[IEEE Energy Society General Meeting - Detroit, MI, USA (2011.07.24-2011.07.29)] 2011 IEEE Power and...

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1 Transmission Expansion Planning by Meta- heuristic Techniques: A comparison of Shuffled Frog Leaping Algorithm, PSO and GA Mehdi Eghbal, Member; IEEE, Tapan Kumar Saha, Senior Member, IEEE and Kazi Nazmul Hasan, Student Member, IEEE Abstract- This paper presents the application of a memtic meta-heuristic optimization technique known as Shuffled Frog Leaping Algorithm (SFLA) to the problem of transmission network expansion planning. The main objective of the proposed problem is to minimize total cost by finding the place, number and type of new transmission lines required to ensure that the power system meets the forecasted demand in the most economic and reliable way. The proposed static transmission expansion planning problem is formulated as a mixed integer programming optimization problem to minimize the total cost comprised of investment cost of building new lines, congestion costs and the cost of load curtailment due to contingencies. The proposed algorithm has been successfully applied to IEEE RTS 24-bus test system and the performance of the proposed algorithm has been compared with other heuristic optimization techniques such as particle swarm optimization (PSO) and Genetic Algorithm (GA). The comparison results testify to the feasibility and efficiency of the developed algorithm in solving the transmission expansion planning problem. Index Terms—Transmission expansion planning, Shuffled Frog Leaping Algorithm (SFLA), Particle Swarm Optimization (PSO), Genetic Algorithm (GA). I. NOMENCLATURE F total total cost r interest rate a number of years in the planning horizon ij right-of-way i-j between bus i and j Q set of existing circuits UQ number of new circuits in right-of-way ij c if j cost of adding a circuit in right-of-way ij N D number of load levels t m duration of each load level LMP™ Locational Marginal Price at bus i under load level m 0 set of selected contingencies p m ' k probability of contingency k under load level m d m,k duration of contingency k under load level m This work was supported by the Queensland Geothermal Energy Centre of Excellence (QGECE), in The University of Queensland, Brisbane, Australia. M. Eghbal ([email protected]) is with the Queensland Geothermal Energy Centre of Excellence (QGECE), The University of Queensland, Brisbane, QLD 4072, Australia. T. K. Saha (e-mail: [email protected]) and K. N. Hasan (e-mail: [email protected]) are with the School of Information Technology and Electrical Engineering and the Queensland Geothermal Energy Centre of Excellence (QGECE), The University of Queensland, Brisbane, QLD 4072, Australia. 978-1-4577-1002-5/11/S26.00 ©2011 IEEE m,k Sy m,k Zy r B e G S L fij Vij rtij n% "ij 0t Sy gy Sy ly P m n D Umax X w x b x g amount of load curtailment due to contingency k under load level m cost of load curtailment due to contingency k under load level m set of load buses susceptance matrix vector of voltage angles vector of active power generation vector of load curtailment vector of system loads power flow in right-of-way ij susceptance of the branch in right-of-way ij total number of circuits in right-of-way ij number of existing circuits in right-of-way ij maximum number of circuits in right-of-way ij voltage angle at bus i generation at bus y in MW maximum generation limit at bus y in MW amount of load curtailment at bus y amount of load at bus y population size of SFLA number of memeplexes in SFLA number of frogs in each memeplex step size vector maximum step size vector position of frog with worst fitness value in each memeplex position of frog with best fitness value in each memeplex position of frog with best fitness value in the entire population II. INTRODUCTION L ocation constrained transmission projects are required to facilitate the large scale integration of renewable energy sources into the Australian electricity market. Major renewable energy resources such as wind and geothermal are located in areas with insufficient power transfer capability or even without transmission infrastructure. Major wind sources are located in South Australia where, the load growth rate is minimum in the country. Existing network is not able to deliver the clean energy to major load centers in Victoria and New South Wales as the national grid was build based on a state approach and suffers from weak interconnections

Transcript of [IEEE Energy Society General Meeting - Detroit, MI, USA (2011.07.24-2011.07.29)] 2011 IEEE Power and...

