# Novel Intelligent Control Technology for Enhanced Stability Performance of an Ocean Wave Energy Conversion System

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## Abstract

**:**

## 1. Introduction

## 2. Modeling of the Studied System

#### 2.1. Structure of the System

#### 2.2. Wave Energy Characteristics

_{wave}is as follows [25]

#### 2.3. Wells Turbine Modeling

_{A}and V

_{B}represent the axial velocity and blade tip velocity (m/s), respectively, k is the coefficient of the Wells turbine and C

_{1}to C

_{8}are the power coefficients.

#### 2.4. DFIG Modeling

## 3. Design of the Novel FLWRBFN with DEPSO Control System

#### 3.1. Function-Link Based Wilcoxon Radial Basis Function Network (FLWRBFN)

_{1}x

_{2}] are extended to ${\varphi}_{E}={\left[\begin{array}{cccc}{\varphi}_{1}& ,{\varphi}_{2}& \cdots & ,{\varphi}_{8}\end{array}\right]}^{}={\left[\begin{array}{cccccccc}1& ,{x}_{1}& ,\mathrm{sin}(\pi {x}_{1})& ,\mathrm{cos}(\pi {x}_{1})& ,{x}_{2}& ,\mathrm{sin}(\pi {x}_{2})& ,\mathrm{cos}(\pi {x}_{2})& ,{x}_{1}{x}_{2}\end{array}\right]}^{}$. The second layer output ${\mathsf{\Gamma}}_{j}^{(2)}$ of the extended input variable is:

#### 3.2. Learning and Training Procedures of FLWRBFN

#### 3.3. DEPSO Online Adjusts Learning Rate

## 4. Analysis of Convergence

## 5. Simulation Results and Case Studies

_{DFIG}= 20 MW, 3.76 A, 3000 r/min, T

_{R}= 0.69/33 kV, J = 0.00132 Nm s2, B = 0.00577 Nm s/rad, V = 15 KV, PF = 0.976, f = 60 Hz, C

_{dc}= 0.6 pu.

