Comp090520.qxd


The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

_________________________________________________
*Corresponding author’s email: manojmaharana@gmail.com

A Corrective Strategy to Alleviate Overloading in
Transmission Lines Based on Particle Swarm Optimization

Method
Manoj Kumar Maharana* and K. Shanti Swarup

Department of Electrical Engineering, Indian Institute of Technology, Madras, Chennai 600 036, India

Received 20 May 2009; accepted 23 August 2009

Abstract : This paper presents novel corrective control actions to alleviate overloads in transmission lines by
the Particle Swarm Optimization (PSO) method. Generator rescheduling and/or load shedding is performed
locally, to restore the system from abnormal to normal operating state. The appropriate identification of gener-
ators and load buses to perform the corrective control action is an important task for the operators.  A new Direct
Acyclic Graph (DAG) technique for selection of participating generators and buses with respect to a contin-
gency is presented. The effectiveness of the proposed approach is demonstrated with the help of the IEEE 30
bus system. The result shows that the proposed approach is computationally fast, reliable and efficient, in restor-
ing the system to normal state after a contingency with minimal control actions.

Keywords: Direct Acyclic Graph, Participating Generators, Corrective Control Strategy, Particle Swarm Opti-
mization, Generator Rescheduling, Load Shedding

Nomenclatures

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ÜhQGƒ°S »àfÉ°T .∑ ,ÉfQÉ¡e QÉeƒc êƒfÉeCG

::áá°°UUÓÓÿÿGG)  äÉÄjõ÷G ~°ûM á«∏YÉa á≤jôW ᣰSGƒH π«°UƒàdG •ƒ£N ‘ ¬° FÉØdG ∫É≤K’G ∞«Øîàd »ë«ë°üJ ~j~L π©a åëÑdG Gòg Ω~≤jPSO∫GõfEG hCG ~dƒŸG â«bƒJ √OÉYEG â“ (

᪡e »g √ô£«°ù∏d á«ë«ë°üJ äGAGôLG RÉ‚E’ äÉMÉÑdG ∫É≤KCG h  äG~dƒª∏d Ö°SÉæŸG ¢ü«î°ûàdG .á«©«Ñ£dG ádÉ◊G ¤G á«©«ÑW ÒZ πª©dG ádÉM øe ΩɶædG IOÉY’ É«∏fi õ‚G ~b π≤ãdG

) »μ«∏jôcC’G ÊÉ«ÑdG §£îª∏d I~j~L ¥ôW .äÓ¨°ûª∏d G~LDAGìÎ≤ŸG ܃∏°S’G ih~L .É¡Á~≤J ” ~b áFQÉ£dG á«MÉædG øe äÉMÉÑdG h áªgÉ°ùŸG äG~dƒŸG QÉ«àN’ ä~ªàYG ~b (

) Ωɶf I~YÉ°ùà ɡ뫰VƒJ ” ~b(IEEE 30πbCÉH áFQÉ£dG ádÉ◊G ~©H á«©«Ñ£dG ádÉë∏d ΩɶædG √OÉY’ AƒØch ¥ƒKƒe h ,É«HÉ°ùM ™jô°S ƒg ìÎ≤ŸG ܃∏°S’G ¿ÉH èFÉàædG ÚÑJ .

.Iô£«°S äGAGôLG

áá««MMÉÉààØØŸŸGG  ääGGOOôôØØŸŸGG .π≤ãdG õjõ©J ,√OƒŸG 𫨰ûJ IOÉ©Z ,äÉÄjõ÷G ~°ûM á«∏YÉa ,á«ë«ë°üJ Iô£«°S á«é«JGΰSEG ,áªgÉ°ùe äG~dƒe ,ô°TÉÑe »μ«∏jôcCG ÊÉ«H §£fl :

N :    number of particles in the swarm.   
n :    number of elements in a particle. 
w :     initial weight of the particle.    
t :     generation number. 
rand () :     uniform random value in the range [0, 1].   
c1, c2 :     acceleration constant. 
Vi    :     voltage of the generator buses.   
Pt

i  :     best position of particle i so far.   
Sij :     the MVA flow on the line.  
Pi & Qi  :     real and reactive power of bus ‘i’.    
Sf   :     factor of safety (generally 0.9 to 0.95). 
ai, bi, ci :     are the cost coefficient of generators.   
NG :     number of participating generators. 
NB :     number of participating buses in the group.  