Page 1: [IEEE Energy Society General Meeting - Detroit, MI, USA (2011.07.24-2011.07.29)] 2011 IEEE Power and Energy Society General Meeting - Transmission expansion planning by meta-heuristic

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Transmission Expansion Planning by Meta-heuristic Techniques: A comparison of Shuffled

Frog Leaping Algorithm, PSO and GA Mehdi Eghbal, Member; IEEE, Tapan Kumar Saha, Senior Member, IEEE and Kazi Nazmul Hasan,

Student Member, IEEE

Abstract- This paper presents the application of a memtic meta-heuristic optimization technique known as Shuffled Frog Leaping Algorithm (SFLA) to the problem of transmission network expansion planning. The main objective of the proposed problem is to minimize total cost by finding the place, number and type of new transmission lines required to ensure that the power system meets the forecasted demand in the most economic and reliable way. The proposed static transmission expansion planning problem is formulated as a mixed integer programming optimization problem to minimize the total cost comprised of investment cost of building new lines, congestion costs and the cost of load curtailment due to contingencies. The proposed algorithm has been successfully applied to IEEE RTS 24-bus test system and the performance of the proposed algorithm has been compared with other heuristic optimization techniques such as particle swarm optimization (PSO) and Genetic Algorithm (GA). The comparison results testify to the feasibility and efficiency of the developed algorithm in solving the transmission expansion planning problem.

Index Terms—Transmission expansion planning, Shuffled Frog Leaping Algorithm (SFLA), Particle Swarm Optimization (PSO), Genetic Algorithm (GA).

I. NOMENCLATURE

Ftotal total cost r interest rate a number of years in the planning horizon ij right-of-way i-j between bus i and j Q set of existing circuits UQ number of new circuits in right-of-way ij cifj cost of adding a circuit in right-of-way ij ND number of load levels tm duration of each load level LMP™ Locational Marginal Price at bus i under load level m 0 set of selected contingencies pm'k probability of contingency k under load level m dm,k duration of contingency k under load level m

This work was supported by the Queensland Geothermal Energy Centre of Excellence (QGECE), in The University of Queensland, Brisbane, Australia.

M. Eghbal ([email protected]) is with the Queensland Geothermal Energy Centre of Excellence (QGECE), The University of Queensland, Brisbane, QLD 4072, Australia.

T. K. Saha (e-mail: [email protected]) and K. N. Hasan (e-mail: [email protected]) are with the School of Information Technology and Electrical Engineering and the Queensland Geothermal Energy Centre of Excellence (QGECE), The University of Queensland, Brisbane, QLD 4072, Australia.

978-1-4577-1002-5/11/S26.00 ©2011 IEEE

m,k Sy

m,k Zy

r B

e G S L fij Vij rtij

n% "ij

0t Sy

gy

Sy

ly P m n D Umax Xw

xb

xg

amount of load curtailment due to contingency k under load level m cost of load curtailment due to contingency k under load level m set of load buses susceptance matrix vector of voltage angles vector of active power generation vector of load curtailment vector of system loads power flow in right-of-way ij susceptance of the branch in right-of-way ij total number of circuits in right-of-way ij number of existing circuits in right-of-way ij maximum number of circuits in right-of-way ij

voltage angle at bus i generation at bus y in MW maximum generation limit at bus y in MW

amount of load curtailment at bus y amount of load at bus y population size of SFLA number of memeplexes in SFLA number of frogs in each memeplex step size vector maximum step size vector position of frog with worst fitness value in each memeplex position of frog with best fitness value in each memeplex position of frog with best fitness value in the entire population

II. INTRODUCTION

Location constrained transmission projects are required to facilitate the large scale integration of renewable energy

sources into the Australian electricity market. Major renewable energy resources such as wind and geothermal are located in areas with insufficient power transfer capability or even without transmission infrastructure. Major wind sources are located in South Australia where, the load growth rate is minimum in the country. Existing network is not able to deliver the clean energy to major load centers in Victoria and New South Wales as the national grid was build based on a state approach and suffers from weak interconnections

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between states. The tentative aim of the Australian geothermal industry is 4000MW base-load capacity by 2030 of which, major parts are located in areas at least 500 km far from the nearest existing transmission network infrastructure. To deliver such clean base-load power to the major load centers, two types of transmission projects are required. One is building new transmission lines to connect the new generation zone to the existing network and the other is enhancing the power transfer capability of the existing network. Due to huge investment cost and restricted environmental constraints, determining the most economic and efficient transmission expansion scenario is very important to both the Australian Energy market Operator (AEMO) and transmission service providers.

