# Modelling and Performance Analysis of a Tidal Current Turbine Connected to the Grid Using an Inductance (LCL) Filter

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Tidal Overview

^{3}[23]. The ${C}_{p}$ variations depend on the pitch angle of the blades $\left(\beta \right)$ and the tip-speed ratio λ, defined as the ratio between the rotor tip speed and the tides’ velocity ${C}_{p}(\lambda ,\beta )$ curve [23].

## 3. Modelling of Tidal Generation Connected to Grid Using LCL Filter

## 4. Control Scheme

#### 4.1. Modelling of Phase-Locked Loop (PLL)

#### 4.1.1. Outer-Loop Controller

#### 4.1.2. Inner-Loop Control

#### 4.2. Modulation Control

_{d}and u

_{q}are the current errors output signals.

#### 4.3. Modelling of Permanent Magnet Synchronous

#### 4.4. Modelling of LCL Filter

#### 4.5. Filter Capacitor

#### 4.6. Current Ripple

#### 4.7. Modelling of Back-to-Back Converters

_{dc}. A grid-coupled inverter changes the DC electricity back into a fixed-frequency AC current [40]. The inverter can separately control the reactive and active power that is injected, and it can also balance the active power by adjusting the DC bus voltage. The active rectifier is a three-phase IGBT voltage source converter that employs field-oriented control (FOC) to adjust the generator current based on the alignment of the stator current with the electromotive force (EMF).

#### 4.8. PID Controller

**Figure 7.**A PID controller with a feedback loop block diagram [44].

#### 4.9. Generic Three-Phase VSC Electrical Topology

_{s}, R

_{s}), six separate IGBT switches, and a DC-link capacitor C on the DC side.

#### 4.10. Modelling of DC-Link Voltage

## 5. Case System Description

## 6. Results and Analysis

#### 6.1. Control

#### 6.2. Inverter Characteristics

#### 6.3. Case Studies

^{−7}VAR), whereas the active power was 2.5 MW. Between t = 0 and t = 0.3 s, the active power signal overshoots were 14.557%, while between t = 0.3 and t = 0.4 s, the value fell short by approximately 1.998% at time t = 0.6 s according to Equation (18) presented in Energies Standard 2021, volume 14 (page 688).