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The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

ing generators and load buses for generator
rescheduling/load shedding.  With respect to the contin-
gency, the participating generators are classified into two
groups based on the power flow directions. Generation in
one group of generators is increased while in the other
group it is decreased. Generators which are contributing to
the contigency line (generator flows contributing to the
contingency line) to the contingency line identified as the
Generator Decrease (GD) group and the generators which
are not contributing to the contingency line are catego-
rized as the Generator Increase (GI) group.  The corrective
control strategy is modeled as an optimization problem.
From the literature it has been found that the Particle
Swarm Optimization (PSO) method proposed by Kennedy
and Eberhart (1995) is robust and fast in solving non-lin-
ear, non-differentiable problems. The corrective control
action for overload-alleviation is a PSO-based-generator-
rescheduling and/or load-shedding method applied to the
GI and GD groups. The proposed corrective control action
provides an optimal solution of generator-rescheduling
and load-shedding which would bring back the system to
normal state.

2.  Graph Theoretic Approach

In a power system, all generators do not supply power
to all loads.  The generators which  supplying power to a
particular load can be identified easily by graph theory.
Graph theory converts the entire power system into a uni-
directional hierarchical structure, based on the power flow
contribution from the generators to the loads.  Graph the-
ory organizes the buses and lines of the network into a
homogeneous group according to the concept of 'reach of
a generator', 'generator area' and 'links'. The homogeneous
group is called the direct acyclic graph (DAG) and it is
unidirectional in nature. 

2.1 Directed Acyclic Graph (DAG) 
A graph is a set of nodes and a set of edges.  A cycle is

a path with the same node at the beginning and the end. An
acyclic graph is a graph with no path that starts and ends
at the same node. A directed acyclic graph (DAG) con-
tains no cycles; this means that if there is a route from
node 'a' to node 'b', then there is no way back. 

2.1.1 Reach of a Generator (ROG): 
The reach of a generator is defined as the set of buses

which are reached by power produced by that generator.

1. Introduction

When a major power system disturbance occurs, pro-
tection and control actions are required to stop the power
system’s degradation. The aim of corrective control strat-
egy is to avoid cascading outages or system collapse, and
to maintain system reliability. The selection of generators
and load buses for corrective control action is a crucial
task for the system operator. A fast identification of the
participating generators, load buses and a proper control
action are essential for secure and reliable operation of a
power system. Under this condition, a minimum number
of control actions like rescheduling of generators/load
shedding for the participating generators and loads are
efficient for the affected power system.

In literature many methods for transmission line over-
load alleviation via corrective strategies have been report
ed. Alleviation of line overloads by generator reschedul-
ing/load shedding based on Redial Basic Function (RBF)
neural network is reported by Ram et al. (2007).
Conjugate gradient technique to minimize the line over-
loads in conjunction with the local optimization is given
by Shandilya et al. (1993). There are several publications
available that describe direct methods of line overload
alleviation using generation rescheduling and load shed-
ding (Talukdar et al. (2005); Medicheral et al.  (1981);
Chan et al. (1979) and Christie et al. (2000). In these
methods the system operator has no choice over the selec-
tion of the generators or tagged buses to alleviate the over-
loads.    

Relative-Electrical-Distance-based (RED-based) real
power rescheduling for the participating generators to
alleviate overload of lines is proposed by Yesuratnam et
al. (2007), whereas multi-objective-PSO-based generator
rescheduling/load shedding for alleviation of overload in
a transmission network is proposed by Hazra et al.;
(2007). Sensitivity-optimized-based participating genera-
tor selection and alleviating overloads by rescheduling
generators is proposed by Dutta et al.; (2008). In this type
of control, all the generators in a system may be divided
into two groups, but in practical cases some generators do
not supply power to the congested lines. In such cases, all
the generators are handled unnecessarily, increasing the
complexity of the control strategy. The Optimal Power
Flow (OPF) technique is the most accurate method for
overload alleviation. However, OPF calculation is compu-
tationally expensive and time-consuming. 

The main intent of the paper is to propose a technique
to identify the participating generators for corrective con-
trol actions. In this DAG is used to identify the participat

NL :     number of lines in the group.  
Pgi  :     real power generated by the generator ‘i’.   
Pd & PL :     are the total demand and loss of the system.  
Gij &Bij :     conductance and susceptance of the line ‘ i to j’.  
Pt

i , g
  :     global best position of particle in the population.  

