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40220140504001

  1. 1. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 1 STATUS OF ALL BRANCHES OF DISTRIBUTION NETWORKS IN CHRONOLOGICAL ORDER FOR COMPOSITE LOADS USING DISTRIBUTED GENERATION D Banerjee, S K Saha, S Banerjee Electrical Engineering Department, Dr. B. C. Roy Engineering College, Durgapur, India ABSTRACT This paper presents status of all branches of radial distribution networks in chronological order for loads of composite type using distributed generation at optimal position by considering the concept of reactive loading index technique. Although under different situations for all the branches the identified weakest branch remains same up to some specified conditions but the corresponding loading at different branches in chronological order has been categorically identified. The effectiveness of the proposed idea has been successfully tested on 12.66 kV radial distribution systems consisting of 33 nodes and the results are found to be in very good agreement. Keywords: Active Power Loss; Composite Load; Distributed Generation; Reactive Loading Index; Radial Distribution Networks; Weakest Branch. I. INTRODUCTION VOLTAGE stability [1] is one of the important factors that may be explained as the ability of a power system to maintain voltage at all the nodes of the system so that with the increase of load, load power will increase and both the power and voltage are controllable. The problem of voltage stability [1] has been defined as inability of the power system to provide the reactive power [2] or non- uniform consumption of reactive power by the system itself. Therefore, voltage stability is a major concern in planning and assessment of security of large power systems in contingency situation, specially in developing countries because of non-uniform growth of load demand and lacuna in the reactive power management side [3]. The loads generally play a key role in voltage stability analysis and therefore the voltage stability is known as load stability. Literature survey shows that a major work has been done on the voltage stability analysis of transmission systems, but so far the researchers have paid very little attention on the voltage stability analysis for a radial distribution network [4-10] in power system. Radial distribution systems having a low reactance to resistance ratio, which causes a high power loss whereas the transmission system having a high reactance to resistance ratio. So, the INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY (IJEET) ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME: www.iaeme.com/ijeet.asp Journal Impact Factor (2014): 6.8310 (Calculated by GISI) www.jifactor.com IJEET © I A E M E
  2. 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 2 conventional load flow methods like Newton Raphson and fast decoupled method cannot be effectively used for the load flow analysis of radial distribution systems. The current article has been developed a novel and simple theory [11-12] to identify the weakest branch of a radial distribution system for loads of composite type. The effectiveness of the proposed idea is then tested on 33 node radial distribution system. II. METHODOLOGY We consider a simple 2-node system as shown in Fig. 1. Fig 1: A simple 2-node system Here a load having an impedance of φ∠= LL ZZ r is connected to a source having an impedance of α∠= SS ZZ r . If line shunt admittances are neglected, the current flowing through the line equals the load current; From Figure 1, * L LL S LS V jQP Z VV rr rr − = − (1) Using simple calculation, we can write load reactive power LQ as ( ) αδαδ sinsin 2 S L SL S LS L Z V Z VV Q −−+= (2) The load voltage LV can be varied by changing the load reactive power LQ . The load reactive power LQ becomes maximum when the following condition is satisfied. 0= L L dV dQ (3) Now, from (2) and (3) ( ) 0sinsin2 =−+− SL S L V V δαδα (4) LLL VV δ∠= α∠= SS ZZ φ∠= LL ZZ SI LI SSS VV δ∠=
