VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR. A Thesis by. Hong-Tuan Nguyen Vu

Transcription

1 VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR A Thesis by Hong-Tuan Nguyen Vu Eletrial Engineer, Polytehni University of HCMC, 1993 Submitted to the College of Engineering and the faulty of the Graduate Shool of Wihita State University in partial fulfillment of the requirements for the degree of Master of Siene Deember 2005

2 VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR I have examined the final opy of this Thesis form and ontent and reommend that it be aepted in partial fulfillment of the requirement for the degree of Master of Eletrial and Computer Engineering. Dr Ward T. Jewell, Committee Chair We have read this Thesis and reommend its aeptane: Dr Andrew Aker, Committee Member Dr Paul K. York, Committee Member ii

3 DEDICATION To my parents who sarifie their whole lives to enourage me to learn and to my family, my wife Huyen and three kids Chi, Emily, and Luke, for their lak of my are, as I was busy to omplete this Thesis. iii

4 ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Ward Jewell, who led me from the very first year in my Graduate Shool, for his patiene as well as the professional advies to help me to obtain this ahievement. iv

5 ABSTRACT A previous thesis [1] showed that the voltage on a distribution line with high R/X ratio will atually derease as shunt apaitane is added. This thesis develops a new distribution feeder model and onfirms this unexpeted result. Then the IEEE radial test feeders are modeled to further study the effet and provide additional insight into voltage ontrol on feeders with high R/X ratio. v

6 TABLE OF CONTENTS Chapter CHAPTER I INTRODUCTION CHAPTER II METHODOLOGY Page Radial Distribution Feeder Problem Formulation 02 CHAPTER III EXAMPLE SYSTEM CHAPTER IV LOAD IMPEDANCES CHAPTER V VOLTAGE CONTROL Example Example Example 3 16 LIST OF REFERENCES 19 APPENDIXES 21 APPENDIX A: IEEE 37-NODE TEST FEEDERS..22 APPENDIX B: LINE IMPEDANCES CALCULATIONS.24 APPENDIX C: EXAMPLES CALCULATIONS 27 vi

7 LIST OF TABLES Table TABLE 1 Page LIST OF R/X FACTOR OF EACH LINE SEGMENTS ON IEEE 37-NODE TEST FEEDERS SEGMENTS.09 TABLE 2 SPOT LOADS OF IEEE 37-NODE TEST FEEDERS 11 vii

8 LIST OF FIGURES Figure Page Figure 1 Feeder Model. 3 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Equivalent Ciruit Model..3 Combined All Impedanes in Zt Model...4 Reeiving End Phasor Diagrams. 7 One line Diagram of IEEE 37-Node Test Feeder.10 Results for Example 1.14 Results for Example 2.15 Results for Example 3.16 viii

9 CHAPTER I INTRODUCTION As early as 1910, apaitor banks were applied to improve both quality and quantity of eletri power transmission and distribution. Still today they are used to orret power fator in order to lower line losses, to raise power transfer apabilities, and to improve a line s voltage profile. They an help ontrol power flow through tie lines and redue operating osts. In most ases, apaitor banks play the role of reative power generator; however they may be onsidered as apaitive reative loads too. This thesis extends the work of a previous thesis [1]. In this thesis, it was shown that injeting reative power into lines with high R/X ratio (R/X > 2), sometimes ause the reeiving voltage V R to derease, not inrease, as expeted. That thesis [1] seeks to further explain these results, and also to extend the basi understanding of the operation of apaitors on a power system. 1

10 CHAPTER II METHODOLOGY 2.1 Radial Distribution Feeder A radial distribution feeders supplies all loads from only one substation. The feeder may have the following omponents: Three-phase main feeder Three-phase, two-phase, or single-phase laterals. Step-type voltage regulators. In-line transformers Shunt apaitor banks Distribution transformers Loads 2.2 Problem Formulation: A radial distribution feeder was modeled as shown in Figure 1. Variables are soure voltage Vs, line impedanes R and j*x, and load impedanes Rl and j*xl. The shunt apaitor, whih was paralleled with the load to injet rated reative power, Q, into the feeder, has rated apaitive reatane X. The negative sign on j*x indiates that apaitive reative power Q has the opposite sign to indutive reative power Ql. The reeiving end voltage Vl is supplied to the load, and the shunt apaitor is onneted in parallel with the load. The soure voltage is ideal; onstant magnitude and infinite power. 2

