optimal power flow methods: a comprehensive survey 7... · the optimal power flow problem is...

International Electrical Engineering Journal (IEEJ)

Vol. 7 (2016) No. 4, pp. 2228-2239

ISSN 2078-2365

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2228 Khamees et. al., Optimal Power Flow Methods: A Comprehensive Survey

Abstract - Power flow study (load-flow study) is a steady-state

analysis whose target is to determine the voltages, currents,

and real and reactive power flows in a system under a given

load conditions. The objective of an Optimal Power Flow

(OPF) study is to find steady state operation point which

minimizes generation cost, loss, emission etc. Over the past

half-century, OPF has become one of the most important and

widely studied nonlinear optimization problems while

maintaining an acceptable system performance in terms of

limits on generators’ real and reactive powers, line flow

limits, output of various compensating devices etc.

Traditionally, classical optimization methods were used to

effectively solve OPF. But more recently due to incorporation

of FACTS devices and deregulation of a power sector, the

traditional concepts and practices of power systems are

superimposed by an economic market management.

Therefore, OPF has become complex. In recent years,

Artificial Intelligence (AI) methods have been emerged which

can solve highly complex OPF problems. The purpose of this

paper is to present a comprehensive survey of various

optimization methods like traditional and AI methods used to

solve OPF problems.

Index Terms

Artificial Intelligence, Optimal Power Flow

I. INTRODUCTION

A first comprehensive survey regarding optimal power

dispatch was given by H.H. Happ [1] and then an IEEE

working group [2] presented bibliography survey of

major economic-security functions in 1981. Then in

1985, Carpentair [3] presented a survey and classified

the OPF algorithms based on their solution

methodology. In 1990, Chowdhury [4] presented a

survey on economic dispatch methods. In 1999, J.A.

Momoh et al. [5] presented a review of some selected

OPF techniques. In 2008, K.S. Pandya [6] made a survey

on traditional and Artificial Intelligence optimization

methods. In 2009, Qiu et al. [7] presented a survey of the

key algorithms used to solve OPF problems. In 2010,

Zhang [8] summarized the common deterministic OPF

methods. In 2012 and 2013, Stephen Frank, Ingrida

Steponavice, and Steffen Rebennack [9, 10] provided an

introduction and survey of the deterministic and

stochastic optimization methods.

II. PROBLEM FORMULATION

The optimal power flow problem is concerned with

optimization of steady state power system performance

with respect to an objective function while subjected to

various equality and inequality constraints. For optimal

active power dispatch, the objective function F (total

generation cost) is given by the following equation

- Minimize

Where,

Fт: Total quadratic cost function; it could be also a

cubic function

Pᵢ: Real power generated

Ng: Number of generation busses

aᵢ, bᵢ, cᵢ: Fuel cost coefficients for ith unit

- Subject to various constraints.

(a) Active power balance in the network

Pi (V, δ) - Pgi + Pdi = 0 (i=1, 2, ……, NB)

(b) Reactive power balance in the network

Qi (V, δ) - Qgi + Qdi = 0

(i= NV +1, NV + 2, ……, NB)

(c) Security-related constraints called soft constraints.

Limits on real power generations

Pgimin Pgi Pgimax (i=1, 2, NG)

Limits on voltage generation

ViminViVimax

(i= NV +1, NV + 2, ……, NB)

Limits on voltage angles

Optimal Power Flow Methods:

A Comprehensive Survey

Amr Khaled Khamees*, N. M. Badra*, Almoataz Y. Abdelaziz**

*Department of Engineering Physics and Mathematics, Faculty of Engineering, Ain Shams University, Cairo, Egypt

**Department of Electrical Power & Machines, Faculty of Engineering, Ain Shams University, Cairo, Egypt

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δimin δ i δ imax (i=1, 2,……, NB)

- Real power flow equations are:

Pi (V,δ) = Vi

NB

j 1

Vj(Gijcos(δ i - δ j ) + Bijsin(δ i - δ j )

- Reactive power flow equations are

Qi (V,δ) = Vi

NB

j 1

Vj(Gijsin(δ i - δ j ) - Bijcos(δ i - δ j )

where NG is the number of generator buses, NB is

number of buses, NV is number of voltage controlled

buses, Pi is active power injection into bus i, Qi is

reactive power injection into bus i, Pdi is active load on

bus i, Qdi is reactive load on bus i, Pgi is active power

generation on bus i, Qgi is reactive power generation on

bus i, Vi is magnitude of the voltage at ith bus, δi is

voltage phase angle of bus i, and Yij = Gij + jBij are the

elements of admittance matrix.

