Static security enhancement using fuzzy particle

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COMPEL 35,1

Static security enhancement using fuzzy particle swarm optimization

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Received 5 December 2014 Revised 8 May 2015 23 July 2015 Accepted 26 July 2015

K. Pandiarajan Department of Electrical and Electronics Engineering, Pandian Saraswathi Yadav Engineering College, Arasanoor, India, and

C.K. Babulal Department of Electrical and Electronics Engineering, Thiagarajar College of Engineering, Madurai, India Abstract Purpose – The electric power system is a complex system, whose operating condition may not remain at a constant value. The various contingencies like outage of lines, transformers, generators and sudden increase of load demand or failure of equipments are more common. This causes overloads and system parameters to exceed the limits thus resulting in an insecure system. The purpose of this paper is to enhance the power system security by alleviating overloads on the transmission lines. Design/methodology/approach – Fuzzy logic system (FLS) with particle swarm optimization based optimal power flow approach is used for overload alleviation on the transmission lines. FLS is modeled to find the changes in inertia weight by which new weights are determined and their values are applied to particle swarm optimization (PSO) algorithm for velocity and position updation. Findings – The proposed method is tested and examined on the standard IEEE-30 bus system under base case and increased load conditions at different contingency. This method gives better results in terms of optimum fuel cost and fast convergence under base case and could alleviate the line overloads at different contingency with optimum generation cost, when compared to adaptive particle swarm optimization (APSO) and PSO. Originality/value – FLS is modeled in MATLAB environment. The effectiveness of the proposed method is tested and examined on the standard IEEE-30 bus system and their results are compared with APSO and PSO under MATPOWER environment. The results show that the proposed algorithm is capable of improving the transmission security with optimum generation cost. Keywords Power systems, Fuzzy logic, Particle swarm optimization, Security enhancement, Generator rescheduling, TCSC, Severity index, Overload alleviation Paper type Research paper

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Vol. 35 No. 1, 2016 pp. 172-186 © Emerald Group Publishing Limited 0332-1649 DOI 10.1108/COMPEL-12-2014-0334

1. Introduction Congestion in the transmission network in a power system may occur due to lack of coordination between generation and transmission utilities or as a result of unexpected contingencies such as line outages, sudden increase of load demand or failure of equipments. The power dispatch is a nonlinear programming problem. It is classified into two parts, namely, real and reactive power dispatch problems. The reactive power dispatch helps to minimize the real power loss in a transmission network. The real power dispatch is the most widely used control for network overload alleviation because of ease of control and require no additional reserves. Optimal power flow (OPF) is an important tool for power system management. The aim of OPF problem is to optimize one or more objectives by adjusting the power system control variables while satisfying a set of physical and operating constraints such as generation and load balance, bus voltage limits, power flow equations, and

