Download - Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
1/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
1
Multi-Objective based Congestion Management
using Generation Rescheduling and Load SheddingS. Surender Reddy, Member, IEEE
AbstractThis paper proposes a new congestion managementapproach by using the generation rescheduling and load shed-ding, with the realistic voltage-dependent load modeling. Thepaper presents several objective functions such as Generationand Load shedding Cost Minimization (GLCM)/ Social WelfareMaximization including demand response offers (SWM), LoadShedding Minimization (PshdM), Load Served Maximization(LSM), and Load Served Error (LSE) minimization. To the bestof our knowledge, all previous congestion management effortsconsidered constant load models. Using voltage-dependent loadmodels, the paper clearly brings out the inappropriateness ofconventional single objectives for congestion management, such
as GLCM/SWM andPshd
M, due to the reduction of amount ofload served. Therefore, multi-objective optimization is requiredand the objectives can be judiciously combined depending on theloading condition. Multi-objective Strength Pareto EvolutionaryAlgorithm 2+ has been employed to solve the proposed conges-tion management problem. The effectiveness of the developedapproach is confirmed from the simulation results on IEEE 30bus test system.
Index TermsCongestion management, generation reschedul-ing, load shedding, load modeling, contingency, multi-objectiveoptimization.
NOMENCLATURE
ai, bi, ci Generator cost coefficients ofith generating
unit.a
k, b
k, c
k Demand response cost coefficients of kth
load bus.
Gij , Bij Transfer conductance and susceptance be-tween bus i and bus j .
NG Number of generating units.NBU S Total number of buses in the system.NL Number of demands/loads.NC Number of shunt capacitors.NT Number of regulating transformers.np, nq Voltage exponents.PGi Generation output of i
th generator.
Pshd,k Amount of load shed atkth bus.
P0Di, PcDi Nominal and actually supplied load activepower demand.
LS0 Nominal load served.Qci Reactive power injected by i
th capacitor
bank.
QGi Reactive power output ofith generator.PDi, QDi Active and reactive load demands.PminGi , P
maxGi Minimum and maximum generation capac-
ities ofith generator.
S Surender Reddy (email: [email protected]) is with theDepartment of Railroad and Electrical Engineering, Woosong University,Daejeon, Republic of Korea.
QminGi , QmaxGi Minimum and maximum reactive capacities
ofith generator.Sij MVA flow between busi and bus j .Smaxij Thermal limit of the line connected between
busi and bus j .Ti Tap settings of i
th transformer.
Pl0, Ql0 Nominal values of active and reactive powerloads.
V0 Nominal values of voltage magnitudes.Nobj Number of objective functions to be opti-
mized simultaneously.Meq, Nineq Set of equality and inequality constraints.M Number of non-dominated solutions.N Population size.N Archieve size.VGi Bus voltage ofith generator.VmaxGi , V
minGi Maximum and minimum limits of generator
bus voltage magnitudes.
VLi Bus voltage ofith load.VmaxLi , V
minLi Maximum and minimum limits of load bus
voltage magnitudes.
x Vector of decision variables.i, j Voltage angles at busi and busj .
I. INTRODUCTION
POWER system experiences variations in operating con-ditions all the time. Contingency situations may occurdue to sudden increase of electrical load, forced outage of
a transmission line or generator, or any defect in equipment
of the system. Optimal generation rescheduling and load
shedding during the contingency situations is one of the critical
issues in planning secured operation of power systems. Load
shedding is defined as the set of controls, which results in
a decrease of load demand in the power system in order to
achieve a new equilibrium state. Load shedding schemes have
become more important in deregulated power systems, where
there is lack of adequate spinning reserve (SR) or a shortageof tie line power capacity to make up for the lost generation
[1]. The load shedding schemes are necessary to prevent the
phenomena such as voltage collapse, line overload, etc., which
may lead to cascade outages and then black out. Load shedding
is considered as a powerful tool to avoid the system wide
blackouts [2].
A common characteristic of large regional electricity mar-
kets is that they have sub-hourly energy markets that are jointly
optimized with the ancillary services markets, in which all
generators and load demands can participate. In Pennsylvania-
New Jersey-Maryland Interconnection (PJM) energy market,
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
2/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
2
the Curtailment Service Providers (CSPs) [3], and in California
Independent System Operator (CAISO) energy market, the
Demand Response Providers (DRPs) [4], submit demand/load
reduction bids individually, or in aggregated fashion. Cus-
tomers may have the capability to curtail their normal con-
sumption in order to participate in the market clearing [5]. A
client bids individually only when it is large enough to do so,
else a group of customers bid in aggregation. In CAISO, the
DRPs are designed to enable end use customers to contribute
energy load reduction. The integration of demand response
into PJM electricity markets recognizes the importance of load
response to a fully functioning market, and the effect of load
response on the reliability of electrical grid. PJM emergency
load response enables demand response resources that reduce
the load demand during the emergency situations, and in turn
to receive payment for those reductions [3]. Various classes of
demand-side resources are defined as follows:
Demand-side resources in the energy only option of
emergency load response are defined as the demand
resources that receive only an energy payment for the
load reductions. Demand-side resources in capacity only option of emer-
gency load response are defined as the demand response
resources that receive only a capacity payment for load
demand reduction.
Demand-side resources in the full emergency load re-
sponse are defined as the demand resources that receive
both an energy payment for load reductions and a capac-
ity payment.
Optimal Power Flow (OPF) is one of the most accurate
methods for the Congestion Management (CM) in power sys-
tem with existing transmission and operational constraints [6].
An OPF based method that minimizes the cost of congestionand the service costs has been described in [7]. A coordination
mechanism between the generating companies (GENCOs)
and the Independent System Operator (ISO) for congestion
management (CM) using Benders decomposition has been
discussed in [8]. From the point of view of operations, load
shedding plays a major role. As a traditional control action it
prevents occurrence and extension of voltage instability. It also
helps in over-load mitigation in the electrical power systems
[9]. Optimum steady state load shedding schemes are proposed
in [10]-[13]. The combined/composite effect of optimizing
economic dispatch (ED), fast action by the spinning reserves
and load shedding, in order to withstand sudden loss of
generation, without system collapse due to cascading effects,is presented in [14]. The utilization of an approximate event
cost technique in a load shedding strategy under emergency
condition is illustrated in [15].
