Optimal Compensation of Reactive Power in Transmission ... · 1 [email protected] 2 Sri Satya...

22
Optimal Compensation of Reactive Power in Transmission Networks using PSO, Cultural and Firefly Algorithms Subhash Shankar Zope 1 and 2 Dr. R.P. Singh 1 Sri Satya Sai University of Technology & Medical Sciences. Opposite OILFED, Bhopal Indore Highway, Pachama, Sehore (India) 466001 1 [email protected] 2 Sri Satya Sai University of Technology & Medical Sciences. Opposite OILFED, Bhopal Indore Highway, Pachama, Sehore (India) 466001 2 [email protected] Abstract Increased demand for electrical energy and free market economies for electricity exchange, have pushed power suppliers to pay a great attention to quality and cost of the latter, especially in transmission networks. To reduce power losses due to the high level of the reactive currents transit and improve the voltage profile in transmission systems, shunt capacitor banks are widely used. The problem to be solved is to find the capacitors optimal number, sizes and locations so that they maximize the cost reduction. This paper is constructed as a function of active and reactive power loss reduction as well as the capacitor costs. To solve this constrained non- linear problem, a heuristic technique, based on the sensitivity factors of the system power losses, has been proposed. The proposed algorithm has been applied to numerous feeders and the results International Journal of Pure and Applied Mathematics Volume 114 No. 9 2017, 367-388 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu 367

Transcript of Optimal Compensation of Reactive Power in Transmission ... · 1 [email protected] 2 Sri Satya...

Page 1: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Optimal Compensation of Reactive Power in Transmission Networks using PSO, Cultural and Firefly Algorithms

Subhash Shankar Zope1and 2Dr. R.P. Singh

1Sri Satya Sai University of

Technology & Medical Sciences. Opposite OILFED, Bhopal Indore Highway,

Pachama, Sehore (India) 466001

[email protected]

2 Sri Satya Sai University of

Technology & Medical Sciences.

Opposite OILFED, Bhopal Indore Highway,

Pachama, Sehore (India) 466001

2 [email protected]

Abstract

Increased demand for electrical energy and free

market economies for electricity exchange, have

pushed power suppliers to pay a great attention to

quality and cost of the latter, especially in

transmission networks. To reduce power losses

due to the high level of the reactive currents

transit and improve the voltage profile in

transmission systems, shunt capacitor banks are

widely used. The problem to be solved is to find

the capacitors optimal number, sizes and locations

so that they maximize the cost reduction. This

paper is constructed as a function of active and

reactive power loss reduction as well as the

capacitor costs. To solve this constrained non-

linear problem, a heuristic technique, based on

the sensitivity factors of the system power losses,

has been proposed. The proposed algorithm has

been applied to numerous feeders and the results

are compared with those of the authors having

International Journal of Pure and Applied MathematicsVolume 114 No. 9 2017, 367-388ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

367

Page 2: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

treated the problem. The optimal location SVC is

studied on the basis of Heuristic methods; Particle

Swarm Optimization (PSO), Cultural Algorithm

(CA), and Firefly Algorithm (FF) to minimize

network losses. Validation of the proposed

implementation is done on the IEEE-14 and

IEEE-30 bus systems.

Key Words andPhrases:CA, FDL, FF, PSO,

SVC.

1 Introduction

The rapid growth of the population as well as the industry are

primarily the factors influencing the consumption of electrical

energy which is on the other hand continuously increasing.

Since storing the electrical energy is a challenging task, it

requires a permanent balance between consumption and

production for that it is at first sight necessary to increase the

number of power stations, and of the various structures

(Transformers, Transmission lines, etc.), this leads to an

increase in cost and a degradation of the natural environment

[1].

1.1 Classification of the Variables of Power Flow Equations

In an electrical network each busbar is connected with four

fundamental magnitudes: The modulus of the voltage , the

phase of the voltage , the active power injected and the

reactive power injected . It is very important to note that for

each busbar; two variables must be specified beforehand and the

other two must be calculated. These different variables each

have a name following their role in the electrical network. The

state of the system is determined only after calculating the

values of the state variables [2]:

The disturbance variables: These are uncontrolled variables

representing the power demands of loads, the perturbation

variables are: and | |.

