75

CHAPTER - 5

NETWORK RECONFIGURATION

_______________________________________________________________________________________________________

5.1 INTRODUCTION

Network Reconfiguration is the process of operating switches to

change the circuit topology so that operating costs are reduced while

satisfying the specified constraints. These constraints include radial

configuration, serving all loads, coordination of protective devices,

keeping all the equipment within current capacity limits and the

voltage drop within limits. Distribution network reconfiguration for

loss reduction and load balancing is a complicated combinatorial, non

- differentiable, constrained optimization problem since the

reconfiguration involves many candidate-switching combinations. The

problem precludes algorithms that guarantee a global optimum. Most

existing reconfiguration algorithms fall into two categories. In the first,

branch exchange, the system operates in a feasible radial

configuration and the algorithm opens and closes candidate switches

in pairs. In the second, loop cutting, the system is completely meshed

and the algorithm opens candidate switches to reach a feasible radial

configuration.

An algorithm for minimum loss reconfiguration of distribution

system is proposed based on Sensitivity and Heuristics [100]. A

codification algorithm is proposed for network reconfiguration for loss

reduction [101]. The loss minimum distribution system

reconfiguration is obtained using hyper cube ant colony optimization

76

[102]. The algorithm proceeds towards final configuration by

introducing variations according to heuristic rules from the initial

configuration. A sequential method for loss minimum reconfiguration

and an extended algorithm for service restoration are presented in

[108]. The network reconfiguration based on a Benders decomposition

approach integrated with optimal power flow is presented [109]. A

mixed integer quadratic constrained program for solving

reconfiguration problem is proposed [116]. A Meta – heuristic method

using modified Tabu – search algorithm is proposed for distribution

system reconfiguration [120]. Implementation of an evolutionary

algorithm [122] is presented for network reconfiguration to minimize

loss and disruption costs. The efficiency of loss estimation technique

and reconfiguration approach affects the efficiency of network

reconfiguration of distribution systems [125]. A coloured Petri net

algorithm for load balancing in radial distribution system is proposed

[67]. A method using GA is presented for load balancing through

reconfiguration [90].

This chapter presents PGSA for radial distribution system

network reconfiguration to minimize power loss and/or to keep load

balancing while satisfying its constraints. The proposed method

handles objective function inclusive of the constraints. One of the

major advantages of PGSA is better searching performance than the

published random algorithms in the literature [73]. The effectiveness

of PGSA to network reconfiguration is illustrated with the help of

examples.

77

5.2 PROBLEM FORMULATION FOR LOSS REDUCTION

The objective function of the network reconfiguration to

minimize the power loss in the system is given below.

Minimize F = min P + λ S + λ SV IT, Loss CV CI (5.1)

where, PT,Loss is the total active power loss in the system.

λV and λI parameters are the penalty constants.

SCI is the squared sum of the violated current constraints and SCV is

the squared sum of the violated voltage constraints.

Moreover, the penalty constants are determined as follows:

(i) Constant λI (λV) is given a value of ‘0’, if the associated current

(voltage) constraint is not violated.

(ii) λI (λV) is given a significant value if the associated current (voltage)

constraint is violated. These considerations make the objective

function to move away from the unfeasible solutions.

The voltage magnitude at each node must be maintained within

specified limits. The current in each branch must satisfy the branch

current carrying capacity.

These constraints are expressed as follows:

maximin VVV (5.2)

max,jj II (5.3)

where iV is voltage magnitude of node i, minV and maxV are

minimum and maximum node voltage magnitude limits, jI and Ij,max

are current magnitude and maximum current limit of branch j,

78

respectively. Backward - forward sweep power flow method is used as

described in the section 2.2 to prevent complicated computation.

5.3 LOAD BALANCING

Usually it appears a mixture of domestic, commercial and

industrial type of loads, varying from time to time, on distribution

lines. Each of these has different characteristics and requirements.

From this one can understand that some parts of the distribution

system are heavily loaded at certain times and less loaded at other

times in a day. In order to reschedule the load currents more

efficiently for loss minimization, it is required to transfer the loads

between the substations or feeders and modify the topology of the

distribution feeders without changing the radial structure.

5.3.1 Load Balancing Problem Formulation

The objective function for load balancing is presented in this

section. The function consists of two components. One is the system

load balancing index and the other is the branch load balancing

index. The branch Load Balancing index (LBj) is defined as a measure

of how much a branch can be loaded without exceeding the rated

capacity of that branch. The load on the entire system is indicated by

system Load Balancing index (LBsys). The objective is to optimize the

branch load balancing indices so that the system load balancing index

is minimized. In other words, all the branch load balancing indices are

set to be more or less the same value and are also nearly equal to the

system load balancing index.

