 Open Access
 Total Downloads : 22
 Authors : M. V. S. Ram, Dr. G. Srinivasa Rao
 Paper ID : IJERTCONV4IS07010
 Volume & Issue : ETE – 2016 (Volume 4 – Issue 07)
 Published (First Online): 24042018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Load Flow analysis for Radial Distribution Network with Network Topology Method
M. V. S. Ram Dr. G. Srinivasa Rao
M. Tech. Power Systems Engineering Associate Professor

Siddhartha Engineering College (Autonomous) V.R. Siddhartha Engineering College (Autonomous) Vijayawada, Andhra Pradesh, India Vijayawada, Andhra Pradesh, India
Abstract Voltage stability has become an important issue of power system stability. This paper work concentrated on simple a n d e f f i c i e n t load flow analysis of radial distribution system for finding voltage magnitudes without trigonometric equations. Various methods are identified in literature survey for indication of voltage magnitude. The proposed analysis will be implemented on any IEEE standard test systems for composite load modeling. This feature enables us to set an index threshold to monitor and predict system stability online so that a proper action can be taken to prevent the system from collapse.
Keywords: Distribution load flow, Branch Injection and Branch Current (BIBC), mathematical techniques, stability index.

INTRODUCTION

The transmission system is distinctly different, in both its operation and characteristics, from the distribution system. Whereas the latter draws power from a single source and transmits it to individual loads, the transmission system not only handles the largest blocks of power but also the system.
The main difference between the transmission system and the distribution system shows up in the
network structure. The former tends to be a loop structure and the latter generally, a radial structure. The modern power distribution network is constantly being faced with an evergrowing load demand. Distribution networks e x p e r i e n c e a distinct change from low to high load level every day.
Literature survey shows that a lot of work has been done on the voltage stability analysis of transmission systems [2].
Power transmission systems may include sub transmission stages to supply intermediate voltage levels. Subtransmission stages are used to enable a more practical or economical transition between transmission and distribution systems. It operates at the highest voltage levels (typically, 230 kV and above). The generator voltages are usually in the range of 11 kV to 35 kV. There are also a few transmission networks operating in the extremely high voltage class (345 kV to 765 kV). As compared to transmission system subtransmission system transmits energy at a lower voltage level to the distribution substations. Generally, subtransmission systems supply power directly to the industrial customers. The distribution system is the final link in the transfer of electrical energy to the individual customers. Between 30 to 40% of total investment in the electrical sector goes to distribution systems, but nevertheless, they havent received the technological improvement in the same manner as the generation
and transmission systems. The distribution network differs from its two of siblings in topological structure as well as its associated voltage levels. The distribution networks are generally of radial or tree structure and hence referred as Radial Distribution Networks (RDNs). Its primary voltage level is typically between 4.0 to 35 kV, while the secondary distribution feeders supply residential and commercial customers at 120/240/440 volts. It generally consists of feeders, laterals (circuit breakers) and the service mains.
According to these studies, power flow analysis of RDNs may be divided into two categories. The first group of methods includes: ladder network methods for radial structure distribution systems using basic laws of circuit theories like Kirchhoffs Current Law (KCL) and Kirchhoffs Voltage Law (KVL ) [1]. On the other hand, the second category includes Gauss Seidel, Newton Raphson and Decoupled Newton Raphson methods for transmission systems and is usually based on nodal analysis method. The characteristics of RDNs are dynamic in nature and general features of RDS are

Uncertainties and Imperfection of network parameters.

High R/X ratio

Extremely large number of nodes and branches.

Dynamic change in imposed load.
line shunt capacitances at distribution voltage level are very small and thus can be neglected. The base values taken for calculation of voltages in the system are
11 KV and 200 KVA. The simplified mathematical model of a section of a RDN is shown in Fig.1.
Fig 1: Single Line of an Existing Distribution Feeder
I(i)=S(J)/V*(J) ———————(1)
I(i)=P(J)Q(J)/V*(J) ———————–(2)
Fig 2: 33bus Radial Distribution Network single line diagram
and also
I(i)=V(i) (i)V(j) (j)/(R(i)+X(j))—–(3)
V(2)={[(P(j)*R(i)+Q(j)*X(i)0.5V(i)2)2
(R2(i)+X2(i))(P2(j)+Q2(j))]1/2(P(j)*R(i)+Q(j)*X(i)
2 1/2

MATHEMATICALMODEL OF A RDN 0.5V(i) )} ———–(4)
The real and reactive power losses in branch ij are given by:
In RDNs, the large R/X ratio causes problems in convergence of conventional load flow algorithms. For a balanced RDN, the network can be represented by an equivalent singleline diagram. The
LP(j)=R(j)*[P2(m2)+Q2(m2)]/V(m2)2 ——(5)
QP(j)=X(j)*[P2(m2)+Q2(m2)]/V(m2)2 ——(6)
Fig 3: Voltage magnitudes of 33bus Radial Distribution Network
Initially, if LP(j) and LQ(j) are set to zero for all j, then initial estimates of P(m2) and Q(m2) will be the sum of the loads of all the nodes beyond node m2 plus the load of the node m2 itself.