The state variables: Modules and phases are called unknown

state variables which characterize the state of the system, these

variables are: | |and .

Control variables: In a generic way, the active and reactive

powers injected are called control. It is also possible, depending

on the case, to consider tensions at the generation nodes or the

transformation ratios of transformers with load adjuster as

control variables, these variables are: [2].

1.3 Types of busbars

In the power flow analysis, the busbars in the system are

classified in three categories:

International Journal of Pure and Applied Mathematics Special Issue

368

Page 3: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Reference busbar (slack bus): It is also called the swing bus or

swing bus, it is a fictional element created for the study of the

distribution of power, and it has for role to provide the

additional power necessary to compensate for transmission

losses, as these are not known in advance. In general, by

convention, this busbar is identified by the set of busbars𝑁° = 1

connected to a voltage source from which the module | | and

phase (δ) of the voltage are known, these values are taken as

references = 1𝑝𝑢 and δ = 0°. The active powers ( ) and ( ) are

therefore unknown and must be calculated after solving the

problem of the power flow [2] and [3].

Busbars (control bus): Also known as generator or voltage

controlled busbars; they may include games of barriers to which

generators, capacitor banks, static compensators or

transformers with adjustable plug are connected to control the

voltage. The parameters specified here are: the active power ( )

and the voltage modulus ( ) from which the term: busbars therefore the remaining parameters must be calculated ( ) and

(δ) [2] and [3].

Loadbars (Loadbus): Also called the busbars (P Q), the specified

values are the active powers ( ) and ( ), the values to be

computed are the modulus and the phase (δ) of the voltage [2]

and [3].

This paper is organized into nine sections. Section 2 gives

analytical methods. Then in 3, relative unit (Static VAr

Compensator) is explained. Section 4 details about modeling

branches and loads. Section 5 explains the optimization of the

reactive energy compensation by fixed batteries using heuristic

method. Section 6 describes load flow analysis using Newton-

Raphson method. Section 7 provides optimal location using

heuristic techniques. Results and analysis is described in

section 8 and finally, a conclusion summarizes the contributions

of the paper.

2 Analytical Methods

The pioneer in the field is Cook [4]. In 1959, he studied the

effects of capacitors on power losses in a radial distribution

network where the charges are uniformly distributed. It

considered the reduction of power losses as an objective function

by considering a periodic reactive charging cycle. Cook then

developed a network of convenient curves to determine the most

economical power of the capacitor bank and the location of the

capacitor bank on the line. The equation giving the optimal

location to be assigned to a specified size battery is given by:

2.1 Methods of Digital Programs

The development of methods has led researchers to become

increasingly interested in the optimization of reactive energy

International Journal of Pure and Applied Mathematics Special Issue

369

Page 4: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

compensation. Therefore, they have developed numerical

methods for the analysis of the electrical network.

Baran and Wu [5] in 1989, presented a method for solving the

problem of placing capacitor banks in distribution networks. In

this problem, the locations of the batteries, their sizes, their

types, the stresses of the voltage and the variations of the load

are taken into account. The problem is considered to be a non-

linear programming problem where load flow is explicitly

represented.

To solve this problem, it is broken down into a slave problem

and a master problem. They exploit for this purpose the

property of optimization where:

𝑢 { 𝑢 } (1)

3 Relative Unit (Static

VArCompensator)

The normalization of the resistance of the line is obtained by

relating it to a calculated basic resistance by means of the

voltage and the power . If the base voltage is given

in kV and the power in kVA then, this resistance is given by:

(2)

The normalized resistance is then:

(3)

Standardized load ratings are obtained by:

{

(4)

4 Modeling Branches and Loads

4.1 Modeling Branches

The distribution networks have a radial configuration and

consist of a set of branches. Each branch of this network is

modeled as a series resistor with a pure inductance. The

impedance of any branch "i" of this network (see Fig. 1) is given

by:

(5)

International Journal of Pure and Applied Mathematics Special Issue

370

Page 5: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Fig. 1. Single line diagram of a branch

The shunt admittances are negligible because the line is of

medium voltage.

