Here, the power system oscillations are minimized by tuning of the scaling factors using GA. The aim is to minimize the error between the steady-state power (*Pref* ) flowing through the line in which the TCSC is installed and the actual power flowing through that line (*Pactual*) after a disturbance [12, 19]. Several performance indices can be used to represent the above goal mathematically. The integral of the squared error (ISE) [12] as shown in eqn. (1) has been selected as it tends to place a greater penalty on large errors. This goal can be formulated as the minimization of the objective function F where,

$$F = \int\_0^{t\_{\rm sat}} e^{2}(t)dt\tag{1}$$

In eqn. (1), *e*(*t*)= *Pref* −*Pactual* is the error in power flow in the line following a disturbance and *tsim* is the total time period of simulation. As the objective function of eqn. (1) is nonconvex in nature, GA has been used to minimize F. A basic introduction to GA is given in Section 2.

### *2.2.1. Genetic algorithm (GA)*

Various conventional optimization techniques are available in the literature, which can be used to optimize the controller parameters effectively. The conventional optimization approach, based on gradient descent technique, sometimes gets stuck at local minima giving suboptimal controllers.

Genetic Algorithms (GAs) offer promising potential for optimizing controller parameters and it uses the concept of Darwin's theory of evolution. As per this theory, the existence of all living things is based on the rule of "survival of the fittest" [1]. GA makes use of three fundamental operators, namely, reproduction, crossover, and mutation, which are explained later in this section. The basic principle of GA is to initially form different possible solutions to a problem and then test them for their performance. By using the rule of "survival of the fittest," only a fraction of the better solutions are selected, eliminating the remaining ones. Genetic operators (reproduction, crossover, and mutation) are then applied to the selected solutions resulting in a new generation of possible solutions (which are expected to perform better than the previous generation). The above steps are repeated until a specific termination criterion is met (such as maximum number of generations, negligible variation in performance or fitness value, etc.). Search space of GA does not confine to a narrow expected region (as in the case of gradient descent), but rather includes a broad spectrum of possible solutions. It is capable of obtaining the global solution of a wide variety of functions such as differentiable or nondifferentiable, linear or nonlinear, continuous or discrete, and analytical or procedural [1]. GA tries to perform an intelligent search for a solution from a nearly infinite number of possible solutions.

### *2.2.2. Basic tuning procedure*

**Δe/e NB NM NS ZE PS PM PB NB** VB VB VB B SB S ZE **NM** VB VB B B MB S VS **NS** VB MB B VB VS S VS **ZE** S SB MB ZE MB SB S **PS** VS S VS VB B MB VB **PM** VS S MB B B VB VB **PB** ZE S SB B VB VB VB

Here, the power system oscillations are minimized by tuning of the scaling factors using GA. The aim is to minimize the error between the steady-state power (*Pref* ) flowing through the line in which the TCSC is installed and the actual power flowing through that line (*Pactual*) after a disturbance [12, 19]. Several performance indices can be used to represent the above goal mathematically. The integral of the squared error (ISE) [12] as shown in eqn. (1) has been selected as it tends to place a greater penalty on large errors. This goal can be formulated as

2

( )

In eqn. (1), *e*(*t*)= *Pref* −*Pactual* is the error in power flow in the line following a disturbance and *tsim* is the total time period of simulation. As the objective function of eqn. (1) is nonconvex in nature, GA has been used to minimize F. A basic introduction to GA is given in Section 2.

Various conventional optimization techniques are available in the literature, which can be used to optimize the controller parameters effectively. The conventional optimization approach, based on gradient descent technique, sometimes gets stuck at local minima giving suboptimal

Genetic Algorithms (GAs) offer promising potential for optimizing controller parameters and it uses the concept of Darwin's theory of evolution. As per this theory, the existence of all living things is based on the rule of "survival of the fittest" [1]. GA makes use of three fundamental operators, namely, reproduction, crossover, and mutation, which are explained later in this section. The basic principle of GA is to initially form different possible solutions to a problem and then test them for their performance. By using the rule of "survival of the fittest," only a fraction of the better solutions are selected, eliminating the remaining ones. Genetic operators (reproduction, crossover, and mutation) are then applied to the selected solutions resulting in

*F e t dt* = ò (1)

0

*sim t*

**Table 2.** Rule Base for α

146 Fuzzy Logic - Tool for Getting Accurate Solutions

*2.2.1. Genetic algorithm (GA)*

controllers.

**2.2. Scaling factor's tuning using genetic algorithm (GA)**

the minimization of the objective function F where,

The overall flowchart for optimization using GA is shown in Fig. 4. Initially, a number of populations (N) have been generated for the scaling factors. Each of the populations consists of the binary strings corresponding to the scaling factors Ge, GΔe, and Gu. These strings are created in a random fashion with the constrain that the values of Ge, GΔe, and Gu should lie within their specified ranges. The ranges chosen for each of these scaling factors are shown in Table 3. For each of these N sets of values of Ge, GΔe, and Gu, time domain nonlinear simulation studies have been carried out for evaluating the objective function F of eqn. (1). For this, *tsim* has been taken as 80 s. Based on the values of the objective function, out of these N possible solutions, the good solutions are retained and the others are eliminated (following the principle of survival of the fittest) [1, 15, 19]. The selected solutions undergo the processes of reproduc‐ tion, crossover, and mutation to create a new generation of possible solutions (which are expected to perform better than the previous generation). This process of production of a new generation and its evaluation is performed repetitively. The algorithm stops when a predefined maximum number of generations is achieved [1, 15, 19]. The parameters used for GA are shown in Table 4. 2.2.2. Basic tuning procedure The overall flowchart for optimization using GA is shown in Fig. 1.4. Initially, a number of populations (N) have been generated for the scaling factors. Each of the populations consists of the binary strings corresponding to the scaling factors Ge, G∆e, and Gu. These strings are created in a random fashion with the constrain that the values of Ge, G∆e, and Gu should lie within their specified ranges. The ranges chosen for each of these scaling factors are shown in Table 1.3. For each of these N sets of values of Ge, G∆e, and Gu, time domain nonlinear simulation studies have been carried out for evaluating the objective function F of eqn. (1). For this, tsim has been taken as 80 s. Based on the values of the objective function, out of these N possible solutions, the good solutions are retained and the others are eliminated (following the principle of survival of the fittest) [1, 15, 19]. The selected solutions undergo the processes of reproduction, crossover, and mutation to create a new generation of possible solutions (which are expected to perform better than the previous generation). This process of production of a new generation and its evaluation is performed repetitively. The algorithm stops when a predefined maximum number of generations is achieved [1, 15, 19]. The

Table 3. Ranges for the different scaling factors

Table 4. Parameters used in genetic algorithm

3. Case studies

Section 3.1.1.

Parameters Ge G∆e Gu Minimum range 0 0 0 Maximum range 0.5 1 1

Parameter Value/Type Maximum generations 50 Population size 25 Mutation rate 0.1 Crossover operator Scattered

The efficacy of the projected STFPIC has been validated on two different multimachine power systems: (a) two-area 4 machine system [16] and (b) 10-machine 39-bus system [16, 19]. The details of these two systems are presented in

parameters used for GA are shown in Table 1.4.

Figure 4. Flowchart of the GA optimization algorithm **Figure 4.** Flowchart of the GA optimization algorithm

**Table 3.** Ranges for the different scaling factors

**Table 4.** Parameters used in genetic algorithm

### **3. Case studies**

The efficacy of the projected STFPIC has been validated on two different multimachine power systems: (a) two-area 4-machine system [16] and (b) 10-machine 39-bus system [16, 19]. The details of these two systems are presented in Section 3.

#### **3.1. Study systems** 3.1. Study systems

The schematic diagram of the two-area 4-machine system is shown in Fig. 5. In this system, machines 1, 2 and 3, 4 form two different coherent groups. The three tie lines connect these two coherent areas. As shown in Fig. 5, a TCSC has been installed in the middle of one of these tie lines [17, 19]. The schematic diagram of the two-area 4-machine system is shown in Fig. 1.5. In this system, machines 1, 2 and 3, 4 form two different coherent groups. The three tie lines connect these two coherent areas. As shown in Fig. 1.5, a TCSC has been installed in the middle of one of these tie lines [17, 19]. The one line diagram of the second study system of this work, i.e., the 10-machine 39-bus system is shown in Fig. 1.6.

has been assumed to be installed in the middle of the tie line connecting buses #39 and #36.

In this diagram, the generators are identified by their bus numbers to which they are connected. In this system, a TCSC

Figure 5. TCSC in a two-area 4-generator system **Figure 5.** TCSC in a two-area 4-generator system

12 11

2

19

18

17 15

3.2. Simulation results

1

14

13

16

31

3

Figure 6. Schematic diagram of 10-machine, 39-bus system

20

33

32

10 8 28 26 29 The one line diagram of the second study system of this work, i.e., the 10-machine 39-bus system is shown in Fig. 6. In this diagram, the generators are identified by their bus numbers

24

27

36

39

34 35

30

25

38 37

6

23

The effectiveness of the self-tuning fuzzy PI controller (STFPIC) has been studied through detailed nonlinear time domain simulation studies for a three-phase, 5-cycle, solid short-circuit faults on both the test systems shown above. The short-circuit faults have been assumed to occur at t = 5 s. The simulation studies have been carried out in the MATLAB/SIMULINK environment [18]. For illustrating the efficacy of the fuzzy controllers developed in this work, results pertaining to two different situations are presented. These situations are: (a) study system with a TCSC

2221

4 5 7

9

11

12

4

3

G3

The schematic diagram of the two-area 4-machine system is shown in Fig. 1.5. In this system, machines 1, 2 and 3, 4 form two different coherent groups. The three tie lines connect these two coherent areas. As shown in Fig. 1.5, a TCSC

The one line diagram of the second study system of this work, i.e., the 10-machine 39-bus system is shown in Fig. 1.6. In this diagram, the generators are identified by their bus numbers to which they are connected. In this system, a TCSC

8

to which they are connected. In this system, a TCSC has been assumed to be installed in the middle of the tie line connecting buses #39 and #36. G2 G4

has been assumed to be installed in the middle of the tie line connecting buses #39 and #36.

5 6 9 10 8 7

1 2

4

TCSC

3

9 7

Load A Load B

11

has been installed in the middle of one of these tie lines [17, 19].

5

6

3.2. Simulation results **Figure 6.** Schematic diagram of 10-machine, 39-bus system

Figure 6. Schematic diagram of 10-machine, 39-bus system

3.1. Study systems

1

G1

2

10

Figure 5. TCSC in a two-area 4-generator system

#### The effectiveness of the self-tuning fuzzy PI controller (STFPIC) has been studied through detailed nonlinear time **3.2. Simulation results**

**Parameters Ge GΔe Gu** Minimum range 0 0 0 Maximum range 0.5 1 1

**Parameter Value/Type**

The efficacy of the projected STFPIC has been validated on two different multimachine power systems: (a) two-area 4-machine system [16] and (b) 10-machine 39-bus system [16, 19]. The

The schematic diagram of the two-area 4-machine system is shown in Fig. 5. In this system, machines 1, 2 and 3, 4 form two different coherent groups. The three tie lines connect these two coherent areas. As shown in Fig. 5, a TCSC has been installed in the middle of one of these

has been assumed to be installed in the middle of the tie line connecting buses #39 and #36.