NETWORK TOPOLOGY FOR MATRIX FORMATION
The branch current B is calculated with the help of BusInjection to BranchCurrent matrix (BIBC)[4]. The BIBC matrix is the result of the relationship between the bus current injections and branch currents.The e l e m e n t s of B I B C m a t r i x consists of 0s or 1s. [B]Nnb*1=[BIBC]nb*(n1)*[I](n1)*1———————(7)
Where nb is the number of branches, [I] is the vector of the equivalent current injection for each bus except the reference bus. This produced matrix is used for
calculation of voltage magnitudes. The building Step for the BIBC matrix is shown in Fig .1.
Fig 4: Graphical view of BIBC matrix
Step (1): For a distribution system with nb branch sections and n buses, the dimension of the BIBC matrix is nb Ã— (n1) Step (2): If a line section (Bk) is located between Bus i and Bus j, copy the column of the ith bus of the BIBC matrix to the column of the jth bus and fill +1 in the position of the jth bus column as shown below. Step (3): Repeat Step (2) until all the line sections are
Fig 5: stability index of 33bus Radial Distribution Network
included in the BIBC matrix. The building Step (2) for the BIBC matrix is shown in Fig. 4.
The BIBC matrix is responsible for the relations between the bus current injections and branch currents. (iii) The corresponding variation of the branch currents, which is generated by the variation at the current injection buses, can be found directly by using the BIBC matrix.

MATHEMATICALMODEL OF STABILITY INDEX For a distribution line model, given in fig.1, the
quadratic equation which is mostly used for the calculation of the line sending end voltages in load flow analysis can be written in general form as
2 2 2 2 2
Vr4+2 V 2(PR+QX) Vr V +(P +Q )Z =0——(8)
and from this equation a feasible solution has considered , line receiving end active and reactive power can e written
2 4 2 2 2 2
2 4 2 2 2 2
2Vr2 Vr – Vr 2Vr (PR+QX)Z (P +Q )0——–(9)
The above equation is most feasible of Eq (8).From the last equation, it is clearly seen that the value of the Eq.9 is decrease with the increase of the transferred power and impedance of the line, and it can be used as a bus stability index for a distribution networks as
SI(m2)= V(m1)4 4{P(m2)r(jj) Q(m2)x(jj)}2
4{P(m2)r(jj)+ Q(m2)x(jj)}V(m1)2 ——————(10)
In this study the above simple stability criterion, given in eq. 10, is used to find the stability index for
each line receiving end bus in radial distribution
r r networks. After the load flow study, the voltages of all nodes and the branch currents are known, therefore P and Q at the receiving end of each line
can easily be calculated and hence using Eq. 5 the voltage stability index of each node can easily be calculated. The node, at which the value of the stability index is at minimum, is the most sensitive to the voltage collapse.