## 7. Discussion

## 8. Conclusions

^{−7}VAR) from t = 0 to t = 0.3 s. There were some harmonics at the PMSG output restrictions and some with voltage sag in the tidal power generation. The LCL filter lowered the switching frequency ripple and aided in coupling with a current-like performance to the utility grid, and the intermediate circuit’s voltage ripples were reduced and stabilised at the predetermined value. Therefore, it meets industry standards and allows for the occurrence of a THD within. The outcomes of the simulation demonstrate that the controller’s operation presents no issues and offers a superior dynamic and steady-state performance of the grid-connected tidal energy system with low overall harmonic distortion, which was around 0.12% for voltage and 0.07% for current. To prevent over-modulation, its minimum operating voltage was higher than the grid peak voltage. However, during this investigation, 85% efficiency was attained. The goal of future studies should be to validate these results with a test bench setup and conduct a sensitivity analysis to measure how the system responds to changes in its parameters. Furthermore, future analysis should focus on more advanced and intelligent control strategies to enhance the performance of single-stage inverters. Another factor that needs to be investigated in the framework of smart grids is how to incorporate two-way communication into these systems.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Ranjan, A.; Giribabu, D. Design of LCL Filter For Grid Connected Three Phase Three Level Inverter to Meet IEEE 519 Standards. In Proceedings of the 2023 IEEE International Students’ Conference on Electrical, Electronics and Computer Science (SCEECS), Bhopal, India, 18–19 February 2023; pp. 1–6. [Google Scholar] [CrossRef]
- Kangaji, L.; Orumwense, E.; Abo-Al-ez, K. Modelling and simulation of tidal energy generation system: A systematic literature review. Int. J. Adv. Technol. Eng. Explor.
**2022**, 9, 1028–1055. [Google Scholar] [CrossRef] - Zhou, Z.; Scuiller, F.; Charpentier, J.F.; El Hachemi Benbouzid, M.; Tang, T. Power Control of a Nonpitchable PMSG-Based Marine Current Turbine at Overrated Current Speed with Flux-Weakening Strategy. IEEE J. Ocean. Eng.
**2015**, 40, 536–545. [Google Scholar] [CrossRef] - Elghali, S.E.B.; Benbouzid, M.E.H.; Charpentier, J.F.; Ahmed-Ali, T.; Munteanu, I. High-order sliding mode control of a marine current turbine driven permanent magnet synchronous generator. In Proceedings of the 2009 IEEE International Electric Machines and Drives Conference, Miami, FL, USA, 3–6 May 2009; pp. 1541–1546. [Google Scholar] [CrossRef]
- Melikoglu, M. Current status and future of ocean energy sources: A global review. Ocean Eng.
**2018**, 148, 563–573. [Google Scholar] [CrossRef] - Thiébot, J.; Bois, P.B.D.; Guillou, S. Numerical modeling of the effect of tidal stream turbines on the hydrodynamics and the sediment transport—Application to the Alderney Race (Raz Blanchard), France. Renew. Energy
**2015**, 75, 356–365. [Google Scholar] [CrossRef] - Sousounis, M.C.; Shek, J.K.H.; Sellar, B.G. The effect of supercapacitors in a tidal current conversion system using a torque pulsation mitigation strategy. J. Energy Storage
**2019**, 21, 445–459. [Google Scholar] [CrossRef] - Reznik, A.; Simões, M.G.; Al-Durra, A.; Muyeen, S.M. LCL filter design and performance analysis for small wind turbine systems. In Proceedings of the 2012 IEEE Power Electronics and Machines in Wind Applications, Denver, CO, USA, 16–18 July 2012. [Google Scholar] [CrossRef]
- Carballo, D.; Escala, E.; Balda, J.C. Modeling and Stability Analysis of Grid-Connected Inverters with Different LCL Filter Parameters. In Proceedings of the 2018 IEEE Electronic Power Grid (eGrid), Charleston, SC, USA, 12–14 November 2018; pp. 1–6. [Google Scholar] [CrossRef]