5 6 9 10 8 7

1 2 3 4

9 7

11

Area 1 Area 2

28 26

34 35

30

27

The one line diagram of the second study system of this work, i.e., the 10-machine 39-bus system is shown in Fig. 6. In this diagram, the generators are identified by their bus numbers

36

39

24

Load A Load B

has been installed in the middle of one of these tie lines [17, 19].

5 6

The schematic diagram of the two-area 4-machine system is shown in Fig. 1.5. In this system, machines 1, 2 and 3, 4 form two different coherent groups. The three tie lines connect these two coherent areas. As shown in Fig. 1.5, a TCSC

The one line diagram of the second study system of this work, i.e., the 10-machine 39-bus system is shown in Fig. 1.6. In this diagram, the generators are identified by their bus numbers to which they are connected. In this system, a TCSC

8

12 TCSC

6

23

The effectiveness of the self-tuning fuzzy PI controller (STFPIC) has been studied through detailed nonlinear time domain simulation studies for a three-phase, 5-cycle, solid short-circuit faults on both the test systems shown above. The short-circuit faults have been assumed to occur at t = 5 s. The simulation studies have been carried out in the MATLAB/SIMULINK environment [18]. For illustrating the efficacy of the fuzzy controllers developed in this work, results pertaining to two different situations are presented. These situations are: (a) study system with a TCSC

2221

4 5 7

29

9

3

4

G4

11

G3

Maximum generations 50 Population size 25 Mutation rate 0.1 Crossover operator Scattered

details of these two systems are presented in Section 3.

3.1. Study systems

1

G1

10

**Figure 5.** TCSC in a two-area 4-generator system

12 11

2

19

18

17 15

3.2. Simulation results

1

14

13

2

G2

Figure 5. TCSC in a two-area 4-generator system

8

16

31

3

Figure 6. Schematic diagram of 10-machine, 39-bus system

20

33

32

25

38 37

10

**Table 3.** Ranges for the different scaling factors

148 Fuzzy Logic - Tool for Getting Accurate Solutions

**Table 4.** Parameters used in genetic algorithm

**3. Case studies**

**3.1. Study systems**

tie lines [17, 19].

domain simulation studies for a three-phase, 5-cycle, solid short-circuit faults on both the test systems shown above. The short-circuit faults have been assumed to occur at t = 5 s. The simulation studies have been carried out in the MATLAB/SIMULINK environment [18]. For illustrating the efficacy of the fuzzy controllers developed in this work, results pertaining to two different situations are presented. These situations are: (a) study system with a TCSC The effectiveness of the self-tuning fuzzy PI controller (STFPIC) has been studied through detailed nonlinear time domain simulation studies for a three-phase, 5-cycle, solid short-circuit faults on both the test systems shown above. The short-circuit faults have been assumed to occur at t = 5 s. The simulation studies have been carried out in the MATLAB/SIMULINK environment [18]. For illustrating the efficacy of the fuzzy controllers developed in this work, results pertaining to two different situations are presented. These situations are: (a) study system with a TCSC controlled by FPIC and (b) study system with a TCSC controlled by STFPIC. For following figures, the rotor angles of the machines have been measured with respect to the Centre of Inertia (COI) reference [16].

### *3.2.1. Two-area 4-machine system*

For this system, initially the short-circuit fault has been assumed to occur at bus 9. The variations of the rotor angles of the two machines (machine 1 and machine 4) and active power flow in line 11–10 (P11-10) for the base case loading condition (the loading condition as described in [16, 21]) are displayed in Figs. 7 and 8, and 9(a), corresponding to scenarios (a) and (b), respectively. In Figs. 7– 9, the dotted lines show the variation of rotor angle with TCSC FPIC, whereas the variation of rotor angle with TCSC STFPIC is depicted with solid lines. For implementing STFPIC, K has been set equal to 3. From Figs. 7 to 8, and 9(a), it is observed that there is perceptible improvement in the performance of the system as the oscillations are damped earlier by the STFPIC proposed for TCSC. The variations of the TCSC reactance (XTCSC) are shown in Fig. 9(b) for situations (a) and (b).

To investigate the performance of the TCSC STFPIC controller at enhanced loading condition, simulation studies were carried out by increasing the system loads by 10% from the base case loading condition. The results are shown in Figs. 10 and 11, and 12, corresponding to scenarios (a) and (b), respectively. From Figs. 10 to 11 and 12(a), it is evident that at 10% higher loading, the TCSC STFPIC improves the system performance. Figure 12(b) shows the variation of the TCSC reactance for this case with TCSC FPIC and TCSC STFPIC. It can be observed from Figs. 9(b) and 12(b) that STFPIC has been able to improve the damping with smaller variation in XTCSC as compared to FPIC for the base case and 110% loading conditions respectively with fault at bus 9.The variations of α for fault at bus 9 are shown in Fig. 13, corresponding to both base case and 10% increased loading conditions. From these figures it is observed that for different loading conditions, the TCSC STFPIC always improves the system performance, showing the robustness of the controller.

The performance of the TCSC STFPIC has also been studied with faults at different locations for both base case and 10% increased loading conditions. The simulation results for faults at bus 8 are shown in Figs. 14– 19 with the variations of α depicted in Fig. 20. Similarly, the results corresponding to fault at bus 5 are shown in Figs. 21– 26 with the variations of α displayed in Fig. 27. From these figures, it is observed that irrespective of the fault location, the TCSC STFPIC always improves the system performance.

### *3.2.2. 10-machine 39-bus system*

In this system, initially the short-circuit fault has been assumed to occur at bus 24. From the fault simulation studies carried out at the base case loading condition (the loading condition as described in [16, 19]), it has been observed that the proposed TCSC STFPIC improved the system performance. Subsequently, a great number of fault studies have been carried out at several increased system loading situations to inspect the effectiveness of the developed STFPIC for improving the performance of the system. After all these studies, it has been found that the TCSC STFPIC helps to further increase the damping for the system. Only a few representative results are presented below to illustrate the effectiveness of the developed STFPIC in further enhancing the performance of the system under study.

controlled by FPIC and (b) study system with a TCSC controlled by STFPIC. For following figures, the rotor angles of

For this system, initially the short-circuit fault has been assumed to occur at bus 9. The variations of the rotor angles of the two machines (machine 1 and machine 4) and active power flow in line 11–10 (P11-10) for the base case loading condition (the loading condition as described in [16, 21]) are displayed in Figs. 1.7 and 1.8, and 1.9(a), corresponding to scenarios (a) and (b), respectively. In Figs. 1.7–1.9, the dotted lines show the variation of rotor angle with TCSC FPIC, whereas the variation of rotor angle with TCSC STFPIC is depicted with solid lines. For implementing STFPIC, K has been set equal to 3. From Figs. 1.7 to 1.8, and 1.9(a), it is observed that there is perceptible improvement in the performance of the system as the oscillations are damped earlier by the STFPIC proposed for TCSC. The variations of

To investigate the performance of the TCSC STFPIC controller at enhanced loading condition, simulation studies were carried out by increasing the system loads by 10% from the base case loading condition. The results are shown in Figs. 1.10 and 1.11, and 1.12, corresponding to scenarios (a) and (b), respectively. From Figs. 1.10 to 1.11 and 1.12(a), it is evident that at 10% higher loading, the TCSC STFPIC improves the system performance. Figure 1.12(b) shows the variation of the TCSC reactance for this case with TCSC FPIC and TCSC STFPIC. It can be observed from Figs. 1.9(b) and 1.12(b) that STFPIC has been able to improve the damping with smaller variation in XTCSC as compared to FPIC for the base case and 110% loading conditions respectively with fault at bus 9.The variations of α for fault at bus 9 are shown in Fig. 1.13, corresponding to both base case and 10% increased loading conditions. From these figures it is observed that for different loading conditions, the TCSC STFPIC always improves the system performance, showing

The performance of the TCSC STFPIC has also been studied with faults at different locations for both base case and

the machines have been measured with respect to the Centre of Inertia (COI) reference [16].

the TCSC reactance (XTCSC) are shown in Fig. 1.9(b) for situations (a) and (b).

3.2.1. Two-area 4-machine system

the robustness of the controller.

the TCSC STFPIC always improves the system performance.

Figure 7. Rotor angle of generator 1 with STFPIC for base case with fault at bus 9 **Figure 7.** Rotor angle of generator 1 with STFPIC for base case with fault at bus 9

*3.2.1. Two-area 4-machine system*

150 Fuzzy Logic - Tool for Getting Accurate Solutions

(XTCSC) are shown in Fig. 9(b) for situations (a) and (b).

showing the robustness of the controller.

*3.2.2. 10-machine 39-bus system*

STFPIC always improves the system performance.

For this system, initially the short-circuit fault has been assumed to occur at bus 9. The variations of the rotor angles of the two machines (machine 1 and machine 4) and active power flow in line 11–10 (P11-10) for the base case loading condition (the loading condition as described in [16, 21]) are displayed in Figs. 7 and 8, and 9(a), corresponding to scenarios (a) and (b), respectively. In Figs. 7– 9, the dotted lines show the variation of rotor angle with TCSC FPIC, whereas the variation of rotor angle with TCSC STFPIC is depicted with solid lines. For implementing STFPIC, K has been set equal to 3. From Figs. 7 to 8, and 9(a), it is observed that there is perceptible improvement in the performance of the system as the oscillations are damped earlier by the STFPIC proposed for TCSC. The variations of the TCSC reactance

To investigate the performance of the TCSC STFPIC controller at enhanced loading condition, simulation studies were carried out by increasing the system loads by 10% from the base case loading condition. The results are shown in Figs. 10 and 11, and 12, corresponding to scenarios (a) and (b), respectively. From Figs. 10 to 11 and 12(a), it is evident that at 10% higher loading, the TCSC STFPIC improves the system performance. Figure 12(b) shows the variation of the TCSC reactance for this case with TCSC FPIC and TCSC STFPIC. It can be observed from Figs. 9(b) and 12(b) that STFPIC has been able to improve the damping with smaller variation in XTCSC as compared to FPIC for the base case and 110% loading conditions respectively with fault at bus 9.The variations of α for fault at bus 9 are shown in Fig. 13, corresponding to both base case and 10% increased loading conditions. From these figures it is observed that for different loading conditions, the TCSC STFPIC always improves the system performance,

The performance of the TCSC STFPIC has also been studied with faults at different locations for both base case and 10% increased loading conditions. The simulation results for faults at bus 8 are shown in Figs. 14– 19 with the variations of α depicted in Fig. 20. Similarly, the results corresponding to fault at bus 5 are shown in Figs. 21– 26 with the variations of α displayed in Fig. 27. From these figures, it is observed that irrespective of the fault location, the TCSC

In this system, initially the short-circuit fault has been assumed to occur at bus 24. From the fault simulation studies carried out at the base case loading condition (the loading condition as described in [16, 19]), it has been observed that the proposed TCSC STFPIC improved the system performance. Subsequently, a great number of fault studies have been carried out at several increased system loading situations to inspect the effectiveness of the developed STFPIC for improving the performance of the system. After all these studies, it has been found that the TCSC STFPIC helps to further increase the damping for the system. Only a few representative results are presented below to illustrate the effectiveness of the developed

STFPIC in further enhancing the performance of the system under study.