4.2 Modeling of Loads

The loads are generally modeled as being voltage dependent. We

write for the active and reactive powers of a charge placed at the

node "i" the following expressions:

(

)

(6)

(

)

(7)

Where,

and are the nominal active and reactive powers.

is the nominal voltage.

and are the active and reactive power of the load at node ‘ ’ for a voltage equal to .

The coefficients and determine the character of the load.

If the coefficients and are both zero, the load is considered to

be constant power. If, on the other hand, and are equal to 1,

the load is considered to be constant current. When they are

equal to 2 the load is considered to have a constant impedance.

In the remainder, and will be zero, i.e. consider constant

power loads.

The apparent power of the load connected to the node is in this

case:

(8)

5 Method of Solution

The voltage drop method is an iterative method. Its principle

consists in calculating, first and for each section of the line, the

powers at the end of the branch, the losses of active and reactive

powers and the powers at the beginning of the branch. From

these, the currents of the branches are determined by raising

the line to the source. These currents are calculated from the

estimated values of the voltages, the powers at the beginning of

i

International Journal of Pure and Applied Mathematics Special Issue

371

Page 6: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

the branch and the values of the impedances of each line section

between two successive busbars.

5.1 Formulation of the Problem

Power losses, low power factor and degradation of the voltage

profile are the result of strong current flow in power

systems.These phenomena are more pronounced in distribution

networks where the branch currents are stronger compared to

those circulating in the transport networks. The problem is

therefore to decide the number of batteries, their powers and

their locations which would make an objective function "F"

maximum. This objective therefore makes the problem of

reactive energy compensation an optimization problem.

However, owed to the discrete nature of the battery sizes and

their locations, this problem is non-linear with constraints. It is

generally modelled as follows:

{

𝑢 𝑢

𝑢 𝑢 𝑢

(9)

Where,

: is the objective function to maximize.

: is the equality constraint. It is the set of equations of the

power flow

: is the control variable vector

𝑢: is the state variable vector.

5.2 Objective Function

The objective function on which all the authors who have dealt

with the problem of optimization of reactive energy

compensation is the so-called "economic return" function or cost

reduction noted as "∆S". Mathematical expression is given by:

∑ (10)

Where,

: is the total number of batteries installed.

: is the cost of kW produced (₹ /kW).

: is the annual price of kVAr installed depreciation and life

included.

: is the size of the installed battery at node " ".

: is the reduction of the active power losses.

International Journal of Pure and Applied Mathematics Special Issue

372

Page 7: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

5.3 Reduction of Active Power Losses

The reduction of the power losses due to a battery "k" is equal to

the difference of the losses of active power in the network before

and after the installation of the said capacitor bank. It is given

by:

(11)

Where,

: are the active power losses in line before compensation.

: are active power losses in line after compensation.

5.4 Reduction of Reactive Power Losses

The reduction of the reactive power losses due to a battery

installed at node " " of the distribution line is defined by the

difference between the losses before and after the installation of

batteries in question of capacitors. It is given by:

(12)

Where,

: are the losses of reactive power in line before

compensation.

: are the losses of reactive power in line after compensation.

5.5 Reactive Power Losses

The losses of reactive power in a distribution network line

composed of n branches are given by the following formula:

(13)

Where,

is the reactance of branch

is the line current of the branch.

As with the active power losses, the active and reactive

components of the branch current thus allow to write the losses

of reactive power as follows:

(14)

The losses of reactive power when a capacitor bank is placed on

a node are given by:

(15)

International Journal of Pure and Applied Mathematics Special Issue

373

Page 8: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

The reduction of reactive power losses by calculating the

difference between equation (14) and equation (15), will be equal

to:

∑ (16)

5.6 Heuristic Method

Heuristic methods are based on experience and practice. They

are easy to understand and simple in their implementation.