79

The load balancing problem is formulated in the form of branch

load balancing and system load balancing indices [20] as

The branch load balancing index,SjLB = maxj Sj

(5.4)

The system load balancing index, Snb j1LB =sys maxnb Sj=1 j

(5.5)

where, nb is the total number of branches in the system.

Sj is apparent power of branch j

maxSj is maximum capacity of branch j

5.3.1.1 Objective function

Snb j1Minimize F = maxnb Sj=1 j

(5.6)

By rescheduling the loads the branch load balancing indices

can be optimized and thereby the system load balancing index will be

minimized. In effect, it is made all the branch load balancing indices,

(LBj) are approximately equal to each other and also closely

approximate to the system load balancing index (LBsys).

Mathematically this can be represented as,

SSS nbS j121 n= = ..... = =m ax m ax m ax m axnbS S S Sj=1n1 2 j (5.7)

The objectives to be achieved are,

(i) The system loss must be reduced.

(ii) The voltage magnitude of each node must fall within permissible

limits i.e. maximin VVV

80

(iii) Current capacity of each branch, max,jj II

The condition of a branch will become critical when the load

balancing index of the branch is equal to 1 and if it is greater than 1

the branch rated capacity will be exceeded. The system load balancing

index will be low if the system is lightly loaded and its value will be

closer to zero and the individual branch load balancing indices will

also be low. The load balancing indices of individual branches will

differ widely when the loads are unbalanced. On the other hand the

balanced load will make the load balancing indices of all the branches

nearly equal. Practically it is not possible to make all the branch load

balancing indices exactly equal. However, the branch load balancing

indices can be adjusted with the help of reconfiguration and hence the

system load balancing index can be improved.

5.4 IMPLEMENTATION OF PGSA TO RECONFIGURATION

This section presents implementation of PGSA to the network

reconfiguration problem for loss reduction and/or load balancing.

5.4.1 Decision Variables Design

The switch, usually considered as the decision variable, can be

assigned either a value 0 (zero for open switch) or 1

(one for closed switch) in the distribution network optimization

problem. However, two problems exist, (i) the rudimentary techniques

are unsuitable for the large-scale optimization problem as the number

of possible network states grows exponentially with the number of

81

switches, (ii) the optimal reconfiguration may not be obtained since a

lot of unfeasible solutions will appear in the iterative procedure. The

design of decision variables requires more sophisticated techniques to

overcome the above mentioned problems. The independent loops can

be taken as decision variables in distribution system reconfiguration

problem since the number of independent loops is the same as the

number of tie switches.

The network optimization problem to minimize system real

power loss is identical to the problem of selection of an appropriate tie

switch for each independent loop in the system. This can greatly

reduce the network model as the number of the decision variables are

reduced and cause unfeasible solutions to a marked decrease in the

iterative procedure.

Consider an IEEE 16 node distribution system consisting of 13

sectionalizing and 3 tie switches as shown in fig.5.1, to illustrate the

new decision variables. The dotted lines represent initial tie switches

and the sectionalizing switches are represented as thick lines. The

basic procedure to design the new decision variables is given below.

(i) An initial radial network is to be formed with all the sectionalizing

switches in close and all the tie switches in open.

(ii) The first independent loop (nominated loop 1) is to be formed by

closing the first tie switch (S5).

(iii) Number the switches in loop 1 using consecutive integers

assuming the decision variable of loop-1 as x1, and then the numbers

of all switches in loop-1 constitute the possible solution set of x1. For

82

example, number the switches S1, S2, S5, S9, S8, S6 in loop-1 using

1, 2, 3, 4, 5, 6 and then get the possible solution set of x1 i.e., integral

set [1 6]. In the same manner, define other decision variables as x2 for

loop 2, x3 for loop 3, and then get their respective possible solution

sets.

Fig. 5.1 Initial configuration of 16 node distribution system

5.4.2 Switch State Description

In the iterative procedure the unfeasible solutions cannot be

avoided when independent loops are taken as decision variables. Here,

to reduce the chance to appear the unfeasible solutions in the iterative

procedure the switches are described in four states. Further it

improves the efficiency of the solution method.

(i) Open state - switch is open in a feasible solution.

(ii) Closed state - switch is closed in a feasible solution.

(iii) Permanent closed state - switch is closed in all feasible solutions.

(iv) Temporary closed state - switch must be closed in a feasible

solution because another switch is open and the switch will be open

83

or closed state when the opened switch is closed in another feasible

solution.

The above description makes no need to number the

permanent closed state switches while forming the possible solution

sets of the selected decision variables. Also the number of switches in

temporary closed state can be temporarily deleted in the possible

solution set of the corresponding variable.

Some illuminations about the temporary closed state and

permanent closed state of a switch for fig.5.1 are as given below.

(i) In any feasible and reasonable solution a switch which is close to

the source node should be closed. The switches S1, S6 and S12 in

fig.5.1 belong to such case. Hence no need to number the switches S1,

S6, and S12 while forming the possible solution set of each decision

variable. This reduces the search domain.

