Ant Lion Optimized Fractional Order Fuzzy Pre-Compensated Intelligent Pid Controller for Frequency Stabilization of Interconnected Multi-Area Power Systems
Abstract
:1. Introduction
- A new application for the FOFP-iPID controller is proposed for the LFC strategy.
- The SFs of the controllers are adjusted employing the ALO algorithm.
- The proposed FOFP-iPID controller is evaluated on an interconnected two-area power system in which the physical constraints are taken into account for challenging realization.
- The performance of the suggested controller is evaluated by comparing the results with other controllers, such as FOiPD and FOPID controllers for the same plant [17].
- Sensitivity analysis is carried out to show the robustness of the FOFP-iPID controller under a wide range of parameter variations and LPs.
2. Mathematical Modelling of Investigated Power System
3. Controller Structure
3.1. Design of the Fopid Controller
3.2. Design of the Foipid Controller
3.3. Design of the Fractional Order Fuzzy Pre-Compensated Intelligent PID (FOFP-iPID) Controller
4. Objective Function and Its Solution
4.1. Objective Function for Controller Design
4.2. ALO Algorithm
4.2.1. Random Walk of Ants
4.2.2. Trapping in Antlions Traps
4.2.3. Building Traps
4.2.4. Sliding Ants against toward Antlion
4.2.5. Catching Preys and Rebuilding the Traps
4.2.6. Flowchart of the ALO Algorithm
5. Simulation Results and Discussion
- (1)
- Performance evaluation under different perturbations (LPs):
- Performance evaluation of the suggested FOFP-iPID controller under step load perturbation (SLP) in area-1.
- Performance evaluation of the suggested FOFP-iPID controller under sinusoidal load change (SLC) in area-1.
- Performance evaluation of the suggested FOFP-iPID controller under random load perturbation (RLP) in area-1.
- (2)
- Sensitivity analysis is also carried out to appraise the robustness of the current controller against uncertainty in system parameters.
5.1. Performance Evaluation under SLP
5.2. Performance Evaluation of the Controller for Sinusoidal Load Changes
5.3. Performance Evaluation of the Controller under Random Load Perturbations
5.4. Sensitivity Analysis
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. System Parameters
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Governor time constant of steam turbine | Time constant of the valve positioner | ||
Steam turbine time constant | Hydro turbine governor time constant | ||
Steam turbine reheat time constant | Compressor discharge volume time constant | ||
Steam turbine reheat constant | Gas turbine valve positioner | ||
Lead time constant of gas turbine governor | Gas turbine fuel time constant | ||
Lag time constant of gas turbine governor | Gas turbine combustion reaction time delay | ||
Starting time of water in hydro turbine | Hydro turbine speed governor reset time | ||
Power system time constants | Participation factors of thermal unit | ||
Participation factors of hydro unit | Participation factors of gas unit | ||
Power system gains | Synchronizing coefficient | ||
Governor speed regulation parameters of thermal unit | Governor speed regulation parameters of hydro unit | ||
