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Table 4. Time response gain measurement values in the presence of ISE objective functions using the proposed DE + FPID + IPFC controller.

Table 4 Time response gain measurement values in the presence of ISE objective functions using the proposed DE + FPID + IPFC controller.

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and is shown in Figure 2. To make the system more stable, an IPFC FACTS device was incorporated in the system as depicted in Figure 3. After developing the system, initially, a MATLAB code with a DE and PSO algorithm was developed and interfaced with the system model by using the controller tools such as the integral, PI, and FPID for the comparison. During optimization, an error signal occurred due to the change in the load sensed by the feedback signal that was compared with the reference, and the controller took the appropriate action to take the system to a steady state.
and is shown in Figure 2. To make the system more stable, an IPFC FACTS device was incorporated in the system as depicted in Figure 3. After developing the system, initially, a MATLAB code with a DE and PSO algorithm was developed and interfaced with the system model by using the controller tools such as the integral, PI, and FPID for the comparison. During optimization, an error signal occurred due to the change in the load sensed by the feedback signal that was compared with the reference, and the controller took the appropriate action to take the system to a steady state.
Figure 1. Three-area power system model. Figure 2. Structure of the proposed FPID controller.
Figure 1. Three-area power system model. Figure 2. Structure of the proposed FPID controller.
Table 1. Time response gain measurement values in the presence of ITAE objective functions using the proposed DE + FPID + IPFC controller. In this paper, before choosing the ITAE as an objective function, a comparison analysis with other objective functions such as ITSE, ISE, and IAE was performed using time domain specification, namely the peak undershoot, peak overshoot, and settling time, as per the objective of minimizing the ACE control error using DE, which are given in Equations (2)-(5). Tables 1-4 present the time response gain measurement values for the objective functions ITAE, IAE, ITSE, and ISE, respectively. It was found that better results were obtained by using the ITAE than the others.
Table 1. Time response gain measurement values in the presence of ITAE objective functions using the proposed DE + FPID + IPFC controller. In this paper, before choosing the ITAE as an objective function, a comparison analysis with other objective functions such as ITSE, ISE, and IAE was performed using time domain specification, namely the peak undershoot, peak overshoot, and settling time, as per the objective of minimizing the ACE control error using DE, which are given in Equations (2)-(5). Tables 1-4 present the time response gain measurement values for the objective functions ITAE, IAE, ITSE, and ISE, respectively. It was found that better results were obtained by using the ITAE than the others.
Table 2. Time response gain measurement values in the presence of IAE objective functions using the proposed DE + FPID + IPFC controller. Table 3. Time response gain measurement values in the presence of ITSE objective functions using the proposed DE + FPID + IPFC controller.
Table 2. Time response gain measurement values in the presence of IAE objective functions using the proposed DE + FPID + IPFC controller. Table 3. Time response gain measurement values in the presence of ITSE objective functions using the proposed DE + FPID + IPFC controller.