(ii) Some switches, which belong to the same two or three independent

loops, are interrelated. Only one of the interrelated switches may be in

open state in a feasible solution. In other words, the possible switches

corresponding to two independent loops must be temporarily closed

while only one switch is in open state. The unfeasible solutions due to

the interrelation of some switches can be avoided by introducing the

concept of temporary closed state.

5.4.3 Constraints Treatment

In PGSA, the constraints are treated in the following way.

(i) Adopting independent loops as decision variables the radial

characteristic of the network is enforced.

84

(ii) The branch capacity and node voltage limits are executed by

checking every possible solution obtained.

Fig.5.2 Flow chart for Network Reconfiguration

5.4.4 Algorithm for Network Reconfiguration

The flow chart is shown in fig.5.2.

Step 1: Read the distribution system data such as line and load data,

constraints limits, Nmax etc. and set iteration count N=0.

85

Step 2: Form the search domain by giving possible tie-line switches,

which corresponds to the length of the trunk and the branch of a

plant.

Step 3: Give the initial solution X0 (X0 is initial configuration) which

corresponds to the root of a plant, and calculate the initial value of

objective function (power loss or load balancing index).

Step 4: Let the initial value of the basic point Xb, which corresponds to

the initial preferential growth node of a plant, and the initial value of

optimization Xbest equal to X0, and let Fbest that is used to save the

objective function value of the best solution Xbest be equal to f(X0),

namely, Xb = Xbest = X0 and Fbest = f(X0).

Step 5: For k=1: n (n is the number of tie lines)

Step 6: For j=1: m (m is the maximum number of possible switches for

kth tie line)

Step 7: Get a possible solution (configuration) Xp from basic point Xb

(initial or updated configuration) by replacing kth element in the basic

point Xb with jth possible switch of kth tie line.

Step 8: Calculate the corresponding objective function (power loss or

load balancing index) for Xp (new configuration).

Step 9: Check for limit constraints and if the objective function f(Xp) <

f(Xb), then save the Xp in feasible solution set, otherwise abandon the

possible solution Xp.

Step 10: From the set of all feasible solutions find the minimal

solution.

86

Step 11: Calculate the probabilities C1, C2, C3,…., Ck of feasible

solutions X1, X2, X3,…., Xk by using equation (3.1), which corresponds

to the morphactin concentration of the nodes of a plant.

Step 12: Calculate the accumulating probabilities ∑C1, ∑C2,………,∑Ck

of the solutions X1, X2, … Xk. Select a random number β from the

interval [0 1], β must belong to one of the intervals [0 ∑C1], [∑C1, ∑C2],

….,[∑Ck-1, ∑Ck], the accumulating probability of which is equal to the

upper limit of the corresponding interval, and in the next iteration this

will be the new basic point Xb, which corresponds to the new

preferential growth node of a plant for next step.

Step 13: Check for N>=Nmax, if yes go to next step else set N=N+1 and

go to step 6 by replacing Xb and Fbest with new growth point and its

corresponding objective function respectively.

Step 14: Print the results for the optimal configuration obtained.

Step 15: Stop.

5. 5 ILLUSTRATIVE EXAMPLES

The proposed method is demonstrated through two different cases.

Case-I: Three different systems consisting of 16, 33 and 69-node

radial distribution systems are tested to demonstrate the loss

reduction through network reconfiguration.

Case-II: Illustrates testing of the Load Balancing through network

reconfiguration of 2 different systems consisting of 33 and 69-node

radial distribution systems.

87

5.5.1 Case I

5.5.1.1 Example - 1

The line and load data of 16 node system is given in table C.1.

The results obtained from the PGSA for a 16 node system are

compared with the existing method [116] in table 5.1. The minimum

voltage is improved in PGSA. The average real power loss reduction is

8.86%. The convergence characteristics are shown in fig.5.3. The node

voltages are tabulated in table 5.2. The power losses are given in table

5.3. The voltage profile is shown in fig.5.4. The final configuration

arrived is shown in fig.5.5 (b).

Table5.1. Results of 16-node radial distribution networkreconfiguration for loss reduction

ItemInitial

Configuration

Final Configuration

Existingmethod

[116]

ProposedPGSA

Tie Switches 5,11,16 7,9,16 7, 9,16

Real Power Loss (kW) 511.44 466.1 466.13

Loss Reduction (%) - 8.85 8.86

Min. Voltage (pu) 0.9693 0.9716 0.9717

No. of Switches Changed - 2 2

Table5.2. Node voltages before and after reconfiguration for 16node system

NodeNo.

|V| (pu) beforeReconfiguration

|V| (pu) afterReconfiguration

1 1.0000 1.0000

2 1.0000 1.0000

3 1.0000 1.0000

88

4 0.9906 0.9907

5 0.9878 0.9879

6 0.9859 0.9860

7 0.9848 0.9849

8 0.9791 0.9814

9 0.9711 0.9734

10 0.9769 0.9899

11 0.9709 0.9879

12 0.9693 0.9717

13 0.9944 0.9923

14 0.9948 0.9907

15 0.9918 0.9897

16 0.9913 0.9891

Table5.3. Power loss before and after reconfiguration for 16 nodesystem

BranchNo.

