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\author[1,\Letter]{Mehrdad Ahmadi Kamarposhti}
\author[2]{Ersan Kabalci}
\affil[1]{\small{Department of Electrical Engineering,Jouybar Branch, Islamic Azad University, Jouybar, Iran}}
\affil[2]{\small{Department of Electrical and Electronics Engineering, Nevsehir Haci Bektas Veli University,Nevsehir, Turkey}}
\affil[\Letter]{\footnotesize{\href{mailto:mehrdad.ahmadi.k@gmail.com}{mehrdad.ahmadi.k@gmail.com}}}
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\begin{document}
\title{Optimal Transmission Expansion Planning considering Distributed
Generations by using Non-dominated sorting genetic algorithm-II (NSGAII)}
\vspace{-1em}
\date{}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
Reconstructing power systems has changed the traditional planning of
power systems and has raised new challenges in transmission expansion
planning (TEP). In this paper, investment cost, cost of density and
dependability have been considered three objectives of optimization.
Also, multi-objective genetic algorithm NSGAII was used to solve this
non-convex and mixed integer problem. A fuzzy decision method has been
used to choose the final optimal answer from the Pareto solutions
obtained from NSGAII. Moreover, to confirm the efficiency of NSGAII
multi-objective genetic algorithm in solving TEP problem, the algorithm
was implemented in an IEEE 24 bus system and the gained results were
compared with previous works in this field. ~
\par\null%
\end{abstract}%
\sloppy
\textbf{Keywords}: dynamic programming, TEP, NSGAII, fuzzy decision.
\section{Introduction}
{\label{481040}}
Transmission Expansion Planning (TEP) is one of the main parts of
planning development power systems aiming at identifying time, place and
number of new transmission lines to optimize construction cost and
efficiency of these lines In order to achieve the adequacy of the power
to the centers of load. TEP is usually classified into dynamic and
static. In static planning the number and spots of needed power lines
are determined for one year, while in dynamic planning, the needed
construction time is also considered ~\hyperref[csl:1]{[1]}. TEP is a
nonlinear and complex problem one which is getting more complicated by
increasing of the studied network scale. It was started by L. L. Grinver
in 1970 to minimize efficiency cost and taking account generation
constraints of power plants and power lines capacity using linear
planning ~\hyperref[csl:2]{[2]} . But in the recent year, most studies have
been done on reconstructed power systems. The major difference between
the TEPs in exclusive and competitive environments is that the main
problem in exclusive environments include generation, transmission, and
distribution all together while in competitive environments these
sections are considered separately~\hyperref[csl:3]{[3]}; \hyperref[csl:4]{[4]}. Another important
difference is that unlike exclusive environments which mostly include
definite data, competitive environments include uncertainty data as a
main parameter~\hyperref[csl:5]{[5]}; \hyperref[csl:6]{[6]}. Objective function of exclusive
environment is based on minimal cost while in competitive environment
the objective function is maximum profit. Also, TEP solutions in
competitive and traditional environments are classified into innovative
optimization such as l{inear programming \hyperref[csl:6]{[6]},} dynamic
programming~\hyperref[csl:7]{[7]}, nonlinear programming~\hyperref[csl:8]{[8]}
in mathematical optimization and mathematical methods such as genetic
algorithm~\hyperref[csl:9]{[9]}, objective-oriented models
\hyperref[csl:10]{[10]}, metal plating \hyperref[csl:11]{[11]}, expert systems
\hyperref[csl:12]{[12]} and fuzzy theory \hyperref[csl:13]{[13]}.
The purpose of this paper is to study the effects of distributed
generation on TEP in reconstructed environments. Since there is no
contribution between generation companies and transmission companies in
reconstructed environments, TEP needs to predict producers' behaviors.
In this study, generation valuing method was used to predict producers'
behaviors and planning was researched using dynamic approach in a
five-year period. Moreover, the effects of distributed generation of
windy and solar powers on TEP in reconstructed environments are
considered. The rest of the paper is organized as follows: market
exploitation model is introduced in section 2. Problem formulation and
planning indexes is discussed in section 3. Simulation results and
conclusion have been presented in section 4 and section 5.