- Zhang, Z.; Wang, P.; Jiang, P.; Gao, F.; Fu, L.; Liu, Z. Robust Control Method of Grid-Connected Inverters with Enhanced Current Quality while Connected to a Weak Power Grid. IEEE Trans. Power Electron.
**2022**, 37, 7263–7274. [Google Scholar] [CrossRef] - Reznik, A.; Simoes, M.G.; Al-Durra, A.; Muyeen, S.M. LCL Filter design and performance analysis for grid-interconnected systems. IEEE Trans. Ind. Appl.
**2014**, 50, 1225–1232. [Google Scholar] [CrossRef] - Ali, S.W.; Sadiq, M.; Terriche, Y.; Naqvi, S.A.; Mutarraf, M.U.; Hassan, M.A.; Yang, G.; Su, C.L.; Guerrero, J.M. Offshore Wind Farm-Grid Integration: A Review on Infrastructure, Challenges, and Grid Solutions. IEEE Access
**2021**, 9, 102811–102827. [Google Scholar] [CrossRef] - Sen, S.; Yenduri, K.; Sensarma, P. Step-by-step design and control of LCL filter based three phase grid-connected inverter. In Proceedings of the 2014 IEEE International Conference on Industrial Technology (ICIT), Busan, Republic of Korea, 26 February–1 March 2014; pp. 503–508. [Google Scholar] [CrossRef]
- Ruiz, G.E.M.; Munoz, N.; Cano, J.B. Modeling, analysis and design procedure of LCL filter for grid connected converters. In Proceedings of the 2015 IEEE Workshop on Power Electronics and Power Quality Applications (PEPQA), Bogota, Colombia, 2–4 June 2015. [Google Scholar] [CrossRef]
- Liu, B.; Song, B.M. Modeling and analysis of an LCL filter for grid-connected inverters in wind power generation systems. In Proceedings of the 2011 IEEE Power and Energy Society General Meeting, Detroit, MI, USA, 24–28 July 2011; pp. 1–6. [Google Scholar] [CrossRef]
- Zabaleta, M.; Burguete, E.; Madariaga, D.; Zubimendi, I.; Zubiaga, M.; Larrazabal, I. LCL grid filter design of a multimegawatt medium-voltage converter for offshore wind turbine using SHEPWM modulation. IEEE Trans. Power Electron.
**2016**, 31, 1993–2001. [Google Scholar] [CrossRef] - Mishra, A.; Chatterjee, K. Harmonic analysis and attenuation using LCL-filter in doubly fed induction generator based wind conversion system using real time simulation based OPAL-RT. Alex. Eng. J.
**2022**, 61, 3773–3792. [Google Scholar] [CrossRef] - Baykov, A.; Dar’enkov, A.; Kurkin, A.; Sosnina, E. Mathematical modelling of a tidal power station with diesel and wind units. J. King Saud Univ. Sci.
**2019**, 31, 1491–1498. [Google Scholar] [CrossRef] - Mora, D.; Núñez, C.; Visairo, N.; Segundo, J.; Camargo, E. Control for three-phase LCL-filter PWM rectifier with Bess-oriented application. Energies
**2019**, 12, 4093. [Google Scholar] [CrossRef] - Lumpkin, R.; Johnson, G.C. Global ocean surface velocities from drifters: Mean, variance, El Niño-Southern Oscillation response, and seasonal cycle. J. Geophys. Res. Ocean.
**2013**, 118, 2992–3006. [Google Scholar] [CrossRef] - Ghefiri, K.; Bouallègue, S.; Haggège, J.; Garrido, I.; Garrido, A.J. Modeling and MPPT control of a tidal stream generator. In Proceedings of the 2017 4th International Conference on Control, Decision and Information Technologies (CoDIT), Barcelona, Spain, 5–7 April 2017; pp. 1003–1008. [Google Scholar] [CrossRef]
- Tiwari, R.; Babu, N.R. Recent developments of control strategies for wind energy conversion system. Renew. Sustain. Energy Rev.
**2016**, 66, 268–285. [Google Scholar] [CrossRef] - Sousounis, M.C.; Shek, J.K.H.; Mueller, M.A. Modelling and control of tidal energy conversion systems with long distance converters. In Proceedings of the 7th IET International Conference on Power Electronics, Machines and Drives (PEMD 2014), Manchester, UK, 8–10 April 2014. [Google Scholar] [CrossRef]
- Elzalabani, M.; Nafeh, A.E.A.E. Modelling and Simulation of Tidal Current Turbine with Permanent Magnet Synchronous Generator. TELKOMNIKA Indones. J. Electr. Eng.
