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51 murthy
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51 murthy
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  • 1. V. V. S. N. Murty, Junior Research Fellow Dr. Ashwani Kumar, Professor Department of Electrical Engg., NIT Kurukshetra
  • 2. INTRODUCTION UNBALANCED DISTRIBUTION SYSTEM LOAD FLOW ANALYSIS ANALYSIS OF UNBALANCED SYSTEM UNDER DIFFERENT LOADING CONDITIONS  ANALYSIS OF UNBALANCED DISTRIBUTION SYSTEM UNDER TYPE-A AND TYPE-B UNBALANCES RESULTS AND DISCUSSIONS CONCLUSIONS
  • 3.  It is well known fact that distribution systems can operate under unbalanced loading conditions.  So, the distribution system planner have to consider these load unbalances for better planning and oper ation of the system.  It is observed from the literature survey that, many authors have done optimal placement of capacitors without consideration of load unbalances.  The prime purpose of this paper is to maintain accep table voltages at all buses along the distribution feed er under all loading conditions and load unbalances by optimal placement of capacitors.  In this paper we consider the impact of two types of load unbalances and different loading conditions on optimal capacitor sizes and locations.
  • 4. The main objective of this paper:  Finding optimal sizes and locations of capacitors in Unbalanced Distribution Systems (ubds) using Index Vector Approach.  Impact of different loading conditions (low, medium and high loading) on optimal placement of capacitors in ubds is analyzed.  Impact of type-A and type-B unbalances on voltage profile, voltage unbalance, total power losses and cost of energy losses in ubds is evaluated.  Impact of type-A and type-B unbalances on optimal capacitor allocation problem is addressed. The results are obtained on 25-bus unbalanced radial distribution system.
  • 5. Three phase three wire radial distribution circuit.
  • 6.  In this article Index Vector is used to find out optimal locations and sizes of capacitors in unbalanced distribution systems.  Index Vector is formulated by running the base case load flow on a given distribution network.  Index Vector directly gives the optimal locations and estimated capacitor sizes.  Index Vector, identifies the sequence of nodes to be compensated. The buses with high Index Vector value are the potential locations for capacitor placement.
  • 7. Cost of Energy Losses (CL): (Total Real power Loss)*(Ec*8760) $ Ec: energy rate ($/kWh) =0.06 $/kWh Cost of capacitor for reactive power support
  • 8.  The load demand at the distribution substation is fluctuating with respect to time.  Distribution feeders are lightly loaded at the mid night and early in the morning and are heavily loaded during the office hours.  Higher load demand also results into lower voltage magnitudes and higher power losses.  Similarly, light load demand also results into high voltage magnitudes and low power losses.
  • 9. In this paper we have consider three different loading conditions i.e. light, medium and high. The total system load is 50%, 100% and 130% of total load for light load, medium and high load operation. By injecting required amount of shunt reactive power, voltage profile can be improved and thereby the power losses will reduce. It means the reactive power supplied by capacitors is proportional to loading conditions.
