Real power loss diminution by camelopard optimization algorithm

Real power loss diminution by camelopard optimization algorithm

Kanagasabai Lenin 

Department of EEE, Prasad V.Potluri Siddhartha, Institute of Technology, Kanuru, Vijayawada, Andhra Pradesh 520007, India

Corresponding Author Email: 
knlenin@gmail.com
Page: 
601-616
|
DOI: 
https://doi.org/10.3166/EJEE.20.601-616
Received: 
|
Accepted: 
|
Published: 
31 December 2018
| Citation

OPEN ACCESS

Abstract: 

 In this work Camelopard optimization Algorithm (COA) has been formulated &utilized for solving the optimal reactive power problem. Activities of Camelopard & itsSocial hierarchies are imitated to formulate this algorithm. Normally males use necking, and as a weapon in assaut portion. Among mammals, the tallest living terrestrial animal and it possess the largest ruminants. It has special approach to explore the grass land in quick mode& this aspect has been utilized in the formulation of the algorithm. Efficiency of the projected Camelopard optimization Algorithm (COA) is validated by evaluating in standard IEEE 30, 57, 118, 300 bus test systems. Also by considering the voltage stability evaluation the proposed algorithm has been tested in standard IEEE 30 bus system simulated outcomes shows that genuine power loss has been reduced considerably with variables are in the limits.

Keywords: 

 optimal reactive power, transmission loss, camelopard optimization algorithm

1. Introduction

Real power loss reduction is the main aspect in this problem. Reactive power optimization plays a dominant role in power system operation & control. Reactive power and voltage control are one of the ancillary services to maintain voltage profile through injecting or absorbing reactive power in electricity market (Genco et al., 2018). Various techniques problem (Lee et al., 1984; Deeb and Shahidehpour, 1988; Bjelogrlic et al., 1990; Granville 1994; Grudinin, 1998; Yan et al., 2006) have been utilized but have the complexity in handling constraints. Different types of evolutionary optimization algorithms (Aparajita et al., 2015; Hu et al., 2010; Mahaletchumi et al., 2015; Sulaiman et al., 2015; Pandiarajan et al., 2016; Mahaletchumi et al., 2016; Rebecca et al., 2016; Genco et al., 2017) have been utilized in various stages to solve the problem. But evolutionary algorithms are also stuck into local optimal solution. In this work Camelopard optimization Algorithm (COA) is applied for solving reactive power optimization problem. As herds Camelopards live with related females & offspring, but bachelor herds of adult males are gathered in large aggregations in the grass lands. Social hierarchies are established by males through necking, is used as a weapon in combat bout. Special tactic of searching the grass land in fast mode has been utilized in the formulation of the algorithm. Projected Camelopard optimization Algorithm (COA) efficiency has been verified by testing it in standard IEEE 30, 57, 118,300 bus test systems. Also by considering the voltage stability evaluation the proposed algorithm has been tested in standard IEEE 30 bus system. Simulation output shows that real power loss has been reduced & control variables are within the limits.

2. Problem formulation

Modal analysis for voltage stability evaluation

Power flow equations of the steady state system is given by,

$\left[ \begin{array} { c } { \Delta \mathrm { P } } \\ { \Delta \mathrm { Q } } \end{array} \right] = \left[ \begin{array} { l } { \mathrm { J } _ { \mathrm { p } \theta } \mathrm { J } _ { \mathrm { pv } } } \\ { \mathrm { J } _ { \mathrm { q } \theta } \mathrm { J } _ { \mathrm { QV } } } \end{array} \right] \left[ \begin{array} { l } { \Delta \theta } \\ { \Delta V } \end{array} \right]$   (1)

Where

ΔP = bus real powerchange incrementally.

ΔQ = bus reactive Power injectionchange incrementally.

Δθ = bus voltage angle change incrementally.

ΔV = bus voltage Magnitudechange incrementally.

Jpθ, JPV, JQθ, JQV are sub-matrixes of the System voltage stability in jacobian matrix and both P and Q get affected by this.