The problem of transmission expansion planning (TEP) involves determining the optimal location, size and time for building new transmission lines in order to meet the forecasted demand in the most reliable and economic way. Mathematically, it is formulated as a mixed integer nonlinear programming (MINLP) problem, where optimal solution cannot be obtained easily for large-scale power systems with many constraints.

The literature on TEP includes a large number of publications. Latorre et al. [1] have classified publications and models on TEP during the last few decades. Most of the proposed methods for solving the TEP problem are based on DC power flow model. However, in [2, 3] AC model is used to solve the problem.

Static transmission network expansion planning determines only the place and size of the new lines that should be added to each right-of-way (ROW) where the total expansion investment is carried out at the beginning of the planning horizon [2-11]. On the other hand, in dynamic approach, the planning horizon is divided into several stages, and then new circuits to be added during each stage are determined in a way that total investment cost is minimized [12-19].

Traditionally, the main objective function of the TEP problem is to minimize the investment and operation costs. New electricity market environment has introduced new objectives and requirements for the TEP problem. California ISO has developed a comprehensive methodology, called Transmission Economic Assessment Methodology (TEAM), to evaluate the economic benefits of transmission expansion in competitive electricity markets [20]. Hyung et al [9] have developed a market-based model to simulate the interaction between market participants and ISO in order to help investors and system planners on deciding locations and amounts of new generation and transmission facilities. In [17], the Bender decomposition approach has been used to solve a multi-year TEP problem considering the transmission congestion and the impact of generation investment cost in the planning horizon. In [8], a multi-objective optimization framework has been used to solve a static TEP problem in deregulated environments.

Recently used models to solve the TEP problem are mixed integer linear programming [6], branch and bound [7, 21], bender decomposition [9, 10, 17], simulated annealing (SA)

[12], differential evolution algorithm [16], particle swarm optimization [22], and genetic algorithm (GA) [4, 5, 8, 13].

In this paper, a DC based power flow model is used to find the best location, number and type of new lines to be added to the existing and new right-of-ways in order to minimize the total cost. The total cost represents the present value of investment cost, congestion cost and the cost of load curtailment under N-l contingency states. In practice, to transfer bulk amount of power, it is common to build new right-of-ways with higher voltages than existing voltage levels. Increasing the voltage level increases the power transfer capability of the line at the price of higher investment cost. Therefore, it is important to consider the type of the new lines in the process of transmission expansion planning. In the proposed algorithm in order to keep a practical approach, the possibility of installing new circuits at different standard voltage levels is considered.

The uncertainties associated with generation expansion and load forecast are not considered in this paper, however, for a given scenario a stepwise load duration curve is considered for loads in each area of the system.

The proposed problem is formulated as a mixed integer optimization problem and solved by a new meta-heuristic optimization method known as shuffled frog leaping algorithm (SFLA). SFLA is a mimetic meta-heuristic algorithm developed by Eusuff and Lansey [23] and has been applied successfully to several engineering optimization problems such as bridge deck repairs [24], water resource distribution [25], job-shop scheduling arrangement [26] as well as power system problems such as unit commitment problem [27] and optimal reactive power flow [28]. Comparison of the performance of SFLA with other recent evolutionary based algorithms such as GA, mimetic algorithm, PSO and ant-colony systems proves the fast convergence speed of SFLA [27, 29]. To evaluate the feasibility of the proposed algorithm in solving the transmission expansion planning problem, PSO and GA have been also applied to the problem and performances have been compared.

The paper is organized as follows. Section III is devoted to the problem formulation. Section IV explains the overview of shuffled frog leaping algorithm (SFLA) and illustrates the proposed structure of the random generated population. Then, section V illustrates simulation results and compares the performance of the developed algorithm with PSO and GA. Finally, section VI concludes the paper.

III. PROBLEM FORMULATION

This section outlines the mathematical model of the proposed TEP problem. The objective functions of the TEP problem are to minimize: 1) the investment cost of the new circuits to be installed at the existing and new right-of-ways, 2) total congestion cost and 3) the amount of load shedding due to N-l contingencies. The problem is formulated as a single objective optimization problem. The objective function and constraints can be expressed as in (l)-(3):

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r(l + r)a _ Minimize FTntnl = , , / 2^ ui,j£t,j

(l + r f - L J ^ ND( \

+ZkZ ^ " ' I c ^ r

(1)

Subject to

B0+G+S =L

K\*nvfv 0 < » , <^7 n.. = u .. + n ?. , u .. > 0

0 , ( i j e a )

(2)