K1, K2, K3 :   the penalty factors (normally large positive real value).  



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The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

branches of a link are all in the same direction.
Furthermore, this flow in a link is always from a genera-
tor areas of rank N to a generator area of rank M where M
is always strictly greater than N. 

The construction of DAG with the help of ROG, GA
and links will be understood easily by an example given
below. For example consider a 6-bus 11-line system.
Figure  3(a) shows the real power flows from generator to
load.  By  definition the ROG of generator G1 encompass-
es all the buses  generator G2 includes buses 2, 3, 4, 5, 6
and the ROG of generator G3 includes buses 3, 5 and 6.
Bus 1, which is supplied by generator G1 only comes
under Generator area GA1 and the rank is one as only G1
power to it.  Similarly buses 2 and 4 come under genera-
tor area GA2 and the rank is 2 as power is supplied by
both generator G1 and G2.  Buses 3, 5 and 6 come under
generator area GA3 and these buses are supplied power
from all the three generators, so their rank is 3.  Lines 1-2
and 1-4 are links between generator areas GA1 and GA2,
whereas lines 2-3, 2-5, 2-6 and 4-5 are links between gen-
erator area GA2 and GA3. The line 1-5 is the link between
generator areas GA1 and GA3.  The DAG for a six-bus
system is shown in Fig. 3(b).  

3.  Particle Swarm Optimization (PSO)

PSO is a simple and efficient population-based opti-
mization method proposed by Kennedy and Eberhart
(1995). PSO is motivated by social behavior of organisms
such as fish-schooling and bird-flocking.  In PSO, poten-
tial solutions called particles fly around in a multidimen-
sional problem space. A population of particles is called a
swarm. Each particle in a swarm flies in the search space
towards the optimum or a quasi-optimum solution based
on its own experience, experience of nearby particles, and 

Power from a generator reaches a particular bus if it is
possible to find a path through the network from the gen-
erator to the bus for which the direction of travel is always
consistent with the direction of the flow as computed by a
power flow program or a state estimator proposed by
Bialek; (1996) and Kirschen et al. (1997). For large sys-
tems, the reach of a generator (ROG) can be determined
using the algorithm, explained in the flowchart shown in
Fig. 1.

2.1.2 Generator Area (GA): 
The generator area is defined as a set of contiguous

buses supplied by the same generator. Unconnected sets of
buses supplied by the same generator are treated as sepa-
rate generator area. A bus therefore belongs to one and
only one generator area. The rank of generator area is
defined as the number of generators supplying power to
the buses. It can never be lower than one or higher than the
number of generators in the system. For networks of a
more realistic size, the generator area can be determined
using the algorithm which is explained in the flowchart
shown in Fig. 2.

2.1.3 Links: 
Having divided the buses into generator areas, each

branch is either internal (ie. it connects two buses which
are part of the same generator area) or external (ie. it con-
nects two buses which are part of different generator area)
to a generator area. One or more external branches con-
necting the different generator area will be called a link.  It
is very important to note that the actual flows in all the

Start 

Count all the generator bus in the system (Set k = 1)  

Check for all the  
connected branches  

Add to ROG  

End

No 

Check for last bus  

Is the bus in ROG  

No 

Yes 
Print ROG and Stop  

Select a generator bus and Add to ROG  

No 
Yes 

Check for the flows from 
generator bus  

Yes 
No 

Yes 

No 

Yes 

Check for all the generator bus  
(k = generator)  

k = k +1  

Figure 1.  Flow  Chart   for Reach   of  a   Generator
(ROG)

Start 

Construct Reach of Generator (ROG)  

Find Common Bus 

Add the bus to GA supply by the 
generator as ROG  

End 

Is the bus in GA  

Print GA and Stop  

Compare buses of ROG (n) with ROG (n -i) 

No 

Yes 

Yes 

No 

i = i +1  

n= n -1 
& n  i 

Figure 2.  Flowchart for Generator Generator Area
(GA)



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The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

is very low, the particle may not explore sufficiently, and
if Vmax is very high, it may oscillate about optimal solu-
tion. Velocity clamping effect has been introduced to
avoid the phenomenon of "swarm explosion".  In the pro-
posed method, velocity is controlled within a band as   

(4)

where Vmax,t is maximum velocity at generation t, and Vmax
and Vmin are initial and final velocity, respectively. 