0 5 10 15 20 25 30 35 40

(b) XTCSC

0 5 10 15 20 25 30 35 40

Figure 9. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 9

Time (sec.)

(a) Power flow in line 11-10

with TCSC STFPIC with TCSC FPIC

with TCSC FPIC with TCSC STFPIC

Figure 8. Rotor angle of generator 4 with STFPIC for base case with fault at bus 9 **Figure 8.** Rotor angle of generator 4 with STFPIC for base case with fault at bus 9

p.u.

0

0.5

p.u.

1

radian

Time (sec.)

Figure 8. Rotor angle of generator 4 with STFPIC for base case with fault at bus 9

δ4

with TCSC FPIC with TCSC STFPIC

Figure 9. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 9 **Figure 9.** Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 9

0 5 10 15 20 25 30 35 40 45 50

Time (sec.)

Figure 11. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 9

δ4

with TCSC FPIC with TCSC STFPIC

Figure 10. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 9 **Figure 10.** Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 9

radian

Time (sec.)

Figure 10. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 9

δ1

with TCSC FPIC with TCSC STFPIC

Figure 11. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 9 **Figure 11.** Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 9

0

0.05

0.1

0.15

radian

0.2

0.25

0.3

0.35

0 5 10 15 20 25 30 35 40

δ4

with TCSC FPIC with TCSC STFPIC

with TCSC STFPIC with TCSC FPIC

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

> with TCSC FPIC with TCSC STFPIC

Time (sec.)

(a) Power flow in line 11-10

0 5 10 15 20 25 30 35 40

(b) XTCSC

0 5 10 15 20 25 30 35 40

Time (sec.)

Figure 9. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 9 **Figure 9.** Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 9

δ1

0 10 20 30 40 50

δ4

0 5 10 15 20 25 30 35 40 45 50

Time (sec.)

Figure 11. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 9

Time (sec.)

Figure 10. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 9

**Figure 10.** Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 9

Figure 8. Rotor angle of generator 4 with STFPIC for base case with fault at bus 9

152 Fuzzy Logic - Tool for Getting Accurate Solutions

0

radian

0.05

0.1

0.15

radian

0.2

0.25

0.3

0.35

p.u.

p.u.

0 0.5 1 1.5

radian

Figure 12. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 9 (a) Base case **Figure 12.** Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 9

0 10 20 30 40 50 60

(b) 110% loading

0 10 20 30 40 50 60

Time (sec.)

Figure 13. Variation of α for base case and 110% loading with fault at bus 9

0

1

0

0.5

α

0.5

α

1

p.u.

p.u.

0 5 10 15 20 25 30 35 40 45 50

(b) XTCSC

with TCSC FPIC with TCSC STFPIC

Figure 12. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 9

with TCSC STFPIC with TCSC FPIC

Time (sec.)

(a) Power flow in line 11-10

Figure 13. Variation of α for base case and 110% loading with fault at bus 9 **Figure 13.** Variation of α for base case and 110% loading with fault at bus 9

0 5 10 15 20 25 30 35 40

δ4

with TCSC FPIC with TCSC STFPIC

Time (sec.)

Figure 15. Rotor angle of generator 4 with STFPIC for base case with fault at bus 8

Figure 14. Rotor angle of generator 1 with STFPIC for base case with fault at bus 8 **Figure 14.** Rotor angle of generator 1 with STFPIC for base case with fault at bus 8

radian

Time (sec.)

Figure 14. Rotor angle of generator 1 with STFPIC for base case with fault at bus 8

δ1

with TCSC FPIC with TCSC STFPIC

Figure 15. Rotor angle of generator 4 with STFPIC for base case with fault at bus 8 **Figure 15.** Rotor angle of generator 4 with STFPIC for base case with fault at bus 8

0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

radian

0 5 10 15 20 25 30 35 40 45 50

(b) XTCSC

with TCSC FPIC with TCSC STFPIC

Figure 12. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 9

with TCSC STFPIC with TCSC FPIC

0 5 10 15 20 25 30 35 40 45 50

Time (sec.)

(a) Base case

0 10 20 30 40 50 60

(b) 110% loading

0 10 20 30 40 50 60

Time (sec.)

δ1

with TCSC FPIC with TCSC STFPIC

0 5 10 15 20 25 30 35 40

Time (sec.)

Figure 14. Rotor angle of generator 1 with STFPIC for base case with fault at bus 8

δ4

with TCSC FPIC with TCSC STFPIC

0 5 10 15 20 25 30 35 40

Time (sec.)

Figure 15. Rotor angle of generator 4 with STFPIC for base case with fault at bus 8

Figure 13. Variation of α for base case and 110% loading with fault at bus 9 **Figure 13.** Variation of α for base case and 110% loading with fault at bus 9

(a) Power flow in line 11-10

0

1

0

0.06

radian

**Figure 14.** Rotor angle of generator 1 with STFPIC for base case with fault at bus 8

0.08

0.1

0.12

0.14

radian

0.16

0.18

0.2

0.22

0.24

0.5

α

0.5

α

1

p.u.

p.u.

Figure 16. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 8 δ1 **Figure 16.** Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 8

with TCSC FPIC with TCSC STFPIC

0 10 20 30 40 50 60

Time (sec.)

Figure 17. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 8

0.05

0.1

0.15

radian

0.2

0.25

p.u.

0.05 0.1

0

0 0.2 0.4 0.6 0.8 1

p.u.

0 5 10 15 20 25 30 35 40

(b) XTCSC

Time (sec.)

Figure 16. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 8

(a) Power flow in line 11-10

with TCSC STFPIC with TCSC FPIC

with TCSC FPIC with TCSC STFPIC

**Figure 17.** Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 8 Figure 17. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 8

0 10 20 30 40 50 60

(b) XTCSC

with TCSC FPIC with TCSC STFPIC

Figure 19. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 8

with TCSC STFPIC with TCSC FPIC

0 10 20 30 40 50 60

Time (sec.)

(a) Power flow in line 11-10

Figure 18. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 8 **Figure 18.** Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 8

0

p.u.

0.05

0.1

0

0.5

p.u.

1

0 10 20 30 40 50 60

δ4

with TCSC FPIC with TCSC STFPIC

Time (sec.)

Figure 18. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 8

radian

0 5 10 15 20 25 30 35 40

(b) XTCSC

0 5 10 15 20 25 30 35 40

Figure 16. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 8

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

Time (sec.)

δ1

0 10 20 30 40 50 60

0 10 20 30 40 50 60

Time (sec.)

Figure 18. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 8

**Figure 18.** Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 8

(a) Power flow in line 11-10

0 10 20 30 40 50 60

(b) XTCSC

with TCSC FPIC with TCSC STFPIC

Figure 19. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 8

with TCSC STFPIC with TCSC FPIC

0 10 20 30 40 50 60

Time (sec.)

Time (sec.)

δ4

**Figure 17.** Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 8 Figure 17. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 8

(a) Power flow in line 11-10

with TCSC STFPIC with TCSC FPIC

with TCSC FPIC with TCSC STFPIC

0 0.2 0.4 0.6 0.8 1

156 Fuzzy Logic - Tool for Getting Accurate Solutions

0.05

0

p.u.

0.05

0.1

0

0.5

p.u.

1

1.5

radian

0.1

0.15

radian

0.2

0.25

0.3

p.u.

0.05 0.1

0

p.u.

**Figure 19.** Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at Figure 19. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 8 bus 8

0 5 10 15 20 25 30 35 40

δ1

with TCSC FPIC with TCSC STFPIC

Time (sec.)

Figure 21. Rotor angle of generator 1 with STFPIC for base case with fault at bus 5

Figure 20. Variation of α for base case and 110% loading with fault at bus 8 **Figure 20.** Variation of α for base case and 110% loading with fault at bus 8

0.05

0.1

0.15

0.2

radian

0.25

0.3

0.35

0.2 0.4 0.6 0.8

α

0 0.2 0.4 0.6 0.8

α

0 10 20 30 40 50 60

(b) 110% loading

Time (sec.)

Figure 20. Variation of α for base case and 110% loading with fault at bus 8

(a) Base case

**Figure 21.** Rotor angle of generator 1 with STFPIC for base case with fault at bus 5 Figure 21. Rotor angle of generator 1 with STFPIC for base case with fault at bus 5

0 5 10 15 20 25 30 35 40

(b) XTCSC

0 5 10 15 20 25 30 35 40

Time (sec.)

(a) Power flow in line 11-10

with TCSC STFPIC with TCSC FPIC

with TCSC FPIC with TCSC STFPIC

Figure 23. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 5

Figure 22. Rotor angle of generator 4 with STFPIC for base case with fault at bus 5 **Figure 22.** Rotor angle of generator 4 with STFPIC for base case with fault at bus 5

0

p.u.

0.5

p.u.

1

with TCSC FPIC with TCSC STFPIC

Time (sec.)

Figure 22. Rotor angle of generator 4 with STFPIC for base case with fault at bus 5

δ4

radian

0 10 20 30 40 50 60

(b) 110% loading

0 10 20 30 40 50 60

δ1

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

0 5 10 15 20 25 30 35 40

Time (sec.)

δ4

0 5 10 15 20 25 30 35 40

Time (sec.)

with TCSC STFPIC with TCSC FPIC

with TCSC FPIC with TCSC STFPIC

Figure 23. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 5

Figure 22. Rotor angle of generator 4 with STFPIC for base case with fault at bus 5

**Figure 22.** Rotor angle of generator 4 with STFPIC for base case with fault at bus 5

(a) Power flow in line 11-10

0 5 10 15 20 25 30 35 40

(b) XTCSC

0 5 10 15 20 25 30 35 40

Time (sec.)

**Figure 21.** Rotor angle of generator 1 with STFPIC for base case with fault at bus 5 Figure 21. Rotor angle of generator 1 with STFPIC for base case with fault at bus 5

Time (sec.)

Figure 20. Variation of α for base case and 110% loading with fault at bus 8

(a) Base case

0 0.2 0.4 0.6 0.8

0 0.2 0.4 0.6 0.8

158 Fuzzy Logic - Tool for Getting Accurate Solutions

0.05

0

p.u.

0.5

p.u.

1

1.5

radian

0.1

0.15

0.2

radian

0.25

0.3

0.35

0.4

α

α

**Figure 23.** Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 5 Figure 23. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for base case with fault at bus 5

0 5 10 15 20 25 30 35 40 45 50

δ4

with TCSC FPIC with TCSC STFPIC

Time (sec.)