\section{Market exploitation model}
{\label{279514}}
In reconstructed power systems, independent system operator (ISO)
manages generator productions to provide load with minimum cost while
keeping dependability and quality of the power system. It is assumed
that in a specified interval, all power producers inform to ISO their
suggested price for one electric power and their minimum and maximum
generation. Consumers send their minimum and maximum load demand and
their suggestion of cutting off the load as well. Then, ISO executes
optimum load distribution and determines quantity of Locational Marginal
Price (LMP) and generations and loads. Market exploitation models have
been modeled by applying the following equations~\hyperref[csl:14]{[14]}:~
\(Min:\ \ J(P_G,P_D)=P_{Base}[P_G\cdot(a^T\cdot P_G+b) \ \ \ \\ \ \ +C_T^D\cdot(P_D^{\max}-P_D)]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)\)~
~ ~ ~ ~ ~ ~ ~ ~~\[s.t.:\ B\delta=P_G-P_D-P_{tie}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)\]
\[-P_i^{\max}\le H\delta\le P_i^{\max}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3)\]~~~~ \[P_G^{\min}\le P_G^{ }\le P_G^{\max}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(4\right)\]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\[P_D^{\min}\le P_D^{ }\le P_D^{\max}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(5\right)\]
In which~\(J(P_G,P_D)\)~ represents total exploitation cost (\$/h) ,
~\(P_{Base}\) is base active power (MW),~\(C_D^T\) ~is
the transposed of suggested vector of cost load (\$/MWh) ,~\emph{a}
and~\emph{b} are constant coefficients vector in the generator price
suggestion function, ~\(P_G\) and~\(P_D\)~ are
vectors of generators output~ active power and active loads in perunit~
(P.U.) (these vectors are the output of Optimal Power Flow),
~\(P_{tie}\) is the output power vector from the studied area to
other areas in P.U. , and~\(B\)~ is the linearized
Jacobian matrix to P.U.. The term H is the linear matrix of the passing
flow from lines to P.U. and~\(\delta\) ~is the buses' voltage
angle vector in radian. Objective function of Eq. (1) shows the total
exploitation cost. The first part of this equation shows the
exploitation cost of generators and the second part shows the deficiency
cost of load. Equation (2) is for DC load distribution. The passing
power limitation from lines is shown in equation (3). Equations (4) and
(5) show generation limits and load limits, respectively. Losses are
deleted in this model. Second-order optimization programing method can
be used to solve this problem. ~
\section{Formulation of problem}
{\label{780124}}
The main purpose of TEP in competitive environment is to provide a
competitive, unprejudiced and sure environment for all the market actors
and in minimum cost. The prerequisite for providing such an environment
is to consider some indices in designing and development of transmission
network. Considered indexes in the paper are the level of competition,
dependability, and investment cost which are presented in the following.
\subsection{Investment cost index}
{\label{715983}}
Economic justifying is important in competitive environment. Thus,
development costs have to be considered in TEP to minimize investment
budgets and transmission tariffs. Thus, the present value of total
investment cost is formulated during the planning {{period as follows:
}}\[ic^k=\sum_{p-1}^{np}\frac{IC^P}{(1+r)^{p-1}}\ \ \ p=1,2,\dots,np\ \ \ \ \ \ \ \ \ \ \ \ \left(6\right)\]
{While~}\(IC^P\){ ~is the investment cost for the new lines
installed in year~}\emph{{p}}{ (\$) and~}\(ic^k\){~ is the}
present pure value of investment cost during programming horizon. Also,
k is programming horizon.
\par\null
\subsection{Lines density cost index ~}
{\label{206878}}
Density cost is a function of density level and its duration in a
network. Here, density cost is calculated according to load peak over
time and it is going to be minimized as a goal of TEP. Line density cost
(as shown in Figure 1 ) is formulated as follows:
\par\null
\[CC_i=(lmp_{i1}-lmp_{i2})P_{li1,i2}\ \ \ \ \ \ \ \ \ \ i=1,2,\dots,N_i\ \ \left(7\right)\]
\par\null
In which ~\(CC_i\)~is density cost in line in (\$/h) ,
~\(lmp_i\) is LMP in ~\(i_2\) base in (\$/MWh) ,
~\(P_{lti}\)is the sent power from ~\(i_1\) base
to~\(i_2\)~ through line \(i\) and
\(N_i\) ~is the number of lines of transmission network~
\hyperref[csl:14]{[14]}.