LOAD MODELING
For the purpose of voltage stability analysis of radial distribution networks, composite load modeling is considered. The real and reactive power loads of node `i' is given as:
PL (i) =PLo(i)(c1+c2V(i)+c3V(i)2) —– (11)
QL (i) =QLo(i)(d1+d2V(i)+d3V(i)2) —– (12)
In the above equations, loads are gradually increased at every node. Constants (c1, d1), (c2, d2) and (c3, d3) are the compositions of constant power, constant current and constant impedance loads, respectively.
To demonstrate the effectiveness of the proposed method, a 33bus radial distribution network [3] is considered. Fig.2 shows a 33node radial distribution network. Line data and nominal load data (i.e. r, x, PLo and QLo) are given in Appendix A and Appendix B. In the present work, a composition of
40% constant power=c1=d1= 0:4; 30% of constant current=c2
=d2= 0.3; and 30% of constant impedance
=c3 =d3 =0.3; are considered.
Table 1: Voltages at different nodes
branch
Voltage(pu)
1
1
2
0.995894
3
0.976348
4
0.96592
5
0.955601
6
0.929896
7
0.92505
8
0.918269
9
0.90949
10
0.901343
11
0.900134
12
0.898013
13
0.889443
14
0.886274
15
0.884297
16
0.882379
17
0.879547
18
0.878696
19
0.995177
20
0.990319
21
0.989363
22
0.988498
23
0.971436
24
0.962298
25
0.957741
26
0.927204
27
0.923625
28
0.907613
29
0.896112
30
0.891151
31
0.885285
32
0.883993
33
0.883593
The above table shows the voltage magnitudes (pu) for 33bus network .The first bus voltage is as obtained to be 1pu and further it continues with
respect to algorithm of proposed method. The above voltages are obtained for composite loads which are in algebraic form which are shown in Eqns (8) & (9). The Fig.3. shows how voltages are changes with respect their busses, at 19th bus the a sudden increase had obtained as this is because of the reason that the bus is nearer to substation bus and it continues.
Table 2: Line flows of P and Q of 33 bus radial
distribution network
30
7.89E01
7.79E01
31
4.97E01
5.79E01
32
5.25E02
8.16E02
The above table shows the line flow of real and reactive power 33 bus radial distribution network. The total real power loss of the system is 44.80KW and reactive power loss is 33.82KVAR.The stability indices are shown in Fig 5.
Branch number
Real Power loss(KW)
Reactive Power loss(KVAR)
1
3.29E02
1.68E02
2
1.28E01
6.52E02
3
2.06E01
1.05E01
4
4.69E02
2.39E02
5
9.21E02
7.95E02
6
2.65E01
8.74E01
7
1.01E+00
3.35E01
8
1.18E01
8.51E02
9
1.21E01
8.59E02
10
1.67E02
5.52E03
11
5.26E02
1.82E02
12
2.08E01
1.64E01
13
3.32E01
4.37E01
14
6.47E02
5.75E02
15
8.85E02
6.46E02
16
1.53E01
2.05E01
17
2.11E01
1.66E01
18
4.18E02
3.99E02
19
3.85E01
3.47E01
20
1.05E01
1.23E01
21
1.82E01
2.40E01
22
1.29E01
8.80E02
23
5.28E+00
4.17E+00
24
5.29E+00
4.14E+00
25
2.42E02
1.23E02
26
3.40E02
1.73E02
27
1.22E01
1.08E01
28
4.53E01
3.95E01
29
5.96E+00
3.03E+00
Branch number
Real Power loss(KW)
Reactive Power loss(KVAR)
1
3.29E02
1.68E02
2
1.28E0
6.52E02
3
2.06E01
1.05E01
4
4.69E02
2.39E02
5
9.21E02
7.95E02
6
2.65E01
8.74E01
7
1.01E+00
3.35E01
8
1.18E01
8.51E02
9
1.21E01
8.59E02
10
1.67E02
5.52E03
11
5.26E02
1.82E02
12
2.08E01
1.64E01
13
3.32E01
4.37E01
14
6.47E02
5.75E02
15
8.85E02
6.46E02
16
1.53E01
2.05E01
17
2.11E01
1.66E01
18
4.18E02
3.99E02
19
3.85E01
3.47E01
20
1.05E01
1.23E01
21
1.82E01
2.40E01
22
1.29E01
8.80E02
23
5.28E+00
4.17E+00
24
5.29E+00
4.14E+00
25
2.42E02
1.23E02
26
3.40E02
1.73E02
27
1.22E01
1.08E01
28
4.53E01
3.95E01
29
5.96E+00
3.03E+00
Table 3: Stability Index of 33 bus radial distribution
network
Branch number
Stability Index
1
0.983272583
2
0.906940845
3
0.868636821
4
0.832999639
5
0.745868785
6
0.729374704
7
0.706288905
8
0.682070313
9
0.657896675
10
0.656196014
11
0.649589051
12
0.622415428
13
0.613741796
14
0.61041852
15
0.604740201
16
0.595537497
17
0.593828343
18
0.980141808
19
0.955548193
20
0.95627273
21
0.951432533
22
0.888761294
23
0.841258052
24
0.825358375
25
0.7386677
26
0.72715612
27
0.67629338
28
0.640883659
29
0.623765846
30
0.60857052
31
0.607974998
32
0.608448922
The 17th bus in the system is nearer to collapse, so that we must take care of that node by optimal using of distributed generators or shunt capacitors [5].

RESULTS
The rate of convergence of the proposed approach is tested using IEEE 33 node radial distribution systems with varying load conditions ranging from 0.5 to 3.0 times of the given load condition. The voltages had been plotted in Fig 3.and Fig 5. Voltage magnitude and stability index values are obtained from RDS network which is shown in Table 1.The total real power loss of the system is 44.80KW and reactive power loss is 33.82KVAR.