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active and reactive power limits. A variety of optimization techniques had been applied to solve the OPF problem such as gradient method (Alsac and Scott, 1974), linear programming method (Stott and Hobson, 1978) and interior point method Capitanescu et al. (2007). In conventional optimization methods, identification of global minimum is not possible. To overcome the difficulty, evolutionary algorithms like genetic Algorithm (Deb, 2009), enhanced genetic algorithm (Anastasios et al., 2002), particle swarm optimization (PSO) (Abido, 2002a) differential evolution (Varadarajan and Swarup, 2008), modified differential evolution algorithm (Sayah and Zehar, 2008), gravitational search algorithm (Duman et al., 2012), Tabu search algorithm (Abido, 2002b) and artificial bee colony algorithm (Sumpavakup and Chusanapiputt, 2010) had been proposed. In Yu et al. (2011), a self-adaptive learning based PSO algorithm has been proposed to get good performance on a variety of different fitness landscapes. A probability model was used to describe the probability of a strategy being used to update a particle. In Wang et al. (2013), self-adaptive particle swarm optimization (APSO) algorithm has been used to adjust the inertia weight (IW) according to fitness variance of population. Mutation operation was processed for the poor performative particle in population based on K-means. Minimization line overloads and unwanted loop flows under single contingencies through optimal utilization of TCSC have been depicted in Lu and Abur (2002). In Ghahremani and Kamwa (2013), a graphical user interface based genetic algorithm has been used to determine the optimal location and sizing of multi type FACTS devices for power flow reduction on overloaded lines. In Anandakumar and Rambabu (2013), PSO algorithm has been used to solve multi-objective problems such as economical operating condition of the system and system security margin. Security enhancement was made by using TCSC. In Gnanambal and Babulal (2012), hybrid differential evolution with PSO has been used to solve the maximum loadability problem. Alleviation of network overloads using fuzzy logic composite criteria and PSO algorithm has been presented in Vaisakh et al. (2010). Line overloads were removed by using re-dispatching of generation and adjustment of reactive power control variables. A network overload alleviation using improved PSO has been proposed in Baskar and Mohan (2009). The line overloads were relieved through rescheduling of generators with minimum severity index. In Dutta and Singh (2008), PSO based corrective strategy to alleviate the line overloads has been discussed. In Venkaiah and Vinod Kumar (2011b), Fuzzy logic system with particle swarm optimization (FPSO) based congestion management by optimal rescheduling of active powers of generators has been depicted. The generators have been chosen based on the generator sensitivity to the congested line. The fitness of the current location and the current IW were used as inputs of fuzzy inference system (FIS) and correction of IW was considered as output from FIS. An optimal sizing and placement of TCSC for congestion management in an electric power system has been focussed in Abouzar and Peyman (2012). The optimal location of TCSC was done by sensitivity analysis and sizing of TCSC by using genetic algorithm. In Venkaiah and Vinod Kumar (2011a), overload alleviation through redispatch of generators has been experimented. Fuzzy adaptive bacterial foraging algorithm was used for generation redispatch. In this paper, fuzzy PSO based transmission line overload management in power system network is presented with an illustrated example. The organization of the paper is as follows: Section 2 presents overview of optimal location of TCSC. Section 3 presents the optimization problem formulation for transmission line overload management. Section 4 presents overview of PSO. Section 5 presents

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modeling of fuzzy logic system (FLS). Section 6 presents the algorithm of proposed FPSO for transmission line overload management. The simulation results for base case and 30 percent increased load case at different contingency in IEEE-30 bus system is presented in Section 7. Finally, conclusion is given in Section 8.

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2. Optimal location of TCSC To enhance the security of the system, the TCSC is to be placed at the suitable locations. To determine the best location of TCSC, an index called line overload sensitivity index (LOSI) is calculated for the selected contingency cases (Narmatha Banu and Devaraj, 2012). These factors have been obtained as: ! NC X Sl C (1) LOSI l ¼ S l max C¼1 where S l C is the flow in transmission line l in MVA during contingency C, S l max the rating of the transmission line l in MVA and NC the number of considered contingencies. The branches are ranked on their corresponding LOSI values. TCSCs are placed on the branches starting from the top ranking list. 3. Problem formulation 3.1 Objective function 3.1.1 Objective function 1: minimization of total fuel cost FT ¼

NG   X ai P gi 2 ; 1emþ bi P gi þ ci

(2)

i¼1

where FT is the total fuel cost, NG the number of generators, Pgi the active power output of ith generator and ai, bi, ci the cost coefficients of generator i. 3.1.2 Objective function 2: minimization of severity index  n  X S l 2m SI l ¼ (3) S l max l AL o

where Sl is the flow in line l (MVA), S l max the rating of the line l (MVA), Lo the set of overloaded lines and m the integer exponent ¼ 1(assumed) (Devaraj and Yegnanarayana, 2005). 3.2 Problem constraints The constraints (Acharya and Mithulananthan, 2007) are: Generation/load balance equation: NG X i¼1

P gi 

ND X

P Di P L ¼ 0

(4)

i1

where NG is the number of generators, ND the number of loads, Pgi the generation of generator i, PDi the active power demand at bus i, g the generator, D the demand and PL the system active power loss.

