quadratic equation. 5. Conclusions This paper introduces the results of the research for load management of pole-transformers done recently in Korea. This paper seeks to adjust the existing load regression equation aimed to re¯ect the latest power demand pattern of customers, and to develop error reduction methods in estimating the peak load of summer season. To adjust the load regression equation, we installed load data acquisition devices at sample transformers. By assessing a variety of load regression models, the quadratic regression equation has been selected for the optimum model. The modi®ed load regression models were scheduled to be applied to load management of pole-transformers for KEPCO from January 2001. To compensate the error of peak load estimation in the summer season, we propose the indices (CLPC,
ACLP) aimed to estimate customers' cooling load possession levels. Through the case studies, it is revealed that the average estimation error is much reduced when we use the modi®ed load regression equation and the proposed error reduction method in estimating the summer peak load. The proposed error reduction method of the peak load current in the summer season can apply to other utilities that have similar topologies and operation philosophies to those of Korea. Acknowledgements The authors would like to express their appreciation to Prof. Kyoung-Soo Ro at Dongguk University for assistance in revising this paper. References [1] Sargent A, et al. Estimation of diversity and kWh-to-peak-kW factors from load research data. IEEE Trans Power Syst 1994;9(3):1450±6. [2] Broadwater RP, et al. Estimating substation peaks from load research data. IEEE Trans Power Delivery 1997;12(1):451±6. [3] Korea electric power research institute. A study on the improvement of pole-transformer load management (technical report). Korea Electric Power Corporation, 1999;TR.96ES15.S1998.86. [4] IEC Publication 354(1971). Loading guide for oil-immersed power transformers. [5] IEEE Std. C57.91(1981), IEEE guide for loading mineral-oilimmersed overhead and pad-mounted distribution transformers rated 500 kVA and less with 65 or 55 8C average winding rise. [6] Korea electric power research institute. A study for the reduction of the power transformer failures (technical report). Korea Electric Power Corporation, 1989;KRC-88S-J04. [7] Korea electric power economy department. 98 analysis of summer
S.-Y. Yun et al. / Electrical Power and Energy Systems 24 (2002) 743±749
[8] [9] [10] [11] [12] [13]
cooling load (technical report). Korea Electric Power Corporation, 1998. Douglas AP, et al. The impacts of temperature forecast uncertainty on Bayesian load forecasting. IEEE Trans Power Syst 1998;13(4):1507± 13. Asbury CE. Weather load model for electric demand and energy forecasting. IEEE Trans Power Appar Syst 1975;PAS-94(4):1111±6. Thompson RP. Weather sensitive electric demand and energy analysis on a large geographically diverse power system. IEEE Trans Power Appar Syst 1976;PAS-95(1):385±93. Klir GJ, et al. Fuzzy sets, uncertainty, and information. New Jersey: Prentice-Hall, 1988. Korean Industrial Std. KSC9306(1999). Air conditioners. Korea electric power economy department. A study on the plan of middle and long term partial DSM (technical report). Korea Electric Power Corporation, 1997.
Sang-Yun Yun was born in Inchon, Korea, 1970. He received his B.S.E.E. and M.S.E.E. degrees in Electrical Engineering from Soongsil University, Korea, in 1996 and 1998, respectively. He is currently working on his Ph.D. at the Soongsil University. He is a member of KIEE and KIIEE. His areas of interest include power quality, adaptive reclosing, and load management of distribution transformer.
749
Jae-Chul Kim was born in Chonbuk, Korea, 1955. He received his B.S.E.E. degree from Soongsil University, Korea, 1979, and M.S.E.E. and Ph.D. degrees from Seoul National University, Korea, in 1983 and 1987, respectively. He has served as a professor of Electrical Engineering at the Soongsil University since 1988. Prof. Kim is a member of KIEE and KIIEE. His areas of interest are diagnosis of power system equipments, power quality, distribution system automation, and battery energy storage system (BESS).