  3. 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 3 Now, at no load, L SV V= and L Sδ δ= . Therefore at no load, the left hand side (LHS) of (4) will besinα . However, at the maximum reactive power LQ , the equality sign of (4) hold and thus the LHS of (4) becomes zero. Hence the LHS of (4) is considered as a reactive loading index, qL of the system that varies between sinα (at no load) and zero (at maximum reactive power). Thus, ( )SL S L q V V L δαδα −+−= sinsin2 (5) Here, 0sin ≥≥ qLα (6) In radial distribution system the power flow problem can be solved by distflow technique. The active and reactive power flow through the branch near bus i is ( )iP and ( )iQ respectively and the active and reactive power flow through the branch near bus (i+1) is ( )1+iP and ( )1+iQ respectively. Hence we can write ( ) ( ) ( ) ( ) ( ) ( )iR iV iQiP iPiP 1 11 1 2 22 + +++ ++= (7) ( ) ( ) ( ) ( ) ( ) ( )iX iV iQiP iQiQ 1 11 1 2 22 + +++ ++= (8) Here, ( ) ( ))11( +++ ijQiP is the sum of complex load at bus (i+1) and all the complex power flow through the downstream branches of bus (i+1). Now, the voltage magnitude at bus (i+1) is given by ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )iV iXiRiQiP iXiQiRiPiViV 2 2222 22 ))(( )(21 ++ ++−=+ (9) The power flow solution of a radial distribution feeder involves recursive use of (7) to (9) in reverse and forward direction. Now beginning at the last branch and finishing at the first branch of the feeder, we determine the complex power flow through each branch of the feeder in the reverse direction using (7) to (9). Then we determine the voltage magnitude of all the buses in forward direction using (9). III. LOAD MODELING For the purpose of loading status of all branches of radial distribution networks, composite load modeling is considered. The real and reactive power loads of node ‘i’ is given as:
  4. 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 4 ( ) ( ) ( ) ( )( )2 3210 iVciVcciPLiPL ++= (10) ( ) ( ) ( ) ( )( )2 3210 iVdiVddiQLiQL ++= (11) Here ( ),, 11 dc ( ),, 22 dc and ( )33 , dc are the compositions of constant power (CP), constant current (CI) and constant impedance (CZ) loads respectively. Now, for constant power load ,111 == dc ,03322 ==== dcdc for constant current load ,122 == dc ,03311 ==== dcdc and for constant impedance load ,133 == dc 02211 ==== dcdc . Here, for composite load, a composition of 40% of constant power ( ),4.011 == dc 30% of constant current ( )3.022 == dc and 30% of constant impedance ( )3.033 == dc loads are also considered. IV. RESULTS AND DISCUSSIONS With the help of MATLAB programme, the effectiveness of the proposed idea is tested on 12.66 KV radial distribution systems consisting of 33-nodes for composite types of loads. The single line diagram of the 33-node system is shown in Fig. 2 and its data is given in appendix (Table III). Fig. 2: Single line diagram of a main feeder The reactive loading index of all branches of the 33-node system is evaluated using equation (5). Then the reactive loading index of all branches of the system is shown in Fig.3 (normal loading condition only) and the investigation reveals that the value of the reactive loading index qL to be minimum in the branch 5 (connected between buses 5 and 6). Thus branch 5 can be considered as the weakest branch of the system. In nominal loading condition, the active power loss is 179.8 kW and reactive loss is 119.3 kVAr. Under this condition, the minimum system voltage is 0.9186 pu at node 18. 1 3 75 942 6 8 13121110 1514 1716 25 21 20 19 24 23 322827 29 31 3330 26
  5. 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 5 From Fig. 3, a chart has been prepared as depicted below. From the chart we observe that the values of the reactive loading index of different branches are always in ascending order as listed below. B5-B2-B27-B28-B3-B4-B23-B8-B12-B9-B7-B30-B19-B22-B29-B6-B24-B1-B26-B13-B16-B25- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. Now we insert unity power factor DG in the existing 33-node system. DG is considered as an active power source and hence DG is considered as negative load. The maximum size of the DG is assumed to be total load demand of the system. For this test case, DG capacity is assumed to be 3.715 MW. With the help of optimization technique it is seen that the power loss will be minimum if 2600.5 kW unity power factor DG is placed at node 6. In this case, the active power loss is 98.0 kW. With the help of optimization technique it is also seen that that the power loss will be 98.6 kW, if 2229.0 kW unity power factor DG is placed at node 7. Fig. 3: Reactive loading index of all branches of the 33-node system under nominal loading conditions for composite load Now, DG is placed at node 6 and capacity of DG is varied from 10% to 100% in step of 10% of total DG capacity. Now, the reactive loading index of all branches of the modified 33-node system is evaluated using equation (5) at every step. A chart has been prepared as depicted below under head ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘I’, and ‘J’. From the chart we observe that the values of the reactive loading index of different branches are always in ascending order as listed below. This ascending order pattern is changing for different capacities of DG at node 6. The investigation reveals that the value of the reactive loading index )( qL is minimum in branch 5 and B5 can be considered as the weakest branch of the system up to 30% DG capacity at node 6. From 40% to 100% DG capacity, B27 can be considered as the weakest branch of the system. 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Branch number Reactiveloadingindex