0 < g y < g y , ( y e T )

, ( y e n OZSyZly

Bk0k +Gk +Sk =L fij -y>l{ek -ok) = o

0<nk<^

n\ =u.. + n~ , k * ij

1 , k = ij

• ( y e n ( y ^ n

(i,je ft)

^ = w ( / + ^ ( / 0 < S * < g 3

o < / ; < j

(3)

The above sets of equality and inequality constraints are DC optimal power flow constraints during base case and contingencies. Outage of line k is referred as contingency k. Line k can be any of the existing or new circuits. To reduce the calculation time, O can be limited to only a set of the most severe contingencies. In the proposed formulation, the amount of load curtailment at each load bus due to a contingency must be less or equal to the load at that bus. In practice, residential load buses are often the first to be curtailed. In the proposed formulation, priority of load curtailment at load buses can be easily modeled by assigning different load shedding cost to each load bus. However, without loss of generality and for the sake of simplicity, priority of load curtailment is considered the same for all load buses.

The first term in (1) represents the annualized present value of the investment cost for adding new circuits. It is assumed that the total expansion investment is carried out at the beginning of the planning horizon, which is a common assumption in static planning approach. c^ represents the cost of adding a line between buses / andj and includes the cost of the transmission line, which is directly proportional to the length of the line, and additional cost of transformers if voltage level of the line ij is different than voltage levels of

buses / and j \ Moreover, the cost of overhead line was considered as a function of the voltage level of the line.

The second term is the congestion cost under different load levels and defined as the opportunity cost of transmitting power through each line. One of the objectives of the proposed TEP problem is to enhance the competitiveness of the electricity market by reducing the differences among LMPs. For each load level, LMPs are obtained by calculating the Lagrangian multipliers of the power flow constraints.

The third component of the objective function minimizes total cost of the expected energy not supplied due to contingencies (single line outage events). The amount of energy not supplied is calculated by summation of load curtailments in all load buses as below:

EENS=Z\PkdkZ{sky) (5)

Currently, under the Reliability Standard defined by the Australian Energy Market Commission, the level of expected unserved energy should not exceed 0.002% of the annual energy consumption per region [30]. To ensure that the solution of the proposed TEP problem meets the reliability standards, the following constraint is added to the set of constraints:

lKZk*'^2>; (6)

I k l c L< 0.002%

IV. SOLUTION ALGORITHMS

A. Overview of Shuffled Frog Leaping Algorithm SFLA is a population based cooperative search approach

that starts with a virtual population of frogs, leaping in a swamp, searching for a place with maximum amount of available food [23]. Nonlinear, non-differentiable and multi-modal complex optimization problems can be solved by SFLA. It has been reported that SFLA converges faster than other meta-heuristic algorithms [29].

Fig.l illustrates the flowchart of SFLA. Same as other population based algorithms, SFLA starts with initializing the population that is generated randomly within the feasible search space. In this paper, each frog represents the location, type and number of new branches. The performance value of each frog is calculated using (1). Then, the population is sorted in the order of increasing performance value and divided into m memeplexes each including n frogs such that:

Yk = [X(j)k\ X(j)k = X(k + m(j - l)),j = 1, ...,n\k = 1,...,m (6)

Where Y represents the kth memeplex. After / number of mimetic evolutionary steps for each memeplex k, as illustrated in Fig.2, the memeplexes are merged into the population and

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sorted in the order of increasing performance value. The position of the best frog in the entire population is updated and the loop continues until the convergence criteria are satisfied.

Start

Generate random population of frogs (P=m*n), Calculate fitness of each

individual frog J

Sort the population in descending order of fitness values

Divide the population into m memeplexes, each includes n frogs

Local search (Details in Fig.2)

Shuffle evolved memplexes

Yes

Determine the best solution

End

Figure 1. Flowchart of Shuffled Frog Leaping Algorithm (SFLA)

Local search tries to improve only the position of the worst frogs in each memeplex and not all frogs. To do so, a process similar to the PSO algorithm [31] is applied to each memeplex in order to move the position of the worst frog toward the position of the best frog.

f min{int[rand X (Xb — Xw)],Dmax], for positive step | \max{int[rand X (Xb — Xw)], —Dmax], for negative step]

ynew _ v- current , n

(7)

(8)

Where rand is a random number in the range of [0,1], D is the step size vector and has dimensions equal to the number of decision variables. Dmax is the maximum step size that is allowed to be adopted by a frog after being moved and acts as a constraint to control the global exploration ability of the SFLA. If the new frog position does not improve or is not feasible, it is updated using the step size vector based on the best frog position in the entire population as in (9) otherwise, the old frog position is replaced with the new one.

