Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26th, Bologna, Italy
Stochastic Load Flow Analysis by Considering Temperature Sensitivity of Customer Power Consumption M. S. Kang, C. S. Chen,
Member, IEEE,
Abstract-- In this paper, the stochastic load flow analysis has been executed to solve the expected values of system bus voltages and variances. The load models of substations have been determined according to the typical load patterns and load composition of various customer classes. The random load behavior of customers served by each substation has been identified and applied to find the noise level of substation power demand. The dc circuit model of Taipower system is created and the temperature effect of customer power consumption is considered in the stochastic load flow analysis. It is found that the voltage angle difference between system buses has been introduced by the bulk power transmission. Power system operation may be deteriorated by the significant standard deviation of angle difference due to the stochastic load behavior of substations. Index Terms--Load composition, stochastic load flow, temperature sensitivity.
I. INTRODUCTION
T
HE power consumption profile of a load bus depends on the load composition of various types of customers served by the substation[1]. By load survey study, the utility can identify the typical daily load pattern of each customer class [2]. The test customers selected for load study have to be determined by properly sampling method so that the load patterns derived can represent the load behavior of whole population within the same class. The mean value and the standard deviation of total power consumption by all the customers in the same class within the service territory of each substation can therefore be solved according to the typical load patterns and customer billing data. After integrating the power consumption by each customer class, the daily load profile and the standard deviation of power demand caused by the customer random load behavior are determined to represent the stochastic load characteristics of a substation. By representing the load demand of substation as a stochastic model for load flow analysis, it will be different from the load models used in the conventional transient This work was supported in part by the National Science Council of R.O.C. under contract number NSC 91-2213-E-244-006. M. S. Kang is with the Department of Electrical Engineering, Kao Yuan Institute of Technology, Taiwan (e-mail:
[email protected]). C. S. Chen is with Department of Electrical Engineering, National Sun YatSen University, Kaohsiung, Taiwan (e-mail:
[email protected]). Y. L. Ke is with the Department of Electrical Engineering, Kun Shan University of Technology, Taiwan (e-mail:
[email protected]). T. E. Lee is with the Department of Electrical Engineering, National Kaohsiung University of Applied Sciences, Taiwan.
0-7803-7967-5/03/$17.00 ©2003 IEEE
Y.L. Ke, Member, IEEE, and T.E. Lee stability analysis. For transient stability analysis, the transient recorders have been adopted to measure the power consumption as well as the bus voltage and frequency so that the load demand of a substation during the transient process can be expressed as functions of voltage and frequency. By this method, the load model derived cannot represent the power consumption of load buses effectively because the model will be varied from time to time according to the load composition of different types of customers [3]-[5]. On the other hand, the stochastic load models can represent the time dependent load characteristics of substations by considering the hourly load composition and the customer stochastic load behavior. Besides the noise level of substation power consumption can be determined by statistics method to identify the random portion of customer load behavior. By executing the stochastic load flow analysis [6], [7] with the load models derived for each substation, the expected value of bus voltage magnitudes and angles can be solved in a more statistical manner. In this paper, the DC load flow analysis is executed to solve the statistic variance of bus voltage angles by considering the stochastic behavior of bus real power demand. The stochastic voltage magnitude and reactive power flow are ignored in the study to simplify the simulation. Fig. 1 shows the flowchart of stochastic load flow analysis by considering the customer load behavior. Derive the typical daily load patterns and temperature sensitivity (TS) of power consumption for each customer class by load survey
Solve the power consumption profile of substations by load composition and typical daily load patterns
Determine the expected mean value and noise of hourly power demand of each substation by considering the temperature effect of power consumption
Calculate the bus voltage angles and the corresponding standard deviation by stochastic load flow analysis Estimate the power flows of transmission lines by the expected bus voltage angles and dc circuit model
Fig. 1. The process of stochastic load flow analysis.