\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/fig1/fig1}
\caption{{\(i^{th}\) ~line in sample power network \protect\hyperref[csl:14]{[14]}
{\label{181409}}%
}}
\end{center}
\end{figure}
\texttt{}\[TCC^P=\sum_{i=1}^{N_I^P}cc_I=\sum_{i=1}^{N_I^P}\left(lmp_{i1}-lmp_{i2}\right)P_{LI1,I2}\ (8)\]
In which is network total density cost in \(P^{th}\) ~year from
programming horizon and \(N_I^P\) ~is the number of installed
lines until~\(P^{th}\)~ year. In order to considering density
cost in programming horizon, the present value of density cost should be
calculated as follows:
\[CC^k=\sum_{p-1}^{np}\frac{TCC^P}{\left(1+r\right)^{p-1}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(9\right)\]
While ~\(CC^k\)~is the present value of pure density cost
after adding planning~~\(k\) during programming period,
~\(np\) is the number of~ years of programming's horizon and
~\(r\) is the decline rate \hyperref[csl:14]{[14]}.
\subsection{Load deficiency cost}
{\label{711478}}
Load deficiency cost due to line failure in ~year is calculated as
follows ~\hyperref[csl:14]{[14]}.
\[LC_i^P=(P_d^{p\max}-P_d^{i,p})C_d\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(10\right)\]
While~\(P\) is maximum vector of demand in
~\(Pth\) year in (MW),~\(P_d^{i,p}\)~ is provided load
vector after failure of line~\(i\) in ~\(Pth\)
year of planning in (MW) , ~\(C_d\)~is the load deficiency
vector due to failure of line~\(i\)~ in \(Pth\)
year in (MW) , ~\(LC_i^p\)is load deficiency cost due to failure
of line~\(i\) in \(Pth\)~year in (\$/h) . Load
deficiency cost due to failure of all lines in \(Pth\)~year
has been calculated as follows:
\[TLC^P=\sum_{i=1}^{N_i^P}LC_i^P=\sum_{i=1}^{N_i^P}\left(P_d^{p\max}-P_d^{i,p}\right)C_d\ \ \ \left(11\right)\]
Whereas, the number of suggested lines is different in various answers,
average of equation (11) has to calculate. Thus, average of load
deficiency cost due to failure of all lines in ~\(Pth\) year
is computed as below:
\[ALC^P=\frac{(TLC^P)}{N_i^P}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(12\right)\]
Average present value of load deficiency cost during the planning
horizon can be calculated as follows:
\[ALC^k=\sum_{p-1}^{np}\frac{ALC^p}{\left(1+r\right)^{p-1}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(13\right)\]
\section{Modeling of distributed generation in
TEP}
{\label{433419}}
In reconstructed environments, generation planning and transmission
planning are separated and problem is faced a lot of uncertainty in
generation and load. Type, capacity, and location of power plants may
change during the operational phase which indeed may increase the
uncertainty of input data~\hyperref[csl:15]{[15]}. DG units can be valued in
two ways:~
~
1-~~~~ When the share and contribution of DG units be low in market, a
unit of DG is usually modeled in the model of distribution network as a
negative load and the distribution company constructs it when its cost
is lower than buying electricity from market.
2-~~~~ When DG influence level reaches to specific level, each DG can be
considered as a standard power plant generation with technology
\(j\) ~in bus~\(i\)~ and its value is
determined by Net Present Value (NPV) criterion which has been discussed
in below section:
After calculating the knot price during the period of the lifetime of
the power plant, financial circulation of the power plant
\(j\) ~in year ~\(t\) is calculated as
follows:
\par\null
\(CF_i=(Z_i(t)-C_{VO\&M}-C_{fuel})\times f_c_a_p\times8760-C_(_F_O_\&_M_)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(14\right)\)
\par\null
In which~\(C_{VO\&M}\) , ~\(C_{FO\&M}\)~and
~\(C_{fuel}\) are variable cost of repairs and maintenance,
constant cost of repairs and maintenance and the fuel cost of
technology~\(j\) . The term~\(f_{cap}\)~ shows the
capacity coefficient of the power plant. Then, NPV~ is calculated
thorough the below equation:
\[NPV_{i,j}=C_{Cap}+\sum_{i=1}^T(CF_t\times e^{-rt})\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(15\right)\]
While ~is the interest rate without risk and ~is the cost of
constructing the power plant . However, it is possible to consider the
government encouraging schemes in promoting of renewable resource in
investments. Thus, according to equation (15), the current pure value of
each technology in each base can be calculated. Then, candidate cases
for generation are cases with higher NPV in electricity market.