An optimization approach to minimize the load curtailments
that are necessary to restore the equilibrium of operating point
with relaxation of restrictions is described in [16]. A simple
and straight forward approach using the generation reschedul-
ing and load shedding for CM in power system, is presented
in [17]. Minimization of total load shedding by considering
the system operating constraints, like, transmission line flows
and voltage deviation limits is solved in [18]. An algorithm
for CM based on Particle Swarm Optimization (PSO), which
minimizes the deviations of rescheduled values of generator
power outputs from the scheduled levels is proposed in [19].
Reference [20] proposes a cost efficient CM model for smooth
and non-convex cost functions using the multi-objective PSO
technique.
Mostly power system optimization problems involve simul-
taneous optimization of several objectives, which are conflict-
ing and competing with each other. In a single-objective opti-
mization problem there exists a global optimum, while in case
of multi-objective optimization (MOO), no optimal solution is
clearly defined; but a set of solutions called the Pareto optimal
front / Pareto optimal set is present. The main aim of MOO
approaches is to generate a set of non-dominated solutions as
an approximation to this Pareto optimal front. But, majority
of problems of this kind cannot be solved exactly because
of their highly complex and large search spaces. Recently,
several meta-heuristic techniques have become important tools
for solving the MOO problems encountered in the industry and
academia as well [21].
From the literature survey it is clear that most of thetraditional approaches convert the MOO functions into a single
objective function using weighting schemes or optimize single
objective function at a time. Therefore, these approaches do
not truly optimize the multiple objectives simultaneously. Due
to these inherent deficiencies of conventional algorithms, the
use of alternative non-traditional solution algorithms for such
complex problems has become more popular and is used
widely. Multi-objective evolutionary algorithms have received
wide acceptance due to their robustness and quality of solution.
This paper proposes a new congestion management (CM)
mechanism with generation rescheduling and load shedding
using the multi-objective optimization (MOO). Further, the
loads are modeled as voltage-dependent, which were hith-ero modeled as voltage-independent. Handling of demand
response is more complex under voltage-dependent load mod-
eling when compared to constant load modeling. This has
not been investigated so far. The proposed CM approach is
particularly suitable for stressed system-operating conditions,
where the demand elasticity alone cannot yield a feasible
optimal solution. The feasible solution is obtained by invoking
load reduction bids/demand response offers.
It is shown that the single objectives, like, Generation and
Load shedding Cost Minimization (GLCM)/ Social Welfare
Maximization including demand response offers (SWM) and
Load Shedding Minimization (PshdM) are not suitable with
this voltage-dependent load model, due to the reduction ofamount of load served (LS). But, these two objectives can
be combined to get the compromised solution with constant
load modeling. This work then proposes that the MOO is
important to do the justice to this complex optimization
problem. The importance of using the multiple objectives, i.e.,
GLCM/SWM,PshdM, Load Served Maximization (LSM) andLoad Served Error (LSE) minimization are highlighted. This
paper then highlights the requirement for selecting judiciously,
a combination of objective functions best suited for the CM.
In this paper, Strength Pareto Evolutionary Algorithm 2+ is
considered as one such suitable MOO algorithm. The major
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
3/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
3
contributions of the paper are as follows:
It has been shown that the use of conventional single
objective of cost minimization / social welfare maximiza-
tion, while using voltage-dependent load models leads to
an unrealistically low loads being served, due to voltage
reduction inherent in achieving this objective.
In the light of above, a multi objective optimization
is suggested to tackle the above mentioned problem.
This is achieved by adding Load Served Error (LSE)
Minimization as an objective to the original one. The
numerical results confirm the benefit of the proposed
approach.
In critical situations when either conventional gener-
ation reserves are insufficient or cannot be deployed
fast enough due to Generation Rate Constraints (GRCs),
demand-side reserves are being increasingly used despite
their much higher costs. This is because the latter are
not only very fast in response, but also strategically
very well distributed throughout the system. Although,
all these things are very well known, how to handle them
in the context of voltage-dependent load modeling hasnot been investigated so far. Customers providing this
service are to be told, what actual load relief is required
at a specific voltage (obtained from optimization), so that
the difference between nominal load relief and the actual
load relief is clear. This is quite complex, and unlike the
simple, single load relief quantum instruction given, with
constant load model.
The remainder of the paper is organized as follows. Section
II describes the problem formulation. Section III presents
the description about multi-objective congestion management
using generation rescheduling and load shedding. Section IV
addresses the simulation results and discussion. Finally, Sec-
tion V brings out the contributions with concluding remarks.
I I . CONGESTION M ANAGEMENT(CM): PROBLEM
FORMULATION
Elimination/ alleviation of transmission lines overload and
maintaining voltages within stipulated limits, i.e., congestion
management (CM), in contingency/emergency situations, by
means of generators rescheduling and load shedding is formu-
lated as a non-linear optimization problem. Here, we discuss
possible primary as well as supplementary objectives. Sup-
plementary objectives are the ones which can not be used in
isolation. They need to be coupled with the primary objective
function in order to formulate a multi-objective formulation.
Various choices for the optimization problem are presented, as
follows:
A. Generation and Load shedding Cost Minimization (GLCM)
In this case, demand is inelastic to the price hence, the main
objective is to reduce the generation and load shedding cost
(GLC), and it is formulated as,
Minimize,
GLC=
NGi=1
[ai+ bi(PGi) + ci(PGi)2]
+
NLk=1
[ak+ b
k(Pshd,k) +c
k(Pshd,k)2] (1)
B. Social Welfare Maximization including demand response
offers (SWM)
In the presence of demand elasticity, the market is set-
tled with social welfare maximization as objective function.
