Parameter Identification of Pump Turbine Governing System Using an Improved Backtracking Search Algorithm
<p>A simple structure of PTGS.</p> "> Figure 2
<p>The block diagram of the speed governor.</p> "> Figure 3
<p>The characteristic curves of a pump turbine: (<b>a</b>) flow characteristic curve; and (<b>b</b>) moment characteristic curve.</p> "> Figure 4
<p>The <span class="html-italic">WH</span> and <span class="html-italic">WM</span> curves obtained using the improved Suter transform: (<b>a</b>) <span class="html-italic">WH</span> curve; and (<b>b</b>) <span class="html-italic">WM</span> curve.</p> "> Figure 5
<p>The flowchart of the improved backtracking search algorithm.</p> "> Figure 6
<p>The parameter identification model of PTGS based on IBSA.</p> "> Figure 7
<p>Comparison between the outputs of the three parts of the original and the identification systems under frequency disturbance: (<b>a</b>) outputs of the turbine speed; (<b>b</b>) outputs of the guide vane opening; (<b>c</b>) outputs of the controller output; (<b>d</b>) identification error of the turbine speed; (<b>e</b>) identification error of the guide vane opening; and (<b>f</b>) identification error of the controller output.</p> "> Figure 8
<p>Comparison between the outputs of the three parts of the original and the identification systems under load disturbance: (<b>a</b>) outputs of the turbine speed; (<b>b</b>) outputs of the guide vane opening; (<b>c</b>) outputs of the controller output; (<b>d</b>) identification error of the turbine speed; (<b>e</b>) identification error of the guide vane opening; and (<b>f</b>) identification error of the controller output.</p> "> Figure 9
<p>Convergence curves of different optimization algorithms under the frequency and load disturbances.</p> ">
Abstract
:1. Introduction
2. Model of Pump Turbine Governing System
2.1. Model of the Speed Governor
2.1.1. Model of the Controller
2.1.2. Model of the Servomechanism
2.2. Model of the Penstock System
2.3. Model of the Pump Turbine
2.4. Model of the Generator with a Load
3. Improved Backtracking Search Algorithm
3.1. Overview of the Backtracking Search Algorithm
3.2. Improvements of the Backtracking Search Algorithm
3.2.1. The Orthogonal Initialization Technique
3.2.2. The Chaotic Local Search Operator
3.2.3. The Elastic Boundary Processing Strategy
3.2.4. The Adaptive Mutation Scale Factor
3.2.5. The Flowchart of the Improved Backtracking Search Algorithm
4. Parameter Identification Strategy
4.1. Parameter Identification of PTGS Based on IBSA
4.2. Objective Function
5. Experiments and Results Analysis
5.1. Case Study
5.2. Parameter Identification under Frequency and Load Disturbances
5.3. Influence of Signal-To-Noise Ratio (SNR) on Identification Accuracy
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Actual Value | PSO | GSA | BSA | IBSA | |||||
---|---|---|---|---|---|---|---|---|---|
PE | PE | PE | PE | ||||||
Kp | 8.7 | 8.428 | 0.031 | 8.617 | 0.010 | 8.687 | 0.001 | 8.703 | 0.000 |
Ki | 0.35 | 0.463 | 0.323 | 0.32 | 0.086 | 0.331 | 0.054 | 0.356 | 0.017 |
Kd | 1.9 | 2.35 | 0.237 | 1.936 | 0.019 | 1.908 | 0.004 | 1.917 | 0.009 |
Ty | 0.2 | 0.277 | 0.385 | 0.199 | 0.005 | 0.2 | 0.000 | 0.198 | 0.010 |
Tyl | 0.02 | 0.01 | 0.500 | 0.021 | 0.050 | 0.019 | 0.050 | 0.02 | 0.000 |
Tw | 1.3 | 1.445 | 0.112 | 1.135 | 0.127 | 1.207 | 0.072 | 1.293 | 0.005 |
Ta | 10.8 | 9.523 | 0.118 | 11.457 | 0.061 | 11.54 | 0.069 | 10.883 | 0.008 |
en | 1 | 1.205 | 0.205 | 0.918 | 0.082 | 0.958 | 0.042 | 0.996 | 0.004 |
APE | 0.239 | 0.055 | 0.037 | 0.007 |
Actual Value | PSO | GSA | BSA | IBSA | |||||
---|---|---|---|---|---|---|---|---|---|
PE | PE | PE | PE | ||||||
Kp | 6.7 | 7.351 | 0.097 | 6.638 | 0.009 | 6.726 | 0.004 | 6.71 | 0.001 |
Ki | 0.45 | 0.415 | 0.078 | 0.448 | 0.004 | 0.445 | 0.011 | 0.451 | 0.002 |
Kd | 0.5 | 0.45 | 0.100 | 0.412 | 0.176 | 0.427 | 0.146 | 0.481 | 0.038 |
Ty | 0.18 | 0.197 | 0.094 | 0.183 | 0.017 | 0.21 | 0.167 | 0.172 | 0.044 |
Tyl | 0.02 | 0.03 | 0.500 | 0.027 | 0.350 | 0.024 | 0.200 | 0.023 | 0.150 |
Tw | 1.3 | 1.469 | 0.130 | 1.451 | 0.116 | 1.432 | 0.102 | 1.392 | 0.071 |
Ta | 10.8 | 11.44 | 0.059 | 10.873 | 0.007 | 11.21 | 0.038 | 10.854 | 0.005 |
en | 0.9 | 1.259 | 0.399 | 0.96 | 0.067 | 0.947 | 0.052 | 0.906 | 0.007 |
APE | 0.182 | 0.093 | 0.090 | 0.040 |
Actual Value | 90 dB | 50 dB | 20 dB | ||||
---|---|---|---|---|---|---|---|
PE | PE | PE | |||||
Kp | 8.7 | 8.703 | 0.000 | 8.65 | 0.006 | 8.542 | 0.018 |
Ki | 0.35 | 0.356 | 0.017 | 0.35 | 0.000 | 0.341 | 0.026 |
Kd | 1.9 | 1.917 | 0.009 | 1.887 | 0.007 | 2.234 | 0.176 |
Ty | 0.2 | 0.198 | 0.010 | 0.195 | 0.025 | 0.172 | 0.140 |
Tyl | 0.02 | 0.02 | 0.000 | 0.0193 | 0.035 | 0.026 | 0.300 |
Tw | 1.3 | 1.293 | 0.005 | 1.28 | 0.015 | 1.387 | 0.067 |
Ta | 10.8 | 10.883 | 0.008 | 10.92 | 0.011 | 10.583 | 0.020 |
en | 1 | 0.996 | 0.004 | 0.983 | 0.017 | 0.979 | 0.021 |
APE | 0.007 | 0.015 | 0.096 |
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Zhou, J.; Zhang, C.; Peng, T.; Xu, Y. Parameter Identification of Pump Turbine Governing System Using an Improved Backtracking Search Algorithm. Energies 2018, 11, 1668. https://doi.org/10.3390/en11071668
Zhou J, Zhang C, Peng T, Xu Y. Parameter Identification of Pump Turbine Governing System Using an Improved Backtracking Search Algorithm. Energies. 2018; 11(7):1668. https://doi.org/10.3390/en11071668
Chicago/Turabian StyleZhou, Jianzhong, Chu Zhang, Tian Peng, and Yanhe Xu. 2018. "Parameter Identification of Pump Turbine Governing System Using an Improved Backtracking Search Algorithm" Energies 11, no. 7: 1668. https://doi.org/10.3390/en11071668