Generator constraints: P gi;min p P gi p P gi;max

Fuzzy particle swarm (5) optimization

where Pgi,max is the upper limit of active power generation at generator bus i and Pgi, min the lower limit of active power generation at generator bus i: V gi;min p V gi p V gi;max

(6)

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where Vgi is the voltage magnitude at generator bus i, Vgi,max the upper limit of voltage magnitude at generator bus i and Vgi,min the lower limit of voltage magnitude at generator bus i. Voltage constraints: V i;min p V i p V i;max

(7)

where Vi is the voltage magnitude at bus i, Vi,max the upper limit of voltage magnitude at bus i and Vi,min the lower limit of voltage magnitude at bus i: Transmission line flow limits: S l p S l max

(8)

X TCSCi;min p X TCSCi p X TCSCi;max

(9)

TCSC reactance limit:

The working range of TCSC is considered as follows: 0:8X l p X TCSC p 0:2X l

(10)

where XTCSC is the TCSC reactance and Xl the reactance of the line where TCSC is located. 4. Overview of PSO PSO is a simple and efficient population-based optimization method (Kennedy and Eberhart, 1995). PSO simulates the behaviors of bird flocking. It uses a number of agents (particles) that constitute a swarm moving around in the search space looking for the best solution. PSO is initialized with a group of random particles (solutions) and then searches for optima by updating generations (iterations). Each particle is updated by two “best” values such as particle best ( pbest) and global best ( gbest) in every iteration. After finding the two best values, the particle updates its velocity and positions using the following equations:    V i ðu þ 1Þ ¼ w w  V i ðuÞ þ C 1  randðÞ  pbest i P i ðuÞ   þ C 2  randðÞ  gbest i P i ðuÞ (11) P i ðu þ 1 Þ ¼ P i ðu Þ þ V i ðu þ 1 Þ where χ is the constriction  factor, whose  value is set to 1.

The term randðÞ  pbest i P i ðuÞ is called particle memory influence.   The term randðÞ  gbest i P i ðuÞ is called swarm influence. V i ðuÞ is the velocity of ith particle at iteration u.

(12)

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The velocity of ith particle at iteration u must lie in the range as below: V min p V i ðuÞ p V max

(13)

where Vmin is the minimum velocity and Vmax the maximum velocity. The parameter Vmax determines the resolution, or fitness, with which regions are to be searched between the present position and the target position. 5. Modeling of FLS The IW is considered as an important parameter for the convergence of the algorithm. A large IW facilitates exploration, i.e., searching newer areas, while a small value tends to facilitate exploitation, i.e., a finer searching of current search area. The balance between global and local search throughout the course of run is critical to the success of an evolutionary algorithm. Suitable selection of IW provides a balance between global and local search abilities. By changing the IW, the search ability can be dynamically adjusted. The uncertainty in choosing the IW is carried out by fuzzy logic. The fuzzy logic based IW determination is presented in this section. The proposed FLS is developed in MATLAB environment. The system parameter such as IW, iteration (ITER) and normalized fitness value (NFV) are given to FIS as inputs and changes in inertia weight (CIW) [−0.1 0.1] as output. The CIW are represented as zero (Z), positive (P) and negative (N). Triangular membership functions are used in both inputs and output. Three linguistic values, namely, low (L), medium (M) and high (H) are considered. The IW is set according to the following equation (Hazra and Sinha, 2007):   wmax wmin  I TER (14) I W ¼ wmax  I TERmax where IW is the inertia weighting factor, wmax the maximum value of weighting factor, wmin the minimum value of weighting factor, ITERmax the maximum number of iterations and ITER the current number of iteration. The NFV is set according to the following equation (Venkaiah and Vinod Kumar, 2011b):   BFV FV min (15) N FV ¼ FV max FV min where NFV is the normalized fitness value, BFV the best fitness value, FVmin the minimum fitness value, FVmax the maximum fitness value. The fuzzy rules for changing inertial weight are constructed and tabulated in Table I. FIS editor window of FLS is shown in Figure 1. The input membership functions are shown in Figures 2-4, respectively. The output membership function is shown in Figure 5. The FIS sample output for 100th iteration is shown in Figure 6. From Figure 6, it is observed that IW is M (0.7), ITER is M (100), NFV is M (0.5) then CIW is N (  0.074). The IW is reduced from original value. 6. Proposed FPSO algorithm In proposed FPSO, FLS is combined with PSO. The different combinations of IW are applied to PSO and their best fuel cost is observed using Equation (2). The suitable IW

