A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systems
Abstract
:1. Introduction
2. Dynamic Model of One-Area LFC System with Time Delay
3. Delay Margin Computation Using the Sweeping Test
- (i)
- A is stable,
- (ii)
- A + Ad is stable, and
- (iii)
4. Case Study: One-Area LFC System
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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KP | τd, s | KI | ||||||
---|---|---|---|---|---|---|---|---|
Method | 0.05 | 0.1 | 0.15 | 0.2 | 0.4 | 0.6 | 1 | |
0 | Theorem 1 | 30.928 | 15.207 | 9.961 | 7.338 | 3.382 | 2.042 | 0.923 |
[32] | 30.915 | 15.201 | 9.96 | 7.335 | 3.382 | 2.042 | 0.923 | |
[18] | 30.853 | 15.172 | 9.942 | 7.323 | 3.377 | 2.04 | 0.922 | |
[16] | 27.927 | 13.778 | 9.056 | 6.692 | 3.124 | 1.91 | 0.886 | |
0.05 | Theorem 1 | 31.851 | 15.687 | 10.277 | 7.573 | 3.502 | 2.122 | 0.97 |
[32] | 31.875 | 15.681 | 10.279 | 7.575 | 3.501 | 2.122 | 0.97 | |
[18] | 31.498 | 15.647 | 10.258 | 7.561 | 3.496 | 2.119 | 0.969 | |
[16] | 27.874 | 14.061 | 9.284 | 6.866 | 3.215 | 1.974 | 0.927 | |
0.1 | Theorem 1 | 32.769 | 16.127 | 10.575 | 7.793 | 3.61 | 2.194 | 1.012 |
[32] | 32.751 | 16.119 | 10.571 | 7.794 | 3.61 | 2.194 | 1.012 | |
[18] | 30.415 | 15.765 | 10.547 | 7.777 | 3.604 | 2.191 | 1.011 | |
[16] | 27.038 | 13.682 | 9.22 | 6.941 | 3.29 | 2.029 | 0.963 | |
0.2 | Theorem 1 | 34.198 | 16.86 | 11.06 | 8.16 | 3.792 | 2.313 | 1.079 |
[32] | 34.226 | 16.856 | 11.062 | 8.162 | 3.792 | 2.313 | 1.079 | |
[18] | 28.01 | 14.597 | 10.107 | 7.821 | 3.784 | 2.309 | 1.077 | |
[16] | 25.114 | 12.76 | 8.617 | 6.535 | 3.32 | 2.108 | 1.016 | |
0.4 | Theorem 1 | 35.802 | 17.661 | 11.596 | 8.559 | 3.981 | 2.426 | 1.118 |
[32] | 35.834 | 17.658 | 11.594 | 8.559 | 3.98 | 2.426 | 1.118 | |
[18] | 22.457 | 11.835 | 8.287 | 6.505 | 3.718 | 2.419 | 1.116 | |
[16] | 20.364 | 10.426 | 7.065 | 5.384 | 2.832 | 1.912 | 1.017 | |
0.6 | Theorem 1 | 34.906 | 17.198 | 11.28 | 8.311 | 3.826 | 2.281 | 0.947 |
[32] | 34.922 | 17.195 | 11.278 | 8.312 | 3.826 | 2.281 | 0.947 | |
[18] | 16.033 | 8.624 | 6.209 | 4.997 | 3.038 | 2.178 | 0.964 | |
[16] | 14.618 | 7.477 | 5.157 | 3.958 | 2.13 | 1.475 | 0.827 | |
1 | Theorem 1 | 0.595 | 0.586 | 0.575 | 0.564 | 0.516 | 0.463 | 0.361 |
[32] | 0.596 | 0.586 | 0.575 | 0.564 | 0.516 | 0.463 | 0.361 | |
[18] | 0.594 | 0.584 | 0.574 | 0.563 | 0.515 | 0.463 | 0.36 | |
[16] | 0.546 | 0.538 | 0.53 | 0.522 | 0.482 | 0.438 | 0.348 |
θ/rad | KI | ||||||
---|---|---|---|---|---|---|---|
KP | 0.05 | 0.1 | 0.15 | 0.2 | 0.4 | 0.6 | 1.0 |
0 | 1.546 | 1.521 | 1.496 | 1.471 | 1.368 | 1.257 | 0.989 |
0.05 | 1.596 | 1.571 | 1.546 | 1.521 | 1.418 | 1.307 | 1.041 |
0.1 | 1.646 | 1.621 | 1.596 | 1.571 | 1.468 | 1.358 | 1.092 |
0.2 | 1.747 | 1.722 | 1.696 | 1.671 | 1.567 | 1.456 | 1.187 |
0.4 | 1.956 | 1.929 | 1.902 | 1.875 | 1.765 | 1.647 | 1.349 |
0.6 | 2.184 | 2.153 | 2.123 | 2.092 | 1.968 | 1.828 | 1.419 |
1.0 | 1.435 | 1.413 | 1.390 | 1.365 | 1.262 | 1.152 | 0.934 |
ω/(rad/s) | KI | ||||||
---|---|---|---|---|---|---|---|
KP | 0.05 | 0.1 | 0.15 | 0.2 | 0.4 | 0.6 | 1.0 |
0 | 0.0500 | 0.1000 | 0.1502 | 0.2005 | 0.4045 | 0.6153 | 1.0714 |
0.05 | 0.0501 | 0.1002 | 0.1505 | 0.2009 | 0.4050 | 0.6161 | 1.0732 |
0.1 | 0.0502 | 0.1005 | 0.1509 | 0.2016 | 0.4067 | 0.6187 | 1.0784 |
0.2 | 0.0511 | 0.1021 | 0.1534 | 0.2048 | 0.4133 | 0.6295 | 1.1004 |
0.4 | 0.0546 | 0.1092 | 0.1640 | 0.2191 | 0.4434 | 0.6789 | 1.2065 |
0.6 | 0.0626 | 0.1252 | 0.1882 | 0.2518 | 0.5143 | 0.8015 | 1.4981 |
1.0 | 2.4102 | 2.4120 | 2.4151 | 2.4193 | 2.4462 | 2.4861 | 2.5867 |
KI | θ | ω | τd |
---|---|---|---|
0.05 | 1.5460 | 0.0500 | 30.9283 |
0.1 | 1.5212 | 0.1000 | 15.2066 |
0.15 | 1.4963 | 0.1502 | 9.9614 |
0.2 | 1.4712 | 0.2005 | 7.3375 |
0.4 | 1.3678 | 0.4045 | 3.3816 |
0.6 | 1.2566 | 0.6153 | 2.0422 |
1.0 | 0.9889 | 1.0714 | 0.9230 |
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Khalil, A.; Swee Peng, A. A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systems. Energies 2018, 11, 3460. https://doi.org/10.3390/en11123460
Khalil A, Swee Peng A. A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systems. Energies. 2018; 11(12):3460. https://doi.org/10.3390/en11123460
Chicago/Turabian StyleKhalil, Ashraf, and Ang Swee Peng. 2018. "A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systems" Energies 11, no. 12: 3460. https://doi.org/10.3390/en11123460