IJSRD - International Journal for Scientific Research & Development| Vol. 2, Issue 01, 2014 | ISSN (online): 2321-0613

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Backward / Forward Sweep Load Flow Algorithm for Radial Distribution

System A. D. Rana

1 J. B. Darji

2 Mosam Pandya

3

1, 2, 3P. G. Student

1, 2, 3,Eletrical Engg. Department

1, 2, 3L.D.C.E., Abad Abstract---This paper presents Backward / Forward

(BW/FW) Sweep algorithm for load flow analysis of radial

distribution network. In backward sweep, Kirchhoffs Current Law and Kirchhoffs Voltage Law are used to compute the bus voltage from farthest node. In forward

sweep, downstream bus voltage is updated starting from

source node. The procedure stops after the mismatch of the

calculated and the specified voltages at the substation is less

than a convergence tolerance. Line losses are calculated

afterwards using updated bus voltage. Using this method,

load flow solution for a distribution network can be obtained

without solving any set of simultaneous equations. The

proposed algorithm is tested with 15 bus and IEEE 33 bus

radial distribution system. Test results are obtained by

programming using MATLAB.

Keywords: radial distribution system, load flow analysis,

backward/forward sweep

I. INTRODUCTION

Power flow or load flow studies are performed for the

determination of the steady state operating condition of a

power system. This is the most frequently carried out study

by power utilities and are required to be performed for

power system planning, operation, optimization and control.

At the design stage, load flow analysis is used to check

whether the voltage profiles are expected to be within limits

throughout network. At the operation stage, it is run to

explore different arrangements to maintain the required

voltage profile and to minimize system losses.

In addition to the direct use of load flow, in many

other problems it is used as a sub problem, for instance in

the contingency analysis of a system. The main objective of

loaf flow studies is to determine the bus voltage magnitude

with its phase angle, real and reactive power flow in

different lines and the transmission power losses.

Some of the basic power flow algorithms were

developed and applied such as Newton Raphson (NR),

Gauss Seidel (GS) to the transmission network. These

methods may become inefficient for the distribution network

because of its special features like radial structure, high R/X

ratio, unbalanced load etc. These features make the

distribution systems power flow computation different and

somewhat difficult to analyze as compared to the

transmission systems.

In the past, many approaches for distribution

system load-flow analyses have been developed. Among

these approaches, the ladder network theory and the

backward/forward sweep methods are commonly used due

to their computational efficiencies and solution accuracies.

In this paper, standard backward/forward sweep method is

used for radial distribution system load flow analysis.

II. BACKWARD/FORWARD SWEEP ALGORITHM

This method includes two steps: the backward sweep and

the forward sweep. In backward sweep, voltage and currents

are computed using KVL and KCL from the farthest node

from the source node. In forward sweep, the downstream

voltage is calculated starting from source node. The input

data of this algorithm is given by node-branch oriented data.

Basic data required are, active and reactive powers,

nomenclature for sending and receiving nodes, and positive

sequence impedance model for all branches.

Listed below summarize major steps of the

proposed solution algorithm with appropriate equations.

1) Assume rated voltages at end nodes only for 1st iteration and equals the value computed in the forward sweep in

the subsequent iteration.

2) Start with end node and compute the node current using equation (1). Apply the KCL to determine the current

flowing from node i towards node i+1 using equation

(2), start from end nodes.

(1)

(2)

3) Compute with this current the voltage at ith node using equation (3). Continue this step till the junction node is

reached. At junction node the voltage computed is

stored.

(3)

4) Start with another end node of the system and compute

voltage and current as in step 2 and 3.

5) Compute with the most recent voltage at junction node,

the current using equation (1).

6) Similarly compute till the reference node.

7) Compare the calculated magnitude of the rated voltage

at reference node with specified source voltage.

Stop if the voltage difference is less than specified criteria,

otherwise forward sweep begins.