4.  Mathematical Formulation for Corrective 
Control Strategy 

The corrective control strategy by generator reschedul-
ing/load shedding has been divided into two groups (GD
and GI) of optimization problems below.

4.1 Modeling for Generator Decrease (GD) Group 
In the Generator Decrease group, the goal is to reduce

the generation with respect to load such that the bus volt-
age constraints are within the limits. This problem can be
solved by classical economic load dispatch with lineflow
and voltage limits as constraints. The objective of the con-
strained economic dispatch problem (ie. voltage and line
flow constraints) is to determine the most economic load-
ing of the generators such that the load demand in the GD
group are within their limits. The objective is to determine
the optimal set of generation Pgi (i=1,2, . .NG) so as to
minimize the total cost of generation "Ft" given by  

(5)

Subject to Equality constraints

(6)

(1)

(2)

The acceleration constant c1 called cognitive param-
eter pulls each particle towards local best position where-
as constant c2 (called social parameter) pulls the particle
towards a global best position. Usually c1 and c2 range
from 0 to 4 given in PSO Tutorial. [Online].

The inertia weight w is an important factor for the
PSO's convergence.   It is used to control the impact of the
previous history of velocities on the current velocity.  A
large inertia weight factor facilitates global exploration
(ie. searching of a new area) while a small weight factor
facilitates local exploration. Therefore, it is wise to choose
a large weight factor for initial iterations and gradually
reduce the weight  factor  in   successive   iterations   given
by Bhaskar et al. (2008).   This   can   be   done   by   using  

(3)

where wmax and wmin are maximum and minimum weight,
respectively, iter is iteration number, and itermax is maxi-
mum iteration allowed.

With no restriction on the maximum velocity (Vmax) of
the particles, velocity may move towards infinity.  If Vmax

1 

2

3 

4 

5 

6 

G1 

G2 

G3

Figure 3.  (a) Flow diagram of six bus system                                 (b) DAG of six bus system

global best position among particles in the swarm. Let 
us define a search space S as n-dimension while the 
swarm consists of N particles. At time t, each particle i 
has its position defined by 1 2{ , ,...., }

i i i i
t nX x x x  and 

a velocity defined by 1 2{ , ,...., }
i i i i

t nV v v v in variable 
space S.  The position and velocity of each particle 
change with time.  The velocity and position of each 
particle in the next generation (time step) can be 
calculated as   

1 1

,
2

  V   rand()  ( )

  rand()  ( )

i i i i
t t t t

i g i
t t

V w c P X
c P X

      

   

  1, 2,....,
1 1

i i iX X V i N
tt t

  
 

max min    
max

max

w w
w w iter

iter


  

max min    
maxmax,

max

V V
V V iter

t iter


  

2Minimize ( ) ( )
1

     
NG

f x F a P b P ct i gi i gi ii
   



( ) 0 ( ) 0
1

NG
g x P P Pgi Ldi

    




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The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

5.  Algorithm for Proposed Corrective Cont-
rol Strategy

To alleviate  line overloads due to contingency of one
or more lines in the system, the following sequence of
control actions is expected from the operator.

1. Decrease the bus power injections at the sending end
bus of the contingency line. This is incorporated by
decreasing the generation at this bus and/or at the
buses feeding power to it.

2. Maintain the bus power injections constant at the
receiving end bus of the contingency line by increas-
ing the generation at this bus and/or at the buses feed-
ing power to it.

3. If the load demand is not met satisfying all the line
constraints, then curtail the load at the receiving-end
participating loads to which power is being fed from
this bus.

Based on Powerflow/state estimation results the pre
and post-contingency DAG are constructed, and GD and
GI groups are identified, by comparing the pre-and-post-
contingency generator areas. The generator rescheduling
and/or load shedding optimization problems for the GD
and GI group are solved by a PSO technique. Adjustment
of generation and loads for the participating generators
and load buses obtained from the PSO technique are the
corrective control actions for the alleviation of overloads.
In the GD group, adjust the generation to a load within
minimum generation cost,  in the GI group, adjust the gen-
eration and load such that there are no overloads in any
lines in this group. The implementation procedure of the
proposed algorithm is given below. 

Step 1:  Initialize randomly the individual of the popula-
tion according to the limits of each generating unit (except
a slack bus) including individual dimensions, searching
points and velocities. The new velocity strategy equation
is formulated and the maximum and minimum velocity
limits of each individual are calculated using (13) and (14)

(13) 

(14)

Step 2: Compute the slack bus generator vector, losses and
line flows using Newton-Raphson load-flow method for
the above generators.