Presume ΔP = 0, then equation (1) can be written as:

$\left.\Delta \mathrm { Q } = \left[ \mathrm { J } _ { \mathrm { QV } } - \mathrm { J } _ { \mathrm { Q } \theta } \mathrm { J } _ { \mathrm { P } \mathrm { \theta } ^ { - 1 } } \right] _ { \mathrm { PV } } \right] \Delta \mathrm { V } = \mathrm { J } _ { \mathrm { R } } \Delta \mathrm { V }$        (2)

$\Delta \mathrm { V } = \mathrm { J } ^ { - 1 } - \Delta \mathrm { Q }$   (3)

Where

$\mathrm { J } _ { \mathrm { R } } = \left( \mathrm { J } _ { \mathrm { QV } } - \mathrm { J } _ { \mathrm { Q } \theta } \mathrm { J } _ { \mathrm { P } \theta ^ { - 1 } } \mathrm { JPV } \right)$      (4)

JR denote the reduced Jacobian matrix of the system.

2.1. Modes of voltage instability

Voltage Stability characteristics of the system have been identified through computation of the Eigen values and Eigen vectors.

$\mathrm { J } _ { \mathrm { R } } = \xi \wedge \mathrm { \eta }$   (5)

Where,

ξ denote the  right eigenvector matrix of JR, ηdenote the  left eigenvector matrix of JR, ∧ denote the  diagonal eigenvalue matrix of JR.

$\mathrm { J } _ { \mathrm { R } ^ { - 1 } } = \xi ^ { - 1 } \mathrm { \eta }$   (6)

From the equations (5) and (6),

$\Delta \mathrm { V } = \xi \wedge ^ { - 1 } \eta \Delta \mathrm { Q }$  (7)

or

$\Delta \mathrm { V } = \sum _ { \mathrm { I } } \frac { \mathfrak { \xi} _ { 1 } \eta _ { \mathrm { i } } } { \lambda _ { \mathrm { i } } } \Delta \mathrm { Q }$    (8)

ξi denote the ith column right eigenvector & η is the ith row left eigenvector of JR.

λi indicate the ith Eigen value of JR.

reactive power variation ofthe ith modalis given by,

$\Delta \mathrm { Q } _ { \mathrm { mi } } = \mathrm { K } _ { \mathrm { i } } \xi _ { \mathrm { i } }$  (9)

where,

$\mathrm { K } _ { \mathrm { i } } = \Sigma _ { \mathrm { j } } \xi _ { \mathrm { ij } ^ { 2 } } - 1$    (10)

Whereξji is the jth element of ξi

ith modal voltage variation is mathematically given by,

$\Delta \mathrm { V } _ { \mathrm { mi } } = \left[ 1 / \lambda _ { \mathrm { i } } \right] \Delta \mathrm { Q } _ { \mathrm { mi } }$    (11)

When the value of |λi| =0 then the ith modal voltage will get collapsed.

In equation (8), when ΔQ = ek  is assumed ,then ek has all its elements zero except the kth one being 1. Then

 can be formulated as follows,

$\Delta \mathrm { V } = \sum _ { \mathrm { i } } \frac { \mathrm { n } _ { 1 \mathrm { k } } \xi _ { 1 } } { \lambda _ { 1 } }$     (12)

$\eta_{1k}$ is k th element of $\eta_1$

At bus k V –Q sensitivity is given by,

$\frac { \partial \mathrm { v } _ { \mathrm { K } } } { \partial \mathrm { Q } _ { \mathrm { K } } } = \sum _ { \mathrm { i } } \frac { \eta _ { 1 \mathrm { k } } \xi _ { 1 } } { \lambda _ { 1 } } = \sum _ { \mathrm { i } } \frac { \mathrm { P } _ { \mathrm { ki } } } { \lambda _ { 1 } }$     (13)

Minimization of actual power loss and augmentation of static voltage stability margin index (SVSM) is main key to solve optimal reactive power dispatch problem. Voltage stability evaluation has been done through modal analysis method.

2.2. Minimization of real power loss

Real power loss (Ploss) minimization is given as,

$\mathrm { P } _ { \text {loss } } = \sum _ { \mathrm { k } = ( \mathrm { i } , \mathrm { j } ) } ^ { \mathrm { n } } \mathrm { g } _ { \mathrm { k } \left( \mathrm { V } _ { \mathrm { i } } ^ { 2 } + \mathrm { V } _ { \mathrm { j } } ^ { 2 } - 2 \mathrm { V } _ { \mathrm { i } } \mathrm { V } _ { \mathrm { j } } \cos \theta _ { \mathrm { ij } } \right) }$   (14)

Where n is the number of transmission lines, gk is the conductance of branch k, Vi and Vj are voltage magnitude at bus i and bus j, and θij is the voltage angle difference between bus i and bus j.

