A COMPLETE REACTIVE POWER MANAGEMENT STRATEGY USING ANT COLONY OPTIMIZATION ALGORITHM · 2018. 12. 9. · A Complete Reactive Power Management Strategy Using Ant Colony Optimization

Emirates Journal for Engineering Research, 19 (3), 19-31 (2014)

(Regular Paper)

19

A COMPLETE REACTIVE POWER MANAGEMENT STRATEGY

USING ANT COLONY OPTIMIZATION ALGORITHM

Mohamed T. Mouwafi1, Ragab A. El-Sehiemy

2, Adel A. Abou El-Ela

1

and Abdel-Mohsen M. Kinawy1

1 Electrical Engineering Department; Faculty of Engineering, Minoufiya university

Shebin El Kom , 32511 - Egypt 2 Electrical Engineering Department; Faculty of Engineering, Kafrelsheikh university,

Kafrelsheikh, 33511 - Egypt - e-mail: [email protected]

(Received June 2014 and Accepted December 2014)

دارج انقذرج انكهزتيح غيز انفعانح، ف حالاخ انرشغيم انعاديح إنحم يشكهح يقرزححسرزاذيجيح ايقذو هذا انثحس

يرعذد (Ant Colony Optimization Algorithm) وانطارئح نهظى انكهزتيح تاسرخذاو خىارسو يسرعزج انم

هيار جهىد قضثا الأحال إنع حذوز انفعال إجزاء انرحكى انىقائتسرزاذيجيح انقرزحح يق الاذطث ىذ. الأهذاف

جزاءاخ إعرثار انذوال يرعذدج الأهذاف انرانيح: يفاقيذ خطىط انقم، سيادج إ. حيس ذى ف الأظح انكهزتائيح انجهذج

انحذد، وذقهيم انقذرج غيز انفعانح نىحذاخ انرىنيذ يع ذقهيم ذثاعذ جهىد قضثا الأحال ع انجهذقثم؛ انكافحح ي

قيىد يرغيزاخ دانح انهذف )جهىد قضثا انرىنيذ وانقذرج غيز انفعانح ي يصادر انرىنيذ الأخزي( الإعرثارالأخذ ف

فحص ذى .هذهيار انجإوانرغيزاخ انراتعح )جهىد قضثا الأحال وانقذرج غيز انفعانح نهىنذاخ( تالاضافح ان قيذ

دفي قيى إجزاء انرحكى انىقائ ف حالاخ انرشغيم انطارئح تذو إجزاء عهياخ ذصحيحيح، حيس لا ذىجذ ذجاوساخ

. حيس أوضحد انرائج أ أسهىب خىارسو يسرعزج قضية 03الاسرزاذيجيح انقرزحح عه ظاو ذى ذطثيق و.انظا

.ال ف حالاخ انرشغيم انطارئح انخرهفحإجزاء انرحكى انىقائ انفعقذرج عه انم أكثز

This paper proposes a generalized strategy for reactive power management problem during

normal and emergency operating conditions. The proposed problem is solved via multi-objective

ant colony optimization (ACO) algorithm. The proposed strategy solves the reactive power

management problem and is creating efficient control actions to mitigate the occurrence of

voltage collapse in stressed power systems. The proposed multi-objective functions are:

minimizing the transmission line losses, maximizing the control actions by; minimizing the

voltage deviation of load buses with respect to the specified bus voltages and minimizing the

reactive power generation at generation buses based on control variables under voltage collapse,

control and dependent variable constraints. In addition, the proposed control actions are checked

under emergency conditions without making corrective control actions, while all system

constraints are kept within their permissible limits. The proposed ACO-based strategy is tested to

the IEEE standard 30-bus test system. The results show the capability of the proposed ACO

algorithm for the maximal preventive control actions to eradicate different emergency condition

effects.

Keywords: Ant colony optimization algorithm, voltage collapse, corrective action, sensitivity

analysis, security

1. INTRODUCTION

Over the last few decades, reactive power

management problem is one of the main problems for

both power system planners and operators. So, it is

very important issue in the expansion planning and

operation of power systems. The purpose of reactive

power management problem focuses to improve the

voltage stability in the system and to optimize system

losses keeping the voltage security in concern, power

system. The interest in reactive power management

has been growing, mainly because of the way in

which energy supplier charge a customer for reactive

power especially after deregulation. Moreover, the

energy price is growing, what force the

industry plants and individual customers to

minimize energy consumption, including reactive

power. Also, modern power systems are operated

fairly close to their limits due to economic

competition and deregulation [1-3].

The reactive power management in power systems

aims at minimizing reactive power flow in supplying

and distribution systems, minimizing the charge for

reactive power as well as aspire to active energy

limitation, in result, reducing fare for electrical

energy. In the matter of fact, the energy providers

want their customers to compensate reactive power.

Energy suppliers avoid paying for reactive power as

much as possible [2]. The management of reactive

mailto:[email protected]

Mohamed T. Mouwafi, Ragab A. El-Sehiemy, Adel A. Abou El-Ela and Abdel-Mohsen M. Kinawy

20 Emirates Journal for Engineering Research, Vol. 19, No.3, 2014

power resources generation facilities under control of

transmission operators plays an important role in

maintaining voltage stability and system reliability

[3]. The optimization of reactive power management

problem is a very complicated one, main features are:

nonlinear, discrete and large scale, the convergence of

the initial dependence. To make the system network

loss and node voltage offset, it must be combined

minimum power reactive power optimization model

of multi-objective under system certain constraints.

The main objectives of the reactive power

management problem are:

- Maintaining the power factor determined by the

energy supplier in order to reduce paying for

energy consumption.

- Improving power quality

- Decreasing transmission power losses

- Decreasing the cross section of the wires

- Decreasing transformer costs.

- Lowering voltage drop of supplying network and

increasing the transmission capability.

The shortage in reactive power sources or heavy

loading conditions may lead to the occurrence of

voltage collapse problem that occurs when the

voltage magnitudes violate their minimum threshold

of their reasonable limits of voltages. So, it is

necessary to simulate the voltage collapse problem

within the reactive power managing. Also, preparing

sufficient preventive control actions is very important

requirement to alleviate the effects of different

emergency conditions. The preventive control actions

are carried out in the pre-contingency situation by

optimizing the control variables using optimization

techniques to obtain the maximum preventive control

actions by operators or controllers which react to the

stress imposed on the system in order to mitigate the

voltage collapse. While, the corrective control is

carried out in post-contingency to stabilize unstable

power system in order to restore system solvability

Feng et al. [4] presented a comprehensive approach to

systematically compute the corrective and preventive

control strategies to mitigate power system voltage

collapse.

