Voltage Regulators Placement in Unbalanced Radial Distribution Systems for Loss Minimization Using Particle Swarm Optimization

ISSN 2349-7815

International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE) Vol. 1, Issue 3, pp: (11-22), Month: October - December 2014, Available at: www.paperpublications.org

Page | 11 Paper Publications

Voltage Regulators Placement in Unbalanced

Radial Distribution Systems for Loss

Minimization Using Particle Swarm

Optimization

Namrata Sahu

ME Control System, Department of Electrical Engineering, Jabalpur Engineering College, Jabalpur, INDIA

Abstract: The Automatic Voltage Regulators (AVRs) help to reduce energy loss and improve the power quality of

electric utilities. This paper presents selection of optimal location and tap setting for voltage regulators in

Unbalanced Radial Distribution Systems (URDS). Power loss index (PLI) is used for the selection of optimal

location of voltage regulators which will first found at each branch except source bus and the bus that has the

highest power loss index are picked as the best location for the voltage regulators placement. Particle swarm

optimization (PSO), is used for selecting the tap position of voltage regulator in an unbalanced radial distribution

system. This algorithm makes the initial selection and tap position setting of the voltage regulators to minimize

power losses and provide a good voltage profile along the distribution network and then reduce the total cost to

obtain the maximum net savings. The effectiveness of the proposed method is illustrated on a test system of IEEE

33 bus unbalanced radial distribution systems.

Keywords: Unbalanced Radial Distribution Systems (URDS), Load Flow, Power loss index(PLI),Particle swarm

optimization(PSO), Voltage Regulator placement, Loss minimization, cost saving.

I. INTRODUCTION

Distribution systems are the networks that transport the electrical energy from bulk substation to many services or loads.

Losses in a distribution system are significantly high compared to that in a transmission system. The need of improving

the overall efficiency of power delivery has forced the power utilities to reduce the losses at distribution level. By

minimizing the losses, the system may acquire longer life span and has greater reliability. Therefore after proper

installation of voltage regulator losses in the distribution system reduces and hence voltage profile also improved.

Voltage Regulator (VR) or Automatic Voltage Booster (AVB) is essentially an auto transformer consisting of a primary

or existing winding connected in parallel with the circuit and a secondary winding with taps connected in series with the

circuit. Taps of series winding are connected to an automatic tap changing mechanism.

A voltage regulator is a device that keeps a predetermined voltage in a distribution network despite of the load variations

within its rated power [1].In distribution systems operation, shunt capacitor banks and feeder regulators are necessary for

providing acceptable voltage profiles to all end-use customers and reducing power losses on large distribution systems

[2]. A voltage regulator is equipped with controls and accessories for its tap to be adjusted automatically under load

conditions. Moreover, it can be controlled by the installation of devices such as fixed and controlled capacitors banks,

transformers with On Load Tap Changers (OLTCs), and Automatic Voltage Regulators (AVRs) [3].

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1.1 Load Flow Solution

In any radial distribution system, the electrical equivalent of a branch 1, which is connected between nodes 1 and 2 having

impedance Z1 is shown in Figure. 1[C.L.Wadhwa, „Electrical power systems‟]

Figure.1 Electrical equivalent of a typical branch ‘1’

The voltage at source node is taken as 1.0 p.u. The voltage at node 2 is given by[7]

V2 = V1 – I1 Z1

In general Vn2 = V n1 – Ij Z j -- (1)

where „n1‟ and „n2‟ are sending and receiving ends of branch „j‟ respectively.

By using Eqn. (1), the voltage at any node (except node 1) can be calculated.

