Fuzzy harmony search algorithm based optimal power flow for power system security enhancement

Electrical Power and Energy Systems 78 (2016) 72–79

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Fuzzy harmony search algorithm based optimal power flow for power system security enhancement K. Pandiarajan a,⇑, C.K. Babulal b,1 a b

Department of Electrical and Electronics Engineering, Pandian Saraswathi Yadav Engineering College, Arasanoor, India Department of Electrical and Electronics Engineering, Thiagarajar College of Engineering, Madurai, India

a r t i c l e

i n f o

Article history: Received 21 February 2014 Received in revised form 26 September 2015 Accepted 17 November 2015

Keywords: Optimal power flow Harmony search algorithm Fuzzy logic system Optimization Power systems

a b s t r a c t This paper proposes the integration of fuzzy logic system with harmony search algorithm (FHSA) to find the optimal solution for optimal power flow (OPF) problem in a power system. The objective of the method is to minimize the total fuel cost of thermal generating units having quadratic cost characteristics and severity index (SI). The generator active power, generator bus voltage magnitude, transformer taps, VAR of shunts and the reactance of thyristor controlled series capacitor (TCSC) are taken as the control variables. The adjustment of proposed algorithm parameters such as pitch adjustment rate (PAR) and bandwidth (BW) is done through fuzzy logic system (FLS). The effectiveness of the proposed method has been tested on the standard IEEE 30 bus, IEEE 57 bus and IEEE 118 bus systems in MATLAB environment and their results are compared with conventional harmony search algorithm (HSA) and other heuristic methods reported in the literature recently. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction The power system security is the ability of the system to maintain the flow of electricity from the generators to the customers, especially under contingency conditions. A contingency is basically an outage of a generator; transformer and/or transmission line and its effects are monitored with specified security limits. The power system operation is said to be normal, when the power flows and the bus voltages are within acceptable limits in spite of changes in load or generation. In static security analysis, contingency analysis is used to predict the possible systems outage and their effect [1]. When outage of components in a power system occurs, system gets overloaded and the system parameters exceed their limits thus resulting in an insecure system. Hence, static security enhancement by alleviating overloads on the transmission lines is a vital role in an electric power system. Optimal power flow is an important tool for power system management. OPF has been applied to regulate generator real power outputs and voltages, shunt capacitors/reactors, transformer tap settings and other controlled variables to minimize the total fuel cost of generators, real power loss, while satisfying a set of physical and operating constraints such as generation and load balance, bus ⇑ Corresponding author. Tel.: +91 9443495438. E-mail addresses: [email protected] (K. Pandiarajan), [email protected] (C.K. Babulal). 1 Tel.: +91 9843917258. http://dx.doi.org/10.1016/j.ijepes.2015.11.053 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.

voltage limits, power flow equations and active and reactive power limits. The OPF problem has been solved by using conventional and evolutionary based algorithms. Conventional optimization techniques such as gradient method, linear programming method, nonlinear programming method and interior point method have been discussed in [2–5]. In conventional optimization methods, identification of global minimum is not possible. To overcome the difficulty, evolutionary algorithms like genetic Algorithm (GA) [6], tabu search algorithm [7], differential evolution [8], modified differential evolution algorithm (MDE) [9], cuckoo optimization algorithm [10], artificial bee colony algorithm [11], improved harmony search method [12] and improved teaching–learning-based optimization algorithm [13] had been proposed. In [14], chaotic invasive weed optimization algorithm has been used to find the optimal solution for optimal power flow problem in a power system. Different non-smooth and non-convex cost functions were considered to minimize the fuel cost such as quadratic fuel cost function, fuel cost function with valve point effect, and fuel cost function with considering the prohibited zones. In [15], chaotic invasive weed optimization techniques have been used for solving environmental optimal power flow problem. Simultaneous minimization two conflicting objectives such as fuel cost and gaze emission were considered. Fuzzy particle swarm optimization based congestion management by optimal rescheduling of active powers of generators has been depicted in [16]. The