Capitanescn and Cutsem [5] revisited the use of

sensitivities to identify which parameter changes are

most effective to deal with unstable or low voltages.

The proposed sensitivities focused on the weakest bus

voltage, identified in practice as the one experiencing

the largest drop due to the load increase or the

contingency.

Also, Capitanescu et al. [6] proposed an approach

coupling security-constrained optimal power flow

with time-domain simulation to determine an optimal

combination of preventive and corrective controls

ensuring a voltage stable transition of the system

towards a feasible long-term equilibrium, if any of a

set of postulated contingencies occurred.

Lenoir et al. [7] presented a concept overview of an

automatic operator of electrical networks for real-time

alleviation of component overloads and increase of

system static loadability, based on state-estimator

data only.

Fu and Wang [8] proposed unified preventive control

approach considering voltage instability and thermal

overload.

Bruno and Scala [9] proposed a methodology to

assess preventive control actions through adjustments

of unified power flow controllers of (UPFCs)

reference signals that represented a nonlinear model.

The UPFC model included electrical equivalent

circuits, a local control scheme and a centralized

control scheme. Control actions evaluated through a

nonlinear optimization process.

Li et al. [10] proposed an Integer-coded

multiobjective Genetic Algorithm (IGA) applied to

the full Reactive-power Compensation Planning

problem considering both intact and contingent

operating states.

Ant colony optimization (ACO) algorithms were first

proposed by Dorigo [11]. ACO algorithms are based

on the behavior of real ants that are members of a

family of social insects. However, a group of explorer

ants leave the colony for finding the food source in a

randomly directions where they marked their routes

by laying a chemical substance on the ground. Other

ants attractive to the route that has the largest amount

of pheromone that decays with time. So that, a shorter

route will be found that has a largest amount of

pheromone than a longer route. So that, they are

found the shortest route between the nest and food

source by indirect communication media that called

pheromone that laid on the ground as a guide for

another ants. Through few recent years, ACO

algorithms are employed to solve optimization

problems in different fields with more accurate and

efficiently solution compared with conventional and

other modern optimization algorithms.

In the field of power systems, in power systems, the

ACO has been applied to solve the optimum

generation scheduling problems [12], Power system

restoration [13], unit commitment [14], economic

dispatch [15], and for the constrained load flow [16].

The authors in [17] developed a procedure using

ACO algorithm for optimal distributed generation

placement for enhancing protective device in

distribution systems. In literature, there are different

optimization algorithms for solving the reactive

power management problem including the ant colony

algorithm as presented in [18-22].

In our previous work, it was solved the optimal

reactive power dispatch (ORPD) problem using ACO

algorithm [23]. In [24], a multiobjective fuzzy based

procedure is proposed for preparing preventive

control actions from generator and transmission lines

to overcome the emergency effects based on the

optimal power dispatch model. In that paper, the

control actions are customized via maximizing the

possible reserve from generators and the critical lines.

A Complete Reactive Power Management Strategy Using Ant Colony Optimization Algorithm

Emirates Journal for Engineering Research, Vol. 19, No.3, 2014 21

But, it was carried out on active power problem and

didn't consider of reactive power resources on the

emergency mitigation.

So, in present work, a proposed complete strategy is

proposed for solving the reactive power management

problem considering the voltage collapse constraints

at both normal and abnormal operating conditions.

The proposed reactive power management is solved

via the ACO algorithm. The proposed procedure is

checked for alleviating the effects of different

emergency conditions. The proposed procedure is to

take by operator's hands to secure and economize

crossover of emergency conditions. Problem solving

is carried out on IEEE 30 bus test system.

2. PROBLEM FORMULATION

The ORPD problem can be expressed as an

optimization problem as:

Min f x (1)

Subject to : 0

0

g x

h x

(2)

where, f(x) is the objective function such as

transmission line losses, generators fuel costs,...etc,

g(x), h(x) represent the equality and inequality

constraints, respectively and x is the vector of the

control variables.

The reactive power optimization mathematical model

should include object function, variable constraint

equations and power constraint equations. Then, the

objective function f(x) is the transmission line losses

that are a function in the generator voltages and

switchable reactive power, which are defined as:

1

1

/

/

N

L L G G

G

N

L SW SW

SW

Min P P V V

P Q Q

G

SW

(3)

where, ∆PL is the objective function of the change in

transmission line losses, ∆VG and ∆QSW are the

changes in the control variables of generation voltages

and switchable reactive power, respectively, NG is the

number of generation buses, NSW is the number of

buses which the switchable reactive sources are

located.

The changes in transmission line losses with respect

to changes in generator voltage can be derived based

on the load flow equations as:

i i iS V I (4)

Also;

i i iS P jQ (5)

From equations 4 and 5, the active power at bus i can

be formulated as:

1

cos sinN

i i ij ij ij ij j

j

P V G B V

(6)

At i = j, equation 6 can be rewritten as:

2

1,

cos sinN

i i ii i ij ij ij ij j

j j i

P V G V G B V

(7)

Now, the values of ∂Pi /∂Vi and ∂Pj /∂Vi can be

calculated by differentiating equation 7 as:

1,

/ 2 cos sinN

i i i ii ij ij ij ij ji NGj j i

P V V G G B V

(8)

/ cos sinj i j ji ij ji ijj NGP V V G B

(9)

where, Yij = -1 / Zij = Gij +j Bij is the line admittance

between buses i and j.

δi and δj are the angles of the voltages at buses i and

j, respectively.

Also, the change in transmission line losses due to

changes in switchable reactive power can be written

as:

/ / /L SW L SW SW SWP Q P V V Q (10)

where, ∂VSW / ∂QSW is the change of switchable

voltage buses with respect to change in switchable

reactive power at that bus, and determined based on

sensitivity that will be illustrated in the next Section.

The objective function (3) is subjected to the

following constraints:

a) Control variable constraints

Generation voltage constraints

The change in generator voltage must be within their

permissible limits as:

min max

G G GV V V (11)

where,

min min init

G G GV V V and max max init

G G GV V V

VGinit

is the initial value of the generator voltage at

each generator bus.

VGmin

and VGmax

are the minimum and maximum of

generation voltages, respectively.

∆VGmin

and ∆VGmax

are the minimum and maximum

changes in generation voltages, respectively.

Switchable reactive power constraints

The change in switchable reactive power must be

within their permissible limits as:

min max

SW SW SWQ Q Q (12)

where,

min min init

SW SW SWQ Q Q and max max init

SW SW SWQ Q Q



QSWinit

is the initial value of the switchable reactive

power.