#### 5.1. Load Change

#### 5.2. Short Circuit Fault

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Halamay, D.A.; Simmons, A.; McArthur, S.; Brekken, T.K.A. Reserve requirement impacts of large-scale integration of wind, solar, and ocean wave power generation. IEEE Trans. Sustain. Energy
**2011**, 2, 321–328. [Google Scholar] [CrossRef] - Zhao, X.; Yan, Z.; Zhang, X.-P. A wind-wave farm system with self-energy storage and smoothed power output. IEEE Access
**2016**, 4, 8634–8642. [Google Scholar] [CrossRef] - Linda, S.; Rachel, S.; Thomas, D. What drives energy consumers: Engaging people in a sustainable energy transition. IEEE Power Energy Mag.
**2018**, 16, 20–28. [Google Scholar] - Romain, G.; Josh, D.; John, V.R. Adaptive control of a wave energy converter. IEEE Trans. on Sustain. Energy
**2018**, 1, 1. [Google Scholar] - Nicola, D.; Davide, B.; Francesco, G.; Paolo, C.; Giampaolo, B. Review of oscillating water column converters. IEEE Trans. Indust. Appl.
**2016**, 52, 1698–1710. [Google Scholar] - Sunil, K.M.; Aradhna, P. Wells turbine modeling and PI control scheme for OWC plant using Xilinx system generator. In Proceedings of the International Conference on Power, Control & Embedded Systems (ICPCES), Allahabad, India, 9–11 March 2017; pp. 1–6. [Google Scholar]
- Francesco, F.; Ringwood, J.V. A simple and effective real-time controller for wave energy converters. IEEE Trans. Sustain. Energy
**2013**, 4, 21–30. [Google Scholar] - Bacelli, G.; Nevarez, V.; Coe, R.G.; Wilson, D.G. Feedback Resonating Control for a Wave Energy Converter. IEEE Trans. Ind. Appl.
**2019**, 56, 1862–1868. [Google Scholar] [CrossRef] - Foster, S.; Xu, L.; Fox, B. Coordinated reactive power control for facilitating fault ride through of doubly fed induction generator- and fixed speed induction generator-based wind farms. IET Renew. Power Gener.
**2010**, 4, 128–138. [Google Scholar] [CrossRef] - López, J.; Gubía, E.; Olea, E.; Ruiz, J.; Marroyo, L. Ride through of wind turbines with doubly fed induction generator under sym-metrical voltage dips. IEEE Trans. Ind. Electron.
**2009**, 56, 4246–4254. [Google Scholar] [CrossRef] - Meegahapola, L.G.; Littler, T.; Flynn, D. Decoupled-DFIG fault ride-through strategy for enhanced stability performance during grid faults. IEEE Trans. Sustain. Energy
**2010**, 1, 152–162. [Google Scholar] [CrossRef] [Green Version] - Yang, L.; Xu, Z.; Ostergaard, J.; Dong, Z.Y.; Wong, K.P. Advanced control strategy of DFIG wind turbines for power system fault ride through. IEEE Trans. Power Syst.
**2012**, 27, 713–722. [Google Scholar] [CrossRef] [Green Version] - Kennedy, J.; Eberhart, R.C. Particle swarm optimisation. In Proceedings of the IEEE International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December 1995; pp. 1942–1948. [Google Scholar]
- Storn, R.; Price, K. Differential Evolution-A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces; Technical Report TR-95-012; International Computer Science Institute: Berkley, CA, USA, 1995. [Google Scholar]
- Mohammadmehdi, S.; Rasoul, R.; Saad, M.; Amanullah, M.T.O.; Alex, S.; Tey, K.S.; Alireza, S.G. Simulation and hardware im-plementation of new maximum power point tracking technique for partially shaded PV system using hybrid depso method. IEEE Trans. Sustain. Energy
**2015**, 6, 850–862. [Google Scholar] - Huo, J.; Ma, L.; Yu, Y.; Wang, J. Hybrid algorithm based mobile robot localization using DE and PSO. In Proceedings of the 32nd Chinese Control Conference, Xi’an, China, 26–28 July 2013; pp. 5955–5959. [Google Scholar]
- Wang, P.; Liang, L.; Ji, Y.; Liu, X.; Chen, S.; Xie, G.; Fan, L. Parameter identification of steam turbine governor system based on DEPSO algorithm. In Proceedings of the 2017 3rd IEEE International Conference on Control Science and Systems Engineering (ICCSSE); Institute of Electrical and Electronics Engineers (IEEE), Beijing, China, 17–19 August 2017; pp. 228–232. [Google Scholar]
- Elgammal, A.A.A. Adaptive fuzzy sliding mode controller for grid interface ocean wave energy conversion. J. Intell. Learn. Syst. Appl.