Presently, most of the electric power markets have introduceddemand-side bidding in the market clearing process. The con-
cept of maximizing social welfare can be applied for the cen-
tralized market with demand elasticity. This traditional social
welfare includes the total surplus of generators and customers.
In this case, the system operator optimally dispatches the
generators in such a way that the social welfare is maximized
while satisfying the operation and security related constraints.
The CSPs or DRPs can bid into the market in terms of fixed
bids, linear bids or quadratic bids. In case of CAISO, the
demand response offers (load reduction bids) exactly similar
to generation bids are solicited. Hence, the modified social
welfare is the traditional social welfare including demand
response offers. This can be formulated as follows,
Maximize,
modified SW=NL
k=1
[BDk(PDk )] NGi=1
[CGi(PGi)]
NLk=1
[ak+ b
k(Pshd,k) +c
k(Pshd,k)2] (2)
where
NLk=1
[BDk(PDk)] =
NLk=1
[dk ek(PDk) fk(PDk )2] (3)
NGi=1
[CGi(PGi)] =
NGi=1
[ai+ bi(PGi) + ci(PGi)2] (4)
i=1,2,...,NG. PDk and Pshd,k are demand bids and amountof load reduction/demand response at bus k, BDk(PDk) isdemand cost function at bus k, CGi(PGi) is cost functionfor generating real power PGi; dk, ek and fk are demandcoefficients ofk th load bus.
C. Amount of Load Shedding Minimization (PshdM)
The amount of load shedding is the sum of difference
between nominal load, and actually supplied active power
demands, and it is formulated as,
minimize Pshd=
NBUSi=1
(P0Di Pc
Di) (5)
D. Load Served Error (LSE) Minimization
This objective function is formulated as follows,
minimize LSE= (LS LS0)2 (6)
whereLS0 is nominal load served i.e., amount of load servedwith the constant load modeling. LS is the amount of load
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
4/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
4
served with the voltage-dependent load modeling, and it is
formulated as,
LS=
NBUSi=1
Pil0
ViV0i
np(7)
Equation (7) is also considered as a single objective function
to be optimized, and it is called as Load Served Maximization
(LSM). The practical loads/demands are function of voltages,therefore voltage-dependent load modeling is used. Improve-
ment of system voltage increases the amount of load served
(LS). The LSE minimization objective function will never
be used as an independent objective. LSE will be used as
a supplementary objective, to ensure that load served (LS)
reduction is prevented to the extent possible.
The above objectives are achieved by the optimal determi-
nation of control variables. The control variables considered
in this problem are shown in Figure 1. where PcGi, Pc
Di are
Fig. 1. Control Variables for Proposed Congestion Management (CM)Approach
the active power generation and load active power demand in
contingency/ emergency state. The equality and inequality con-
straints for the proposed optimization problem are described
next:
E. Equality Constraints
1) Nodal Power Balance Constraints: These constraints are
typical load flow equations, and they include the active and
reactive power balances.
PGi PDi = Vi
NBUSj=1
Vj (Gijcos ij+ Bijsin ij ) (8)
QGi QDi= Vi
NBUSj=1
Vj (Gijsin ij Bijcos ij ) (9)
In Equations (8) and (9),i=1,2,...,NBUS. Whereij =i jis the voltage phase angle difference between bus i and busj .
F. Inequality Constraints
These constraints represent system operating limits.1) Generation Constraints: The outputs of generating units
are restricted by their minimum and maximum limits, and they
are represented as,
PminGi PGi Pmax
Gi (10)
The reactive power limits of generator are expressed as,
QminGi QGi QmaxGi (11)
The generator bus voltage limits are represented by,
VminGi VGi Vmax
Gi (12)
2) Constraints on Control Variables: The limits on control
variables are represented by,
PminGi Pc
Gi Pmax
Gi (13)
PminDi Pc
Di P0
Di (14)
where P0
Di is load active power demand in the normal stateand PminDi is amount of load which must be supplied.
3) Constraints on Switchable var Sources: The switchable
var sources are restricted by,
Qminci Qci Qmaxci i= 1, 2,...,NC (15)
4) Constraints on Demand response offers/ Amount of load
shed: This constraint provides relation between Pshd,k andPDk.
0 Pshd,k (PDk Pmin
Dk ) (16)
that is0 Pshd,k P
maxshd,k (17)
wherePmaxshd,k is the amount of load shed provided by the loaddemands.
5) Security Constraints: The security constraints are ex-
pressed as follows:
The load bus voltage limits are represented by,
VminLi VLi Vmax
Li i= 1, 2,...,NL (18)
The line flows are restricted by,
|Sij| Smaxij (19)
The transformer taps have minimum and maximum setting
limits as,
Tmini Ti Tmax
i i= 1, 2,...,NT (20)
The proposed CM problem with the above objectives is
solved using Genetic Algorithm (GA). The variables have been
represented in binary strings and the corresponding description
about their representation, encoding of chromosomes and
genetic operators can be found in [22]. A penalty function [23]
is added to the objective function if the functional operatingconstraints violate any of their limits.
It is worth noting that there is a conflict between the two
objectives (i.e., GLCM/SWM and PshdM) presented in thispaper. For example, when GLCM/SWM is optimized indepen-
dently, then the cost is minimum/ social welfare is maximum
but the amount of load shedding is more. On the other hand,
when the amount of load shedding minimization is optimized
independently, then the amount of load shed is minimum but
GLC is more/ social welfare is less. Hence, multi-objective
based CM approach using generation rescheduling and load
shedding is proposed in this paper.