II. LOAD STUDY P
A. Typical Load Patterns of Customer Classes To identify the load demand by considering the load composition and customer load behavior for each substation in Taipower system, the load survey study has been performed to find the load behavior of each customer class. The load study has been applied to find the customer load behavior with certain confidential level. The hourly power consumption of all customers within the same class is then integrated to solve the mean value and standard deviation of substation power demand. Fig. 2 shows the load patterns of residential, commercial, and industrial customers respectively. It is found that the residential customers consume most of their power during the night time period when people stay at home and use a lot of electric appliances such as air conditioners (A/C), lamps, TV sets and etc. For the commercial customers, the peak loading occurs during the daytime business hours with very high percentage of the A/C loading. With high temperature and humidity during the summer season in Taiwan, the A/C units contribute more than 70% of power demand for the commercial customers. For the industrial customers, the hourly loading factor has been improved and maintained above 80% with the implementation of load management.
1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
T
Fig. 3. The relationship of power consumption and temperature for the commercial customers.
P = 0.87 − 0.13T + 0.30T 2 (1) where P is the power consumption and T is the temperature. By executing the derivative of power consumption with respect to the temperature, the temperature sensitivity (TS) can be solved. Fig. 4 shows the temperature sensitivities of power consumption for three customer classes. It is found that the temperature sensitivity becomes more significant with the usage of air conditioners. For instance, temperature has more significant effect to the power demand of commercial customers during the daytime period. For the residential customers, temperature effect to the power consumption is more obvious during the night time period. On the other hand, the temperature change has less impact to the power consumption of industrial customers.
1.0
TS
0.9
Industrial
0.8 0.7
Commercial & Office
0.6 0.5 0.4
Residential
0.3 0.2 0.1
2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
Commercial & Office
Residential
Industrial 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time(hour)
0.0 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time(hour ) Fig. 2. The typical load patterns of three customer classes.
B. Temperature Effect to Customer Power Consumption Due to the usage of air conditioners by the commercial and residential customers, the temperature rise always introduces dramatic increase of system demand. More than 35% of Taipower system peak loading has been contributed by the air conditioners and the power demand is increased by 650 MW for each 1 ℃ temperature rise. The investigation of temperature sensitivity of the power consumption for each customer class can be used to estimate the system demand with temperature change[8],[9]. By performing the statistic regression analysis [10] of the customer power consumption with respect to the temperature, the power consumption can be represented as a polynomial function of temperature. Fig. 3 shows that the relationship between power consumption and temperature rise for the commercial customers at 3 PM with 264 data points over one year period. Equation (1) shows the expected mean value of power consumption as the solid line and the dash lines illustrate the 95% confidential intervals.
Fig. 4. Temperature sensitivity of power consumption for three customer classes.
C. Load Composition of Substations The power demand of each substation or load bus can be determined according to the load composition by all customer classes. With the typical load patterns and the total power consumption by all customers in each class within the service territory, the daily power profile of substations can be obtained. Fig. 5 shows the load window of Shijr substation, which is located in northern Taiwan and serves high percentage of commercial and residential areas. Its peak load demand is 1688 MW at 2 PM and the load composition by commercial and residential customers is 51% and 46% respectively. Fig. 6 shows the load window of Kaokang substation, which serves several heavy industrial parks in Kaohsiung area. The substation peak load demand is 2691MW at 3PM and the loading percentages of industrial, residential, and commercial customers are 50%, 31%, and 19% respectively. By comparing Fig. 5 and Fig. 6, significantly different daily power profiles have been illustrated due to the differences of load composition between this two substations. Besides, the power consumption by industrial customers remains very consistent over the daily period, while the commercial customers
consume more power during the daytime business hours because of the usage of air conditioners. 1800
Residential
Load(MW)
Commercial
Industrial
1600 1400 1200 1000
is estimated by the load composition and the covariance matrix of power consumption. For each study hour, PiT is the mean value of power consumption by all test customers in class i and Pi is the substation load composition of the customer class. The standard deviation of substation power consumption can be solved as (3). R ,C , I
Pi ) (3) P i iT For instance, the mean power consumption of Shijr substation at 3 PM is solved as 1679 MW with noise level as 90 MW. S = ∑ ( Cεi ×
800 600 400 200 0 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Time(hour) Fig. 5. Synthesized daily power profiles of Shijr substation.