Chang-Ho Park was born in Jindo, Korea, 1956. He received his B.S.E.E. degree from Chungang University, Korea, in 1979, and received his M.S.E.E. in Electrical Engineering from Yonsei University, Korea in 1982. He is a member of KIEE and KIIEE. He is presently a senior researcher at the Power System Laboratory, Korea Electric Power Research Institute, Korea Electric Power Corporation. His areas of interest include load management of distribution transformer, distribution system automation, and power quality.
www.elsevier.com/locate/ijepes
Peak load estimation of pole-transformer using load regression equation and assumption of cooling load for customer Sang-Yun Yun a,*, Jae-Chul Kim a, Chang-Ho Park b a
Power System Laboratory, Department of Electrical Engineering, Soongsil University, 1-1 Sangdo 5-Dong, Dongjak-Ku, Seoul 156-743, South Korea b Korea Electric Power Research Institute, 103-16, Munji-Dong, Yuseong-Ku, Taejoen 103-16, South Korea Received 28 November 2000; revised 5 July 2001; accepted 20 September 2001
Abstract This paper summarizes the results of the research for load management of pole-transformers done in 1997±1999 in Korea. The purpose of the research is to enhance the peak load estimation of pole-transformers. For this purpose, we concentrate on two parts. One is to modify the load regression equation for load management of pole-transformers. The other is to estimate the cooling load possessions of customers and reduce estimation errors of the peak load for pole-transformers in the summer season. To do this, we propose indices of cooling load estimation using the increment of electric energy from spring to summer. Case studies for sample pole-transformers show that the proposed peak load estimation method could reduce estimating error of the peak load in the summer season, compared with the conventional method in Korea. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Load management of pole-transformer; Load regression equation; Peak load estimation; Cooling loads
1. Introduction As the social framework has shifted to the information and industrialization-centered society, the electrical power demands steadily increase. Among other things augmented is a concern about load management of distribution transformers that directly supply electrical power to customers. Utilities have implemented a variety of load management methods [1,2]. These methods have merits of showing direct and clear results for the speci®c topology and operation philosophy of each utility because a distribution transformer is the equipment that directly re¯ects the load pattern of customers. In Korea, pole-transformers far exceed other kinds of distribution transformers, and load management is performed mostly on the pole-transformers. To optimize the load management, each pole-transformer should be managed. However, it is impossible to manage individually pole-transformers because their number is about 1.3 million, and their types and capacities are various. For this reason, the load management has been traditionally performed through the peak load estimation using the load regression equation. The parameters of the load regression equation are electric energy (kWh) and peak load current (A). The * Corresponding author. Tel.: 182-2-817-7966; fax: 182-2-817-0780. E-mail addresses: [email protected] (S.-Y. Yun), [email protected] (J.-C. Kim), [email protected] (C.-H. Park).
coef®cients of the load regression equation can be estimated by surveying the electric demand of customers through load data acquisition for sample pole-transformers. These attempts were made in 1975 and 1986. Compared with the electric demand in 1986 when the latest load regression coef®cients were adjusted, the current electric demand has increased tremendously. Therefore, to re¯ect such electric demand increase, it necessitates adjusting the load regression equation coef®cients. This paper summarizes the results of the research for load management of pole-transformers done in 1997±1999 in Korea [3]. The object of this research is to enhance the peak load estimation for pole-transformer through the readjustment of load regression coef®cients that is suitable for distribution circumstances and customers' load demand recently. For this purpose, we installed the load data acquisition devices to the 144 sample pole-transformers. The modi®ed load regression model is selected as the most suitable one from among the various types. The peak load estimation using the load regression equation will have inherent errors. In the summer season when the load generally peaks in a year, the error is very important. To reduce the error in peak load estimation in the summer season, we propose the indices indicating the cooling load possession of customer (CLPC). By compensating the peak load estimation using the proposed indices, the accuracy of peak load estimation in the summer season could be enhanced.