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Rule No.

IW

ITER

NFV

CIW

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

L L L L L L M M M M M M M M M H H H H H H H H H

M M M H H H L L L M M M H H H L L L M M M H H H

L M H L M H L M H L M H L M H L M H L M H L M H

Z P P Z P P Z N N N N N N N N N N N N N N N N N

Fuzzy particle swarm optimization 177

Table I. FIS rules

Figure 1. FIS editor window of FLS

is selected based on minimum fuel cost among the possibilities. The selected IW is between 0.9 and 0.4. The suitable value of IW between the selected ranges is decided by the FLS. The suitable weight is given to PSO for velocity and position updation. FPSO algorithm codings are carried out in MATLAB environment.

COMPEL 35,1 Degree of membership

L

M

H

0.8 0.6 0.4 0.2 0

Figure 2. Membership function of input variable IW

0.4

0.5

0.6

0.7 IW

L

0.8

0.9

M

1

H

1

Degree of membership

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178

1

0.8

0.6

0.4

0.2

Figure 3. Membership function of input variable ITER

0 0

20

40

60

80

100

120

140

160

180

200

ITER

The step by step procedure of FPSO algorithm is given below: Step 1: initialize the PSO parameters such as the particle size (Np), number of generations or iterations (G), number of variables to be optimized, limits of each variable in the particle, acceleration constants and IW. PSO parameter values are: Particle size: 20, No. of generation: 100, cognitive constant, C1 ¼ 2, social constant, C2 ¼ 2 and IW: 0.9-0.4. Step 2: an initial population is randomly generated considering the variables to be optimized. Step 3: for each particle in the population, run Newton Raphson power flow under base case/30 percent increased load case at different contingency and evaluate the objective function.

L

M

H

1

Fuzzy particle swarm optimization

Degree of membership

179

0.6

0.4

0.2

0 0

1

Degree of membership

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0.8

0.1

0.2

0.3

0.4

N

0.5 NFV

0.6

0.7

0.8

0.9

Z

1

Figure 4. Membership function of input variable NFV

P

0.8

0.6

0.4

0.2

0 –0.1 –0.08 –0.06 –0.04 –0.02

0

0.02 0.04 0.06 0.08

0.1

CIW

Step 4: find particle best ( pbest) and global best ( gbest). Step 5: increase the iteration count. Step 6: a new population is created by changing the velocity and position of the particle. Step 7: evaluate the objective function values for each new individual. Step 8: update pbest and gbest values by comparing current fitness values with local best and global best values. Step 9: find the new IW using FLS and update the velocity and position of the particles using Equations (11) and (12). Step 10: if stopping criteria is satisfied, then the best individual is obtained, otherwise repeat the procedure from step 5.

Figure 5. Membership function of output variable CIW

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Figure 6. FIS sample output of 100th iteration