Before Reconfiguration After Reconfiguration

Ploss (kW) Qloss (kVAr) Ploss (kW) Qloss (kVAr)

1 61.63 82.18 67.80 90.40

2 7.51 10.33 10.63 14.62

3 11.95 23.89 11.94 23.89

4 1.52 1.52 1.52 1.52

5 278.34 278.34 0.25 0.25

6 2.09 2.09 220.94 220.94

7 87.01 119.64 76.53 105.23

8 0.71 0.71 19.61 26.97

9 19.71 27.09 42.51 42.51

10 29.08 29.08 7.87 10.82

11 7.84 10.77 3.71 4.94

12 2.01 2.68 0.74 0.74

13 2.06 2.06 2.07 2.07

Total 511.44 590.38 466.13 544.9

89

Fig.5.3 Convergence characteristics of 16 node system

Fig.5.4 Voltage profile of 16 node radial distribution systembefore and after reconfiguration

(a) Initial Configuration (b) Final configurationFig.5.5 Reconfiguration of 16 node distribution system

90

5.5.1.2 Example - 2

The single line diagram of initial configuration of 33 node RDS is

shown in fig.5.6. The line and load data is tabulated in table C.2. The

node voltages and power loss before and after reconfiguration are

given in table 5.4 and table 5.5 respectively. The proposed PGSA

results are compared with the existing method [116] in the table 5.6.

The loss reduction is 31.39%, which is better compared to existing

method. The minimum voltage is 0.9381 whereas it is 0.9378 with the

existing method. The node voltages before and after reconfiguration

are shown in fig.5.7. The convergence characteristics are shown in

fig.5.8. The final configuration of the 33 node RDS obtained by PGSA

is shown in fig.5.8. It is seen that the PGSA is converged 94 times to

optimum solution.

Table5.4. Node voltages before and after reconfiguration of 33node system

Node No. |V| (pu) beforeReconfiguration

|V| (pu) afterReconfiguration

1 1.0000 1.0000

2 0.9970 0.9971

3 0.9830 0.9870

4 0.9755 0.9825

5 0.9681 0.9781

6 0.9499 0.9673

7 0.9462 0.9667

8 0.9414 0.9626

9 0.9351 0.9592

10 0.9290 0.9627

91

11 0.9282 0.9628

12 0.9269 0.9631

13 0.9208 0.9605

14 0.9185 0.9597

15 0.9171 0.9532

16 0.9157 0.9514

17 0.9137 0.9485

18 0.9132 0.9475

19 0.9965 0.9951

20 0.9929 0.9782

21 0.9922 0.9736

22 0.9916 0.9701

23 0.9794 0.9834

24 0.9727 0.9768

25 0.9694 0.9735

26 0.9478 0.9655

27 0.9452 0.9632

28 0.9337 0.9526

29 0.9254 0.9451

30 0.9220 0.9419

31 0.9178 0.9385

32 0.9169 0.9381

33 0.9166 0.9472

Table5.5. Power loss before and after reconfiguration of 33 nodesystem

BranchNo.

Before Reconfiguration After Reconfiguration

Ploss (kW) Qloss (kVAr) Ploss (kW) Qloss (kVAr)

1 12.24 6.33 11.87 6.14

2 51.79 26.38 26.79 13.65

3 0.16 0.15 2.26 2.16

4 0.83 0.75 18.06 16.27

92

5 0.10 0.12 4.23 4.94

6 0.04 0.06 1.18 1.56

7 19.90 10.14 5.62 5.62

8 3.18 2.17 1.24 0.89

9 5.14 4.06 1.74 1.74

10 1.29 1.01 0.45 0.33

11 18.70 9.52 0.48 0.65

12 37.12 33.02 0.15 0.12

13 1.91 6.33 0.02 0.02

14 2.60 1.32 2.15 2.15

15 3.33 1.69 0.03 0.01

16 11.30 6.86 0.46 0.36

17 7.83 6.82 0.08 0.10

18 3.90 1.98 0.01 0.00

19 1.59 1.58 7.55 3.84

20 0.21 0.25 3.16 2.16

21 0.01 0.02 5.10 4.03

22 4.84 1.60 1.28 1.00

23 4.18 3.00 6.65 3.39

24 3.56 2.52 13.19 11.39

25 0.55 0.18 0.06 0.21

26 0.88 0.29 2.23 1.14

27 2.69 2.10 2.84 1.45

28 0.73 0.96 9.60 8.46

29 0.36 0.32 6.62 5.77

30 0.28 0.21 3.25 1.65

31 0.25 0.34 1.09 1.08

32 0.05 0.04 0.12 0.14

TotalLoss

201.54 132.11 138.46 102.42

93

Table5.6. Results of 33-node radial distribution networkreconfiguration for loss reduction