Figure 25. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 5

Figure 24. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 5 **Figure 24.** Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 5

radian

0.05

0.1

0.15

0.2

0.25

radian

0.3

0.35

0.4

0.45

Time (sec.)

Figure 24. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 5

δ1

with TCSC FPIC with TCSC STFPIC

Figure 25. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 5 **Figure 25.** Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 5

Figure 26. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 5 (a) Base case **Figure 26.** Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 5

0 10 20 30 40 50 60

(b) 110% loading

0 10 20 30 40 50 60

Time (sec.)

In this system, initially the short-circuit fault has been assumed to occur at bus 24. From the fault simulation studies carried out at the base case loading condition (the loading condition as described in [16, 19]), it has been observed that the proposed TCSC STFPIC improved the system performance. Subsequently, a great number of fault studies have been carried out at several increased system loading situations to inspect the effectiveness of the developed STFPIC for improving the performance of the system. After all these studies, it has been found that the TCSC STFPIC helps to further increase the damping for the system. Only a few representative results are presented below to illustrate the

The performance of the TCSC STFPIC at 160% loading condition (w.r.t. the base case loading condition as described in [16]) is shown in Figs. 1.28–1.31. From these figures it is observed that at 160% loading condition, substantial improvement in the system performance is achieved by the proposed TCSC STFPIC. For implementing STFPIC, K has been set equal to 10. When the system loading level is further increased to 175% of the base case loading condition, the proposed TCSC STFPIC is able to improve the system performance significantly as illustrated in Figs. 1.32 and 1.33. It

effectiveness of the developed STFPIC in further enhancing the performance of the system under study.

Figure 27. Variation of α for base case and 110% loading with fault at bus 5

3.2.2. 10-machine 39-bus system

0

1

0

0.5

α

0.5

α

1

with TCSC STFPIC with TCSC FPIC

with TCSC FPIC with TCSC STFPIC

Figure 26. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 5

0 10 20 30 40 50 60

(b) XTCSC

0 10 20 30 40 50 60

Time (sec.)

(a) Power flow in line 11-10

Figure 27. Variation of α for base case and 110% loading with fault at bus 5 **Figure 27.** Variation of α for base case and 110% loading with fault at bus 5

0

0

0.05 0.1

p.u.

0.5

p.u.

1

1.5

0 5 10 15 20 25 30 35 40 45 50

δ4

0 5 10 15 20 25 30 35 40 45 50

Time (sec.)

(a) Power flow in line 11-10

0 10 20 30 40 50 60

(b) XTCSC

0 10 20 30 40 50 60

Time (sec.)

(a) Base case

**Figure 26.** Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at

0 10 20 30 40 50 60

(b) 110% loading

0 10 20 30 40 50 60

Time (sec.)

Figure 27. Variation of α for base case and 110% loading with fault at bus 5

3.2.2. 10-machine 39-bus system

Figure 25. Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 5 **Figure 25.** Rotor angle of generator 4 with STFPIC for 110% loading with fault at bus 5

Time (sec.)

Figure 24. Rotor angle of generator 1 with STFPIC for 110% loading with fault at bus 5

δ1

with TCSC FPIC with TCSC STFPIC

> with TCSC FPIC with TCSC STFPIC

with TCSC STFPIC with TCSC FPIC

with TCSC FPIC with TCSC STFPIC

Figure 26. Active power flow in line 11-10 and TCSC capacitive reactance with STFPIC for 110% loading with fault at bus 5

In this system, initially the short-circuit fault has been assumed to occur at bus 24. From the fault simulation studies carried out at the base case loading condition (the loading condition as described in [16, 19]), it has been observed that the proposed TCSC STFPIC improved the system performance. Subsequently, a great number of fault studies have been carried out at several increased system loading situations to inspect the effectiveness of the developed STFPIC for improving the performance of the system. After all these studies, it has been found that the TCSC STFPIC helps to further increase the damping for the system. Only a few representative results are presented below to illustrate the

The performance of the TCSC STFPIC at 160% loading condition (w.r.t. the base case loading condition as described in [16]) is shown in Figs. 1.28–1.31. From these figures it is observed that at 160% loading condition, substantial improvement in the system performance is achieved by the proposed TCSC STFPIC. For implementing STFPIC, K has been set equal to 10. When the system loading level is further increased to 175% of the base case loading condition, the proposed TCSC STFPIC is able to improve the system performance significantly as illustrated in Figs. 1.32 and 1.33. It

effectiveness of the developed STFPIC in further enhancing the performance of the system under study.

0

160 Fuzzy Logic - Tool for Getting Accurate Solutions

0

0

1

0

0.5

α

0.5

α

bus 5

1

0 0.05 0.1

p.u.

0.5

p.u.

1

1.5

radian

0.05

0.1

0.15

0.2

0.25

radian

0.3

0.35

0.4

0.45

3.2.2. 10-machine 39-bus system In this system, initially the short-circuit fault has been assumed to occur at bus 24. From the fault simulation studies carried out at the base case loading condition (the loading condition as described in [16, 19]), it has been observed that the proposed TCSC STFPIC improved the system performance. Subsequently, a great number of fault studies have been carried out at several increased system loading situations to inspect the effectiveness of the developed STFPIC for improving the performance of the system. After all these studies, it has been found that the TCSC STFPIC helps to further increase the damping for the system. Only a few representative results are presented below to illustrate the effectiveness of the developed STFPIC in further enhancing the performance of the system under study. The performance of the TCSC STFPIC at 160% loading condition (w.r.t. the base case loading condition as described in [16]) is shown in Figs. 28– 3 From these figures it is observed that at 160% loading condition, substantial improvement in the system performance is achieved by the proposed TCSC STFPIC. For implementing STFPIC, K has been set equal to 10. When the system loading level is further increased to 175% of the base case loading condition, the proposed TCSC STFPIC is able to improve the system performance significantly as illustrated in Figs. 32 and 33. It can be noticed from Figs. 31(b) and 33(b) that STFPIC has been able to improve the damping with smaller variation in XTCSC as compared to FPIC for 160% and 175% loading conditions, respectively, with fault at bus 24. The variations of α for fault at bus 24 are shown in Fig. 34, corresponding to 160% and 175% loading conditions.

The performance of the TCSC STFPIC at 160% loading condition (w.r.t. the base case loading condition as described in [16]) is shown in Figs. 1.28–1.31. From these figures it is observed that at 160% loading condition, substantial improvement in the system performance is achieved by the proposed TCSC STFPIC. For implementing STFPIC, K has been set equal to 10. When the system loading level is further increased to 175% of the base case loading condition, the proposed TCSC STFPIC is able to improve the system performance significantly as illustrated in Figs. 1.32 and 1.33. It Additional fault simulation studies have also been carried out with faults at different locations, for various loading conditions, to investigate the robustness of the proposed control scheme. For all the simulation studies carried out in this work, the TCSC STFPIC has improved the damping of the system (as compared to the damping obtained with FPIC). Some representative results obtained at 175% loading condition are shown in Figs. 35– 38. Figures 35 and 36 show the results for fault at bus 38, while the results for fault at bus 23 are shown in Figs. 37 and 38. These results amply demonstrate that the TCSC STFPIC helps to enhance the damping capability of the system quite significantly. The variations of α for fault at bus 38 and 23 corresponding to 175% loading conditions are shown in Fig. 39. Variation of the rotor angle of generator 3 only has been shown for 175% loading condition.

can be noticed from Figs. 1.31(b) and 1.33(b) that STFPIC has been able to improve the damping with smaller variation in XTCSC as compared to FPIC for 160% and 175% loading conditions, respectively, with fault at bus 24. The variations of

α for fault at bus 24 are shown in Fig. 1.34, corresponding to 160% and 175% loading conditions.

can be noticed from Figs. 1.31(b) and 1.33(b) that STFPIC has been able to improve the damping with smaller variation in XTCSC as compared to FPIC for 160% and 175% loading conditions, respectively, with fault at bus 24. The variations of

Additional fault simulation studies have also been carried out with faults at different locations, for various loading conditions, to investigate the robustness of the proposed control scheme. For all the simulation studies carried out in this work, the TCSC STFPIC has improved the damping of the system (as compared to the damping obtained with FPIC). Some representative results obtained at 175% loading condition are shown in Figs. 1.35–1.38. Figures 1.35 and 1.36 show the results for fault at bus 38, while the results for fault at bus 23 are shown in Figs. 1.37 and 1.38. These results amply demonstrate that the TCSC STFPIC helps to enhance the damping capability of the system quite significantly. The variations of α for fault at bus 38 and 23 corresponding to 175% loading conditions are shown in Fig.

Additional fault simulation studies have also been carried out with faults at different locations, for various loading conditions, to investigate the robustness of the proposed control scheme. For all the simulation studies carried out in this work, the TCSC STFPIC has improved the damping of the system (as compared to the damping obtained with FPIC). Some representative results obtained at 175% loading condition are shown in Figs. 1.35–1.38. Figures 1.35 and 1.36 show the results for fault at bus 38, while the results for fault at bus 23 are shown in Figs. 1.37 and 1.38. These

significantly. The variations of α for fault at bus 38 and 23 corresponding to 175% loading conditions are shown in Fig.

with TCSC FPIC

1.39. Variation of the rotor angle of generator 3 only has been shown for 175% loading condition.

α for fault at bus 24 are shown in Fig. 1.34, corresponding to 160% and 175% loading conditions.

1.39. Variation of the rotor angle of generator 3 only has been shown for 175% loading condition.

(a) δ1

Figure 28. Rotor angles of generator 1 and 2 with STFPIC for 160% loading with fault at bus 24 **Figure 28.** Rotor angles of generator 1 and 2 with STFPIC for 160% loading with fault at bus 24 Figure 28. Rotor angles of generator 1 and 2 with STFPIC for 160% loading with fault at bus 24

Figure 29. Rotor angles of generator 7 and 8 with STFPIC for 160% loading with fault at bus 24 **Figure 29.** Rotor angles of generator 7 and 8 with STFPIC for 160% loading with fault at bus 24

Figure 30. Rotor angles of generator 9 and 10 with STFPIC for 160% loading with fault at bus 24 **Figure 30.** Rotor angles of generator 9 and 10 with STFPIC for 160% loading with fault at bus 24 Time (sec.)

8

can be noticed from Figs. 1.31(b) and 1.33(b) that STFPIC has been able to improve the damping with smaller variation in XTCSC as compared to FPIC for 160% and 175% loading conditions, respectively, with fault at bus 24. The variations of

α for fault at bus 24 are shown in Fig. 1.34, corresponding to 160% and 175% loading conditions.

can be noticed from Figs. 1.31(b) and 1.33(b) that STFPIC has been able to improve the damping with smaller variation in XTCSC as compared to FPIC for 160% and 175% loading conditions, respectively, with fault at bus 24. The variations of

Additional fault simulation studies have also been carried out with faults at different locations, for various loading conditions, to investigate the robustness of the proposed control scheme. For all the simulation studies carried out in this work, the TCSC STFPIC has improved the damping of the system (as compared to the damping obtained with FPIC). Some representative results obtained at 175% loading condition are shown in Figs. 1.35–1.38. Figures 1.35 and 1.36 show the results for fault at bus 38, while the results for fault at bus 23 are shown in Figs. 1.37 and 1.38. These results amply demonstrate that the TCSC STFPIC helps to enhance the damping capability of the system quite significantly. The variations of α for fault at bus 38 and 23 corresponding to 175% loading conditions are shown in Fig.