QSWmin

and QSWmax


switchable reactive power, respectively.

∆QSWmin

and ∆QSWmax


changes in switchable reactive power,

respectively.

a) Dependent variable constraints

Load voltage constraints

The voltage at each load bus must be within their

permissible limits as:

min max

L L LV V V (13)

where,

min min init

L L LV V V and

max max init

L L LV V V

VLinit

is the initial value of the voltage at each load

bus.

VLmin

and VLmax


load bus voltages, respectively.

∆VLmin

and ∆VLmax


changes in load bus voltages, respectively.

Generation reactive power constraints

The reactive power of each generator must be within

their permissible limits as:

min max

G G GQ Q Q (14)

where,

min min init

G G GQ Q Q and

max max init

G G GQ Q Q

QGinit

is the initial value of reactive power at

generation buses.

QGmin

and QGmax


values of reactive power at generation buses,

respectively.

∆QGmin

and ∆QGmax


changes in reactive power at generation buses,

respectively.

3. VOLTAGE COLLAPSE

CONSTRAINT

Based on Thevenin's theorem that provides an

extremely valuable means for reducing a complex

circuit to a simple circuit containing an ideal voltage

source in series with equivalent impedance, thus, the

complex power circuit shown in Figure 1(a) can

always be reduced to the Thevenin's equivalent as

shown in Figure 1(b). From this circuit, the real

power transmitted to load can be calculated as:

2

2

L i i

i TH TH

i ii i ii

iTH

i ii

P real V I

Z E Ereal

Z Z Z Z

Zreal E

Z Z

(15)

To obtain the maximum power transmitted (PLmax

) to

the load, ∂PL/∂Zi is calculated and equals to zero as

follows:

0

i

L

Z

P

02

4

222

iii

iiiTHiTHiii

ZZ

ZZEZEZZreal

Hence, the maximum power transmitted to the load

occurs at Zi = Zii can be calculated as:

ii

THL

Z

ErealP

4

2max (16)

For preventing the occurrence of the voltage collapse

in power systems, it should satisfy the following

inequality constraint:

NiZZ iii ,....1;0.1/ (17)

where,

Zii is the ith

diagonal elements of the Thevenin's

equivalent impedance matrix.

N is the number of load buses.

Zi is the load impedance, which is calculated as:

iLii SVZ /2

(18)

where, |VLi| is the magnitude of the load voltage under

normal and emergency conditions at bus i. Si* is the

conjugate of the apparent power at bus i.

4. PROPOSED SENSITIVITY

PARAMETERS

The fast decoupled power flow (FDPF) method is one

of the load flow methods that assumed the changes in

active power flows due to changes in voltage phase

angles are higher than the changes due to voltage

Complex

Circuit

Bus i

ZL

Ii

Vi

ZL=Zi

Bus i ZTH = Zii

ETH

(a) Original circuit (b) Thevenin equivalent circuit

Figure 1. Reduction network using Thevenin's theorem



magnitudes. On the other hand, the changes in

reactive power flows due to changes in voltage

magnitudes are higher than the changes due to voltage

phase angles. So, it can be written as:

[∆P/V] = [B'] [∆δ] and [∆Q/V] = [B"] [∆V]

where, [∆P] and [∆Q] are the vectors of active and

reactive power mismatches, respectively. [B'] and

[B"] are the susceptance matrices. [∆δ] and [∆V] are

the vectors of changes in voltage angles and

magnitudes, respectively.

In this paper, the ORPD problem is based on the

second equation of the FDPF as:

[∆Q/V]=[B"][∆V] (19)

where, B" is the susceptance matrix as:

1"

1,

" "

1/ ; 1,2,....., 1

1/ ; , 1,2,....., 1

N

ii ij

j j i

ij ji ij

B X i N

B B X i j N

where, Xij is the line reactance between buses i and j.

Now, equation 19 can be rewritten in terms of control

and dependent variables as:

/

/

G G GGG GL

LG LLL L L

Q V VB B

B BQ V V

(20)

The sensitivity parameters between control and

dependent variables can be derived based on equation

20 as follows:

a) The load bus voltages related to control

variables

No changes in the reactive power at load-bus

(∆QL=0)

The sensitivity parameters relating the changes in

load-bus voltages due to the changes in generation-bus

voltages are given as:

GLGLLL VBBV 1

G

L

GL VSV (21)

where, LGLL

L

G BBS1

No changes in generation voltages (∆VG=0)

The sensitivity parameters relating to the changes in

load-bus voltages due to the changes in switchable

reactive power sources can be given as:

SW

L

SWL QSV (22)

where, 11 SWLL

L

SW VBS and, VSW is the vector

of bus voltages that connected to VAR sources.

b) Generation reactive power related to control

variables

The sensitivity parameters relating to the changes

in generated reactive power due to the changes in

generation-bus voltages can be written as:

LGLGGGGG VBVBVQ / (23)

By substituting from equation 21 into 23, we obtain:

G

L

GGLGGGGG VSBVBVQ /

G

G

GG VSQ (24)

where, L

GGLGGG

G

G SBBVS

The sensitivity parameters relating to the changes

in generated reactive power due to the changes in

switchable reactive power sources can be written

as:

LGLL

L

GGGGG VBVSBVQ 1

/ (25)

By substituting from equation 22 into 25, we get:

1

/ L LG G GG G GL SW SWQ V B S B S Q

SW

G

SWGG QSVQ / (26)

where, L

SWGL

L

GGGG

G

SW SBSBVS 1

Now, the proposed sensitivity between the control

and the dependent variables can be formulated based

on equations 21, 22, 24 and 26 in a compact matrix

form as:

L L

GL G SW

G GG SWG SW

VV S S

Q QS S

(27)

5. PROPOSED CONTROL ACTIONS

The proposed control actions are carried out as multi-

objective functions in the pre-contingency situation

by optimizing the control variables to avoid any

violation limit, which may occur at the emergency

condition.

a) Preventive control actions of load voltages

based on each generation voltage

The maximal effect of the preventive control actions

of load voltages obtained by minimizing the voltage

deviation with respect to the specified voltage can be

expressed as:

Max. YVLi

LiG

L

G

init

LiLsp YVVSVV . (28)

where, VLisp is the specified load voltage (equals to

one); VLiinit

is the initial value of load voltage at bus i;



YVLi is the maximal Preventive control actions due to

decrease the voltage deviation at load buses.