K. Pandiarajan, C.K. Babulal / Electrical Power and Energy Systems 78 (2016) 72–79

generators had been chosen based on the generator sensitivity to the congested line. The results were compared with fitness distance ratio particle swarm optimization and conventional PSO. A contingency constrained economic load dispatch using improved particle swarm optimization to alleviate transmission line overloads has been discussed in [17]. The line overloads were relieved through rescheduling of generators with minimum fuel cost and minimum severity index. In [18], fuzzy adaptive bacterial foraging has been used to alleviate overload through redispatch of generators. The participating generators were selected based on the generator sensitivity to the congested line. An alleviation of congestion in a power system by optimal sizing and placement of TCSC have been depicted in [19]. Minimization of severity index was taken as objective function. The optimal location of TCSC was done by sensitivity analysis and sizing of TCSC by using genetic algorithm. HS algorithm was first proposed by Geem et al. in 2001 [20]. It is a population-based meta-heuristic optimization algorithm. It is inspired by the music improvisation process in which the musician searches for harmony and continues to polish the pitches to obtain a better harmony. In HSA, PAR and BW is very important parameters in fine tuning of optimized solution vectors and can be potentially useful in adjusting convergence rate of algorithm to get optimal solution. The fine adjustment of these parameters is of great interest. The conventional HSA uses fixed value of PAR and BW. The PAR and BW is adjusted in initialization only and cannot be changed during new iterations. The main drawback of this method is to take more number of iterations to get an optimal solution. Small PAR values and large BW can cause to poor performance of an algorithm and great increase in iterations to find optimal solution. Large PAR values with small BW values usually cause the improvement of best solutions in final iterations which algorithm converged to optimal solution vector. In this paper, fuzzy logic based PAR and BW adjustment is presented. The organization of the paper is as follows: section ‘Optimal location of TCSC’ presents overview of optimal location of TCSC. Section ‘Problem formulation’ presents the optimization problem formulation for power system security enhancement. Section ‘Modeling of fuzzy logic system’ presents modeling of fuzzy logic system. Section ‘Proposed FHSA algorithm’ presents the algorithm of proposed FHSA to find the optimal solutions. The results achieved by applying the proposed method on the standard IEEE 30 bus, IEEE 57 bus and IEEE 118 bus systems are presented in section ‘Simulation results’. Finally, conclusion is given in section ‘Conclusion’.

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 [21]. These factors have been obtained as:

LOSIl ¼

NC X C¼1

SCl

SCl Smax l

! ð1Þ

Smax l

where = flow in line l (MVA) in contingency C; = rating of the line l (MVA); N c = Number of considered contingencies. TCSC’s are placed on the branches starting from the top of the ranking list.

73

Problem formulation The objective of the proposed method is to minimize the total fuel cost and severity index. Objective functions Objective 1: Minimization of total fuel cost

FT ¼

NG  X

ai P 2gi þ bi Pgi þ ci



ð2Þ

i¼1

where FT = total fuel cost, NG = number of generators, Pgi = Active power output of ith generator and ai, bi, ci = cost coefficients of generator i. Objective 2: Minimization of severity index

SIl ¼

2m n  X Sl max Sl l2Lo

ð3Þ

where Sl = flow in line l (MVA), Smax = rating of the line l (MVA), l Lo = set of overloaded lines and m = integer exponent = 1 (Assumed) [22]. For secure system, the value of SI is zero. When the SI value is greater, the contingency becomes severe. Problem constraints The constraints are: Generation/load balance Equation NG ND X X Pgi  PDi  P L ¼ 0 i¼1

ð4Þ

i1

where N G = Number of generators, N D = Number of loads, Pgi = Generation of generator i, PDi = Active power demand at bus i, g = Generator, D = Demand and PL = System active power loss. Generator constraints

Pgi;min 6 Pgi 6 Pgi;max

ð5Þ

where P gi;max = Upper limit of active power generation at generator bus i and Pgi;min = Lower limit of active power generation at generator bus i.