ItemInitial

Configuration

Final Configuration

Existingmethod

[116]by PGSA

Tie Switches 33,34,35,36,37 7,9,14,37,32 7,14,9,32,37

Real Power

Loss (kW)201.54 139.55 138.46

Loss

Reduction

(%)

- 30.76 31.39

Min. Voltage

(pu)0.9132 0.9378 0.9381

No. of

Switches

Changed

- 4 4

Fig.5.6 Initial configuration of 33 node system

94

Fig.5.7 Voltage profile of 33 node radial distribution systembefore and after reconfiguration

Fig.5.8 Convergence characteristics of 33 node system

Fig.5.9 Final configuration of the 33 node system

95

5.5.1.3 Example – 3

The initial configuration of the 69 node system is shown in

fig.5.10. The line and load data is given in the table C.3. In table 5.7

the summary of results obtained by the PGSA for the 69 node system

is given. It is run for 100 times out of which PGSA converged to

optimum solution 94 times with an average loss reduction of 55.59%.

The convergence characteristics are shown in fig.5.11. The node

voltages before and after reconfiguration is given in table 5.8 and also

is shown in fig.5.12. The power losses are given in table 5.9. The

reconfigured 69 node radial distribution system is shown in fig.5.13.

Fig.5.10 Initial configuration of 69 node system

Table5.7. Results of 69-node radial distribution networkreconfiguration for loss reduction

ItemInitial

ConfigurationFinal Configurationby proposed PGSA

Tie switches 69,70,71,72,73 69,70,14,56,61

96

Real Power loss (kW) 224.44 99.62

Power loss reduction (%) - 55.59

Min. Voltage (pu) 0.9094 0.9428

No. of switches changed - 3

Fig.5.11 Convergence characteristics of 69 node system

Fig.5.12 Voltage profile of 69 node radial distribution system

before and after reconfiguration

97

Fig.5.13 Final configuration of the 69 node systemTable5.8. Node voltages before and after reconfiguration of 69

node system

NodeNo.

|V| (pu) beforeReconfiguration

|V| (pu) afterReconfiguration

1 1.0000 1.0000

2 1.0000 1.0000

3 0.9999 0.9999

4 0.9998 0.9999

5 0.9990 0.9997

6 0.9901 0.9975

7 0.9808 0.9954

8 0.9786 0.9947

9 0.9775 0.9945

10 0.9726 0.9917

11 0.9715 0.9912

12 0.9684 0.9900

13 0.9653 0.9898

14 0.9624 0.9898

15 0.9596 0.9802

16 0.9590 0.9792

98

17 0.9581 0.9774

18 0.9580 0.9773

19 0.9578 0.9761

20 0.9575 0.9752

21 0.9569 0.9739

22 0.9569 0.9738

23 0.9569 0.9734

24 0.9566 0.9723

25 0.9565 0.9703

26 0.9565 0.9694

27 0.9563 0.9689

28 0.9999 0.9999

29 0.9998 0.9999

30 0.9997 0.9997

31 0.9997 0.9997

32 0.9996 0.9996

33 0.9994 0.9993

34 0.9992 0.9990

35 0.9990 0.9989

36 0.9999 0.9999

37 0.9997 0.9990

38 0.9996 0.9980

39 0.9996 0.9977

40 0.9995 0.9977

41 0.9988 0.9914

42 0.9987 0.9888

43 0.9985 0.9884

44 0.9985 0.9883

45 0.9984 0.9874

46 0.9984 0.9874

47 0.9998 0.9997

99

48 0.9986 0.9964

49 0.9948 0.9854

50 0.9942 0.9828

51 0.9788 0.9947

52 0.9788 0.9947

53 0.9747 0.9944

54 0.9716 0.9943

55 0.9669 0.9942

56 0.9627 0.9942

57 0.9402 0.9942

58 0.9291 0.9523

59 0.9248 0.9523

60 0.9197 0.9484

61 0.9126 0.9428

62 0.9124 0.9628

63 0.9118 0.9628

64 0.9112 0.9630

65 0.9094 0.9654

66 0.9715 0.9911

67 0.9715 0.9911

68 0.9679 0.9896

69 0.9679 0.9896

Table5.9. Power loss before and after reconfiguration of 69 nodesystem

BranchNo.

