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Fig. 3 The modified Phillips-Heffron model of SMIB with TCSC The Phillips-Heffron model of the single machine infinite bus (SMIB) system with TCSC is obtained using the linearized equations (10-13). The corresponding block diagram model is shown in Fig. 3 [16].

Figure 3 The modified Phillips-Heffron model of SMIB with TCSC The Phillips-Heffron model of the single machine infinite bus (SMIB) system with TCSC is obtained using the linearized equations (10-13). The corresponding block diagram model is shown in Fig. 3 [16].

Related Figures (14)

Fig. 1 Single machine infinite bus power system with TCSC The single-machine infinite-bus power system shown in Fig. 1 is considered in this study. The generator is equipped with a PSS and the system has a TCSC installed in transmission line. In the figure X; and X, represent the reactance of the transformer and the transmission line respectively, V7 and Vx, are the generator terminal and infinite bus voltage respectively.
Fig. 1 Single machine infinite bus power system with TCSC The single-machine infinite-bus power system shown in Fig. 1 is considered in this study. The generator is equipped with a PSS and the system has a TCSC installed in transmission line. In the figure X; and X, represent the reactance of the transformer and the transmission line respectively, V7 and Vx, are the generator terminal and infinite bus voltage respectively.
The non-linear differential equations of the single machine nfinite bus power system with TCSC are [1, 9]:
The non-linear differential equations of the single machine nfinite bus power system with TCSC are [1, 9]:
Fig. 4 Deception of velocity and position updates in PSO. number. Fig. 4 shows the velocity and position updates of a particle for a two-dimensional parameter space. The computational flow chart of PSO algorithm is shown in Fig. 5.
Fig. 4 Deception of velocity and position updates in PSO. number. Fig. 4 shows the velocity and position updates of a particle for a two-dimensional parameter space. The computational flow chart of PSO algorithm is shown in Fig. 5.
Fig. 5 Flowcharts of particle swarm optimization algorithm B. Genetic Algorithm (GA)
Fig. 5 Flowcharts of particle swarm optimization algorithm B. Genetic Algorithm (GA)
Fig. 7 Structure of the TCSC controller The commonly used lead-lag structure is chosen in this study as a TCSC controller. The structure of the TCSC controller is shown in Fig. 7. It consists of a gain block with gain Ky, a signal washout block and two-stage phase compensation block as shown in figure. The phase compensation block provides the appropriate phase-lead characteristics to compensate for the phase lag between input and the output signals. The signal washout block serves as a high-pass filter, with the time constant Twr, high enough to allow signals associated with oscillations in
Fig. 7 Structure of the TCSC controller The commonly used lead-lag structure is chosen in this study as a TCSC controller. The structure of the TCSC controller is shown in Fig. 7. It consists of a gain block with gain Ky, a signal washout block and two-stage phase compensation block as shown in figure. The phase compensation block provides the appropriate phase-lead characteristics to compensate for the phase lag between input and the output signals. The signal washout block serves as a high-pass filter, with the time constant Twr, high enough to allow signals associated with oscillations in
The computational flow chart of GA is shown in Fig. 6.
The computational flow chart of GA is shown in Fig. 6.
PARAMETERS USED IN PSO AND GA
PARAMETERS USED IN PSO AND GA
Fig. 9 Variation of computational time for PSO and GA with generation. Fig. 8 Convergence of objective function for PSO and GA optimization techniques.
Fig. 9 Variation of computational time for PSO and GA with generation. Fig. 8 Convergence of objective function for PSO and GA optimization techniques.
OPTIMIZED PARAMETERS OBTAINED BY PSO AND GA
OPTIMIZED PARAMETERS OBTAINED BY PSO AND GA
SYSTEM EIGENVALUES WITHOUT AND WITH CONTROL
SYSTEM EIGENVALUES WITHOUT AND WITH CONTROL
Fig. 10 System response for a 5 % step increase in mechanical power input.(a) speed @ (b) power angle 6 (c) accelerating power P, (d) terminal voltage Vy
Fig. 10 System response for a 5 % step increase in mechanical power input.(a) speed @ (b) power angle 6 (c) accelerating power P, (d) terminal voltage Vy
For completeness, the effectiveness of the proposed controllers is also tested for a disturbance in reference voltage setting. The reference voltage is increased by a step of 5% at t=1 sec. Fig. 11 shows the system response for the above contingency for all the three controllers. The figures illustrate the advantage of the PSOTCSC and GATCSC compared to CPSS. These positive results of the proposed PSOTCSC can be attributed to its faster response with less overshoot compared to that of CPSS. Further, it is also clear that the both PSOTCSC and GATCSC give almost similar responses. The controllers have good damping characteristics to low frequency oscillations and stabilize the system much faster. This extends the power system stability limit and the power transfer capability.
For completeness, the effectiveness of the proposed controllers is also tested for a disturbance in reference voltage setting. The reference voltage is increased by a step of 5% at t=1 sec. Fig. 11 shows the system response for the above contingency for all the three controllers. The figures illustrate the advantage of the PSOTCSC and GATCSC compared to CPSS. These positive results of the proposed PSOTCSC can be attributed to its faster response with less overshoot compared to that of CPSS. Further, it is also clear that the both PSOTCSC and GATCSC give almost similar responses. The controllers have good damping characteristics to low frequency oscillations and stabilize the system much faster. This extends the power system stability limit and the power transfer capability.
NE Fig. 11 System response for a 5 % step increase in reference voltage setting (a) speed w (b) power angle 6 (c) accelerating power P, (d) terminal voltage Vy
NE Fig. 11 System response for a 5 % step increase in reference voltage setting (a) speed w (b) power angle 6 (c) accelerating power P, (d) terminal voltage Vy
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