V gi;min 6 V gi 6 V gi;max

ð6Þ

where V gi = Voltage magnitude at generator bus i, V gi;max = Upper limit of voltage magnitude at generator bus i and V gi;min = Lower limit of voltage magnitude at generator bus i. Voltage constraints

V i;min 6 V i 6 V i;max

ð7Þ

where V i = Voltage magnitude at bus i, V i;max = Upper limit of voltage magnitude at bus i and V i;min = Lower limit of voltage magnitude at bus i. Transformer constraints

T i;min 6 T i 6 T i;max

ð8Þ

where T i;min and T i;max are minimum and maximum tap settings limits of transformer i. Shunt VAR constraints

Q ci;min 6 Q ci 6 Q ci;max

ð9Þ

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K. Pandiarajan, C.K. Babulal / Electrical Power and Energy Systems 78 (2016) 72–79

Fig. 1. FIS editor window of FLS.

Medium

Low

High

0.8

0.6

0.4

0.2

0

High

0.8

0.6

0.4

0.2

0 0

20

40

60

80

100

120

140

160

180

200

Iteration

Medium

Low

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.9

Fig. 4. Membership function of output variable BW.

High

TCSC reactance limit

X TCSCi;min 6 X TCSCi 6 X TCSCi;max Degree of membership

0.85

BW

Fig. 2. Membership function of input variable iteration.

1

Medium

Low

1

Degree of membership

Degree of membership

1

0.8

ð11Þ

The working range of TCSC is considered as follows.

0.6

0:8X l 6 X TCSC 6 0:2X l

ð12Þ

0.4

where X TCSC = TCSC reactance and X l = Reactance of the line where TCSC is located.

0.2

Modeling of fuzzy logic system 0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

PAR Fig. 3. Membership function of output variable PAR.

where Q ci;min and Q ci;max are minimum and maximum VAR injection limits of shunt capacitor i. Transmission line flow limits

Sl 6 Smax l

ð10Þ

The balance between global and local search throughout the course of run is critical to the success of an evolutionary algorithm. Suitable selection of pitch adjustment rate and bandwidth provides a balance between global and local search abilities. FLS gives suitable value of PAR and BW during execution. Triangular membership functions are used in both input and output and three linguistic values are considered. The values are Low, Medium and High. The fuzzy system model is developed in MATLAB environment. Fuzzy logic system is modeled to increase the PAR and to reduce the BW corresponding to number of iterations. The fuzzy

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K. Pandiarajan, C.K. Babulal / Electrical Power and Energy Systems 78 (2016) 72–79

Fig. 5. FIS sample output of 50th iteration.

Table 1 Comparison of control variables and statistical analysis of fuel cost – IEEE 30 bus system.

814 HSA FHSA

Control variables (p.u.)

HSA

FHSA

Control variables (p.u.)

HSA

FHSA

P1 P2 P5 P8 P11 P13 V1 V2 V5 V8 V11 V13 T11

1.77747 0.48584 0.21539 0.21278 0.11014 0.12266 1.0951 1.0747 1.0410 1.0531 1.0976 1.0892 0.9789

1.76804 0.49229 0.21147 0.21043 0.11977 0.12062 1.100 1.085 1.054 1.062 1.098 1.095 1.011

T12 T15 T36 QC10 QC12 QC15 QC17 QC20 QC21 QC23 QC24 QC29

0.9395 1.0125 0.9452 0.0138 0.0060 0.0398 0.0430 0.0346 0.0352 0.0002 0.0221 0.0482

0.934 1.008 0.976 0.031 0.045 0.041 0.011 0.038 0.013 0.045 0.023 0.034

800.397 800.421 800.444 0.0152 195

799.914 799.924 799.942 0.0146 178

Best cost ($/h) Average cost ($/h) Worst cost ($/h) Standard deviation No. of iteration

Table 2 Comparison of fuel cost of different methods – IEEE 30 bus system. Method

Fuel cost ($/h)

Method

Fuel cost ($/h)

GA [22] GA [25] PSO [26] DE [27] PSO [27] GA [28] GA fuzzy [28]

803.05 801.7165 800.41 801.8436 801.8441 801.96 801.21

PSO [28] FPSO [28] PSO [29] MOTLBO [30] ABC [31] HSA FHSA

800.96 800.72 801.6954 800.6797 800.6600 800.397 799.914

rules for changing the pitch adjustment rate and bandwidth are given below. 1. If iteration is Low then PAR is Low and BW is High. 2. If iteration is Medium then PAR is Medium and BW is Medium. 3. If iteration is High then PAR is High and BW is Low. FIS editor window of FLS is shown in Fig. 1. The input and output membership functions are shown in Figs. 2–4, respectively. The FIS sample output for 50th iteration is shown in Fig. 5.