Before Reconfiguration After ReconfigurationPloss (kW) Qloss (kVAr) Ploss (kW) Qloss (kVAr)

1 0.08 0.18 0.07 0.17

2 0.08 0.18 0.07 0.17

3 0.20 0.47 0.12 0.30

4 0.00 0.00 0.00 0.00

5 0.00 0.00 0.03 0.07

6 0.02 0.04 0.42 1.02

100

7 0.02 0.02 0.64 0.75

8 0.01 0.01 0.19 0.22

9 0.00 0.00 0.01 0.01

10 0.05 0.06 3.93 4.59

11 0.02 0.02 1.67 1.95

12 0.00 0.00 0.22 0.26

13 0.00 0.00 0.05 0.06

14 0.01 0.01 0.58 0.73

15 0.00 0.00 0.00 0.01

16 0.00 0.01 4.25 4.25

17 0.01 0.00 0.84 0.28

18 0.00 0.00 1.38 0.46

19 0.01 0.00 0.01 0.00

20 0.01 0.00 0.81 0.27

21 0.01 0.00 0.52 0.17

22 0.00 0.00 0.84 0.28

23 1.94 2.27 0.02 0.01

24 0.02 0.06 0.23 0.07

25 0.58 1.43 0.49 0.16

26 1.63 4.00 0.91 0.30

27 0.12 0.28 0.37 0.12

28 28.30 14.41 0.19 0.06

29 28.40 14.98 1.03 1.03

30 6.91 7.10 0.71 0.36

31 3.38 2.92 0.01 0.00

32 0.00 0.00 0.00 0.00

33 0.00 0.00 0.00 0.01

34 4.79 1.58 0.01 0.00

35 5.79 2.95 0.00 0.00

36 6.73 3.43 0.01 0.00

37 9.14 4.66 0.01 0.00

38 8.81 4.49 0.01 0.00

101

39 49.78 16.71 0.00 0.00

40 24.54 8.23 0.11 0.13

41 9.52 3.15 0.17 0.41

42 10.69 3.25 4.19 10.25

43 14.05 7.16 13.29 32.52

44 0.11 0.06 2.55 6.25

45 0.14 0.07 38.24 38.24

46 0.66 0.34 0.00 0.00

47 0.04 0.02 6.33 1.92

48 1.02 0.34 8.32 4.24

49 2.20 0.73 1.59 0.81

50 0.00 0.00 1.64 0.84

51 0.00 0.00 0.35 0.36

52 1.29 0.43 0.12 0.11

53 0.02 0.01 0.00 0.00

54 0.00 0.00 0.00 0.00

55 1.25 0.41 1.43 0.47

56 1.21 0.40 0.01 0.00

57 0.22 0.07 0.00 0.00

58 0.32 0.11 0.00 0.00

59 0.00 0.00 0.00 0.00

60 0.10 0.03 0.00 0.00

61 0.07 0.02 0.29 0.09

62 0.11 0.04 0.32 0.11

63 0.00 0.00 0.00 0.00

64 0.01 0.00 0.00 0.00

65 0.01 0.00 0.00 0.00

66 0.01 0.00 0.02 0.01

67 0.00 0.00 0.00 0.00

68 0.00 0.00 0.00 0.00

TotalLoss 224.44 107.14 99.62 114.9

102

5.5.2 Case II

5.5.2.1 Example – 1

The proposed method for load balancing is tested on 33 node

radial distribution system shown in fig.5.6. The node voltages and

power loss before and after load balancing is given in tables 5.10 and

5.11 respectively. The summary of results obtained from the PGSA is

given in table 5.12. The minimum voltage is improved from 0.9132 pu

to 0.9171 pu. The configuration of the 33 node system after load

balancing is shown in fig.5.14. The voltage profile and convergence

curves are shown in fig.5.15 and 5.16 respectively.

Table5.10. Node voltages of a 33 node system before and after

Load Balancing

NodeNo.

|V| (pu) before loadbalancing

|V| (pu) after loadbalancing

1 1.0000 1.0000

2 0.9970 0.9970

3 0.9830 0.9830

4 0.9755 0.9755

5 0.9681 0.9681

6 0.9499 0.9498

7 0.9462 0.9463

8 0.9414 0.9415

9 0.9351 0.9353

10 0.9291 0.9331

11 0.9282 0.9328

12 0.9269 0.9325

13 0.9208 0.9316

14 0.9185 0.9270

103

15 0.9171 0.9277

16 0.9157 0.9264

17 0.9137 0.9244

18 0.9132 0.9238

19 0.9965 0.9965

20 0.9929 0.9929

21 0.9922 0.9922

22 0.9916 0.9916

23 0.9794 0.9794

24 0.9727 0.9727

25 0.9694 0.9694

26 0.9478 0.9478

27 0.9452 0.9453

28 0.9337 0.9338

29 0.9254 0.9256

30 0.9220 0.9221

31 0.9178 0.9179

32 0.9169 0.9175

33 0.9166 0.9171

Table5.11. Power loss before and after Load balancing

BranchNo.