b) Preventive control actions of load voltages

based on each switchable reactive power

Equation 28 can be restated as a function of

switchable reactive power as:

Max. YVL

Subject to:

LiSW

L

SW

init

LiLsp YVQSVV . (29)

c) Preventive control actions of load voltages

based on all of generation voltage, switchable

reactive power and all of them

Equations 28 and 29 can be composed as multi-

objective functions to obtain the maximal preventive

control actions as:

Max. YVLi

SWGLiLi

init

LiLsp NNiYVVVV ,...,2,1,,...,2,1;. (30)

where, ∆VLi is the incremental change of load voltage

based on control variables using sensitivity

parameters of reactive power.

d) Preventive control actions of all generation

reactive power based on each generation

voltage

The maximal effect of the preventive control actions

of generation reactive power obtained by minimizing

the generation reactive power can be expressed as:

Max. YQGi

GiG

G

G

init

Gi YQVSQMin (31)

where, QGiinit

is the initial value of generation reactive

power of unit i; YQGi is the maximal Preventive

control actions due to decrease the reactive power at

generation buses.

e) Preventive control actions of all generation

reactive power based on each switchable

reactive power

Equation 31 can be restated as a function of

switchable reactive power as:

Max. YQGi

GiSW

G

SW

init

Gi YQQSQMin (32)

f) Preventive control actions of all generation

reactive power based on all of generation

voltage, switchable reactive power and all of

them

Equations 31 and 32 can be composed as multi-

objective functions to obtain the maximal preventive

control actions as:

Max. YQGi

SWGGiGi

init

Gi NNiYQQQMin ,...,2,1,,...,2,1; (33)

where, ∆QGi is the incremental change of generation

reactive power based on control variables using

sensitivity parameters of reactive power.

6. MATHEMATICAL MODEL OF ACO

ALGORITHM

A random amount of pheromone is deposited in each

rout after each ant completes it is tour, anther antes

attract to the shortest route according to the

probabilistic transition rule that depends on the

amount of pheromone deposited and a heuristic guide

function as equal to the inverse of the distance

between beginning and ending of each route. The

probabilistic transition rule of ant k to go from city i

to city j can be expressed as in Traveling Salesman

Problem (TSP) [13] as:

ki

qiqiq

ijijkij Nqj

tt

tttP

,;

)()(

)()()(

(34)

where, τij is the pheromone trail deposited between

city i and j by ant k, ηij is the visibility or sight and

equal to the inverse of the distance or the transition

cost between city i and j ( ηij = 1/dij ). α and β are two

parameters that influence the relative weight of

pheromone trail and heuristic guide function,

respectively. If α=0, the closest cities are more likely

to be selected that corresponding to a classical greedy

algorithm. On the contrary, if β=0, the probability

will be depend on the pheromone trial only. These

two parameters should be tuned with each other,

Dorigo [12] founds experimentally the good values of

α and β are 1 and 5, respectively, q is the cities that

will be visited after city i. While, Nrk is a tabu list in

the memory of ants that recode the cities which will

be visited to avoid stagnations After each tour is

completed, a local pheromone update is determined

by each ant depending on the route of each ant as in

equation 35, after all ants attractive to the shortest

route, a global pheromone update is considered to

show the influence of the new addition deposits by

the other ants that attractive to the best tour as shown

in equation 36:

)(1)1( tt ijij (35)

)()(1)1( ttt ijijij (36)

where, τij (t+1) is the pheromone after one tour or

iteration, ρ is the pheromone evaporation constant

equals to 0.5 as a good value by Dorigo in [8], ε is the

elite path weighting constant, τo = 1 / dij is the

incremental value of pheromone of each ant. While,

∆τij is the amount of pheromone for elite path as:



( ) 1/ij bestt d (37)

where, d best is the shortest tour distance found as in

TSP.

7. ACO ALGORITHM FOR ORPD

PROBLEM

ACO algorithm is applied to solve the ORPD problem

as an optimization technique with control and

dependent variable constraints. Also, it is applied to

solve a multi-objective functions to obtain the

maximal effect of preventive control action based on

control variables under control and dependent

variable constraints in addition to voltage collapse

constraint where artificial ants travels in search space

to find the shortest route that having the strongest

pheromone trail and a minimum objective function.

Our objectives in this paper are: minimize the power

losses as described in (3) with control variable

constraints in (11) and (12), and dependent variable

constraints in (13) and (14). Also, maximize

preventive control actions with equations 28-33 with

the same control and dependent variable constraints

with addition voltage collapse constraint in equation

17. So that, the heuristic guide function is the inverse

of each objective function for each ant that positioned

in the reasonable limit of the control variable to the

visibility of each ant. While, heuristic guide function

of the problem is the inverse of the total value of

objective functions at iteration t +1, e.g., for ORPD

problem, the heuristic guide function can be

expressed as:

1

1

( 1) 1/ /

/

N

L G G

G

N

L SW SW

SW

t P V V

P Q Q

G

SW

(38)

In ACO algorithm, a search space creates with

dimensions of stages on number of control variables

and states or the randomly distributed values of

control variables within a reasonable threshold.

Artificial ant's leaves colony to search randomly in

the search space based on the probability in (34) to

complete a tour matrix that consists of the positions

of ants with the same dimension of the search space.

Then, tour matrix is applied on the objective function

to find a heuristic guide function to find the best

solution and update local and global pheromone to

begin a next iteration. System parameters are adjusted

by trial and error to find the best values of theses

parameters. The ACO algorithm can be applied to

solve the proposed problem using the following steps:

Step 1: Initialization

Insert the lower and upper boundaries of each control

variable [(∆VGmin

, ∆VGmax

) and (∆QSWmin

, ∆QSWmax

)],

system parameters, and create a search space with a

dimensions of number of control variables (∆VG,

∆QSW) and the length of randomly distributed values

with the same dimension of the initial pheromone that

contains elements with very small equal values to

give all ants with the same chance of searching.

Step 2: Provide first position

Each ant is positioned on the initial state randomly

within the reasonable range of each control variable

in a search space with one ant in each control variable

in the length of randomly distributed values.

Step 3: Transition rule

Each ant decide to visit a next position in the range of

other control variables according to the probability

transition rule in equation 34 that depends on the

amount of pheromone deposited and the visibility that

is the inverse of objective function. Where, the effect

of pheromone and visibility on each other depends on

the two parameters α and β.

Step 4: Local pheromone updating

Local updating pheromone is different from ant to

other because each ant takes a different route. The

initial pheromone of each ant is locally updated as in

equation 35.