\section{Simulation Results}
{\label{200155}}
In the paper, multi-objective genetic algorithm was used to solve TEP
problem in an IEEE standard 24-bus experimental system
Fig.~{\ref{879677}}. The basis data of the network were
provided from reference~\hyperref[csl:16]{[16]} and the data related to
initial investment cost were taken from reference \hyperref[csl:15]{[15]}. It
is assumed that the system has to be developed for future condition in
which load and generation demand is 2.2 times higher than the initial
level (initial load was 3054, initial generation was 3404 MW, so 2.2
times higher equals a load of 6720 MW and generation level of 7490 MW.
This is equal to increase rate of 8\% per year in a five-year planning's
horizon.~
In addition, it is assumed that the candidate branches of network
development can be done simultaneously in all current 34 lines, and 7
new lines to be added in future, the their data of which are presented
in Table ~{\ref{tab:1}}. It is noteworthy that the
information of candidate lines which are in parallel with previous
lines, be like them exactly. Due to environmental limitations, 3 lines
can be installed in each route. It is also assumed that all generators
can be upgraded to 1.3 times higher than their current capacity and if
more capacity is needed, new plants have to be constructed.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/fig2/fig2}
\caption{{IEEE 24-bus system
{\label{879677}}%
}}
\end{center}
\end{figure}
% Please add the following required packages to your document preamble:
% \usepackage[normalem]{ulem}
% \useunder{\uline}{\ul}{}\selectlanguage{english}
\begin{table}\center
\caption {{ Configurations and investment costs of new lines}} \label{tab:1}
\begin{tabular}{|c|c|c|}
\toprule
from & To & Construction cost (\$10000) \\
\toprule
1 & 8 & 35 \\
2 & 8 & 33 \\
6 & 7 & 50 \\
19 & 23 & 84 \\
13 & 14 & 62 \\
14 & 23 & 86 \\
16 & 23 & 114 \\
\hline
\end{tabular}
\end{table}
\subsection{The first scenario: two-objective
optimizations}
{\label{201053}}
In the first scenario, two generators are installed in 11 and 24 buses
from the second year onwards and each of them can produce electricity
until maximum 1500 MW. Also, all generators can have produce 1.3 higher
than their initial capacity. The increasing of generation can answer
load growth until five next year, because we have to increase the
generation as much as 4000 MW until end of the fifth year of development
of transmission network with 3000 MW of which will be provided by two
new installed power plants 1500 MW in the second year and 1000 MW will
be supplied by increasing the generation level of existing power plants.
Moreover, only two objective such as investment cost and distributed
cost of lines have been considered and problem is solved as
two-objective as seen in Table ~{\ref{tab:2}}.~ Gained
Pareto's diagram from simulation is shown in
Fig.~{\ref{253454}}.
\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/fig3/fig3}
\caption{{Pareto's diagram for solving considered problem with two objective
functions, reducing the cost of construction and congestion of lines
{\label{253454}}%
}}
\end{center}
\end{figure}
% Please add the following required packages to your document preamble:
% \usepackage[normalem]{ulem}
% \useunder{\uline}{\ul}{}\selectlanguage{english}
\begin{table}\centering
\caption{{Maximum and minimum of gained quantity for objective function in Pareto's diagram for objective functions, reducing the cost of construction and congestion of lines}}\label{tab:2}
\begin{tabular}{|c|c|c|}
\hline
& Min amount & Max. amount \\ \hline
Congestion cost & 49404 & 54251 \\
Construction cost & 1.2396609 & 1.4473605 \\
\hline
\end{tabular}
\end{table}
\par\null
Also, weighted values of 0.5 have been assigned to both objective
functions. In Table~{\ref{tab:3}}, values of objective
function of Pareto's spots and corresponding membership function are
displayed. From comparing the membership function of Pareto's answers
with Fig.~{\ref{253454}} can be said that spot 7 is the
best of problem's answer. Corresponding planning with this answer has
been brought in Table~{\ref{tab:4}}. In Table
~{\ref{tab:5}}, the obtained results for this scenario
have been compared with reference~\hyperref[csl:14]{[14]}. The results states
that however investment cost in the planning period in
reference~\hyperref[csl:14]{[14]}~ is almost half of the gained investment
cost in this paper, but the cost of congestion lines is very high in
this reference.