The load current at node „i‟ is calculated by

IL i = PL i+j QL i, for i = 2,3, ----,nn -- (2)

Vi

Where,

PL i = Real or Active power load at node i

QL i = Reactive power load at node i

nn= Number of nodes

The real and reactive power losses of branch „j‟ can be calculated as

LP j = Ij2 r j -- (3)

LQ j = Ij2 x j for j=1, 2, ----, nb. -- (4)

where nb= Number of branches

The current in each branch is calculated by applying KCL at node „2‟ shown in Figure 1 the branch current equation

obtained is as follows:

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I1= I2 +I5 +I7+IL2 -- (5)

From the above, the current can be calculated in any branch. Initially, a flat voltage profile is assumed at all nodes i.e., 1.0

p.u. Load currents are computed iteratively with the updated voltages at each node.

II. PROBLEM FORMULATION

In a distribution system with an ever increasing load demand there is reduction in voltage and hence power losses

increases. Therefore in order to maintain the constant voltage profile and to reduce the power losses, voltage regulators

are installed in the distribution system.

2.1 Optimal location of Automatic Voltage Regulators (AVR)

Voltage Regulator (VR) or Automatic Voltage Booster (AVB) is essentially an auto transformer consisting of a primary

or existing winding connected in parallel with the circuit and a second winding with taps connected in series with the

circuit. In order to maintain the voltage profile and to reduce the power losses these are installed in the distribution

systems [6].

• VR provides 10% boost of voltage

• It boosts voltage in four steps of 2.5% each and it also boosts voltage in 32 steps of 0.625% each.

• It has line drop compensation to maintain constant voltage at its location.

The optimal location of voltage regulator (AVR) is defined as function of two objectives, one representing power loss

reduction and the other one representing the voltage deviations but both are essential to secure the power supply.

The objective function to be minimized is given below

Minimize f = ∑ lossj

abc --(6)

Where, P loss jabc

is the active power loss in the jth branch after voltage regulator placement.

„nb‟ is the number of branches in the system.

2.2 Tap Position Selection

By finding the optimal number and location of Voltage regulators then tap positions of VR is to be determined as follows.

In general, VR position at node „i‟ can be calculated as [5]

V1

i = Vi ± tap× Vrated --(7)

Tap position (tap) can be calculated by comparing voltage obtained before VR installation with the lower and upper limits

of voltage

„+‟ for boosting of voltage

„-‟ for bucking of voltage

The node voltages are computed by load flow analysis, described in section 1.1

2.3 Candidate Node Identification using PLI

Power Loss Index (PLI) is power loss based approach to determine the suitable location for placement of voltage

regulators. After running the load flows, the total active power loss is given by 281.5877 kW. Therefore Power Loss

Index (PLI) are calculated as:

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PLI[j] = (Loss. reduction[j] -Min reduction) --(8)

(Max. reduction - Min. reduction)

2.4 Calculations for Net Savings

The maximum net savings after voltage regulator placement can be calculated is given below [4]

F = Ke× Plr ×8760 ×Lsf – KVR× N(α+β) --(9)

Where,

Plr = Reduction in power losses due to installation of VR

Ke = Cost of energy in Rs./kWh

Lsf= Loss factor = 0.2 Lf + 0.8 Lf2

Lf= Load factor

N = Number of VRs

KVR= Cost of each VR

α= Regulator Setting for resistance compensation

β = Regulator Setting for reactance compensation.

III. IMPLEMENTATION OF PSO

After calculating the total power losses by using load flow analysis and candidate node identification by power loss index,

the voltage regulator tap setting at candidate node of the unbalanced radial distribution system is selected using PSO.

3.1 Initialization of PSO Parameters

The control parameters such as lower and upper bounds of node voltage and tap setting of voltage regulators are selected

as initialize parameters. Randomly generate an initial swarm (array) of particles with random positions and velocities.

3.2 Evaluation of Fitness Function

The fitness function should be capable of reflecting the objective and directing the search towards optimal solution For

each particle or swarm, the voltage regulators are placed at the nodes and run the load flow to calculate the losses and

these losses becomes the fitness function of the PSO.