Additional fault simulation studies have also been carried out with faults at different locations, for various loading conditions, to investigate the robustness of the proposed control scheme. For all the simulation studies carried out in this work, the TCSC STFPIC has improved the damping of the system (as compared to the damping obtained with FPIC). Some representative results obtained at 175% loading condition are shown in Figs. 1.35–1.38. Figures 1.35 and 1.36 show the results for fault at bus 38, while the results for fault at bus 23 are shown in Figs. 1.37 and 1.38. These results amply demonstrate that the TCSC STFPIC helps to enhance the damping capability of the system quite significantly. The variations of α for fault at bus 38 and 23 corresponding to 175% loading conditions are shown in Fig.

α for fault at bus 24 are shown in Fig. 1.34, corresponding to 160% and 175% loading conditions.

1.39. Variation of the rotor angle of generator 3 only has been shown for 175% loading condition.

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

1.39. Variation of the rotor angle of generator 3 only has been shown for 175% loading condition.

0 5 10 15 20 25 30 35 40 45 50

0 5 10 15 20 25 30 35 40 45 50

(b) δ2

(a) δ1

(b) δ2

0 5 10 15 20 25 30 35 40 45 50

Figure 28. Rotor angles of generator 1 and 2 with STFPIC for 160% loading with fault at bus 24

0 5 10 15 20 25 30 35 40 45 50

Time (sec.)

with TCSC FPIC with TCSC STFPIC

> with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

Figure 28. Rotor angles of generator 1 and 2 with STFPIC for 160% loading with fault at bus 24

Time (sec.)

(a) δ7

0 5 10 15 20 25 30 35 40 45 50

(b) δ8

0 5 10 15 20 25 30 35 40 45 50

(b) δ8

0 5 10 15 20 25 30 35 40 45 50

Figure 29. Rotor angles of generator 7 and 8 with STFPIC for 160% loading with fault at bus 24

Figure 29. Rotor angles of generator 7 and 8 with STFPIC for 160% loading with fault at bus 24 **Figure 29.** Rotor angles of generator 7 and 8 with STFPIC for 160% loading with fault at bus 24

0 5 10 15 20 25 30 35 40 45 50

Time (sec.)

Time (sec.)

(a) δ7

**Figure 28.** Rotor angles of generator 1 and 2 with STFPIC for 160% loading with fault at bus 24

(a) δ1

0.2

0

radian

radian

radian

radian

0

0

0.5

0.5

0

0

0.2

0.2

radian

radian

0

0.2

0

0.2

162 Fuzzy Logic - Tool for Getting Accurate Solutions

radian

radian

(a) Power flow in line 39-36

Figure 30. Rotor angles of generator 9 and 10 with STFPIC for 160% loading with fault at bus 24

**Figure 31.** Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 160% loading with fault at Figure 31. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 160% loading with fault at bus 24 bus 24

radian

δ3

Figure 32. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 24 **Figure 32.** Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 24

10

(a) Power flow in line 39-36

Figure 32. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 24

Time (sec.)

with TCSC FPIC

**Figure 33.** Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at Figure 33. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 24 bus 24

Figure 34. Variation of α for 160% and 175% loading with fault at bus 24 **Figure 34.** Variation of α for 160% and 175% loading with fault at bus 24 Figure 34. Variation of α for 160% and 175% loading with fault at bus 24

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

Time (sec.)

δ3

δ3

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

Time (sec.)

Figure 32. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 24

**Figure 32.** Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 24

(a) Power flow in line 39-36

Figure 32. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 24

(a) Power flow in line 39-36

0 10 20 30 40 50 60 70 80

(b) XTCSC

0 10 20 30 40 50 60 70 80

(b) XTCSC

0 10 20 30 40 50 60 70 80

Time (sec.)

with TCSC FPIC with TCSC STFPIC

> with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

Figure 33. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 24

**Figure 33.** Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at Figure 33. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 24

with TCSC FPIC with TCSC STFPIC

0 10 20 30 40 50 60 70 80

Time (sec.)

0

p.u.

p.u.

bus 24

0.01 0.02

0

p.u.

0

p.u.

10

5

5

10

radian

radian

0

0.1

0

0.1

164 Fuzzy Logic - Tool for Getting Accurate Solutions

Figure 35. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 38

0 10 20 30 40 50 60 70 80 Time (sec.) **Figure 35.** Rotor angle of generator 3 for 175% loading with STFPIC for fau Figure 35. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 38 lt at bus 38

0.1

radian

Figure 36. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 38 δ3 **Figure 36.** Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 38 0 10 20 30 40 50 60 70 80 -0.02 Time (sec.)

Figure 36. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 38

Time (sec.)

Figure 37. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 23

Figure 37. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 23 **Figure 37.** Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 23

0 10 20 30 40 50 60 70 80

(b) XTCSC

0 10 20 30 40 50 60 70 80

(b) XTCSC

(a) Power flow in line 39-36

with TCSC FPIC with TCSC STFPIC

Figure 36. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 38

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

> with TCSC FPIC with TCSC STFPIC

with TCSC FPIC with TCSC STFPIC

0 10 20 30 40 50 60 70 80

Time (sec.)

δ3

**Figure 36.** Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at

0 10 20 30 40 50 60 70 80

Time (sec.)

δ3

Figure 36. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 38

0 10 20 30 40 50 60 70 80

Time (sec.)

Figure 37. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 23

Figure 37. Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 23 **Figure 37.** Rotor angle of generator 3 for 175% loading with STFPIC for fault at bus 23

0 10 20 30 40 50 60 70 80

Time (sec.)

(a) Power flow in line 39-36

p.u.

p.u.

radian

radian

0

0.05 0.1

0

0.05

0.1

0 0.01 0.02

0

5

p.u.

bus 38

0

10

p.u.

5

10

166 Fuzzy Logic - Tool for Getting Accurate Solutions

Figure 38. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 23 (a) Fault at bus 38 **Figure 38.** Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 23 0 10 20 30 40 50 60 70 80 Time (sec.)

cases involving three-phase, 5-cycle, solid short-circuit faults have been investigated on both the study systems discussed earlier, for different loading conditions as well as different fault locations. From the simulation results, it has

Figure 38. Active power flow in line 39-36 and TCSC capacitive reactance with STFPIC for 175% loading with fault at bus 23

In this scheme, the output scaling factor of the FPIC is modulated on-line by a gain updating factor (α) whose value is determined by a second fuzzy logic scheme. Hence, the output scaling factor of STFPIC does not remain fixed while

the controller is in operation, rather it is modified at each sampling instant by a gain updating factor "α."

In this chapter, a methodology has been discussed for designing an adaptive FPIC using self-tuning mechanism (STFPIC). The simulation studies have been carried out in MATLAB/SIMULINK environment. A large number of fault cases involving three-phase, 5-cycle, solid short-circuit faults have been investigated on both the study systems discussed earlier, for different loading conditions as well as different fault locations. From the simulation results, it has

In this scheme, the output scaling factor of the FPIC is modulated on-line by a gain updating factor (α) whose value is determined by a second fuzzy logic scheme. Hence, the output scaling factor of STFPIC does not remain fixed while

been observed that the proposed STFPIC for TCSC improves the system stability significantly.

the controller is in operation, rather it is modified at each sampling instant by a gain updating factor "α."

been observed that the proposed STFPIC for TCSC improves the system stability significantly.

In this chapter, a methodology has been discussed for designing an adaptive FPIC using self-tuning mechanism (STFPIC). The simulation studies have been carried out in MATLAB/SIMULINK environment. A large number of fault Figure 39. Variation of α for 175% loading with fault at bus 38 and 23 **Figure 39.** Variation of α for 175% loading with fault at bus 38 and 23

4. Conclusion

0.6 0.8

### **4. Conclusion**

In this chapter, a methodology has been discussed for designing an adaptive FPIC using selftuning mechanism (STFPIC). The simulation studies have been carried out in MATLAB/ SIMULINK environment. A large number of fault cases involving three-phase, 5-cycle, solid short-circuit faults have been investigated on both the study systems discussed earlier, for different loading conditions as well as different fault locations. From the simulation results, it has been observed that the proposed STFPIC for TCSC improves the system stability signifi‐ cantly.

In this scheme, the output scaling factor of the FPIC is modulated on-line by a gain updating factor (α) whose value is determined by a second fuzzy logic scheme. Hence, the output scaling factor of STFPIC does not remain fixed while the controller is in operation, rather it is modified at each sampling instant by a gain updating factor "α."

The effectiveness of the developed STFPIC has been studied through detailed nonlinear fault simulation studies on both the test systems. The same fault cases have also been studied with FPIC and the performances obtained by STFPIC have been compared to those obtained by FPIC. From the comparative simulation results, it can be observed that the proposed STFPIC for TCSC improves the system damping further (as compared to the system damping obtained by FPIC).

The STFPIC, which comprises of two fuzzy logic blocks, requires increased computational time and memory for implementation. Therefore, it would be advantageous to reduce the size of the rule base so that the requirement of computational time and memory for implementation is reduced.

The performances of FPIC and STFPIC discussed in this chapter have been tested with predesigned scaling factors. However, in real life, the operating point in the system may vary continuously, thereby making it almost impossible to predesign the scaling factors. Thus, it is necessary to determine the scaling factors on-line based on some suitable measurements. In future, such a scheme for on-line determination of the scaling factors will be described.

The proposed self-tuning philosophy may possibly be applied for the tuning of input SFs or for tuning of both input and output SFs simultaneously, which may lead to superior perform‐ ances of the FLCs.

The efficacy and suitability of the proposed techniques can be explored further by applying it to larger power systems for different operating conditions.

### **Author details**

Salman Hameed\*

Address all correspondence to<EMAIL_ADDRESS>
Department of Electrical Engineering, Aligarh Muslim University, Aligarh, India

### **References**

**4. Conclusion**

168 Fuzzy Logic - Tool for Getting Accurate Solutions

cantly.

by FPIC).

is reduced.

ances of the FLCs.