Table 5. System and simulation coding parameters for the system under study [12]. The main control parameters were the change in frequency and the change in ACE, while the main measurement parameters were the settling time, overshoot, undershoot, and rise time. Additionally, the main controllers were the integral, PI, and FPID including the IPFC FACTS device. In the optimization, the minimum solution was taken as a solution after running the program more than 30 times, and the optimization was initialized with 0 as the lower bound range and 2 as the upper bound range. Tables 6-11 show the optimized gain parameters of the FPID, IPFC, I, optimized IPFC in the presence of the integral, PI. and optimized IPFC in the presence of the PI controller, respectively. The comparison of the FPID, I, and PI controllers in the presence of the IPFC with the time response parameters is given in Tables 12-14, and the FPID + IPFC with the reduced ST, OS, and US provided a satisfying result when compared with the fuzzy integral and fuzzy PI controllers. Table 15 discusses the time response results obtained by optimizing the PID with the PSO in the presence of the IPFC FACTS device. Compared to the other controllers, the reduced-error [TAE objective function was achieved in the case of the FPID controller by using the DE technique, which resulted in a value of 0.2545 pu; for the PSOPID controller in the presence of IPFC, the value was 3.2976 pu, and in the case without the controller, the value was 187.5810 pu, and these values are given in Table 16. Figures 5-7 show the comparison of DE + FPID + IPFC, DE + 1+ IPFC, DE + PI + IPFC, and PSO + PID + IPFC for the change in frequency f1, f2, and f3, respectively, and they show that with the DE + FPID + IPFC reduced settling time, an overshoot and undershoot were achieved; similarly, Figures 8-10 depict the results of the comparison of the changes in ACE1, ACE2, and ACES3, respectively, and better result were achieved with the proposed DE + FPID + IPFC controller. Compared to the other controllers, the fast that was created by using the D convergence characteristics of the proposed controller E method are given in Figure 11. The performance of the time response parameters is also shown in Figures 12-14, which revealed that the FPID optimized by DE performed be tter with the reduced undershoot, reduced settling time, and reduced overshoot. The results of the analysis on the application of the random load change to the system is shown in Figures 15-25, and the discussion for each is also given, which corresponds to each simu ation result figure.
Table 5. System and simulation coding parameters for the system under study [12]. The main control parameters were the change in frequency and the change in ACE, while the main measurement parameters were the settling time, overshoot, undershoot, and rise time. Additionally, the main controllers were the integral, PI, and FPID including the IPFC FACTS device. In the optimization, the minimum solution was taken as a solution after running the program more than 30 times, and the optimization was initialized with 0 as the lower bound range and 2 as the upper bound range. Tables 6-11 show the optimized gain parameters of the FPID, IPFC, I, optimized IPFC in the presence of the integral, PI. and optimized IPFC in the presence of the PI controller, respectively. The comparison of the FPID, I, and PI controllers in the presence of the IPFC with the time response parameters is given in Tables 12-14, and the FPID + IPFC with the reduced ST, OS, and US provided a satisfying result when compared with the fuzzy integral and fuzzy PI controllers. Table 15 discusses the time response results obtained by optimizing the PID with the PSO in the presence of the IPFC FACTS device. Compared to the other controllers, the reduced-error [TAE objective function was achieved in the case of the FPID controller by using the DE technique, which resulted in a value of 0.2545 pu; for the PSOPID controller in the presence of IPFC, the value was 3.2976 pu, and in the case without the controller, the value was 187.5810 pu, and these values are given in Table 16. Figures 5-7 show the comparison of DE + FPID + IPFC, DE + 1+ IPFC, DE + PI + IPFC, and PSO + PID + IPFC for the change in frequency f1, f2, and f3, respectively, and they show that with the DE + FPID + IPFC reduced settling time, an overshoot and undershoot were achieved; similarly, Figures 8-10 depict the results of the comparison of the changes in ACE1, ACE2, and ACES3, respectively, and better result were achieved with the proposed DE + FPID + IPFC controller. Compared to the other controllers, the fast that was created by using the D convergence characteristics of the proposed controller E method are given in Figure 11. The performance of the time response parameters is also shown in Figures 12-14, which revealed that the FPID optimized by DE performed be tter with the reduced undershoot, reduced settling time, and reduced overshoot. The results of the analysis on the application of the random load change to the system is shown in Figures 15-25, and the discussion for each is also given, which corresponds to each simu ation result figure.
Table 6. FPID controller gain parameters.
Table 6. FPID controller gain parameters.
Table 7. IPFC model gain parameters. Table 8. Optimized gain parameter values of integral controller.
Table 7. IPFC model gain parameters. Table 8. Optimized gain parameter values of integral controller.
Table 9. Optimized IPFC gain parameters in the presence of integral controller.
Table 9. Optimized IPFC gain parameters in the presence of integral controller.