Fuel Cost ($/h)

812 810 808 806 804 802 800 798

0

20

40

60

80

100

120

140

160

180

200

Iteration Number Fig. 6. Fuel cost convergence characteristics of HSA and FHSA-IEEE 30 bus system.

Proposed FHSA algorithm The step by step procedure of FHSA algorithm is given below. Step 1: Initialize the HSA parameters such as harmony memory size (HMS) or population number, harmony memory considering rate (HMCR), pitch adjustment rate (PAR), bandwidth (BW), number of iterations, number of variables to be optimized, limits on each variables and iteration count. HSA parameter values are: HMS: 20, No. of iteration: 200, HMCR = 0.9 PAR = 0.3–0.9, BW = 0.9–0.4. Step 2: An initial harmony memory (HM) is randomly generated considering the variables to be optimized. The harmony memory is a memory location where all the solution vectors (sets of decision variables) are stored. Step 3: Run Newton Raphson power flow and evaluate the objective function. Step 4: Build the HM. Step 5: Increase the iteration count.

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K. Pandiarajan, C.K. Babulal / Electrical Power and Energy Systems 78 (2016) 72–79

Table 3 Comparison of control variables and statistical analysis of fuel cost – IEEE 57 bus system. Control variables (p.u.)

HSA

FHSA

Control variables (p.u.)

HSA

FHSA

Control variables (p.u.)

HSA

FHSA

P1 P2 P3 P6 P8 P9 P12 V1 V2 V3 V6 V8

1.46823 0.81023 0.46231 0.67613 4.49781 0.94476 3.78699 1.053 1.056 1.046 1.068 1.088

1.42020 0.83589 0.47086 0.74987 4.53261 0.98136 3.65870 1.077 1.075 1.066 1.081 1.090

V9 V12 T4–18 T4–18 T21–20 T24–25 T24–25 T24–26 T7–29 T34–32 T11–41 T15–45

1.066 1.047 0.912 0.926 0.996 0.962 0.916 0.991 0.939 0.962 0.904 0.952

1.086 1.063 0.927 0.947 0.998 1.052 0.942 0.976 0.916 0.955 0.922 0.957

T14–46 T10–51 T13–49 T11–43 T40–56 T39–57 T9–55 QC18 QC25 QC53

0.938 0.962 0.905 0.905 0.991 0.936 0.960 0.079 0.044 0.125

0.967 0.983 0.946 0.907 1.003 0.949 0.940 0.154 0.235 0.008

41684.36 41684.39 41684.41 0.0153 188

41658.18 41658.20 41658.22 0.0148 184

Best cost ($/h) Average cost ($/h) Worst cost ($/h) Standard deviation No. of iteration

Table 4 Comparison of fuel cost of different methods – IEEE 57 bus system. Method

Fuel cost ($/h)

ABC [31] Fuzzy-GA [32] EADDE [33] DE-PS [34] GSA [35] HSA FHSA

41693.9589 41716.2808 41713.62 41685.295 41695.8717 41684.36 41658.18

4.34

x 10

4

Simulation results HSA FHSA

4.32

Fuel Cost ($/h)

4.3 4.28 4.26 4.24 4.22 4.2 4.18 4.16

Step 7: Evaluate the objective function values for each New Harmony. Step 8: Update the HM by comparing the New Harmony vector and worst one stored in HM. If the New Harmony is better than worst one in HM from the point of view of objective function values, the New Harmony [23] is included in the HM and the existing worst harmony is excluded from HM. Step 9: Find the new value of PAR and BW using FLS and update them. Step 10: If stopping criteria is satisfied, then the best individual is obtained, otherwise repeat the procedure from step 5.