Forward Sweep:

1) Start with reference node at rated voltage. 2) Compute the node voltage in forward direction from

reference node to end nodes using equation (4).

(4) 3) Again start backward sweep with updated bus voltage

calculated in forward sweep.

After calculating node voltages and line currents using

standard BW/FW sweep algorithm, the line losses are

calculated. The complex power, Sij from bus i to bus j and

Sji from bus j to bus i, as are calculated using equation (5)

and (6).

Sij = ViIij* (5)

Backward / Forward Sweep Load Flow Algorithm for Radial Distribution System

(IJSRD/Vol. 2/Issue 01/2014/102)

All rights reserved by www.ijsrd.com 399

Sji = VjIji* (6)

III. SIMULATION RESULTS

The proposed algorithm has been tested on 15 bus and IEEE

33 bus radial distribution system, using MATLAB. 15 bus

system is shown in Figure 1. This system is consisting of 15

nodes and 14 branches, where node 1 is the reference node

or substation.

Fig. 1: 15 bus Radial Distribution System

The base voltage is 11 kV and base KVA

is 100. The tolerance is 0.00001 p.u. and number

of iteration required is 5. Results are shown in

Table 1 and Table 2. Bus voltage magnitude in

p.u. and phase angle in degree at each bus are

shown in Table 1 and real and reactive line losses

in each branch in kW and kVAR respectively, are

shown in Table 2. Voltage profile of the system is

shown in Figure 2. Bus

Number

Voltage Magnitude

(pu)

Phase Angle

(degree)

1 1.0000 0

2 0.9714 0.0131

3 0.9569 0.0659

4 0.9511 0.0693

5 0.9501 0.0840

6 0.9585 0.1729

7 0.9563 0.2007

8 0.9573 0.1869

9 0.9681 0.0571

10 0.9671 0.0714

11 0.9502 0.1508

12 0.9461 0.1974

13 0.9447 0.2153

14 0.9488 0.0976

15 0.9485 0.0978

Table. 1: Voltage magnitude and Phase angle

Fig. 2: Voltage profile of 15 bus system

Branch Active Line

Losses (kW)

Reactive Line

Losses (kVAR) Sending

End

Receiving

End

1 2 37.0603 37.0600

2 3 11.6679 10.5011

3 4 2.4601 2.4601

4 5 0.0572 0.0352

2 9 0.4826 0.3123

9 10 0.0594 0.0382

2 6 5.7275 3.8186

6 7 0.3936 0.2624

6 8 0.1091 0.0764

3 11 2.1985 1.4657

11 12 0.5943 0.4160

12 13 0.0756 0.0489

4 14 0.1999 0.1333

4 15 0.4445 0.3112

Table. 2: Active and Reactive line losses of 15 bus system

IEEE 33 bus system consists of 33 nodes and 32

branches is shown in Figure 3. The base voltage for this

system is 12.66 kV and base MVA is 10.

The tolerance is 0.00001 p.u. and number of

iteration required is 2. Bus voltage magnitude in p.u. and

phase angle in degree at each bus are shown in Table 3 and

real and reactive line losses in each branch in kW and kVAR

respectively, are shown in Table 4. Voltage profile of the

system is shown in Figure 4.

Fig. 3: IEEE 33 bus distribution system

Bus

Number

Voltage Magnitude

(pu)

Phase Angle

(degree)

1 1.0000 0

2 0.9972 0.0147

3 0.9839 0.0904

4 0.9770 0.1516

5 0.9701 0.2138

6 0.9531 0.1275

7 0.9498 -0.0864

8 0.9373 -0.2323

9 0.9316 -0.3029

10 0.9262 -0.3637

11 0.9254 -0.3575

12 0.9241 -0.3476

13 0.9185 -0.4349

14 0.9164 -0.5085

15 0.9151 -0.5439

16 0.9139 -0.5660

17 0.9120 -0.6380

18 0.9115 -0.6472

19 0.9967 0.0039

20 0.9931 -0.0629

Backward / Forward Sweep Load Flow Algorithm for Radial Distribution System

(IJSRD/Vol. 2/Issue 01/2014/102)