III. OPTIMAL POWER FLOW METHODS

The optimal power flow solution methods are classified

into two categories: Traditional methods and Artificial

Intelligence based methods as shown in Fig. 1.

Fig. 1 – Optimal Power Flow Solution Methods

IV. TRADITIONAL METHODS

Traditional methods are called deterministic or

conventional optimization methods.

The application of these methods had been an area of

active research in the recent past. The conventional

methods are based on mathematical programming

approaches and used to solve different size of OPF

problems. To meet the requirements of different

objective functions, types of application and nature of

constraints, the popular conventional methods are further

subdivided into the following:

1. Linear Programming

2. Gradient methods

3. Quadratic Programming

4. Newton-Raphson

5. Nonlinear Programming

6. Interior Point

Even though, excellent advancements have been made in

classical methods, they suffer from the following

disadvantages:

1. Some required linearization

2. Some required differentiability

3. May get stuck at local optimum

4. Poor convergence

5. Weak in handling qualitative constraints

6. Become too slow if number of variables are large

7. Can find only a single optimized solution in a single

simulation run

a) LINEAR PROGRAMMING

Linear programming formulation requires linearization

of objective function as well as constraints with

nonnegative variables.

Mukherjee, S.K. [11] presented a linear

programming based optimization method for optimal

power flow. Results show that a 220 kV five-bus system

convergence within only one iteration was achieved with

a considerable reduction in CPU time. The technique has

been recommended to Florida Power and Light

Company's Power System Control Division and has

proved successful for a 15 bus system using real-time

data.

T.S. Chung et al. [12] presented a linear

programming method for minimizing power loss and

finding the optimal location for capacitor in a

distribution system. Calculation is carried at 14-bus

system and this method does not require any matrix

inversion, thus saves computational time and memory

space.

E. Lobato et al. [13] presented a linear

programming based method for OPF for minimization of

OPF methods

Traditional methods

Artificial

Intelligence (AI) methods

1. Linear Programming

2. Gradient methods

3. Quadratic Programming

4. Newton-Raphson

5. Nonlinear Programming

6. Interior Point

1. Genetic algorithm

2. Particle swarm

3. Artificial neural network

4. Bee colony optimization

5. Differential evolution

6. Grey wolf optimizer

7. Shuffled frog-leaping


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power loss and generator reactive margins for Spanish

power system. Shunt reactors and capacitors are discrete,

modeled by integer variables. Both the objective

function and the constraints are linearized in each

iteration.

Rau, N. [14, 15] presented DC power flow

formulation which involves simplifying assumptions and

linearization with a linear (or linearized) objective

function. Since the DC power flow constraint set is fully

linear, no further constraint linearization is needed. In

contrast to other linearization techniques, DC-OPF is

non-iterative; only a single solve is required to yield the

optimal solution. Because of its simplicity, speed, and

robust nature, DC-OPF is widely used in industry.

b) GRADIENT METHOD

Gradient methods were among the first attempts to solve

practical OPF problems at the end of the 1960s. Gradient

methods use the 1st order derivative vector of the

objective function of a non-linear optimization (that is,

the gradient) to determine improving directions for the

solution in iterative steps. Gradient methods are reliable,

easy to implement, and guaranteed to converge for well-

behaved functions. However, gradient methods are slow

compared to higher-order methods.

Dommel and Tinney [16] presented a gradient

method to OPF problem, using penalty techniques to

enforce the limits on the dependent variables and the

functional constraints. This work relied on 1st order

information of the (nonlinear) objective and the

constraints derived from the Jacobian matrix computed

from a conventional power flow.