Table 10. Optimized gain parameter values of PI controller.
Table 10. Optimized gain parameter values of PI controller.
Table 11. Optimized IPFC gain parameters in the presence of PI controller.
Table 11. Optimized IPFC gain parameters in the presence of PI controller.
Table 12. Time response gain values for measured parameters in the presence of DE + FPID 4 IPFC controller.
Table 12. Time response gain values for measured parameters in the presence of DE + FPID 4 IPFC controller.
Table 13. Time response gain values for measured parameters in the presence of DE + I + IPFC controller.
Table 13. Time response gain values for measured parameters in the presence of DE + I + IPFC controller.
Figure 5. Frequency change f1 in area 1. Table 16. ITAE error function values for various simulation cases.
Figure 5. Frequency change f1 in area 1. Table 16. ITAE error function values for various simulation cases.
Table 14. Time response gain values for measured parameters in the presence of DE + PI + IPFC controller. Table 15. Time response gain values for measured parameters in the presence of PSOPID with IPFC FACTS controller.
Table 14. Time response gain values for measured parameters in the presence of DE + PI + IPFC controller. Table 15. Time response gain values for measured parameters in the presence of PSOPID with IPFC FACTS controller.
Figure 6. Frequency change f2 in area 2.
Figure 6. Frequency change f2 in area 2.
Figure 7. Frequency change f3 in area 3. Figure 9. ACE 2 change.
Figure 7. Frequency change f3 in area 3. Figure 9. ACE 2 change.
Figure 12. Settling time comparison using conventional and intelligent controllers with IPFC for change in frequency and ACE.
Figure 12. Settling time comparison using conventional and intelligent controllers with IPFC for change in frequency and ACE.
Figure 10. ACE 3 change.
Figure 10. ACE 3 change.
Figure 11. Convergence characteristics comparison.
Figure 11. Convergence characteristics comparison.
Figure 13. Undershoot comparison using conventional and intelligent controllers with IPFC for change in frequency and ACE.
Figure 13. Undershoot comparison using conventional and intelligent controllers with IPFC for change in frequency and ACE.
Figure 15. A load change pattern ranging from [—0.2 to 0.2]. Figure 14. Overshoot comparison using conventional and intelligent controllers with IPFC for change in frequency and ACE.
Figure 15. A load change pattern ranging from [—0.2 to 0.2]. Figure 14. Overshoot comparison using conventional and intelligent controllers with IPFC for change in frequency and ACE.
Figure 16. Frequency responses due to a random load change.
Figure 16. Frequency responses due to a random load change.
Figure 17. Frequency changes in each area for random load changes in area 1 only.
Figure 17. Frequency changes in each area for random load changes in area 1 only.
Figure 18. Tie-line power changes in each area for random load changes in area 1 only.
Figure 18. Tie-line power changes in each area for random load changes in area 1 only.
Figure 19. ACE changes in each area for random load changes in area 1 only.
Figure 19. ACE changes in each area for random load changes in area 1 only.
Figure 20. Frequency changes in each area for random load changes in area 2 only.
Figure 20. Frequency changes in each area for random load changes in area 2 only.
Figure 21. Only area 2 experienced tie-line power adjustments for random load changes.
Figure 21. Only area 2 experienced tie-line power adjustments for random load changes.
Figure 24. Only area 3 tie-line power adjustments for random load changes. Figure 23. Frequency changes in each area for random load changes in area 3 only.
Figure 24. Only area 3 tie-line power adjustments for random load changes. Figure 23. Frequency changes in each area for random load changes in area 3 only.
Figure 22. Only area 2 saw ACE fluctuations due to random load changes.
Figure 22. Only area 2 saw ACE fluctuations due to random load changes.
Figure 25. Only area 3 ACE adjustments for random load changes.
Figure 25. Only area 3 ACE adjustments for random load changes.
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Pid ControllerAutomatic Generation Control
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