3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 0
Residential
Load(MW)
Commercial
Industrial
B. Stochastic Load Flow Analysis After solving the expected mean value and the corresponding variance of power consumption for each substation, the voltage angles of a power system can be obtained by stochastic load flow analysis. In this paper, the dc circuit model is used to represent the simplified power system and the load flow equation is expressed as (4). F ( X , D) = 0 (4) where X is the voltage angles of system buses and D is the power demands of substations. By Taylor’s expansion, the power mismatch ∆F can be expressed as (5). ∂F ∆X + η (5) ∂X where η is the noise associated with the substation power demand. In this paper, the least square method is applied to solve the best estimate of standard deviation of bus voltage angles in (6). ∆F =
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time(hour) Fig. 6. Synthesized daily power profiles of Kaokang substation.
III. STOCHASTIC LOAD FLOW A. Stochastic Load Model According to the above discussion, the power consumption of each customer class during each study hour will be varied with the temperature and be stochastically changed with the customer random load behavior. The temperature effect can be used to explain the variation of customer power consumption in (1). The customer random load behavior can be treated as the noise ε of bus loading, which is expressed as the difference of actual power consumption and its expected mean value in (2).
ε = Pi − Pˆi (Ti ) (2) Here, the noise is assumed to have the following properties. 1. E (ε) = 0 2. ε is a Gaussian’s distribution 3. E (ε − ε ) 2 = Cov(ε) = Cε After solving the covariance of power consumption for each customer class, the stochastic load demand of each substation
∂F t −1 ∂F C ∆Xˆ = ∂X η ∂X
−1
∂F t −1 Cη ∆F ∂X
(6)
IV. CASE STUDY To demonstrate the stochastic load flow analysis by considering the customer load behavior, Taipower system has been selected to perform the stochastic load flow analysis to find the bus voltage angles. Fig. 7 shows the simplified single line diagram of Taipower system. There are 16 power generation stations and hundreds of substations have been integrated as 17 equivalent load buses. Bus 1 is the swing bus with voltage magnitude as 1.0 pu and voltage angle as zero degree. The hourly power consumption of substations and the power generation by each power plant have been collected by the SCADA system in Taipower. The average power demand of substations and power generation at 3 PM have been solved as Pl and Pg respectively in Table I. By taking into account the temperature effect to the power consumption of each customer class and the load composition, the standard deviation of substation power consumption is derived and represented as C η . It is found that the average loading at bus 7 is 1369 MW with variance as 84 MW2. The bus voltage
magnitudes V and angles θ have been obtained by NewtonRaphson load flow analysis to verify the accuracy of the proposed stochastic load flow analysis with the simplified dc power system model. To solve the stochastic load flow of Taipower system by considering the random load behavior of customers served by each substation, only the real power component and network reactance are included in the dc circuit model. The real power flow of transmission lines and voltage angles of system buses are calculated by (7). Yθ = P + ε
(7)
Here Y is the system admittance matrix, θ is the bus voltage angles and P is the mean value of power consumption of substations. The variance of bus voltage angles is introduced by the random load behavior ε of the customers served by the substation. The expected values of bus voltage angles are then derived as (8). θˆ = Y −1P (8) From Table I, the deviation between the actual θ and the expected θˆ is introduced by using the simplified dc circuit model and due to the customer random load behavior. It is found that the largest angle difference between the northern buses and southern buses has reached 65.5° because of the large amount of power transfer by the bulk transmission lines. A diagonal matrix with variances Var corresponding to the stochastic power loading of substations has been applied to solve the standard deviation of bus voltage angles in (9).
σθ2ˆ
[
= Diag Y Var Y
＃28
＃29 G
＃5
＃31
＃15 ＃16
G
＃1
＃24
G
＃2
G
＃8
＃3 ＃4
＃14
＃9
G
＃30
＃7 ＃6
＃17 ＃10
＃20 ＃21
G
＃19
−1
∂F t −1 Cη ∆F (11) ∂θ
∂H 2 ∂H σ (12) ∂θ θˆ ∂θ Table II shows the expected mean value and standard deviation of power flows for partial of the transmission lines in Taipower. Although the dc circuit model is used in the load flow analysis, the expected values of line flows derived are still very consistent to those solved by Newton-Raphson method with detail circuit model.
＃32
G
＃33
＃18 G
Fig. 7. The single-line diagram of Taipower transmission system. Angle(degree) 70 Upper
60
P
＃11
(9)
W = H (θ ) (10) The standard deviation and covariance of power flows over the transmission lines are basically related to the uncertainty of bus voltage angles in (11) and (12) respectively.