0

20

40

60

80

100

120

140

160

180

200

Iteration Number Fig. 7. Fuel cost convergence characteristics of HSA and FHSA-IEEE 57 bus system.

Step 6: Generate New Harmony vector, based on memory consideration, pitch adjustment and random selection (Improvisation). The New Harmony vector can be stated as follows.

X 0 ¼ ðX 01 ; X 02 ; . . . ; X 0N Þ

ð13Þ

The value of first decision variable for the new vector can be chosen from any value in the specified HM range which can be stated as follows.

X 01  X HMS 1

ð14Þ

The value of other design variables is chosen in the same manner. HMCR, which varies between 0 and 1, is the rate of choosing one value from the historical values stored in the HM,

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 [24]. Two different cases are considered for the study. In case 1, the proposed FHSA algorithm is applied to minimize the total fuel cost on the standard IEEE 30 bus, IEEE 57 bus and IEEE 118 bus systems under normal conditions. In case 2, the proposed algorithm is applied to alleviate line overloads in the above systems under selected severe contingency cases. In order to verify the robustness of the proposed FHSA method, simulation is carried out for 25 independent runs with different initial population. The final parameters are selected based on minimum objective value. Case 1: Minimization of fuel cost The objective function is to minimize the total fuel cost of the thermal generating units with smooth cost functions. The generator active power, generator bus voltage magnitude, transformer taps and VAR of shunts are taken as optimization variables. The upper and lower limits of all the generator bus voltages are taken as 1.10 p.u. and 0.95 p.u. respectively. The upper and lower limits of all the transformers are taken as 1.10 p.u. and 0.9 p.u. respectively. The upper and lower limits of all shunt VAR supports in IEEE 30 bus is taken as 0.05 p.u. and 0 p.u. respectively. The upper and lower limits of all shunt VAR supports in both IEEE 57 bus and IEEE 118 bus system are taken as 0.3 p.u. and 0 p.u. respectively. IEEE 30 bus system The IEEE 30 bus system consists of 6 generators, 2 shunt reactors, 41 lines and 4 transformers. The proposed FHSA method is applied to IEEE 30 bus system; the obtained results of control variables

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K. Pandiarajan, C.K. Babulal / Electrical Power and Energy Systems 78 (2016) 72–79 Table 5 Comparison of control variables and statistical analysis of fuel cost. Control variables (p.u.)

HSA

FHSA

Control variables (p.u.)

HSA

FHSA

Control variables (p.u.)

HSA

FHSA

P10 P12 P25 P26 P31 P46 P49 P54 P59 P61 P65 P66 P69 P80 P87 P89 P100 P103 P111 V10 V12

3.76172 1.25530 2.21641 3.64199 0.20521 0.36254 2.14182 0.49287 1.95554 1.83933 4.34887 3.21314 4.54593 4.58026 0.05038 5.22268 3.00638 0.36508 0.43047 1.0546 0.9691

4.30072 1.29886 2.32628 2.79056 0.14399 0.25568 2.10069 0.51226 1.62384 1.76540 4.31309 3.86225 4.54298 4.65377 0.12305 6.17429 2.34367 0.30349 0.33079 1.0358 0.9996

V25 V26 V31 V46 V49 V54 V59 V61 V65 V66 V69 V80 V87 V89 V100 V103 V111 T8–5 T30–17 T38–37 T38–37

1.0387 1.0443 1.0448 1.0230 1.0137 0.9583 1.0007 1.0126 1.0029 1.0459 1.0312 1.0231 1.0121 1.0138 0.9903 0.9986 0.9892 0.9719 1.0603 1.0210 1.0578

1.0446 0.9546 0.9511 1.0497 1.0094 0.9547 0.9782 0.9889 1.0530 1.0040 0.9930 0.9957 0.9659 1.0102 1.0102 0.9640 0.9892 1.0696 1.0729 1.0507 1.0664