Alsac and Stott [17] extended the work of

Dommel and Tinney to security-constrained OPF

(SCOPF) by adding predetermined contingency cases to

the power flow equations and penalizing security

violations of these cases in the objective function.

Peschon et al. [18] presented an application of

the Generalized Reduced Gradient (GRC) method to

OPF, presenting the benefits of the GRC method. These

benefits include the avoidance of penalty terms and the

straightforward computation of sensitivities.

c) QUADRATIC PROGRAMMING

Quadratic Programming (QP) is a special form of non-

linear programming whose objective function is

quadratic and constraints are linear.

J.A. Momoh [19] presented a generalized

Quadratic-based model for OPF. The construction of the

OPF algorithm includes the conditions for feasibility,

convergence and optimality. It is also capable of using

hierarchical structures to include multiple objective

functions. The algorithm using sensitivity of objective

functions with optimal adjustments in the constraints

yields a global optimal solution. Computational memory

and execution time required have been reduced.

N. Grudinin [20] presented a reactive power

optimization model based on Successive Quadratic

Programming (SQP) methods. Six other optimization

methods were used to test the IEEE 30-bus and 278-bus

systems. It is found that the SQP methods provide more

fast and reliable optimization in comparison with other

classical methods.

Reid and Hasdorff [21] presented QP OPF

using the Lagrange multiplier method and Taylor

expansion. Economic dispatch problem is formulated as

a quadratic programming problem and solved using

Wolfe's algorithm. The method is capable of handling

both equality and inequality constraints on p, q, and v

and can solve the load flow as well as the economic

dispatch problem. Convergence was obtained in three

iterations for all test systems considered and solution

time is small enough to allow the method to be used for

on-line dispatching at practical time intervals.

d) NEWTON – RAPHSON MEHTOD

Newton method is a second order method for

unconstrained optimization based on the application of a

2nd order Taylor series expansion about the current

candidate solution.

S. Chen et al. [22] presented Newton-Raphson

(NR) method to solve emission dispatch in real-time

with sensitivity factors incorporated. The Jacobian

matrix and the coefficients have been developed in terms

of the generalized generation shift distribution factor.

Penalty factor and the incremental losses are easily

obtained. Run time is lesser than that of the conventional

one.

K.L. Lo et al. [23] presented two Newton-like

load flow methods, the Fixed Newton method and the

modification of the right-hand-side vector method for

line outage simulation that is a part of contingency

analysis. These two methods are compared with the

Newton-based full AC load flow method and the fast

decoupled load flow to show their better convergence

characteristics.

H. Ambriz-Pérez [24] presented unified power

flow controller (UPFC) modeling within the context of

optimal power flow (OPF) by Newton Method. The

networks are modified to include several UPFCs are

solved with equal reliability. The UPFC model itself is

very flexible; it allows the control of active and reactive

powers and voltage magnitude simultaneously. It can



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also be set to control one or more of these parameters in

any combination or to control none of them.

e) NON LINEAR PROGRAMMING

Nonlinear programming (NLP) deals with problems

involving nonlinear objective and/or constraint

functions. The main advantage of NLP formulations for

OPF is that they accurately capture power system

behavior. However, the computational and theoretical

challenges associated with NLP motivated the

development of simplified formulations, as discussed

below. In addition, certain NLP formulations redefine

the problem variables to reduce the degree of

nonlinearity.

J.A. Momoh et al. [25] presented a new

nonlinear convex network flow programming

(NLCNFP) model for solving the multi-area security

constrained economic dispatch (MAED) problem. A

combined method of quadratic programming and

network flow programming used to solve MAED

problem. The tie-line security and transfer constraints

are considered in each area. Method is tested in four

interconnected power systems.

D. Pudjianto et al. [26] presented LP and NLP

for reactive OPF for allocating reactive power among

generators in a deregulated environment. It was found

that the overall cost associated with the system reactive

requirement calculated by LP method was reasonably

accurate, but the generator’s individual commitment

may vary considerably. Whereas, NLP offers a faster

computation speed and accuracy for the solution but the

convergence could not be guaranteed for every

condition.

