This document presents an improved differential evolution algorithm for congestion management in power systems with wind turbine generators. The algorithm determines the optimal location of new wind farms based on bus sensitivity factor and wind availability factor. It then uses an enhanced differential evolution approach to reschedule generators and install new wind farms to relieve transmission line congestion. The algorithm is tested on the IEEE 30-bus system and is shown to be more effective at congestion management than other approaches.

1. Contents lists available at ScienceDirect
Renewable and Sustainable Energy Reviews
journal homepage: www.elsevier.com/locate/rser
An Improved Differential Evolution algorithm for congestion management
in the presence of wind turbine generators
S.T. Suganthia,⁎
, D. Devarajb
, K. Ramarc
, S. Hosimin Thilagard
a
Dept of EEE, Sri Shakthi Institute of Engineering and Technology, Coimbatore, India
b
Dept of EEE, Kalasalingam University, Srivilliputur, India
c
Faculty of Engineering Multimedia University, Cyberjeya, Malaysia
d
Dept of EEE, College of Engineering, Anna University, Chennai, India
A R T I C L E I N F O
Keywords:
Congestion management
Generation rescheduling
Wind Availability Factor
Bus Sensitivity Factor
Improved Differential Evolution
A B S T R A C T
Congestion management is imperative for reliable and secure system operation in restructured power systems.
Since the installation of wind farms at proper locations offers the possibility of congestion relief, this paper
investigates congestion management in power systems with specific consideration of wind energy sources. The
optimal location of a wind farm is determined by the Bus Sensitivity Factor and the Wind Availability Factor.
Differential Evolution is a population-based heuristics algorithm used for solving non-linear optimization
problems. We propose an Improved Differential Evolution based approach to ease congestion in transmission
lines by generator rescheduling and installation of new wind farms. In this approach, an enhanced mutation
operator is introduced to improve the performance of the Differential Evolution algorithm. A standard IEEE-30
bus system is used to evaluate the proposed algorithm under critical line outages. The simulation results show
that the proposed approach is more effective than other approaches.
1. Introduction
In competitive electricity markets, due to Transmission Open
Access (TOA) the transmission networks are loaded up near to their
stability limits. The electrical power that is transmitted has various
limits, such as thermal, voltage, and stability limits. The system is
congested if any one of these limits is reached [1]. The security of the
power system will be violated if the system does not operate within its
limits. This failure can cause the power system to experience wide-
spread blackouts, leading to severe economic and social consequences.
Congestion Management (CM) is thus the fundamental transmission
problem to be addressed to ensure that transfer limits are observed [2].
Rescheduling generators, load curtailment, regulaing or tap setting
transformers, FACTS devices, etc. can relieve congestion. The ISO
generally prefers the approach of rescheduling generators as it does not
alter the system topology. For CM, several techniques like optimum
power dispatch and a price-based framework have been reported in [3].
In [4,5], CM techniques for different market structures like Bilateral/
Multilateral and pool market structures are proposed. Voltage stability
enhancement during congestion is discussed in [6]. In [7], the
applications of FACTS devices, such as TCSC and TCPAR, for CM are
discussed. In [8], the CM problem is formulated in an OPF framework.
The congestion cluster-based method and ac transmission congestion
distribution factor approach for CM are reported in [9] and [10].
Sensitivity Index has been proposed in [11] to identify generators to be
rescheduled to alleviate congestion.
The CM is intuitively an optimization problem with ample con-
straints. Traditional techniques for relieving congestion can be found in
[12–14]. Specifically, the Lagrangian Relaxation (LR) based algorithm
and Linear Programming (LP) and Sequential Quadratic Programming
(SQP) based approaches have been proposed for CM in these articles.
As these techniques face difficulty handling the constraints of CM, they
do not guarantee the global optimum solution. Recently, advancements
in computation technology, like parallel computation, have stimulated
many researchers to focus on the application of Artificial Intelligence
(AI) techniques for CM problems in restructured power systems
[15,16]. The CM problem has been successfully solved with the help
of the Differential Evolution (DE) algorithm, which was originally
proposed by Storn and Price [17,18]. Although DE is a very simple and
efficient optimization algorithm, it sometimes suffers from slow con-
vergence. It has been observed that mutation plays the key role in the
convergence process. A new operator named the Double Best Mutation
Operator (DBMO) has therefore been developed in order to speed up
convergence and to obtain the optimal solution [24].
http://dx.doi.org/10.1016/j.rser.2017.08.014
Received 30 September 2016; Received in revised form 26 June 2017; Accepted 7 August 2017
⁎
Corresponding author.