T63–59 T64–61 T65–66 T68–69 T81–80 QC5 QC34 QC37 QC44 QC45 QC46 QC48 QC74 QC79 QC82 QC83 QC105 QC107 QC110

1.0556 1.0353 0.9853 0.9392 0.9672 0.2929 0.1331 0.1875 0.0724 0.1978 0.2765 0.2406 0.2027 0.2900 0.1832 0.0758 0.2293 0.1930 0.0087

1.0581 1.0452 1.0180 0.9761 0.9239 0.2900 0.2058 0.2261 0.2953 0.1522 0.1165 0.1658 0.1302 0.2647 0.2933 0.0484 0.0412 0.0838 0.0842

132319.60 132319.63 132319.65 0.0143 181

132138.30 132138.32 132138.34 0.0133 163

Best cost ($/h) Average cost ($/h) Worst cost ($/h) Standard deviation No. of iteration

x 10

2.8

Table 7 Overloaded line details before rescheduling.

5

HSA FHSA

2.6

Fuel Cost ($/h)

2.4

System

Outage Overloaded Line flow line lines (MVA)

Line flow OF limit (MVA)

IEEE 30 Bus

2–5

1–2 1–3 2–4 3–4 2–6 4–6 5–7 6–7 6–8

220.1530 143.2545 93.0656 132.5710 128.0934 152.3131 126.2165 148.5759 58.5808

130 130 65 130 65 90 70 130 32

IEEE 57 Bus

1–15

3–15

112.6383 100

1.1264 1.2687

12–14 13–15 12–16 15–17 16–17

107.2030 103.0672 143.6514 223.4804 160.2231

1.0720 6.3471 1.0307 1.1050 1.1174 1.2325

2.2 2 1.8 1.6 1.4 1.2

IEEE 118 Bus 8–5

0

20

40

60

80

100

120

140

160

180

200

Iteration Number

SI

1.6935 21.7216 1.1019 1.4318 1.0198 1.9707 1.6924 1.8031 1.1429 1.8306

100 100 130 200 130

Fig. 8. Fuel cost convergence characteristics of HSA and FHSA-IEEE 118 bus system. Table 8 Control variable setting for IEEE 30 bus system.

Table 6 Normalized LOSI values. System

Branches

LOSI value

Rank

IEEE 30 bus

6–8 1–2 2–4

1.0000 0.7895 0.7164

1 2 3

3–15 7–29

1.0000 0.7833

1 2

IEEE 57 bus

compared with conventional HSA and statistical analysis of fuel cost are tabulated in Table 1. The fuel cost of FHSA compared with HSA and other methods reported in different literatures are shown in Table 2. The fuel cost convergence characteristics of the proposed FHSA compared with HSA is shown in Fig. 6.

Control variables (p.u.)

HSA

FHSA

Control variables (p.u.)

HSA

FHSA

P1 P2 P5 P8 P11

1.88718 0.365932 0.470382 0.346886 0.287646

1.783505 0.424438 0.46706 0.34897 0.29713

P13 TCSC 1 TCSC 2 TCSC 3

0.301985 0.02099 0.01688 0.05494

0.33211 0.02675 0.01554 0.04073

In IEEE 30 bus system, convergences reach at 195th iteration and 178th iteration in HSA and FHSA methods, respectively. From Table 2, it is clear that the proposed FHSA method gives less generation cost of 799.914 $/h (cost difference of 0.483 $/h), when compared to conventional HSA and other reported methods. From Fig. 6, it is noted that the proposed FHSA method gives better

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that the proposed FHSA method gives better results in terms of minimum fuel cost with fast convergence when compared to HSA.

Table 9 Control variable setting for IEEE 57 bus system. Control variables (p.u.)

HSA

FHSA

P1 P2 P3 P6 P8 P9 P12 TCSC 1 TCSC 2

1.8464 0.739583 0.462264 0.616489 4.775099 0.898928 3.397702 0.02507 0.01373

1.183915 0.970564 0.534861 0.811342 4.786272 0.754314 3.685741 0.02714 0.04583

Table 10 Control variable setting for IEEE 118 bus system. Control variables (p.u.)

HSA

FHSA

Control variables (p.u.)