H. Habibollahzadeh [27] presented

hydrothermal OPF based on a combined LP and NLP

methods. Hydraulic modeling of systems with

considerable share of hydraulic generation is also

considered. It used the LP technique to help the

Generalized Reduced Gradient technique in a feasibility

adjustment step and feasible directions method for

solving nonlinear programming problems has been used.

f) INTERIOR POINT METHOD

Interior Point Methods (IPMs) are a family of projective

scaling algorithms for solving linear and nonlinear

optimization problems that constrain the search to the

feasible region by introducing barrier terms to the

objective function. In general, IPMs attempt to

determine and follow a central path through the feasible

region to the optimal solution.

Sergio Granville [28] presented IPM to the

optimal reactive power dispatch problem. It is based on

the primal dual logarithmic. This method was applied on

large power systems and it converged in 40 iterations at

CPU time 398.9 seconds. IPM advantages are: number

of iterations is not very sensitive to network size or

number of control variables, numerical robustness, hot

starting capability, no active set identification difficulties

and effectiveness in dealing with optimal reactive

allocation.

Torres, G.L. [29] presented the solution of an

optimal power flow (OPF) problem in rectangular form

by an IPM for nonlinear programming. OPF problem is

solved via a primal-dual IPM for NLP. Objective

function and constraints are quadratic. Desirable

properties of a quadratic function are: (a) its Hessian is

constant, (b) its Taylor expansion terminates at the

second-order without error, and (c) the higher-order

term is easily evaluated. Such quadratic features allow

for ease of matrix setup and inexpensive incorporation of

higher order information in a predictor-corrector

procedure that reduces the number of IPM iterations to

convergence.

Edgardo D. Castronuovo [30] presented new

versions of interior point methods applied to the optimal

power flow problem. Search for the optimum is based on

the combination of two directions: the affine-scaling and

the centralization, it is shown that the suitable

combination of these directions can increase the

potential of the optimization algorithm in terms of speed

and reliability. To solve optimization problems through

the IPM for Nonlinear Programming (NLP) a

perturbation parameter is introduced in the

complementarily Karush-Kuhn-Tucker (KKT) condition.

Hua Wei et al. [31] presented a new interior

point nonlinear programming algorithm for optimal

power flow problems (OPF) based on the perturbed

KKT conditions of the primal problem. Through the

concept of the centering direction, authors extend this

algorithm to classical power flow (PF) and approximate

OPF problems. Compared with the conventional data

structure of Newton OPF, the number of fill-ins of the

proposed scheme is roughly halved and CPU time is

reduced by about 15% for large scale systems. The

proposed algorithm includes four kinds of objective

functions and two different data structures. Extensive

numerical simulations on test systems that range in size

from 14 to 1047 buses have shown that the proposed

method is very promising for large scale application due

to its robustness and fast execution time.

V. ARTIFICIAL INTELLIGENCE METHODS


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The intelligent search has become a very important

technique in searching the global or near-global optimal

solution. It also called Non-deterministic or stochastic

method, major advantages of these methods are:

1. Able to handle various qualitative constraints

2. Can find multiple optimal solutions in single

simulation run

3. Suitable in solving multi-objective optimization

problems

4. Can find the global optimum solution

Number of non-deterministic optimization methods have

been developed and applied to global optimization

problems to overcome the weak global search

capabilities of many conventional deterministic

optimization algorithms. Many of these techniques have

been applied to OPF problems like:

1. Genetic algorithm

2. Particle swarm

3. Artificial neural network

4. Bee colony optimization

5. Differential evolution

6. Grey wolf optimizer

7. Shuffled frog-leaping

a) GENETIC ALGORITHM

Genetic Algorithm (GA) operates on the encoded binary

string of the problem parameters rather than the actual

parameters of the system. Each string can be thought of

as a chromosome that completely describes one

candidate solution to the problem. A simple Genetic

Algorithm is an iterative procedure.