E-mail address: suganthi.sb@gmail.com (S.T. Suganthi).
Renewable and Sustainable Energy Reviews 81 (2018) 635–642
Available online 18 August 2017
1364-0321/ © 2017 Elsevier Ltd. All rights reserved.
MARK

2. In competitive electricity markets, as conventional energy tends to
be exhausted, it is important to give exceptional attention to the
advancement of renewable energy sources. Wind power has surpassed
other renewable energy sources because of its reduced operational and
maintenance costs [20]. Recently, incorporation of Wind Farms (WF)
into power systems for congestion alleviation has been on the rise.
Integration of wind energy sources not only provides congestion relief
but can also help reduce active power losses in addition to improving
the voltage profile [20]. An approach based on locational marginal
prices (LMPs) for incorporating wind energy for CM is discussed in
[19]. Incorporation of WF with congestion management problems
using sensitivity factors is discussed in [20]. However, the WF locations
were selected in [20] without considering wind availability at the
locations.
Installation of a WF into a power system to alleviate congestion
should be based on the following significant aspects:
1) Availability of the required quantity of wind.
2) The sensitivity of the location of the WF for alleviating congestion.
A new strategy for identifying the location of wind farms based on
the Wind Availability Factor (WAF) and Bus Sensitivity Factor (BSF) is
proposed in this paper.
Development of a CM strategy for integration of a wind energy
conversion system using an Improved Differential Evolution (IDE)
algorithm is the objective of this work. A standard IEEE-30 bus system
is used to test the proposed technique. The paper is organized as
follows. In Section 2, the wind farm model is presented. Section 3
describes the proposed methodology for placement of wind farms.
Section 4 presents the congestion management problem in a deregu-
lated environment. Section 5 provides an overview of the IDE
algorithm. The CM solution methodology using IDE is elaborated in
Section 6. Results showing the effectiveness of the projected method
are discussed in Section 7. The major contributions and conclusions are
discussed in Section 8.
2. Modeling of the wind turbine generator
The bus in which the wind turbine generator is connected is
modelled as a PQ bus. The steady-state model of the wind turbine
generator (induction generator) [21] is shown in Fig. 1. In order to
compensate for the reactive power consumption of the induction
generator a shunt capacitor is connected as shown in Fig. 1.
According to Boucherot's theorem, the reactive power consumption
of the wind farm generator can be written as [21]:
Q V
X X
X X
X
V RP
R X
X
V RP P R X
R X
=
−
+
+ 2
2( + )
−
( + 2 ) − 4 ( + )
2( + )
c m
c m
2 2
2 2
2 2 2 2
2 2
(1)
Q V
X X
X X
X
V
P≈
−
+ ,c m
c m
2
2
2
(2)
where
V is the rated voltage,
X is the sum of the stator and rotor leakage reactance per phase,
Xm is the magnetizing reactance per phase,
Xc is the reactance of the capacitor bank per phase,
R is the sum of the stator and rotor resistance per phase, and
P is the real power generated by the wind generator (positive when
injected into the grid).
The real power output of the induction generator is expressed as
[21]:
P ρAU C=
1
2
,P
3
(3)
where
ρ is air density (kg/m3
)
A is the area of rotor (m2
)
U is the wind velocity (m/sec), and
Cp is the coefficient of power.
3. Proposed method for placement of wind farm
A method for the placement of wind farms based on bus sensitivity
and wind availability is proposed in this section.
3.1. Bus Sensitivity Factor (BSF)
The BSF for a congested line k connected between buses i and j is
defined as the change in the active power flow in the transmission line
due to a unit change in power injection at bus n [20]. Mathematically,
the BSF for line k is defined as,
BSF
ΔP
ΔP
= ,n
k ij
n (4)
where ΔPij is the change in real power flow of line k for an active power
injection ΔPn at bus n. The BSF is calculated as follows.