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
5/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
5
G. Voltage-dependent Load Modeling
The power systems in the developed world were earlier
conservatively designed. This was due to relative abundance
of resources with the utilities till 1970s. The situation changed
dramatically during 1980s due to various factors such as:
deteriorating economic health of utilities, Right of Way (ROW)
restrictions, and environmental considerations. Deregulation,
which started a little later, compounded the problems signifi-cantly. Economic compulsions resulted in power flow patterns
for which the system was never designed. The effects were
seen in the large number of voltage collapses in power system
all over the world. In short, the pre 1980 networks were
strong, robust and maintaining near nominal voltage profile
was easy. This made the voltage-dependent load representation
almost redundant. Post 1980 power systems were subjected to
operations scenarios with low voltages, including the extreme
ones threatening voltage collapse. As mentioned in [24]-[26],
voltage-dependent load models are essential in such situations
of power systems operation, without which the results will be
impractical.
The load modeling has a major influence on the operationof electrical power systems. Generally, the power system
loads are modeled as the constant loads. But, this kind of
model is not suitable for practical voltage-dependent loads.
This is even more true for the aggregated load representation
seen from the EHV buses. This is due to the fact that the
effects of sub-transmission and distribution system are also
reflected in this equivalent load representation. More realistic
and practical approach is brought into this paper by modeling
the loads/demands as the voltage-dependent [26]-[27]. For the
steady state power system analysis, exponential load model or
constant Impedance-Current-Power (ZIP) load model [27] are
used.
In this paper, exponential load model is used and the activeand reactive powers of the load bus are related to the bus
voltage through an exponential function,
PDi = Pi
l0
Vi
V0i
np(21)
QDi= Qil0
ViV0i
nq(22)
In Equations (21) and (22),i=1,2,...,NBU S. Wherenp and nqare voltage exponents, and they depends on the composition
and type of load demand. PDi and QDi are the active andreactive power demands at ith bus; Pil0, Q
il0 and V0i are the
nominal values of the active, reactive power demands and the
voltage magnitude at ith bus, respectively.
III. MULTI-OBJECTIVE C ONGESTION M ANAGEMENT
USINGG ENERATION R ESCHEDULING ANDL OAD
SHEDDING
In this paper, single objective based CM problem is solved
by using a Genetic Algorithm (GA). In order to find the
optimal decision variables to optimize an objective function
and to satisfy the constraints, the variables are represented
in binary strings. Most of the real-world problems naturally
involve multiple and conflicting objectives to be optimized si-
multaneously. Defining multiple objectives often gives a better
idea of the problem. Generally, a single attribute that is most
essential and appropriate for a particular operating condition,
has been used as an objective function for the optimization
problem. All other major attributes are incorporated in the
mathematical formulation as constraints with correctly chosen
limits. Many times selecting these limits is not so simple. This
is a rigorous approach and does not provide the room for trade-
off between various attributes, which can be beneficial form
the system operation point of view. However, such a flexibility
is contributed by the multi-objective optimization (MOO). The
MOO problem is formulated as,
M inimize/Maximize fi(x) i= 1, 2,...,Nobj (23)
subjected to gj(x) = 0 j = 1, 2,...,Meqhk(x) 0 k= 1, 2,...,Nineq
Essentially, there are two different methods for solving the
MOO problem. The first method reduces the MOO problem
to a single objective optimization problem, by generating
a composite objective c(x), from a linear sum of multipleobjective functionsfi(x).
c(x) =min
Nobji=1
[Wifi(x)] (24)
The above objective function can be optimized by using the
existing single objective optimization algorithms. However,
the weights Wi (which by convention are non-negative andthe sum is equal to 1) must be pre-set. The solution to
this optimization problem will then be a single vector ofcontrol variables, rather than entire Pareto optimal set. This can
have undesirable consequences: setting the weights implicitly,
introduces the designers preconceptions about the relative
trade-off between the objectives. The practical world prob-
lems can produce surprising Pareto optimal fronts/sets which
may profoundly affect design decisions, and the potential to
generate novel designs is a key benefit of optimization [28].
The second method for solving the MOO problem, is to search
directly for the entire Pareto optimal set. This can be achieved
in a number of ways, and needs modification to the existing
single objective optimization algorithms.
Multi-objective evolutionary algorithms can yield a whole
set of potential solutions, which are all optimal, in somesense. The multi-objective evolutionary algorithms were first
proposed by Schaffer [29]. The principle of an ideal MOO pro-
cedure is to determine the multiple trade-off optimal solutions
with a wide range of values for objective functions and then
choose one of the solutions using higher level information. In
this paper, Strength Pareto Evolutionary Algorithm 2+ (SPEA
2+) has been used to solve the proposed CM problem, which
provides a set of points on the Pareto optimal front. The
user/System Operator can then select a point which is suitable
to his needs best. In this paper, a best compromise solution
can be determined through a fuzzy min-max approach [30].
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
6/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
6
A. Multi-objective Optimization (MOO) using Strength Pareto
Evolutionary Algorithm 2+ (SPEA 2+)
The MOO problem is minimization/ maximization of mul-
tiple evaluation criteria that conflict with each other. The
solution which is an optimum for one criterion is may not
be an optimal solution for MOO, because the multiple criteria
have trade-off relationships with each other. The SPEA 2+ is a
multi-objective genetic algorithm (MOGA) that improves thesearch performance of SPEA 2. The SPEA 2+ is SPEA 2 with
the addition of following three mechanisms [31]:
Mating Selection: This reflects all good chromo-
somes/solutions preserved in the archive.
Neighborhood Crossover: This crossover allow crossing
over individuals located close to each other in the objec-
tive space.
The application of two archives to maintain diverse
solutions in the objective space and design variable space.
The description of Mating selection and Neighborhood
crossover are presented in [31]-[32]. The algorithm for im-
plementation of SEPA 2+ is presented next:
Step 1: Generate the initial population (P0). Empty theobjective archive population (OA0), and design variablearchive population(V A0). Initially, the generation countk=0.
Step 2: The fitness values of all individuals Pk, OAk
and V Ak are determined using the SPEA 2s fitnessassignment technique [33].
