Abstract- This paper presents status of all branches of radial
distribution networks in chronological order 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.
Index Terms-Active Power Loss; 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 conventional load flow methods like Newton Raphson and fast decoupled method cannot be effectively used for the load flow analysis of radial distribution systems.
Chandan Kumar Chanda3 3Department of Electrical Engineering
Bengal Engineering and Science University, Shibpur, Howrah, India 3 eke _ math@yahoo. eom
The current article has been developed a novel and simple theory [11-17] to represent status of all branches of radial distribution systems in chronological order using distributed generator at optimal position by considering the concept of reactive loading index technique. 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. I. A simple 2-node system.
Here a load having an impedance of ZL = ZLL¢ is
connected to a source having an impedance of Zs = ZsLa . If line shunt admittances are neglected, the current flowing through the line equals the load current; From Figure 1,
ZS VL' (1)
Using simple calculation, we can write load reactive power QL as
VSVL . ( ) V/ . Q = --sm 0 +a-o --" sma L Zs L S Zs (2)
The load voltage VL can be varied by changing the load
reactive power QL' The load reactive power QL becomes
maximum when the following condition is satisfied.
Now, from (2) and (3)
dQL = 0 (3) dVL
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Proceedings of 2014 1st International Conference on Non Conventional Energy (ICONCE 2014)
2VLsina-sin (6L +a-6 s ) = 0 (4) Vs
Now, at no load, VL = Vs and aL = as . Therefore at no load,
the left hand side (LHS) of (4) will besina. However, at the maximum reactive powerQL , 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, L of the system that varies between sin a (at no load) q and zero (at maximum reactive power).
Thus,
L =2VL sina-sin(oL +a-os )
q Vs
(5)
Here, sin a::: Lq ::: 0 (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 P (i) and Q (i) respectively and the active and reactive power flow through the branch near bus (i+ 1) is P (i+ 1) and Q (i+ 1) respectively.
Hence we can write
(.) (
. )
P2(i+l)+Q2(i+l) (.) (7) Pl=Pl+l+
2(.
) Rl
V 1 +1
( .) ( . ) P2(i+I)+Q2(i+I)X(') (8) Q I = Q I + I + V 2 (i + I)
I
Here, (P (i + I ) + jQ (i + I ) 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
V2 (i + 1 ) = V 2 (i )- 2 (P (i ) R (i )+ Q (i ) x (i ) +
(P2 (i )+ Q 2 (i ) ( R2 (i )+ X2 (i ) (9)
V 2 (i ) 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. RESULTS AND DISCUSSIONS
With the help of MA TLAB programme, the effectiveness of the proposed idea is tested on 12.66 K Y radial distribution systems consisting of 33-nodes. The single line diagram of the 33-node system is shown in Fig. 2 and its data is given in appendix (Table III).
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 Lq 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 203.1 kW and reactive loss is 135.0 kYAr. Under this condition, the minimum system voltage is 0.9130 pu at node 18.
Fig. 3. Reactive loading index of all branches of the 33-node system under nominal loading conditions.
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.
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 104.1 kW. With the help of optimization technique it is also seen that that the power loss will be 105.5 kW, if 2600.5 kW unity power factor DG is placed at node 7.
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 ofDG at node 6.
The investigation reveals that the value of the reactive loading index (Lq) is minimum in branch 5 and B5 can be considered as the weakest branch of the system up to 30% DG
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capacity at node 6. From 40% to 100% DG capacity, B27 can be considered as the weakest branch of the system.
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 and reactive power loss will decrease, up to 70% DG capacity is inserted at node 6 and
after that both the losses will increase. But minimum system voltage will increase up to maximum size ofDG.
TABLE I. ACTIVE POWER LOSS, REACTIVE POWER LOSS AND MINIMUM SYSTEM VOLTAGE AFTER INSERTING DG AT NODE 6.
DG Ploss Qloss Minimum Node capacity kW kVAr Voltage number
(%) (pu) 10 175.7 118.0 0.9188 18
20 153.1 104.0 0.9244 18
30 134.9 92.8 0.9299 18
40 121.1 84A 0.9354 18
50 IliA 78.6 0.9408 18
60 105.8 75.5 0.9462 18
70 104.1 74.8 0.9514 18
80 106.3 76.6 0.9566 18 90 112.1 80.8 0.9618 18
100 121.5 87.2 0.9668 18
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', '0', '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 ofDG at node 7.
The investigation reveals that the value of the reactive loading index (Lq) 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.
TABLE II. ACTIVE POWER LOSS, REACTIVE POWER LOSS AND MINIMUM SYSTEM VOLTAGE AFTER INSERTING DG AT NODE 7.
DG capacity Ploss Qloss Minimum Node
(%) kW kVAr Voltage (pu) number
10 174.6 115.0 0.9193 18
20 151.3 99.2 0.9254 18
30 133.0 87.6 0.9314 18
40 119.4 79.9 0.9374 18
50 110.4 76.0 0.9432 18
60 105.8 75.8 0.9489 18
70 105.5 79.2 0.9546 18
80 109.4 86.0 0.9598 33
90 117.2 96.1 0.9649 33 100 128.9 109.5 0.9698 33
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 ofDG 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 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 ofDG.
IV. 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 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. SOI-SII, 2003.
[4] M. Chakravorty, D. Das, "Voltage stability analysis of radial
distribution networks", Electric Power and Energy Systems, Vol. 23, pp. 129-13S, 2001.
[S] Das, D., Nagi, H. S., and Kothari, D. P., "Novel method for solving radial distribution networks", lEE 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. 33S-346, 1995.
[8] Goswami, S. K., and Basu, S. K., "Direct solution of distribution systems", lEE 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. 1029-103S.
[II] 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, lIT 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 TEN CON 2009, Singapore, 23-26 November 2009.
[13] Sumit BaneIjee, A. Mukherjee and C. K. Chanda, "Voltage Stability Margin of Radial Distribution Systems for Composite Loads using Distributed Generators," International Journal on
Systems Applications and Algorithms, vol. 3, issue ICEEC 13, pp. 130-134,2013.
[14] Deblina Maity, Sumit Banerjee, and C. K. Chanda, "Impact of Distributed Generators on Voltage Stability Margin of Distribution Networks", Second IntI. Conf. on Advances in Electronics, Electrical and Computer Engineering-EEC 2013, pp. 96-101, Dehradun, India, 22-23 June, 2013.
[IS] Sumit Banerjee, C. K. Chanda, S. C. Konar and C. M. Khan, "Loading Status of all Branches of Distribution Networks in Chronological order for Loads of Different Types," 4th
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International Conference on Electronics Computer Technology (ICECT 2012), Kanyakumari, April 6-8, 2012.
[16] Sumit Banerjee, C. K. Chanda, S. C. Konar and P K. Ghosh, "Study of Loading Status for all Branches in chronological order at different Conditions in a Radial Distribution Systems using Reactive Loading Index Technique" PEDES 2010 & Power India International Conference, December 20-23, 2010. (IEEE Xplore).
[17] Sum it Banerjee, Sudipta Ghosh, C. K. Chanda and Debraj
Sarkar, "Placement of Distributed Generator in Optimal Position on a Network System"; ACTE-2009; Manipal Institute of Technology, Manipal University; 2-4 April 2009.
APPENDIX
TABLE III. LINE DATA AND NOMINAL LOAD DATA OF 33-NODE RADIAL DISTRIBUTION NETWORK.
Bf. Sending Receiving Branch Branch Nominal load at
Receiving end node no. end node end node resistance reactance
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