The active power flow on the congested line can be written as
P V Y θ VV Y θ δ δ= − cos + cos( + − )ij i ij ij i j ij ij j i
2
(5)
P
P
δ
δ
P
δ
δ
P
V
V
P
V
VΔ =
∂
∂
Δ +
∂
∂
Δ +
∂
∂
Δ +
∂
∂
Δ .ij
ij
i
i
ij
j
j
ij
i
i
ij
j
j
(6)
Eq. (6) can be rewritten as
P a δ b δ c V d VΔ = Δ + Δ + Δ + Δ ,ij ij i ij j ij i ij j (7)
where
a VV Y θ δ δ= sin( + − )ij i j ij ij j i (8)
b VV Y θ δ δ= − sin( + − )ij i j ij ij j i (9)
c V Y θ δ δ VY θ= cos( + − ) − 2 cosij j ij ij j i i ij ij (10)
d VY θ δ δ= cos( + − ).ij i ij ij j i (11)
We know that
Fig. 1. Static model of Induction machine.
S.T. Suganthi et al. Renewable and Sustainable Energy Reviews 81 (2018) 635–642
636

3. P
Q
J δ
V
J J
J J
δ
V
Δ
Δ
= Δ
Δ
= Δ
Δ
.11 12
21 22
⎡
⎣
⎢
⎤
⎦
⎥
⎡
⎣
⎢
⎤
⎦
⎥
⎡
⎣
⎢
⎤
⎦
⎥
⎡
⎣
⎢
⎤
⎦
⎥
(12)
Neglecting P-V and Q-δ coupling,
P J δΔ = [ ][Δ ]11 (13)
Q J VΔ = [ ][Δ ].22 (14)
From (13)
δ J P M PΔ = [ ] [Δ ] = [ ][Δ ]11
−1
(15)
∑δ m P iΔ = Δ = 2, …, N, (assuming bus 1 is the slack bus),i
l
N
il l
=2 (16)
where N is the number of buses.
As the coupling between ΔP and ΔV has been neglected, Eq. (7) can
be written as
P a δ b δΔ = Δ + Δ .ij ij i ij j (17)
Substituting (16) in (17) we get
∑ ∑P a m P b m P
P a m b m P a m b m P
a m b m P
Δ = Δ + Δ
Δ = ( + )Δ + ( + )Δ
+ ... + ( + )Δ .
ij ij
l
N
il l ij
l
N
jl l
ij ij i ij j ij i ij j
ij in ij jn n
=2 =2
1 1 1 2 2 2
(18)
The above equation can be written as
P BSF P BSF P BSF PΔ = Δ + Δ + ... + Δ .ij
k k
n
k
n1 1 2 2 (19)
Therefore, the BSF corresponding to the nth bus and line k
connected between buses i and j is
BSF a m b m= + .n
k
ij in ij jn (20)
The BSFs of all buses (including load buses) except the slack bus
can be calculated using Eq. (20). Congestion Management can be
performed by placing a WF at a load bus. Hence the PQ wind generator
model is considered in this work. The BSF values may be used to
identify sensitive buses at which a change in power injection can relieve
the transmission line congestion. The buses with high BSF values are
identified as the most sensitive buses, where the WFs may be placed.
3.2. Wind Availability Factor (WAF)
The installation of wind farms not only helps alleviate conges-
tion in transmission lines but also increases benefits for investors
by enhancing system stability. The key factor that decides the
location of a WF is the WAF. Wind availability depends on the
geological location of a region. Wind speed maps are available for
almost all regions in the world. A sample wind speed map is given
in Fig. 2. Based on the wind speed map, the WAF is calculated.
There must also be enough space (area) for WF installation.
Considering space and wind speed, the Wind Availability Factor
(WAF) for each location is defined as
WAF f SA AW
SA
AW
= ( , )
= 0 or 1
0 ≤ ≤ 1
i i i i
i
i (21)
In (21) SAi is the space available at location i, AWi is the average
wind speed at that location, and fi is the appropriate function relating
SA and AW to WAF. Generally, the function is defined as
f SA AW SA AW( , ) = * .i i i i i (22)
The value for the space factor is either 0 or 1. If there is enough space
for wind installation, then the space factor is 1; otherwise it is zero. The
WAF can be calculated with the aid of a wind speed map of each location.
3.3. Placement of wind farm
A potential wind farm location can be identified by considering both
the BSF and WAF values. To identify the optimal location, the Wind
Farm Factor (WFF) is introduced. The WFF is defined as
WFF f BSF WAF= ( , ).i i i i (23)
The function can be written as
f BSF WAF BSF α WAF( , ) = + .i i i i i i (24)
Here αi is the weighting factor, which is in the range [0, 1].
