Design of a Damping Controller Using a Metaheuristic Algorithm for Angle Stability Improvement of an MIB System
Abstract
:1. Introduction
2. Modelling of SMIB with AVR and PSS Damping Controllers
3. Objective Function to Tune the PSS Parameters
- , min ≤ ≤ , max,
- , min ≤ ≤ , max,
- , min ≤ ≤ , max.
4. SCA
5. Moth Flame Optimisation (MFO) Algorithm
6. Evolutionary Programming Algorithm
7. Advantages of SCA over MFO and EP
8. Results and Discussion
Modules | Parameters |
---|---|
Generator | H = 3.50, = 1.0 < 36°, ′ = 0.30, = 0.0030, = 1.810, = 1.760, = 8, = 0.84910, = 0.84910. |
Power line | = 0.650, = 0.160, = 0.0 |
AVR with PSS-LL controller | = 0.020, = 1.40, = 200.0 |
9. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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SCA Pseudocode |
---|
Initialise the population for i = 1:size(X,1) Objective values(1,i) = fobj(X(i,:)); if i == 1 Destination position = X(i,:); Destination fitness = Objective values(1,i); elseif Objective values(1,i) < Destination fitness Destination position = X(i,:); Destination fitness = Objective values(1,i); end if All objective values(1,i) = Objective values(1,i); end for whilst iteration maximum iterations do r1 = a − t*((a)/max_iteration) calculate the number using Equation () for i = 1 to n do for j = 1 to n do r2 = 2 * pi * rand() r3 = 2 * (rand()) r4 = rand() Update r2, r3 and r4 for Equation () if r4 < 0.5 % Equatoin () X(i,j) = X(i,j) + (r1 * sin(r2) * abs(r3 * Destination position(j) − X(i,j))); else % Equation () X(i,j) = X(i,j) + (r1 * cos(r2) * abs(r3 * Destination position(j) − X(i,j))); if Objective values(1,i) < Destination fitness Destination position = X(i,:); Destination fitness = Objective values(1,i); end if end if end for end for Convergence curve(t) = Destination fitness; if mod(t,50) == 0 display([‘At iteration’, num2str(t), ‘the optimum is’, num2str(Destination fitness)]); end show the best amongst solutions end whilst |
MFO Algorithm Pseudocode |
---|
Randomly initialise the population for the moth flame by moth position Ni for i = 1 to n do calculate fitness function fi end for whilst iteration maximum iterations do reform the location of Ni calculate the number of flames using Equation () weigh up fi, the fitness function fi if iteration == 1 next F = rank(N) and OF = rank(ON) else F= rank(Nt − 1, Nt) and OF = rank(ONt − 1, ONt) end if for i = 1 to n do for j = 1 to n do reform the values of t and r determine the value of G using Equation () update N(i,j) to its moth using Equation () end for end for end whilst show the best amongst solutions P |
Evolutionary Programming Algorithm Pseudocode |
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Initialise the population for i = 1 to n do //parents/// for j = 1 to K populations do describe (i) and J((i)) end for ///offspring/// for j = 1 to N populations do (i) = α × ( − ) × Calculate (i) end for merge both offspring and parents sort x(i) in descending arrangement of J(x(i)) pick best one-half x(i) value, the same as brand-new (i) if | − | < then end if i = i + 1 end for |
Loading Conditions | Active Power, P (p. u) | Reactive Power, Q (p. u) |