- i min{int[rand X (Xg

max[int[rand X [Xg --Xw)]fDmi

Xw)l~Dm

.}, for positive step |

x), for negative stepj (9)

If the new frog position updated by (9) and (8) is either infeasible or not better than the old position, a random frog is generated within the feasible range to replace the old frog position. This step is known as censorship in SFLA.

(

r^ { k=i

I ( i = 1

i

S ta r t

J ^ f

IK t

{

j

k=k+l

i=i+l

r*

~^ J^

Determine Xw and Xb for kth memeplex and X„

Improve the worst frog position using (7) and (8)

S^ Yes^^-^^ls new frog position better\^^

^ ^ \ 4 h a n the worst posit ion^^^^

i Improve the worst frog position using (9) and (8)

"X" ^r^^^^ ^""^\^^ Yes

^^^vs, new frog position bet te i^^ ^ ^ \ ^ h a n the worst position^--^^^

J N O

Creat a new frog randomly

W Replace the worst frog with the new frog ~*

^^^ l f i=number o f " \ - N o ^ \ ^ iterations ^

jjYes

^^lfk=number-"of--^ No ^ ^ - ^ m e m p l e x e s ^

j Yes

( End )

Figure 2. Flowchart of the local search

B. Structure of the initial population of SFLA In the developed SFLA, each frog position (Xa) is a

sequence of integer numbers representing the number and voltage level of new branches to be installed in each right-of-way as shown in Fig.3. The length of Xa is equal to the number of candidate right-of-ways for constructing new lines including existing and new right-of-ways. Theoretically, new branches can be added to all existing right-of-ways considering the maximum allowed number of parallel circuits per right-of-way. However, to reduce the size of the search space and calculation time, it is recommended to limit the set of candidate right-of-ways.

Right-of-way

xa

ii-ji u i l j l > v i l j l

l2"J2 U i2j2 > Vi2j2

in-jn Uinjn •> Vinjn

Figure 3. Structure of the initial population of SFLA (frog positions)

unji and vuji are the number and the voltage level of the circuits to be added in the right-of-way i rji, respectively, UUJI is an integer value between zero and maximum number of branches allowed to be installed in the right-of-way ij. VUJI is a discrete integer value generated randomly from the set of [138, 230, 345, 500, 765] which, represents the standard voltage levels considered in this paper.

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The same structure is used for particles in PSO algorithm and chromosomes in GA.

V. SIMULATION RESULTS

Simulation results were conducted in MATLAB 7.10.0 [32] environment and MATPOWER [33] functions were used to solve the power flow equations. The developed program was carried out on a personal computer with Intel Core 2 Duo CPU at 3GHz, 2.99GHz and 3GB of RAM. IEEE RTS 24-bus test system was used to validate the proposed TEP algorithm and network data for this system was taken from [34]. In the test system, it was assumed that new lines could be constructed in any existing right-of-way as well as a set of new right-of-ways up to a total number of four. The cost data for construction of new lines were taken from [35]. The Value of Customer Reliability (VCR), equal to $13,250 per MWh for the residential sector, defined by the Australian Energy Market Commission [30] was used as the load curtailment cost in the simulations. For the sake of simplicity, load curtailment priority for all load buses was assumed to be the same. To reduce the calculation time, only a set of severe contingencies including line outages in right-of-ways 14-16, 20-23, 15-21, 3-24 and 15-24 were considered.

Fig.4 illustrates the diagram of the test system. In this diagram, dotted lines show the candidate new right-of-ways.

Table I shows the typical voltage levels and line parameters for the overhead transmission lines [36] considered for new circuits in this paper.

TABLE I. TYPICAL VALUES FOR OVERHEAD TRANSMISSION LINES[36]

Nominal voltage R(Q/km) XL=lo) (O/km) Bc=a)C (mS/km)

230kV

0.05 0.488

3.371

345 kV

0.037 0.367

4.518

500 kV

0.028 0.325

5.2

765 kV

0.012 0.329

4.978

To evaluate the performance of the developed SFLA, the proposed TEP problem were solved using PSO and GA and the results were compared. Table II lists the optimization parameters of the proposed SFLA, PSO and GA algorithms. For the sake of comparison, maximum number of iterations was considered 100 for all the optimization methods.