3.3 Optimal Solution

PSO simulates the behaviors of bird flocking. Suppose the following scenario: a group of birds are randomly searching

food in an area. There is only one piece of food in the area being searched. All the birds do not know where the food is,

But they know how far the food is in each iteration. So what's the best strategy to find the food? The effective one is to

follow the bird which is nearest to the food.

PSO learned from the scenario and used it to solve the optimization problems. In PSO, each single solution is a "bird" in

the search space. We call it "particle". All of particles have fitness values which are evaluated by the fitness function to be

optimized, and have velocities which direct the flying of the particles. The particles fly through the problem space by

following the current optimum particles.

PSO is initialized with a group of random particles (solutions) and then searches for optima by updating generations. In

every iteration, each particle is updated by following two "best" values. The first one is the best solution (fitness) it has

achieved so far. (The fitness value is also stored.) This value is called pbest. Another "best" value that is tracked by the

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particle swarm optimizer is the best value, obtained so far by any particle in the population. This best value is a global

best and called gbest.

The modification can be represented by the concept of velocity (modified value for the currentpositions). Velocity of each

particle can be modified by the following equation,

Vik+1

=WVik + C1 rand1 × (Pbesti − Xi

k) + C2 rand2 ×( Gbest – Xi

k ) --(10)

The rand1, rand2 are the two random numbers with uniform distribution with range of { 0.0 to 1.0 }

W is the inertia weight which shows the effect of previous velocity vector on the new vector.

A larger inertia weight „W‟ facilitates global exploration, while smaller inertia weight „W‟ tends to facilitates local

exploration to fine tune. where,

Vik: Velocity of particle i at iteration k,

Vik+1

: Modified velocity of particle i at iteration k+1,

W : Inertia weight,

C1, C2 : Acceleration Constants,

rand1, rand2 : Two random numbers

Xik: Current position of particle i at iteration k,

Pbesti : Pbesti of particle i,

Gbest : Gbest of the group.

In the equation (10),

The term rand1 × (Pbesti – Xik ) is called particle memory influence

The term rand 2×(Gbest – Xik) is called swarm influence.

W=Wmax - Wmax- Wmin × iter --(11)

itermax

Where,

Wmax: Initial value of the Inertia weight,

Wmin: Final value of the Inertia weight,

itermax : Maximum iteration number,

iter : current iteration number.

Accordingly, the optimal types and sizes of voltage regulators to be placed at each compensation node can be determined.

3.4 Algorithm for Optimal Location using PLI and Tap setting of VR using PSO

The detailed algorithm is to determine optimal location along with tap setting of voltage regulator is given below.

Step 1: Read system data such as line data and load data of distribution system.

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Step 2: Initialize the PSO parameters such as Number of Agents (M), Number of Particles (N), Number of Iterations

(Kmax), Initial value of Inertia weight (Wmax), Final value of Inertia weight (Wmin), Acceleration Constants (C1 & C2).

Step 3: Initialize the parameters as explained in section 5.

Step 4: Obtain the optimal location of VR by using PLI (Power Loss Index) as input.

Step 5: Initialize the swarm by assigning a random position and velocity in the problem hyperspace to each particle,

where each particle is a solution of tap setting of VR.

Step 6: Run the load flow and compute the fitness value of each particle using equation (10).

Step 7: Compare the present fitness value of ith particle with its historical best fitness value. If the present value is better

than Pbest updating the Pbest, else retain Pbest as same.

Step 8: Find the Gbest value from the obtained Pbest values.

Step 9: Update the particle positions & velocity using eqns. (10) & (11).

Step 10: Apply boundary conditions to the particles

Step 11: Execute steps 6-10 in a loop for maximum number of iterations (Kmax).

Step 12: Stop the execution and display the Gbest values as the final result for optimal tap setting of voltage regulator.