7. Simulation results The simulation studies are performed on system having 2.27 GHz Intel 5 processor with 2 GB of RAM in MATLAB environment. The power flow is obtained using MATPOWER (Zimmerman et al., 2011). Two cases are considered for the study. In order to verify the robustness of the proposed FPSO method, simulation is carried out for 100 independent runs with different initial population. The final parameters are selected based on minimum objective value. 7.1 IEEE-30 bus system 7.1.1 Case 1: optimal scheduling for the base case. The objective function in this case is minimization of total fuel cost. Generator active power outputs and the generator bus voltages are taken as optimization variables. The proposed FPSO method is applied to IEEE-30 bus system; the obtained results of control variables along with statistical analysis of fuel cost are compared with APSO (Kaushik et al., 2008) and conventional PSO and tabulated in Table II. The minimum generation cost (best value) obtained by various methods are shown in Table III. The fuel cost convergence characteristics of the proposed FPSO method are compared with APSO and simple PSO and shown in Figure 7. In the simple PSO method, convergence is reached at 98th iteration and the best cost is equal to 800.816 $/h. In APSO method, convergence is reached at 91th iteration and the best cost is equal to 800.477 $/h. In proposed FPSO method, convergence is reached at 85th iteration and the best cost is equal to 800.103 $/h. It is clear that, the proposed FPSO method gives less fuel cost and fast convergence when compared to other methods. From Table III, it is also clear that the proposed FPSO method gives less fuel cost of 800.103 $/h, when compared to FPSO, (Kumar and Chaturvedi, 2013) which has the cost of 800.72 $/h. This highlights originality of the proposed FPSO. 7.1.2 Case 2: overload alleviation under 30 percent increased load conditions. 7.1.2.1 Generation rescheduling without TCSC. To test the ability of the proposed algorithm, the active and reactive loads at all load buses except bus no. 5 are increased

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Control variables (p.u.) P1 P2 P5 P8 P11 P13 V1 V2 V5 V8 V11 V13 Best cost ($/h) Average cost ($/h) Worst cost ($/h) SD No. of iteration

PSO

APSO

FPSO

1.7800 0.4913 0.2149 0.2194 0.1000 0.1200 1.100 1.100 1.100 1.087 1.100 1.100 800.816 800.883 800.895 0.0221 98

1.7567 0.4939 0.1934 0.1952 0.1437 0.1394 1.100 1.084 1.055 1.079 1.100 1.100 800.447 800.468 800.494 0.0217 91

1.7669 0.4846 0.2120 0.2069 0.1217 0.1306 1.100 1.100 1.075 1.083 1.100 1.100 800.103 800.132 800.145 0.0214 85

Methods MATPOWER (Zimmerman et al., 2011) GA (Devaraj and Yegnanarayana, 2005) EP (Somasundaram et al., 2004) GA (Narmatha Banu and Devaraj, 2009) DE (Sen et al., 2011) PSO (Sen et al., 2011) PSO (Ahmed et al., 2014) GA (Kumar and Chaturvedi, 2013) GA fuzzy (Kumar and Chaturvedi, 2013) PSO (Kumar and Chaturvedi, 2013) FPSO (Kumar and Chaturvedi, 2013) ABC (Rezaei Adaryani and Karmi, 2013) PSO APSO FPSO

Fuzzy particle swarm optimization 181

Table II. Control variables and statistical analysis of fuel cost

Fuel cost ($/h) 802.20 803.05 802.4 801.7165 801.8436 801.8441 801.6954 801.96 801.21 800.96 800.72 800.6600 800.816 800.477 800.103

to 30 percent from its base case value (only 10 percent is increased at bus no. 5). Contingency analysis is carried out on the system under the load of 349.58 MW. Outage is created for the most critical lines such as line 1-2 and 2-5. The overloads due to above said outages can be alleviated by changing the active power generations and their values along with the final value of severity index and generation cost is shown in Table IV. The overloaded line details before and after rescheduling are shown in Tables V and VI, respectively. From Tables IV and VI, it is clear that the proposed FPSO method could alleviate the overloads under line 1-2 outage with a minimum generation cost of 1,169.59 $/h and minimum average CPU time of 15.82 seconds when compared to APSO and PSO

Table III. Comparison of fuel cost of different methods

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835 PSO

Fuel Cost ($/h)