A more predominant factor in alleviating congestion is the identi-
fication of buses that are more sensitive to the power flow in that line.
In consideration of this, BSF can be weighted more heavily than WAF.
The bus with the highest WFF value is thus identified as the location for
placement of a WF.
4. Problem statement – congestion management
The main objective of the congestion management problem considered
here is to find the total amount of rescheduling power required to alleviate
transmission congestion. This article proposes a CM technique incorporat-
ing wind energy sources. Though wind power alone may be adequate to
alleviate congestion in some cases, in this paper we propose rescheduling
existing generators along with the wind power generation for congestion
management, as the actual power generation by the wind turbines may be
quite random [23]. The amount of rescheduling power of conventional
generators is calculated based on the bids provided by the generating units.
The CM problem is formulated as an optimization problem with the
objective of minimizing congestion cost. Here the congestion cost is only
the cost required to reschedule the active power of generating units. The
objective function for this problem is stated as follows:
Minimize Re-dispatch Cost (RC)
∑RC R P R P R P= ( Δ + Δ ) +
i
N
i
u
gi
u
i
d
gi
d
w w
=1
g
(25)
Subject to
P PΔ , Δ ≥ 0gi
u
gi
d
(26)
P P P P P P= + Δ or = − Δgi gi gi
u
gi gi gi
d0 0
(27)
P P P i N≤ ≤ = 1, …,gi gi gi g
min max
(28)
Here PΔ gi is the active power to be rescheduled by the ith
generator.Pgi is the active power generation at bus i and Pgi
0
is the
original active power generation from the market clearing operation. Ng
is the total number of generating units, Pw is the active power
generation of the WF, Ru
is the incremental bid submitted for a unitFig. 2. Sample wind speed map at Amagro weather station, Spain, 1999.
S.T. Suganthi et al. Renewable and Sustainable Energy Reviews 81 (2018) 635–642
637

4. increase in the active power, and Rd
is the decremental bid submitted
for a unit decrease in the active power generation. As wind is a
naturally available energy source, the bidding cost of wind Rw is
considered to be zero in this problem formulation. The Independent
System Operator (ISO) has to ensure the system security for this
reschedule. Any reschedule in active power, either for an increase or
decrease, involves payment to the corresponding generating unit.
The additional constraints are
Equality Constraints at all nodes:
∑P V V G δ δ B δ δ= [ cos( − ) + sin( − )]i i
i
N
j ij i j ij i j
=1 (29)
∑Q V V G δ δ B δ δ i N= [ sin( − ) − cos( − )] = 1, …,i i
i
N
j ij i j ij i j
=1 (30)
Inequality Constraints:
Voltage Constraint at all load buses:
V V V≤ ≤i i i
min max
(31)
Constraint on reactive power at all generator buses:
Q Q Q≤ ≤Gi Gi Gi
min max
(32)
Transmission line flow limit at all lines:
F F≤ .l l
max
(33)
Eqs. (29) and (30) represent the power balance in all the buses. N is
the total number of buses in the system. P Qandi i are the injected
active and reactive powers at bus i. Vi and Vj are the voltage magnitude
at buses i and j. Similarly, δi and δj are the voltage angles of buses i and
j.Gij and Bij are the conductance and susceptance between buses i and j.
Eq. (31) enforces the voltage limits of all the load buses, with minimum
and maximum values of 0.95 and 1.05 p.u., respectively. Eq. (32)
represents the limits of reactive power production of the generators. In
Eq. (33), Fl
max
is the maximum MVA limit of the lth
transmission line,
and Fl is the actual MVA flow in that line. The above optimization
problem is solved using the Improved Differential Evolution algorithm,
the details of which are given in the next section.
5. Proposed method – Improved Differential Evolution
Differential Evolution (DE) [17,18] is a simple and robust meta-
heuristics algorithm that possesses self-adapting capabilities at differ-
ent stages of the search process. During the initial stages of the search
process the perturbations are large since the distance between the
solutions in the population is huge. In the mature stages, all of the
population converges to a small region, and the DE adapts accordingly.
This allows the algorithm to perform faster than other metaheuristic
algorithms.