During each iteration step (generation) three genetic

operators (Selection, crossover, and mutation) are

performing to generate new populations (offspring).

Bakritzs, V. [32] presented economic dispatch problems

using genetic algorithm method. Its merits are: the non-

restriction of any convexity limitations on the generator

cost function and effective coding of GAs to work on

parallel machines. GA is superior to dynamic

programming, as per the performance observed in

Economic dispatch problem. The run time of the second

GA solution (EGA method) proportionately increases

with size of the system.

Po-Hung Chen [33] presented a large scale

economic dispatch problem by GA. He designed new

encoding technique where in, the chromosome has only

an encoding normalized incremental cost. There is no

correlation between total number of bits in the

chromosome and number of units. The unique

characteristic of Genetic Approach is significant in big

and intricate systems which other approaches fails to

accomplish. Dispatch is made more practical by

flexibility in GA, due to consideration of network losses,

ramp rate limits and prohibited zone’s avoidance. This

method takes lesser time compared to Lambda –iteration

method in big systems.

M. Younes and M. Rahl [34] presented hybrid

Genetic Algorithm (combination of GA and Mat power)

that was used to solve OPF including active and reactive

power dispatches. The method uses GA to get a close to

global solution and the package of MATLAB – m files

for solving power flow and optimal power flow problem

(mat power) to decide the optimal global solution. Mat

power is employed to adjust the control variables to

attain the global solution. The method was validated on

the modified IEEE 57–bus system and the results show

that the hybrid approach provides a good solution as

compared to GA or Mat power alone.

M. Sailaja Kumari [35] presented OPF problem

formulated as a multi-objective optimization problem,

where optimal control settings for simultaneous

minimization of fuel cost and loss, loss and voltage

stability index, fuel cost and voltage stability index and

finally fuel cost, loss and voltage stability index are

obtained, it combines a new Decoupled Quadratic Load

Flow (DQLF) solution with Enhanced Genetic

Algorithm (EGA) to solve the OPF problem. A Strength

Pareto Evolutionary Algorithm (SPEA) based approach

with strongly dominated set of solutions is used to form

the pareto-optimal set.

b) PARTICLE SWARM OPTIMIZATION

Particle Swarm Optimization (PSO) is a population-

based stochastic optimization Technique. PSO is based

on processes arising naturally in socially organized

colonies such as flocks of birds and schools of fish. PSO

exploits a population of individuals to explore promising

regions within the search space. In the search procedure,

each individual (particle) moves within the decision

space over time and changes its position in accordance

with its own best experience and the current best particle

according to the model shown in Fig. 2.



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Fig. 2 - Particle Swarm Model [36]

El-Gallad et al. [37] presented PSO to solve the

traditional economic dispatch problem. The objective

function was formulated as a combination of piecewise

quadratic cost functions with non-differential regions,

instead of adopting a single convex function for each

generating unit. This innovation in problem formulation

is due to the incorporation of practical operating

conditions, like valve-point effects and fuel types where

system demand and the balance of power, with network

losses incorporated and the generating capacity limits.

Djillani Ben Attous [38] presented economic

dispatch problem with a valve point effects. A valve

point effects is the rippling effects added to the

generating unit curve when each steam admission valve

in a turbine starts to open. Proposed method using PSO

has been examined and tested for standard IEEE 30-bus

system, it has been found that PSO method is highly

competitive for its better general convergence

performance.

Sanjeev Kumar [39] presented PSO and

integration of GA-fuzzy and PSO-fuzzy optimization to

calculate optimal power flow. The four algorithms GA,

GA-fuzzy, PSO, and FPSO are tested for solving

modified IEEE 30 bus test system. It is found that

integration of fuzzy with Genetic Algorithm and particle

swarm optimization techniques improve the performance

of average fitness obtained with the help of optimal

power flow method. The results of integrated GA-Fuzzy

and PSO-fuzzy are compared with simple GA and PSO

and found synergetic approaches are better.

