International Journal of Research In Science & Engineering
Volume: 3 Issue: 3 May-June 2017
e-ISSN: 2394-8299
p-ISSN: 2394-8280
WIND-THERMAL COORDINATION USING GREY WOLF
OPTIMIZATION
M.Anand1, Mr.Sp.Sela Kumar2
1
P.G.Student, Department of EEE, Mahath Amma Institute Of Engineering And Technology
[email protected]
2
Assistant Professor, Department of EEE, Mahath Amma Institute Of Engineering And
Technology
ABSTRACT
Now a day in world, the load on power system enormously increases. The conventional power
generation plants never satisfy the power demand. So the power generating sectors turn into
renewable energy sources. Electrical power systems are designed and operated to meet the
continuous variation of power demand. In power system, minimization of the generation and
operation cost is very important. The rise of environmental protection and the progressive
exhaustion of traditional fossil energy sources have increased the interest in integrating
renewable energy sources into existing power systems. With increasing fuel prices and
environmental concerns the governments all over the world has commissioned research on
renewable energy applications under the consideration of diversifying energy sources. Among
the various renewable energy sources, wind energy could be in short term, one of the most
promising renewable energy sources. It could provide a much greater proportion of energy
production in places with good wind. Wind energy is also commonly regarded as problematic
for power system operation due to its limited predictability and variability. The output
fluctuation of wind energy can be compensated by employing exchange schedules with
neighboring systems when there is only limited penetration exceeds specific scale, the often
and only solution is to use conventional generation units to cover the variability of wind
power. The Economic Dispatch (ED) of electric power generation is one of the most important
optimization problems in power system. Its task is to allocate load over the set of dispatch able
units such that the required power is generated at the least cost. Since wind power does not
consume fossil fuel, the government has regulated in its renewable energy law that the power
grid should buy all electricity produced by renewable energy plant. Thereafter, adoption and
variation of high penetration wind power will have notable impact to economic dispatch of
power system. Recently, a optimization technique known as grey wolf optimization algorithm
has become a candidate for many optimization applications due to its flexibility and efficiency.
This thesis focuses on investigating whether the conventional generation system can balance
wind power and what the wind power will bring to our power system. Economic dispatch of ten
units system incorporating a wind power plant is analyzed using grey wolf optimization
algorithm.
1.2 LITERATURE REVIEW
Chowdhury and Rahman presented a survey of papers and reports which address various aspects
of economic load dispatch. The time period considered is 1977-88. This is done to avoid any
repetition of previous studies which were published prior to 1977. Four very important and
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International Journal of Research In Science & Engineering
Volume: 3 Issue: 3 May-June 2017
e-ISSN: 2394-8299
p-ISSN: 2394-8280
related areas of economic load dispatch are identified and papers published in the general area of
economic dispatch are classified as follows.
The areas are: (i) Optimal power flow, (ii) Economic dispatch in relation to AGC, (iii) dynamic
dispatch and (iv) Economic dispatch with non-conventional generation sources.
Megahed et al. developed a method for solving the economic load dispatching problem by
changing it from constrained nonlinear programming problem to a sequence of constrained linear
programming problems. The formulation of the load scheduling is exact in the sense that all the
system voltages, active and reactive generation, as well as the phase angles are considered as
independent variables. In addition, the effect of bus voltages on the loads is taken into
consideration. 3 Fink L. H., et al. Described the valve-point loading logic which is intended to
meet at any time in the most economical fashion a generation commitment. This objective is
approached by insuring that as great a portion of the load as practicable will be carried by units
loaded to valve points, that the remainder of the load will be carried by units reserved for
regulation, and that in both categories the assignments will be made to those units which can
provide the requisite capacity at the lowest cost.
Walters and Sheble used genetics-based algorithm to solve an economic dispatch problem for
valve point discontinuities. The algorithm utilizes payoff information of candidate solutions to
evaluate their optimality. Thus, the constraints of classical Lagrange techniques on unit curves
are circumvented. The formulations of an economic dispatch computer program using genetic
algorithms are presented and the program's performance using two different encoding techniques
is compared. The results are verified for a sample problem using a dynamic programming
technique Chen and Chang presented a new genetic approach for solving the economic dispatch
problem in large-scale systems. A new encoding technique is developed. The chromosome
contains only an encoding of the normalized system incremental cost in this encoding technique.