% Please add the following required packages to your document preamble:
% \usepackage[normalem]{ulem}
% \useunder{\uline}{\ul}{}\selectlanguage{english}
\begin{table}\center
\caption{{Pareto's spots and calculating their membership function and detecting the best spot for objective functions, reducing the cost of construction and congestion of lines}}
\label{tab:3}
\begin{tabular}{|lcc|}
\toprule
& Value of membership & Congestion cost \\ \toprule
1 & 0.0513 & 54251 \\
2 & 0.0513 & 49404 \\
3 & 0.0731 & 51354 \\
4 & 0.0472 & 54106 \\
5 & 0.0509 & 50181 \\
6 & 0.0512 & 50423 \\
7 & 0.075 & 50818 \\
8 & 0.0613 & 50568 \\
9 & 0.0644 & 50797 \\
10 & 0.065 & 50723 \\
11 & 0.0613 & 50568 \\\toprule
& Construction cost & \\ \toprule
1 & 1.2396609 & \\
2 & 1.4473605 & \\
3 & 1.2755295 & \\
4 & 1.2625938 & \\
5 & 1.4155655 & \\
6 & 1.4036662 & \\
7 & 1.2910195 & \\
8 & 1.3570774 & \\
9 & 1.334906 & \\
10 & 1.3352972 & \\
11 & 1.3570774 & \\ \hline
\end{tabular}
\end{table}\selectlanguage{english}
\begin{table}
\caption{{Final planning for construction of added lines in the network during 5 year}}\label{tab:4}
\begin{tabular}{|c|c|c|c|} \hline
& first year & second year & third year \\ \hline
Line 1 & 24-3 & 24-3 & 4-1 \\
Line 2 & 10-6 & 8-2 & 9-4 \\
Line 3 & 10-5 & 8-7 & 6-2 \\
Line 4 & 11-9 & 8-9 & 12-10 \\
Line 5 & 18-15 & 13-12 & 23-16 \\
Line 6 & 23-20 & 7-1 & 20-13 \\
Line 7 & 14-13 & 4-8 & 2-16 \\
Line 8 & 21-18 & - & 21-15 \\
Line 9 & - & - & 2-1 \\ \hline
& & forth year & Fifth year \\ \hline
Line 1 & & 8-23 & 24-3 \\
Line 2 & & 23-14 & 23-16 \\
Line 3 & & - & 21-15 \\
Line 4 & & - & 9-8 \\
Line 5 & & - & 2-1 \\
Line 6 & & - & 23-19 \\
Line 7 & & - & 23-14 \\
Line 8 & & - & - \\
Line 9 & & - & - \\ \hline
\end{tabular}
\end{table}\selectlanguage{english}
\begin{table}
\caption{{Comparing the gained results in the paper with reference [14]}}\label{tab:5}
\begin{tabular}{|c|c|c|}
\hline
& Proposed Method & Ref. {[}14{]} \\ \hline
Congestion Cost & 50818 & 68916 \\ \hline
Investment Cost & 14.03 & 7.91 \\ \hline
\end{tabular}
\end{table}
\subsection{The second scenario: three-objective optimization with
regard to distributed
generation}
{\label{535524}}
In this scenario, in addition two objective, initial investment cost and
congestion cost of transmission lines, average cost of cutting the load
has been considered as the third objective of the optimization.
Moreover, the effects of windy and solar distributed generations in TEP
has been taken attention. In the scenario 1 and 2, it is assumed that
generators increase the power output as much as 1.3 higher than their
initial value and new generators in 11 and 24 buses with capacity 1500
MW have been installed during the planning period in the second year.
But, in this scenario for construction of the new generators, we will
use generation valuation method and the generators with the highest
value in market are the better options for the investors in generation
section. Also, it's assumed that solar and windy power plant are only
constructed in load buses. In order to considering the government's
politics for encouraging applying of the renewable resource, a tariff
coefficient is considered for solar and windy powers plants. The value
of the electricity from wind and solar power plants is equal to the
price of the spot market in its tariff. Requirements parameters for
calculating of generation value have been stated in Table
~{\ref{tab:6}} .