Step 3:All the non-dominated solutions/individuals in the
Pk, OAk and V Ak are copied to OAk+1 and V Ak+1.If the number of individuals ofOAk+1 andV Ak+1 haveexceeded the archive size, archive truncation in objective
space is applied to the individuals inOAk+1 , and archive
truncation in variable space is V Ak+1
to reduce thenumber of individuals. If the number of individuals of
OAk+1 or V Ak+1 is less than archive size, individualswith good fitness from Pk, OAk and V Ak are used tofill OAk+1 and V Ak+1.
Step 4: Stop the search if maximum number of gener-
ations are reached or other termination conditions are
satisfied.
Step 5: Pk+1 is generated by copying OAk+1. Theneighborhood crossover and mutation operations are per-
formed. Go to Step 2, and increase k to k+1.
B. Best Compromise SolutionAfter determining the Pareto optimal set of non-dominated
solutions (i.e., Pareto optimal front) using the SPEA 2+
approach, the fuzzy min-max approach [30] provides the best
compromise solution to the system operator/decision maker.
Due to the imprecise nature of the decision makers judgement,
the ith objective function Fi is expressed using the fuzzymembership functioni, and is expressed as,
i=
1 if Fi Fmin
iFmaxi Fi
Fmaxi Fmini
if Fmini < Fi< Fmax
i
0 if Fi Fmaxi
(25)
where Fmaxi and Fmin
i are the maximum and minimum
values of the ith objective function among all non-dominatedsolutions, respectively. For each non-dominated solution k, thenormalized membership function (k) is determined using,
k =
Nobji=1
kiM
k=1
Nobji=1
ki
(26)
The best compromise solution is the one having maximumvalue ofk. The description of fitness function evaluation ispresented in [34], [35].
IV. RESULTS ANDD ISCUSSION
In this paper, IEEE 30 bus test system [36] is used to test the
effectiveness of the proposed congestion management (CM)
approach. The single line diagram of IEEE 30 bus system is
depicted in Figure 2. This system consists of 6 generating
units, 21 load demands and 41 lines/branches. Among these
41 branches, 4 branches are tap setting transformer branches.
Buses 10, 12, 15, 17, 20, 21, 23, 24 and 29 have been
selected as shunt compensation buses. It is assumed that, the
system operator receives generator bids and load shedding costoffers from customers to perform the congestion management
analysis [17], [20]. The Genetic Algorithm (GA) encoding
is accomplished by using different gene/chromosome lengths
for each set of control variables, depending on the desired
accuracy level. All the optimization programs are coded in
MATLAB and implemented on a PC-Core2 Quad computer
with 3.24GB of RAM.
A. Study 1: Simulation Results Considering Demand is Inelas-
tic to the Price
In this Study, 6 generator active power outputs, 21
power demands are selected as the control variables. Thegene/chromosome length for the unit of generation or load
power is 12 bits and they are considered as the continuous
controls. In view of this, the chromosome length for proposed
congestion management approach is (6*12)+(21*12) = 324.
In this paper, exponential load modeling with np = 1 andnq = 2 are used [26]. The emergency/contingency situationis obtained by taking line 36 out (i.e., line connecting the
buses 27 and 28 in IEEE 30 bus system). It is considered that
PminDi = 0.7 P0
Di for all load buses. This equation means
that, load shedding at bus i cannot be greater than 30 percentof load demand in this bus. The generator and load shedding
cost coefficients are taken from [17]. The CM problem by
generation rescheduling and load shedding is first solved byoptimizing the single objective at a time, and later it is solved
by using the multi-objective SPEA 2+ technique, considering
appropriate multiple objective functions to be optimized. The
effect of realistic/practical voltage-dependent load modeling
on the same is evaluated. In each case, the optimization
algorithm is stopped when all the chromosomes/population
members assume similar fitness values.
The value of a particular objective function shows a ten-
dency to move away from the optimum value, if the problem
is optimized with respect to some other objective function.
When MOO is performed, it leads to the formation of a
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
7/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
7
Fig. 2. Single Line Diagram of IEEE 30 Bus Test System.
Pareto optimal front/set. In this paper, a multi-objective based
SPEA 2+ technique has been used to solve the proposed CM
problem. The GA and SPEA 2+ parameters used are shown
in Table I. The justification of chromosome length has been
explained earlier. The population and archieve sizes have been
considered for this optimization problem, after some trials.
These are not case dependent or operating condition depen-
dent. The last 4 parameters in Table I are considered based
on the experience of many researchers, for a wide variety of
problems [29], [31]-[33], [37]-[39]. A set of strong dominatedsolutions is selected from population of chromosomes to form
the Pareto optimal set. If the Pareto optimal set size exceeds
maximum size, a hierarchical clustering technique is used to
limit its size.
TABLE IGA A ND SPEA 2+ PARAMETERS.
Paramaters GA SPEA 2+
Chromosome length 324 324
Population size (N) 60 100
Archieve size (N) 100
Reproduction Operator Roulette Wheel Mating
Mutation operator, Rate Bitwise, 0.001 Bitwise, 0.001
Crossover operator Uniform Neighborhood
Maximum iterations/generations 200 100
Two different cases - one for constant load modeling and
the other for voltage-dependent load modeling have been
simulated. The simulation results for Study 1 are presented
next:
1) Study 1 - Case 1: Congestion Management (CM) by opti-
mal generation rescheduling and load shedding with constant
load modeling: Table II presents the control variables and
objective function values when the individual and combined
objective functions are optimized, considering the constant
load modeling. The variables are generator active power
outputs and load active power demands in contingency state
at corresponding buses. In the table, GC is the generation cost
and LC is the load shedding cost. When Generation and Load
shedding Costs (GLC) is optimized independently, then the
optimum value obtained is 550515.5076 Rs/h, but the amount
of load shedding is 11.0192 MW. When the amount of load
shedding minimization (PshdM) is optimized independently,its value is restricted to 3.7831 MW, but the GLC has
increased to 568757.7146 Rs/h. This shows that when conges-
tion management (CM) problem with one objective function
is optimized, then the other objective function value deviates
from the optimum value. Thus, there is a scope for solving
a trade-off between conflicting objectives. The CM problem
with these conflicting objective functions, should be solved
using the multi-objective optimization (MOO) algorithms.