**2014**, 6, 53–69. [Google Scholar] [CrossRef] [Green Version] - Hong, Y.; Waters, R.; Bostrom, C.; Eriksson, M.; Engstrom, J.; Leijon, M. Review on electrical control strategies for wave energy conversion systems. Renew. Sustain. Energy Rev.
**2014**, 31, 329–342. [Google Scholar] [CrossRef] - Lin, W.-M.; Hong, C.-M.; Huang, C.-H.; Ou, T.-C. Hybrid control of a wind induction generator based on grey-elman neural network. IEEE Trans. Control. Syst. Technol.
**2013**, 21, 2367–2373. [Google Scholar] [CrossRef] - Patra, J.C.; Pal, R.N. A functional link artificial neural network for adaptive channel equalization. Signal Process.
**1995**, 43, 181–195. [Google Scholar] [CrossRef] - Ou, T.-C.; Lu, K.-H.; Huang, C.-J. Improvement of transient stability in a hybrid power multi-system using a designed NIDC (novel intelligent damping controller). Energies
**2017**, 10, 488. [Google Scholar] [CrossRef] [Green Version] - Lin, W.; Lu, K.; Ou, T. Design of a novel intelligent damping controller for unified power flow controller in power system connected offshore power applications. IET Gener. Transm. Distrib.
**2015**, 9, 1708–1717. [Google Scholar] [CrossRef] - Vinal, P.; Vaibhav, G.; Shashank, H.; Nithin, V.G. Design of adaptive exponential functional link network-based nonlinear filters. IEEE Trans. Circ. Syst. I. Regular Papers
**2016**, 63, 1434–1442. [Google Scholar] - Brekken, T.K.A.; Ozkan-Haller, H.T.; Simmons, A. A methodology for large-scale ocean wave power time-series generation. IEEE J. Ocean. Eng.
**2012**, 37, 294–300. [Google Scholar] [CrossRef] - Cashman, D.P. Electrical Machine Characterisation and Analysis for Renewable Energy Applications. Ph.D. Thesis, University College Cork, Cork, Ireland, 2010. [Google Scholar]
- Wang, L.; Chen, Z.-J. Stability analysis of a wave-energy conversion system containing a grid-connected induction generator driven by a wells turbine. IEEE Trans. Energy Convers.
**2009**, 25, 555–563. [Google Scholar] [CrossRef] - Kiran, D.R.; Palani, A.; Muthukumar, S.; Jayashankar, V. Steady grid power from wave energy. IEEE Trans. Energy Convers.
**2007**, 22, 539–540. [Google Scholar] [CrossRef] - Hogg, R.V.; McKean, J.W.; Craig, A.T. Introduction to Mathematical Statistics, 6th ed.; Prentice-Hall: New Jersey, NJ, USA, 2005. [Google Scholar]
- Lin, W.M.; Hong, C.M. Intelligent approach to maximum power point tracking control strategy for variable-speed wind turbine generation system. Energy
**2010**, 35, 2440–2447. [Google Scholar] [CrossRef] - Lin, C.T.; Lee, G.C.S. Neural Fuzzy Systems; Prentice-Hall, Inc.: Upper Saddle River, NJ, USA, 1996. [Google Scholar]
- Elsayed, S.M.; Sarker, R.A.; Essam, D.L. An improved self-adaptive differential evolution algorithm for optimization problems. IEEE Trans. Ind. Inform.
**2012**, 9, 89–99. [Google Scholar] [CrossRef] - Xin, B.; Chen, J.; Zhang, J.; Fang, H.; Peng, Z.-H. Hybridizing differential evolution and particle swarm optimization to design powerful optimizers: A review and taxonomy. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev.
**2011**, 42, 744–767. [Google Scholar] [CrossRef] [Green Version] - Ben, N.; Li, L. A novel PSO-DE-based hybrid algorithm for global optimization. Comp. Sci.
**2008**, 5227, 156–163. [Google Scholar] - Wu, Y.C.; Lee, W.P.; Chien, C.W. Modified the performance of differential evolution algorithm with dual evolution strategy. Int. Conf. Machine Learn. Comp.
**2011**, 3, 57–63. [Google Scholar] - Yoo, S.J.; Choi, Y.H.; Park, J.B. Generalized predictive control based on self-recurrent wavelet neural network for stable path tracking of mobile robots: Adaptive learning rates approach. IEEE Trans. Circuits Syst. I Regul. Pap.
**2006**, 53, 1381–1394. [Google Scholar] [CrossRef] - Wai, R.J.; Li, C.M. Design of dynamic petri recurrent fuzzy neural network and its application to path-tracking control of nonho-lonomic mobile robot. IEEE Trans. Indust. Electron.
**2009**, 56, 2667–2683. [Google Scholar] - Lin, W.-M.; Hong, C.-M. A new Elman neural network-based control algorithm for adjustable-pitch variable-speed wind-energy conversion systems. IEEE Trans. Power Electron.
**2010**, 26, 473–481. [Google Scholar] [CrossRef] - Lu, K.-H.; Hong, C.-M.; Han, Z.; Yu, L. New Intelligent Control Strategy Hybrid Grey–RCMAC Algorithm for Ocean Wave Power Generation Systems. Energies
**2020**, 13, 241. [Google Scholar] [CrossRef] [Green Version]