  • 10. A-ph B-ph C-ph 14 12 Index vector 10 8 6 4 2 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 25 Bus Number Index Vector profile for 25 bus system at light load
  • 11. Va without Capacitor Vb without Capacitor Vc without Capacitor Va with Capacitor Vb with Capacitor Vc with Capacitor 1.01 1 Voltage (p.u) 0.99 0.98 0.97 0.96 0.95 0.94 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 Bus Number Voltage profile for 25 bus system at light load
  • 12. Bus No. 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 Total (kVAr) Qa 0 0 0 0 27.66 0 0 0 41.85 23.23 0 32.6 23.26 0 95.41 0 0 0 41.89 0 0 32.4 0 0 41.96 360.26 Qb 0 0 0 0 27.66 0 0 0 41.85 23.23 0 32.6 23.26 0 95.41 0 0 0 41.89 0 0 32.4 0 0 41.96 360.26 Qc 0 0 0 0 27.66 0 0 0 41.85 23.23 0 32.6 23.26 0 95.41 0 0 0 41.89 0 0 32.4 0 0 41.96 360.26
  • 13. Without capacitor A-phase TPL (kW) TQL (kVAr) Vmin (p.u) B-phase C-phase Total A-phase B-phase C-phase Total 12.39318 13.06759 9.906581 35.367 8.013701 8.428882 6.392486 22.835 13.69854 39.491 8.824555 8.061579 8.512255 25.398 12.5513 13.24069 0.965432 0.965328 0.969208 0.98073 0.979209 0.983683 (%) 2.513073 2.46686 2.161777 1.401089 1.467985 1.119791 Qc (kVAr) ---- ---- ---- Voltage unbalance 360.26 360.26 Cost of energy loss 18589.08 12002.11 capacitor ($) ---- 4242.34 Total cost ($) 18589.08 16244.45228 Savings ($) ---- 2344.6 ($) Cost of 360.26
  • 14. C-ph 12 Va with Capacitor Vc with Capacitor 1.02 10 1 8 Voltage (p.u) Index Vector Vb without Capacitor Vb with Capacitor B-ph Va without Capacitor Vc without Capacitor A-ph 6 4 0.98 0.96 0.94 0.92 2 0.9 0.88 0 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Index Vector profile for 25 bus system at medium load 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Voltage profile for 25 bus system at medium load
  • 15. Bus No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Total (kVAr) Qa 0 0 0 0 0 0 0 0 87.502 48.734 0 68.539 48.905 0 199.54 0 0 0 86.595 0 0 67.097 0 0 86.898 693.81 Qb 0 0 0 0 0 0 0 0 87.502 48.734 0 68.539 48.905 0 199.54 0 0 0 86.595 0 0 67.097 0 0 86.898 693.81 Qc 0 0 0 0 0 0 0 0 87.502 48.734 0 68.539 48.905 0 199.54 0 0 0 86.595 0 0 67.097 0 0 86.898 693.81
  • 16. Without capacitor With capacitor A-phase B-phase C-phase Total A-phase B-phase C-phase Total 52.81328 55.4431 41.86151 150.12 33.66803 35.31495 26.58381 95.567 TQL (kVAr) 58.29014 53.29408 55.69108 167.28 37.02202 33.85069 35.33719 106.21 Vmin (p.u) 0.928412 0.928396 0.936595 0.96067 0.957692 5.334261 5.215524 4.544444 2.975958 3.097951 693.81 693.81 TPL (kW) 0.966898 Voltage unbalance (%) Qc (kVAr) Cost of 78901.97 energy loss ($) 50229.9 Cost of capacitor ($) Total cost 7244.29 78901.97 57474.19459 ($) Savings ($) 21427.7754 2.366941 693.81
  • 17. A-ph B-ph C-ph Va without Capacitor Vc without Capacitor 12 Vb without Capacitor Va with Capacitor Vb with Capacitor 1.02 10 Vc with Capacitor 8 0.98 Voltage (p.u) Index Vector 1 6 4 0.96 0.94 0.92 0.9 0.88 2 0.86 0 0.84 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Index Vector profile for 25 bus system at high load 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Voltage profile for 25 bus system at high load
  • 18. Bus No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Qa 0 0 0 0 0 0 0 0 117.15 65.4 0 92.11 65.72 0 267.2 0 0 0 0 0 0 0 0 0 115.53 Qb 0 0 0 0 0 0 0 0 117.15 65.4 0 92.11 65.72 0 267.2 0 0 0 0 0 0 0 0 0 115.53 Qc 0 0 0 0 0 0 0 0 117.15 65.4 0 92.11 65.72 0 267.2 0 0 0 0 0 0 0 0 0 115.53
  • 19. Without capacitor With capacitor A-phase B-phase C-phase Total A-phase B-phase C-phase Total 93.0239 97.35278 73.28935 263.67 62.20085 65.02331 48.8517 176.08 102.5659 93.62979 97.2082 293.4 68.45781 62.53135 64.90851 195.9 0.904789 0.904949 0.916012 0.945143 0.941683 0.953737 7.208388 7.028391 6.099434 4.496543 4.595769 3.624808 755.66 755.66 755.66 TPL (kW) TQL (kVAr) Vmin (p.u) Voltage unbalance (%) Qc (kVAr) Cost of energy loss 138582.9 92545.47 ($) Cost of capacitor ($) Total cost ($) Savings ($) 7507.99 138582.9 100053.4608 38529
  • 20. Type A Unbalance Type b Unbalance where lub is the load unbalance factor which determines unbalance in the loads at all nodes in the study system. lub = 0.0 represents the balanced system base case study. In this paper work lub is taken as 5, 10, 15 and 20%.