Inequality constraints

(7)

Fitness function  F*t used in PSO for this group is for-
mulated including all the constraints as follows. 

(8)

4.2 Modeling for Generator Increase (GI) Group
The aim of the Generator Increase group is to increase

the generation within the generator limits so as to meet the
demand, and if not possible, switch to load-shedding. As
generation increases in this group, there may be an over-
load in some of the lines. Alleviation of overloads in the
GI group can be formulated as an optimization problem as
follows:

The objective function 

(9)

Subject to Equality constraints:

(10)

Inequality constraints:

(11)

The fitness function F*t used in PSO for this group is
formulated as follows:

(12)

min max

min max

max

( ) 0
gi gi gi

i i i

ij ij

P P P

h x V V V

S S

  


   




1 2

3

* 2 max 2( ) ( )
1 1

2( )

NB NLLimF F K V V K S St t ij ijLi Lii j
LimK P PSlack Slack

     
 

 

2max( ) 0 ( ) 0
  

f x S S Sfij ijij all
   



2 [ cos( )
  all

sin( )] 0
( ) 0

2 [ cos( )
  all

sin( )] 0

P G v v v Gi ij i j ij i ji
j

Bij i j
g x

Q B v v v Bi ij i j ij i ji
j
Gij i j

 

 

 

 












  


  
 

  


  

min max

min max( ) 0
min max

P P Pi i i

h x Q Q Qi i i

V V Vi i i

 

   

 







* max 2 2(  ) ( )11 1

NL NB LimF S S Sf K V Vt ij ij Li Lij i
    

 

max min
max   

2

P Pd dVd 


 
 
 
 
 

max min
min   

2

P Pd dVd 


  
 
 
 
 

     Where  max max
1

n
P Pid i

 


 and min min
1

n
P Pid i

 


   

i= 1, 2,. . . n (number of generators) and  â = 0.01 a 
smaller value for smooth convergence.  



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The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

Load Reduction Factor (LRF) = 

Present modified load = (1.LRF x Initial MVA (18)
load at the bus

Step 13: The latest Gbest value generated by the individ-
ual is the optimal generation for each unit, which is
obtained by satisfying the reduced loads and all con-
straints in GI the group. 

6.  Simulation and Results

6.1  Case 1: Outage  of  line 4-12 of  IEEE 30 Bus 
The buses occupied by the generator areas for the base

case and the changes of buses due to outage of lines 4-12
are given in Table-1. The base-case power-flow diagram
indicating different generator areas is given in Fig. 4.

The base case Direct Acyclic Graph (DAG) acquired
from Table 1 is shown in Fig.  5(a). The bus numbers
occupied by the generator areas GA11, GA13 and GACom
are altered,  there is no change of buses in the generator
areas GA1, GA2, GA5, and GA8 after the outage of line 4-
12 as given in Table 1. Before outage the flows in the lines
4-12 are supplied from GA1 and GA2.  The generator areas
GA1 and GA2 are considered as GD group where as gen-
erator areas GA8, GA11, GA13 and GACom are considered
as the GI group as shown in Fig.  5(b). 

The nature of PSO convergence characteristics for the
GD and GI groups is shown in Fig.  6.  The convergence
time for the GD group varies from 1.93 sec to 2.2 sec and
for the GI group it varies from 9.1 sec to 9.8 sec respec-
tively.

Step 3:  To account for slack unit limit violation, and volt-
age limit violation, the total operating cost is augmented
by non-negative penalty terms K1, K2 and K3. Calculate
augmented cost  F*t using (8) for GD group and (12) for
GI group.

Step 4: Among the population, the minimum augmented
fuel cost value is taken as the best value. The best-aug-
mented fuel cost value in the population is denoted as the
Gbest. Remaining individuals are assigned as the Pbest.

Step 5: Modify the velocity V of each individual real
power-generating unit Pgi  using (1).

Step 6:   Check the limits on velocity using (15)

(15)

Step 7:   Modify the member position of each individual
Pgi using (16).

(16)

(17)

Step 9:  Modified member positions in step 8 are taken as
the initial value for the N-R load-flow method. Compute
slack bus power and line-flows using the N-R load flow
method.