% Please add the following required packages to your document preamble:
% \usepackage[normalem]{ulem}
% \useunder{\uline}{\ul}{}\selectlanguage{english}
\begin{table}
\caption{{Specifications of new generators}}\label{tab:6}
\begin{tabular}{lcc} \\ \hline
Technology & Solar \\ \hline
Initial Investment (M\$/MW) & 4.9 \\
Fixed production cost (\$/MW/Year) & - \\
Fixed production cost (\$/MWh) & 45.5 \\
life span (Year) & 25 \\
capacity (MW) & 200*5 \\
Capacity coefficient (\%) & 56 \\ \hline
Technology & combined \\ \hline
Initial Investment (M\$/MW) & 1.314 \\
Fixed production cost (\$/MW/Year) & 1550000 \\
Fixed production cost (\$/MWh) & 38.21 \\
life span (Year) & 30 \\
capacity (MW) & 1200 \\
Capacity coefficient (\%) & 60 \\ \hline
Technology & Coal \\ \hline
Initial Investment (M\$/MW) & 2.239 \\
Fixed production cost (\$/MW/Year) & 7200000 \\
Fixed production cost (\$/MWh) & 17.02 \\
life span (Year) & 40 \\
capacity (MW) & 1500 \\
Capacity coefficient (\%) & 85 \\ \hline
Technology & Wind \\ \hline
Initial Investment (M\$/MW) & 2.8 \\
Fixed production cost (\$/MW/Year) & 600000 \\
Fixed production cost (\$/MWh) & - \\
life span (Year) & 25 \\
capacity (MW) & 200*5 \\
Capacity coefficient (\%) & 40 \\ \hline
\end{tabular}
\end{table}\selectlanguage{english}
\begin{table}
\caption{{Generation Valuation Results (solar FIT=2, Wind FIT=2)}}\label{tab:7}
\begin{tabular}{|l|c|c|c|c|} \hline
Technology & Cap. (MW)& Bus No. & NPV(M\$) \\ \hline
Coal & 1500 & 11 & 14570 \\
Coal & 1500 & 20 & 13255.46 \\
Combined & 1500 & 11 & 11522.45 \\
Wind & 1000 & 17 & 8232.05 \\
Wind & 1000 & 11 & 6307.15 \\ \hline
\end{tabular}
\end{table}
\par\null
Also, candidate generation options assuming different tariff have been
shown in Table ~{\ref{tab:7}} and Table
~{\ref{tab:8}} . In calculation of
Table~{\ref{tab:7}} , the values of tariff for windy
and solar power plants have been considered 2. Then, it can be observed
that with this tariff, solar power plants are not competitive case in
electricity market and they have not any place among candidate options,
but windy power plant are more competitive.~
As observed in Table ~{\ref{tab:8}} , with increasing
the tariff coefficient of solar power plant to 3, this power plant
converts to one of the options with higher generation value which can be
replaced instead of hybrid power plant among the selective options. The
achieved results show that these two renewable technology are not
competitive with fossil power plant technology and they need government
support in order to development of their market.\selectlanguage{english}
\begin{table}
\caption{{Generation Valuation Results (solar FIT=3, Wind FIT=2)}}\label{tab:8}
\begin{tabular}{|l|c|c|c|}
\hline
Technology & Bus No. & Capacity (MW) & NPV(M\$) \\ \hline
Coal & 17 & 1000 & 12850.32 \\
Coal & 11 & 1000 & 9650.31 \\ \
Solar & 9 & 5*200 & 7450.42 \\
Solar & 11 & 5*200 & 3740.11 \\
Wind & 1000 & 11 & 6307.15 \\ \hline
\end{tabular}
\end{table}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/fig4/fig4}
\caption{{Pareto's diagram of three-objective algorithm NSGAII
{\label{999307}}%
}}
\end{center}
\end{figure}
Now with considering two coal power plants 1000 MW in buses 11, 17 and
also, five power plants 200 MW in bus 9, TEP has been done. Pareto's
diagrams of three-objective problem with the generation structure of the
above mentioned has been displayed in
Fig.~{\ref{999307}}. As seen in F
ig.~{\ref{999307}} , the eight spot of Pareto have been
recommended as final answer by Non dominated sorting genetic algorithm
(NSGA-II) algorithm for TEP. Maximum and minimum value of each objective
function based on Figure ~is according to the Table
~{\ref{tab:9}}.~In order to determining the membership
function for each answers, equal weighting coefficients have been
considered for three objective function. The obtained final answer (the
biggest membership function) is according to Table
~{\ref{tab:10}}. The gained optimization values of
objective functions according to planning of
Table~~{\ref{tab:10}} in comparison with results of
reference~\hyperref[csl:14]{[14]} have been presented in Table
~{\ref{tab:11}}.~
As observed from results, the proposed method in the paper, with
increasing of the investment cost as much as 44 percent, the cost of
congestion lines as much as 32 percent and average cost of cutting off
the load as much as 89 percent are decreased. Only problem of the
optimization method is high calculating time, because of this reason for
solving above problem in personal computer need one day. In order to
decreasing calculating time can choose{} outlet of a number selected
lines instead of outlet of every single line. As observed from results,
the proposed method in the paper, with increasing of the investment cost
as much as 44 percent, the cost of congestion lines as much as 32
percent and average cost of cutting off the load as much as 89 percent
are decreased.~Only problem of the optimization method is high
calculating time, because of this reason for solving above problem in
personal computer need one day. In order to decreasing calculating time
can choose outlet of a number selected lines instead of outlet of every
single line.