11 ~ Figure 1. Feeder Model The equivalent iruit in Figure 2 puts the load in parallel with the apaitor, reating the new load with the omplex impedane Z. Figure 2. Equivalent iruit model Equation 1 gives the new load impedane Z of Figure 2. 3

12 Z = j. x.( Rl jxl ) ( 01) Rl j Xl x The equivalent iruit in Figure 3 ombines the load, omplex impedane Z, in series with the line impedane to form the new total omplex impedane Zt, whih is alulated in equation 2. Figure 3. Combined All Impedanes In Zt Model Zt = j. x.( Rl jxl) ( R jx) Rl j Xl x 4

13 Zt = j. x.( Rl jxl) ( R jx). Rl j Xl x Rl j Xl x Rl j Xl x Zt = jrl. x Xl. x RRl. jr. Xl jr. x jrl. X XXl. Xx. Rl j Xl x Rl j Xl x Zt = Xl. x RRl. XXl. Xx. j. Rlx. RXl Rx. Rl. X (02) Rl j Xl x Applying Ohm's law for load Z and again for total line and load Zt: Vl = ZI. Vs = Zt. I Assuming that Vs is the base voltage, its per-unit value will be Vs = 1 pu with an angle of 0, so the per unit reeiving end voltage Vl/Vs does not depend on the urrent I, beause the urrent I is eliminated from both numerator and denominator, as shown in equation 3. Vl Vs = j. x.( Rl j. Xl) Xlx. RRl. XXl. Xx. jrlx.. RXl. Rx. RlX. (03) Equation 03 gives the reeiving end voltage in per unit The apaitive reative power, Q, at nominal apaitor voltage is used to rate a apaitor. Capaitive reatane, X, an be alulated from voltage and reative power. The equation for the shunt apaitor reative power is: 5

14 Q =-kv 2 /X Where: X: Shunt Capaitive reatane (Ohm) Q: rated apaitive reative power (MVAr) kv: rated apaitor voltage (kv) The apaitive reatane X is given by equation 4. x kv 2 Q ( Ω ) ( 4) The value of apaitive reatane X will have the opposite sign from indutive reatane Xl, and from Q, whih is positive when supplied to the system. Most loads are indutive, Figure 4a, and added ompensation supplies reative power, Figure 4b. In the ase of overompensation, the reative power supplied by the added apaitive reatane is greater than that onsumed by the load. The ombination beomes apaitive, as shown in Figure 4. 6

15 a/ Indutive load b/ Power fator orretion 1 > pf > pf, adding shunt apaitor: I = I+I () Overompensation Figure 4. Reeiving End Phasor Diagrams (a) Without adding shunt apaitor. (b) With adding shunt apaitor. () Overompensated 7

16 CHAPTER III EXAMPLE SYSTEM A feeder from the IEEE 37-node test feeder [5] is used as the example system in the rest of this thesis. Simple positive-sequene line impedanes were alulated from the 37 node feeder data. IEEE 37 Node Test Feeder The positive-sequene R and X are needed for eah feeder segment of the 37-node test feeder. From the available feeder data [5], the impedane matrix [Zab] is plaed into the modified Carson and the Kron redution equations [6]: Zs 1. 3 Zab 0, 0 Zab 11, Zab 22, Zm 1. 3 Zab 01, Zab 1, 2 Zab 2, 0 The positive sequene impedane, Z11, is : Z11 = Zs Zm The alulations for eah segment are presented in Appendix B. The results are shown in Table 1. 8

17 TABLE 1: R/X FACTOR OF EACH LINE SEGMENT Node A Node B OF IEEE 37-NODE TEST FEEDERS Line Segment Data Positive Seq. Positive Seq. (Ω/mile) (Ω) r x R X R/X Length (mile.) Config. 9

18 Figure 5: One line diagram of IEEE 37-Node Test Feeder 10

19 CHAPTER IV LOADS IMPEDANCES Load data for a distribution feeder is ommonly modeled as onstant real power, P, and reative power, Q. This load power data is onverted to a onstant impedane model by assuming a load voltage, and from the load data shown in Table 2 [5]: TABLE 2: SPOT LOADS OF IEEE 37-NODE TEST FEEDERS Node Load Ph-1 Ph-1 Ph-2 Ph-2 Ph-3 Ph-4 Model MW MVAr MW MVAr MW MVAr 701 D-PQ D-PQ D-PQ D-I D-Z D-PQ D-I D-Z D-PQ D-PQ D-PQ D-I D-Z D-Z D-PQ D-I D-PQ D-PQ D-Z D-I D-PQ D-PQ D-I D-Z D-PQ Total

