Real-Time LFO Damping Enhancement in Electric Networks Employing PSO Optimized ANFIS
Abstract
:1. Introduction
- Two versions of SMIB electric networks were considered to demonstrate the proposed approach of LFO mitigation. For both the networks, optimized PSS parameters were found offline for a large number of operating conditions using a heuristic optimization technique.
- The PSO inspired ANFIS model was developed by taking the range of operating points as the inputs and the PSS key parameters as the outputs. Different statistical parameters were used to check the efficacy of the developed model.
- The proposed ANFIS model was assessed to provide the optimal PSS parameter in real-time, under any loading condition. Time-domain analysis, eigenvalues, and the damping ratios were used to measure the developed approach’s performance.
2. Power System Models
2.1. Example 1: SMIB Electric Network without UPFC
2.2. Example 2: SMIB Electric Network Equipped with PSS and UPFC
3. Proposed Optimization Method
3.1. Adaptive Neuro-Fuzzy Inference System (ANFIS)
3.2. Particle Swarm Optimization (PSO)
4. Data Processing and ANFIS Model Development
4.1. Data Generation and Processing
4.2. PSO-ANFIS Model Development
5. Results and Discussion
5.1. Example 1: SMIB Electric Network with PSS only
5.1.1. Eigenvalues and Minimum Damping Ratio Analyses
5.1.2. Time-Domain Simulation under Disturbance
5.2. Example 2: SMIB System with UPFC Coordinated PSS
5.2.1. Eigenvalues and Minimum Damping Ratio Analysis
5.2.2. Time-Domain Simulation under Disturbance
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
ANFIS | Adaptive neuro-fuzzy inference system |
ANN | Artificial neural networks |
AVR | Automatic voltage regulator |
BT | Boosting transformer |
ET | Excitation transformer |
FACTS | Flexible alternating current transmission system |
LFO | Low-frequency oscillations |
MAPE | Mean absolute percentage error |
MDR | Minimum damping ratio |
PSO | Particle swarm optimization |
PSS | Power system stabilizer |
RMSE | Root mean squared error |
RSR | RMSE-observations to standard deviation ratio |
R2 | Coefficient of determination |
SMIB | Single machine infinite bus |
SPI | Statistical performance indices |
UPFC | Unified power flow controller |
VSC | Voltage source converter |
WIA | Willmott’s index of agreement |
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Limit | Real Power (Pe) | Reactive Power (Qe) | Terminal Voltage (Vt) |
---|---|---|---|
Minimum | 0.40 | −0.30 | 0.90 |
Maximum | 1.10 | 0.40 | 1.10 |
Cluster Number | Gain Parameter (K) | Time Constant Parameter (T1) | ||
---|---|---|---|---|
MAPE | R2 | MAPE | R2 | |
2 | 3.5455 | 0.9867 | 2.1450 | 0.9900 |
3 | 4.3358 | 0.9882 | 2.3695 | 0.9887 |
4 | 2.4405 | 0.9939 | 2.5640 | 0.9873 |
5 | 4.8319 | 0.9836 | 2.0364 | 0.9903 |
6 | 2.8576 | 0.9935 | 2.2844 | 0.9884 |
7 | 4.0036 | 0.9868 | 2.6272 | 0.9862 |
8 | 3.7293 | 0.9874 | 1.9038 | 0.9928 |
9 | 2.4318 | 0.9948 | 1.9486 | 0.9926 |
10 | 3.9331 | 0.9872 | 2.1869 | 0.9854 |