There exist many strategies for population reproduction resulting in
different variants. Price and Storn proposed several DE strategies using
the notation DE/x/y/z, where x, which is either a randomly chosen
vector or the best vector of the current generation, is the vector to be
mutated; y is the number of vectors used in the mutation; and z is the
crossover method. The performance of DE depends on the selection of
a strategy and its three key control parameters: population size NP,
scaling factor F, and crossover rate CR. Proper choice of the strategy
and associated control parameters leads to the best searching perfor-
mance of the algorithm.
Mutation therefore plays a key role in the convergence process; an
attempt is made here to speed up the convergence process by
introducing the Double Best Mutation Operator (DBMO) [25]. The
main procedure of the proposed IDE algorithm is depicted in Table 1.
6. Implementation of IDE algorithm for CM problem
The implementation of the proposed IDE algorithm for the CM
problem is summarized as follows.
Table 1
Proposed IDE Algorithm.
1. Parameter setup: identify the control parameters (Decision
variables Xi), and set the Population size (NP), Scaling factor
(F), Crossover constants (CR) and Maximum number of
generations (Gmax).
2. Initialization: generate initial values for all variables in the
population of NP vectors randomly. The variables must lie
within the boundaries of the entire search area:
X X rand X X= + (0, 1)( − ),i i i i
0 min max min
where i = 1,…,D and Xi
min
and Xi
max
are the lower and upper
bounds of the ith
decision variable.
3. Mutation: generate new parameter vectors called mutant vectors,
with the fixed Scaling Factor (F)
X X F X X i NP= + ( − ), ∈ ,i
g
a
g
b
g
c
g/ +1
where X X X, anda
g
b
g
c
g
are selected randomly from NP.
A modification made with the existing mutant vector is called the
Double Best Mutation Operator
(DBMO). The DBMO is described by
X X C rand X X C rand X X= + × × ( − ) + × × ( − ),i
g
gbest
g
ibest
g
i
g
gbest
g
i
g/ +1
1 1 2 2
where Xgbest
g
is the global best solution of all the individuals in the
population; Xibest
g
denotes the
individual best solution; rand1 and rand2 are uniform random
numbers in [0, 1]; and C1, and C2
are constants, preferably taking the value 2.
4. Cross over: With the predetermined CR, a trial vector Xi
g//
is
generated by
X
X if ρ C
X otherwise
j D=
≤
,
∈ ,ji
g ii
g
R
ji
//
/ +1
0
⎪
⎪
⎧
⎨
⎩
where D is the number of decision variables and ρ is a random
number with uniform distribution on [0,1].
5. Evaluation/Selection: The trial vector Xi
g// +1
generated in Step
4 will compete with its parent individuals Xi
0
using the following
selection criterion:
X
X if f X f X
X otherwise
=
( ) ≤ ( )
,
.i
g i
g
i
g
i
i
+1
// +1 // +1 0
0
⎪
⎪
⎧
⎨
⎩
6. Termination: The process is repeated until the number of
generations reaches the preset Gmax.
Table 2
Power flow violations in the congested lines.
Congested lines Line flow
(MVA)
Maximum limit
(MVA)
Violation
(MVA)
1–3 170.4604 130 40.46
3–4 162.1420 130 32.14
4–6 102.5795 90 12.57
S.T. Suganthi et al. Renewable and Sustainable Energy Reviews 81 (2018) 635–642
638

5. 6.1. Representation of decision variables
Considering the objective function as well as the constraints on the
CM problem, a generator's active power change (ΔPgi) and active power
generation of WF (Pw) are considered as decision variables. In the
initialization process, these decision variables are randomly selected,
within the maximum and minimum limits, using Eq. (28). The strategy
(DE/rand/1/bin) and parameters then have to be assigned. The
representation of the variables is presented as follows.