Before load balancing After load balancing

Ploss (kW) Qloss (kVAr) Ploss (kW) Qloss (kVAr)

1 12.24 6.33 12.20 6.31

2 51.79 26.38 51.61 26.29

3 0.16 0.15 0.16 0.15

4 0.83 0.75 0.83 0.75

5 0.10 0.12 0.10 0.12

6 0.04 0.06 0.04 0.06

7 19.90 10.14 19.80 10.09

8 3.18 2.17 3.18 2.17

9 5.14 4.06 5.14 4.06

104

10 1.29 1.01 1.29 1.01

11 18.70 9.52 18.60 9.48

12 37.12 33.02 38.05 32.85

13 1.91 6.33 1.89 6.26

14 2.60 1.32 2.60 1.32

15 3.33 1.69 3.33 1.69

16 11.30 6.86 11.30 9.96

17 7.83 6.82 7.83 6.82

18 3.90 1.98 3.89 1.98

19 1.59 1.58 1.59 1.57

20 0.21 0.25 0.21 0.25

21 0.01 0.02 0.01 0.02

22 4.84 1.60 4.77 1.58

23 4.18 3.00 4.11 2.95

24 3.56 2.52 0.49 0.35

25 0.55 0.18 2.64 2.63

26 0.88 0.29 0.09 0.08

27 2.69 2.10 0.28 0.20

28 0.73 0.96 0.25 0.33

29 0.36 0.32 0.05 0.04

30 0.28 0.21 0.05 0.02

31 0.25 0.34 0.05 0.02

32 0.05 0.04 0.05 0.04

TotalLoss 201.54 132.12 196.48 131.15

Table5.12. Summary results of 33-node system for load balancing

Item Before load balancing Proposed PGSA

Tie Switches 33,34,35,36,37 33,13,35,36,37

LB Index 0.9438 0.7543

LBsys Reduction (%) - 18.95

Minimum Voltage (pu) 0.9132 0.9171

105

Fig.5.14 Final configuration of 33 node distribution systemafter load balancing

Fig.5.15 Voltage profile of 33 node radial distribution systembefore and after load balancing

Fig.5.16 Convergence curve of 33 node radial distribution systembefore and after load balancing

106

5.5.2.2 Example – 2

Consider 69-node radial distribution network as shown in

fig.5.10. The results obtained from the PGSA are compared with GA

[90] in the table 5.13. The convergence characteristic is shown in

fig.5.17. The PGSA is converged to same solution for 95 times out of

100 times with an average system load balancing index of 0.5667,

whereas genetic algorithm is converged to solution for 59 times, with

an average system load balancing index of 0.6187. The network

diagram after load balancing is shown in fig.5.18. The node voltages

before and after load balancing is given in table 5.14 and also shown

in fig.5. 19. The power loss is given in table 5.15.

Table5.13. Results of 69-node system for load balancing

ItemBeforeload

balancing

After load balancing

GA [90] PGSA

Tie Switches69, 70, 71,

72, 7310,20,13,57,25

10,20,13,58,

25

LB Index 0.9438 0.6187 0.5699

LBsys Reduction (%) - 32.51 37.39

No. of Switches

Changed- 5 5

No. of times best

solution occurred- 59 95

Average execution

time (seconds)- 45.7687 27.3468

107

Fig.5.17 Convergence characteristics of 69 node system for loadbalancing

Fig.5.18 Final configuration of 69 node distribution system afterload balancing

Fig.5.19 Voltage profile of 69 node distribution system before andafter load balancing

108

Table5.14. Node voltages of 69 node system before and after Load

Balancing

NodeNo.