  • 21.  The total network load remains constant under type A unbalance scenario.  The total network load reduces under type B unbalance scenario.  The load unbalances in the system directly impacts the total power losses and voltage profile.  The main objective of this study to determine required amount of capacitive reactive power needed in the presence of different unbalance scenarios to improve system performance.
  • 22. Without capacitor considering unbalance of type-A for 25 bus system Phase Unbalance 0% 5% 10 % 15 % 20 % A 52.81328 51.53396 50.25238 48.96833 47.68162 B 55.4431 50.70412 46.20817 41.94849 37.91851 C 41.86151 48.23329 55.07561 62.39956 70.21673 Total 150.11789 150.47136 151.53616 153.31637 155.81686 A 58.29014 58.48702 58.67479 58.85355 59.02338 B 53.29408 46.22705 39.66439 33.59785 28.01959 C 55.69108 63.31257 71.48492 80.22349 89.5443 Total 167.27529 168.02664 169.82410 172.67489 176.58727 A 0.928412 0.929145 0.929886 0.930633 0.931388 B 0.928396 0.932337 0.936244 0.94012 0.943964 C 0.936595 0.931385 0.926135 0.920844 0.91551 A 5.334261 5.271712 5.208695 5.145201 5.081221 B 5.215524 4.9143 4.617142 4.323945 4.034603 C 4.544444 4.953752 5.369119 5.790749 6.218856 Cost of energy loss ($) 78901.97 79087.75 79647.41 80583.09 81897.34 Total cost ($) 78901.97 79087.75 79647.41 80583.09 81897.34 TPL (kW) TQL (kVAr) Min Voltage (p.u) Un balance (%)
  • 23. Phase 0% 5% 10 % 15 % 20 % A 33.66803 33.46699 32.73168 31.84653 30.70615 B 35.31495 34.2367 30.55031 28.20139 27.5183 C 26.58381 29.11303 33.51727 37.30539 41.23329 Total 95.56678 96.8167 96.79925 97.35331 99.45773 A 37.02202 36.11431 36.70106 36.53679 35.97869 B 33.85069 32.42506 27.39659 23.82588 21.91705 C 35.33719 41.14802 45.10282 50.35751 56.63392 Total 106.20989 109.68739 109.20047 110.72017 114.52965 A 0.96067 0.961326 0.962004 0.96303 0.964316 B 0.957692 0.955607 0.959332 0.959304 0.956215 C 0.966898 0.967949 0.963476 0.960642 0.958713 A 2.975958 2.944228 2.88706 2.811096 2.709989 B 3.097951 3.177551 2.916197 2.91857 3.122641 C 2.366941 1.913179 2.279138 2.433346 2.578057 A 693.81 693.653 693.127 693.304 693.127 B 693.81 642.18 641.689 575.07 459.043 C 693.81 953.323 952.743 1009.236 1065.603 Total 2081.43 2289.156 2287.559 2277.61 2217.773 Cost of energy loss ($) 50229.9 50886.86 50877.69 51168.9 52274.99 Cost of capacitor ($) 7244.29 7867.468 7865.89 7832.83 7653.319 Total cost ($) 57474.19459 58754.33008 58743.57928 59001.73113 59928.30411 Savings ($) 21427.77541 20333.41992 20903.83072 21581.35887 21969.03589 TPL (kW) TQL (kVAr) Min Voltage (p.u) Un balance (%) Qc (kVAr)