Step 5: Fitness function

After all ants attractive to the shortest path that

having a strongest pheromone, the best solution of the

objective function is obtained.

Step 6: Global pheromone updating

Amount of pheromone on the best tour becomes the

strongest due to attractive of ants for this path.

Moreover, the pheromone on the other paths is

evaporated in time.

Step 7: Program termination

The program will be terminated when the maximum

iteration is reached or the best solution is obtained

without the ants stagnations.

8. APPLICATIONS

a) Test Systems

The IEEE 30-bus standard test system [25] is used to

show the capability of the proposed technique to find

the ORPD problem and maximal preventive control

actions using ACO algorithm. The MVA base is

taken 100 and the cost of power losses is assumed

0.07 E.P. /KWh while, the cost of reactive power is

assumed 15 E.P. /KVar. The best values of ACO

algorithm parameters are α =1, β=5 ρ=0.5 and ε=5.

The load flow is done using the Newton-Raphson

load flow to get the initial values of power loss that

are 17.528 and 22.811 MW for 30-bus system.

Seven cases have been studied to obtain the maximal

preventive control actions which have the following

definitions:

Case (1): ACO algorithm is applied for the ORPD

problem considering the minimization of

transmission power losses.



Case (2): ACO algorithm is applied for maximizing

the preventive actions of load voltages

based on each generation voltage,

individually.



based on each switchable reactive power,

individually.



based on all of generation voltages,

switchable reactive power and all of them.

Case (5): The ACO algorithm is applied for

maximizing the preventive actions of all

generation reactive power based on each

generation voltage, individually.



generation reactive power based on each

switchable reactive power, individually.



generation reactive power based on all of

generation voltages, switchable reactive

power and all of them.

The considered emergency conditions that may occur

are:

a. Forced outage of line 2.

b. Unexpected outage of generation number 5.

Six cases are considered for post emergency

conditions and corrective actions due to emergency

conditions as:

Case (8): Load flow calculations for post-emergency

conditions depending on the initial state.


conditions depending on the ORPD

(Case1).


conditions depending on the maximum

preventive actions with the minimal

transmission line losses from Cases 2-7.

Case (11): Corrective actions with ORPD solutions

depending on case 8 as initial values.


depending on case 9 as initial values.


depending on case 10 as initial values).

B) Results and discussion

B.1) Normal conditions

Table 1 shows the results of the initial, ORPD

problem (Case 1) and the preventive control actions

of all load voltages based on each generation voltage

(Case 2). However, Cases (2-a)-(2-f) represent the

maximal effect of the preventive control actions from

generation voltage 1, 2, 5, 8, 11 and 13, respectively

while, all the system constraints are satisfied. In Case

1, the violation of generation reactive power at bus 13

is removed, while the transmission line losses (P.L)

are decreased by about 6.9% with respect to the initial

condition. In Cases (2-a)-(2-f), the maximal

preventive control actions with minimum line losses

and cost of power loss (CPL) obtained in case (2-b),

while case (2-a) has maximal preventive actions with

minimum root mean square of load-bus voltage

deviation (V.Dr.m.s) than other cases. Case (2-c) has

maximum preventive actions with maximum reactive

power reserve (RPR) and minimum cost of the

connected reactive power (CRP). However, line

losses are increased than Case 1.

Table 1. Preventive control actions of Cases 1 and 2

Variables Min.

Limit

Max.

Limit

Initial Case (1)

ORPD

Case (2)

2-a 2-b 2-c 2-d 2-e 2-f

Vg 1 1.00 1.10 1.050 1.0120 1.0952 1.0623 1.0786 1.0758 1.0804 1.0724

Vg 2 0.95 1.05 1.034 1.0217 1.0377 1.0315 1.0365 1.0269 1.0151 1.0379

Vg 5 0.95 1.05 1.006 1.0137 1.0352 1.0317 1.0358 1.0011 1.0062 1.0306

Vg 8 0.95 1.05 1.023 1.0148 1.0183 1.0267 1.0327 1.0085 1.0329 1.0104

Vg 11 1.00 1.10 1.091 1.0430 1.0568 1.0784 1.0546 1.0446 1.0449 1.0631

Vg 13 1.00 1.10 1.099 1.0380 1.0216 1.0516 1.0258 1.0662 1.0235 1.0662

Qsw 10 0.00 0.20 0.000 0.1023 0.1060 0.1547 0.1027 0.1027 0.1168 0.1723

Qsw 17 0.00 0.15 0.000 0.0886 0.0552 0.1426 0.0200 0.0910 0.0198 0.1166

Qsw 24 0.00 0.10 0.000 0.0822 0.0541 0.0023 0.0145 0.0338 0.0435 0.0652

QG 1 -0.30 1.00 -0.026 -0.230 0.3231 0.3821 0.2237 0.3731 0.2134 0.5874

QG 2 -0.40 0.50 -0.103 -0.187 -0.2773 -0.3311 -0.2451 -0.3286 -0.2324 -0.3921

QG 5 -0.20 0.60 0.036 0.511 0.2365 0.2921 0.2342 0.2683 0.1881 0.4226

QG 8 -0.20 0.70 0.048 0.185 0.1255 0.1458 0.1105 0.1425 0.1052 0.19501

QG 11 -0.06 0.34 0.308 0.236 0.3271 0.3294 0.3378 0.3317 0.3351 0.33951

QG 13 0.06 0.37 0.379* 0.335 0.3756 0.3684 0.3700 0.3700 0.3689 0.34621

P.L. (pu.) -- -- 0.17528 0.1631 0.1761 0.1728 0.1732 0.1756 0.1744 0.1745

CPL (EP) -- -- 1227 1141.7 1232.8 1209.6 1212.1 1229 1220.8 1221.6

(V.D.)rms -- -- 0.0182 0.0135 0.0127 0.0138 0.0170 0.0137 0.0142 0.0178

RPR -- -- 0.45 0.1769 0.2339 0.1504 0.3098 0.2230 0.2699 0.0960

CRP ( EPx103) -- -- 0.00 409.65 324.107 449.42 210.27 341.17 270.09 531

* Denotes violation of its limit



Table 2, Figures 2 and 3 show the maximal effect of

preventive actions for cases (3) and (4). For case (3),

the maximum preventive actions of load voltages

based on each switchable reactive power at buses 10,

17 and 24, respectively. Case (3-b) gives the

maximum preventive actions with minimum power

losses, CPL, while case (3-a) gives maximum

preventive actions with minimum V.Dr.m.s. Case (3-c)

gives maximum preventive actions with maximum

RPR and minimum CRP. However, line losses are

increased than case (1). For case (4), the maximum

preventive actions of load voltages based on all

generation voltages, all switchable reactive power and

all both of them. In this case, the system operators can

choice between taking more the preventive control

actions from all system generation voltages or from

all switchable reactive power or from both of them,

simultaneously. Figures 2 and 3 show the dependent

variables of load-bus voltages for cases (3) and (4),

respectively.