They use sensitivity factors which they incorporate into

optimization methods in order to achieve qualitative solutions

with small computational efforts. Since the problem of

determining the suitable battery locations has been separated

from that of optimum power determination since the locations

are determined by the sensitivity factors then the size

calculation is generally modeled as follows:

{

𝑢

(17)

5.7 New Modeling of the Problem

By substituting the constraint on the tension with that made on

the branch current, the new mathematical model of the problem

becomes:

{

𝑢

(18)

5.8 Optimal Operation of Batteries

The reduction in power losses for a given node "k" is defined as

the difference between the power losses before canceling the

reactive current of the load at node " " and after the latter has

been canceled. It is given by:

(19)

The power losses before the cancellation of the reactive current

of the load at the node " " are given by:

(20)

The power losses after the cancellation of the reactive current of

the load at the node " " are given by:

(21)

After simplification, the reduction in power losses will have the

International Journal of Pure and Applied Mathematics Special Issue

374

Page 9: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

following expression:

(22)

5.9 Determination of Optimal Sizes

To calculate the optimum sizes of the batteries, the currents

they generate are first determined. This current is calculated so

as to make the objective function the maximum cost

reduction. This current is acquired by undertaking the

accompanying condition:

(23)

The expression of the current is then given by:

(24)

The initial optimum power is calculated by the following

expression:

(25)

The maximum value of the cost reduction in this case:

* ∑ ∑

+

( ∑ ∑

)

(26)

The value of the equivalent power loss reduction is given by:

(∑

)

(∑

)

( ∑ ∑

)

∑ [ ∑

]

( ∑ ∑

)

(27)

5.10 Solution Strategy

By optimally compensating the reactive energy we expect the

battery locations to be busbars in the network and that the

optimum battery power is available commercially or multiple of

these batteries. If the constraint on the locations, which can

only be busbars of the network, has found a solution by means

of sensitivity factors, the optimum powers of the batteries

remain to be determined by solving the problem with the

following constraints:

International Journal of Pure and Applied Mathematics Special Issue

375

Page 10: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

{

𝑢

(28)

The detailed solution algorithm of the problem of determination

will be detailed in the following section.

5.11 Calculation Algorithm

The algorithm for solving the overall problem, i.e., the suitable

locations of the capacitor banks and their sizes is detailed in

what follows. A MATLAB 14a environment program has been

developed for this purpose.

Step 1: Read the network data.

Step 2: Perform the program of the power flow before

compensation to determine the active and reactive power losses,

branch currents, node voltages and their phases at the origin.

Step 3: Initialize reduction of power losses and cost.

Step 4: as long as the reductions in power losses and cost are

positive.

Step 4.1: Determine the sensitivities of the nodes according to

equation (22) and rank them in descending order.

Step 4.2: If the most sensitive node considered has already

received a battery, ignore it.

Step 4.3: Calculate the initial value of the optimum size of the

battery to be placed there, the reduction of the cost and the

reduction of the power losses.

Step 4.4: Perform load flow to update electrical quantities

(voltage, current, power).

Step 4.5: Adjust the optimal size of the battery.

Step 4.6: If the battery size is negative, smaller than the

smallest standard battery or greater than the total power and

the reduction of negative power losses then:

Step 4.6.1: Remove the battery.

Step 4.6.2: Give the voltages at their origin and branch currents

the values d before the battery.

Step 4.7: Otherwise, take as the optimum size of the battery, the

lower standard size where higher giving the greatest cost

reduction.

International Journal of Pure and Applied Mathematics Special Issue

376

Page 11: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Step 4.8: Re-calculate the load flow.

Step 4.9: If the battery produces overcompensation then:

Step 4.9.1: Replace the standard battery with a smaller one that

does not overcompensate.

Step 4.9.2: Test if the battery is not smaller than the smallest

standard battery.

Step 4.9.3: Perform load flow and calculate the reduction in

power losses and cost based on the actual installed kVAr power.

Step 4.10.4: Verify that the reduction in power loss and cost

reduction are positive.

Step 4.10: End if

Step 4.11: Go to Step 4

Step 5: Display the results.

