# Validation of a Coupled Electrical and Hydrodynamic Simulation Model for a Vertical Axis Marine Current Energy Converter

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Söderfors Experimental Station

#### 2.1. The Turbine, the Generator and Load Control

#### 2.2. Electrical Layout and Control System

#### 2.3. Water Speed Measurements

## 3. Coupling of the Electrical and the Hydrodynamic Vortex Model

#### 3.1. Electrical Model in Simulink

^{TM}because of its $powergui$ blocks that have stiff solvers. Since the vortex code and the rest of the system updates at different time steps a variable step solver is best suited in order to maximize simulation speed and retain solver accuracy.

#### 3.2. Hydrodynamic Vortex Model for Vertixal Axis Turbines

## 4. Calibrating the Simulation Model

#### 4.1. Calibration of Generator and Electrical System Losses

#### 4.2. Calibration of Drag Losses

## 5. Validating the Simulation Model

#### 5.1. Simulations of the Power Capture of the Turbine

#### 5.2. Step Response of Change in Target DC Bus Voltage

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Day, A.; Babarit, A.; Fontaine, A.; He, Y.P.; Kraskowski, M.; Murai, M.; Penesis, I.; Salvatore, F.; Shin, H.K. Hydrodynamic modelling of marine renewable energy devices: A state of the art review. Ocean Eng.
**2015**, 108, 46–69. [Google Scholar] [CrossRef] [Green Version] - Khan, M.J.; Bhuyan, G.; Iqbal, M.T.; Quaicoe, J.E. Hydrokinetic energy conversion systems and assessment of horizontal and vertical axis turbines for river and tidal applications: A technology status review. Appl. Energy
**2009**, 86, 1823–1835. [Google Scholar] [CrossRef] - Uihlein, A.; Magagna, D. Wave and tidal current energy—A review of the current state of research beyond technology. Renew. Sustain. Energy Rev.
**2016**, 58, 1070–1081. [Google Scholar] [CrossRef] - Zhou, Z.; Scuiller, F.; Charpentier, J.F.; Benbouzid, M.; Tang, T. An up-to-date review of large marine tidal current turbine technologies. In Proceedings of the 2014 International Power Electronics and Application Conference and Exposition, Shanghai, China, 5–8 November 2014; pp. 480–484. [Google Scholar]
- Bahaj, A.S. Marine current energy conversion: The dawn of a new era in electricity production. Philos. Trans. A Math. Phys. Eng. Sci.
**2013**, 371. [Google Scholar] [CrossRef] [PubMed] - Domenech, J.; Eveleigh, T.; Tanju, B. Marine hydrokinetic (MHK) systems: Using systems thinking in resource characterization and estimating costs for the practical harvest of electricity from tidal currents. Renew. Sustain. Energy Rev.
**2018**, 81, 723–730. [Google Scholar] [CrossRef] - Paraschivoiu, I.; Allet, A. Aerodynamic analysis of the darrieus wind turbines including dynamic-stall effects. J. Propuls. Power
**1988**, 4, 472–477. [Google Scholar] [CrossRef] - Strickland, J.H.; Webster, B.T.; Nguyen, T. A vortex model of the darrieus turbine: An analytical and experimental study. J. Fluids Eng.
**1979**, 101, 500–505. [Google Scholar] [CrossRef] - Murray, J.; Barone, M. The development of CACTUS, a wind and marine turbine performance simulation code. In Proceedings of the 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, FL, USA, 4–7 January 2011. [Google Scholar]
- Sorensen, J.; Shen, W.Z. Numerical modeling of wind turbine wakes. J. Fluids Eng.