Step 10: Calculate the augmented fuel cost using (8) for
the GD group and (12) for the GI group.  Gbest and Pbest
values are assigned. If the Gbest value is better than Gbest
value in Step 4 then current value is set to Gbest. If the
present Pbest value is better than the Pbest value in Step
4, current value is set to Pbest.

Step 11: In the  GD group if the iteration reaches the max-
imum go to Step 13, otherwise go to Step 4 and the Gbest
and Pbest values obtained in Step4 are replaced by the lat-
est Gbest and Pbest values acquired in Step 10.  In the GI
group if the iteration reaches the maximum and the solu-
tion does not converge, then go to step 12.

Step 12: Reduce the load using the load-reduction factor
given in Eq. (18) and jump to Step 4 after replacing Gbest
and Pbest values with the latest values obtained in Step
10.

( 1) ( 1)max maxIf ,  then 

( 1) ( 1)min minIf ,  then 

t tV V V Vid d id d
t tV V V Vid d id d

 
 

 
 

( 1) ( ) ( 1)t t tPg Pg Vid id id
 

 

Step 8:   ( 1)tidPg
 must satisfy the capacity limits  of the 

generators and are given by  (17) 

( 1) ( 1)max maxIf Pg ,  then Pg

( 1) ( 1)min minIf Pg ,  then Pg

t tPg Pgid id id id
t tPg Pgid id id id

 
 

 
 

Net Load at overload bus - Allowable  Po wer to the bus

Total MVA Load

     To verify the effectiveness of the proposed 
corrective control strategy, simulation was carried out 
on the IEEE 30 bus power system. The simulation was 
done in a 2.66 GHz Pentium IV, 512 MB RAM 
personal computer. Cost Coefficients and MW limits of 
the generators are given in Appendix A. The selection 
of contingency cases was considered randomly. The 
upper and lower limits of load bus voltages were taken 
as 1.05 p.u. and 0.95 p.u. respectively. The generator 
bus voltages were fixed to their specified values. Line- 
loading (MVA) limits of 125% of base case were 
considered. In the PSO-based optimization method, a 
population size of 10 with number of iterations limited 
to a maximum of 50 was taken. An increases in 
population size provides better optimal results 
sacrificing more computation time.  PSO parameters 
c1= 2.0, c2= 2.1, wmax = 0.9, wmin= 0.4 were selected 
from Hazra et al.; (2007) and Bhaskar et al.; (2008). 
For each test case, 50 independent trials were carried 
out. An acceptable variation from 1% to 10% is 
observed in few worst cases among the 50 trials. 



37

The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

Table-2 shows the results of the corrective control strat-
egy of generator rescheduling/load shedding for the out-
age of line 4-12. It can be observed from Table-2 that the
line flows after the occurrence of contingency (B) exceeds
the MVA limits (A). The line overloading is removed by
rescheduling generators 1, 2, 8, 11, 13 and a 30.13 MVA
of load shedding, shared by load buses 12, 14-19, 23 and
24 respectively.  The post-contingency flows (C) are with-
in the MVA limits (A) after the control strategy as seen
from Table-2.  The pre-contingency and post-contingency
voltage magnitudes after corrective control action are
given in Table 3.  From Table 3 it is observed that all load
bus voltages are with in the voltage limits.

Sl.  
No. 

Generator 
Area 

Bus Numbers 
occupied 

(base case) 

Bus Numbers 
occupied 

(after outage 
of line 4-12) 

1 GA1 1, 3 1, 3 
2 GA2 2, 4 2, 4 
3 GA3 6, 7, 8, 27-30 6, 7, 8, 27-30 
4 GA4 12-16, 18, 23 13 
5 GA5 5 5 
6 GA6 9, 10, 11, 20-

22 
9, 10, 11, 16-

26 
7 GA7 17, 19, 24-26 12, 14, 15 

Table 1.  Buses occupied by generator areas for IEEE
30 bus system

5 

16 
17 

G8
8 

G1
1 

G5

G2

G1
1 

2 

3 
4 

6 

7 

9 

10 11 

12 13 

14 
15 

26 

27 
18 

19 

20 
21 

22 

23 24 

25 

28 

29 30 

G1
3 

Figure  4.  Base  case flow diagram indicating genera-
tor area of IEEE 30 bus system

Figure 5.  (a) Base case DAG for IEEE 30 bus system

  G D  G r ou p  

G I G r o u p  

G A 1 

L ink 1  

G A C o m  

G A 2 

G A 5 
G A 8 

G A 1 3 
G A 1 1 

L in k 2  

L ink 3  

L ink 5  

L ink 6  

L ink  8 L in k 9  

Figure 5.  (b) DAG after outage of line 4-12

(a) GD group

(b) GI group

Figure 6.  PSO convergence characteristics for outage
of line 4-12



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The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

1. Overload Condition 2. Corrective Control Strategies 
Generation Load Line  

4-12 
 out 

(A) 
Max 
Cap. 