T. Saravanan [40] presented the application of

PSO technique to solve OPF with inequality constraints

on line flow. Algorithm is implemented on a six-bus

three-unit system and the results are compared with

linear programming method.

J. Praveen and B. Srinivasa Rao [41] presented

optimization problem solved by PSO with power

injection model of the FACTS device. The proposed

methodology is tested on standard IEEE 30-bus test

system and the results are compared for single objective

optimization with and without FACTS device.

c) ARTIFICIAL NEURAL NETWORK

Artificial neural network (ANN) is an interconnected

group of artificial neurons that use a mathematical model

or computational model for information processing

based on a connection list approach to computation.

Mat Syai’in [42] presented a novel algorithm of an

optimal power flow (OPF). The proposed algorithm uses

neural networks (NNs) to model the generator capability

curves and set them as the output power constraints of

the generators. In addition, it also uses NNs to replace an

OPF based on the particle swarm optimization (PSO)

method so as to run in real time. Also, in order for the

proposed algorithm to be able to account for various

load conditions, a 500 kV Java-Bali power system

consisting of 23 buses is used as a benchmark system to

validate the proposed NN-based OPF. The simulation

results show that that the values obtained from the

proposed algorithm are in great agreement with those

calculated from the PSO-OPF. Method procedure is

shown in Fig. 3.

Nakawiro and Erlich [43] presented a speedup

strategy for OPF that uses a dedicated ANN to perform

the function of a power flow program. The ANN is

combined with a GA, which performs the optimization.

Tests show that their method significantly speeds up the

solution process compared to GAs alone, while

providing solutions of similar quality.



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Fig. 3 - Flowchart design of ANN-OPF [41]

Chowdhury [44] presented Integrated Security

Constrained Optimal Dispatch (ISCOD) which could

solve the OPF problem when it was constrained by both

static and dynamic security. ISCOD utilized the

diagnostic and decision making capabilities of

Knowledge Base System (KBS), massive parallellisms

and learning features of an ANN along with

conventional power system network solution

methodologies to provide real-time control and

optimization. The KBS and the ANN are used

indifferent configuration for adding the dispatch or in

making control decisions.

d) BEE COLONY OPTIMIZATION

Artificial Bee colony (ABC) simulates the intelligent

foraging behavior of a honeybee swarm. ABC is simple

in concept, easy to implement, and has fewer control

parameters. Foraging artificial bees are divided into

three groups:

1. Employed bee

It stays on a food source and provides the neighborhood

of the source in its memory.

2. Onlooker bee

It gets the information of food sources from the

employed bees in the hive and selects one of the food.

3. Scout bee

It is responsible for finding new food, the new nectar

sources. The process is shown in Fig. 4.

Fig. 4 - Foraging behavior of honeybees to find food

sources [45]

Sumpavakup et al. [46] presented ABC to solve

the optimal power flow problems. The effectiveness of

the Bees Algorithm was verified by testing with IEEE-

14 and IEEE-30 bus system. The technique was also

compared with other swarm intelligence techniques

namely, Genetic Algorithms and Particle Swarm

Optimization and its simulation results show that Bees

Algorithm can converge towards the better solution

slightly faster than the rest methods.

Khorsandi [47] presented a fuzzy based

modified artificial bee colony (MABC) algorithm to

solve discrete optimal power flow (OPF) problem that

has both discrete and continuous variables considering

valve point effects. The OPF problem is formulated as a

multi-objective mixed-integer nonlinear problem, where

optimal settings of the OPF control variables for

simultaneous minimization of total fuel cost of thermal

units, total emission, total real power losses, and voltage

deviation are obtained. The proposed approach is applied

to the OPF problem on IEEE 30-bus and IEEE 118-bus

test systems. The performance and operation of the

proposed approach is compared with the conventional

methods. The results confirm that the MABC algorithm

is more effective in global search exploration and faster

than the other algorithms.