σ 2ˆ =
G
G
＃13 ＃12
With the random load behavior of substations, significant variation of bus voltage angles has been introduced as shown by the 95% confidential interval in Fig. 8. To determine the effect of random load behavior to the power flow of transmission lines, the power flow equation in (10), is used in this study.
t
＃27 ＃25
Swing
G
∂H ˆ ∂H ∂F t −1 ∂F Cη ∆Wˆ = ∆θ = ∂θ ∂θ ∂θ ∂θ
G
＃26
G
]
G
＃23
＃22
−1 −1
t
To investigate the effect of loading level to the stochastic load flow, the power demand and the corresponding standard deviation of Taipower substations for the off peak operation at 5 AM have been solved in Table III. After executing the load flow analysis by the Newton-Raphson method and the proposed stochastic method with the simplified dc circuit model, the bus voltages and angles are obtained. It is found that the power consumption by the commercial customers in the northern region has been reduced dramatically during the off peak period. The balance of area generation and load demand is therefore improved to result in the reduction of power transfer over the transmission lines. The largest angle difference between the system buses has been reduced from 65.5° in peak hours to 21.7 ° for the off peak operation.
50
Expected value
40 30
Lower
20 10 0 -10 -20
2
4
6
8
10
12
14
16
18
20
22
24
Bus no.
-30
Fig. 8. The 95% confidential interval of bus voltage angles.
26
28
30
32
TABLE I THE STOCHASTIC BUS VOLTAGE ANGLES FOR PEAK OPERATION (BASE: 100 MVA) Bus voltage Pg Cη Pl Bus No. θˆ σ θˆ V θ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Line segment 2 3 4 10 12 17 18 22 26 28 30 34 36 39 41 43 45 46
8.3 0.3 0.3 35.0 21.2 13.7 5.3 8.7 10.9 2.0 5.0 14.2 0.5 20.8 20.8 10.9 18.2 26.9 18.5 18.5 19.2 27.3 21.1 9.0 16.8 19.4 11.5 18.1 6.0 11.5 21.0 8.7
0.383 0.007 0.007 1.768 1.604 0.838 0.127 2.061 0.063 0.506 0.001 2.061 3.123 3.126 1.866 0.235 0.813 -
1.000 0.973 1.011 1.004 0.965 1.004 1.020 0.964 1.015 1.010 1.015 1.008 1.022 1.025 1.028 1.024 1.015 1.038 1.014 1.024 1.024 1.015 0.979 1.000 1.009 1.013 1.021 1.006 1.022 1.015 1.015 1.015 1.015
0.0 -3.7 23.8 11.2 -12.6 25.5 24.9 -1.8 11.7 33.4 24.3 11.1 12.3 12.7 13.1 26.2 33.5 41.9 37.0 36.5 36.5 32.6 -17.2 -16.0 -15.4 -14.8 -13.3 -14.0 -13.7 24.1 1.3 43.0 41.8
-3.6 26.0 12.8 -12.8 28.1 27.3 -1.1 13.3 37.3 26.6 12.7 14.0 14.5 14.9 28.7 37.4 47.0 41.5 40.5 40.5 34.7 -17.9 -16.6 -16.2 -15.6 -14.2 -14.7 -14.4 26.4 1.4 47.7 46.4
2.4 4.6 4.1 3.1 5.1 4.6 3.7 4.1 5.8 4.6 4.1 4.2 4.2 4.2 4.6 5.7 6.0 6.1 5.7 5.7 5.1 3.4 3.4 3.4 3.4 3.4 3.4 3.4 4.6 2.4 6.1 6.1
TABLE II THE STOCHASTIC POWER FLOWS OF TAIPOWER SYSTEM (BASE: 100 MVA) Expected Transmission Power Power line flow σ Pˆ 1.96σ Pˆ flow From To P(pu) Pˆ 31 11 32 27 18 26 25 5 7 13 12 6 6 29 16 15 30 9
2 3 19 26 17 24 24 4 3 12 4 22 10 26 7 14 3 4
11.5 2.0 21.0 4.3 9.8 5.3 3.5 -9.8 3.6 4.3 -0.7 -19.1 -5.3 15.5 17.3 2.9 6.0 8.7
11.5 2.0 21.0 3.9 9.2 4.7 2.7 -11.1 3.5 4.3 -0.5 -17.6 -6.4 15.2 17.3 2.9 5.9 8.7
0.01 0.01 0.01 0.11 0.38 0.45 0.37 0.63 0.65 0.45 0.51 0.07 0.60 0.33 0.27 0.02 0.01 0.01
0.02 0.02 0.02 0.21 0.74 0.87 0.72 1.23 1.27 0.88 1.00 0.14 1.17 0.64 0.52 0.03 0.03 0.02
TABLE III THE STOCHASTIC BUS VOLTAGE ANGLES FOR OFFPEAK OPERATION (100 MVA BASE) Bus voltage Pg Cη σ θˆ Pl Bus No θˆ V θ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
10.8 1.3 1.3 18.3 7.3 5.3 5.3 15.6 6.3 2.0 2.3 5.6 0.5 17.2 17.2 6.3 18.2 20.7 10.4 10.4 2.5 7.8 5.8 4.3 6.1 16.0 11.5 18.1 10.4 3.2 9.6 8.7
0.392 0.058 0.058 4.396 1.129 0.309 0.316 2.229 1.163 0.037 0.046 0.285 0.003 1.163 3.148 0.0001 0.488 0.264 0.106 0.209 0.991 -