IV. RESULTS AND DISCUSSION

The PSO Parameter values for voltage regulator placement: Number of Particles (N) =10, Number of Iterations (Kmax)

=30, Initial value of the inertia weight (Wmax) =0.9 ,Final value of the inertia weight (Wmin) =0.4, Acceleration

constants, (C1 & C2)=4. The performance of the proposed algorithm is evaluated for test system of 11kV, 100MVA,33

bus URDS for voltage regulator placement. Proper allocation of VR gives minimum losses and improves voltage profile

of the system.The proposed method is illustrated with test system consisting of 33 bus URDS.

4.1 Case Study

Power loss indices for 33 bus URDS is shown in the Figure.2. The proposed algorithm is tested on IEEE 33 bus URDS

ans the single line diagram of IEEE 33 bus URDS is shown in Figure.3

Figure 2: Power loss indices for IEEE 33 bus URDS

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Branch Number

Pow

er

loss index

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Line and load data, active and reactive power flows are given in tables 1.Summary of test results of bus IEEE 33 bus

URDS for voltage regulator placement are given in table 2. Voltage, Power loss indices, Power loss values before VR

placement and Voltage, Power loss values and Tap setting of Voltage regulator of 33-node RDS after VR placement are

given in table 3.

From table 2 it is observed that the Active Power loss is reduced from 281.5877 kW to 171.8373 kW i.e, 38.97 % and

Reactive Power loss is reduced from 187.9595 kW to 114.0787 kW i.e, 39.30 % .The minimum voltage at node 18 is

0.8819 and after VR placement it is improved by 1.1133. The maximum net saving is Rs. 4383529.7838 after VRs

placement. Hence, there is an improvement in the minimum voltage, reduction in active and reactive power losses and

maximizing the net savings when compared with before and after voltage regulator placement.

Table. 1: Line data and Load data of IEEE 33 bus Radial Distribution System

Branch

Number

Sending

end bus

Receiving

end bus

Resistance

R (Ω)

Reactance

X (Ω)

Bus

Number

Active Power

PL (kW)

Reactive

Power

QL (kVAr)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

0.0922

0.4930

0.3660

0.3811

0.8190

0.1872

0.7114

1.0300

1.0440

0.1966

0.3744

1.4680

0.5416

0.5910

0.7463

1.2890

0.7320

0.0470

0.2511

0.1864

0.1941

0.7070

0.6188

0.2351

0.7400

0.7400

0.0650

0.1238

1.1550

0.7129

0.5260

0.5450

1.7210

0.5740

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

0

100

90

120

60

60

200

200

60

60

45

60

60

120

60

60

60

0

60

40

80

30

20

100

100

20

20

30

35

35

80

10

20

20

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18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

2

19

20

21

3

23

24

6

26

27

28

29

30

31

32

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

0.1640

1.5042

0.4095

0.7089

0.4512

0.8980

0.8960

0.2030

0.2842

1.0590

0.8042

0.5075

0.9744

0.3105

0.3410

0.1565

1.3554

0.4784

0.9373

0.3083

0.7091

0.7011

0.1034

0.1447

0.9337

0.7006

0.2585

0.9630

0.3619

0.5302

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

90

90

90

90

90

90

420

420

60

60

60

120

200

150

210

60

40

40

40

40

40

50

200

200

25

25

20

70

600

70

100

40

Table.2: Test results of 33-node system before and after VRs placement

Parameters

Before VRs

placement

After VRs placement

(VR at buses 2,5,27)

Reduction in %age

Total Active Power PL (kW) 281.5877 171.8373 38.97 %

Total Reactive Power QL(kVAr) 187.9595 114.0787 39.30 %

Minimum Voltage (p.u) 0.8819 1.1133 -

Voltage regulation 0.4418 0.2341 -

Net saving(Rs.) - 4383529.7838 -

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Figure.3: IEEE 33- Bus Radial Distribution Network

Table.3: Voltage, Power loss indices, Power loss values before VR placement and Voltage, Power loss values and

Tap setting of Voltage regulator of 33-node RDS after VR placement

Branch

No.