|V| (pu) before loadbalancing

|V| (pu) after loadbalancing

1 1.0000 1.0000

2 1.0000 1.0000

3 0.9999 0.9999

4 0.9998 0.9999

5 0.9990 0.9998

6 0.9901 0.9989

7 0.9808 0.9980

8 0.9786 0.9978

9 0.9775 0.9977

10 0.9726 0.9976

11 0.9715 0.9848

12 0.9684 0.9828

13 0.9653 0.9816

14 0.9624 0.9856

15 0.9596 0.9856

16 0.9590 0.9854

17 0.9581 0.9850

18 0.9581 0.9850

19 0.9578 0.9850

20 0.9575 0.9850

21 0.9569 0.9808

22 0.9569 0.9808

23 0.9569 0.9807

24 0.9566 0.9807

25 0.9565 0.9807

26 0.9565 0.9245

27 0.9563 0.9243

109

28 0.9999 0.9999

29 0.9998 0.9999

30 0.9997 0.9997

31 0.9997 0.9997

32 0.9996 0.9996

33 0.9994 0.9993

34 0.9992 0.9990

35 0.9990 0.9989

36 0.9999 0.9999

37 0.9997 0.9989

38 0.9996 0.9979

39 0.9996 0.9976

40 0.9995 0.9976

41 0.9988 0.9909

42 0.9987 0.9881

43 0.9985 0.9877

44 0.9985 0.9877

45 0.9984 0.9874

46 0.9984 0.9874

47 0.9998 0.9997

48 0.9986 0.9958

49 0.9948 0.9827

50 0.9942 0.9796

51 0.9788 0.9978

52 0.9788 0.9978

53 0.9747 0.9977

54 0.9716 0.9976

55 0.9669 0.9975

56 0.9627 0.9975

57 0.9402 0.9975

58 0.9291 0.9975

59 0.9248 0.9407

110

60 0.9197 0.9357

61 0.9126 0.9282

62 0.9124 0.9279

63 0.9118 0.9275

64 0.9112 0.9255

65 0.9094 0.9246

66 0.9715 0.9848

67 0.9715 0.9848

68 0.9679 0.9825

69 0.9679 0.9825

Table5.15. Power loss before and after Load balancing for 69 nodedistribution system

BranchNo.

Before load balancing After load balancing

Ploss (kW) Qloss (kVAr) Ploss (kW) Qloss (kVAr)

1 0.08 0.18 0.07 0.18

2 0.08 0.18 0.07 0.18

3 0.20 0.47 0.12 0.30

4 0.00 0.00 0.00 0.00

5 0.00 0.00 0.03 0.08

6 0.02 0.04 0.46 1.13

7 0.02 0.02 0.71 0.83

8 0.01 0.01 0.21 0.24

9 0.00 0.00 0.01 0.01

10 0.05 0.06 4.40 5.13

11 0.02 0.02 1.86 2.18

12 0.00 0.00 0.25 0.29

13 0.00 0.00 0.01 0.01

14 0.01 0.01 1.41 1.41

15 0.00 0.00 0.88 0.29

16 0.00 0.01 0.00 0.00

17 0.01 0.00 0.00 0.00

111

18 0.00 0.00 0.24 0.08

19 0.01 0.00 0.02 0.01

20 0.01 0.00 0.00 0.00

21 0.01 0.00 0.11 0.11

22 0.00 0.00 0.00 0.00

23 1.94 2.27 0.00 0.00

24 0.02 0.06 0.00 0.00

25 0.58 1.43 0.00 0.00

26 1.63 4.00 0.06 0.08

27 0.12 0.28 0.00 0.00

28 28.30 14.41 0.27 0.27

29 28.41 14.98 0.00 0.00

30 6.91 7.10 0.05 0.02

31 3.38 2.92 0.05 0.02

32 0.00 0.00 0.00 0.00

33 0.00 0.00 0.00 0.00

34 4.79 1.58 0.00 0.00

35 5.79 2.95 0.00 0.01

36 6.73 3.43 0.01 0.00

37 9.14 4.66 0.00 0.00

38 8.81 4.49 0.01 0.00

39 49.78 16.71 0.01 0.00

40 24.54 8.23 0.01 0.00

41 9.52 3.15 0.00 0.00

42 10.69 3.25 0.02 0.02

43 14.05 7.16 0.23 0.57

44 0.11 0.06 5.77 14.13

45 0.14 0.07 18.52 45.31

46 0.66 0.34 3.79 9.28

47 0.04 0.02 62.44 62.44

48 1.02 0.34 10.68 3.24

49 2.20 0.73 14.04 7.15

112

50 0.00 0.00 0.13 0.07

51 0.00 0.00 0.16 0.08

52 1.29 0.43 0.77 0.39

53 0.02 0.01 0.09 0.04

54 0.00 0.00 0.01 0.01

55 1.25 0.41 0.00 0.00

56 1.21 0.40 0.26 0.13

57 0.22 0.07 0.27 0.14

58 0.32 0.11 0.05 0.05

59 0.00 0.00 0.01 0.01

60 0.10 0.03 0.00 0.00

61 0.07 0.02 0.00 0.00

62 0.11 0.04 0.01 0.00

63 0.00 0.00 0.01 0.00

64 0.01 0.00 0.00 0.00

65 0.01 0.00 0.00 0.00

66 0.01 0.00 0.00 0.00

67 0.00 0.00 0.00 0.00

68 0.00 0.00 0.00 0.00

TotalLoss 224.45 107.14 128.59 155.92

5.6 CONCLUSIONS

In this chapter, the PGSA has been proposed to reconfigure

distribution network for loss reduction and/or to keep load balancing.

The problem is formulated as a non-linear optimization problem with

an objective function of minimizing system losses and/or load

balancing index subject to security constraints. The test results have

been presented for loss minimization and/or load balancing through

the network reconfiguration.