TABLE n. OPTIMIZATION PARAMETERS OF SFLA, PSO AND GA

SFLA

PSO

GA

Number of memeplexes=10 Number of frogs in each memeplex=30 Max. number of evolutionary iterations in each memeplex=5 Number of populations=40 wmax=0.9; wmin=0.4;Vmax=10; ct=2; c2=2 Number of populations=40 Mutation probability=0.1 Cross over probability^ 0.9

Figure 4. Diagram of IEEE RTS 24 bus test system

In real power systems, annual generation and load growth of all areas are not uniform during the long-term planning horizon. Furthermore, generation and load zones are not evenly distributed. Therefore, in this paper, TEP problem were solved for two scenarios of generation and demand growth as follows:

Scenario 1) Original values of demand and installed generation capacity at every bus were increased by 2.2 times. Fig.5 depicts the stepwise load duration curve during the planning year.

Percentage of peak

load i

100%

90%

75%

-'Percentage of year

Figure 5. Load duration curve

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Table III compares the solutions obtained by SFLA, PSO and GA methods. Total cost of the expansion plans obtained by SFLA, PSO and GA are 10L18M$, 108M$ and 134M$, respectively.

TABLE EL OPTIMAL SOLUTIONS TO THE TRANSMISSION EXPANSION PLANNING PROBLEM OBTAINED BY SFLA, PSO AND GA METHODS FOR

UNIFORM LOAD AND GENERATION GROWTH SCENARIO

SFLA

t 2 3-15 3-11 1-2

9-12 14-16 16-17

«4-H

o ft rt u i i i 2 1 1

| B > 230 345 138 230 230 230

PSO

t 2 3-15 3-24 5-10 9-12 14-16 16-17

«4-H

o ft ^

11 1 2 2 1 1 1

| B > 345 230 138 230 230 230

GA

2 9-15 1-2

3-24 4-9 5-10 9-12 14-16 16-17

«4-H

o ft ^

11 1 B > 230 138 138 138 138 138 230 230

Scenario 2) To simulate the situation of unevenly distributed generation and load centers, generation capacity and loads at different areas of the test system were increased by different growth rates as listed in Table IV. Areas 1 and 2 were considered as load centers where loads and generation were increased by 2.4 and 1.4 times, respectively. Areas 3 and 4 were considered as generation dominant areas where loads and generation were increased by 1.4 and 2.4 times, respectively.

TABLE IV. BASECASE AND FUTURE GENERATION AND DEMAND DATA

Area

Area 1 Area 2 Area 3

Area 4

Bus Numbers

1,2,3,4,5,9 6,7,8,10

11,12,13,14,19,2 0,23

15,16,17,18,21,2 2,24

Base case Generation

capacity (MW) 384 300

1251

1470

Demand (MW)

705 627

768

750

Future condition Generation

capacity (MW) 691 510

2877

3234

Demand (MW)

1551 1442

1382

1275

Load duration curve for this scenario is assumed to be the same as in Fig.5. Table V lists the optimal solutions of the proposed TEP problem obtained by SFLA, PSO and GA methods after 100 iterations. Total cost of the expansion plans obtained by SFLA, PSO and GA are 139M$, 142M$ and 162M$, respectively.

In this scenario, because of the uneven distribution of generation and demand in the system, new line between buses 17 and 11 was suggested to deliver the power directly from the generation zone to the lower area where is a load dominant area. Detailed analysis of the results obtained by the SFLA showed that building the right-of-way 11-17 with higher voltage level (345 kV) is more economic compared to using the existing voltage level, which was 230kV. It was observed that when the possibility of building new lines with higher voltage levels was disabled, the program suggested adding

three 230kV lines in the 17-16, 16-14 and 14-11 right-of-ways. Total cost in this case, was higher compared to building one right-of-way with higher voltage level.