**2002**, 124, 393–399. [Google Scholar] [CrossRef] - Lundin, S.; Forslund, J.; Carpman, N.; Grabbe, M.; Yuen, K.; Apelfröjd, S.; Goude, A.; Leijon, M. The söderfors project: Experimental hydrokinetic power station deployment and first results. In Proceedings of the 10th European Wave and Tidal Energy Conference (EWTEC13), Aalborg, Denmark, 2–5 December 2013. [Google Scholar]
- Yuen, K.; Lundin, S.; Grabbe, M.; Lalander, E.; Goude, A.; Leijon, M. The Söderfors Project: Construction of an Experimental Hydrokinetic Power Station. In Proceedings of the 9th European Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 5–9 September 2011; pp. 1–5. [Google Scholar]
- Forslund, J.; Lundin, S.; Thomas, K.; Leijon, M. Experimental results of a DC bus voltage level control for a load controlled Marine Current Energy Converter. Energies
**2015**, 8, 4572–4586. [Google Scholar] [CrossRef] - Grabbe, M.; Yuen, K.; Goude, A.; Lalander, E.; Leijon, M. Design of an experimental setup for hydro-kinetic energy conversion. Int. J. Hydropower Dams
**2009**, 15, 112–116. [Google Scholar] - Lundin, S.; Forslund, J.; Goude, A.; Grabbe, M.; Yuen, K.; Leijon, M. Experimental demonstration of performance of a vertical axis marine current turbine in a river. J. Renew. Sustain. Energy
**2016**, 8, 064501. [Google Scholar] [CrossRef] [Green Version] - Grabbe, M.; Yuen, K.; Apelfröjd, S.; Leijon, M. Efficiency of a directly driven generator for hydrokinetic energy conversion. Adv. Mech. Eng.
**2013**, 2013, 1–8. [Google Scholar] [CrossRef] - Lundin, S.; Goude, A.; Leijon, M. One-dimensional modelling of marine current turbine runaway behaviour. Energies
**2016**, 9, 309. [Google Scholar] [CrossRef] - Yuen, K.; Apelfröjd, S.; Leijon, M. Implementation of control system for hydro-kinetic energy converter. J. Control Sci. Eng.
**2013**, 2013, 10. [Google Scholar] [CrossRef] - Cottet, G.H.; Koumoutsakos, P.D. Vortex Methods: Theory and Practice; Cambridge University Press: Cambridge, UK, 2008. [Google Scholar]
- Goude, A. Fluid Mechanics of Vertical Axis Turbines: Simulations and Model Development. Ph.D. Thesis, Uppsala University, Uppsala, Sweden, 2012. [Google Scholar]
- Dyachuk, E. Aerodynamics of Vertical Axis Wind Turbines. Development of Simulation Tools and Experiments. Ph.D. Thesis, Uppsala University, Uppsala, Sweden, 2015. [Google Scholar]
- Dyachuk, E.; Goude, A. Numerical validation of a vortex model against experimental data on a straight-bladed vertical axis wind turbine. Energies
**2015**, 8, 11800–11820. [Google Scholar] [CrossRef] - Sheldahl, R.E.; Klimas, P.C. Aerodynamic Characteristics of Seven Symmetrical Airfoil Sections through 180-Degree Angle of Attack for Use in Aerodynamic Analysis of Vertical Axis Wind Turbines; Sandia National Laboratories: Albuquerque, New Mexico, 1981.
- Dyachuk, E.; Goude, A.; Bernhoff, H. Dynamic stall modeling for the conditions of vertical axis wind turbines. AIAA J.
**2014**, 52, 72–81. [Google Scholar] [CrossRef] - Goude, A.; Bülow, F. Robust VAWT control system evaluation by coupled aerodynamic and electrical simulations. Renew. Energy
**2013**, 59, 193–201. [Google Scholar] [CrossRef] - Goude, A.; Lundin, S. Forces on a marine current turbine during runaway. Int. J. Mar. Energy
**2017**, 19, 345–356. [Google Scholar] [CrossRef]

**Figure 1.**The Marine Current Energy converter rated at 7.5 kW, that can be placed on the river or sea bed. A five-bladed fixed pitch Vertical Axis Current Turbine is connected directly (no gearbox) to a Permanent Magnet Synchronous Generator. The radius, r, is 3 m and the height is 3.5 m to give a projected cross sectional area of 21 m${}^{2}$.