(B) 
Contin 
-gency 
 Flows 

Pre -  
contingency 

Control 
action  

Pre - 
contingency 

Control  
action 

(C) 
Post  
cont. 
Flow 

Lines MVA MVA Bus MW MW Bus MVA MVA MVA 

Remarks 
 

4-6 
6-9 

6-10 
9-10 

12-13 
16-17 
18-19 
19-20 
10-20 
10-17 
22-24 
23-24 
24-25 
25-27 
28-27 
6-28 

48.23 
20.86 
14.79 
41.15 
23.38 

5.11 
3.57 
9.09 

12.19 
8.56 
8.98 
3.19 
1.88 
4.32 

21.84 
16.33 

62.68 
30.13 
20.34 
47.67 
28.34 

9.56 
4.49 

13.77 
16.44 
18.92 

9.85 
5.91 
5.46 
8.28 

22.17 
17.03 

1* 
2* 
5 
8* 

11* 
13* 

138.69 
57.56 
24.56 
35.00 
17.93 
16.91 

105.58 
59.17 
24.56 
37.12 
22.41 
18.24   

2 
3 
4 

10 
12* 
14* 
15* 
16* 
17* 
18* 
19* 
20 
21 
23* 
24* 
26 

25.14 
2.68 
7.77 
6.14 

13.48 
6.40 
8.57 
3.94 

10.71 
3.33 

10.09 
2.31 

20.77 
3.57 

10.98 
4.18 

25.14 
2.68 
7.77 
6.14 
7.81 
3.71 
4.69 
2.28 
6.21 
1.93 
5.85 
2.31 

20.77 
2.07 
6.36 
4.18 

46.35 
14.64 
12.09 
35.22 
20.73 

2.17 
0.78 
6.61 
9.05 
8.28 
8.16 
1.12 
1.18 
4.16 

18.17 
12.88 

30.13 
MVA load 
shedding 
and there 

are no 
overload 

in any 
lines 

 

 

Table 2.  Simulation results for outage of line 4-12 of IEEE 30 bus system

The ‘*’ indicates the alteration of generation and loads as corrective control action at that bus

Pre Contingency Bus Voltage Post Contingency Voltage (After control action) 
Sl. No. Voltage  (pu) Sl. No. Voltage  (pu) Sl. No. Voltage  (pu) Sl. No. Voltage  (pu) 

1 1.050 16 1.047 1 1.050 16 1.046 
2 1.045 17 1.043 2 1.045 17 1.048 
3 1.023 18 1.031 3 1.039 18 1.046 
4 1.017 19 1.028 4 1.036 19 1.047 
5 1.010 20 1.033 5 1.010 20 1.050 
6 1.014 21 1.036 6 1.032 21 1.049 
7 1.004 22 1.036 7 1.015 22 1.049 
8 1.010 23 1.030 8 1.035 23 1.042 
9 1.053 24 1.024 9 1.045 24 1.039 

10 1.048 25 1.019 10 1.044 25 1.037 
11 1.082 26 1.002 11 1.082 26 1.019 
12 1.060 27 1.025 12 1.048 27 1.043 
13 1.071 28 1.009 13 1.071 28 1.029 
14 1.045 29 1.005 14 1.049 29 1.024 
15 1.041 30 0.993 15 1.048 30 1.013 

Table 3.  Pre and post contingency voltage magnitude

Generator Rescheduling (MW) P Generator  
Number Result Reported on Dutta et al. (2008)  Proposed Approach  

1 -59.0 -55.59 
2 19.9 18.70 
5 13.0 18.30 
8 6.0 4.60 
11 6.5 9.20 
13 7.0 Idle 

Total (MW)  111.4 106.39 

Table 4.  Comparison result for congestion management of lines 1-2 and 2-6



39

The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

Participating Generators for outage of line 4-12 
Generator Number Max (MW) Min (MW) Best (MW) 