0142-0615/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0142-061 5(01)00076-X
744
S.-Y. Yun et al. / Electrical Power and Energy Systems 24 (2002) 743±749
2. Present state of load management for poletransformer in Korea The capacities of pole-transformers in Korea range from 10 to 100 kVA [3]. For the load management, the types of customers are divided into commercial, residential, and farming and ®shing. Those customers have limits in their contract powers according to their types. Commercial, farming and ®shing customers are limited to 10 kW, but residential customers are not limited. Also, customers receiving power from pole-transformers are called `lamp-use load'. Load management of pole-transformers in Korea aims to estimate the peak load of each transformer in the next summer and winter season, and to prevent the transformer from being overloaded. Through this estimation, utilities are able to determine the replacement time and the new capacities of pole-transformers. The load management is done in ®ve steps. Step 1. We need to estimate the peak load current for each pole-transformer at present, 12 and 24 months ago. This estimation can result from a regression equation between the monthly electric energy (kWh) and peak load current (A) of each pole-transformer. A linear regression model has been used so far in Korea. Thus, the peak load current of the ith pole-transformer is Iti AXti 1 B:
1
here, Iti denotes the peak load current (A) of the ith pole-transformer at the tth month. A and B are regression coef®cients and Xti represents the monthly electric energy (kWh) of the ith pole-transformer at the tth month. Table 1 shows the conventional regression coef®cients of poletransformers in the summer season. Step 2. The average peak load current (A) of customers for the ith pole-transformer at present, 12 and 24 months ago is computed as ICUti
Iti ; Nti
2
where ICUti is the average peak load current of customers for the ith pole-transformer at the tth month, and Nti denotes the total number of customers for the ith pole-transformer at the tth month. Table 1 Load regression coef®cients for pole-transformers in summer season Area
Electric energy (kWh)
A
B
Commercial
under 2000 2001±10,000 over 10,000
0.0680 0.0438 0.0197
0 48.0 287.0
Residential
under 1000 1001±7500 over 7500
0.1010 0.0422 0.0166
0 59.0 260.0
Farming and ®shing
under 500 over 500
0.1199 0.0339
0 43.0
Step 3. The result of step 2 is used for calculating the increasing rate of load current for the ith pole-transformer, Ri : ! ! 1 ICU2i 2 ICU4i 21 1 21 3 Ri 1 1 3 ICU0i 3 ICU2i in Eq. (3), ICU4i ; ICU2i and ICU0i represent the average peak load current of customers for the ith pole-transformer at present, 12 and 24 months ago, respectively. Step 4. The peak load current in the next summer or winter season can be computed as I6i I4i £ Ri :
4
here, I6i represents the estimation value of the peak load current after 12 months from the present month. Monthly electric energy demands (kWh) for the summer and winter season mean the ones for August and January, respectively. Thus, in the case of the peak load current estimation for the next summer, I4i and I6i are the peak load currents for August this year and the next year. As shown in Eq. (4), the number of customers up to this year is only taken into account, without considering the number of customers related to the next year. This is because we estimate the peak load of the next summer at this summer. Step 5. The peak load (kVA) of pole-transformers for the next summer or winter season, kW6i ; can be calculated as kW6i Vi £ I6i £ 1023
5
in Eq. (5), Vi is the secondary voltage (V) of the ith poletransformer. From this result, we forecast an overload for the ith pole-transformer in the next summer or winter season, and determine a replacement of the ith poletransformer. From the above steps, it is important to estimate the peak load at step 1 using the load regression equation. If step 1 had many errors, the overall estimation process would be wrong. 3. Modi®cation of load regression equation for poletransformer load management The regression coef®cients in Table 1 were estimated in 1986 for which the power demand was low. To re¯ect increases of the power demand, the regression coef®cients need to be readjusted. Therefore, we utilize the load data acquisition devices for pole-transformers. The measurement devices are able to record voltages, currents, power demands and temperatures automatically. The measurement devices are installed at 144 points in six distribution branch of®ces in Seoul. This is because Seoul is the largest city in Korea where all customers with the highest and lowest power demand exist. Of the 144 devices installed, 72 units are installed in residential areas while the remainders are installed in commercial areas. The farming and ®shing areas were excluded from this research.