1.000 1.003 1.012 1.012 1.001 1.015 1.021 0.998 1.011 1.017 1.012 1.015 1.025 1.027 1.028 1.024 1.022 1.038 1.012 1.024 1.024 1.001 0.998 1.012 1.015 1.017 1.021 1.006 1.022 1.001 1.015 1.015 1.015
0.0 -1.5 1.9 -0.7 -1.3 3.8 4.2 -2.9 -1.7 10.0 1.4 -0.2 1.7 2.0 2.4 5.2 10.1 17.7 12.3 11.7 11.7 3.8 0.7 3.5 4.7 5.4 6.5 5.4 6.2 1.3 -0.2 15.0 17.1
-1.6 1.4 -0.8 -1.3 3.3 3.8 -3.0 -1.9 10.4 0.8 -0.4 1.7 2.1 2.5 4.9 10.3 18.7 12.8 12.1 12.1 2.3 0.7 3.7 4.9 5.6 6.8 5.6 6.5 0.8 -0.2 15.7 17.8
2.3 4.4 4.1 2.9 4.8 4.4 3.6 4.1 5.4 4.4 4.1 4.1 4.1 4.1 4.4 5.3 5.6 5.8 5.4 5.4 4.8 2.9 3.0 3.0 3.0 3.0 3.0 3.0 4.4 2.3 5.8 5.8
V. CONCLUSION In this paper, the stochastic load flow analysis has been performed to solve the mean value and standard deviation of voltage angles for system buses. The stochastic power flows of transmission lines are then calculated according to the bus voltage derived. To find the customer load behavior, the load survey system has been used to derive the typical daily load patterns of each customer class by statistic analysis. After retrieving the power consumption of all customers in the same class, the hourly power consumption by each customer class in the service territory of each substation can be obtained according to the load patterns derived. The hourly bus loading is therefore represented as the expected power demand and the corresponding standard deviation by considering the load composition. The noise level of bus loading, which has been introduced by the customer random load behavior, is also identified. To execute the stochastic load flow analysis, the dc circuit model of Taipower system has been used in this study to solve the mean value and standard deviation of voltage angles for system buses. To verify the accurancy of the proposed stochastic load flow analysis, the Newton-Raphson method by considering the detail circuit model is also performed. To represent the stochastic phenomenon of substation loading due
to customer random load behavior, the temperature effect of power consumption have been included in the load flow analysis. For the summer peak operation, the power consumption in northern Taipower substations has been increased dramatically due to the usage of air conditioners in the commercial and residential oriented areas. A bulk power transfer has to be transmitted from the southern region to the northern region over the bulk transmission lines. By executing the stochastic load flow analysis, the largest voltage angle difference of Taipower system buses can reach 65.6° with the average standard deviation of 4.8°. During the off peak period, the largest voltage angle difference between system buses has been reduced to 21.7° because of the balance of generation and load demand in each service region. To assess the security margin of bus voltage angle difference for system operation, it is suggested that the random load behavior of each substation should be considered in the stochastic load flow analysis to evaluate the variation of bus voltage angles in a power system. VI. REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7] [8]
[9]
[10]