3 4 6 7 9 10 12 1415161718192021222324252627282930VLmin.

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

VLmax.

Load buses

Load b

us v

oltage (

pu.)

Vsp.VL (case 3.a)VL (case 3.b)VL (case 3.c)

Figure 1. Load voltages of case 3

3 4 6 7 9 10 12 14151617181920212223242526272829300.995

1

1.005

1.01

1.015

1.02

1.025

1.03

1.035

1.04

1.045

VLmax.

Load buses

Load b

us v

oltage (

pu.)

Vsp.VL (case 4.a)VL (case 4.b)VL (case 4.c)


Table 3 and Figure 4 show the results of case (5) that

obtained dependent on the maximal effects of

preventive actions of all generation reactive power

based on each generation voltage, while the system

constraints are satisfied. From this Table, case (5-d)

gives the maximum preventive actions based on

generation voltage at bus 8 with minimum

transmission line losses and CPL. While, case (5-a)

has maximal effect preventive actions with minimum

V.Dr.m.s than other cases. Case (5-e) has maximum

preventive actions with maximum RPR and minimum

CRP. However, line losses are increased than case

(1). Figure 4 shows the dependent variables of load-

bus voltages this case.

3 4 6 7 9 10 12 14151617181920212223242526272829300.99

1

1.01

1.02

1.03

1.04

VLmax.

Load buses

Load b

us v

oltage (

pu.)

Vsp.VL (case 5.a)VL (case 5.b)VL (case 5.c)VL (case 5.d)VL (case 5.e)VL (case 5.f)


Table 4 shows the maximal effect of preventive

actions for cases (6) and (7). For case (6), the

maximum preventive actions of all generation

reactive power based on each switchable reactive

power at buses 10, 17 and 24, respectively. Case (6-a)

gives the maximum preventive actions with minimum

power losses, CPL and V.Dr.m.s. While, case (6-c)

gives the maximum effect preventive actions with

maximum RPR and minimum CRP. However, line

losses are increased than case (1). For case (7), the

maximum preventive actions of all generation

reactive power based on all generation voltages, all

switchable reactive power and all both of them, In

this case, the system operators can choice between

taking more the preventive control actions from all

system generation voltages or from all switchable

reactive power or from both of them, simultaneously.

b.2) Emergency conditions

Unexpected outage of transmission line

Table 5 shows the post emergency condition cases

and corrective actions based on the pre-emergency

cases of initial, case (1) and case (2-b) that have the

maximal preventive actions with minimal line losses.

From Table 5, cases 8-10 based on initial, case (1)

and (2-b), respectively, while cases 11-13 show the

corrective actions based on initial values of control

variables of cases 8-10, respectively. From these

cases, it can be shown that, case 8 has violation limits

in generation reactive power at buses 5 and 13. Also,

case 9 has violation limits in generation reactive



power at bus 1 in addition voltage collapse at buses

26 and 30. While, case 10 hasn't any violations in

control or dependent variables, this means that the

preventive control actions are capable of avoid

voltage collapse under emergency conditions. Case

13 has a minimum transmission line loses and V.Dr.m.s

than cases 11 and 12, while case 12 has a maximum

RPR with minimum CRP. Figure 6 shows the

dependent variables of load-bus voltages for

corrective actions of cases 11-13, all of these voltages

are within their permissible limits.

Unexpected outage of generation unit

Table 6 shows the post emergency condition cases

and corrective actions based on the pre-emergency

cases of initial, case (1) and case (2-b) that have the

maximal preventive actions with minimal line losses.

From this table, case 8 has a violation limit in

generation reactive power at bus 13. Also, case 9 has

violation limits in generation reactive power at bus 1

in addition voltage collapse at buses 26 and 30.

While, case 10 hasn't any violations in control or

dependent variables, this means that the preventive

control actions are capable of avoid voltage collapse

under emergency conditions. Case 12 has a minimum

transmission line loses, CPL, while case 13 has a

minimum V.Dr.m.s. Case 11 has a maximum RPR with

minimum CRP than cases 12 and 13.

Table 2. Proposed preventive control actions of Cases 3 and 4

Variables Min.

Limit

Max.

Limit

Initial Case (3) Case (4)

3-a 3-b 3-c 4-a 4-b 4-c

Vg 1 1.00 1.10 1.050 1.0761 1.0832 1.0733 1.0893 1.0689 1.0932

Vg 2 0.95 1.05 1.034 1.0385 1.0195 1.0378 1.0211 1.0115 1.0235

Vg 5 0.95 1.05 1.006 1.0341 1.0333 1.0235 1.0135 1.0188 1.0333

Vg 8 0.95 1.05 1.023 1.0315 1.0105 1.0152 1.0192 1.0372 1.017

Vg 11 1.00 1.10 1.091 1.0447 1.0693 1.0578 1.0249 1.0379 1.0693

Vg 13 1.00 1.10 1.099 1.0536 1.0216 1.0762 1.0647 1.0517 1.0216

Qsw 10 0.00 0.20 0.000 0.1614 0.1737 0.1545 0.0328 0.1825 0.1075

Qsw 17 0.00 0.15 0.000 0.1377 0.1354 0.1268 0.0294 0.1351 0.0751

Qsw 24 0.00 0.10 0.000 0.0478 0.0816 0.0479 0.0381 0.0389 0.0841

QG 1 -0.30 1.00 -0.026 0.2667 0.5194 0.2416 0.2393 0.5332 0.4516

QG 2 -0.40 0.50 -0.103 -0.2683 -0.3983 -0.2384 -0.2491 -0.3953 -0.3621

QG 5 -0.20 0.60 0.036 0.2282 0.3752 0.1973 0.2163 0.3721 0.3068

QG 8 -0.20 0.70 0.048 0.1214 0.1817 0.1112 0.1116 0.1786 0.1592

QG 11 -0.06 0.34 0.308 0.3286 0.3400 0.3316 0.3308 0.3400 0.3382

QG 13 0.06 0.37 0.379* 0.3682 0.3634 0.3586 0.3700 0.3627 0.3498

P.L. (pu.) -- -- 0.17528 0.1741 0.1738 0.1758 0.1771 0.1730 0.1764

CPL (EP) -- -- 1227 1218.6 1216.5 1230.4 1239.9 1210.9 1234.5

(V.D.)rms -- -- 0.0182 0.0239 0.0251 0.0280 0.0165 0.0262 0.0197

RPR -- -- 0.45 0.1030 0.0593 0.1208 0.3494 0.0935 0.1833

CRP ( EPx103) -- -- 0.00 520.44 586 493.82 150.89 534.77 399.99

Table 3. Proposed control actions of case 5

Variables Min.