Therefore, the total number of bits of chromosome is entirely independent of the number of
units. The salient feature makes the proposed genetic approach attractive in large and complex
systems which other methodologies may fail to achieve. Moreover, the approach can take
network losses, ramp rate limits, and prohibited zone avoidance into account.
Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Andrew Lewis presented a new
optimization techniques it is applicable to challenging problems with unknown search spaces and
with different constraints.
1.3 OBJECTIVE OF THE WORK
 To find solution of economic dispatch problem so that the total fuel cost is minimized
while satisfying equality and inequality constraints like the power generation limits.
 To use global search techniques like GA/GWO to find the optimal settings.
 Investigate the effectiveness of these methods for solving ED problem while neglecting
the transmission losses.
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International Journal of Research In Science & Engineering
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2.ECONOMIC DISPATCH & WIND THERMAL CO-ORDINATION
2.1 INTRODUCTION TO ECONOMIC DISPATCH
Economic dispatch is the process of allocating the required load demand between the available
generation units so as to minimize the cost of operation. It is a straight forward concept: costs to
serve a given level of electricity demand are minimized by dispatching generation involving
lower cost before dispatching higher cost generation. A number of considerations must be
addressed to ensure that the resulting system operation is secure, reliable and cheap.
2.2 ECONOMIC OPERATION OF POWER SYSTEMS
One of the earliest applications of on-line centralized control was to provide a central facility, to
operate economically, several generating plants supplying the loads of the system. Modern
integrated systems have different types of generating plants, such as coal fired thermal plants,
hydel plants, nuclear plants, oil and natural gas units etc. The capital investment, operation and
maintenance costs are different for different types of plants. The operation economics can again
be subdivided into two parts.
 Problem of economic dispatch, which deals with determining the power output of each
plant to meet the specified load, such that the overall fuel cost is minimized.
 Problem of optimal power flow, which deals with minimum – loss delivery, where in the
power flow, is optimized to minimize losses in the system. In this chapter we consider the
problem of economic dispatch.
2.3 ECONOMIC DISPATCH PROBLEM
The economic dispatch problem is defined as the one that minimizes the total operating cost of a
power system while meeting the total load plus transmission losses within generator limits.
When long distance transmission of power is involved, transmission losses do occur. If the
transmission losses are neglected, then the total system load can be optimally divided among the
various generating plants using the equal incremental cost criterion. A modern electric utility is
capable of serving a vast area of relatively low load density. The transmission losses may vary
from 5 to 15 per cent of total load. It is very necessary to keep an account for transmission losses
while developing an economic dispatch policy. Mathematically, the problem is defined as
2.3.1 Economic Load Dispatch without Losses
The simplest economic load dispatch problem is the case when transmission line losses are
neglected. Due to this the total demand 𝑃𝐷 is the sum of all generations. A cost function 𝐹𝑖 ( ) is
assumed to be known for each plant. The problem is to find the real power generation, 𝑃𝑔𝑖 for
each plant such that the total operating cost (𝑃𝑔𝑖)is minimum and the generation remains within
the lower generation 𝑃𝑔𝑖𝑚𝑖𝑛and upper generation𝑃𝑔𝑖𝑚𝑎𝑥. Suppose there is a station with NG
generators committed and the active power load demand PD is given, the real power generation
𝑃𝑔𝑖 for each generator has to be allocated so as to minimize the total cost. The optimization
problem can be therefore be stated as Minimize (𝑃𝑔𝑖)=Σ𝐹𝑖( 𝑃𝑔𝑖 ) transmission losses may vary
from 5 to 15 per cent of total load. It is very necessary to keep an account for transmission losses
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International Journal of Research In Science & Engineering
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e-ISSN: 2394-8299