6 Load Flow Analysis using Newton-

Raphson Method

This method requires more time per iteration where it does not

requires only a few iterations even for large networks. However,

it requires storage as well as significant computing power. Let

us assume:

(29)

(30)

(31)

We know that:

Equation (29) then becomes:

(32)

By separating the real and the imaginary part, one obtains:

{ ∑

(33)

International Journal of Pure and Applied Mathematics Special Issue

377

Page 12: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Positions:

(34)

(35)

Where,

{

Then, the equation (33) becomes:

{ ∑

(36)

Where,

{ ∑

(37)

It is a system of nonlinear equations. The active power and

the reactive power are, and the real and imaginary

components of the voltage and are unknown for all Bus bars

except the reference bus bar, where the voltage is specified and

fixed. The Newton-Raphson method requires that non-linear

equations be formed of expressions linking the powers and the

components of the voltage.

[

]

[

|

|

|

]

[

]

(38)

Where the last set of bars is the reference bar. The outline of the

matrix is given by:

*

+ *

|

+ *

+ (39)

Or

[

] [

] (40)

Where [J] is the Jacobian of the matrix. are the

differences between the planned values and the values

calculated respectively for active and reactive powers.

International Journal of Pure and Applied Mathematics Special Issue

378

Page 13: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Equation (37) can be written as follows:

{

(38)

From where, one can draw the elements of the Jacobian:

The diagonal elements of : ∑

The non-diagonal elements of

The diagonal elements of ∑

The non-diagonal elements of

The diagonal elements of ∑

The non-diagonal elements of

The diagonal elements of ∑

The non-diagonal elements of

(39)

(40)

Because of the quadratic convergence of the Newton-Raphson

method, a solution of accuracy can be achieved in just a few

iterations. These characteristics make the success of the Fast

Decoupled Load Flow and the Newton-Raphson.

7 Optimal Location using Heuristic

Techniques

In the proposed system, the location of SVC in a particular bus

system is decided by PSO, CA, FF algorithms. The objective

function is minimized using the abovementioned techniques.

7.1 Particle Swarm Optimization (PSO)

James Kennedy and Russell C. Eberhart proposed a PSO

approach in 1995. This approach is a heuristic method [6]. The

evaluation of candidate solution of current search space is done

on the basis of iteration process (as shown in Fig. 2). The

minima and maxima of objective function is determined by the

candidate’s solution as it fits the task’s requirements. Since PSO

International Journal of Pure and Applied Mathematics Special Issue

379

Page 14: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

algorithm do not accept the objective function data as its inputs,

therefore the solution is randomly away from minimum and

maximum (locally/ globally) and also unknown to the user. The

speed and position of candidate’s solution is maintained and at

each level, fitness value is also updated. The best value of

fitness is recorded by PSO for an individual record. The other

individuals reaching this value are taken as the individual best

position and solution for given problem. The individuals

reaching this value are known as global best candidate solution

with global best position. The up gradation of global and

individual best fitness value is carried out and if there is a

requirement then global and local best fitness values are even

replaced. For PSO’s optimization capability, the updation of

speed and position is necessary. Each particle’s velocity is

simplified with the help of subsequent formula:

(41)

Fig. 2. Flow chart of PSO algorithm [6]

7.2 Cultural Algorithm

Cultural algorithm corresponds to modeling inspired by the

evolution of human culture [7]. Thus, just as we speak of

biological evolution as the result of a selection based on genetic

variability, we can speak of a cultural evolution resulting from a

selection exercising on the variability Cultural development.

From this idea, Reynolds developed a model whose cultural

evolution is considered as a process of transmission of

experience at two levels: a micro-evolutionary level in terms of

transmission of genetic material between individuals of a

population and a macro level -evolutionary in terms of

No

Start

Initialization on early searching points of all agents

Assessment of searching points of all agents

Amendment of every searching point using state equation

Extent to extreme iteration

Stop

International Journal of Pure and Applied Mathematics Special Issue

380

Page 15: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

knowledge acquired on the basis of individual experiences. The

following figure presents the basic CA framework.

As Fig. 3 shows, the population space and the belief space can

evolve respectively. The population space consists of the

autonomous solution agents and the belief space is considered

as a global knowledge repository. The evolutionary knowledge

that stored in belief space can affect the agents in population

space through influence function and the knowledge extracted

from population space can be passed to belief space by the

acceptance function.