**Author details**

Salman Hameed\*

In this chapter, a methodology has been discussed for designing an adaptive FPIC using selftuning mechanism (STFPIC). The simulation studies have been carried out in MATLAB/ SIMULINK environment. A large number of fault cases involving three-phase, 5-cycle, solid short-circuit faults have been investigated on both the study systems discussed earlier, for different loading conditions as well as different fault locations. From the simulation results, it has been observed that the proposed STFPIC for TCSC improves the system stability signifi‐

In this scheme, the output scaling factor of the FPIC is modulated on-line by a gain updating factor (α) whose value is determined by a second fuzzy logic scheme. Hence, the output scaling factor of STFPIC does not remain fixed while the controller is in operation, rather it is modified

The effectiveness of the developed STFPIC has been studied through detailed nonlinear fault simulation studies on both the test systems. The same fault cases have also been studied with FPIC and the performances obtained by STFPIC have been compared to those obtained by FPIC. From the comparative simulation results, it can be observed that the proposed STFPIC for TCSC improves the system damping further (as compared to the system damping obtained

The STFPIC, which comprises of two fuzzy logic blocks, requires increased computational time and memory for implementation. Therefore, it would be advantageous to reduce the size of the rule base so that the requirement of computational time and memory for implementation

The performances of FPIC and STFPIC discussed in this chapter have been tested with predesigned scaling factors. However, in real life, the operating point in the system may vary continuously, thereby making it almost impossible to predesign the scaling factors. Thus, it is necessary to determine the scaling factors on-line based on some suitable measurements. In future, such a scheme for on-line determination of the scaling factors will be described.

The proposed self-tuning philosophy may possibly be applied for the tuning of input SFs or for tuning of both input and output SFs simultaneously, which may lead to superior perform‐

The efficacy and suitability of the proposed techniques can be explored further by applying it

Department of Electrical Engineering, Aligarh Muslim University, Aligarh, India

at each sampling instant by a gain updating factor "α."

to larger power systems for different operating conditions.

Address all correspondence to<EMAIL_ADDRESS>

[16] K. R. Padiyar, *Power System Dynamics - Stability and Control*, Interline Publishing Ltd.,

[17] B. Chowdhury, R. Majumder and B. C. Pal, "Application of multiple-model adaptive control strategy for robust damping of interarea oscillations in power system", IEEE Transactions on Control Systems Technology, vol. 12, no. 5, September 2004, pp.

[19] S. Hameed, "A self-tuning fuzzy PI controller for TCSC to improve power system

[20] S. Hameed, "Power system stability enhancement using reduced rule base self-tun‐

[21] S. Hameed, "Reduced rule base self-tuning fuzzy PI controller for TCSC", Int J Elect

[18] MATLAB/SIMULINK Software, Version 7.0.1, Release 14, The Math Works Inc.

ing fuzzy PI controller for TCSC", IEEE PES T&D, 2010, 04/2010

Bangalore, India 1996.

170 Fuzzy Logic - Tool for Getting Accurate Solutions

stability", Elect Power Sys Res, 10/2008

Power Energy Sys, 11/2010

727-736.

### *Edited by Elmer P. Dadios*

This book is a collection of chapters, concerning the developments within the Fuzzy Logic field of study. The book includes scholarly contributions by various authors pertinent to Fuzzy Logic. Each contribution comes as a separate chapter complete in itself but directly related to the books topics and objectives. The target audience comprises scholars and specialists in the field.

Fuzzy Logic - Tool for Getting Accurate Solutions

Fuzzy Logic

Tool for Getting Accurate Solutions

*Edited by Elmer P. Dadios*

Photo by mjaud / iStock


**4.2 Management practices that could be adopted in the dairy industries**

## **4.3 Ensuring the production of beef and milk products that are free of antibiotic residues**

In the developed countries such as the USA, most dairy farmers do accept responsibility for the safety of the milk and beef produced from their farms [22]. The linkage between farm production practices and the quality of processed products could however be weak.

In order to ensure the production of beef and milk products that are free of antibiotic residues, the beef and dairy cattle farmers should adhere to the antibiotic drugs withdrawal times as specified on the label use of the drug manufacturer [27].

Again, meat and milk samples should be collected from individual the beef and dairy animals and also from the milk bulk tanks and tested for presence of antibiotic residues. The observation of the antibiotic treatments withdrawal period specified is very important as this could dictate the need to discard milk or withhold the cattle from slaughter in order to ensure drug residues are below the determined maximum residue limit allowed by the food and drug administration (FDA) after an animal has received an antibiotic treatment [28]. These previous researchers [28] emphasized that it is important to ensure that meat, milk and milk products are of high quality, safe and free of antibiotic residues before being sent out for human consumption and these could go a long way in enhancing food safety and food security.


*3.3. The Application of FAHP for Weight Calculation*

*3.3. The Application of FAHP for Weight Calculation* After defining the five sustainable project criteria, as shown in the previous subsection, the first step in determining the priority weights of these criteria is collecting the opinions of experts in sustainability and sustainable development regarding the relative importance of these criteria in sustainable project selection. In this research, a number of literature publications related to sustainable project selection and sustainable development as well as some prominent project management literature covering the chosen criteria were selected and evaluated, as part of the literature review for this research, to serve as the voice of experts in determining preferences among the five different criteria shown in Table 1. These studies were closely reviewed in an effort to determine the relative importance of these criteria and preference patterns, as presented by the After defining the five sustainable project criteria, as shown in the previous subsection, the first step in determining the priority weights of these criteria is collecting the opinions of experts in sustainability and sustainable development regarding the relative importance of these criteria in sustainable project selection. In this research, a number of literature publications related to sustainable project selection and sustainable development as well as some prominent project management literature covering the chosen criteria were selected and evaluated, as part of the literature review for this research, to serve as the voice of experts in determining preferences among the five different criteria shown in Table 1. These studies were closely reviewed in an effort to determine the relative importance of these criteria and preference patterns, as presented by the authors of these publications. The list of the chosen literature publications is shown in Table 2.

authors of these publications. The list of the chosen literature publications is shown in Table 2.

**Expert Source(s)** E1 Malik et al. [20] E2 Alyamani et al. [10] E3 Sabaghi et al. [17]

E5 Chen et al. [33] E6 Wang et al. [28] E7 Işik and Aladağ [34] E8 Hatefi and Tamošaitienė [16]

**Table 2.** Selected expert literature used for the evaluation of criteria.

**Table 2.** Selected expert literature used for the evaluation of criteria.

The second step in determining the priority weights of the five sustainable project criteria is utilizing the expert opinions from the literature in Table 2 based on the linguistic variables and triangular fuzzy numbers (TFNs), shown in Table 3, as presented by Ballı and Koruko˘glu [25]. In this step, expert opinions are gathered from the literature and translated into the linguistic variables. After creating the pairwise comparison matrix representing the opinions of each of the ten experts shown in Table 1 using the linguistic variables, these ten matrices are then combined to form the combined pairwise comparison matrix shown in Table 4.

**Table 3.** Linguistic variables and triangular fuzzy number scale.

Source: adapted from Ballı and Koruko˘glu [25].

**Table 4.** Pairwise comparison matrix using linguistic variables.

**Table 4.** *Cont.*

These linguistic variables in the combined matrix are then further translated into the corresponding triangular fuzzy numbers (TFNs) and reciprocal TFNs based on the scale shown in Table 3, resulting in the combined TFN pairwise comparison matrix, shown in Table 5.

**Table 5.** Pairwise comparison matrix using TFNs.

**Table 5.** *Cont.*

Once the TFN pairwise comparison matrix is created, as shown above, it can be used to calculate the weight of importance for the five criteria. This calculation is performed in three main steps. The first step is to combine the fuzzy pairwise comparison from all ten experts for each of the five criteria. This can be done by calculating the geometric mean of the experts' opinions. To calculate the fuzzy geometric mean, the geometric mean method introduced by Buckley [37] is used leading to the fuzzy geometric mean pairwise comparison matrix shown in Table 6.

**Table 6.** Fuzzy geometric mean pairwise comparison matrix.

The second step in calculating the criteria weights of importance is determining the fuzzy relative importance weight or the fuzzy synthetic extent of each of the five criteria. To do that, the extent analysis method introduced by Chang [38] is applied in this research, as shown in Equations (2–5). Let *G* = *g*1, *g*2, *g*3, . . . , *gn* be a goal set. Each criterion is taken and the extent analysis for each goal *gi* is performed, respectively [25,39]. Accordingly, the *m* extent value for each criterion is obtained as follows: *M*1 *gi* , *M*2 *gi* , *M*3 *gi* , . . . , *Mm gi* , where *gi* (*i* = 1, 2, 3, . . . , *n*) is the goal set and *M j gi* (*j* = 1, 2, 3, . . . , *m*) are all TFNs. The value of the fuzzy synthetic extent (*Si* ) with respect to the *i*th criterion is defined as shown in Equation (2).

$$S\_{\bar{i}} = \sum\_{j=1}^{m} M\_{\mathcal{G}i}^{j} \otimes \left[ \sum\_{i=1}^{n} \sum\_{j=1}^{m} M\_{\mathcal{G}i}^{j} \right]^{-1} \tag{2}$$

In order to calculate P*m j*=1 *M j gi* , a fuzzy addition operation of the *m* extent is used for a certain matrix, as shown in Equation (3). This can be done following the addition of the fuzzy number process shown in Sun [27].

$$\sum\_{j=1}^{m} M\_{\mathcal{G}i}^{j} = \left(\sum\_{j=1}^{m} l\_{j\prime} \sum\_{j=1}^{m} m\_{j\prime} \sum\_{j=1}^{m} u\_{j}\right) \tag{3}$$

where the variables *l*, *m*, and *u* indicate the lowest possible value, the modal or most likely value, and the upper or highest possible value, respectively, as explained earlier in this research. The next logical operation is to calculate P*n i*=1 P*m j*=1 *M j gi* by performing another fuzzy addition operation of *M j gi* (*j* = 1, 2, 3, . . . , *m*), as shown in Equation (4).

$$\sum\_{i=1}^{n}\sum\_{j=1}^{m}M\_{\mathcal{G}i}^{j} = \left(\sum\_{i=1}^{n}l\_{i\prime}\sum\_{i=1}^{n}m\_{i\prime}\sum\_{i=1}^{n}u\_{i}\right) \tag{4}$$

Finally, P*n i*=1 P*m j*=1 *M j gi* −1 is determined by calculating the inverse of the vector above as shown in Equation (5).

$$\left[\sum\_{i=1}^{n}\sum\_{j=1}^{m}M\_{\mathcal{G}i}^{j}\right]^{-1} = \left(\frac{1}{\sum\_{i=1}^{n}u\_{i}}, \frac{1}{\sum\_{i=1}^{n}m\_{i}}, \frac{1}{\sum\_{i=1}^{n}l\_{i}}\right) \tag{5}$$

Equations (2)–(5) are now applied to the TFNs obtained in this research. To determine the fuzzy synthetic extent to the criteria chosen in this research, the P*m j*=1 *M j gi* value is first calculated for each row of the matrix shown in Table 6. For example, for C1:

C1 = (1 + 1.676 + 1.446 + 4.143 + 3.187, 1 + 2.647 + 2.125 + 6.221 + 4.904, 1 + 3.657 + 3.071 + 8.262 + 7.020)

C1 = (11.452, 16.897, 23.010)

Accordingly, the P*n i*=1 P*m j*=1 *M j gi* value is calculated for each of the five criteria in Table 6 by applying Equation (4) as follows:

 $\sum\_{i=1}^{n} \sum\_{j=1}^{m} M\_{\S i}^{j} = (11.452, 16.897, 23.010) \oplus (4.813, 6.883, 9.404) \oplus (4.760, 6.457, 8.915) \oplus (2.425, 3.205, 4.302) \oplus (2.425, 3.074, 4.345)$   $\oplus (2.425, 3.205, 4.345) \oplus (2.425, 3.6516, 4.9.976)$

Based on that, the reciprocal value hP*n i*=1 P*m j*=1 *M j gi* i−1 is calculated by applying Equation (5) as follows:

$$\left[\sum\_{i=1}^{n}\sum\_{j=1}^{m}M\_{\mathbb{S}\_{i}}^{j}\right]^{-1} = \left(\frac{1}{49.976}, \frac{1}{36.516}, \frac{1}{25.862}\right) = (0.020, 0.027, 0.039)$$

Finally, the value of the fuzzy synthetic extent (*Si* ) with respect to the *i*th criterion is calculated for each criterion, as shown in Equation (2). For example, the value of the fuzzy synthetic extent for the first criterion *S*1 is calculated as follows:

$$S\_1 = (11.452, 16.897, 23.010) \text{ @ } (0.020, 0.027, 0.039) \\ = (0.229, 0.436, 0.893)$$

The fuzzy synthetic extent or the fuzzy relative importance weights resulting from applying the same process to the remaining criteria is presented in Table 7.