**Figure 3.**The dynamic simulation results of the studied system under load change: (

**a**) Turbine speed; (

**b**) AC line voltage; (

**c**) DC link voltage; (

**d**) Grid side real power.

**Figure 5.**The transient simulation results of the studied system under short circuit: (

**a**) Turbine speed; (

**b**) AC line voltage; (

**c**) DC link voltage; (

**d**) Grid side real power.

Method | Iterative Number | CPU Run Time (10^{2} s) | Mean Square Error (10^{−3}) | Accuracy (%) |
---|---|---|---|---|

FLWRBFN + DEPSO | 57 | 1.48 | 1.235 | 98.76 |

FLWRBFN + MPSO | 90 | 2.34 | 5.017 | 94.98 |

FLWRBFN + PSO | 54 | 1.40 | 7.581 | 92.42 |

RBFN | 94 | 2.44 | 10.051 | 89.95 |

Methods | Interative Number | CPU Run Time (10^{2} s) | Mean Square Error (10^{−3}) | Accuracy (%) |
---|---|---|---|---|

FLWRBFN + DEPSO | 64 | 1.66 | 15.965 | 84.03 |

FLWRBFN + MPSO | 94 | 2.44 | 20.071 | 79.93 |

FLWRBFN + PSO | 91 | 2.36 | 29.057 | 70.94 |

Method | FLWRBFN + DEPSO | FLWRBFN + MPSO | FLWRBFN + PSO | RBFN |
---|---|---|---|---|

Grid-Side Voltage | 1.0003125 | 1.0005316 | 1.0004338 | 0.9976911 |

DC-Side Voltage | 1.0012123 | 1.0026557 | 1.0013670 | 0.9896110 |

Max. Transient Over Shoot Voltage | 1.0043437 | 1.0060341 | 1.0071922 | 1.0085975 |

Max. Transient Under Shoot Voltage | 0.9965313 | 0.9954371 | 0.9957687 | 0.991125 |

Method | FLWRBFN + DEPSO | FLWRBFN + MPSO | FLWRBFN + PSO | RBFN |
---|---|---|---|---|

Grid-Side Voltage | 1.0204878 | 1.0257873 | 1.0310922 | 1.0214457 |

DC-Side Voltage | 1.006251 | 1.0069122 | 1.0052166 | 1.0071458 |

Max. Transient Over Shoot Voltage | 1.0780488 | 1.0993411 | 1.1477012 | 1.1931707 |

Max. Transient Under Shoot Voltage | 0.9609756 | 0.0922378 | 0.0912409 | 0.0902439 |

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**MDPI and ACS Style**

Lu, K.-H.; Hong, C.-M.; Tan, X.; Cheng, F.-S.
Novel Intelligent Control Technology for Enhanced Stability Performance of an Ocean Wave Energy Conversion System. *Energies* **2021**, *14*, 2027.
https://doi.org/10.3390/en14072027

**AMA Style**

Lu K-H, Hong C-M, Tan X, Cheng F-S.
Novel Intelligent Control Technology for Enhanced Stability Performance of an Ocean Wave Energy Conversion System. *Energies*. 2021; 14(7):2027.
https://doi.org/10.3390/en14072027

**Chicago/Turabian Style**

Lu, Kai-Hung, Chih-Ming Hong, Xiaojing Tan, and Fu-Sheng Cheng.
2021. "Novel Intelligent Control Technology for Enhanced Stability Performance of an Ocean Wave Energy Conversion System" *Energies* 14, no. 7: 2027.
https://doi.org/10.3390/en14072027