Governor speed regulation parameters of gas unit | Frequency bias coefficients of area-1 | ||
Frequency bias coefficients of area-2 |
ACE | |||||||
---|---|---|---|---|---|---|---|
NL | NM | NS | Z | PS | PM | PL | |
NL | PL | PL | PL | PM | PM | PS | Z |
NM | PL | PM | PM | PM | PS | Z | NS |
NS | PL | PM | PS | PS | Z | NS | NM |
Z | PM | PM | PS | Z | NS | NM | NM |
PS | PM | PS | Z | NS | NS | NM | LN |
PM | PS | Z | NS | NM | NM | NM | LN |
PL | Z | NS | NM | NM | LN | LN | LN |
Controller | Controller Gains | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
FOPID [17] | 0.8413 | 1.3263 | 1.4395 | - | - | - | - | 0.8512 | 0.8768 | - | - |
FOiPID | 0.9413 | 0.9663 | 1.0432 | - | - | - | - | 0.9765 | 0.7986 | - | - |
Proposed controller | 0.7458 | 1.0115 | 1.9765 | 0.5670 | 0.6961 | 0.9552 | 0.6785 | 0.5611 | 0.7654 | 0.9045 | 0.8563 |
Controller | Settling Time (Sec) for 5% Band | Peak Overshoot | Peak Undershoot () | ITAE | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
FOPID [17] | 11.57 | 10.72 | 11.450 | 9.951 | 0.0076 | 0.0069 | 0.0001 | 0.0023 | 0.0302 | 0.0371 | 0.0063 | 0.0187 | 1.1780 |
FOiPID | 8.058 | 7.684 | 8.764 | 6.009 | 0.0052 | 0.0047 | 0.0 | 0.0014 | 0.0282 | 0.0330 | 0.0058 | 0.0176 | 0.9714 |
Proposed controller | 5.325 | 4.371 | 8.750 | 4.250 | 0.0034 | 0.0033 | 0.0 | 0.0 | 0.0243 | 0.0307 | 0.0053 | 0.0157 | 0.7057 |
Controller Parameter Variation | %Change | Settling Time (Sec) for 5% Band | Peak Overshoot | Peak Undershoot () | ITAE | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Nominal | No change | 5.325 | 4.371 | 8.750 | 0.0034 | 0.0033 | 0.0 | 0.0243 | 0.0307 | 0.0053 | 0.7057 |
Loading condition | 5.892 | 5.670 | 8.801 | 0.0035 | 0.0035 | 0.0 | 0.0283 | 0.0353 | 0.0061 | 0.8718 | |
4.942 | 4.001 | 8.475 | 0.0014 | 0.0015 | 0.0 | 0.0192 | 0.0237 | 0.0041 | 0.5038 | ||
5.351 | 4.382 | 8.740 | 0.0034 | 0.0033 | 0.0 | 0.0243 | 0.0307 | 0.0053 | 0.7238 | ||
5.315 | 4.365 | 8.760 | 0.0035 | 0.0034 | 0.0 | 0.0243 | 0.0307 | 0.0053 | 0.6913 | ||
6.021 | 5.341 | 8.750 | 0.0035 | 0.0034 | 0.0 | 0.0248 | 0.0315 | 0.0054 | 0.7458 | ||
4.567 | 3.925 | 8.752 | 0.0025 | 0.0012 | 0.0 | 0.0264 | 0.0269 | 0.0045 | 0.6576 | ||
5.325 | 4.371 | 8.750 | 0.0035 | 0.0034 | 0.0 | 0.0243 | 0.0307 | 0.0053 | 0.7110 | ||
3.325 | 4.371 | 8.750 | 0.0034 | 0.0033 | 0.0 | 0.0243 | 0.0307 | 0.0053 | 0.6982 |
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Gomaa Haroun, A.H.; Li, Y.-Y. Ant Lion Optimized Fractional Order Fuzzy Pre-Compensated Intelligent Pid Controller for Frequency Stabilization of Interconnected Multi-Area Power Systems. Appl. Syst. Innov. 2019, 2, 17. https://doi.org/10.3390/asi2020017
Gomaa Haroun AH, Li Y-Y. Ant Lion Optimized Fractional Order Fuzzy Pre-Compensated Intelligent Pid Controller for Frequency Stabilization of Interconnected Multi-Area Power Systems. Applied System Innovation. 2019; 2(2):17. https://doi.org/10.3390/asi2020017
Chicago/Turabian StyleGomaa Haroun, A. H., and Yin-Ya Li. 2019. "Ant Lion Optimized Fractional Order Fuzzy Pre-Compensated Intelligent Pid Controller for Frequency Stabilization of Interconnected Multi-Area Power Systems" Applied System Innovation 2, no. 2: 17. https://doi.org/10.3390/asi2020017