Limit

Max.

Limit

Initial Case (5)

5-a 5-b 5-c 5-d 5-e 5-f

Vg 1 1.00 1.10 1.050 1.0937 1.0905 1.0772 1.0741 1.0725 1.0716

Vg 2 0.95 1.05 1.034 1.0381 1.0351 1.0383 1.0331 1.0450 1.0411

Vg 5 0.95 1.05 1.006 1.0385 1.0325 1.0389 1.0347 1.0383 1.0357

Vg 8 0.95 1.05 1.023 1.0414 1.0442 1.0414 1.0472 1.0412 1.0291

Vg 11 1.00 1.10 1.091 1.0654 1.0579 1.0935 1.0373 1.0932 1.0581

Vg 13 1.00 1.10 1.099 1.0271 1.0512 1.0635 1.0632 1.0416 1.0774

Qsw 10 0.00 0.20 0.000 0.1532 0.1151 0.19821 0.1303 0.0835 0.1769

Qsw 17 0.00 0.15 0.000 0.1120 0.1246 0.1030 0.1131 0.0548 0.0553

Qsw 24 0.00 0.10 0.000 0.0055 0.0443 0.0762 0.0258 0.0436 0.0909

QG 1 -0.30 1.00 -0.026 0.4971 0.5341 0.6195 0.4421 0.2893 0.5337

QG 2 -0.40 0.50 -0.103 -0.3826 -0.400 -0.3893 -0.3589 -0.2855 -0.3798

QG 5 -0.20 0.60 0.036 0.3553 0.3921 0.4265 0.3227 0.2293 0.3621

QG 8 -0.20 0.70 0.048 0.1721 0.1793 0.2273 0.1625 0.1186 0.2539

QG 11 -0.06 0.34 0.308 0.3357 0.3285 0.3400 0.3371 0.3296 0.3183

QG 13 0.06 0.37 0.379* 0.3683 0.3699 0.3634 0.3700 0.3700 0.3482

P.L. (pu.) -- -- 0.17528 0.1779 0.1788 0.1785 0.1746 0.1755 0.1753

CPL (EP) -- -- 1227 1245.3 1251.2 1249.3 1222.3 1228.5 1227.1

(V.D.)rms -- -- 0.0182 0.0204 0.0215 0.0226 0.0218 0.0263 0.0270

RPR -- -- 0.45 0.1793 0.1659 0.0726 0.1808 0.2681 0.1269

CRP ( EPx103) -- -- 0.00 406.03 426.13 566.18 403.88 272.91 484.65



Table 4. Proposed control actions of case 6 and 7

Variables Min.

Limit

Max.

Limit

Initial Case (6) Case (7)

6-a 6-b 6-c 7-a 7-b 7-c

Vg 1 1.00 1.10 1.050 1.0612 1.0735 1.0893 1.0927 1.0724 1.0833

Vg 2 0.95 1.05 1.034 1.0282 1.0272 1.0287 1.0381 1.0325 1.0467

Vg 5 0.95 1.05 1.006 1.0381 1.0284 1.0255 1.0385 1.0283 1.0272

Vg 8 0.95 1.05 1.023 1.0437 1.0314 1.0384 1.0414 1.0214 1.0252

Vg 11 1.00 1.10 1.091 1.0695 1.0285 1.0267 1.0633 1.0253 1.0452

Vg 13 1.00 1.10 1.099 1.0583 1.0617 1.0783 1.0267 1.0752 1.0758

Qsw 10 0.00 0.20 0.000 0.1813 0.1667 0.1379 0.0973 0.1872 0.1513

Qsw 17 0.00 0.15 0.000 0.1287 0.1420 0.1146 0.1030 0.1390 0.1394

Qsw 24 0.00 0.10 0.000 0.0267 0.0247 0.0338 0.0035 0.0218 0.0653

QG 1 -0.30 1.00 -0.026 0.5355 0.5653 0.5791 0.3225 0.5682 0.3295

QG 2 -0.40 0.50 -0.103 -0.3862 -0.3653 -0.400 -0.3162 -0.400 -0.3210

QG 5 -0.20 0.60 0.036 0.4132 0.3735 0.4115 0.2337 0.3924 0.2661

QG 8 -0.20 0.70 0.048 0.2673 0.1667 0.3584 0.1125 0.2398 0.1538

QG 11 -0.06 0.34 0.308 0.3218 0.3395 0.3372 0.3400 0.3385 0.3400

QG 13 0.06 0.37 0.379* 0.3596 0.3671 0.3598 0.3700 0.3651 0.3700

P.L. (pu.) -- -- 0.17528 0.1730 0.1734 0.1788 0.1773 0.1736 0.1776

CPL (EP) -- -- 1227 1210.7 1214.1 1251.5 1241.1 1215.3 1242.9

(V.D.)rms -- -- 0.0182 0.0304 0.0318 0.0333 0.0228 0.0350 0.0283

RPR -- -- 0.45 0.1133 0.1167 0.1638 0.2462 0.1021 0.0940

CRP ( EPx103) -- -- 0.00 505.03 499.9 429.38 305.67 521.87 533.95

Table 5. Proposed procedures for forced line 2 outage

Variables Min.

Limit

Max.