  • 24. Type A-Un balance (%) A-ph 0 0 0 0 0 0 0 0 87.48 48.712 0 5 B-ph 0 0 0 0 0 0 0 0 0 0 0 A-ph 0 0 0 0 0 0 0 0 87.458 48.691 0 10 B-ph 0 0 0 0 0 0 57.314 0 0 0 0 A-ph 0 0 0 0 0 0 0 0 87.436 48.668 0 15 B-ph 0 0 0 0 0 0 0 0 0 0 0 C-ph 0 0 46.793 75.387 57.054 0 0 57.054 87.48 48.712 61.829 68.515 68.515 48.886 0 A-ph 0 0 0 0 0 0 0 0 87.412 48.646 0 20 B-ph 0 0 0 0 0 0 0 0 0 0 0 C-ph 0 0 46.79 75.386 57.047 0 0 57.046 87.458 48.691 61.809 C-ph 0 0 46.786 75.383 57.04 0 0 57.037 87.436 48.668 61.787 C-ph 0 0 46.782 75.381 57.032 56.564 0 57.028 87.412 48.646 61.766 68.515 68.491 68.491 68.491 68.466 68.466 68.466 68.44 68.44 68.44 48.886 66.816 48.886 66.816 48.867 0 48.867 66.8 48.867 66.8 48.847 0 48.847 0 48.847 66.784 48.827 0 0 0 48.827 66.767 199.5 0 0 0 86.59 0 0 199.5 0 57.328 0 0 0 0 0 0 57.328 56.83 86.59 0 0 199.44 0 0 0 86.585 0 0 199.44 0 0 0 0 0 0 0 0 57.314 56.829 86.585 0 0 199.39 0 0 0 86.579 0 0 199.39 0 57.3 0 0 0 0 0 0 57.3 56.829 86.579 0 56.307 199.34 0 0 0 86.572 0 0 199.34 0 57.285 0 0 0 0 0 0 57.285 56.827 86.572 0 56.296 67.086 0 67.086 0 0 0 67.076 0 67.076 0 0 0 67.064 0 67.064 0 0 0 67.052 0 0 0 0 0 0 47.165 47.165 0 47.157 47.157 0 47.149 47.149 0 47.14 47.14 86.884 86.884 86.884 86.869 86.869 86.869 86.854 86.854 86.838 86.838 86.838 86.838
  • 25. Va without Capacitor Vb without Capacitor Vc without Capacitor Va with Capacitor Va without Capacitor Vc without Capacitor Va with Capacitor Vb with Capacitor Vb with Capacitor Vb without Capacitor Vc with Capacitor Vc with Capacitor 1.02 1.02 1 0.98 Voltage (p.u) Voltage (p.u) 1 0.96 0.94 0.98 0.96 0.94 0.92 0.92 0.9 0.9 0.88 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Voltage profile for 25 bus system with Type-A unbalance case-1 0.88 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Voltage profile for 25 bus system with Type-A unbalance case-2
  • 26. Va without Capacitor Vb without Capacitor Va without Capacitor Vb without Capacitor Vc without Capacitor Va with Capacitor Vc without Capacitor Va with Capacitor Vb with Capacitor Vc with Capacitor Vb with Capacitor Vc with Capacitor 1.02 1.02 1 0.98 0.98 Voltage (p.u) Voltage (p.u) 1 0.96 0.94 0.96 0.94 0.92 0.92 0.9 0.9 0.88 0.88 0.86 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Number Voltage profile for 25 bus system with Type-A unbalance case-3 Voltage profile for 25 bus system with Type-A unbalance case-4
  • 27. Unbalance 0% 5% 10% 15% 20% Unbalance 0% 160 10% 15% 20% 0.98 0.97 140 0.96 120 0.95 100 0.94 80 60 40 20 0 Vmin (p.u) Total Real Power Loss (kW) 180 5% 0.93 0.92 0.91 0.9 0.89 0.88 Total Real Power Loss with and without Capacitor considering Unbalances Minimum Voltage with and without Capacitor considering Unbalances
