KP |
KI |
KD |
1 |
0.25 |
0.28 |
Table 1: Coefficients of the reference PID controller [8]
|
Transfer function |
Parameter limits |
Used parameter values |
Amplifire |
Ka/(1+sτa) |
10≤Ka≤40, 0.02≤τa≤0.1 |
Ka =10, τa=0.1 |
DC Exciter |
Ke/(1+sτe) |
1≤Ke≤10, 0.4≤τe≤1.0 |
Ke =1, τe=0.4 |
Generator |
Kg/(1+sτg) |
0.7≤Kg≤1.0, 1.0≤τg≤2.0 |
Kg =1, τg=1 |
Sensor |
Ks/(1+sτs) |
Ks=1, 0.001≤τs≤0.06 |
Ks =1, τs=0.05 |
Table 2: Parameters of the AVR system model
Yi limitation |
2-3 |
τi limitation |
0.4-0.7 |
Table 3: Limitation of optimized parameters of CDM
Ƴ 1 |
Ƴ 2 |
Ƴ 3 |
Ƴ 4 |
Ƴ 5 |
τ(s) |
2.0475 |
2.0349 |
2.4618 |
2.1936 |
2.8168 |
0.6334 |
Table 4: Optimized key parameters of CDM
Control strategy |
Ts(sec) , Vt |
Tp(sec) , Vt |
ITSE (Ve) |
Oscillatory modes |
MDR (ζ) |
PID |
1.2604 |
1.5500 |
0.0552 |
-0.1080 ±4.4191i |
0.0244 |
Optimal CDM |
1.0024 |
1.2300 |
0.0105 |
-2.13e+00 ± 6.01e+00i |
0.3338 |
Table 5: Numerical comparison of the outcomes of various control techniques
Parameter variation |
Nominal |
KA |
TA |
KE |
TE |
KG |
TG |
KS |
TS |
% change |
0 |
+ 5 0 % |
+ 5 0 % |
+ 5 0 % |
+50% |
+ 5 0 % |
+ 5 0 % |
+ 5 0 % |
+ 5 0 % |
MDRPID |
0.0244 |
-0.0643 |
-0.0169 |
-0.0643 |
0.0347 |
-0.0643 |
0.0884 |
-0.0643 |
-0.0070 |
MDROptimal CDM |
0.3338 |
0.1946 |
0.2150 |
0.1946 |
0.3030 |
0.1946 |
0.4136 |
0.1946 |
0.2429 |
Table 6: Sensitivity analysis with changes in the range of dynamic parameters
Figure 2: The practical representation of the AVR system
Figure 3: The block diagram of AVR system
Figure 4: The block diagram of the structure of CDM controller
Figure 5: A whirlpool that is formed by (a) a centripetal force that is caused by rotating motion, and (b) the action of centrifugal force, as well as the updating of the locations of particles
Figure 6: the block diagram of the AVR control system in conjunction with the proposed CDM-TFWO controller
Figure 7: The flowchart of designing the optimal CDM using the TFWO method for the AVR system
Figure 8: Convergence curve of TFWO for CDM controller
Figure 9: Convergence curve of TFWO for CDM controller
Figure 10: Coefficient diagram of designed proposed controller
Figure 11: Generator terminal voltage with two strategies: Reference PID control and the proposed optimal CDM
Tables at a glance
Figures at a glance