HSA

FHSA

P10 P12 P25 P26 P31 P46 P49 P54 P59 P61

3.31485 1.71229 2.95600 2.79018 0.48573 0.42453 2.58239 0.88048 1.22244 1.24278

2.37931 1.73129 1.94245 3.39844 0.17384 1.00969 2.69539 1.17557 2.48988 2.56982

P65 P66 P69 P80 P87 P89 P100 P103 P111

4.46001 3.68187 4.76872 4.57690 0.65181 3.94129 3.28845 0.16343 0.72531

1.86592 3.01082 4.58771 5.16858 0.38132 3.98808 3.12856 1.26335 0.84298

results in terms of minimum fuel cost with fast convergence compared to HSA. IEEE 57 bus system The IEEE 57 bus system consists of 7 generators, 3 shunt reactors, 80 lines and 17 transformers. The proposed FHSA method is applied to IEEE 57 bus system; the obtained results of control variables compared with conventional HSA and statistical analysis of fuel cost are tabulated in Table 3. The fuel cost of FHSA compared with HSA and other methods reported in different literatures are shown in Table 4. The fuel cost convergence characteristics of proposed FHSA compared with HSA is shown in Fig. 7. In IEEE 57 bus system, convergence is reached at 188th iteration and 184th iteration for HSA and FHSA methods respectively. From Table 4, it is clear that the proposed FHSA method gives less generation cost of 41658.18 $/h (cost difference of 26.18 $/h), when compared to HSA and other reported methods. From Fig. 7, it is clear

IEEE 118 bus system The IEEE 118 bus system consists of 54 generators, 14 shunt reactors, 186 lines and 9 transformers. The proposed FHSA method is applied to IEEE 118 bus system; the obtained results of control variables compared with conventional HSA and statistical analysis of fuel cost are tabulated in Table 5. The fuel cost convergence characteristics of proposed FHSA compared with HSA is shown in Fig. 8. In IEEE 118 bus system, convergence is reached at 181th iteration and 163rd iteration for HSA and FHSA methods respectively. From Table 5, it is clear that the proposed FHSA method gives less generation cost of 132138.30 $/h (cost difference of 181.3 $/h), when compared to HSA. From Fig. 8, it is clear that the proposed FHSA method gives better results in terms of minimum fuel cost with fast convergence when compared to HSA. Case 2: Overload alleviation through generation rescheduling and/or optimal placement of TCSC The proposed FHSA method is applied to alleviate the line overload on the standard IEEE 30 bus, IEEE 57 bus and IEEE 118 bus systems under selected severe contingency cases. Generator active power and the reactance of thyristor controlled series capacitor (TCSC) are taken as the control variables to alleviate the line overloads in IEEE 30 bus and IEEE 57 bus systems. Generator active power is taken as the control variables to alleviate the line overloads for IEEE 118 bus system. The optimal selection of TCSC is computed using Eq. (1) and shown in Table 6. In IEEE 30 bus system, contingency analysis is carried out on the system under 30% increased load case in all the load buses except bus no. 5 and 1.1 times the base load conditions in bus no. 5. In IEEE 57 bus and IEEE 118 bus systems, contingency analysis is carried out on the system under base load conditions. The overloaded line details for the test systems before rescheduling are shown in Table 7. Tables 8–10 presents the optimal control variable setting for IEEE 30 bus, IEEE 57 and IEEE 118 bus system. The overloaded line details for the test systems after rescheduling are shown in Table 11. The CPU time per trial (100 iterations) in HSA and FHSA methods is 17.50 s & 16.09 s, 19.73 s & 18.37 s and 23.61 s & 22.87 s for line outages of 2–5, 1–15 and 8–5 in IEEE 30 bus system, IEEE 57 bus system and IEEE 118 bus system, respectively. In line 2–5 outage, the active power loss is reduced from 50.743 MW to

Table 11 Overloaded line details after rescheduling. System with outage line

Line flow (MVA)

OF

SI

Best Cost ($/h)