Hence, in this case, Generation and Load shedding Cost
Minimization (GLCM) and amount of load shedding mini-
mization (PshdM) objectives are combined to get the compro-mise solution. In this paper, multi-objective SPEA 2+ approach
is employed to get the Pareto optimal front, and fuzzy min-maxapproach is used to get the best compromise solution. The best
compromise solution has the GLC of 556432.4382 Rs/h, and
amount of load shed (Pshd) of 7.3691 MW. Figure 3 depictsthe Pareto optimal front of GLCM and PshdM with constantload modeling. The computational time required when GLCM
andPshdM objectives are optimized independently using GAare 55.2809s and 61.4772s, respectively. When GLCM and
PshdM objectives are optimized simultaneously using multi-objective SPEA 2+ approach, the computational time required
is 126.5041s, and this has been shown in Table II.
5.54 5.56 5.58 5.6 5.62 5.64 5.66 5.68
x 105
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
X: 5.564e+005Y: 7.369
Cost minimization ($/hr)
Loadshedminimization(MW)
Cost and Load Shed Minimization
Fig. 3. Pareto optimal front of GLCM and PshdM with constant load
modeling for Study 1.
The results of CM with constant load modeling are also
compared using Interior Point Method (IPM). Table III
presents the simulation results using IPM. When GLCM
objective is optimized independently using IPM, then the
optimum generation and load shedding cost (GLC) obtained
is 550844.4960 Rs/h, which is higher compared to the value
presented in Table II using GA (i.e., 550515.5076 Rs/h).
When the amount of load shedding minimization (PshdM)objective is optimized independently using IPM, then the
optimum value of load shed obtained is 4.8262MW, which
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
8/12
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
9/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
9
is less than the nominal load demand of 283.4 MW. Hence,
GLCM and PshdM are not appropriate multiple objectives tobe optimized with voltage-dependent load modeling. But, in
case of constant load modeling, the GLCM and PshdM areappropriate multiple objective functions to be optimized.
Hence, to get the better compromise solution GLCM,
PshdM and LSE minimization objectives are optimized si-multaneously. Then the compromise solution has GLC of
550935.1685 Rs/h, Pshd of 7.0274 MW and amount of loadserved (LS) is 283.4312 MW. Here, the LSE minimization
objective is combined with GLCM and PshdM to get theload served (LS) approximately equal to the nominal load
served. Figure 4 depicts the Pareto optimal front of GLCM
and PshdM objectives, where as Figure 5 depicts the Paretooptimal front of GLCM, PshdM and LSE minimizations withvoltage-dependent load modeling.
4.9 4.95 5 5.05 5.1 5.15 5.2 5.25 5.3 5.35
x 105
5.1
5.15
5.2
5.25
5.3
5.35
X: 4.976e+005Y: 5.284
Cost minimization ($/hr)
Loadshedminimization(MW
)
Cost and Load Shed Minimization
Fig. 4. Pareto Optimal Front of GLCM and PshdM with Voltage-dependentLoad Modeling for Study 1.
5.4 5.45
5.55.55
5.65.65
x 105
5
6
7
8
90
0.2
0.4
0.6
0.8
Cost minimization ($/hr)
Cost, Load Shed and LSE minimization
X: 5.509e+005Y: 7.027Z: 0.031
Load shed minimization (MW)
LSEminimization(MW)
Fig. 5. Pareto Optimal Front of GLCM, PshdM and LSE Minimizationswith Voltage-dependent Load Modeling for Study 1.
B. Study 2: Simulation Results Considering Demand is Elastic
to the Price
In this Study also, two different cases - one with constant
load modeling and the other with voltage-dependent load
modeling have been simulated at stressed loading conditions
with 140% loading (emergency situation). This emergency
situation can be because of increased load demand, generator
outage and transmission line outage etc. Here, 140% loading
is assumed only to show how the demand response offers
are utilized to relieve the congestion. It is observed that, the
demand elasticity bids alone can not yield a feasible optimal
solution. Load reduction bids/demand response offers have
used to obtain the same. The simulation results for Study 2
are described next:
1) Study 2 - Case 1: CM by Optimal Generation Reschedul-
ing and Load Shedding with Constant Load Modeling: Table
V presents the optimum objective function values obtained
when Social Welfare Maximization including load reduction
cost/demand response offers (SWM) is optimized, considering
the constant load model. The variables are the generator active
power outputs, load demands, and the demand response offers
at corresponding buses.
When SWM objective is optimized, the optimum social
welfare (SW) obtained is 37492.5024 Rs/h, and the amount
of load shed (Pshd) is 17.6443 MW. The net amount of load
served is 369.7271 MW. The net amount of load supplied is thedifference between the total demand supplied and the amount
of load reduced.
2) Study 2 - Case 2: CM by Optimal Generation Reschedul-
ing and Load Shedding with Voltage-dependent Load Model-
ing: Any voltage between the minimum and maximum limits
is acceptable from operations point of view. However, with
voltage-dependent load modeling it can be seen that an attempt
to maximize the social welfare will result in load served
reduction through voltage reduction. Hence, social welfare
maximization can not be the sole objective for these type of
loads. There are two alternative approaches to prevent this load
reduction. The first is through the appropriate enforcement of
hard constraints on voltages, and the second being throughthe proposed multi-objective optimization approach. The first
approach requires that the minimum voltage limit should be
nominal voltage of the load bus so that, satisfaction of the same
will not allow load reduction. Apparently this logic is perfect.
However, achieving the same through the proposed multi-
objective optimization alternative provides us with significant
advantages. Distributed nature of the reactive resources do
not normally allow perfect voltage control at all the buses
simultaneously. In such situations, the former optimization
technique may simply result in an infeasible solution. The
proposed approach however attempts to keep the loads near
to their nominal values, thereby having better chances of pro-
viding a feasible solution. The proposed approach is flexible,attempting to strike a compromise between two conflicting
requirements. Such a compromise by very nature, results in a
feasible solution, unlike that in the previous approach.