Fig. 3. CA framework [8]

7.3 Firefly Algorithm

Fireflies are small flying beetles capable of producing a cold

flashing light for mutual attraction. In the common language

between fireflies, they are also used synonymous lighting bugs

or glow worms. These are two beetles that can emit light, but

fireflies are recognized as species that have the ability to fly.

These insects are able to produce light inside their bodies

through special organs located very close to the surface of the

skin. This light production is due to a type of chemical reaction

called bioluminescence [9].

Principle of operation of the algorithm of Fireflies

The algorithm takes into account the following three points:

• All fireflies are unisex, which makes the attraction

between these is not based on their gender.

• The attraction is proportional to their brightness, so for

two fireflies, the less bright will move towards the

brighter. If no firefly is luminous that a particular

Belief Space

Update

Acceptance Function Influence Function Communication

Protocol

Population Space

Inherit

Evaluation Adaption,

Reproduction

International Journal of Pure and Applied Mathematics Special Issue

381

Page 16: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

firefly, the latter will move randomly.

• The luminosity of the fireflies is determined according

to an objective function (to be optimized).

Based on these three rules, the Firefly algorithm is as follows:

Fig. 4. Pseudo code for Firefly Algorithm

8 Results Analysis

On the IEEE-14 and IEEE-30 bus test systems (shown in Fig. 5

and Fig. 6) the proposed heuristic techniques (PSO, CA and FF)

have been tested.

Fig. 5. Single line diagram of the IEEE-14 bus test system

G

C

G

C

C

1

2

3

4

5

6 7 8

9

10 11

12

1

3 1

4

G Gener

ators C Synchro

nous

Compe

nsators

Three Winding

Transformer

Equivalent

C

4 8

9

7

Define an objective function Generate a population of fireflies Define the intensity of light at a point by the objective function Determine the absorption coefficient As long as ( Max Generation) For to For to If

Move the firefly to the firefly End if Vary the attraction as a function of the distance via 𝑝 Evaluation of new solutions and updating light intensity End For End For Classify fireflies and find the best solution End as long as View results

International Journal of Pure and Applied Mathematics Special Issue

382

Page 17: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Fig. 6. Single line diagram of the IEEE-30 bus test system

Fig. 7. Active & Reactive power losses in IEEE-14 bus system

using PSO

NRPF NRPF with SVC (PSO)0

10

20

30

40

50

60

Pow

er

Loss (

MW

& M

Var)

Active & Reactive Power Losses in IEEE Bus System

13.7214

56.5404

13.5531

54.7546P

Q

International Journal of Pure and Applied Mathematics Special Issue

383

Page 18: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Fig. 8. Active & Reactive power losses in IEEE-30 bus system

using PSO

Fig. 9. Active & Reactive power losses in IEEE-14 bus system

using CA

NRPF NRPF with SVC (PSO)0

10

20

30

40

50

60

70

Pow

er

Loss (

MW

& M

Var)

Active & Reactive Power Losses in IEEE Bus System

17.8162

69.4087

17.8162

69.4087

P

Q

NRPF NRPF with SVC (CA)0

10

20

30

40

50

60

Pow

er

Loss (

MW

& M

Var)

Active & Reactive Power Losses in IEEE Bus System

13.7214

56.5404

12.789

53.1876P

Q

International Journal of Pure and Applied Mathematics Special Issue

384

Page 19: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Fig. 10. Active & Reactive power losses in IEEE-30 bus system

using CA

Fig. 11. Active & Reactive power losses in IEEE-14 bus system

using FF

NRPF NRPF with SVC (CA)0

10

20

30

40

50

60

70

Pow

er

Loss (

MW

& M

Var)

Active & Reactive Power Losses in IEEE Bus System

17.8162

69.4087

16.764

67.678

P

Q

NRPF NRPF with SVC (FF)0

10

20

30

40

50

60

Pow

er

Loss (

MW

& M

Var)