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while developing an economic dispatch policy. Mathematically, the problem is the simplest
economic load dispatch problem is the case when transmission line losses are neglected. Due to
this the total demand 𝑃𝐷 is the sum of all generations. A cost function 𝐹𝑖 ( ) is assumed to be
known for each plant. The problem is to find the real power generation, 𝑃𝑔𝑖 for each plant such
that the total operating cost (𝑃𝑔𝑖)is minimum and the generation remains within the lower
generation 𝑃𝑔𝑖𝑚𝑖𝑛and upper generation𝑃𝑔𝑖𝑚𝑎𝑥. Suppose there is a station with NG generators
committed and the active power load demand PD is given, the real power generation 𝑃𝑔𝑖 for
each generator has to be allocated so as to minimize the total cost. The optimization problem can
be therefore be stated as
Minimize (𝑃𝑔𝑖)=Σ𝐹𝑖( 𝑃𝑔𝑖 ) (2.1)𝑁𝐺𝑖=1
Subject to
i. the power balance equation
Σ𝑃𝑔𝑖𝑁𝐺𝑖=1=𝑃𝐷 (2.2)
ii. the inequality constraints
𝑃𝑔𝑖𝑚𝑖𝑛≤𝑃𝑔𝑖≤𝑃𝑔𝑖𝑚𝑎𝑥 (𝑖=1,2,…………,𝑁𝐺) (2.3)
Where
𝑃𝑔𝑖is the decision variable, i.e. real power generation
𝑃𝐷is the real power demand
NG is the number of generation plants
𝑃𝑔𝑖𝑚𝑖𝑛 is the lower permissible limit of real power generation
𝑃𝑔𝑖𝑚𝑎𝑥 is the upper permissible limit of real power generation
(𝑃𝑔𝑖) is the operating fuel cost of the i th plant and is given by the quadratic equation
(𝑃𝑔𝑖)=𝑎𝑖𝑃𝑔𝑖2+𝑏𝑖𝑃𝑔𝑖+𝑐𝑖
WIND THERMAL CO-ORDINATION
The impact of conventional electricity generation on the environment is being minimized and the
efforts are made to generate electricity from renewable source. The problem of low cost of
energy generation and its environmental advantages, using wind energy in electric power
generation, has been seemed useful. The drastic changes in environment and climate can be
avoided by replacing fossil energy sources with clean and fuel free energy generation. The main
advantages of electricity generation from renewable sources are the absence of harmful
emissions and the in principle infinite availability of the prime mover that is converted into
electricity. One way of generating electricity from renewable sources is to use wind turbines that
convert the energy contained in flowing air into electricity . The growing concern for
environment has asked for rapid developments in wind power generation technology. On the
other hand because of variability and uncertainty of this energy, using it has made some
challenges to power system operators. In order to adjust the unforeseeable nature of the wind
power, planned productions and uses in electricity market must be improved during the real
operation of the power system . Wind energy is a clean renewable resource, its exploitation and
utilization has recently been paid more attention in the world. It has become apparent that wind
energy is a good alternative to thermal energy power generation. Additionally, wind power
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generation would yield profit, as there is essentially no fuel cost involved in the production of
power from wind energy conversion system except specific investment costs. Therefore, it
becomes apparent that there is a need for alternatives to a concern . Since the cost of wind
turbine generators (WTGs) has been reduced rapidly, installation of WTGs as fuel savers is
economically and environmentally attractive in windy regions. It would be beneficial to increase
the power supply capacity by the installation of power plants using wind energy sources.Due to
the uncertain nature of wind power, it is widely believed that large wind penetrations would put
an increased burden on system operations. One of these issues is the provision of emergency
reserve for the system security.
GENETIC ALGORITHM
3.1 INTRODUCTION TO GENETIC ALGORITHM
The genetic algorithm is essentially a search algorithm based on the mechanics of natural
selection and natural genetics. It combines solution evaluation with randomized, structured
exchanges of information between solutions to obtain optimality. Genetic algorithm is a robust
approach because no restrictions on the solution space are made during the search process. The
power of this algorithm comes from its ability to exploit historical information structures from
previous solution guesses in an attempt to increase performance of future solution structures. By
simulating “the survival of the fittest” criterion of Darwinian evaluation among chromosome
structures, the optimal solution is searched by randomized information exchange. The three
prime operators associated with the GA are reproduction, crossover and mutation.