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Data used for this research are categorized into two parts. One contains the status information of pole-transformers, which was measured by load data acquisition devices. The other part contains data of customers belonging to sample pole-transformers. We obtained these data from the database of KEPCO (Korea Electric Power corporation). The latter includes monthly electric energy (kWh), contract power (kW) and types of customers. The load data acquisition was performed for 12 months from September 1997 to August 1998. Using the data measured, we attempt to adjust the load regression equation explained in Eq. (1). A comparison measurement that is used to select the load regression equation is the good-of-®tness of data and is expresses as 2 P Iti 2 IREti r 2 P 6 2 P 2 ; Iti 2 IREti 1 IREti 2 Iti where r 2 0 # r 2 # 1 is the good-of-®tness between the actual and estimation values. Also, Iti ; IREti and IREti denote the estimated current by the selected regression equation, the mean of actual current and the actual current by measurement, respectively. Four types (linear, quadratic, logarithmic and exponential regression models) of equations are compared, and the equation with the largest r 2 value is selected for the load regression equation in the customers' area. Fig. 1 shows a selection procedure of the load regression equation. The comparison of good-of-®tness for the load regression equation is shown in Table 2. Through the calculation of standard deviation s; over ^3s data are excluded from the calculation of load regression coef®cients. From this result, we decided that the quadratic model ®ts the load regression equation. A typical formulation of the quadratic regression model is I ti AXti2 1 BXti 1 C:
7
here, A, B and C are regression coef®cients. We could not consider load saturation in the conventional model in Eq. (1), the linear regression equation. However, we considered a
Fig. 1. Selection procedure of a modi®ed load regression equation.
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Table 2 Comparison of good-of-®tness r2 for each load regression equation Area
Season
Regression equation, Model
r2
Residential
Summer
Linear Quadratic Logarithmic Exponential Linear Quadratic Logarithmic Exponential
0.805 0.806 0.693 0.798 0.688 0.714 0.708 0.685
Linear Quadratic Logarithmic Exponential Linear Quadratic Logarithmic Exponential
0.716 0.719 0.611 0.622 0.738 0.740 0.679 0.646
Winter
Commercial
Summer
Winter
load saturation problem by using the quadratic regression equation in Eq. (7). Fig. 2 shows the quadratic regression models selected for the summer and winter seasons for residential and commercial areas. The formulations in Fig. 2 are the selected quadratic regression equations. 4. Accuracy enhancement of peak load estimation in summer season Though we chose the ®ttest load regression model, it still has an error when compared with the actual value in Fig. 2. The accuracy of peak load estimation for summer season is more important than in the other seasons because the magnitude of the peak load in summer has the largest value. The large current increases the oil-temperature of pole-transformers in the summer season, and this eventually causes a failure [4,5]. The failures of pole-transformers in Korea occur mostly in the summer season [6]. For this reason, we propose an error reduction method of peak load estimation in the summer season. We analyzed why customers using similar electric energy in the summer season differ greatly in the peak load. The load of each pole-transformer can be calculated by the sum of the load of each customer. Therefore, it would not be dif®cult to estimate the peak load if we exactly knew the customers' load pattern. However, the load capacity and load pattern of each customer is very uncertain and it is dif®cult to forecast the load change. The main causes that have an effect on customers' load pattern are economy, time, weather, and irregular demand. Among the causes, we thought that the cooling load (air conditioners) has the greatest effect on the customers' peak load in summer [7]. To analyze the power demand pattern of customers, we classify them into two categories. One group of customers changes its monthly electric energy pattern greatly in the
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Fig. 2. Quadratic load regression models of residential and commercial area pole-transformers in summer and winter season. (a) Residential area (summer), (b) Residential area (winter), (c) Commercial area (summer), (d) Commercial area (winter).