Active & Reactive Power Losses in IEEE Bus System

13.7214

56.5404

13.789

54.1876P

Q

International Journal of Pure and Applied Mathematics Special Issue

385

Page 20: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

Fig. 12. Active & Reactive power losses in IEEE-30 bus system

using FF

Table 1. Comparative analysis for IEEE-14 bus system

Heuristic

Method

Active

Power

Loss

Reactive

Power

Loss

PSO 13.5531 54.7546

Cultural

Algorithm

12.789 53.1876

Firefly

Algorithm

13.789 54.1846

Table 2. Comparative analysis for IEEE-30 bus system

Heuristic

Method

Active

Power

Loss

Reactive

Power

Loss

PSO 17.8162 69.4087

Cultural

Algorithm

16.764 67.678

Firefly

Algorithm

17.162 69.076

9 Conclusion

In our work in this paper, we presented a solution for the

problem of the circulation of strong reactive currents in

balanced distribution networks. A heuristic solution technique

based on a loss-of-power sensitivity factor has been proposed. In

this method, the choice of the candidate nodes to receive the

capacitor banks is arbitrated by the sensitivity of the power

losses of the entire electrical system studied to the reactive load

NRPF NRPF with SVC (FF)0

10

20

30

40

50

60

70

Pow

er

Loss (

MW

& M

Var)

Active & Reactive Power Losses in IEEE Bus System

17.8162

69.4087

17.162

69.076

P

Q

International Journal of Pure and Applied Mathematics Special Issue

386

Page 21: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

current of each node. The most sensitive node is therefore the

one whose reactive current of charge produces the most loss

reduction.

During this work, the problem of the power flow in the

distribution networks, which is a prerequisite for the conduct of

the reactive energy compensation, is also taken care of, the

calculation of the power flow is imperative. An iterative method

has been developed for this purpose where a technique specific

to us has been given to recognize the configuration of the

network. Load flow analysis is also done using Newton-Raphson

method. Three Heuristic methods are used to optimize the

location of SVC using the MATLAB model; Particle Swarm

Optimization, Cultural Algorithm and Firefly algorithm. The

tests were performed taking SVC as the FACTS device. It was

found that the Cultural Algorithm has less power losses as

compared to other methods.

References [1] Preedavichit, P. and Srivastava, S.C., 1998. Optimal reactive

power dispatch considering FACTS devices. Electric Power

Systems Research, 46(3), pp.251-257.

[2] Park, J.B., Lee, K.S., Shin, J.R. and Lee, K.Y., 2005. A particle

swarm optimization for economic dispatch with nonsmooth

cost functions. IEEE Transactions on Power systems, 20(1),

pp.34-42.

[3] Driesen, J. and Katiraei, F., 2008. Design for distributed

energy resources. IEEE Power and Energy Magazine, 6(3).

[4] Cook, R.F., 1959. Analysis of capacitor application as affected

by load cycle. Transactions of the American Institute of

Electrical Engineers. Part III: Power Apparatus and Systems,

78(3), pp.950-956.

[5] Baran, M.E. and Wu, F.F., 1989. Optimal capacitor placement

on radial distribution systems. IEEE Transactions on power

Delivery, 4(1), pp.725-734.

[6] Kennedy, J., 2011. Particle swarm optimization. In

Encyclopedia of machine learning (pp. 760-766). Springer US.

[7] Reynolds, R.G., 1994, February. An introduction to cultural

algorithms. In Proceedings of the third annual conference on

evolutionary programming (Vol. 131139). Singapore.

[8] Reynolds, R.G. and Peng, B., 2004, November. Cultural

algorithms: modeling of how cultures learn to solve problems.

In Tools with Artificial Intelligence, 2004. ICTAI 2004. 16th

IEEE International Conference on (pp. 166-172). IEEE.

[9] Yang, X.S., 2010. Firefly algorithm, stochastic test

functions and design optimization. International Journal

of Bio-Inspired Computation, 2(2), pp.78-84.

International Journal of Pure and Applied Mathematics Special Issue

387

Page 22: Optimal Compensation of Reactive Power in Transmission ... · 1 sszope@rediffmail.com 2 Sri Satya Sai University of Technology & Medical Sciences . Opposite OILFED, Bhopal Indore

388