**2015**, 13, 57–64. [Google Scholar] [CrossRef] - Sousounis, M.C.; Shek, J.K.H. Assessment of pulsating torque mitigation control strategy through tidal turbine emulation. J. Eng.
**2019**, 2019, 5059–5063. [Google Scholar] [CrossRef] - Odedele, N.; Olmi, C.; Charpentier, J.F. Power extraction strategy of a robust kW range marine tidal turbine based on permanent magnet synchronous generators and passive rectifiers. In Proceedings of the 3rd Renewable Power Generation Conference (RPG 2014), Naples, Italy, 24–25 September 2014. [Google Scholar] [CrossRef]
- Ugalde-Loo, C.E.; Amézquita-Brooks, L.A.; Licéaga-Castro, E.; Licéaga-Castro, J. Analysis and efficient control design for generator-side converters of PMSG-based wind and tidal stream turbines. In Proceedings of the 2014 Power Systems Computation Conference, Wroclaw, Poland, 18–22 August 2014. [Google Scholar] [CrossRef]
- Esmaeilian, H.R.; Fadaeinedjad, R.; Moschopoulos, G. Dynamic operation and control of a stand-alone PEM fuel cell system. In Proceedings of the 2014 IEEE Applied Power Electronics Conference and Exposition—APEC 2014, Fort Worth, TX, USA, 16–20 March 2014; pp. 3378–3384. [Google Scholar] [CrossRef]
- Rix, A.J. Model Predictive Control of a Grid-Connected Converter with LCL-Filter. Master’s Thesis, Stellenbosch University, Stellenbosch, South Africa, 2019. [Google Scholar]
- Biweta, M.; Mamo, M. Closed loop control strategy of back to back PWM converter fed by PMSG using PLECS toolbox on Matlab/Simulink for wind energy application. In Proceedings of the 2017 IEEE AFRICON, Cape Town, South Africa, 18–20 September 2017; pp. 1313–1318. [Google Scholar] [CrossRef]
- Tripura, P. Power Maximization and Control of PMSG Wind Energy System without Wind Speed Sensors. Int. J. Control Theory Appl.
**2017**, 10, 253–260. [Google Scholar] - Ghefiri, K.; Bouallègue, S.; Garrido, I.; Garrido, A.J.; Haggège, J. Complementary power control for doubly fed induction generator-based tidal stream turbine generation plants. Energies
**2017**, 10, 862. [Google Scholar] [CrossRef] - Nguyen, T.; Yoo, H.; Kim, H. A Flywheel Energy Storage System Based on a Doubly Fed Induction Machine and Battery for Microgrid Control. Energies
**2015**, 8, 5074–5089. [Google Scholar] [CrossRef] - Vidal, J.D.; Carranza, O.; Rodriguez, J.J.; Gonzalez, L.G.; Ortega, R. Analysis of the response of L and LCL filters in controlled rectifiers used in wind generator systems with permanent magnet synchronous generators. IEEE Lat. Am. Trans.
**2018**, 16, 2145–2152. [Google Scholar] [CrossRef] - Guerreiro, J.F.; Arruda, V.C.; Guillardi, H.; Pomilio, J.A. LCL Filter Design and Damping Analysis for Grid-Connected Inverters in Modern Uncertain Grid Impedance Conditions. In Proceedings of the 2021 IEEE Southern Power Electronics Conference (SPEC), Kigali, Rwanda, 6–9 December 2021. [Google Scholar] [CrossRef]
- Yang, L.; Xiong, C.; Teng, Y.; Hui, Q.; Zhu, Y. Harmonic Current Suppression of Grid-Connected PV Based on PR Control Strategy. In Proceedings of the 2015 Sixth International Conference on Intelligent Systems Design and Engineering Applications (ISDEA), Guiyang, China, 18–19 August 2015; pp. 433–436. [Google Scholar] [CrossRef]
- Tarasantisuk, C.; Suyata, T.; Tarateeraseth, V.; Witheephanich, K. Active and reactive power control for three-phase grid inverters with proportional resonant control strategies. In Proceedings of the 2016 13th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), Chiang Mai, Thailand, 28 June–1 July 2016. [Google Scholar] [CrossRef]
- Benzazah, C.; Lazrak, L.; Lafkih, M.A. Design and performance analysis of energy conversion chain, from multilevel inverter until the grid. In Proceedings of the 2015 27th International Conference on Microelectronics (ICM), Casablanca, Morocco, 20–23 December 2015; pp. 311–314. [Google Scholar] [CrossRef]