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APSO FPSO

830

Figure 7. Fuel cost convergence characteristics of PSO, APSO and FPSO methods

825 820 815 810 805 800

0

20

40

60

80

100

120

140

160

180

200

Iteration Number

Outage line PSO

1-2 APSO

FPSO

PSO

2-5 APSO

FPSO

129.80 79.45 49.68 34.77 29.82 39.74 0 1,169.74 16.63

129.86 79.43 49.67 34.76 29.81 39.74 0 1,169.65 15.94

129.91 79.42 49.66 34.76 29.81 39.73 0 1,169.59 15.82

127.74 80.00 50.00 35.00 30.00 40.00 1.0361 1,171.39 16.52

127.74 80.00 50.00 35.00 30.00 40.00 1.0361 1,171.39 15.98

127.74 80.00 50.00 35.00 30.00 40.00 1.0361 1,171.39 15.85

Control variables P1 P2 P5 P8 P11 P13 Table IV. SI Control variable setting for corrective Generation cost ($/h) action without TCSC Average CPU time (s)

Outage line 1-2

2-5

Table V. Overloaded line details before rescheduling

Overloaded lines

Line flow (MVA)

Line flow limit (MVA)

OF

SI

1-3 2-4 3-4 4-6 6-8 4-12 1-2 1-3 2-4 3-4 2-6 4-6 5-7 6-7 6-8

501.8866 114.3787 406.3835 267.5090 118.8391 67.6588 220.1530 143.2545 93.0656 132.5710 128.0934 152.3131 126.2165 148.5759 58.5808

130 65 130 90 32 65 130 130 65 130 65 90 70 130 32

3.8607 1.7597 3.1260 2.9723 3.7137 1.0409 1.6935 1.1020 1.4318 1.0198 1.9707 1.6924 1.8031 1.1429 1.8306

50.8503

21.7216

Outage line 1-2

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2-5

PSO Line flow (MVA) 129.8217 20.2676 121.5842 79.3186 8.1506 30.3844 65.1979 63.1129 50.0450 58.0980 66.1626 71.2196 62.9885 87.9033 8.2506

APSO Line flow (MVA)

OF 0.9986 0.3118 0.9353 0.8813 0.2547 0.4675 0.5015 0.4855 0.7699 0.4469 1.0179 0.7913 0.8998 0.6762 0.2578

129.8729 20.2777 121.6324 79.3472 8.1578 30.3888 65.1979 63.1129 50.0450 58.0980 66.1626 71.2196 62.9885 87.9033 8.2506

OF 0.9990 0.3119 0.9356 0.8816 0.2549 0.4675 0.5015 0.4855 0.7699 0.4469 1.0179 0.7913 0.8998 0.6762 0.2578

FPSO Line flow (MVA) 129.9243 20.2877 121.6809 79.3749 8.1658 30.3946 65.1979 63.1129 50.0450 58.0980 66.1626 71.2196 62.9885 87.9033 8.2506

OF 0.9994 0.3121 0.9360 0.8819 0.2552 0.4676 0.5015 0.4855 0.7699 0.4469 1.0179 0.7913 0.8998 0.6762 0.2578

Fuzzy particle swarm optimization 183

Table VI. Overloaded line details after rescheduling

methods. In line 2-5 outage, the overloads are not relieved completely. This shows generation rescheduling is not sufficient to alleviate the line overloads under a few contingency cases. 7.1.2.2 Generation rescheduling with TCSC. TCSC is included in addition to generation rescheduling to alleviate the line overloads due to line outage 2-5. The LOSI values are calculated using Equation (1) for each branch of the considered system for the selected contingency cases. The branches, which have high values of LOSI, are 6-8, 1-2 and 2-4 and their LOSI values are 1.0000, 0.7895 and 0.7164, respectively. TCSCs are placed in all the above three lines. Generator active power and the reactance of the TCSCs are taken as control variables for overload alleviation for the contingency 2-5. Table VII presents the optimal control variable setting for the contingency 2-5 along with the final value of severity index and generation cost. The overloaded line details after rescheduling are shown in Table VIII.