⏟⏟ ⏟⏟ ⏟ ⏟
13.5 11.8 0.6 3.5 3.6 14
P P P P P PΔ Δ Δ Δ Δg g g g g w2 5 8 11 13
6.2. Fitness function
The fitness function is the modified objective function formulated in
accordance with the equality and inequality constraints. Normally
constraints on the dependent variables can be added with penalty
functions on the original objective function. Hence the fitness function
is
∑ ∑ ∑F RC VP QP FP= + + + .
j
N
j
j
N
j
j
N
j
=1 =1 =1
l g t
(34)
Here N N N, , andl g t are the total number of load buses, generator
buses, and transmission lines, respectively. Similarly VPj, QPj and SFj
are the penalty terms for load bus voltage limit violations, reactive
power generation limit violations and line power flow limit violations,
respectively. These penalty terms are normally introduced to reduce
violations in the dependent variables of the objective function. They
can be defined as
VP
K V V if V V
K V V if V V
otherwise
=
( − ) >
( − ) <
0
j
v j j j j
v j j j j
max 2 max
min 2 min
⎧
⎨
⎪
⎩
⎪
(35)
QP
K Q Q if Q Q
K Q Q if Q Q
otherwise
=
( − ) >
( − ) <
0
j
q j j j j
q j j j j
max 2 max
min 2 min
⎧
⎨
⎪
⎩
⎪
(36)
FP
K F F if F F
otherwise
=
( − ) >
0
,j
f j j j j
max 2 max⎧
⎨
⎩ (37)
where Kv, Kq and Kf are penalty factors. Proper selection of the penalty
parameters plays a key role in obtaining the optimal solution. For
simplicity, here we only use one penalty factor k as a combination of all
the factors.
Since all evolutionary algorithms try to find the maximum value, a
proper transformation is needed to find the minimum value of the
objective function. The fitness function can thus be transformed as
fitness
k
F
= ,
(38)
where k is a constant having a large value that is fixed based on F.
7. Simulation studies
To verify the effectiveness of the proposed method in solving the
Table 3
BSF and WAF values of load buses on the congested lines.
S. No. Bus No. Congested lines WAF S. No. BusNo. Congested lines WAF
1–3 3–4 4–6 1–3 3–4 4–6
1 3 −0.8429 −0.6696 −0.2621 0.12 13 19 0.2129 0.1692 0.0662 0.2
2 4 −0.2662 −0.2115 −0.0828 0.32 14 20 −0.9996 −0.7305 −0.2859 0.61
3 6 −0.5062 0.9879 0.4484 0.25 15 21 0.1156 0.0918 0.0359 0.6
4 7 −0.0887 −0.0705 −0.0276 0.32 16 22 −0.4189 −0.1535 −0.0649 0.15
5 9 −0.4045 −0.1008 −0.0811 0.12 17 23 −0.6322 −0.5022 −0.1966 0.14
6 10 0.3488 0.2771 0.1084 0.32 18 24 −0.2325 −0.1847 −0.0723 0.39
7 12 0.1806 0.1435 0.0562 0.24 19 25 −0.4260 −0.2488 −0.0558 0.98
8 14 0.3263 0.2592 0.1014 0.61 20 26 −0.5178 −0.4592 −0.1797 1.26
9 15 −0.2467 −0.1960 −0.0767 0.6 21 27 −0.4258 −0.2932 −0.0246 0.84
10 16 −0.5780 −0.4592 −0.1797 0.15 22 28 −0.4284 −0.3578 0.0835 0.98
11 17 0.2248 0.1786 0.0699 0.14 23 29 -0.5601 −0.6696 −0.262 1.26
12 18 −0.6322 −0.5022 −0.1966 0.39 24 30 0.1909 0.1516 0.0593 0.84
Table 4
Optimum location of WF for congested line (1–3).
S No. Bus No. BSF WAF WFF
1 3 −0.8429 0.12 0.8909
2 16 −0.5780 0.15 0.6380
3 18 −0.6322 0.39 0.7882
4 20 −0.9996 0.61 1.2436
5 23 −0.6322 0.14 0.6882
6 26 −0.5178 1.26 1.0218
7 29 −0.5601 1.26 1.0641
Fig. 3. Convergence characteristics of IDE with and without WF.
Table 5
Optimal setting of decision variables and congestion cost obtained by IDE algorithm.
Control Variables Without WF With WF at bus 20
ΔP2 (MW) 26.2114 12.0799
ΔP5 (MW) 18.9032 7.5229
ΔP8 (MW) 0.6118 0
ΔP11 (MW) 2.4753 2.2432
ΔP13 (MW) 0.6777 0
Pw (MW) 0 32.0243
Congestion Cost ($/h) 1684.9 1004.57
S.T. Suganthi et al. Renewable and Sustainable Energy Reviews 81 (2018) 635–642
639

6. CM problem, we tested it on the standard IEEE-30 bus test system
[25]. MATLAB code was developed for the proposed IDE algorithm.