summer season compared with other seasons, while the other group does not. Fig. 3 demonstrates the change of monthly electric energy of residential customers from January 1996 to December 1996. The horizontal axis denotes months and the ordinate axis represents monthly electric energy consumptions (kWh). The symbols in the ®gure denote the customers. Fig. 3 demonstrates that the deviation in the monthly electric energy between summer and the other seasons varies according to customers. This electric energy deviation in the summer season is attributed to the cooling load. We compared the daily load patterns of two sample poletransformers for the same day of April and August in 1998. The peak load current in Fig. 4(a) far more increases in
Fig. 3. Change of monthly electric energy of each customer.
Fig. 4. Comparison of daily load pattern of a sample pole-transformer in spring and summer. (a) Large difference pattern, (b) Small difference pattern.
S.-Y. Yun et al. / Electrical Power and Energy Systems 24 (2002) 743±749
summer than in spring. However, Fig. 4(b) demonstrates that the peak load currents in spring and summer are similar. From these patterns, it can be said that the cooling loads of customers increases the peak load current of pole-transformers in Fig. 4(a). This is because the cooling load is simultaneously loaded by temperature [8±10]. The concept of the proposed method is as follows. If a certain customer's monthly electric energy in summer (August) is largely increased compared to that in spring (April), it could be assumed that such a customer possesses a cooling load. For the proposed concept of the cooling load in each customer, we propose the CLPC index. The CLPC of the jth customer is formulated into a membership function [11] and is illustrated as l 1 2 y l21 Xj 2 a CLPCj 8 l l ; 1 2 y l21 Xj 2 a 1y l21 b 2 Xj where Xj is an increment of electric energy (kWh) for the jth customer from spring (April) to summer (August) and a and b are the lower and upper limits of increment kWh for the customer, respectively. y represents an in¯ection point and is assumed as 0.5. Also l is a transition rate. For the estimation of the peak load current for each poletransformer, it is necessary to calculate its average. To do this, we propose an average cooling load possession of poletransformers (ACLP). The ACLP of the ith pole-transformer can be calculated as Nj X
ACLP i
j1
CLPCj Nj
;
9
where Nj represents the total number of customers for the ith sample pole-transformer. The peak load estimation equation is ®nally formulated as IPLi Iti 1 f ACLPi £ S:
10
here, IPLi denotes the ultimate estimation value of peak load current (A) of the ith sample pole-transformer in summer by the proposed peak load estimation method, and Iti is the estimation value of the peak load current (A) for the ith pole-transformer by the modi®ed regression equation (quadratic equation). Also, f ACLPi represents the regressive equation between ACLP of the ith pole-transformer and standard deviations (s ) of the peak load current for each ACLP value. It means that the deviation of the peak load current due to the cooling load is represented by the regressive equation using the value of each ACLP and the standard deviations of the peak load current for each ACLP of sample pole-transformers. S in Eq. (10) denotes the actual current value for standard deviation u ^ 1su: Therefore, f ACLP i £ S is the compensation value of the peak load current estimated by the load regression equation.