Table VI presents the optimum objective function values,
when individual and combined objectives are optimized, con-
sidering voltage-dependent load models. When social welfare
maximization is the sole objective, voltage profile is pushed
down to maximize the social welfare, as a result the net amount
of load served (LS) is decreased. The obtained optimum values
are: social welfare is 41953.1932 Rs/h, amount of load shed
(Pshd) is 14.7613 MW, and the net amount of load served
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
10/12
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
11/120885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more informa
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
11
TABLE VICM WITHD EMANDR ESPONSEOFFERSC ONSIDERINGVOLTAGE-DEPENDENTLOAD M ODELING USINGGA A ND SPEA 2+ F OR S TUDY2 .
Obj ective Fun ction Valu e SWM S WM & LSE min.
Social Welfare ( Rs/h ) 41953.1932 38967.0596
Amount of Load Shed (MW) 14.7613 14.8829
Generation Supplied (MW) 371.3211 382.5908
Demand Supplied (MW) 372.3524 386.1622
Net Load Supplied (MW) 357.5911 371.2793
V. CONCLUSIONS
The paper proposes a new multi-objective based conges-
tion management approach by generation rescheduling and
load shedding, with realistic voltage-dependent load modeling.
The objectives considered in this paper are Generation and
Load shedding Cost Minimization (GLCM)/ Social Welfare
Maximization including demand response offers (SWM), Load
Shedding Minimization (PshdM), Load Served Error (LSE)minimization and Load Served Maximization (LSM). The
simulation studies on IEEE 30 bus test system show the
suitableness of choice of multiple objective functions to be
used for given load modeling. For constant load modeling,GLCM and PshdM are appropriate multiple objective func-tions to be optimized. But, when the loads are modeled as
the voltage-dependent, then it is shown that GLCM/ SWM,
PshdM are not valid single or multiple objectives with thisload model, due to the reduction in the amount of load served
(LS). With voltage-dependent load modeling, GLCM, PshdMand LSE minimizations; SWM and LSE minimization are best
suited multiple objectives to be optimized simultaneously. The
Pareto curve/Pareto optimal front provided by the SPEA 2+,
allows the system operator/decision maker to make a better
informed decision, regarding the compromise between the
various conflicting objectives.
ACKNOWLEDGMENTS
The author would like to thank Prof. P.R. Bijwe and Dr.
A.R.Abhyankar, Department of Electrical Engineering, Indian
Institute of Technology Delhi, India, for their guidance and
support for completing this work.
REFERENCES
[1] M. S. Pasand, M. Davarpanah, A new adaptive multi dimensional loadshedding scheme using genetic algorithm, Canadian Conference on
Electrical and Computer Engineering, pp. 1974-1977, May 2005.[2] C. Concordia, L. H. Fink, and G. Poullikkas, Load Shedding in An
Isolated System, IEEE Trans. Power system, vol. 10, no. 3, pp 1467
1472, Aug 1995.[3] PJM Manual: Energy and Ancillary Services Market Operations [On-
line]. Available: http://www.pjm.com[4] [Online]. Available: http://www.caiso.com[5] J. Wang, N.E. Redondo, and F.D. Galiana, Demand-Side Reserve Offers
in Joint Energy/Reserve Electricity Markets, IEEE Trans. Power Syst.18 (2003), 13001306.
[6] R.D. Christie, B. Wollenberg, I. Wangensteen, Transmission manage-ment in the deregulated environment, invited paper, Proc. IEEE, vol.88, no. 2, pp. 170195, 2000.
[7] F. Jian and J.W. Lamont, A combined framework for service identifi-cation and congestion management, IEEE Trans. Power Syst., vol. 16,no. 1, pp. 56-61, Feb. 2001.
[8] H.Y. Yamina, S.M. Shahidehpour, Congestion management coordina-tion in the deregulated power market, Electric Power Systems Research,vol. 65, no. 2, pp. 119-127, May 2003.
[9] T. Amraee, A.M. Ranjbar, B. Mozafari and N. Sadati, An enhanced un-der voltage load shedding scheme to provide voltage stability, ElectricPower Systems Research, vol. 77, no. 8, pp. 10381046, Jun. 2007.
[10] M.A. Mostafa, M.E. EL-Hawary, G.A. N.Mbamalu, M.M. Mansour,K.M. EL-Nagar, and A.N. EL-Arabaty, Steady state load sheddingschemes: A performance comparison,Electric Power Systems Research,vol. 38, pp. 105-112, 1996.
[11] W.M. AL-Hasawi, K.M. ELNaggar, Optimum Steady State Load Shed-ding Scheme Using Genetic Based Algorithm, IEEE MELECON, pp.605-609, May 2002.
[12] M.A. Mostafa, M.E. El-Hawary, G.A.N. Mbamalu, M.M. Mansour,K.M. El-Nagar, and A.M. El-Arabaty, A Computational Comparisonof Steady State Load Shedding Approaches in Electric Power Systems,
IEEE Trans. Power system, vol. 12 , no. 1, pp 30-37, Feb. 1997.
[13] B.F. Rad, M. Abedi, Application of Meta-heuristics Algorithms in
Discrete Model of Steady-State Load-Shedding, In proc. of OPTIM,2008, pp. 173177.
[14] O.E. Moya, A Spinning Reserve, Load Shedding, and EconomicDispatch Solution by Benders Decomposition, IEEE Trans. Power syst.,vol. 20, no. 1, pp. 384388, Feb. 2005.
[15] W. Wangdee, R. Billinton, Utilization of time varying event-basedcustomer interruption cost load shedding schemes, Electrical Powerand Energy Systems, vol. 27, pp. 674-681, 2005.