HSA

FHSA

HSA

FHSA

HSA

FHSA

HSA

FHSA

30 Bus (2–5)

123.8357 66.7213 63.9953 61.4812 64.2394 81.5387 66.3950 91.2879 11.2858

113.3441 66.2673 59.6465 61.0716 64.8946 79.1064 66.6423 91.6255 10.9610

0.9526 0.5132 0.9845 0.4729 0.9883 0.9060 0.9485 0.7022 0.3527

0.8719 0.5097 0.9176 0.4698 0.9984 0.8790 0.9520 0.7048 0.3425

0

0

1126.93

1126.82

57 Bus (1–15)

89.6258

87.6003

0.8963

0.8760

0

0

42126.50

42018.88

118 Bus (8–5)

76.5008 83.9875 194.7629 121.3951 102.1882

76.6926 84.2355 177.5038 118.7207 93.5700

0.76501 0.64606 0.97381 0.93381 0.78606

0.7669 0.6480 0.8875 0.9132 0.7198

0

0

147554.60

147131.30

K. Pandiarajan, C.K. Babulal / Electrical Power and Energy Systems 78 (2016) 72–79

16.421 MW and 15.741 MW by HSA and FHSA methods, respectively. In line 1–15 outage, the active power loss is reduced from 42.016 MW to 22.847 MW & 21.901 MW, respectively. In line 8–5 outage, the active power loss is reduced from 197.029 MW to 144.947 MW & 138.300 MW, respectively. From Table11, it is clear that the proposed FHSA method is able to alleviate the line overloads completely in the considered cases in terms of minimum fuel cost (cost difference of 0.11 $/h in line 2–5 outage, cost difference of 107.62 $/h in line 1–15 outage and cost difference of 423.30 $/h in line 8–5 outage) and active power loss with least computation time, when compared to conventional HSA. Conclusion In this paper, a FHSA based optimal power flow for security enhancement in power system is proposed. Two different objectives such as minimization of fuel cost and severity index are considered. The fuel cost is minimized by changing generator active power, generator bus voltage magnitude, transformer taps and VAR of shunts. The line overloads are relieved through generation rescheduling and/or inclusion of TCSC by minimizing severity index. The proposed method is tested and examined on the standard IEEE 30 bus, IEEE 57 bus and IEEE 118 bus systems under two different cases. In case 1, the proposed method gives better results in terms of optimum fuel cost with fast convergence, when compared to HSA and other reported methods. In case 2, line overloads are relieved in considered contingency case for the considered systems through generation rescheduling and/or inclusion of TCSC in terms of optimum fuel cost, when compared to HSA. The result shows that the proposed algorithm is capable of improving the transmission security with optimal fuel cost. References [1] Oonsivilai A, Greyson. Power system contingency analysis using multiagent systems. IEEE Trans Power Syst 2009;14(3):355–60. [2] Alsac O, Scott B. Optimal load flow with steady state security. IEEE Trans Power Syst 1974;93(3):745–51. [3] Stott B, Hobson E. Power system security control calculations using linear programming. IEEE Trans Power Apparatus Syst 1978;97(5):1713–20. [4] Burchett RC, Happ HH, Vierath DR. Quadratically convergent optimal power flow. IEEE Trans Power Apparatus Syst 1984;PAS-103:3267–76. [5] Deb K. Optimization for engineering design: algorithms and examples. PHI; 2009. [6] Todorovski Mirko, Rajicic Dragoslav. An initialization procedure in solving optimal power flow by genetic algorithm. IEEE Trans Power Syst 2006;21 (2):480–7. [7] Abido MA. Optimal power flow using tabu search algorithm. Electr Power Compon Syst 2002;30(5):469–83. [8] Abou EL, Ela AA, Abido MA, Spea SR. Optimal power flow using differential evolution. Electr Power Syst Res 2010;80:875–85. [9] Sayah Samir, Zehar Khaled. Modified differential evolution algorithm for optimal power flow with non smooth cost functions. Energy Convers Manage 2008;49(11):3036–42. [10] Rajabioun Ramin. Cuckoo optimization algorithm. Appl Soft Comput 2011;11 (8):5508–18. [11] Sumpavakup C, Chusanapiputt S. A solution to the optimal power flow using artificial bee colony algorithm. In: Int conf power system technology; 2010. p. 1–5.

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