- Brantsæter, H.; Kocewiak, Ł.; Årdal, A.R.; Tedeschi, E. Passive Filter Design and Offshore Wind Turbine Modelling for System Level Harmonic Studies; Elsevier B.V.: Amsterdam, The Netherlands, 2015; Volume 80. [Google Scholar]
- Bracke, X.; De Kooning, J.D.M.; Van De Vyver, J.; Vandevelde, L. Effective capture of wind gusts in small wind turbines by using a full active rectifier. In Proceedings of the 3rd Renewable Power Generation Conference (RPG 2014), Naples, Italy, 24–25 September 2014. [Google Scholar] [CrossRef]
- Wang, R.; Wu, Y.; He, G.; Lv, Y.; Du, J.; Li, Y. Impedance modeling and stability analysis for cascade system of three-phase PWM rectifier and LLC resonant converter. Energies
**2018**, 11, 3050. [Google Scholar] [CrossRef] - Sanjuan, S.L. Voltage Oriented Control of Three-Phase Boost PWM Converters. Master’s Thesis, Chalmers University of Technology, Göteborg, Sweden, 2010. [Google Scholar]
- Benelghali, S.; Benbouzid, M.E.H.; Charpentier, J.F.; Ahmed-Ali, T.; Munteanu, I. Experimental validation of a marine current turbine simulator: Application sliding mode control. IEEE Trans. Ind. Electron.
**2011**, 58, 118–126. [Google Scholar] [CrossRef] - Thamizhanban, M.C.; Sathish Kumar, G.K. Hybrid Energy System of Offshore Wind and Tidal Energy with Power Quality Improvement. In Proceedings of the National Conference on Emerging Trends in Electronics, Instrumentation, Automation & Control (ETEIAC), Coimbatore, India, 11 March 2016; pp. 33–37. [Google Scholar]
- Brito, R.; Carvalho, A.; Gericota, M. A new three-phase voltage sourced converter laplace model. In Proceedings of the 2015 9th International Conference on Compatibility and Power Electronics (CPE), Costa da Caparica, Portugal, 24–26 June 2015; pp. 160–166. [Google Scholar] [CrossRef]
- Malinowski, M.; Stynski, S.; Kolomyjski, W.; Kazmierkowski, M.P. Control of Three-Level PWM Converter Applied to Variable-Speed-Type Turbines. IEEE Trans. Ind. Electron.
**2009**, 56, 69–77. [Google Scholar] [CrossRef] - Brezina, T.; Hejc, T.; Kovar, J.; Huzlik, R. Modeling and control of three-phase rectifier of Swirl turbine. In Mechatronics: Recent Technological and Scientific Advances; Springer: Berlin/Heidelberg, Germany, 2011; pp. 285–291. [Google Scholar] [CrossRef]
- Tan, X.; Dai, J.; Wu, B. A novel converter configuration for wind applications using PWM CSI with diode rectifier and buck converter. In Proceedings of the 2011 IEEE International Electric Machines & Drives Conference (IEMDC), Niagara Falls, ON, Canada, 15–18 May 2011; pp. 359–364. [Google Scholar] [CrossRef]
- Bao, J.; Bao, W.; Gong, J. A PWM Multilevel Current-Source Inverter Used for Grid-Connected Wind Energy Conversion System. Energy Procedia
**2012**, 16, 461–466. [Google Scholar] [CrossRef] - Meshram, S.; Agnihotri, G.; Gupta, S. Performance analysis of grid integrated hydro and solar based hybrid systems. Adv. Power Electron.
**2013**, 2013, 697049. [Google Scholar] [CrossRef] - Elbaset, A.A.; Hassan, M.S.; Ali, H. Performance analysis of grid-connected PV system. In Proceedings of the 2016 Eighteenth International Middle East Power Systems Conference (MEPCON), Cairo, Egypt, 27–29 December 2016; pp. 675–682. [Google Scholar] [CrossRef]
- Hamad, K.B.; Luta, D.N.; Raji, A.K. A Grid-Tied Fuel Cell Multilevel Inverter with Low Harmonic Distortions. Energies
**2021**, 14, 688. [Google Scholar] [CrossRef] - Jayalakshmi, N.S.; Gaonkar, D.N.; Kumar, K.S.K. Dynamic modeling and performance analysis of grid connected PMSG based variable speed wind turbines with simple power conditioning system. In Proceedings of the 2012 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Bengaluru, India, 16–19 December 2012. [Google Scholar] [CrossRef]