[16] T.S.P. Fernandes, J.R. Lenzi, and M.A. Mikilita, Load Shedding Strate-gies Using Optimal Load Flow With Relaxation of Restrictions, IEEETrans. Power syst., vol. 23, no. 2, pp. 712718, May 2008.
[17] B.K. Talukdar, A.K. Sinha, S. Mukhopadhyay, A. Bose, A computation-ally simple method for cost-efficient generation rescheduling and loadshedding for congestion management, Electrical Power and EnergySystems, vol. 27, pp. 379-388, 2005.
[18] M.T. Hagh, S. Galvani, A Multi Objective Genetic Algorithm forWeighted Load Shedding, In proc. of ICEE, May 2010, pp. 867873.
[19] S. Dutta and S.P. Singh, Optimal Rescheduling of Generators forCongestion Management Based on Particle Swarm Optimization, IEEETrans. Power syst., vol. 23, no. 4, pp. 15601569, Nov. 2008.
[20] J. Hazra, and A.K. Sinha, Congestion Management Using Multiobjec-tive Particle Swarm Optimization, IEEE Trans. Power syst., vol. 22, no.4, pp. 17261734, Nov. 2007.
[21] R. Banos, C. Gil, B. Paechter and J. Ortega, A Hybrid Meta-Heuristicfor Multi-Objective Optimization: MOSATS,Journal of Mathematical
Modelling and Algorithms, Springer Netherlands, 2006.
[22] M.S. Osman, M.A. Abo-Sinna, and A.A. Mousa, A solution to theoptimal power flow using genetic algorithms, Appl. Math. Comput.,vol. 155, no. 2, pp. 391-405, Aug. 2004.
[23] L.L. Lai, J.T. Ma, R. Yokoyama, and M. Zhao, Improved geneticalgorithms for optimal power flow under both normal and contingentoperation states, Int. J. Elect. Power Energy Syst., vol. 19, no. 5, pp.287-292, Jun. 1997.
[24] C.W. Taylor, Power system voltage stability, USA: Mc Graw-Hill, Inc.,1994.
[25] T.V. Cutsem, C. Vournas, Voltage stability of electric power systems,Springer, 1998.
[26] P. Kundur, Power System Stability and Control, McGraw-Hill, Inc.,New York, 1994.
[27] L.T.M. Mota and A.A. Mota, Load modeling at electric power dis-tribution substations using dynamic load parameters estimation, Inter-national Journal of Electrical Power and Energy Systems , vol. 26, pp.805811, Dec. 2004.
[28] Suppapitnarm, A. Seffen, K. Parks, G. Clarkson, A simulated annealingalgorithm for multi-objective optimization, Engineering Optimization,vol. 33, pp. 5985, 2000.
[29] A. Abraham, L. Jain, R. Goldberg (Eds),Evolutionary Multi-objectiveOptimization, Theoretical Advances and Applications, Springer-VerlagLondon limited, 2005.
-
7/26/2019 Multi-Objective based Congestion Management using Generation Rescheduling and Load Shedding
12/12
his article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.256960
Transactions on Power Systems
12
[30] M.A. Abido, J.M. Bakhashwain, Optimal var Dispatch using a Multi-objective Evolutionary algorithms, Electric Power and Energy systems,vol. 27, pp. 1320, 2005.
[31] T. Hiroyasu, S. Nakayama, M. Miki, Comparison Study of SPEA 2+,SPEA 2, and NSGA-II in Diesel Engine Emissions and Fuel EconomyProblem,IEEE Congress on Evolutionary Computation, 2005, pp. 236242.
[32] S. Watanabe, T. Hiroyasu and M. Miki, Neighborhood Cultiva-tion Genetic Algorithm for Multi-Objective Optimization Problems,Proc. of the 4th Asia-Pacific Conference on Simulated Evolution And
Learning(SEAL-2002), 2002, pp. 198202.[33] E. Zitzler, M. Laumanns and L. Thiele, SPEA 2: Improving the
Performance of the Strength Pareto Evolutionary Algorithm, TechnicalReport 103, Computer Engineering and Communication Networks Lab
(TLK), Swiss Federal Institute of Technology (ETH), Zurich, 2001.[34] S. Surender Reddy, A.R. Abhyankar, P.R. Bijwe, Reactive power price
clearing using multi-objective optimization, Energy, vol. 36, pp. 35793589, 2011.
[35] S. SurenderReddy, A.R. Abhyankar, P.R. Bijwe, Multi-Objective Day-Ahead Real Power Market Clearing with Voltage Dependent LoadModels, International Journal of Emerging Electric Power Systems,vol. 12, no. 4, pp. 1-22, 2011.
[36] [Online]. Available: http://www.ee.washington.edu/research/pstca.[37] M.A. Abido, Environmental/Economic Power Dispatch using Multiob-
jective Evolutionary Algorithms, IEEE Trans. Power Syst., vol. 18, no.4, pp. 15291537, 2003.
[38] K. Deb, Multi-objective Optimization using Evolutionary algorithms,
John Wiley and Sons, Inc., New York, 2001.[39] M. Kim, T. Hiroyasu, M. Miki, SPEA 2+: Improving the Performance
of the Strength Pareto Evolutionary Algorithm 2, Parallel ProblemSolving from Nature-PPSN VIII, pp. 742751, 2004.
S. Surender Reddy (S12-M15) received the Ph.D. degree in electricalengineering from the Indian Institute of Technology, New Delhi, India, in2013.
He was a Post-Doctoral Researcher at Howard University, Washington,DC, USA, from 2013 to 2014. He is currently an Assistant Professor withthe Department of Railroad and Electrical Engineering, Woosong University,Daejeon, Republic of Korea. His current research interests include powersystem restructuring issues, ancillary service pricing, real and reactive powerpricing, congestion management, and market clearing, including renewableenergy sources, demand response, smart grid development with integration ofwind and solar photovoltaic energy sources, artificial intelligence applicationsin power systems, and power system analysis and optimization.