~\selectlanguage{english}
\begin{table}
\caption{{Minimum and maximum of gained quantity for objective function in three-objective Pareto's diagram}}\label{tab:9}
\begin{tabular}{|l|c|c|}
\hline
& Min amount & Max amount \\ \hline
Congestion cost & 49041 & 52061 \\ \hline
Construction cost & 11.452 & 14.815 \\ \hline
Av. Interr. Cost & 2793.56 & 4983.06 \\ \hline
\end{tabular}
\end{table}\selectlanguage{english}
\begin{table}
\caption {{final planning for construction of added lines in network during 5 year for three-objective problem}} \label{tab:10}
\begin{tabular}{|l|c|c|c|} \hline
& first year & second year & third year \\ \hline
Line 1 & 4-3 & 4-3 & 3-1 \\
Line 2 & 10-6 & 8-10 & 9-4 \\
Line 3 & 10-12 & 8-7 & 6-2 \\
Line 4 & 16-7 & 8-9 & 12-10 \\
Line 5 & 14-13 & 13-12 & 23-16 \\
Line 6 & 23-20 & 9-10 & 20-13 \\
Line 7 & - & 13-14 & 2-16 \\
Line 8 & - & - & 21-15 \\
Line 9 & - & - & 2-1 \\ \hline
& & forth year & fifth year \\ \hline
Line 1 & & 8-2 & 24-3 \\
Line 2 & & 17-16 & 23-16 \\
Line 3 & & - & 21-15 \\
Line 4 & & - & 9-8 \\
Line 5 & & - & 2-1 \\
Line 6 & & - & - \\
Line 7 & & - & - \\
Line 8 & & - & - \\
Line 9 & & - & - \\
- & & & \\
- & & & \\
- & & & \\
- & & & \\ \hline
\end{tabular}
\end{table}\selectlanguage{english}
\begin{table}
\caption{{Comparing the gained results in the paper with reference [14] }} \label{tab:11}
\begin{tabular}{|l|c|c|}
\hline
& Proposed Method & Ref. {[}14{]} \\ \hline
Congestion cost & 47061 & 68916 \\ \hline
Construction cost & 14.21 & 7.91 \\ \hline
Av. Interr. Cost & 2938.52 & 2683.257 \\ \hline
\end{tabular}
\end{table}
\section{Conclusion}\label{conclusion}
Condition and requirements of new reconstructed environment necessitates
reviewing available classic methods in TEP problem. In the paper, a
multi-objective model for TEP has been recommended for overcoming on
challenges which are created in effect of reconstruction of electricity
network. In this model, TEP is as a multi-objective nonlinear
optimization with the minimizing of investment cost during planning
period, distributed cost of transmission lines and average cost of load
deficiency (dependability objective). Multi-objective genetic algorithm
has been used for solving this problem. This method unlike the
one-objective methods necessitates set of optimization answers which are
lead to more flexibility in planning process. In order to obtaining a
final optimization answer, Fuzzy membership function method has been
applied for planning of network development from Pareto's answers. The
gained results from this technique have been compared with other works
in this field which is shown that distributed cost of line as much as 32
percent and average cost of cutting off the load as much as 89 percent
can be decrease with more investing in planning period which are lead to
better competitive and more dependability of system. ~
\selectlanguage{english}
\FloatBarrier
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\phantomsection
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\end{document}