11 | 3.2829 | 0.9911 | 1.9155 | 0.9924 |
12 | 3.3876 | 0.9895 | 2.1047 | 0.9915 |
Cluster Number | Gain Parameter (K) | Time Constant Parameter (T1) | ||
---|---|---|---|---|
MAPE | R2 | MAPE | R2 | |
2 | 1.3557 | 0.9779 | 0.2414 | 0.8196 |
3 | 2.1198 | 0.9564 | 0.2667 | 0.7990 |
4 | 1.0857 | 0.9864 | 0.1834 | 0.8838 |
5 | 2.0702 | 0.9522 | 0.1039 | 0.9703 |
6 | 0.8781 | 0.9915 | 0.1213 | 0.9548 |
7 | 0.7446 | 0.9942 | 0.1376 | 0.9277 |
8 | 1.4883 | 0.9774 | 0.1553 | 0.9356 |
9 | 1.5006 | 0.9781 | 0.0786 | 0.9824 |
10 | 1.2636 | 0.9807 | 0.1255 | 0.9607 |
11 | 1.3736 | 0.9770 | 0.1305 | 0.9484 |
12 | 1.4426 | 0.9770 | 0.1304 | 0.9497 |
#ID | Value | #ID | Value | #ID | Value | #ID | Value | #ID | Value | #ID | Value |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.0912 | 16 | 0.9188 | 31 | 0.0841 | 46 | 25.1397 | 61 | 0.0215 | 76 | 0.0742 |
2 | 0.7817 | 17 | −1.8641 | 32 | 0.0125 | 47 | 0.0235 | 62 | 0.9653 | 77 | 0.0230 |
3 | 0.0919 | 18 | 18.7428 | 33 | 0.0822 | 48 | 0.9688 | 63 | 0.0247 | 78 | 0.9509 |
4 | 0.7248 | 19 | 0.0799 | 34 | 0.7026 | 49 | 0.0238 | 64 | 0.4873 | 79 | −0.0283 |
5 | 0.1297 | 20 | −0.1893 | 35 | −2.1530 | 50 | 0.9967 | 65 | −0.5668 | 80 | 0.0102 |
6 | 0.4261 | 21 | 0.0835 | 36 | 4.9097 | 51 | 0.0308 | 66 | 6.0841 | 81 | 0.0159 |
7 | 0.0994 | 22 | −0.1487 | 37 | 0.0237 | 52 | 1.0634 | 67 | −0.0078 | 82 | 0.9918 |
8 | 0.5793 | 23 | −2.1377 | 38 | 0.9641 | 53 | −0.3098 | 68 | 0.0228 | 83 | −0.0069 |
9 | −0.4695 | 24 | −1.0173 | 39 | 0.0233 | 54 | 24.8816 | 69 | 0.0219 | 84 | 0.0181 |
10 | −18.226 | 25 | 0.0832 | 40 | 0.9745 | 55 | 0.0026 | 70 | 0.9659 | 85 | 0.0208 |
11 | 0.0987 | 26 | −0.0634 | 41 | −0.0309 | 56 | −0.0072 | 71 | −0.0717 | 86 | 0.9667 |
12 | 0.7177 | 27 | −2.1694 | 42 | 1.3100 | 57 | 0.0218 | 72 | 0.1264 | 87 | 0.1009 |
13 | 0.1114 | 28 | 1.3801 | 43 | 0.0235 | 58 | 0.9682 | 73 | −0.2241 | 88 | −0.2637 |
14 | 0.3909 | 29 | 0.0810 | 44 | 0.9856 | 59 | −0.0049 | 74 | 3.6773 | 89 | 0.0768 |
15 | 0.0294 | 30 | −0.1725 | 45 | 0.0525 | 60 | 0.0149 | 75 | 0.0033 | 90 | −24.141 |
Parameter | RMSE | MAPE | RSR | PIBIAS | R2 | WIA | |
---|---|---|---|---|---|---|---|
K | First network | 0.2640 | 0.0032 | 0.0401 | −0.0736 | 0.9992 | 0.9996 |
Second network | 0.2003 | 0.0058 | 0.0853 | 0.0539 | 0.9964 | 0.9982 | |
T1 | First network | 0.0011 | 0.0032 | 0.0219 | 0.0248 | 0.9998 | 0.9999 |
Second network | 0.0001 | 0.0001 | 0.0187 | −0.0004 | 0.9998 | 0.9999 |
Case | Pe (pu) | Qe (pu) | Vt (pu) | Gain Parameter (K) | Time Constant Parameter (T1) | ||
---|---|---|---|---|---|---|---|
PSO-ANFIS | Conventional | PSO-ANFIS | Conventional | ||||
Loading condition # 1 | 1.000 | 0.015 | 1.050 | 18.365 | 7.090 | 0.263 | 0.685 |
Loading condition # 2 | 0.894 | −0.281 | 0.955 | 13.526 | 0.325 | ||
Loading condition # 3 | 0.955 | 0.276 | 1.031 | 25.639 | 0.194 |
Item | Conventional PSS | Ref. [37] | Proposed |
---|---|---|---|
Eigenvalues | −0.337 | −0.346 | −0.346 |
−18.703 1.127 ± j4.333 −4.4618 ± j7.483 | −18.207 −2.982 ± j5.6949 −3.006 ± j5.342 | −18.206 −2.928 ± j5.386 −3.061 ± j5.653 | |