Bus

No. Before VR Placement After VR Placement at buses 2, 5,27

Voltage

(p.u)

Active

power

loss

P(kW)

Reactive

power

loss

Q(kVAr)

Power loss

index

(PLI)

Voltage

(p.u)

Active

power

loss

P(kW)

Reactive

power

loss

Q (kVAr)

Bus

No. to

place

VR

Tap

setting of

Voltage

regulato

r (p.u)

1

2

3

4

5

6

7

8

9

10

11

1

2

3

4

5

6

7

8

9

10

11

1.0000

0.9960

0.9770

0.9668

0.9568

0.9318

0.9271

0.9205

0.9119

0.9040

0.9028

16.8042

71.3939

27.6696

26.0406

53.2996

2.6787

6.7909

5.8918

5.0230

0.7815

1.2449

8.5661

36.3631

14.0918

13.2629

46.0108

8.8546

2.2442

4.2329

3.5604

0.2584

0.4116

0.2352

1.0000

0.3874

0.3646

0.7465

0.0373

0.0949

0.0823

0.0701

0.0107

0.0172

1.0000

1.0946

1.0793

1.0715

1.1723

1.1533

1.1494

1.1441

1.1373

1.1309

1.1300

11.1904

46.2350

16.3019

15.0653

30.7251

1.7128

4.3250

3.7341

3.1794

0.4942

0.7864

5.7044

23.5489

8.3024

7.6730

26.5234

5.6618

1.4293

2.6827

2.2536

0.1634

0.2600

2

5

15

17

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12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

0.9008

0.8924

0.8893

0.8874

0.8855

0.8828

0.8819

0.9953

0.9906

0.9896

0.9888

0.9722

0.9632

0.9588

0.9291

0.9257

0.9101

0.8989

0.8941

0.8883

0.8871

0.8867

3.7715

1.0322

0.5062

0.3993

0.3571

0.0754

0.2142

1.1081

0.1342

0.0581

4.2998

6.9559

1.7431

3.6496

4.6773

15.8975

11.0276

5.4873

2.2543

0.3017

0.0186

2.9674

1.3586

0.4505

0.2916

0.4768

0.0591

0.2044

0.9985

0.1568

0.0769

2.9380

5.4927

1.3640

1.8590

2.3814

14.0165

9.6070

2.7950

2.2279

0.3516

0.0290

0.0526

0.0142

0.0068

0.0053

0.0047

0.0008

0.0027

0.0153

0.0016

0.0006

0.0600

0.0972

0.0242

0.0509

0.0653

0.2225

0.1542

0.0766

0.0313

0.0040

0

1.1284

1.1217

1.1192

1.1177

1.1162

1.1139

1.1133

1.0939

1.0896

1.0887

1.0880

1.0749

1.0669

1.0628

1.1514

1.2651

1.2540

1.2460

1.2427

1.2385

1.2376

1.2373

2.3793

0.6507

0.3186

0.2512

0.2245

0.0474

0.1770

0.9155

0.1109

0.0480

3.5047

5.6673

1.4191

1.9061

2.4191

8.2091

5.6895

2.8287

1.1567

0.1547

0.0096

1.8720

0.8565

0.2836

0.1834

0.2997

0.0372

0.1689

0.8250

0.1295

0.0635

2.3948

4.4752

1.1104

0.9709

1.2317

7.2378

4.9566

1.4408

1.1432

0.1803

0.0149

27

18

Before voltage regulator placement

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After voltage regulator placement

Voltage comparison before and after VR placement

V. CONCLUSIONS

The proposed PSO based methodology was applied to IEEE 33 bus URDS. The obtained solution has succeeded in

reducing total active power loss 38.97 % in IEEE 33 bus URDS. From the test results, it is concluded that the proposed

model is valid and reliable .The power loss of unbalanced distribution system can be reduced by proper placement of

voltage regulator. In addition to power loss reduction, the voltage profile also improved by the proposed method and then

obtained the maximum net savings.

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pp. 185–193, 1996.

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