20 Apply Ohm's law to alulate the load impedanes: S = P - j*q S = V*I = V. V Z Then Z = V I So, Z = P V 2 j. Q Hene, R = l Re( Z) (Ω) (05) X = l Im( Z) (Ω) (06) Note: V is in kv P is in MW, and Q in MVAr 12

21 CHAPTER V VOLTAGE CONTROL In this setion, the effets of shunt apaitane on the reeiving end voltage are illustrated in three examples. Beause of its relatively high R/X ratio, phase a of the feeder at node 744 of the IEEE 37-node test feeder was used in the examples. Calulations for all three examples are presented in Appendix C. 13

22 5.1 Example 1: Substitute the feeder data into equations 1, 2, 3, 5, and 6. Then plot the graph of Vr, the reeiving end (load) voltage and power fator versus the rating of apaitor Q. These are shown in Figure 6. Note that the apaitor rating is not the atual apaitive reative power injeted into the line, beause redued Vr lowers the atual Q. So in some ases, a greater value of rated Q may supply less apaitive reative power than a smaller apaitor. 1 Plotting of Reeived End Voltages 0.98 Reeived Voltage Per Unit V 1 pf Q 1 Rating Capaitor (MVA) Figure 6. Results for Example 1. 14

23 5.2 Example 2: Inrease the R/X ratio from its original value of 3 to 31. The results, shown in Figure 7 show that the higher value of k results in the reeiving end voltage to starts dereasing earlier. 1 Plotting of Reeived End Voltages 0.97 Reeived Voltage Per Unit V 1 pf Q 1 Rating Capaitor (MVA) Figure 7. Results for example 2 15

24 5.3 Example 3: Example 3 repeats the ase simulated in a previous thesis [1]. This example verifies agreement between the proedure developed in this thesis with the previous work. Results are shown in Figure Plotting of Reeived End Voltages 0.97 Reeived Voltage Per Unit V 1 pf Q Added Capaitive Power (KVAr) Figure 8. Results for example 3. 16

25 In all three examples, the line s R/X ratio is greater than 2. In eah, reeiving end voltage Vr is observed inreasing to its maximum value, and then dereasing, as the apaitor rating inreases. Also in eah, the plot of power fator has an M shape. In example 1, the onept of power fator orretion apaitane, or reative power generator an explain the behavior of the shunt apaitor within the first interval, 0 < Q < The reative power produed by the shunt apaitor, ompensated for the reative power onsumed by the load, whih orrets the power fator, and inreases pf to unity. In the seond interval, 26.6 < Q < 83.7, the apaitor reative power flow is greater than that onsumed by the load, so the power fator beomes leading thus and starts to derease from unity. The voltage ontinues to inrease with inreasing apaitive reative power. In the last interval, 83.7 < Q < 200, the system beomes overompensated; the apaitive reatane is greater than that onsumed by the load and the line. The surplus apaitive reatane an be onsidered as a apaitive load. Then the apaitive omponent, X, of the load impedane Z beomes smaller and fores Z to do so as well. The voltage drop on the line insreases, and the reeiving end voltage starts dropping with inreasing apaitor rating. The atual apaitive reative power injeted is dereasing due to the derease in the reeiving end voltage, returning the power fator to unity. In example 2, the R/X ratio is inreased by lowering the line reatane X. That hange also redues the demand of reative power that ombine the 17

26 reative load and the reative power loss on the line. So the ase of overompensation omes earlier results in the reeiving end voltage start dropping as soon as the rating apaitor is 30 MVAr. Example 3 repeats an example from an earlier thesis [1]. The results were the same as in [1]. This was used to verify the model developed in previous hapters. Future work: o As shown in example 2, the reeiving end voltage drops earlier with inreasing R/X. Further work should be done to quantify this effet. o Study the effets of plaing more than one apaitor on the line. 18