CONCLUSION
It has been shown that the load flow solutions of radial distribution networks are unique. The power system issues Distributed Generation for optimally placed and sized at Radial Distribution Feeder where the voltage stability index value are minimum and most sensitive to voltage collapse. Optimal sizing of Distributed Generation can be calculated using
analytical expression and an efficient approach is used to determine the optimum location for distributed generators. The effectiveness of the proposed technique has been demonstrated through a
33 bus radial distribution network and it can be evaluated for any IEEE test system.

REFERENCES


Das D, Kothari DP, Kalam A. A simple and efficient method for load flow solution of radial distribution networks. International Journal of Electrical Power and Energy Systems 1995;17(5):335Â±46.

Ajjarapu V, Lee B. Bibliography on voltage stability. IEEE Transactions on Power Systems
1998;13(1):115Â±25

S. Ghosh., D. Das, Method for load flow solution of radial distribution network, IEE Proc. Gener. Transm. Distrib. Vol. 146, No. 6, pp.641
648, 1999

W. H. Kersting, D. L. Mendive, An application of ladder network theory to the solution of three phase radial load flow problem IEEE PES winter meeting, New York, Jan. 1976

Mesut EB, Wu FF. Optimal capacitor placement on radial distribution systems. IEEE Transactions on Power Delivery 1989;4(1):725Â±34.
Appendix A
Line data of 33bus radial distribution network
16
BRANCHNUMBE 
SENDINGNODE 
RECEIVINGNODE 
RESISITANCE 
REACTANCE 
1 
1 
2 
0.000152388 
7.77E05 
2 
2 
3 
0.00081483 
0.000415018 
3 
3 
4 
0.000604925 
0.000308082 
4 
4 
5 
0.000629882 
0.000320808 
5 
5 
6 
0.001353643 
0.00116853 
6 
6 
7 
0.000309404 
0.001022753 
7 
7 
8 
0.001175802 
0.000388573 
8 
8 
9 
0.001702384 
0.001223072 
9 
9 
10 
0.001725523 
0.001223072 
10 
10 
11 
0.00032494 
0.000107432 
11 
11 
12 
0.000618808 
0.000214533 
12 
12 
13 
0.00242631 
0.001908984 
13 
13 
14 
0.000895156 
0.001178281 
14 
14 
15 
0.000976805 
0.000869373 
15 
15 
16 
0.001233485 
0.000900776 
16 
17 
0.002130459 
0.002844469 

17 
17 
18 
0.00120985 
0.000948707 
18 
2 
19 
0.000271059 
0.000258663 
19 
19 
20 
0.002486142 
0.002240205 
20 
20 
21 
0.000676822 
0.0007907 
21 
21 
22 
0.00117167 
0.001549169 
22 
3 
23 
0.000745743 
0.000509558 
23 
23 
24 
0.001484214 
0.001171835 
24 
24 
25 
0.001480909 
0.001158778 
25 
6 
26 
0.000335518 
0.0001709 
26 
26 
27 
0.000469726 
0.00023916 
27 
27 
28 
0.001750315 
0.001543219 
28 
28 
29 
0.001329182 
0.001157952 
29 
29 
30 
0.000838796 
0.000427249 
30 
30 
31 
0.001610488 
0.001591646 
31 
31 
32 
0.000513194 
0.000598148 
32 
32 
33 
0.000563605 
0.000876315 
Appendix B
Bus data of 33bus radial distribution network
Node number 
PL(composite load)pu 
QL(composite load)pu 
1 
0 
0 
2 
0.511344 
0.306806 
3 
0.460209 
0.204538 
4 
0.613613 
0.409075 
5 
0.306806 
0.153403 
6 
0.306806 
0.102269 
7 
1.022688 
0.511344 
8 
1.022688 
0.511344 
9 
0.306806 
0.102269 
10 
0.306806 
0.102269 
11 
0.230105 
0.153403 
12 
0.306806 
0.17897 
13 
0.306806 
0.17897 
14 
0.613613 
0.409075 
15 
0.306806 
0.051134 
16 
0.306806 
0.102269 
17 
0.306806 
0.102269 
18 
0.460209 
0.204538 
19 
0.460209 
0.204538 
20 
0.460209 
0.204538 
21 
0.460209 
0.204538 
22 
0.460209 
0.204538 
23 
0.460209 
0.255672 
24 
2.147644 
1.022688 
25 
2.147644 
1.022688 
26 
0.306806 
0.127836 
27 
0.306806 
0.127836 
28 
0.306806 
0.102269 
29 
0.613613 
0.357941 
30 
1.022688 
3.068063 
31 
0.767016 
0.357941 
32 
1.073822 
0.511344 
33 
0.306806 
0.204538 