  6. 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 6 A. 10% DG capacity B5-B2-B27-B28-B23-B3-B4-B8-B12-B9-B7-B30-B19-B22-B29-B6-B24-B1-B26-B13-B16-B25- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. B. 20% DG capacity B5-B2-B27-B28-B23-B8-B12-B9-B3-B4-B7-B30-B19-B22-B29-B6-B24-B26-B1-B13-B16-B25- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. C. 30% DG capacity B5-B27-B2-B28-B23-B8-B12-B9-B7-B3-B4-B30-B19-B22-B29-B6-B24-B26-B13-B1-B16-B25- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. D. 40% DG capacity B27-B5-B2-B28-B23-B8-B12-B9-B7-B30-B3-B19-B22-B29-B4-B6-B24-B26-B13-B1-B16-B25- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. E. 50% DG capacity B27-B28-B5-B2-B23-B8-B12-B9-B7-B30-B19-B22-B29-B6-B24-B3-B4-B26-B13-B16-B25-B1- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. F. 60% DG capacity B27-B28-B23-B2-B8-B12-B5-B9-B7-B30-B19-B22-B29-B6-B24-B26-B13-B16-B3-B25-B4-B1- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. G. 70% DG capacity B27-B28-B23-B8-B12-B9-B2-B7-B30-B5-B19-B22-B29-B6-B24-B26-B13-B16-B25-B11-B1-B14- B15-B3-B31-B10-B4-B20-B21-B17-B18-B32. H. 80% DG capacity B27-B28-B23-B8-B12-B9-B7-B2-B30-B19-B22-B29-B24-B6-B26-B13-B16-B5-B25-B11-B14- B15-B1-B31-B10-B20-B21-B17-B18-B32-B3-B4. I. 90% DG capacity B27-B28-B23-B8-B12-B9-B7-B30-B19-B22-B29-B24-B6-B2-B26-B13-B16-B25-B11-B14-B15- B1-B31-B10-B20-B21-B17-B18-B32-B5-B3-B4. J. 100% Load B27-B28-B23-B8-B12-B9-B7-B30-B19-B22-B29-B24-B6-B26-B13-B2-B16-B25-B11-B14-B15- B31-B10-B1-B20-B21-B17-B18-B32-B3-B5-B4.
  7. 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 7 Table I: Active power loss, reactive power loss and minimum system voltage after inserting DG at node 6 DG capacity (%) Ploss kW Qloss kVAr Minimum Voltage (pu) Node number 10 156.7 105.0 0.9237 18 20 137.4 93.2 0.9288 18 30 122.0 83.8 0.9338 18 40 110.3 76.9 0.9388 18 50 102.5 72.3 0.9438 18 60 98.3 70.2 0.9488 18 70 98.0 70.4 0.9537 18 80 101.3 73.0 0.9587 18 90 108.4 78.0 0.9636 18 100 119.2 85.4 0.9685 18 Table I shows the active power loss, reactive power loss and minimum system voltage after inserting unity power factor DG at node 6 and capacity of DG is varied from 10% to 100% in step of 10% of total DG capacity. From Table I, we observe that the active power loss loss will decrease, up to 70% DG capacity is inserted at node 6 and after that the active power losses will increase. We also observe that the reactive power loss loss will decrease, up to 60% DG capacity is inserted at node 6 and after that the reactive power losses will increase. But minimum system voltage will increase up to maximum size of DG. Similarly, DG is placed at node 7 and capacity of DG is varied from 10% to 100% in step of 10% of total DG capacity. Now, the reactive loading index of all branches of the modified 33-node system is evaluated using equation (5) at every step. A chart has been prepared as depicted below under head ‘K’, ‘L’, ‘M’, ‘N’, ‘O’, ‘P’, ‘Q’, ‘R’, ‘S’, and ‘T’. From the chart we observe that the values of the reactive loading index of different branches are always in ascending order as listed below. This ascending order pattern is changing for different capacities of DG at node 7. The investigation reveals that the value of the reactive loading index )( qL is minimum in branch 5 and B5 can be considered as the weakest branch of the system up to 30% DG capacity at node 7. From 40% to 100% DG capacity, B27 can be considered as the weakest branch of the system. K. 10% DG capacity B5-B2-B27-B28-B23-B3-B4-B8-B12-B9-B7-B30-B19-B22-B29-B24-B6-B1-B26-B13-B16-B25- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. L. 20% DG capacity B5-B2-B27-B28-B23-B8-B12-B9-B3-B4-B7-B30-B19-B22-B29-B24-B26-B6-B1-B13-B16-B25- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. M. 30% DG capacity B5-B27-B2-B28-B23-B8-B12-B9-B7-B3-B4-B30-B19-B22-B29-B24-B26-B13-B1-B6-B16-B25- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32.