 1   (GD) 109.56 104.43 107.58 
 2   (GD) 61.71 57.55 59.77 
8   (GI) 39.06 30.78 34.43 
11  (GI) 24.89 19.86 22.33 
13  (GI) 21.44 16.39 18.69 

Table 5.  Generators statistical performance for 50 trials

Trial Number Trial Number

G
en

er
at

io
n 

(M
W

)

G
en

er
at

io
n 

(M
W

)

a)  GD group (G1, G2)                                       b)  GI group (G8, G11, G13)

Figure 7.  Trial by trial statistical performance for outage of line 4-12

Trial Number Trial Number

a) GD group                                                                        b) GI group

Figure 8.  Statistical performance of convergence time for outage of line 4-12

T
im

e 
in

 S
ec

T
im

e 
in

 S
ec



40

The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

References

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Dutta, S. and Singh, S.P.,  2008 , "Optimal Rescheduling
of Generators for Congestion Management Based on
Particle Swarm Optimization", IEEE Transactions on
Power Systems, Vol. 23(4),  pp 1560-1569.

Hazra, J. and Sinha, A. K.,  2007, "Congestion
Management using Multi-objective Particle Swarm
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"Generation Rescheduling and Load Shedding to
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PSO Tutorial. [Online]. Available:
http://www.swarmintelligence.org/tutorials.php

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6.2 Comparison study  for overload of line 1-2 and 
2-6

In the IEEE 30 bus systems the lines 1-2 and 2-6 are
overloaded. The generator area for the base case is given
in Table-1, and the DAG is shown in Fig. 5a.  The over-
load in the lines 2-6 is due to the load demand in the gen-
erator areas 5, 8 and 11. The lines 2-6 receive power from
generator areas 1 and 2, so the GA1 and GA2 are declared
as the GD group. The power flows through the lines 2-6 to
supply the loads in the generator areas 5, 8, 11 and GACom.
Generator areas 5, 8, 11 and GACom are declared as GI
group.  The lines 1-2 and 2-6 overloads are removed by
rescheduling the generators 1, 2, 5, 8 and 11. The compar-
ison results for overload alleviation by generator resched-
uling are given in Table 4. 

Before rescheduling  lines 1-2 and 2-6 are loaded to
170.04 MVA and 66.79 MVA with respect to their line
limit 130 MVA and 65 MVA respectively.  After resched-
uling the power flows on the lines 1-2 and 2-6 are 129
MVA and 60 MVA reported in Dutta et al. (2008) where-
as in the proposed approach they are found to be 129.35
MVA and 61.37 MVA respectively. 

6.3 Statistical Performance Analysis
The GD and GI group optimizations are carried out for

50 independent trials for the IEEE 30 bus system. The
maximum and minimum generation output, best output
obtained, and the  maximum number of times for the GD
and GI groups, are given in Table 5.

The trail-by-trail statistical performance in respect of
generation output and convergence times for the GD and
GI groups for outage of lines 4-12 of the IEEE 30 bus sys-
tem are shown graphically in Figs. 7 and  8 respectively.

From the above results, we observe that the proposed
method can alleviate the line overloads due to contin-
gency, in any system within minimal control actions,
thereby preventing the cascading of outages, leading to
blackout or system collapse.

7.  Conclusions

A novel approach to corrective control strategy of gen-
eration-rescheduling and/or load shedding with subject to
contingencies is presented. Identification of effective gen-
erator and/or load buses due to a contingency is achieved
using a Direct Acyclic Graph (DAG). The concept of local
optimization is utilized, wherein the implementation of
control action becomes easy and effective. This enables
the operator to quickly select the appropriate number of
buses for a good sub-optimal solution. This task is
achieved by means of a particle swarm optimization
(PSO) method, which provides the best solution with less
control decision and actions corresponding to generation
and/or load increase/decrease respectively.  The solution
was sufficient for initiating control actions during an
emergency as it protects the system from cascading out-
ages.



41

The Journal of Engineering Research  Vol. 7, No. 1, (2010)  31-41

Cost-efficient Generation Rescheduling and Load
Shedding for Congestion Management," Electrical
power and Energy Systems, Vol. 27, pp. 379-388.

Yesuratnam, G.  and Thukaram, D., 2007, "Congestion
Management in Open Access Based on Relative
Electrical Distance using Voltage Stability Criteria,"
Electric Power System Research, Vol. 77,  pp.1608 -
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