27 LIST OF REFERENCES 19

28 REFERENCES [1] D. K. Mehdi and W. Jewell, Reative power on Radial Distribution Systems: Voltage Control and Line Losses, Wihita State University, Eletrial Computer Engineering Department [2] M.H. Shwedhi and M.R. Sultan, Power Fator Corretion Capaitors; Essentials and Cautions, IEEE Power Engineering Soiety Summer Meeting, vol. 3, pp , [3] B. Milosevi and M. Begovi, Capaitor Plaement for Conservative Voltage Redution on Distribution Feeders, IEEE Transations on Power Delivery, vol. 19, No. 3, July [4] R.T. Saleh and A.E. Emanuel, Optimum Shunt Capaitor for Power Fator Corretion at Busses with Lightly Distorted Voltage, IEEE Transations on Power Delivery, vol PWRD-2, No. 1, pp , January [5] IEEE 34, 37, 123 node test feeders please visit the website [6] William H. Kersting, Distribution System Modeling and Analysis, CRC Press, [7] J. D. Glover and M.S. Sarma, Power System Analysis and Design, 3 rd Edition, Brooks/Cole,

29 APPENDICES 21

30 APPENDIX A IEEE 37 NODE TEST FEEDER PHASE IMPEDANCE AND ADMITTANCE MATRICES Configuration 721 Z (R +jx) in ohms per mile B in miro Siemens per mile Configuration 722 Z (R +jx) in ohms per mile B in miro Siemens per mile

31 Configuration 723 Z (R +jx) in ohms per mile B in miro Siemens per mile Configuration 724 Z (R +jx) in ohms per mile B in miro Siemens per mile

32 APPENDIX B FIND POSITIVE-SEQUENCE R AND X FOR EACH FEEDER SEGMENT OF 37-NODE TEST FEEDER SEGMENTS AND CALCULATE THEIR RATIO R/X: Configuration 721: Zab i i i i i i Using the modified Carson and the Kron redution [6]: Equation 4.68 => Zs Equation 4.69 => 1. 3 Zab Zab 0, 0 11, Zab 22, Zs = i Zm 1. 3 Zab Zab 01, 12, Zab 20, Zm = i Positive sequene impedane, Z11: Z11 Zs Zm Z11 = i Ω/mile Configuration 722: Zab i i i i i i Using the modified Carson and the Kron redution [6]: Equation 4.68 => 1 Zs. 3 Zab Zab 0, 0 11, Zab 22, Zs = i Equation 4.69 => 24

33 Zm 1. 3 Zab Zab 01, 12, Zab 20, Zm = i Positive sequene impedane, Z11: Z11 Zs Zm Z11 = i Ω/mile Configuration 723: Zab i i i i i i Using the modified Carson and the Kron redution [6]: Equation 4.68 => 1 Zs. 3 Zab Zab 0, 0 1, 1 Zab 2, 2 Zs = i Equation 4.69 => Zm 1. 3 Zab Zab 01, 12, Zab 20, Zm = i Positive sequene impedane, Z11: Z11 Zs Zm Z11 = i Ω/mile Configuration 724: Zab i i i i i i Using the modified Carson and the Kron redution [6]: Equation 4.68 => Zs 1. 3 Zab Zab 0, 0 1, 1 Zab 2, 2 Zs = i 25

34 Equation 4.69 => Zm 1. 3 Zab Zab 01, 12, Zab 20, Zm = i Positive sequene impedane, Z11: Z11 Zs Zm Z11 = i Ω/mile 26

35 APPENDIX C EXAMPLES CALCULATION IN MATHCAD FORMAT Example 1 : Node 744, IEEE 37-Node Test Feeder, using Shunt apaitor. From Table 1, We have: R X Line impedanes( Ω ) kv 4.8 ( kv) R X = Calulate the load impedanes (apply equation 04 and equation 05): p 42 ( MW ) q 21 ( MVAr) Z p kv 2 j. q Z = i Rl Xl Re( Z) Rl = Load impedane ( Ω ) Im( Z) Xl = Load impedane ( Ω ) Without adding shunt apaitor: Q 0 0 apaitive reative power = zero Z 0 Rl j. Xl Load impedane (Ω) Zt 0 ( R Rl) j ( X Xl). Total load & line impedane (Ω) Rl j. Xl V 0 ( R Rl) j.( X Xl) Reeived end voltage V 0 = Add shunt apaitor Q (MVAr); Q delivers apaitive reative power up to 200 MVAr. A apaitor absorbs zero real power, P = 0 W, and negative reative power, Q = -V^2/X var. Alternatively, a apaitor delivers positive reative power, +V^2/X [6]. So, we have: 27