---|---|---|
1 | P = 0.9 | Q = 0.2 |
2 | P = 0.9 | Q = 0.3 |
3 | P = 0.9 | Q = 0.4 |
4 | P = 0.5 | Q = 0.5 |
5 | P = 0.2 | Q = 0.7 |
Optimisation Techniques | Parameters Range | Optimised PSS Parameter Range Limit |
---|---|---|
SCA | = 2 to 0, = 0 to 2π, = 0 to 2, = 0 to 1 | = 0.001, = 0.2 = 0.001, = 0.1 = 9, = 200 |
MFO | d = 0.00025, t = −1 to 1 | |
EP | β = 0.1 |
Loading Condition 1 | ||||
---|---|---|---|---|
Methods | PSS−SCA | PSS-MFO | PSS-EP | PSS-U |
PSS optimised parameters | = 0.03224 = 0.00179 = 31.75167 | = 0.03739 = 0.0050 = 31.52837 | = 0.06511 = 0.00142 = 35.44624 | = 0.1 = 0.04 = 9 |
Objective function | 0.7420 | 0.7240 | 0.6770 | 0.1267 |
Number of iterations | 46 | 103 | 19 | NA |
Loading Condition 2 | ||||
---|---|---|---|---|
Methods | PSS-SCA | PSS-MFO | PSS-EP | PSS-U |
PSS optimised parameters | = 0.02499 = 0.00150 = 32.96348 | = 0.02888 = 0.00413 = 32.83729 | = 0.06651 = 0.00152 = 37.41522 | = 0.1 = 0.04 = 9 |
Objective function | 0.7340 | 0.7227 | 0.6609 | 0.1209 |
Number of iterations | 44 | 96 | 23 | NA |
Loading Condition 3 | ||||
---|---|---|---|---|
Methods | PSS-SCA | PSS-MFO | PSS-EP | PSS-U |
PSS optimised parameters | = 0.01780 = 0.001403 = 33.9990 | = 0.02630 = 0.01103 = 33.27788 | = 0.06711 = 0.00154 = 38.34156 | = 0.1 = 0.04 = 9 |
Objective function | 0.7300 | 0.7121 | 0.6337 | 0.1145 |
Number of iterations | 34 | 102 | 23 | NA |
Loading Condition 4 | ||||
---|---|---|---|---|
Methods | PSS-SCA | PSS-MFO | PSS-EP | PSS-U |
PSS optimised parameters | = 0.04316 = 0.05061 = 53.25110 | = 0.05327 = 0.06027 = 54.32393 | = 0.04259 = 0.04422 = 49.64898 | = 0.1 = 0.04 = 9 |
Objective function | 0.7559 | 0.7407 | 0.6764 | 0.1144 |
Number of iterations | 42 | 94 | 20 | NA |
Loading Condition 5 | ||||
---|---|---|---|---|
Methods | PSS-SCA | PSS-MFO | PSS-EP | PSS-U |
PSS optimised parameters | = 0.02396 = 0.04134 = 140.61181 | = 0.03471 = 0.04984 = 147.61060 | = 0.02888 = 0.04339 = 154.93417 | = 0.1 = 0.04 = 9 |
Objective function | 0.8299 | 0.7839 | 0.6384 | 0.0641 |
Number of iterations | 38 | 99 | 13 | NA |
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Khawaja, A.W.; Kamari, N.A.M.; Zainuri, M.A.A.M. Design of a Damping Controller Using a Metaheuristic Algorithm for Angle Stability Improvement of an MIB System. Appl. Sci. 2022, 12, 589. https://doi.org/10.3390/app12020589
Khawaja AW, Kamari NAM, Zainuri MAAM. Design of a Damping Controller Using a Metaheuristic Algorithm for Angle Stability Improvement of an MIB System. Applied Sciences. 2022; 12(2):589. https://doi.org/10.3390/app12020589
Chicago/Turabian StyleKhawaja, Abdul Waheed, Nor Azwan Mohamed Kamari, and Muhammad Ammirrul Atiqi Mohd Zainuri. 2022. "Design of a Damping Controller Using a Metaheuristic Algorithm for Angle Stability Improvement of an MIB System" Applied Sciences 12, no. 2: 589. https://doi.org/10.3390/app12020589
APA StyleKhawaja, A. W., Kamari, N. A. M., & Zainuri, M. A. A. M. (2022). Design of a Damping Controller Using a Metaheuristic Algorithm for Angle Stability Improvement of an MIB System. Applied Sciences, 12(2), 589. https://doi.org/10.3390/app12020589