  8. 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 8 N. 40% DG capacity B27-B5-B2-B28-B23-B8-B12-B9-B7-B30-B3-B19-B22-B29-B4-B24-B26-B13-B1-B16-B25-B6- B11-B14-B15-B31-B10-B20-B21-B17-B18-B32. O. 50% DG capacity B27-B28-B5-B2-B23-B8-B12-B9-B7-B30-B19-B22-B29-B24-B3-B4-B26-B13-B16-B25-B1-B11- B14-B15-B6-B31-B10-B20-B21-B17-B18-B32. P. 60% DG capacity B27-B28-B2-B23-B8-B12-B5-B9-B7-B30-B19-B22-B29-B24-B26-B13-B16-B3-B25-B4-B1-B11- B14-B15-B31-B10-B20-B6-B21-B17-B18-B32. Q. 70% DG capacity B27-B28-B23-B8-B12-B9-B2-B7-B30-B5-B19-B22-B29-B24-B26-B13-B16-B25-B11-B1-B14- B15-B3-B31-B10-B4-B20-B21-B17-B18-B32-B6. R. 80% DG capacity B27-B28-B23-B8-B12-B9-B7-B2-B30-B19-B22-B29-B24-B26-B13-B5-B16-B25-B11-B14-B15- B1-B31-B10-B20-B21-B17-B18-B3-B32-B4-B6. S. 90% DG capacity B27-B28-B23-B8-B12-B9-B7-B30-B19-B22-B29-B24-B2-B26-B13-B16-B25-B11-B14-B15-B1- B31-B10-B20-B21-B17-B18-B32-B5-B3-B6-B4. T. 100% Load B27-B28-B23-B8-B12-B9-B7-B30-B19-B22-B29-B24-B26-B2-B13-B16-B25-B11-B14-B15-B31- B10-B1-B20-B21-B17-B18-B32-B6-B3-B5-B4. Table II: Active power loss, reactive power loss and minimum system voltage after inserting DG at node 7 DG capacity (%) Ploss kW Qloss kVAr Minimum Voltage (pu) Node number 10 155.8 102.4 0.9242 18 20 136.1 89.1 0.9297 18 30 120.5 79.2 0.9351 18 40 109.1 72.9 0.9405 18 50 101.8 70.2 0.9459 18 60 98.6 70.9 0.9513 18 70 99.6 75.1 0.9567 18 80 104.6 82.7 0.9617 33 90 113.7 93.8 0.9666 33 100 126.8 108.4 0.9714 33
  9. 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 9 Table II shows the active power loss, reactive power loss and minimum system voltage after inserting unity power factor DG at node 7 and capacity of DG is varied from 10% to 100% in step of 10% of total DG capacity. From Table II, we observe that the active power loss loss will decrease, up to 60% DG capacity is inserted at node 6 and after that the active power losses will increase. We also observe that the reactive power loss loss will decrease, up to 50% DG capacity is inserted at node 7 and after that the reactive power losses will increase. But minimum system voltage will increase up to maximum size of DG. V. CONCLUSIONS From the above discussion, it is observed that branch 5 has shown the lowest value which is the weakest branch (under nominal loading condition as well as up to 30% DG capacity), although the value of other branches exceeds the value of the weakest branch for different loadings at all node points. From 40% DG capacity at node 6, it is observed that branch 27 has shown the lowest value which is the weakest branch. In this paper the loading status of all branches of radial distribution systems for composite load are arranged in chronological order using reactive loading index. The effectiveness of the proposed idea has been successfully tested on 12.66 kV radial distribution systems consisting of 33 nodes and the results are found to be in very good agreement. REFERENCES [1] H. K. Clark, “New challenges: Voltage stability” IEEE Power Engg Rev, April 1990, pp. 33-37. [2] T. Van Cutsem: “A method to compute reactive power margins with respect to voltage collapse”, IEEE Trans. on Power Systems, No. 1, 1991. [3] R. Ranjan, B. Venkatesh, D. Das, “Voltage stability analysis of radial distribution networks”, Electric Power Components and Systems,Vol. 