2.3. Minimization of voltage deviation

Formula for reducing the voltage deviation magnitudes (VD) is derived as follows,

Minimize $\mathrm { VD } = \sum _ { \mathrm { k } = 1 } ^ { \mathrm { nl } } \left| \mathrm { V } _ { \mathrm { k } } - 1.0 \right|$    (15)

Where nl is the number of load busses and Vk is the voltage magnitude at bus k.

2.4. System constraints

Load flow equality constraints:

$\mathrm { P } _ { \mathrm { Gi } } - \mathrm { P } _ { \mathrm { Di } } - \mathrm { V } _ { \mathrm { i } } \sum _ { \mathrm { j } = 1 } ^ { \mathrm { nb } } \mathrm { v } _ { \mathrm { j } } \left[ \begin{array} { c c } { \mathrm { G } _ { \mathrm { ij } } } & { \cos \theta _ { \mathrm { ij } } } \\ { + \mathrm { B } _ { \mathrm { ij } } } & { \sin \theta _ { \mathrm { ij } } } \end{array} \right] = 0 , \mathrm { i } = 1,2 \ldots , \mathrm { nb }$     (16)

$\mathrm { P } _ { \mathrm { Gi } } - \mathrm { P } _ { \mathrm { Di } } - \mathrm { V } _ { \mathrm { i } } \sum _ { \mathrm { j } = 1 } ^ { \mathrm { nb } } \mathrm { v } _ { \mathrm { j } } \left[ \begin{array} { c c } { \mathrm { G } _ { \mathrm { ij } } } & { \sin \theta _ { \mathrm { ij } } } \\ { + \mathrm { B } _ { \mathrm { ij } } } & { \cos \theta _ { \mathrm { ij } } } \end{array} \right] = 0 , \mathrm { i } = 1,2 \ldots , \mathrm { nb }$    (17)

where, nb is the number of buses, PG and QG are the real and reactive power of the generator, PD and QD are the real and reactive load of the generator, and Gij and Bij are the mutual conductance and susceptance between bus i and bus j.

$\mathrm { V } _ { \mathrm { Gi } } ^ { \min } \leq \mathrm { V } _ { \mathrm { Gi } } \leq \mathrm { V } _ { \mathrm { Gi } } ^ { \max } , \mathrm { i } \in \mathrm { ng }$   (18)

$V _ { \mathrm { Li } } ^ { \min } \leq V _ { \mathrm { Li } } \leq V _ { \mathrm { Li } } ^ { \max } , \mathrm { i } \in \mathrm { nl }$    (19)

$\mathrm { Q } _ { \mathrm { Ci } } ^ { \min } \leq \mathrm { Q } _ { \mathrm { Ci } } \leq \mathrm { Q } _ { \mathrm { Ci } } ^ { \max } , \mathrm { i } \in \mathrm { nc }$       (20)

$\mathrm { Q } _ { \mathrm { Gi } } ^ { \min } \leq \mathrm { Q } _ { \mathrm { Gi } } \leq \mathrm { Q } _ { \mathrm { Gi } } ^ { \max } , \mathrm { i } \in \mathrm { ng }$   (21)

$\mathrm { T } _ { \mathrm { i } } ^ { \mathrm { min } } \leq \mathrm { T } _ { \mathrm { i } } \leq \mathrm { T } _ { \mathrm { i } } ^ { \mathrm { max } } , \mathrm { i } \in \mathrm { nt }$      (22)

$S _ { \mathrm { Li } } ^ { \min } \leq S _ { \mathrm { Li } } ^ { \max } , \mathrm { i } \in \mathrm { nl }$   (23)

3. Camelopard optimization algorithm

As herds Camelopards live with related females & offspring, adult males are in bachelor are in the grass lands in large proposition mode. Social hierarchies are established by males through necking, is used as a weapon in combat bout. Chief distinguishing characteristics are its extremely long neck and legs, its horn-like ossicones, and its distinctive coat patterns. The sole responsibility for raising the young in the herd is by Dominant males.