**Figure 3.**PWM rectifier control scheme [19].

**Figure 5.**The tidal turbine with a PMSG is connected to the grid using an LCL Filter [31].

**Figure 8.**Generic three-phase VSC electrical topology [45].

**Figure 11.**Tidal generator’s active power output (

**a**) and the reactive power of the tide generator (

**b**).

**Figure 12.**Actual and reference DC-link voltage (

**a**), ${\mathrm{I}}_{\mathrm{d}}$ and Id-ref (

**b**), ${\mathrm{I}}_{\mathrm{q}}$ and ${\mathrm{I}}_{\mathrm{q}}$-ef (

**c**), ${\mathrm{V}}_{\mathrm{d}}$ (

**d**), ${\mathrm{V}}_{\mathrm{D}\mathrm{C}}$ and ${\mathrm{V}}_{\mathrm{D}\mathrm{C}\mathrm{r}\mathrm{e}\mathrm{f}}$ (

**e**), and phase-locked loop (PLL) frequency (

**f**).

**Figure 13.**The three-phase voltage before installing the filter (

**a**) and current before installing the filter (

**c**).

**Figure 16.**Load active and reactive power (

**a**), active and reactive power (

**b**), load voltage (

**c**), load current (

**d**), grid voltage (

**e**), and grid current (

**f**).

Control Loop Parameters | Value |
---|---|

${\mathrm{K}}_{\mathrm{p}\mathrm{v}}$ | 133.5 |

${\mathrm{K}}_{\mathrm{i}\mathrm{v}}$ | 133,500 |

Control Loop Parameters | Value |
---|---|

${\mathrm{K}}_{\mathrm{p}\mathrm{i}}$ | 3.24 |

${\mathrm{K}}_{\mathrm{i}\mathrm{i}}$ | 50.625 |

Parameters | Values |
---|---|

${\mathrm{P}}_{\mathrm{n}\mathrm{o}\mathrm{m}}$ | 1.5 MW |

${\mathrm{V}}_{\mathrm{n}\mathrm{o}\mathrm{m}}$ | 600 V |

${\mathrm{R}}_{\mathrm{s}}$ | 0.006 |

${\mathrm{L}}_{\mathrm{d}\mathrm{q}}$ | 0.3 × 10^{−3} |

Φ | 1.48 |

J | 35,000 |

Parameters | Values |
---|---|

Viscous Damping | 0.01 |

Friction | 0 |

${N}_{p}$ | 48 |

Parameters | Values |
---|---|

$\mathrm{Inverter-side}\mathrm{inductor}({\mathrm{L}}_{\mathrm{i}}$) | 0.9 mH |

$\mathrm{Capacitor}\mathrm{filter}({\mathrm{C}}_{\mathrm{f}}$) | 531 μF |

Parameters | Values |
---|---|

Damping resistor (${\mathrm{R}}_{\mathrm{d}}$) | 0.118 Ω |

Resonant frequency (${\mathrm{f}}_{\mathrm{r}\mathrm{e}}\mathrm{e}$) | 845 $\mathrm{H}\mathrm{z}$ |

Grid-side inductor (${\mathrm{L}}_{\mathrm{g}}$) | 0.00761 Ω |

Sampling frequency ${\mathrm{f}}_{\mathrm{s}}$ | 10,000 $\mathrm{H}\mathrm{z}$ |

Crossover frequency ${\mathrm{f}}_{\mathrm{c}}$ | 254 $\mathrm{H}\mathrm{z}$ |

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## Share and Cite

**MDPI and ACS Style**

Kangaji, L.M.; Tartibu, L.; Bokoro, P.N.
Modelling and Performance Analysis of a Tidal Current Turbine Connected to the Grid Using an Inductance (LCL) Filter. *Energies* **2023**, *16*, 6090.
https://doi.org/10.3390/en16166090

**AMA Style**

Kangaji LM, Tartibu L, Bokoro PN.
Modelling and Performance Analysis of a Tidal Current Turbine Connected to the Grid Using an Inductance (LCL) Filter. *Energies*. 2023; 16(16):6090.
https://doi.org/10.3390/en16166090

**Chicago/Turabian Style**

Kangaji, Ladislas Mutunda, Lagouge Tartibu, and Pitshou N. Bokoro.
2023. "Modelling and Performance Analysis of a Tidal Current Turbine Connected to the Grid Using an Inductance (LCL) Filter" *Energies* 16, no. 16: 6090.
https://doi.org/10.3390/en16166090