Congestion can be created in the existing test system by simulating line
outages and by increasing the base loading condition. A contingency
analysis was carried out in order to identify severely congested lines.
From the contingency analysis, the line outage (1–2) is identified as the
most severe contingency, creating power flow violations on lines (1–3),
(3–4) and (4–6). Hence, congestion is created in the system by the
outage of line (1–2) and also by increasing the system load by 20% of
its base case load. The impact of these actions on the IEEE-30 bus
system is shown in Table 2.
7.1. Determining the location of the WF
Bus Sensitivity Factors of all the load buses have been calculated
and are shown in Table 3. The buses with high negative sensitivity
values are considered for location of the WF, as the WF will inject
additional power into the bus. From the table, it is clear that buses 3,
16, 18, 20, 23, 26 and 29 have large BSF values towards all the
congested lines. It can be inferred that power injections at these buses
will have the most significant and desirable impact on flows in the
congested lines. Hence these buses are identified as sensitive buses.
Table 3 also lists the hypothetical WAF value for each bus [22].
To find the optimum location, the sensitive buses are ranked based
on their WFF value, calculated from Eq. (23) by assigning the
weighting factor of α = 0.4. The obtained values are shown in
Table 4. Based on its WFF value, bus 20 is selected for installation of
a WF. It should also be observed that the installation of WFs at other
buses would affect the other transmission lines even though it would
help reduce power flow in the congested lines. Hence bus 20 is selected
for installation of a WF.
7.2. Calculation of congestion cost and rescheduling power
The proposed IDE based approach was implemented in MATLAB
using the MATPOWER toolbox to find the congestion cost and active
power rescheduling. The rescheduling process has been done by ISO
from the market clearing price for the base case to the contingent case.
The convergence characteristics of the proposed IDE method are
shown in Fig. 3. The congestion cost as well as the amount of
rescheduling power obtained with and without the WF are listed in
Table 5. With the installation of the wind farm, the congestion cost is
significantly reduced; it is also clear that only three generators
participate in the rescheduling process. The effect of rescheduling
power on the slack bus with and without installation of the WF is
depicted in Fig. 4. The system voltage profile improvement with the
installation of the wind farm is shown in Fig. 5.
Table 6 shows the line flow details before and after the rescheduling
process; it is clear that power flows in all of the congested lines have
been significantly reduced and have reached safe working limits. Note
also that power flow through the congested lines has been greatly
reduced with the installation of the wind farm. For example, the power
flowing through the congested line (1–3) is reduced to 99.30 MVA from
170.4604 MVA.
From Table 7, it is clear that integration of wind energy also has a
Table 7
Transmission losses and system voltage profile.
Parameter Before rescheduling After rescheduling with WF
Ploss (MW) 20.380 10.40
Vmin(p.u) 0.9841 0.9916
Table 8
Parameters of implemented algorithms.
GA PSO DE IDE
Population size: 50 Population size: 50 Population size: 50 Population size: 50
Crossover Probability: 0.8 Max inertia weight: 0.9 Scaling Factor (F): 0.8 Scaling Factor (C1): 2
Mutation Probability: 0.01 Min inertia weight: 0.4 Crossover Constant (CR): 0.8 Scaling Factor (C2): 2
Maximum Generations: 60 Acceleration Constants (C1,C2): 2 Maximum Generations: 60 Crossover Constant (CR): 0.8
Maximum Generations: 60 Maximum Generations: 60
Fig. 4. Rescheduled real power with and without WF.
Fig. 5. System Voltage Profile of load buses with and without wind.
Table 6
Power flow details of congested lines before and after rescheduling.
Congested
lines
Maximum
limit (MVA)
Power flow
Before
rescheduling
After rescheduling
with WF
1–3 130 170.4604 99.30
3–4 130 162.1420 107.25
4–6 90 102.5795 69.53
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640

7. great impact on reducing the system losses. The system active power
loss has been reduced from 20.38 to 10.40 MW and the minimum
voltage profile of the system with and without installation of wind
farms have also been tabulated.
7.3. Comparison with other solution techniques
In order to demonstrate the superiority of the proposed method, we
compare it with other state-of-the-art methods proposed for CM. The
comparison has been done with both the traditional Sequential
Quadratic Programming (SQP) [14] approach and with recently
proposed heuristic algorithms like the Genetic Algorithm (GA) [15],
Particle Swarm Optimization (PSO) [16], and conventional DE [25]
algorithms. All of the algorithms were implemented on the same
MATLAB platform with the same contingency state. The various
algorithm-specific parameters used in the implementation of heuristics
algorithms to get the optimal solution are listed in Table 8.