3.1.1 Genetic Algorithm Structure
A global optimization technique known as genetic algorithm has emerged as a candidate due to
its flexibility and efficiency for many optimization applications. It is a stochastic searching
algorithm. The method was developed by John Holland (1975). GA is inspired by the
evolutionary theory explaining the origin of species. In nature, weak and unfit species within
their environment are faced with extinction by natural selection. The strong ones have greater
opportunity to pass their genes to future generations via reproduction. In the long run, species
carrying the correct combination in their genes become dominant in their population. Sometimes,
during the slow process of evolution, random changes may occur in genes. If these changes
provide additional advantages in the challenge for survival, new species evolve from the old
ones. Unsuccessful changes are eliminated by natural selection. The Genetic Algorithm (GA) is a
search heuristic that mimics the process of natural evolution. This heuristic is routinely used to
generate useful solutions to optimization and search problems. Genetic algorithms belong to the
larger class of evolutionary algorithms (EA), which generate solutions to optimization problems
using techniques inspired by natural evolution, such as inheritance, mutation, selection, and
crossover.
3.1.2 Genetic Algorithm Steps and Genetic Algorithm Cycle
The basic genetic algorithm steps are
Step (1): Construct an initial population (P) of chromosomes by random process.
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Step (2): Evaluate fitness of each chromosome.
Step (3): Genetic mating pool based on fitness function values.
Step (4): Select mating pair of chromosomes called parent chromosomes from mating pool.
3.1.4 ADVANTAGES AND DISADVANTAGES OF GENETIC ALGORITHM
The advantages associated with a Genetic Algorithm are :
 Ease of implementation.
 Differentiability of the objective function is not required.
 Can handle complex, multi-nodal optimization problems.
 Computational simplicity.
 Power-full search ability to attain the global optimum.
 Extremely robust with respect to the complexity of the problem.
 Diversity of solutions is maintained with mutation.
 Takes into account the overall effect on the system.
 Simultaneously searches from a wide sampling of the cost surface.
 Deals with a large number of variables.
 Optimizes with continuous or discrete variables.
 Provides a list of optimum variables, not just a single solution.
3.2 ALGORITHM FOR ECONOMIC DISPATCH USING GA
The step-wise procedure is outlined below:
1. Read data, namely cost coefficients,,, , no. of iterations, length of string, population size,
probability of crossover and mutations, power demand and Pmin and Pmax .
2. Create the initial population randomly in the binary form.
3. Decode the string, or obtain the decimal integer from the binary string
4.
Calculate
the
power
generated
from
the
decoded
population
𝑃𝑖𝑗=𝑃𝑖𝑚𝑖𝑛+𝑃𝑖𝑚𝑎𝑥−𝑃𝑖𝑚𝑖𝑛2𝑙−1(i NG; j L)
where
L is the number of strings or population size.
𝑦𝑖𝑗 is the binary coded value of the i th substring
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5. Check 𝑃𝑖𝑗
If 𝑃𝑖𝑗> , then set 𝑃𝑖𝑗= 𝑃𝑖𝑚𝑎𝑥
If 𝑃𝑖𝑗< 𝑃𝑖𝑚𝑎𝑥,then set 𝑃𝑖𝑗= 𝑃𝑖𝑚𝑖𝑛
6. Find the fitness or cost function
7. Find population with maximum fitness and average fitness of the population.
8. Perform the Reproduction Process, which includes the following steps:
8(a). Set selection rate and number of mating in a pool.
8(b). Define total fitness as sum of values obtained by using above step for all
chromosomes which are selected.
8(c) Select percentage of each chromosome which is equal to the ratio of its fitness value to the
total fitness value, i.e. find probability which can be written as:
Probability = fitness / Σ Fitness’s.
8(d) Calculate cumulative sum (CS) to normalize the values between 0.0 and 1.0.
9. Perform Crossover Process:
9(a) Choose a pair of random numbers between 0 and 1 to select one mother and one father
chromosome, so as to produce new offspring.
9(b) Pairing the chromosomes from different location, for different locations,
crossover point has to be selected which can be selected randomly. Generate offspring by
applying crossover.