Special tactic of searching the grass land in fast mode has been utilized in the formulation of the algorithm. In the problem space Camelopard is a 1XNvar array & the array can be defined by,

camelopardfe$= \left[ X _ { 1 } , X _ { 2 } , X _ { 3 } , \ldots , X _ { N _ { v a r } } \right]$  (24)

For each Camelopard the function value can be determined by,

Value $= \mathrm { f } ( \text { Camelopard } ) = \mathrm { f } \left( X _ { 1 } , X _ { 2 } , X _ { 3 } , \ldots , X _ { N a r } \right)$    (25)

Self-regulating nature of Camelopard has been incorporated into the modeled Camelopard optimization Algorithm (COA) & written in Equation (26).

$\mathrm { g } _ { \mathrm { k } + 1 } = \mathrm { g } _ { \mathrm { k } } + \mathrm { r } _ { \mathrm { m } 1 } \mathrm { p } _ { 1 } \left( \mathrm { lo } _ { \mathrm { max } } - \mathrm { n } _ { \mathrm { k } } \right) + \mathrm { r } _ { \mathrm { m } 2 } \mathrm { p } _ { 2 } \left( \mathrm { If } _ { \mathrm { max } } - \mathrm { n } _ { \mathrm { k } } \right)$      (26)

Exploration mentioned by gk, exploitation by nk, learning factors are given by

 rm1, rm2, p1, p2 are denoting arbitrary numbers.

Lead Camelopard will be act as an interface with abundant Camelopards as indicated in (equation (26)), there will be a comparison between each Camelopard. Movement to various locations by the Camelopard is articulated by following equation,

$\mathrm { n } _ { \mathrm { k } + 1 } = \lambda \left( \mathrm { g } _ { \mathrm { k } } + \mathrm { n } _ { \mathrm { k } } \right)$    (27)

Fitness of each Camelopard will be computed, lqmax(individual Camelopard location), lsmax(best location of the Camelopard herd) will be found. Fitness of the current is better than (lqmax) location vector then that particular value will be saved. Equations (26), (27) utilized to control the movement of the Camelopard. lsmax, lqmaxboth play lead role in the search other & movement to other areas in search is controlled by equation (26). From the maximum vector

 is subtracted & it will be multiplied by an arbitrary number ,  in the range between 0.00, 0.59 by learning parameter rm1, rm2.

Camelopard optimization Algorithm (COA)

Step a; Initialization

Step b; In solution space Camelopards are initiated in arbitrary mode

Step c; By using equation (26) fitness values are calculated

Step d; By using equation (27) location of the Camelopards are calculated

Step e; when lsmax updating; if yes next step otherwise goes to step b

Step f; when stop criterion is not met, then go back to step c

Step g; optimized value is output

4. Simulation results

Camelopard optimization Algorithm (COA) is tested in standard IEEE 30-bus system. In Table 1control variables are given.

Table 1. Limits

 

Min

Limit

Max

Limit

Generator Bus value

0.95000

1.100

Load Bus value

0.95000

1.0500

Transformer-Tap value

0.9000

1.100

Shunt Reactive Compensator value

-0.1100

0.310

Power limits of the generators are listed in table 2.

Table 2. Generators power limits

Bus

Pg

Pgminimum

Pgmaximum

Qgminimum

Qgmaximum

1

96.000

49.000

200.000

0.000

10.000

2

79.000

18.000

79.000

-40.000

50.000

5

49.000

14.000

49.000

-40.000

40.000

8

21.000

11.000

31.000

-10.000

40.000

11

21.000

11.000

28.000

-6.000

24.000

13

21.000

11.000

39.000

-6.000

24.000

Control variables obtained after optimization given in table 3.COA performance presented in table 4. Comparison of active power loss is given in table 5. Fig 1 gives comparison of real power loss

Table 3. Values of control variable after optimization

Parameters

COA

 

Voltage at 1

1.041200

Voltage at 2

1.041340

Voltage at 5

1.020720

Voltage at 8

1.030180

Voltage at 11

1.070130

Voltage at 13

1.050420

T;4,12

0.0000

T;6,9

0.0000

T;6,10

0.9000

T;28,27

0.9000

Q;10

0.1000

Q;24

0.1000

Value of Real power loss (MW)