**Figure 2.**The turbine and generator are connected to the on-shore measurement and control cabin where the rectifier and DC load control is placed.

**Figure 3.**The Simulink model with the block Vortex simulation that imports the vortex code as a function. The DC load with rectifier block has been replaced with three resistors for the AC-load simulations.

**Figure 5.**Calibration of the generator model using AC-load operation; (

**a**) Power in the load; (

**b**) Generator line-to-line RMS-voltage.

**Figure 6.**Simulated and experimentally measured free-spin operation of the turbine: (

**a**) rotational speed vs water speed; (

**b**) Tip-Speed-Ratio vs water speed.

**Figure 7.**Simulated and experimentally measured ${C}_{P}$-curve: (

**a**) ${C}_{{P}_{turbine}}$ (including generator iron losses); (

**b**) ${C}_{P}$ for the total system (including all mechanical and electrical losses).

**Figure 8.**Experimental data that was used as input for the step response simulation: (

**a**) Measured water speed in the river; (

**b**) Set target DC bus voltage.

**Figure 9.**Simulated and experimental step response of turbine operation close to ${\lambda}_{opt}$, with a step corresponding to an increase of $\lambda $: (

**a**) DC bus voltage; (

**b**) Rotational speed of the turbine.

**Figure 10.**Simulated and experimental step response of turbine operation close to ${\lambda}_{opt}$, with a step corresponding to a decrease of $\lambda $: (

**a**) DC bus voltage; (

**b**) Rotational speed of the turbine.

**Figure 12.**Simulated and experimental step response of turbine operation close from low to high $\lambda $: (

**a**) DC bus voltage; (

**b**) Rotational speed of the turbine.

Turbine and generator rating | 7.5 kW |

Estimated iron, seal and frictional losses | 350 Nm |

The Vertical Axis Current Turbine | |

${C}_{{P}_{max}}$ | 0.26 at $\lambda $ = 3.1 |

Rated water speed | 1.35 m/s |

Rated rotational speed | 15 RPM |

Number of blades | 5 |

Blade pitch | Fixed at 0${}^{\xb0}$ |

Blade profile | NACA0021 |

Rotor Radius | 3 m |

Rotor Height | 3.5 m |

Chord length | 0.18 m |

The Permanent Magnet Synchronous Generator | |

Minimum efficiency | 80 % |

Nominal electrical frequency | 14 Hz |

Poles | 112 |

Rated Line-to-line rms voltage | 138 V |

Rated stator rms current | 31 A |

Stator phase resistance | 0.335 $\mathsf{\Omega}$ |

Armature inductance | 3.5 mH |

The PMSG Generator block | |

Flux linkage | 1.28 Vs |

Estimated moment of inertia | 3000 kgm${}^{2}$ |

DC load parameters | |

Rectifier on-resistance | 1 m$\mathsf{\Omega}$ |

Rectifier forward voltage drop | 0 V |

IGBT on-resistance | 0.1 m$\mathsf{\Omega}$ |

IGBT forward voltage drop | 1 V |

Snubber resistance | 47 k$\mathsf{\Omega}$ |

Snubber capacitance | 470 nF |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Forslund, J.; Goude, A.; Thomas, K.
Validation of a Coupled Electrical and Hydrodynamic Simulation Model for a Vertical Axis Marine Current Energy Converter. *Energies* **2018**, *11*, 3067.
https://doi.org/10.3390/en11113067

**AMA Style**

Forslund J, Goude A, Thomas K.
Validation of a Coupled Electrical and Hydrodynamic Simulation Model for a Vertical Axis Marine Current Energy Converter. *Energies*. 2018; 11(11):3067.
https://doi.org/10.3390/en11113067

**Chicago/Turabian Style**

Forslund, Johan, Anders Goude, and Karin Thomas.
2018. "Validation of a Coupled Electrical and Hydrodynamic Simulation Model for a Vertical Axis Marine Current Energy Converter" *Energies* 11, no. 11: 3067.
https://doi.org/10.3390/en11113067