In Tables 9, 10, the congestion cost obtained by IDE, with and
without incorporation of the WF, is compared with that of other
algorithms, including one traditional technique (SQP). It can be seen
that the solutions obtained from heuristic methods are significantly
more economical than that of the traditional SQP technique. The
solutions, except that of SQP, are also feasible while satisfying all the
constraints in the problem formulation. In the case of SQP, the power
flow results in violation of voltage magnitudes and MVA violations in
other transmission lines. The traditional technique is thus not highly
suitable for CM.
The rescheduling cost obtained by IDE is the minimum in both
scenarios when compared to the other algorithms. The congestion cost
obtained by the proposed IDE is 1684.9 $/h and 1004.57 $/h,
without and with installation of wind generation, respectively. This is
approximately a 5% reduced cost compared to the cost obtained with
the conventional DE algorithm. The proposed IDE algorithm is there-
fore capable of producing the best results among these algorithms. The
real power reschedules by the four aforementioned techniques for both
scenarios are illustrated in Figs. 6 and 8. Figs. 7 and 9 represent the
convergence characteristics of IDE and the other algorithms for the
cases with and without the WF. It can be seen from the figures that IDE
converges to the best solution on the 35th
iteration for the case without
the WF and on the 38th
iteration for the case with the WF. This shows
that the proposed IDE has faster convergence than the other optimiza-
tion algorithms.
Fig. 8. Comparison of real power reschedule by various techniques with WF.
Fig. 9. Average convergence characteristics with WF.
Table 9
Comparison with other solution techniques without WF.
Solution
Technique
Congestion cost ($/h) CPU
time
(Sec)
Performance
Average Minimum Maximum
SQP – 2051.4 – 3.5 Infeasible
GA 1998.57 1929.9 2086.0 4.0 Feasible
PSO 1970.30 1891.9 2098.7 3.2 Feasible
DE 1858.26 1720.3 2089.6 3.8 Feasible
IDE 1840.48 1684.9 2095.8 2.7 Feasible
Table 10
Comparison with other solution techniques with WF.
Solution
technique
Congestion Cost ($/h) CPU
time
(Sec)
Performance
Average Minimum Maximum
SQP – 1146.6 – 3.6 Infeasible
GA 1237.15 1012.4 1490 4.2 Feasible
PSO 1189.75 1010.9 1477.1 3.4 Feasible
DE 1191.25 1008.1 1508.1 3.7 Feasible
IDE 1161.74 1004.5 1478.8 2.8 Feasible
Fig. 6. Comparison of real power reschedule by various techniques without WF.
Fig. 7. Average convergence characteristics without WF.
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641

8. 8. Conclusion
In this paper, a comprehensive analysis of how to alleviate
congestion in transmission lines by incorporating a wind energy source
has been carried out. BSF is used here as a good indicator for
identifying the buses that have a direct impact on the congested line.
Further, a complete analysis has been done to identify the location of a
WF based on the WAF and BSF values, with the aim of congestion
alleviation. The congestion management problem has been formulated
as an optimization problem with the objective of minimizing the
congestion cost, including wind active power as one of the control
variables. The performance of the proposed IDE-based approach has
been tested on a standard IEEE-30 bus system and the results show
that the proposed algorithm is quite efficient and robust with respect to
convergence speed and optimized result. The double best mutation
operation proposed in this research evolved from the idea of Particle
Swarm Optimization, and this operation speeds up the convergence
process effectively. Therefore, the proposed IDE yielded significantly
better solutions to the proposed CM problem than other state-of-the-
art methods.
Acknowledgement
This research work is sponsored by the World Bank under the
Robert S. McNamara Fellowships Program (RSM) grant.
Appendix A
See appendix Table A1 here
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Table A1
Bidding cost of IEEE 30 bus system.
Bus no. Real powerschedule of
generators in MW (Base case)
Bids submitted by GENCOs in $/MWhr
Rgu Rgd
1 176.40 22 18
2 48.91 21 19
5 21.54 42 38
8 22.45 43 37
11 12.29 43 35
13 11.42 41 39
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