A. N. Afandi and H. Miyauchi [48] developed a

Harvest Season Artificial Bee Colony algorithm to

improve performance in terms of the search mechanism



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and convergence speed. The effectiveness of the

proposed method was tested on IEEE-62 bus system and

compared to those obtained by ABC, SFABC, SBABC,

MOABC and IABC. The numerical results showed that

the proposed method reduced the number of iterations.

e) DIFFERENTIAL EVOLUTION

Differential Evolution (DE) is a population-based, direct

stochastic search algorithm. DE combines simple

arithmetic operators with the classical evolutionary

operators of crossover, mutation and selection to evolve

from a randomly generated starting population to a final

solution. DE uses a greedy, rather than stochastic,

approach to solve the problem. DE procedure is shown

in Fig. 5.

Fig. 5 - DE flow chart [48]

Coelho and Mariani [49] presented improved

DE algorithms to solve economic dispatch problems of

electric energy that takes into account nonlinear

generator features such as ramp rate limits and

prohibited operating zones. Two economic dispatch

problems with 6 and 15 thermal units with ramp rate

limits and prohibited operating zones in the power

system operation and transmission loss are employed to

demonstrate the performance of this method. DE

algorithms offer potential advantages: they find the true

global minimum regardless of the initial parameter

values, and they display fast convergence and use few

control parameters.

M. A. Abido [50] presented a multi-objective

differential-evolution-based approach to solve the

optimal power flow (OPF) problem where different

objective functions and operational constraints have

been considered and also clustering algorithm is applied

to manage the size of the Pareto. An algorithm based on

fuzzy set theory is used to extract the best compromise

solution. Results on IEEE 30-bus and IEEE 118-bus

standard test systems show the effectiveness of the

proposed approach in solving true multi-objective OPF

and also finding well-distributed Pareto-optimal

solutions.

Sayah and Zehar [51] presented DE for solving

OPF with non-smooth and non-convex generator fuel

cost curves. They consider effective modifications in the

mutation, enhancing the convergence rate while

improving the solution quality. They also showed that

their modified DE algorithm outperforms the classical

DE algorithms in global convergence speed and obtains

similar results compared to Evolutionary Programming

and Tabu Search methods.

f) GREY WOLF OPTIMIZER

Grey wolf optimizer (GWO) is a population based

heuristics algorithm simulates the leadership hierarchy

and hunting mechanism of gray wolves in nature.

Privileged wolves are alpha wolves – decision makers,

then beta wolves – alpha assistant, and then delta wolves

– lowest ranking and omega are inferior wolves

preceded by scoffed kappa and lambda as in Fig. 6.

Fig. 6 - The hierarchy of the grey wolves

El-Fergany and Hasanien [52] presented the

grey wolf optimizer to solve the optimal power flow

(OPF) problem. The indicator of the static line stability

index is incorporated into the OPF problem. The fuzzy-

based Pareto front method is tested to find the best

compromise point of multi-objective functions.

Algorithm used to determine the optimal values of the

continuous and discrete control variables. These

algorithms are applied to the standard IEEE 30-bus and

118-bus systems with different scenarios.

Sulaiman et al. [53] presented GWO in solving the

optimal reactive power dispatch (ORPD) problem. Two

case studies of IEEE 30-bus system and IEEE 118-bus

system are used to show the effectiveness of GWO

technique compared to other techniques. The results of

this research show that GWO is able to achieve less



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ISSN 2078-2365



power loss and voltage deviation than those determined

by other techniques.

g) SHUFFLED FROG-LEAPING

Shuffled frog Leaping algorithm (SFLA) is memetic

heuristic that is designed to seek a global optimal

solution by performing a heuristic search based on the

evolution of memes carried by individuals and a global

exchange of information among the population. It

combines the benefits of the local search tool of the

particle swarm optimization and the idea of mixing

information from parallel local searches to move toward

a global solution. Shuffling of frogs in memeplexes is

shown in Fig. 7.

Fig. 7 - Shuffled behavior of leaping frogs in search of

food [54]

R. Jahani [55] presented a new method based

on shuffled frog leaping algorithm for distributing the

power optimized distribution to minimize power

production costs and to optimize allocation of every

powerhouse share in addition to providing required

power for a network. An inferior purpose function is

expressed via the basis of units’ productive power and

restrictions are modeled in the form of linear equalities

and inequality equation. The presented method is

simulated on a standard IEEE 30-bus system. Results

demonstrate that the algorithm has great potential in

functions optimization.