4.1024

Value of Voltage deviation

0.9080

Table 4. COA performance

Total number of Iterations

21

Total Time taken

4.97

Value of Real power loss (MW)

4.1024

Table 5. Evaluation of outcome

List of Techniques

Real power loss (MW)

Method SGA (Wu et al., 1998)

4.9800

Method PSO (Zaho et al., 2005)

4.926200

Method LP (mahadevan et al., 2010)

5.98800

Method EP (mahadevan et al., 2010)

4.96300

Method CGA (mahadevan et al., 2010)

4.98000

Method AGA (mahadevan et al., 2010)

4.92600

Method CLPSO (mahadevan et al., 2010)

4.720800

Method HSA (Khazali et al., 2011)

4.762400

Method BB-BC (sakthivel et al., 2013)

4.69000

Method MCS (Tejaswini et al., 2016)

4.8723100

Proposed COA

4.10240

Figure 1. Comparison of real power loss

Table 6. Generator data

Generator No

Pgi minimum

Pgi maximum

Qgi minimum

Qgi maximum

1

25.000

50.000

0.000

0.000

2

15.00

90.00

-17.00

50.00

3

10.00

500.00

-10.00

60.00

4

10.00

50.00

-8.00

25.00

5

12.00

50.00

-140.00

200.00

6

10.00

360.00

-3.00

9.00

7

50.00

550.00

-50.00

155.00

Table 7. Comparison of losses

 

Method CLPSO

(Dai et al., 2009)

Method DE

(Basu et al., 2016)

Method GSA

(Basu et al., 2016)

Method OGSA

(Shaw et al., 2014)

Method SOA

(Dai et al., 2009)

Method QODE

(Basu et al., 2016)

COA

PLOSS (MW)

24.5152

16.7857

23.4611

23.43

24.2654

15.8473

13.086

Figure 2. Comparison of loss

Secondly IEEE 57 bus system is used as test system to validate the performance of the proposed algorithm. Total active and reactive power demands in the system are 1247.89 MW and 338.04 MVAR, respectively. Generator data the system is given in Table 6. The optimum loss comparison is presented in Table 7. Fig 2. Gives the comparaison of losses.

Table 8. Reactive power sources limits

Bus number

5

34

37

44

45

46

48

Maximum value of QC

0.000

14.000

0.000

10.000

10.000

10.000

15.000

Minimum value of QC

-40.000

0.000

-25.000

0.000

0.000

0.000

0.000

Bus number

74

79

82

83

105

107

110

Maximum value of QC

12.000

20.000

20.000

10.000

20.000

6.000

6.000

Minimum value of QC

0.000

0.000

0.000

0.000

0.000

0.000

0.000

Table 9. Evaluation of results

Active power loss – Minimum & Maximum values

Methodology - BBO

(Cao et al., 2014)

Methodology - ILSBBO/

strategy1

(Cao et al., 2014)

Methodology ILSBBO/

Strategy2

(Cao et al., 2014)

COA

Minimum value

128.770

126.980

124.780

124.872

Maximum value

132.640

137.340

132.390

129.734

Average value

130.210

130.370

129.220

126.864

Figure 3. Comparison of actual loss

Table 9. shows the comparaison of results.

Then IEEE 118 bus system is used as test system to validate the performance of the proposed algorithm. Table 8 shows limit values.

Finally IEEE 300 bus system is used as test system and Table10 shows the comparaison of real power loss.

With Considering Voltage Stability Evaluation Criterion in IEEE 30 bus system projected algorithm has been verified. Table 11 shows the optimal control variables.

Table 10. Comparison of real power loss

Parameter

Method EGA

(Reddy et al., 2014)

Method EEA

(Reddy et al., 2014)

COA

PLOSS (MW)

646.2998

650.6027

629.1898

Table 11. COA-ORPD based control variables

Parameter

value

voltage at 1

voltage at 2

voltage at 5

voltage at 8

voltage at 11

voltage at 13

value of T11

value of T12

value of T15

value of T36

value of Qc10

value of Qc12

value of Qc15

value of Qc17

value of Qc20

value of Qc23

value of Qc24

value of Qc29

Real power loss in MW

Value of SVSM

1.03142

1.03418

1.03192

1.02198

1.00032

1.02079

1.00114

1.00021

1.0021

1.0001

3.00

3.00

2.00

0.00

2.00

3.00

3.00

2.00

4.1248

0.2382

Static voltage stability index rises from 0.2382 to 0.2396.