**Table 7.** Fuzzy synthetic extent of sustainable project selection criteria.

The third and final step in calculating the criteria weights of importance is the defuzzification of the fuzzy criteria weights shown in Table 7. To defuzzify these weights, the defuzzification method shown in Equation (6), as presented in Sun [27] and Lespier et al. [7], is used to obtain the best non-fuzzy priority (BNP) or crisp weights of the criteria.

$$\text{BNP}\_{S\_{\hat{i}}} = \frac{\left[\left(u\_{\mathbf{s}\_{\hat{i}}} - l\_{\mathbf{s}\_{\hat{i}}}\right) + \left(m\_{\mathbf{s}\_{\hat{i}}} - l\_{\mathbf{s}\_{\hat{i}}}\right)\right]}{\mathbf{3}} + l\_{\mathbf{s}\_{\hat{i}}} \qquad \text{where } \mathbf{i} = 1, 2, \dots, 5 \tag{6}$$

As an example, applying Equation (6) to calculate the BNP for criterion 1 is done as follows:

$$BNP\_{S\_1} = \frac{\left[\left(0.893 - 0.229\right) + \left(0.463 - 0.229\right)\right]}{3} + 0.229 = 0.528$$

Accordingly, the crisp weights for the remaining criteria are calculated. Using these BNP values, the criteria can be ranked based on importance, where the criterion with the highest BNP is set as the most important, while the criterion with the lowest BNP is set as the least important, as shown in Table 8.

**Table 8.** Best non-fuzzy priority (BNP) or crisp criteria weights.


**2. Study Area**

The description below is based on Veress's work [15]. The parts of the Bakony Region and the names of the features that are mentioned in this study are described in Figure 1. The Bakony Region is the southwestern part of the Transdanubian Mountains. It is surrounded by the Little Hungarian Plain in the NW, by Lake Balaton in the SE and the micro-regions of the Balaton Basin (Balaton Riviera, Tapolca Basin), the Great Hungarian Plain (Mez˝oföld) and the Vértes Mountains in the NE (and Mór Graben with graben structure). Its elevation is 150–700 m and its area is 4300 km2. Its largest area is the Bakony Mountains (2200 km2). Parts of the Bakony Region are the Keszthely Mountains, Northern Bakony, Southern Bakony, Balaton Uplands and Bakonyalja (Figure 1).

The mountains are of horst structure, where more elevated horsts are mountains, while less elevated horsts are basins. They are mainly built up of Triassic dolomite which is significantly widespread on the surface too [16]. However, Triassic, Dachstein and Jurassic limestones frequently occur in great extension on the horsts of higher elevation. Cretaceous and Eocene limestones of smaller thickness can mainly be found in larger and smaller areas on horsts with medium elevation, mostly covered with loess. Horsts of lower elevation (basins) are mostly covered by non-karstic rocks (Middle Oligocene–Lower Miocene gravels, Figure 2).

**Figure 1.** Parts of the Bakony Region. Legend: 1. boundary of mountains, 2. boundary of microregion group, 3. stream, 4. horst, 5. basaltic horst, 6. plateau, 7. basin, 8. karst spring, 9. karst lake, 10. doline group, 11. cave, 12. settlement, 13. Northern Bakony, 14. Southern Bakony, 15. Balaton Uplands, 16. Keszthely Mountains, 17. K˝oris Mountain, 18. Som Mountain, 19. Mester-Hajag, 20. Kab Mountain, 21. S ˝ur ˝u mountain group, 22. Porva basin, 23. Lókút basin, 24. Hárskút basin, 25. Tapolca basin, 26. Dudar basin, 27. Cuha valley, 28. Gerence valley, 29. Ördög valley, 30. Ördög-lik of K˝oris Mountain, 31. Alba-Regia cave, 32. Lóczy cave, 33. Öreg-köves inflow cave, 34. Cserszegtomaj caves, 35. Devecser, 36. Szentbékálla, 37. Tapolca, 38. Márkó, 39. Hajmáskér, 40. Balatonfüred, 41. Hévíz, 42. Eleven-Förtés doline group, 43. Lake Hévíz and its spring cave, 44. Tihany Peninsula, 45. Tapolca cave system.

**Figure 2.** Geological map of the Bakony Region [17]. Legend: 1. fluvial sediment, 2. Holocene peat, 3. Holocene wind-blown sand, 4. Pleistocene loess, 5. Pliocene basalt, 6. Upper-Miocene freshwater limestone, 7. Middle Miocene limestone, 8. Oligocene gravel, 9. Eocene limestone, 10. Upper Cretaceous limestone, 11. Lower Cretaceous limestone, 12. Jurassic limestone, 13. Triassic limestone, dolomite, 14. Permian sandstone, 15. old Paleozoic phyllite.

The uniformly developed karstwater reserves of the mountains (regional groundwater, Figure 3), mostly stored in the main dolomite and preceding karstwater; pumping it resurged not only in karst springs, but also fed karstic swamps and lakes (Lake Balaton) [18,19]. However, it is also transmitted into the basin sediments of the environs [20,21] (Figure 3).

**Figure 3.** Karstwater map of the Bakony Mountains [21]. Regional groundwater of the mountains according to the state of January 2006. Legend: 1. infiltration area, 2. boundary of groundwater storage, 3. altitude of the isoline of groundwater level, 4. hypogene branch, 5. former hypogene branch, 6. termination boundary is not known.

In the Bakony Region, where impermeable intercalations are mainly in the Middle-Eocene limestone (Sz˝oc Limestone Formation) and in Cretaceous limestones, perched water tables developed in some horsts and horst groups [22,23]. Particularly, the percolating water of the gorges of the Bakony Mountains [22] may significantly feed the perched water tables, however, at sites where the aquifuge is absent or already removed by erosion, it feeds the regional groundwater [24].

As the horsts of the mountains performed oscillating movements since the Late Cretaceous period, Pécsi [25] put them into different genetic types (Figure 4). He distinguished

cryptopeneplain (up to 300 m elevation, it is covered with non-karstic impermeable rocks, morphologically basin), low-threshold surface (up to 300 m, its surface is built up of Triassic carbonates), horst elevated to summit position (surface elevation is 400–550 m, constituting rocks are Cretaceous and Eocene limestones, on which mainly permeable loess accumulations are found, morphologically mountain), horst in summit position (surface elevation is 600–700 m, Triassic and Jurassic carbonates are widespread at its surface, cover only occurs in patches) and horst type with basalt cover (basalt caprock and widespread loess cover).

**Figure 4.** Horst types of the mountains [26]. 1. non-karstic rock, 2. Triassic carbonates, 3. Jurassic, Cretaceous and Eocene limestones, 4. impermeable intercalation, clay, marly limestone, silica, etc., 5. basalt, 6. gravel, 7. loess, 8. karst water table, 9. fault, 10. karst water storey, 11. main karst water, 12. basin, graben, 13. mount, 14a. horst in summit position, 14b. horst elevated to summit position, 14c. threshold surface, 14d. cryptopeneplain, 14e. horst covered with basalt.

#### **3. Factors Influencing Its Karstification**

In the Bakony Region, two flow systems are present, a regional and a local. At the ascending branches of regional flows, hypogene karst systems are present, while at the descending branches of regional flows and at local flows, epigene karst systems are present. The main constituent of regional flow is the regional groundwater, which is not exclusively fed by descending waters, but also by the water of the perched water table, which percolates along fractures and faults. The regional flow with a NW–SE direction partly resurges in the karst springs of mountain margins, and, to a larger extent, it arrives at the sediment and at carbonate rocks on the floor of surrounding basins. In the SW, the former hypogene branch extended from the Keszthely Mountains nearly to the NE termination of Lake Balaton (Figure 3). Members of this branch are the Cserszegtomaj Caves [27,28] and the Lóczy Cave [29,30]. The hypogene branch still exists at Lake Hévíz, which is represented by the water of the spring cave of Lake Hévíz with a temperature of 40 ◦C [31].

Local flow occurs at sites where the limestones constituting the horsts are interbedded with impermeable or partly impermeable intercalations (marl, chert, clay). Such local flow is particularly characteristic of the Cretaceous limestone horsts of Northern Bakony (for example on Mester-Hajag Figure 5).

**Figure 5.** Water flow system of Mester-Hajag: Legend: 1. limestone, 2. impermeable intercalation, 3. permeable cover, 4. fault, 5. karstwater level, 6. infiltration, 7. local water inflow, 8. water motion above aquifuge, 9. water drainage along fault, 10. linear seepage, 11. spring, 12. epigenetic valley.

As has already been mentioned, the mountains are separated into horsts of different elevations, expansions and evolutions [21]. The distribution of horst types in the mountains is described in Figure 6.

**Figure 6.** Distribution of horst types in the Bakony Region. Legend: 1. boundary of the mountains, 2. boundary of micro-region group, 3. stream, 4. horst, 5. basaltic horst, 6. plateau, 7. basin, 8. karst spring, 9. karst lake, 10. boundary of horst type, 11. Northern Bakony, 12. Southern Bakony, 13. Balaton Uplands, 14. Keszthely Mountains, 15. horst in summit position, 16. horst elevated to summit position, 17. cryptopeneplain, 18. threshold surface, 19. horst with basalt cap, 20. buttes with basalt cap in karstic and non-karstic environments, 21. hilly country covered with superficial deposit (fluvial sediment, dune sand).