Limit

Pre-emergency Post-emergency condition

Initial Case (1) Case (2-b) Case (8) Case (9) Case (10) Case (11) Case (12) Case (13)

Vg 1 1.00 1.10 1.050 1.0120 1.0623 1.050 1.0120 1.0623 1.0716 1.0637 1.0689

Vg 2 0.95 1.05 1.034 1.0217 1.0315 1.034 1.0217 1.0185 1.0172 1.0213 1.0156

Vg 5 0.95 1.05 1.006 1.0137 1.0317 1.006 1.0137 1.0317 1.0148 1.0285 1.0356

Vg 8 0.95 1.05 1.023 1.0148 1.0267 1.023 1.0148 1.0267 1.0253 1.0148 1.0224

Vg 11 1.00 1.10 1.091 1.0430 1.0784 1.091 1.0430 1.0784 1.0719 1.0831 1.0823

Vg 13 1.00 1.10 1.099 1.0380 1.0516 1.099 1.0380 1.0516 1.0413 1.0552 1.0618

Qsw 10 0.00 0.20 0.000 0.1023 0.1547 0.000 0.1023 0.1547 0.0985 0.1264 0.1475

Qsw 17 0.00 0.15 0.000 0.0886 0.1426 0.000 0.0886 0.1426 0.1482 0.1443 0.1356

Qsw 24 0.00 0.10 0.000 0.0822 0.0023 0.000 0.0822 0.0023 0.0563 0.0117 0.0118

QG 1 -0.30 1.00 -0.026 -0.230 0.3821 0.1335 -0.3085* 0.3935 0.5812 0.3972 0.3562

QG 2 -0.40 0.50 -0.103 -0.187 -0.3311 0.0450 0.4017 -0.3820 -0.3181 -0.3361 -0.3351

QG 5 -0.20 0.60 0.036 0.511 0.2921 -0.2365* -0.0388 0.0266 0.4186 0.3586 0.3263

QG 8 -0.20 0.70 0.048 0.185 0.1458 0.4816 0.5905 0.5405 0.5937 0.2148 0.4618

QG 11 -0.06 0.34 0.308 0.236 0.3294 0.3095 0.2037 0.2785 0.3379 0.3351 0.3351

QG 13 0.06 0.37 0.379* 0.335 0.3684 0.3931* 0.2660 0.2567 0.3641 0.3586 0.3584

P.L. (pu.) -- -- 0.17528 0.1631 0.1728 0.18227 0.1823 0.18187 0.17431 0.17968 0.17387

CPL (EP) -- -- 1227 1141.7 1209.6 1275.9 1276.1 1273.1 1220.2 1257.8 1217.1

(V.D.)rms -- -- 0.0182 0.0135 0.0138 0.0197 0.0306 0.0202 0.0171 0.0130 0.0097

RPR -- -- 0.45 0.1769 0.1504 0.45 0.1769 0.1504 0.147 0.1676 0.1411

CRP ( EPx103) -- -- 0.00 409.65 449.42 0.00 409.65 449.42 454.5 423.6 463.35



Table 6. Proposed procedures for generation outage at bus 5

Variables Min.

Limit

Max.

Limit

Pre-emergency Post-emergency condition

Initial Case (1) Case (2-b) Case (8) Case (9) Case (10) Case (11) Case (12) Case (13)

Vg 1 1.00 1.10 1.050 1.0120 1.0623 1.050 1.0120 1.0623 1.0751 1.0583 1.0827

Vg 2 0.95 1.05 1.034 1.0217 1.0315 1.034 1.0217 1.0185 1.0227 1.0172 1.0155

Vg 5 0.95 1.05 1.006 1.0137 1.0317 1.006 1.0137 1.0317 1.0216 1.0243 1.0227

Vg 8 0.95 1.05 1.023 1.0148 1.0267 1.023 1.0148 1.0267 1.0287 1.0291 1.0243

Vg 11 1.00 1.10 1.091 1.0430 1.0784 1.091 1.0430 1.0784 1.0672 1.0524 1.0812

Vg 13 1.00 1.10 1.099 1.0380 1.0516 1.099 1.0380 1.0516 1.0528 1.0413 1.0681

Qsw 10 0.00 0.20 0.000 0.1023 0.1547 0.000 0.1023 0.1547 0.1089 0.1513 0.1794

Qsw 17 0.00 0.15 0.000 0.0886 0.1426 0.000 0.0886 0.1426 0.1372 0.1426 0.1397

Qsw 24 0.00 0.10 0.000 0.0822 0.0023 0.000 0.0822 0.0023 0.0814 0.0486 0.0472

QG 1 -0.30 1.00 -0.026 -0.230 0.3821 0.2715 -0.3268* 0.5093 0.7554 0.6962 0.6281

QG 2 -0.40 0.50 -0.103 -0.187 -0.3311 -0.1371 0.4363 -0.3911 -0.3391 -0.3491 -0.3295

QG 5 -0.20 0.60 0.036 0.511 0.2921 --- -- --- --- --- ---

QG 8 -0.20 0.70 0.048 0.185 0.1458 0.3381 0.5221 0.4636 0.5917 0.5527 0.4803

QG 11 -0.06 0.34 0.308 0.236 0.3294 0.2859 0.2612 0.2704 0.3394 0.3352 0.3291

QG 13 0.06 0.37 0.379* 0.335 0.3684 0.4127* 0.2475 0.2368 0.3700 0.3593 0.3572

P.L. (pu.) -- -- 0.17528 0.1631 0.1728 0.17658 0.17873 0.17912 0.17552 0.16977 0.17935

CPL (EP) -- -- 1227 1141.7 1209.6 1236.1 1251.1 1253.8 1228.6 1188.4 1255.5

(V.D.)rms -- -- 0.0182 0.0135 0.0138 0.0222 0.0301 0.0208 0.0180 0.0138 0.0094

RPR -- -- 0.45 0.1769 0.1504 0.45 0.1769 0.1504 0.1225 0.1075 0.0837

CRP ( EPx103) -- -- 0.00 409.65 449.42 0.00 409.65 449.42 491.25 513.75 549.45

9. CONCLUSION

This paper presents optimal control actions using ant

colony optimization (ACO) algorithm to mitigate the

occurrence of voltage collapse in stressed power

systems. The optimal control actions from the load

voltages and generation reactive power based on

each generation voltage, each switchable reactive

power and a combination of them are prepared at

normal conditions using multi objective functions

under control, dependent and voltage collapse

constraints. This procedure helps the system

operators to choose easily the optimal feasible

solution of the preventive control action operating

condition. The preventive actions are tested under

different emergency conditions. Also, this paper

proposes an efficient procedure to obtain the optimal

preventive control actions using the ACO technique

to overcome the emergency effects in power

systems. The power system operator can ramp the

load voltages and generation reactive power based

on each generation voltage, each switchable reactive

power and a combination of them corresponding to

the amount of the preventive control actions

requirements. The proposed procedures are suitable

routines that help the decision-maker to give the best

decision for removing emergency effects with

minimum incremental transmission losses, minimum

voltage deviation and switchable devices costs.

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A COMPLETE REACTIVE POWER MANAGEMENT STRATEGY USING ANT COLONY OPTIMIZATION ALGORITHM · 2018. 12. 9. · A Complete Reactive Power Management Strategy Using Ant Colony Optimization