C. S. Chen, J. C. Hwang and C. W. Huang, “Determination of Customer Load Characteristics by Load Survey System at Taipower,” IEEE Transactions on Power Delivery, Vol. 11, No. 3, pp. 1430-1435, July 1996. C. S. Chen, J. C. Hwang and C. W. Huang, “Application of Load Survey Systems to Proper Tariff Design,” IEEE Transactions on Power Systems, Vol. 12, No. 4, pp. 1746-1751, November 1997. Ke Li, “State Estimation for Power Distribution System and Measurement Impacts,” IEEE Transactions on Power Systems, Vol. 11, No. 2, pp. 911-916, May 1996. Atish K. Ghosh, David L. Lubkeman, Matthew J. Downey, and Robert H. Jones, “Distribution Circuit State Estimation Using A Probabilistic Approach,” IEEE Transactions on Power Systems, Vol. 12, No.1, pp. 45-51, February 1997. C. N. Lu, J. H. Teng and W.H.E. Liu, “Distribution System State Estimation,” IEEE Transactions on Power Systems, Vol. 10, No. 1, February 1995, pp. 229-240. Y. Y. Hong, L. H. Lee, “Stochastic Voltage-Flicker Power Flow,” IEEE Transactions on Power Delivery, Vol. 15, No. 1, pp. 407-411, January 2000. O. A. Klitin, “Stochastic load flow,” IEEE Transactions on PAS, vol. PAS-94, no. 2,pp. 299-309, March/April 1975. C.S.Chen, M.S. Kang, J.C. Hwang, C.W. Huang, “Temperature Effect to Distribution System Load Profiles and Feeder Losses,” IEEE Trans. on Power Systems, Vol.16, No.4, November 2001, p916-921. C.S.Chen, M.S. Kang, J.C. Hwang, C.W. Huang, “Temperature Adaptive Switching Operation for Distribution Systems,” IEEE Trans. on Power Delivery, Vol.16, No.4, October 2001, p694-699. Draper,N.R. and H. Smith, Applied Regression Analysis, John Wiley & Sons, Inc., New York, 1966.
VII. BIOGRAPHIES Meei-Song Kang received the M.S., Ph.D. degree in Electrical Engineering from the National Sun Yat-Sen University in 1993 and 2001 respectively. Since August 1993, he has been with Department of Electrical Engineering, Kao Yuan Institute of Technology, Kaohsiung, Taiwan. Currently he is an Associate Professor. His research interest is in the area of load survey and demand subscription service. Chao-Shun Chen received the B.S. degree from National Taiwan University in 1976 and the M.S., Ph.D. degree in Electrical Engineering from the University of Texas at Arlington in 1981 and 1984 respectively. From 1984 to 1994 he was a professor of Electrical Engineering department at National Sun Yat-Sen University. Since 1994, he works as the deputy director general of Department of Kaohsiung Mass Rapid Transit. From Feb.1997 to July 1998, he was with the National Taiwan University of Science and Technology as a professor. From August 1998, he is with the National Sun Yat-Sen University as a full professor. His majors are computer control of power systems and distribution automation. Yu-Lung Ke was born in Kaohsiung, Taiwan, July 1963. He received the BS degree in Control Engineering from National Chiao Tung University, Hsin Chu City, Taiwan in 1988 and received the MS degree in Electrical Engineering from National Taiwan University, Taipei City, Taiwan in 1991. He received the Ph. D degree in Electrical Engineering from National Sun Yat-Sen University, Kaohsiung City, Taiwan in June 2001. Since August 1991, he has been with Department of Electrical Engineering, Kun Shan University of Technology, Tainan, Taiwan. Currently he is an Associate Professor. His research interests include the distribution automation, power quality and artificial intelligence applications in power systems. Dr. Ke is a member of IEEE Power Engineering Society (PES), Industry Applications Society (IAS), Systems, Man, and Cybernetics (SMC) Society and a registered professional engineer at Taiwan. Tsung-En Lee received his Ph.D. from National Sun Yat-Sen University, Taiwan in 1994. He has been with Department of Electrical Engineering, National Kaohsiung University of Applied Sciences while currently he is a associate professor. His research areas are power system operation, and application of operation research and artificial intelligence.