31, pp. 501-511, 2003. [4] M. Chakravorty, D. Das, “Voltage stability analysis of radial distribution networks”, Electric Power and Energy Systems,Vol. 23, pp. 129-135, 2001. [5] Das, D., Nagi, H. S., and Kothari, D. P., “Novel method for solving radial distribution networks”, IEE Proc. C, 1994, (4), pp. 291-298. [6] J.F. Chen, W. M. Wang, “Steady state stability criteria and uniqueness of load flow solutions for radial distribution systems”, Electric Power and Energy Systems,Vol. 28, pp. 81-87, 1993. [7] D. Das, D.P. Kothari, A. Kalam, “Simple and efficient method for load solution of radial distribution networks”, Electric Power and Energy Systems,Vol. 17, pp. 335-346, 1995. [8] Goswami, S. K., and Basu, S. K., “Direct solution of distribution systems”, IEE Proc. C, 1991, 138, (1), pp. 78-88. [9] F. Gubina and B. Strmcnik, “A simple approach to voltage stability assessment in radial network”, IEEE Trans. on PS, Vol. 12, No. 3, 1997, pp. 1121-1128. [10] K. Vu, M.M. Begovic, D. Novosel and M.M. Saha, “Use of local measurements to estimate voltage-stability margin”, IEEE Trans. on PS, Vol. 14, No. 3,1999, pp. 1029-1035. [11] Banerjee,Sumit, Chanda,C.K., and Konar, S.C., “Determination of the Weakest Branch in a Radial Distribution Network using Local Voltage Stability Indicator at the Proximity of the Voltage Collapse Point”, International Conference on Power System,(Published in IEEE Xplore) ICPS 2009, IIT Kharagpur, 27-29 December 2009. [12] Banerjee, Sumit, and Chanda, C.K., “Proposed Procedure for Estimation of Maximum Permissible Load Bus Voltage of a Power System within Reactive Loading Index Range”, IEEE Conference TENCON 2009, Singapore, 23-26 November 2009. [13] Priyanka Das And S Banerjee, “Optimal Allocation of Capacitor in a Radial Distribution System using Loss Sensitivity Factor and Harmony Search Algorithm”, International Journal of Electrical Engineering & Technology (IJEET), Volume 5, Issue 3, 2014, pp. 5 - 13, ISSN Print : 0976-6545, ISSN Online: 0976-6553.
  10. 10. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 4, April (2014), pp. 01-10 © IAEME 10 APPENDIX Table III: Line data and nominal load data of 33 node radial distribution system Line No. From Bus To Bus Branch resistance (ohm) Branch reactance (ohm) Load at Receiving end node PL0 (kW) QL0 (kVAr) 1 1 2 0.0922 0.0477 100.0 60.0 2 2 3 0.4930 0.2511 90.0 40.0 3 3 4 0.3660 0.1840 120 80 4 4 5 0.3811 0.1941 60 30 5 5 6 0.8190 0.7000 60 20 6 6 7 0.1872 0.6188 200 100 7 7 8 0.7114 0.2351 200 100 8 8 9 1.0300 0.7400 60 20 9 9 10 1.0400 0.7400 60 20 10 10 11 0.1966 0.0650 45 30 11 11 12 0.3744 0.1238 60 35 12 12 13 1.4680 1.1550 60 35 13 13 14 0.5416 0.7129 120 80 14 14 15 0.5910 0.5260 60 10 15 15 16 0.7463 0.5450 60 20 16 16 17 1.2890 1.7210 60 20 17 17 18 0.7320 0.5740 90 40 18 2 19 0.1640 0.1565 90 40 19 19 20 1.5042 1.3554 90 40 20 20 21 0.4095 0.4784 90 40 21 21 22 0.7089 0.9373 90 40 22 3 23 0.4512 0.3083 90 50 23 23 24 0.8980 0.7091 420 200 24 24 25 0.8960 0.7011 420 200 25 6 26 0.2030 0.1034 60 25 26 26 27 0.2842 0.1447 60 25 27 27 28 1.0590 0.9337 60 20 28 28 29 0.8042 0.7006 120 70 29 29 30 0.5075 0.2585 200 600 30 30 31 0.9744 0.9630 150 70 31 31 32 0.3105 0.3619 210 100 32 32 33 0.3410 0.5302 60 40

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