10. Perform mutation by randomly selecting the mutation points from the total number of bits in
the population matrix.
11. Update the population.
12. If the number of iterations reaches the maximum, then go to step 13. Otherwise, go to step 6.
13. The fitness that generates the minimum total generation cost is the solution of the problem.
GREY WOLF OPTIMIZATION
4.1 INTRODUCTION
The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in
nature proposed by Mirjalili et al. in 2014. Four types of grey wolves such as alpha, beta, delta,
and omega are employed for simulating the leadership hierarchy. In addition, three main steps of
hunting, searching for prey, encircling prey, and attacking prey, are implemented to perform
optimization.Grey wolf belongs to Canidae family. Grey wolves are considered as apex
predators, meaning that they are at the top of the food chain. Grey wolves mostly prefer to live in
a pack. The group size is 5-12 on average. Of particular interest is that they have a very strict
social dominant hierarchy.
The leaders are a male and a female, called alphas. The alpha is mostly responsible for making
decisions about hunting, sleeping place, time to wake, and so on. The alpha’s decisions are
dictated to the pack. However, some kind of democratic behavior has also been observed, in
which an alpha follows the other wolves in the pack. In gatherings, the entire pack acknowledges
the alpha by holding their tails down. The alpha wolf is also called the dominant wolf since
his/her orders should be followed by the pack. The alpha wolves are only allowed to mate in the
pack. Interestingly, the alpha is not necessarily the strongest member of the pack but the best in
terms of managing the pack. This shows that the organization and discipline of a pack is much
more important than its strength. The second level in the hierarchy of grey wolves is beta. The
betas are subordinate wolves that help the alpha in decision-making or other pack activities. The
beta wolf can be either male or female, and he/she is probably the best candidate to be the alpha
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in case one of the alpha wolves passes away or becomes very old. The beta wolf should respect
the alpha, but commands the other lower-level wolves as well. It plays the role of an adviser to
the alpha and discipliner for the pack. The beta reinforces the alpha's commands throughout the
pack and gives feedback to the alpha. The lowest ranking grey wolf is omega. The omega plays
the role of scapegoat. Omega wolves always have to submit to all the other dominant wolves.
They are the last wolves that are allowed to eat. It may seem the omega is not an important
individual in the pack, but it has been observed that the whole pack face internal fighting and
problems in case of losing the omega. This is due to the venting of violence and frustration of all
wolves by the omega(s). This assists satisfying the entire pack and maintaining the dominance
structure. In some cases the omega is also the babysitters in the pack. If a wolf is not an alpha,
beta, or omega, he/she is called subordinate (or delta in some references). Delta wolves have to
submit to alphas and betas, but they dominate the omega. Scouts, sentinels, elders, hunters, and
caretakers belong to this category. Scouts are responsible for watching the boundaries of the
territory and warning the pack in case of any danger. Sentinels protect and guarantee the safety
of the pack. Elders are the experienced wolves who used to be alpha or beta. Hunters help the
alphas and betas when hunting prey and providing food for the pack. Finally, the caretakers are
responsible for caring for the weak, ill, and wounded wolves in the pack. In addition to the social
hierarchy of wolves, group hunting is another interesting social behavior of grey wolves.
According to Muro et al. the main phases of gray wolf hunting are as follows:
 Tracking, chasing, and approaching the prey
 Pursuing, encircling, and harassing the prey until it stops moving
 Attack towards the prey
4.2 MATHEMATICAL MODEL
The hunting technique and the social hierarchy of grey wolves are mathematically modeled in
order to design GWO and perform optimization. The proposed mathematical models of the social
hierarchy, tracking, encircling, and attacking prey are as follows:
4.2.1 Social Hierarchy
Fig:1 Gwo Social Hierarchy Structure
In order to mathematically model the social hierarchy of wolves when designing GWO, we
consider the fittest solution as the alpha (α). Consequently, the second and third best solutions
are named beta (β) and delta (δ) respectively. The rest of the candidate solutions are assumed to
be omega (ω). In the GWO algorithm the hunting (optimization) is guided by α, β, and δ. The ω
wolves follow these three wolves.
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