  • 28. Without capacitor considering unbalance of type-B for 25 bus system Phase Unbalance 0% A 52.81328 55.4431 53.3283 48.09286 53.83323 41.29643 54.32848 35.03965 54.81446 29.30897 41.86151 33.42204 26.02881 19.63945 14.21441 150.11789 134.84320 121.15846 109.00757 98.33783 A B 58.29014 53.29408 59.29373 48.02609 60.29409 43.05916 61.29132 38.38843 62.28552 34.00912 C 55.69108 43.52779 32.96989 23.95894 16.44025 Total A 167.27529 0.928412 150.84760 136.32313 123.63868 112.73488 B 0.928396 0.927592 0.933194 0.926783 0.937955 0.925983 0.942679 0.925192 0.947367 C 0.936595 0.943955 0.951205 0.95835 0.965394 A 5.334261 5.215524 5.47427 4.472285 5.543272 B 5.404609 4.841294 5.611641 3.74938 C Un balance (%) 20 % Total Min Voltage (p.u) 15 % C TQL (kVAr) 10 % B TPL (kW) 5% 4.544444 3.990296 Total cost ($) 78901.97 78901.97 2.406159 70873.59 Cost of energy loss ($) 3.449616 4.108359 2.921767 63680.89 57294.38 51686.37 70873.59 63680.89 57294.38 51686.37
  • 29. Unbalance Phase TPL (kW) TQL (kVAr) Min Voltage (p.u) Un balance (%) Qc (kVAr) Total Cost of energy loss ($) Cost of capacitor ($) Total cost ($) Savings ($) A B C Total A B C Total A B C A B C A B C 0% 33.66803 35.31495 26.58381 95.56678 37.02202 33.85069 35.33719 106.20989 0.96067 0.957692 0.966898 2.975958 3.097951 2.366941 693.81 693.81 693.81 2081.43 5% 33.87315 30.95504 25.22272 90.05091 37.95326 31.0514 30.65602 99.66067 0.961206 0.959875 0.960363 2.981026 2.889593 2.319529 694.647 643.109 625.647 1963.403 10 % 34.24613 26.33051 19.54578 80.12242 38.9732 27.54172 22.5021 89.01703 0.960645 0.964899 0.964338 3.01902 2.482542 2.177754 695.471 643.881 513.091 1852.443 15 % 34.25481 23.79063 13.79437 71.83980 38.45706 25.4146 17.12555 80.99721 0.960886 0.961139 0.97167 3.018978 2.611763 1.616577 696.292 528.46 513.646 1738.398 20 % 34.25354 18.9619 13.35143 66.56687 40.24009 20.98355 13.34035 74.56399 0.961072 0.967898 0.966326 3.024577 2.129901 1.969987 697.11 529.076 288.776 1514.962 50229.9 47330.76 42112.35 37759 34987.55 7244.29 57474.19459 21427.77541 6890.209 54220.97136 16652.61864 6557.329 48669.67662 15011.21338 6215.194 43974.19514 13320.18486 5544.886 40532.43394 11153.93606
  • 30. Type B- Un balance (%) A 0 0 0 0 0 0 0 0 5 B 0 0 0 0 0 0 0 0 C 0 0 46.838 0 57.116 0 0 57.118 A 0 0 0 0 0 0 0 0 10 B 0 0 0 0 0 0 0 0 C 0 0 46.88 0 57.171 0 0 57.175 A 0 0 0 0 0 0 0 0 15 B 0 0 0 0 0 0 0 0 C 0 0 46.922 0 57.226 0 0 57.231 A 0 0 0 0 0 0 0 0 20 B 0 0 0 0 0 0 0 0 C 0 0 0 0 57.28 0 0 57.286 87.612 0 0 87.722 0 0 87.831 0 0 87.939 0 0 48.795 0 0 0 0 61.935 48.856 0 0 0 0 62.019 48.916 0 0 0 0 62.103 48.976 0 0 0 0 0 68.632 68.632 68.632 68.724 68.724 68.724 68.816 68.816 68.816 68.907 68.907 0 48.97 0 48.97 66.918 0 0 49.035 0 49.035 67.005 0 0 49.1 0 0 0 0 0 49.164 0 0 0 0 0 199.8 0 0 0 199.8 0 57.417 0 0 0 0 0 200.05 0 0 0 200.05 0 57.492 0 0 0 0 0 200.3 0 0 0 200.3 0 57.566 0 0 0 0 0 200.55 0 0 0 200.55 0 57.64 0 0 0 0 0 86.687 0 0 0 0 0 199.8 0 0 86.778 0 0 0 0 0 86.778 0 0 86.868 0 0 0 0 0 86.868 0 0 86.959 0 0 0 0 0 86.959 0 0 67.164 0 67.164 0 0 0 67.231 0 67.231 0 0 0 67.298 0 67.298 0 0 0 67.364 0 67.364 0 0 0 0 47.221 47.221 0 47.269 47.269 0 47.317 47.317 0 47.364 0 86.987 86.987 86.987 87.075 87.075 87.075 87.163 87.163 87.163 87.251 87.251 87.251 694.647 643.109 625.647 695.471 643.881 513.091 696.292 528.46 513.646 697.11 529.076 288.776