The majority of the mountains are covered by impermeable or permeable non-karstic sediment (mainly loess). The caprock thins out in some places (at the mounds of the bedrock or at creeks) as compared to its environment. On horsts covered with impermeable beds, epigenetic valleys of different stages of maturity emerged. These valleys may also have permanent streams at sites where a horst is surrounded by terrains covered with impermeable beds. As a result of the elevated position of the horst relative to its environment of covered terrain, some parts of these valleys are of epigenetic-antecedent origin and constitute gorges. On terrains covered with impermeable beds (for example on Kab Hill which is covered with basalt), mixed allogenic–autogenic karst developed.

The bedrock, therefore, became karstified and dissected into mounds and depressions. The mounds of Cretaceous limestones are partly exhumed. On the terrains between them, the caprock thinned out (Mester-Hajag). However, some parts of threshold surfaces that are uncovered and have a low elevation (below 300 m) are also dissected by mounds.


*BRAF Mutation and Its Importance in Colorectal Cancer DOI: http://dx.doi.org/10.5772/intechopen.82571*

*Advances in the Molecular Understanding of Colorectal Cancer*

**Agents investigated Study**

Encorafenib + cetuximab ±

FOLFOX + bevacizumab vs. FOLFOXIRI + bevacizumab

Dabrafenib + panitumumab vs. dabrafenib + trametinib + panitumumab

Dabrafenib + panitumumab

+ trametinib + panitumumab vs. 5-fluorouracil-based chemotherapy + monoclonal

Trametinib + panitumumab

Encorafenib + cetuximab

vs. dabrafenib

antibody

+ alpelisib

binimetinib

**design**

Phase 3, randomised, open label

Phase 3 open label

4 part phase 1/2, open label

Phase 1b/2, open label, dose escalation

Irinotecan + AZD1775 Phase 1b Recruiting

LGK974 ± PDR001 Phase 1 Recruiting

**Status**

Recruiting

Active, not recruiting

Active, not recruiting

Active, not recruiting

**Therapeutic strategy**

+ MEK inhibition

 + selective Wee 1 inhibitor

+ immunotherapy

agent + cytotoxic chemotherapy

+ MEK inhibition

+ PI3K inhibition

NCT02928224 BRAF + EGFR

NCT02906059 Chemotherapy

NCT01351103 PORCN inhibitor

NCT01640405 Antiangiogenesis

NCT01750918 BRAF + EGFR

NCT01719380 BRAF + EGFR

*Updated 7th November 2018.*

**Table 2.**

**ClinicalTrials. gov number**

Immunotherapy also plays a role in the management of metastatic CRC [36]. Pembrolizumab and nivolumab are immune check point inhibitors against programmed death 1 (PD-1) that have demonstrated significant activity against

MSI-high mCRC [72, 73]. Given the strong association between MSI-high and BRAF MT CRC, this represents a possible therapeutic option. The initial trial of pembrolizumab in MSI-high CRC did not include BRAF MT cases; however, a case report

Nivolumab and combination nivolumab with ipilimumab (cytotoxic T-lymphocyte associated protein 4 inhibitor) in MSI-high/dMMR CRC was examined in the phase 2 CheckMate 142 study [73, 75]. 12 of the 74 patients receiving nivolumab harboured a BRAF mutation. An objective response was seen in 3 patients (25%) and 9 patients achieved disease control for greater than 12 weeks. The ORR for combination immunotherapy was greater at 55% in patients with MSI-high BRAF MT CRC, and disease control rate of 79%. Safety data was not reported by mutation status, however, appeared manageable, with 32% experiencing a grade 3 or 4 adverse event, most commonly raised AST. Discontinuation due to a treatment related adverse event was 13%.

BRAF V600E mutations are present in 7–10% of CRC. It represents a population with poor prognosis and a particular clinical phenotype, being more prevalent in

does suggest activity in the MSI-high BRAF MT population [74].

*Ongoing studies investigating different treatment strategies for BRAF MT mCRC.*

**44**

**7. Conclusion**

women, older than 70 years of age, associated with poorly differentiated histology and right-sided tumours. Chemotherapy with the addition of anti-angiogenesis agent remains the current standard of care in the first line metastatic setting. More aggressive, triplet chemotherapy (FOLFOXIRI) may be appropriate in the selected patient. BRAF inhibition has been extensively investigated for second line therapy and beyond and when in combination with EGFR, MEK and PI3K inhibitors have increased response rates, however, PFS and OS remains poor. Ongoing research remains important to improve outcomes in BRAF MT CRC.


**3. Biofilms in respiratory tract infections**

It is becoming progressively more accepted that biofilm formation is an important cause of morbidity in respiratory tract infections [40]. Biofilms may be involved in some respiratory infections, including ventilator-associated pneumonia, bronchiectasis, bronchitis, cystic fibrosis and upper respiratory airway infections [41].


**Author details**

Ivan Ivanov *Sofia University "St.Kl.Ohridski", Bulgaria*

### **6. References**

22 Will-be-set-by-IN-TECH

*B*0(3)(6, 3) = 13.498; *B*0(3)(5, 3) = 1.285; *B*1(1)(2, 3) = 6.525; *B*1(1)(4, 3) = −5.2; *B*1(2)(2, 1) = −22.99; *B*1(2)(4, 1) = 3.25; *B*1(3)(6, 1) = 6.8466; *B*1(3)(6, 2) = 2.5 . *This choice of the matrices B*0(*i*), *B*1(*i*), *i* = 1, 2, 3 *guaranteed that the matrices R*(*i*, **X**) *are positive semidefinite, i.e. there are symmetric matrices* **X** *which belongs to dom P*†*. The remain coefficient*

We find the maximal solution to (3) - (4) for the constructed example with iterative method (12) and the LMI approach applied to optimization problems (16) and (18). The results are the following. Iteration (12) needs 15 iteration steps to achieve the maximal solution. The

Eig *W*(1)=(4.9558*e* − 5; 0.50058; 0.50004; 0.50002; 0.50001; 0.5),

Eig *W*(3)=(9.33*e* − 5; 0.05041; 0.05005; 0.050018; 0.050011; 0.050003).

The LMI approach for optimization problem (16) does not give a satisfactory result. After 32 iteration step the calculations stop with the computed maximal solution **V**. However, the norm of the difference between two solutions **W** and **V** is �*W*(1) − *V*(1)� = 1.0122*e* −

The LMI approach for optimization problem (18) needs 28 iteration steps to compute the maximal solution to (1). This solution **Z** has the same eigenvalues as in (19). The norm of the difference between two solutions **W** and **Z** is �*W*(1) − *Z*(1)� = 7.4105*e* − 12, �*W*(2) −

The results from this example show that the LMI approach applied to optimization problem (18) gives the more accurate results than the LMI method for (16). Moreover, the results obtained for problem (16) are not applicability. A researcher has to be careful when applied the LMI approach for solving a set of general discrete time equations in positive semidefinite

This chapter presents a survey on the methods for numerical computation the maximal solution of a wide class of coupled Riccati-type equations arising in the optimal control of discrete-time stochastic systems corrupted with state-dependent noise and with Markovian jumping. In addition, computational procedures to compute this solution for a set of discrete-time generalized Riccati equations (7)-(8) are derived. Moreover, the LMI solvers for this case are implemented and numerical simulations are executed. The results are compared

(19)

Eig *W*(2)=(0.00019562; 1.0007; 1.0001; 1; 1; 1),

9, �*W*(2) − *V*(2)� = 2.8657*e* − 6, �*W*(3) − *V*(3)� = 3.632*e* − 6.

*Z*(2)� = 2.8982*e* − 11, �*W*(3) − *Z*(3)� = 3.0796*e* − 11.

and the usefulness of the proposed solvers are commented.

*Sofia University "St.Kl.Ohridski", Bulgaria*

*matrices are already in place.*

case.

**5. Conclusion**

**Author details**

Ivan Ivanov

computed maximal solution **W** has the eigenvalues

	- [17] do Val, J.B.R, Basar, T. (1999). Receding horizon control of jump linear systems and a macroeconomic policy problem, *Journal of Economic Dynamics and Control*, Vol. 23, 1099-1131, ISSN: 0165-1889.
	- [18] Yao, D.D., Zhang, S. & Zhou, X. (2006). Tracking a financial benchmark using a few assets. *Operations Research*, Vol. 54, 232-246, ISSN: 0030-364X.

© 2012 Sokolov, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

 (1)

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Sokolov, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Stochastic Observation Optimization on**

Sergey V. Sokolov

**1. Introduction**

particularly as follows.

functions;

**2. Description of the task**

differential equation in the symmetrized form

of the vector nonlinear observer of form:

http://dx.doi.org/10.5772/39266

Additional information is available at the end of the chapter

**the Basis of the Generalized Probabilistic Criteria**

Till now the synthesis problem of the optimum control of the observation process has been considered and solved satisfactorily basically for the linear stochastic objects and observers by optimization of the *quadratic* criterion of quality expressed, as a rule, through the a posteriori dispersion matrix [1-4]. At the same time, the statement of the synthesis problem for the optimum observation control in a more general case assumes, first, a nonlinear character of the object and observer, and, second, the application of the non-quadratic criteria of quality,

In connection with the fact that the solution of the given problem in such a statement generalizing the existing approaches, represents the obvious interest, we formulate it more

Let the Markovian vector process *t*, described generally by the nonlinear stochastic

0 0 0 , , , , *t t*

where *f*, *f*0 are known *N* – dimensional vector and *N M* – dimensional matrix nonlinear

*nt* is the white Gaussian normalized *M* – dimensional vector - noise; be observed by means

 , , *t ZH t W*

*f t f tn t*

which, basically, can provide the potentially large estimation accuracy[3-6].


**3.1 Mechanism of cracking reaction**

In general, the following steps of the cracking reaction can be identified:

When the bond between hydrogen and carbon atom is broken, a radical is created (initiation step). In the second step of the process, polymer bond breaks at the *β* position, creating one unsaturated molecule and another radical. Depending on the type of polymer, this cracking can follow one of these types of reactions:

In the case of polyolefins, cracking occurs mainly by random scission and backbiting reactions.

In the last step of the process, the radical can react with another radical, creating saturated alkane (recombination), one alkane and one alkene (disproportionation), create cyclic structure (cyclisation), dehydrogenate and condensate and take part in other reactions. In the end, a mixture of different types of hydrocarbons with varying chain lengths is created. When condensation and dehydrogenation reaction progress, polycyclic aromatic hydrocarbons (PAH) are created, which still react and finally create a coke, that is reach in carbon.


**Author details**

Sunil Jain1 \*, Bhagya Kamal Jain2 , Prem Kamal Jain3 and Arvind Singh Kushwaha4

1 Department of Paediatrics, Military Hospital Secunderabad, Telangana State, India

2 Google Inc., India

3 Department of Computational Biology, Indraprastha Institute of Information Technology, New Delhi, India

4 All India Institute of Medical Sciences, Nagpur, India

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Prevention Strategies for Patient Safety in Hospitals: Methodical Paradigm, Managerial… DOI: http://dx.doi.org/10.5772/intechopen.106836*