36 Q = kv2 x Capaitane reatane: x kv 2 Q ( Ω ) (Equation 04) Load impedane (Ω) (Applying equation 01) Z j. x.( Rl j. Xl) Rl j. Xl x ( Ω ) Load & line impedane (Ω) (Applying equation 02) Zt Xl. x RRl. XXl. Xx. j. Rlx. RXl. Rx. Rl. X Rl j. Xl x ( Ω ) The reeived end voltage per unit: (Applying equation 03) V j. x.( Rl j. Xl) Xl. x RRl. XXl. Xx. j. Rlx. RXl. Rx. Rl. X (pu) The power fator pf pf Re V 2 Z V 2 Z Example 2 : Node 744, IEEE 37-Node Test Feeder, using Shunt apaitor. However somehow we an hange the line impedane to fore the fator R/X up ( by lowering X) R X Line impedanes( Ω ) kv 4.8 ( kv) R X =

37 Calulate the load impedanes (applying equation 04 and equation 05): p 42 ( MW ) q 21 ( MVAr) Z p kv 2 j. q Z = i Rl Xl Re( Z) Rl = Load impedane ( Ω ) Im( Z) Xl = Load impedane ( Ω ) Without adding shunt apaitor: Q 0 0 apaitive reative power = zero Z 0 Rl j. Xl Load impedane (Ω) Zt 0 ( R Rl) j( X Xl). Total load & line impedane (Ω) Rl j. Xl V 0 ( R Rl) j.( X Xl) Reeived end voltage V 0 = Add shunt apaitor Q: Q = kv2 x Capaitane reatane: x kv 2 Q ( Ω ) (Equation 04) Load impedane (Ω) (Applying equation 01) Z j. x.( Rl j. Xl) Rl j. Xl x ( Ω ) Load & line impedane (Ω) (Applying equation 02) 29

38 Zt Xl. x RRl. XXl. Xx. j. Rlx. RXl. Rx. Rl. X Rl j. Xl x ( Ω ) The reeived end voltage per unit: (Applying equation 03) V j. x.( Rl j. Xl) Xl. x RRl. XXl. Xx. j. Rlx. RXl. Rx. Rl. X (pu) The power fator pf pf Re V 2 Z V 2 Z Example 3 : Reprodue one of the ases from previous thesis Line impedane Zabs = 0.05 pu, Zbase = 10Ω, R/X = 2.5 Sending Voltage Vs = 1.0 pu with an angle of zero, Vln = 7.62 kv Load S = 1.0 pu with Sbase = 100 MVA Line impedanes Zabs R X Zabs R 2.5 R = ( Ω ) X = ( Ω ) R X = 2.5 Calulate the load impedanes (applying equation 04 and equation 05): p p = ( MW ) 30

39 q ( ) 2 3 q = ( MVAr) kv 7.62 ( kv) Z p kv 2 j. q Z = i Rl Xl Re( Z) Rl = Load impedane ( Ω ) Im( Z) Xl = Load impedane ( Ω ) Without adding shunt apaitor: Q 0 0 apaitive reative power = zero Z 0 Rl j. Xl Load impedane (Ω) Zt 0 ( R Rl) j ( X Xl). Total load & line impedane (Ω) Rl j. Xl V 0 ( R Rl) j.( X Xl) Reeived end voltage V 0 = Add shunt apaitor Q(MVAr) Q = kv2 x Capaitane reatane: x kv 2 Q ( Ω ) (Equation 04) Load impedane (Ω) (Applying equation 01) Z j. x.( Rl j. Xl) Rl j. Xl x ( Ω ) Load & line impedane (Ω) (Applying equation 02) 31

40 Zt Xl. x RRl. XXl. Xx. j. Rlx. RXl. Rx. Rl. X Rl j. Xl x The reeived end voltage per unit: (Applying equation 03) ( Ω ) V j. x.( Rl j. Xl) Xl. x RRl. XXl. Xx. j. Rlx. RXl. Rx. Rl. X (pu) The power fator pf pf Re V 2 Z V 2 Z 32