Control variables P1 P2 P5 P8 P11 P13 TCSC 1 TCSC 2 TCSC 3 SI Generation cost ($/h) Average CPU time (s)

PSO

APSO

135.37 77.55 48.57 33.98 29.18 38.86 −0.00943 −0.01291 −0.039 0 1,159.633 16.32

136.093 77.31 48.43 33.88 29.10 38.75 −0.00953 −0.01304 −0.0394 0 1,158.546 16.11

FPSO 136.25 77.26 48.40 33.86 29.09 38.72 −0.00955 −0.01307 −0.0395 Table VII. 0 Control variable 1,158.304 setting for corrective 16.02 action with TCSC

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184 Table VIII. Overloaded line details after rescheduling with TCSC

Overloaded lines

Line flow limit (MVA)

1-2 1-3 2-4 3-4 2-6 4-6 5-7 6-7 6-8

130 130 65 130 65 90 70 130 32

PSO Line flow (MVA) OF

APSO Line flow (MVA) OF

FPSO Line flow (MVA) OF

76.2269 59.7228 59.7151 54.8869 64.8555 76.1356 64.6093 89.5289 9.8139

76.8067 59.8578 59.9379 55.0135 64.9668 76.3876 64.7692 89.6856 9.9429

76.9368 59.8879 59.9879 55.0418 64.9917 76.4441 64.8051 89.7206 9.9719

0.5864 0.4594 0.9187 0.4222 0.9978 0.8460 0.9230 0.6887 0.3067

0.5908 0.4604 0.9221 0.4232 0.9995 0.8488 0.9253 0.6899 0.3107

0.5918 0.4607 0.9229 0.4234 0.9999 0.8494 0.9258 0.6902 0.3116

From Tables VII and VIII, it is clear that the proposed FPSO method helps to alleviate the overloads for the contingency 2-5 by inclusion of TCSC along with generation rescheduling in terms of minimum generation cost of 1,158.304 $/h and minimum average CPU time of 16.02 seconds when compared to APSO and simple PSO methods. 8. Conclusion In this paper, FPSO method is proposed for transmission line overload management in a contingent power network. The line overloads are relieved through generation rescheduling with or without inclusion of TCSC. To alleviate the line overloads effectively, the best location of TCSCs is identified through sensitivity analysis. The proposed method is tested and examined on the standard IEEE-30 bus system. Line overloads are simulated due to unexpected line outage under 30 percent increased load conditions. In case 1, the proposed method gives better results in terms of optimum fuel cost and fast convergence, when compared to APSO, simple PSO and other reported methods. In case 2, line overloads are relieved in line 1-2 outage. In line 2-5 outage, the proposed method is able to alleviate the line overloads by inclusion of TCSC along with generation rescheduling and gives optimum generation cost, when compared to APSO and simple PSO. The results show that the proposed algorithm is capable of improving the transmission security with optimum generation cost. References Abido, M.A. (2002a), “Optimal power flow using particle swarm optimization”, International Journal of Electrical Power & Energy Systems, Vol. 24 No. 7, pp. 563-571. Abido, M.A. (2002b), “Optimal power flow using tabu search algorithm”, Electric Power Components and Systems, Vol. 30 No. 5, pp. 469-483. Abouzar, S. and Peyman, N. (2012), “A new method for optimal placement of TCSC based on sensitivity analysis for congestion management”, Smart Grid and Renewable Energy, Vol. 3 No. 1, pp. 10-16. Acharya, N. and Mithulananthan, N. (2007), “Locating series FACTS devices for congestion management in deregulated electricity markets”, Electric Power Systems Research, Vol. 77 Nos 3-4, pp. 352-360. Ahmed, E., Yahya, H., Yasmine, A. and Ahmed, E. (2014), “Optimal power flow and reactive compensation using a particle swarm optimization algorithm”, Journal of Electrical Systems, Vol. 10 No. 1, pp. 63-77.

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Corresponding author K. Pandiarajan can be contacted at: [email protected]

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