MDR | 0.252 | 0.464 | 0.476 |
Item | Conventional PSS | Ref. [37] | Proposed |
---|---|---|---|
Eigenvalues | −0.337 | Not available | −0.342 |
−19.123 −1.494 ± j4.408 −4.040 ± j7.551 | −18.508 −2.801 ± j5.583 −3.038 ± j5.676 | ||
MDR | 0.3209 | 0.464 | 0.448 |
Item | Conventional PSS | Ref. [37] | Proposed |
---|---|---|---|
Eigenvalues | −0.338 | Not available | −0.358 |
−18.379 −0.621 ± j3.596 −5.285 ± j7.414 | −17.673 −2.968 ± j4.709 −3.281 ± j4.927 | ||
MDR | 0.170 | 0.534 | 0.533 |
Case | Pe (pu) | Qe (pu) | Vt (pu) | Gain Parameter (K) | Time Constant Parameter (T1) | ||
---|---|---|---|---|---|---|---|
PSO-ANFIS | Conventional | PSO-ANFIS | Conventional | ||||
Loading condition # 4 | 0.980 | −0.160 | 1.000 | 24.005 | 15.000 | 0.984 | 0.500 |
Loading condition # 5 | 0.600 | 0.010 | 0.980 | 25.583 | 0.9839 | ||
Loading condition # 6 | 1.300 | 0.400 | 1.060 | 31.873 | 0.986 |
Item | Conventional PSS | Ref. [28] | Ref. [29] | Proposed |
---|---|---|---|---|
Eigenvalues | −0.206 −6.695 −86.497 −110.705 −994.471 −0.419 ± j4.610 −0.676 ± j0.320 | −0.199 −1.056 −80.726 −125.389 −982.089 −1.493 ± j0.438 −4.159 ± j3.708 | −0.199 −1.184 −80.7544 −125.298 −982.175 −1.459 ± j0.249 −4.118 ± j3.699 | −0.199 −1.683 −80.806 −125.131 −982.332 −1.248 ± j0.136 −4.059 ± j3.673 |
MDR | 0.091 | 0.746 | 0.744 | 0.741 |
Item | Conventional PSS | Ref. [28] | Ref. [29] | Proposed |
---|---|---|---|---|
Eigenvalues | −0.400 −6.593 −87.562 −110.031 −993.512 −0.615 ± j3.969 −0.718 ± j0.295 | −0.391 −1.089 −83.489 −126.897 −977.786 −1.463 ± j0.302 −4.092 ± j2.851 | −0.391 −1.203 −83.489 −126.899 −977.784 −1.415 ± j0.160 −4.084 ± j2.853 | −0.391 −1.466 −83.494 −126.867 −1.291 ± j0.078 −977.816 −4.0744 ± j2.847 |
MDR | 0.153 | 0.821 | 0.820 | 0.820 |
Item | Conventional PSS | Ref. [28] | Ref. [29] | Proposed |
---|---|---|---|---|
Eigenvalues | −0.147 −7.269 −87.048 −112.996 −991.096 −0.427 ± j4.801 −0.677 ± j0.274 | −0.143 −1.936 −82.539 −136.569 −967.917 −1.1471 ± j0.169 −4.683 ± j3.141 | −0.143 −2.025 −82.571 −136.306 −968.192 −1.141 ± j0.128 −4.623 ± j3.107 | −0.141 −1.063 −81.860 −142.793 −961.396 −1.009 ± j0.781 −5.746 ± j3.741 |
MDR | 0.089 | 0.831 | 0.830 | 0.791 |
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Pathan, M.I.H.; Rana, M.J.; Shahriar, M.S.; Shafiullah, M.; Zahir, M.H.; Ali, A. Real-Time LFO Damping Enhancement in Electric Networks Employing PSO Optimized ANFIS. Inventions 2020, 5, 61. https://doi.org/10.3390/inventions5040061
Pathan MIH, Rana MJ, Shahriar MS, Shafiullah M, Zahir MH, Ali A. Real-Time LFO Damping Enhancement in Electric Networks Employing PSO Optimized ANFIS. Inventions. 2020; 5(4):61. https://doi.org/10.3390/inventions5040061
Chicago/Turabian StylePathan, Md Ilius Hasan, Md Juel Rana, Mohammad Shoaib Shahriar, Md Shafiullah, Md. Hasan Zahir, and Amjad Ali. 2020. "Real-Time LFO Damping Enhancement in Electric Networks Employing PSO Optimized ANFIS" Inventions 5, no. 4: 61. https://doi.org/10.3390/inventions5040061