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The proposed method is simulated using residential area data for 16 sample pole-transformers. To determine CLPC, it is necessary to determine the value of a , b and l in Eq. (8). According to Refs. [12,13], we deemed the average time of use of the cooling load in residential areas and average rated capacity as 4.93 h and 1.75 kW, respectively, and set b value at about 280 kWh ù 4:93 £ 1:75 £ 30: Also, we ®xed a value at 0 and adjusted l to induce a coef®cient suitable for the load environment in residential areas. To obtain comparison data useful for selecting l value, on March 2000, we surveyed whether a total of 44 customers for two sample residential transformers possessed cooling loads. Table 3 shows the result. For the assumed l value, the CLPC for each customer was calculated, and to select a l closest to the sum of CLPC, we underwent trial and errors and determined l as about 3. The l value determined is deemed to be suitable for general residential customers. The determination of these coef®cients (a , b and l ) can vary subject to the load environment for each country. The regressive equation of ACLP and standard deviations of the peak load current for each ACLP of sample poletransformers in residential areas is formulated as f ACLPi 1:646 1 1:758 £ ln ACLPi :
11
The logarithmic regression model as in Eq. (11) is selected for the ®ttest regression model. This model is obtained from data acquired from measuring 72 sample pole-transformers for residential areas in September 1997±August 1998. The real current value S [A] for u ^ 1su is about 150 for the 72 sample pole-transformers. We compared the conventional method of peak load estimation with the proposed method. To verify the effectiveness of the proposed method, the error between actual and estimation values, e i ; is calculated as I 2I ESi REi %; 12 ei £ 100 IREi where IREi and IESi are the actual and estimated value of the peak current for the ith pole-transformer in the summer season (August), respectively. For the conventional method, IESi is equal to Iti that is determined by the linear regression equation as Eq. (1). If we estimate the peak load using the improved load regression equation, quadratic equation, IESi Table 3 Comparison of CLPC calculation and survey result of customers P. Tr. ID No.
9721B8741 9721C8421
Item Number of customers
Number of customers that possessed cooling load (surveying result)
Sum of CLPC (calculation result)
24 20
10 6
10.15 6.09
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Table 4 Results of peak load estimation for sample pole-transformers of residential areas in summer season P. Tr. No.
Actual peak current
1 332 2 351 3 381 4 399 5 442 6 459 7 469 8 493 9 515 10 534 11 563 12 576 13 662 14 666 15 711 16 722 Average error (ei )
Linear regression equation (conventional method in Korea)
Quadratic regression equation (modi®ed load regression equation)
Proposed error reduction method of peak load in summer season
IESi (Iti in Eq. (1))
ei
IESi (Iti in Eq. (7))
ei
IESi (IPLi in Eq. (10))
ei
537 547 530 541 607 630 524 542 646 674 526 614 615 628 646 648
61.9 56 39.3 35.7 37.5 37.4 11.9 10.1 25.5 26.3 6.4 6.6 7.1 5.7 9.1 10.2 24.1 (%)
430 444 420 435 528 559 411 437 580 617 414 537 537 555 579 582
29.6 26.7 10.4 9.2 19.4 21.8 12.1 11.2 12.7 15.5 26.3 6.75 18.7 16.5 18.4 19.3 17.2 (%)
330 337 390 378 383 555 466 441 488 596 550 564 665 697 732 723
0.5 3.9 2.3 5.1 13.2 20.9 0.6 10.5 5.1 11.7 2.1 1.9 0.5 4.7 3 0.2 5.3 (%)
will be the same as Iti in Eq. (7). Also, if we use the proposed error reduction method for estimating the summer peak load, IESi will be the same as IPLi in Eq. (10). Table 4 compares the calculation results by each method done in August 1999 for 16 sample pole-transformers. The average error is 24.1% with the existing method used while when using the quadratic equation for estimating the peak load, it is 17.2%, thus being able to reduce about 7% error compared to the existing method. When using the proposed error reduction method in estimating the summer peak load, the average error is calculated as 5.4%. This can reduce the error by about 19% compared to the existing method. It further has an effect on reducing the error by about 12% compared to that which estimates the peak load using the quadratic equation. 5. Conclusions This paper introduces the results of the research for load management of pole-transformers done recently in Korea. This paper seeks to adjust the existing load regression equation aimed to re¯ect the latest power demand pattern of customers, and to develop error reduction methods in estimating the peak load of summer season. To adjust the load regression equation, we installed load data acquisition devices at sample transformers. By assessing a variety of load regression models, the quadratic regression equation has been selected for the optimum model. The modi®ed load regression models were scheduled to be applied to load management of pole-transformers for KEPCO from January 2001. To compensate the error of peak load estimation in the summer season, we propose the indices (CLPC,