All rights reserved by www.ijsrd.com 400

21 0.9924 -0.0821

22 0.9918 -0.1024

23 0.9804 0.0606

24 0.9739 -0.0257

25 0.9707 -0.0681

26 0.9513 0.1644

27 0.9489 0.2169

28 0.9384 0.2978

29 0.9308 0.3731

30 0.9276 0.4713

31 0.9238 0.3959

32 0.9229 0.3752

33 0.9227 0.3683

Table. 3: Voltage magnitude and Phase angle of IEEE 33

bus system

Branch Active Line

Losses (kW)

Reactive Line

Losses (kVAR) Sending

End

Receiving

End

1 2 11.0729 5.5365

2 3 45.9580 23.4266

3 4 17.1532 8.7271

4 5 16.0729 8.1715

5 6 32.7726 28.2832

6 7 1.6564 5.4647

7 8 9.9722 7.1990

8 9 3.5476 2.5490

9 10 3.0097 2.1359

10 11 0.4685 0.1562

11 12 0.7434 0.2446

12 13 2.2398 1.7630

13 14 0.6118 0.8055

14 15 0.2989 0.2657

15 16 0.2353 0.1717

16 17 0.2098 0.2803

17 18 0.0443 0.0347

2 19 0.1583 0.1521

19 20 0.8197 0.7386

20 21 0.0989 0.1156

21 22 0.0429 0.0567

3 23 3.0101 2.0494

23 24 4.8474 3.8260

24 25 1.2097 0.9457

6 26 2.2211 1.1368

26 27 2.8235 1.4357

27 28 9.5845 8.4535

28 29 6.6364 5.7771

29 30 3.2984 1.6752

30 31 1.3406 1.3252

31 32 0.1795 0.2090

32 33 0.0111 0.0172

Table. 4: Active and Reactive line losses of IEEE 33 bus

system

Fig. 4: Voltage profile of IEEE 33 bus system

IV. CONCLUSION

A new method for solving the load flow problem for radial

distribution feeders without using conventional load flow

methods like Gauss Seidel, Newton Raphson, Fast

Decoupled methods is presented in this paper. This method

uses simple algebraic equations to calculate iteratively the

outgoing powers and voltage magnitudes of different nodes

and mismatches at the last nodes of main feeder and laterals

and depending upon mismatches the substation injection is

corrected judiciously and this process is repeated until

convergence. This makes the algorithm very robust and

numerically efficient for convergence for wide variation of

distribution network. Two different radial distribution

systems are used to validate the algorithm.

REFERENCES

[1] Chang, G.W.; Chu, S.Y.; Wang, H.L. An Improved Backward/Forward Sweep Load Flow Algorithm for

Radial Distribution Systems IEEE Trans Power Sys. vol. 22, no. 2, pp. 882-884, 2007.

[2] S. Ghosh and D. Das, Method for load-flow solution of radial distribution network, IEE Proc.-Gener. Transm. Distrib., vol. 146, no. 6, Nov. 1999.

[3] W. H. Kersting, Radial distribution test feeders IEEE distribution planning working group report, IEEE Trans. Power Syst., vol. 6, no.3, pp. 975985, Aug. 1991.

[4] PSR Murthy, C. Radhakrishana, H. S. Jain, Tellegen-

Kirchoff s based Power Flow Solution for Radial

Distribution Networks

[5] W. H. Kersting, Distribution System Modeling and

Analysis Boca Raton, FL: CRC Press, 2002.

[6] D. Shirmohammadi, H. W. Hong, A. Semlyen, and G. X. Luo, A compensation based power flow method for weakly meshed distribution and transmission

networks, IEEE Trans. Power Syst., vol. 3, no. 2, pp. 753762, May 1988.