  • 31. Type-A Type-B 25000 Savings ($) 20000 15000 10000 5000 0 0% 5% 10% Load Unbalance (%) 15% 20%
  • 32. Un balance (%) Type-A 0 5 10 15 20 Un-balance (%) Type-B 0 5 10 15 20 Powers taken from the substation (kVA) Without capacitor With capacitor 3390 +2560.3i 3335.5+417.78i 3390.3+2561i 3336.7+213.48i 3391.5+2562.7i 3336.7+214.54i 3393.3+2565.5i 3337.3+225.96i 3395.8+2569.3i 3339.4+289.56i Power taken from the substation (kVA) Without capacitor 3390+2560.3i 3212.2+2423.8i 3036.1+2289.2i 2861.4+2156.5i 2688.2+2025.5i With capacitor 3335.5+417.78i 3167.5+409.21i 2995+389.47i 2824.3+315.45i 2656.5+472.4i
  • 33. It is observed that 1. The real and reactive power losses are decreasing in phase-B and increasing in phase-C with percentage of type-A unbalance. 2. Voltage magnitudes are decreases with increasing of percentage of type-A unbalance. 3. Voltage unbalance and cost of energy losses are also increasing with increasing of type-A unbalance. 4. Increase in percentage of type-A unbalance results into decrement of required capacitive reactive power in B-phase and increment in Cphase. 5. It is also observed that savings are slightly increasing with increase of load unbalance.
  • 34. It is observed that 1. The real and reactive power losses are decreasing in phase-B and phase-C with percentage of type-B unbalance. 2. Voltage magnitudes are increases with increase of percentage of type-B unbalance. 3. Voltage unbalance and cost of energy losses are also decreasing with increasing of type-B unbalance. 4. Increase in percentage of type-B unbalance results into decrement of capacitive reactive power in B-phase and C-phase. 5. It is also observed that savings are decreasing with increasing of unbalance.
  • 35. The total power losses, voltage unbalance, shunt capacitive requirement and cost of energy losses are varying with loading. The total power losses are increasing with percenta ge of type-A unbalance. Voltage unbalance in phase -B decreasing and in phase-C increasing. Shunt cap acitive reactive power requirement in phase-B is low er than phase-C. Total shunt capacitive reactive power supplied under type-A unbalance is more than type-B unbala nce. Total power losses under type-A unbalance are more than type-B unbalance. Voltage unbalance under type-A unbalance are more than type-B unbalance. Annual cost savings obtained in Type-A unbalance are higher than Type-B unbalance.
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