ACLP) aimed to estimate customers' cooling load possession levels. Through the case studies, it is revealed that the average estimation error is much reduced when we use the modi®ed load regression equation and the proposed error reduction method in estimating the summer peak load. The proposed error reduction method of the peak load current in the summer season can apply to other utilities that have similar topologies and operation philosophies to those of Korea. Acknowledgements The authors would like to express their appreciation to Prof. Kyoung-Soo Ro at Dongguk University for assistance in revising this paper. References [1] Sargent A, et al. Estimation of diversity and kWh-to-peak-kW factors from load research data. IEEE Trans Power Syst 1994;9(3):1450±6. [2] Broadwater RP, et al. Estimating substation peaks from load research data. IEEE Trans Power Delivery 1997;12(1):451±6. [3] Korea electric power research institute. A study on the improvement of pole-transformer load management (technical report). Korea Electric Power Corporation, 1999;TR.96ES15.S1998.86. [4] IEC Publication 354(1971). Loading guide for oil-immersed power transformers. [5] IEEE Std. C57.91(1981), IEEE guide for loading mineral-oilimmersed overhead and pad-mounted distribution transformers rated 500 kVA and less with 65 or 55 8C average winding rise. [6] Korea electric power research institute. A study for the reduction of the power transformer failures (technical report). Korea Electric Power Corporation, 1989;KRC-88S-J04. [7] Korea electric power economy department. 98 analysis of summer
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[8] [9] [10] [11] [12] [13]
cooling load (technical report). Korea Electric Power Corporation, 1998. Douglas AP, et al. The impacts of temperature forecast uncertainty on Bayesian load forecasting. IEEE Trans Power Syst 1998;13(4):1507± 13. Asbury CE. Weather load model for electric demand and energy forecasting. IEEE Trans Power Appar Syst 1975;PAS-94(4):1111±6. Thompson RP. Weather sensitive electric demand and energy analysis on a large geographically diverse power system. IEEE Trans Power Appar Syst 1976;PAS-95(1):385±93. Klir GJ, et al. Fuzzy sets, uncertainty, and information. New Jersey: Prentice-Hall, 1988. Korean Industrial Std. KSC9306(1999). Air conditioners. Korea electric power economy department. A study on the plan of middle and long term partial DSM (technical report). Korea Electric Power Corporation, 1997.
Sang-Yun Yun was born in Inchon, Korea, 1970. He received his B.S.E.E. and M.S.E.E. degrees in Electrical Engineering from Soongsil University, Korea, in 1996 and 1998, respectively. He is currently working on his Ph.D. at the Soongsil University. He is a member of KIEE and KIIEE. His areas of interest include power quality, adaptive reclosing, and load management of distribution transformer.
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Jae-Chul Kim was born in Chonbuk, Korea, 1955. He received his B.S.E.E. degree from Soongsil University, Korea, 1979, and M.S.E.E. and Ph.D. degrees from Seoul National University, Korea, in 1983 and 1987, respectively. He has served as a professor of Electrical Engineering at the Soongsil University since 1988. Prof. Kim is a member of KIEE and KIIEE. His areas of interest are diagnosis of power system equipments, power quality, distribution system automation, and battery energy storage system (BESS).
Chang-Ho Park was born in Jindo, Korea, 1956. He received his B.S.E.E. degree from Chungang University, Korea, in 1979, and received his M.S.E.E. in Electrical Engineering from Yonsei University, Korea in 1982. He is a member of KIEE and KIIEE. He is presently a senior researcher at the Power System Laboratory, Korea Electric Power Research Institute, Korea Electric Power Corporation. His areas of interest include load management of distribution transformer, distribution system automation, and power quality.