TABLE V. OPTIMAL SOLUTION TO THE TRANSMISSION EXPANSION PLANNING PROBLEM OBTAINED BY SFLA, PSO AND GA METHODS FOR

NONUNIFORM LOAD AND GENERATION GROWTH SCENARIO

SFLA

o

s 11-17 3-24 6-10 9-12 10-11

o ft & 1 3

1 2 1 2 2

| B > 345 230 138 230 230

PSO

a 6-10 9-12 10-11 14-16 16-17

o

1 2 2 1 1

B 'o > 138 230 230 230 230

GA

2 2-6 3-24 9-11 10-11 14-16 16-17

o ft ^

1 s

1 1 2 1 1 1

B 'o > 138 138 138 230 230 230

Fig. 6 and Fig. 7 illustrate the convergence characteristic of the SFLA, PSO and GA methods for scenarios 1 and 2, respectively. It can be seen that the performances of SFLA and PSO are better than GA. To verify the robustness of the proposed methods, the problem was solved by each method for 100 times with same initial conditions. It was observed that the results of SFLA and PSO were very similar in most of the cases however, the SFLA had faster convergence speed.

Figure 6. Convegence characteristics of SFLA, PSO and GA methods for solving the TEP problem under scenario 1

Figure 7. Convegence characteristics of SFLA, PSO and GA methods for solving the TEP problem under scenario 2

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Simulation results confirm the effectiveness of SFLA in solving the proposed problem and comply with those reported in [27, 29]. It has to be mentioned that SFLA had slightly faster convergence speed than PSO, but the convergence was more sensitive to the value of initial parameters; the number of frogs and memeplexes. It was observed that total number of frogs (population size) was the most important parameter and increasing the number of frogs and memeplexes improved the performance in the price of more calculation time.

VI. CONCLUSIONS

In this paper, a new meta-heuristic optimization technique, known as shuffled frog leaping algorithm, is applied to the problem of transmission expansion planning. The focus of the proposed problem is to obtain location, type and number of the new lines, which should be added to the network to meet the forecasted demand. Results show that installing new lines at higher voltage levels than the existing network can reduce the total cost. In systems with an uneven distribution of generation and load centers, the impact will be more significant.

Comparison of the meta-heuristic optimization algorithms in solving the proposed problem shows that SFLA and PSO prove to be more suitable for solving the problem than GA. However, in applying the SFLA to the problem, care must be taken in selecting the optimization parameters, especially the number of memeplexes and number of frogs in each memeplex.

To improve the proposed algorithm further, it is suggested to consider the uncertainties associated with demand and generation forecasting scenarios into the problem formulation. Introducing some heuristic techniques to choose the candidate right-of-ways could reduce the calculation time for applying the proposed algorithm to large power systems. Currently, these issues are being investigated and the feasibility of the proposed algorithm will be tested by applying to the large-scale Queensland transmission network.

vn. REFERENCES [1] Latorre, G., et al., Classification of publications and models on

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VIII. BIOGRAPHIES

Mehdi Eghbal (S'05, M' 10) was born in Iran in 1976. He received B.S. in electrical engineering from Ferdowsi University of Mashad, Iran in 1998, M.S. degree in power system engineering in 2001 from Tarbiat Modares University, Tehran, Iran and PhD degree in 2009 from Hiroshima University in the field of Artificial Complex System Engineering. Currently he is with the Queensland Geothermal Energy Centre of Excellence (QGECE), the University of Queensland, Australia. His research interest

lies in application of heuristic techniques in power system planning and operation and renewable energies.

Tapan Kumar Saha (M'93, SM'97) was born in Bangladesh in 1959 and immigrated to Australia in 1989. He received his B. Sc Engineering (electrical and electronic) in 1982 from the Bangladesh University of Engineering & Technology, Dhaka, Bangladesh, M.Tech (electrical engineering) in 19 85 from the Indian Institute of Technology, New Delhi, India and PhD in 1994 from the University of Queensland, Brisbane, Australia. Tapan is currently Professor of Electrical Engineering in the School

of Information Technology and Electrical Engineering, University of Queensland, Australia. Previously he has had visiting appointments for a semester at both the Royal Institute of Technology (KTH), Sweden and at the University of Newcastle (Australia). He is a Fellow of the Institution of Engineers, Australia. His research interests include condition monitoring of electrical plants, power systems and power quality.

Kazi Nazmul Hasan (GS'08) was born in Gazipur, Bangladesh in 1984. He graduated in Electrical and Electronic Engineering from the Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh in 2006. He worked for Huawei Technologies (Bangladesh) Ltd. as trainee engineer of telecommunication network. Then he obtained MEngSc (Power Electronics) from the University of Tasmania,

Hobart, Australia in 2009. He is currently pursuing PhD in the University of Queensland, Brisbane Australia. His research interests include renewable energy applications, power system reliability, and electricity-market operation and planning.