Taher Niknam [56] presented a modified

shuffle frog leaping algorithm for multi-objective

optimal power flow by considering the emission issue. A

modified SLFA called MSLFA algorithm which profits

from a mutation in order to reduce the processing time

and improve the quality of solutions, particularly to

avoid being trapped in local optima. MSLFA algorithm

is applied to the 30-bus IEEE test system. The results

showed that MSFLA method is capable of obtaining

accurate and acceptable solutions

K. Lenin [57] presented an algorithm based on

Modified Shuffled Frog-Leaping Optimization for

solving the multi-objective reactive power dispatch

problem considering various generator constraints in a

power system. This method formulates reactive power

dispatch problem as a mixed integer non-linear

optimization problem and determines control strategy

with continuous and discrete control variables. This

paper introduces a new search-acceleration parameter

into the formulation of the original shuffled frog leaping

algorithm to create a modified form of the shuffled frog

algorithm.

VI. CONCLUSION

This paper presents a review for various optimization

methods used to solve OPF problems. Even though

excellent advancements have been made in classical

methods they suffer from the following disadvantages:

some required linearization and differentiability, may get

stuck at local optimum, poor convergence, weak in

handling qualitative constraints and become too slow if

number of variables are large whereas, the major

advantage of the AI methods is that they are relatively

versatile for handling various qualitative constraints. AI

methods can find multiple optimal solutions in single

simulation run. So they are quite suitable in solving

multi-objective optimization problems. In most cases,

they can find the global optimum solution. Table 1

shows advantages and disadvantages of AI methods

presented in this survey.

Authors strongly believe that this survey article will be

very much useful to the researchers for finding out the

relevant references as well as the previous work done in

the field of OPF methods, so that further research work

can be carried out.

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https://www.researchgate.net/publication/275100723_Mohd_Herwan_Sulaiman_Zuriani_Mustaffa_Mohd_Rusllim_Mohamed_Omar_Aliman_2015_Using_the_gray_wolf_optimizer_for_solving_optimal_reactive_power_dispatch_problem_Applied_Soft_Computing_Vol_32_pp_286-292





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AI method Advantages Disadvantages

Genetic algorithm

- Capability of solving any optimization

problem based on chromosome approach

- Capability to handle multiple solution

search spaces

- Less complex and more straightforward

compared to other algorithms

- Does not always come with global optimum

all the time.

- A tool is dependent on computers speed and

only real time application can produce quick

respond time.

- To a non-professional, the return encoded

result maybe not be able to understand

Particle swarm optimization

- Simple concept and easy implementation

- Robust in controlling the few parameters,

computationally efficient and requires less

memory

- It can be easily applied to nonlinear non-

continuous optimization problem

- It gets trapped in local optima when

handling heavily constraint problems due to

limited local/global searching capabilities

- Updating is performed without considering

quality of solutions and the distance

between solutions

Artificial neural network

- Less formal statistical training,

- Ability to detect all possible interactions

- Availability of multiple training

algorithms.

- Its “black box” nature

- Greater computational burden, proneness to

over-fitting

- The empirical nature of model development.

Bee colony optimization

- It has few parameters

- It is a global optimizer

- Flexible

- High computational time

Differential evolution

- Few control variables and fast

convergence

- Stable and simple

- The convergence to proper target is very

late

Grey wolf optimizer

- Easy to implement due to its simple

structure

- Faster convergence

- Few parameters to control

- Avoids local optima

- The algorithm is still under research and

development

Shuffled frog-leaping

- Robust, accurate, efficient and fast

- It combines the profits of the local search

tool of PSO and the idea of mixing

information from parallel local searches to

move toward a global solution

- It gets trapped in local optima

- The convergence to proper target is very

late

Table 1 - Advantages and disadvantages of AI methods [57]-[62]


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