In table 12 optimal (control variables) are given.

Figure 4. Comparison of  active power loss

Table 12. Value of COA -voltage stability control reactive power dispatch optimal control variables

Parameter

values

voltage at 1

voltage at 2

voltage at 5

voltage at 8

voltage at 11

voltage at 13

value of T11

value of T12

value of T15

value of T36

value of Qc10

value of Qc12

value of Qc15

value of Qc17

value of Qc20

value of Qc23

value of Qc24

value of Qc29

Real power loss in MW

Value of SVSM

1.03279

1.03184

1.03465

1.03254

1.00114

1.03012

0.09001

0.09000

0.09000

0.09000

3.00

3.00

2.00

3.00

0.00

2.00

2.00

3.00

4.9972

0.2396

In Table 13 Eigen values are given.

Table 13. Values of settings

Area of; Contingency

ORPD Setting values

VSCRPD Setting values

28-27

0.14100

0.14240

4-12

0.16380

0.16480

1-3

0.17610

0.17720

2-4

0.20220

0.20410

In table 14 values for limit violation checking has been given with upper & lower limits.

Table 14. Limits of violation

Parameter

Types of Limits values

Values of; ORPD

Values of; VSCRPD

Lower level

Upper

level

At Q1

-20.00

151.0

1.3421

-1.3261

At Q2

-20.00

61.00

8.9902

9.8230

At Q5

-15.00

49.920

25.926

26.000

At Q8

-10.00

63.520

38.8201

40.800

At Q11

-15.00

42.0

2.9309

5.001

At Q13

-15.00

48.0

8.1020

6.030

At V3

0.950

1.050

1.0371

1.0390

At V4

0.950

1.050

1.0304

1.0321

At V6

0.950

1.050

1.0287

1.0290

At V7

0.950

1.050

1.0100

1.0154

At V9

0.950

1.050

1.0466

1.0416

At V10

0.950

1.050

1.0480

1.0492

At V12

0.950

1.050

1.0402

1.0460

At V14

0.950

1.050

1.0476

1.0442

At V15

0.950

1.050

1.0458

1.0412

At V16

0.950

1.050

1.0420

1.0400

At V17

0.950

1.050

1.0384

1.0392

At V18

0.950

1.050

1.0396

1.0402

At V19

0.950

1.050

1.0382

1.0396

At V20

0.950

1.050

1.0110

1.0196

At V21

0.950

1.050

1.0434

1.0248

At V22

0.950

1.050

1.0446

1.0392

At V23

0.950

1.050

1.0476

1.0370

At V24

0.950

1.050

1.0488

1.0374

At V25

0.950

1.050

1.0140

1.0198

At V26

0.950

1.050

1.0490

1.0426

At V27

0.950

1.050

1.0478

1.0458

At V28

0.950

1.050

1.0246

1.0280

At V29

0.950

1.050

1.0432

1.0412

At V30

0.950

1.050

1.0414

1.0390

In table 15 over all comparison of real power loss has been given. It indicates that proposed algorithm efficiently reduced power loss. Fig 5. Gives Comparison of real power loss

Table 15. Comparison of losses

Technique

Loss value in  MW

Method; Evolutionary programming (Wu et al., 1995)

5.01590

Method; Genetic algorithm (Durairaj et al., 2006)

4.6650

Method; Real coded GA with Lindex as SVSM (Devaraj et al., 2007)

4.5680

Method; Real coded genetic algorithm (Aruna et al., 2010)

4.50150

Proposed COA

4.1248

Figure 5. Comparison of real power loss

5. Conclusion

In this work Camelopard optimization Algorithm (COA) efficiently solved the power problem. Mathematical modeling efficiently improved the search of the optimal solution. Both the exploration & exploitation has been comparatively increased in the proposed technique. Camelopard optimization Algorithm (COA) has performed well when evaluated in standard IEEE 30, 57, 118, 300 bus test systems. Also by considering the voltage stability evaluation the proposed algorithm has been successfully tested in standard IEEE 30 bus system. True power loss reduced considerably when compared to another standard algorithm.

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