# Power Oscillation Damping from Offshore Wind Farms Connected to HVDC via Diode Rectifiers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modelling and Control

#### 2.1. Wind Turbine Front-End Converter Controls

#### 2.2. Wind Farm Active Power Control

## 3. Simulation Results

#### 3.1. Open-Loop Tests

#### 3.2. Closed-Loop Tests

#### 3.3. Further Comments

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

AC | Alternating-current |

APC | Active power control |

AVR | Automatic voltage regulator |

C | WT FEC filter capacitance |

CC | Current control |

d axis | Direct axis |

DC | Direct-current |

DR | Diode rectifier |

$\Delta {\omega}_{\mathrm{SM}}$ | SM (angular) speed deviation |

$\Delta {P}_{\mathrm{on}}$ | Onshore (active) power oscillation signal |

$\Delta \widehat{P}$ | WF APC oscillatory/modulating (active) power signal |

$\Delta {\widehat{P}}_{\mathrm{CL}}$ | WF APC oscillatory/modulating (active) power internal/closed-loop signal |

$\Delta {\widehat{P}}_{\mathrm{OL}}$ | WF APC oscillatory/modulating (active) power external/open-loop signal |

${f}_{\mathrm{OL}}$ | WF APC oscillatory/modulating (active) power external/open-loop signal frequency |

${F}_{\mathrm{POD}}$ | WF POD control mode flag |

FC | Frequency control |

FEC | (WT) Front-end converter |

HV | High-voltage |

${I}_{\mathrm{d},k}$ | WT${}_{k}$ output d axis current |

${I}_{k}$ | WT${}_{k}$ output current |

${I}_{\mathrm{q},k}$ | WT${}_{k}$ output q axis current |

${I}_{\phantom{\rule{0.166667em}{0ex}}\mathrm{T},k}$ | WT${}_{k}$ FEC output current |

${I}_{\phantom{\rule{0.166667em}{0ex}}\mathrm{Td},k}$ | WT${}_{k}$ FEC output d axis current |

${I}_{\phantom{\rule{0.166667em}{0ex}}\mathrm{Tq},k}$ | WT${}_{k}$ FEC output q axis current |

${I}_{\phantom{\rule{0.166667em}{0ex}}\mathrm{Td},k}^{*}$ | WT${}_{k}$ FEC output d axis current reference |

${I}_{\phantom{\rule{0.166667em}{0ex}}\mathrm{Tq},k}^{*}$ | WT${}_{k}$ FEC output q axis current reference |

${k}_{\mathrm{Fi}}$ | WF APC PI regulator integral gain |

${k}_{\mathrm{Fp}}$ | WF APC PI regulator proportional gain |

${k}_{\mathrm{Ii}}$ | WT FEC CC PI regulator integral gain |

${k}_{\mathrm{Ip}}$ | WT FEC CC PI regulator proportional gain |

${k}_{\mathrm{Li}}$ | WT${}_{k}$ FEC PLL PI regulator integral gain |

${k}_{\mathrm{Lp}}$ | WT${}_{k}$ FEC PLL PI regulator proportional gain |

${k}_{\mathrm{O}}$ | WF APC POD phase lead compensator gain |

${k}_{\omega}$ | WT FEC FC P regulator gain |

${k}_{\mathrm{Pi}}$ | WT FEC APC PI regulator integral gain |

${k}_{\mathrm{POD}}$ | WF APC POD main gain |

${k}_{\mathrm{Pp}}$ | WT FEC APC PI regulator proportional gain |

${k}_{Q}$ | WT FEC RPC P regulator (reactive-power-frequency droop) gain |

${k}_{\mathrm{Ui}}$ | WT FEC VC PI regulator integral gain |

${k}_{\mathrm{Up}}$ | WT FEC VC PI regulator proportional gain |

${\kappa}_{\mathrm{disp}}$ | WF active power dispatch coefficient |

L | WT FEC filter inductance |

LPF | Low-pass filter |

OTS | Offshore transmission system |

OWF | Offshore wind farm |

$\omega $ | Offshore AC network (angular) frequency |

${\omega}_{0}$ | Offshore AC network (angular) frequency set point |

${\omega}_{k}$ | WT${}_{k}$ FEC (angular) frequency |

${\omega}_{k}^{*}$ | WT${}_{k}$ FEC (angular) frequency reference |

P | Proportional (controller/regulator) |

${P}_{\mathrm{ava}}$ | Overall aerodynamic power available from the wind |

${P}_{\mathrm{ava},k}$ | Aerodynamic power from the wind available to WT${}_{k}$ |

${P}_{F}$ | WF active power output |

${P}_{k}$ | WT${}_{k}$ active power output |

${P}_{\mathrm{on}}$ | Onshore active power |

${P}_{\phantom{\rule{0.166667em}{0ex}}\mathrm{T},k}$ | WT${}_{k}$ FEC active power output |

${P}^{*}$ | WF active power dispatch |

${P}_{\mathrm{F}}^{*}$ | WF active power (output) reference |

${P}_{\mathrm{T},k}^{*}$ | WT${}_{k}$ FEC active power (output) reference |

$\widehat{P}$ | WF APC PI regulator output (control) signal |

PI | Proportional-integral (controller/regulator) |

PLL | Phase-locked loop |

POD | Power oscillation damping |

$\mathrm{pu}$ | Per unit |

PWM | Pulse width modulation |

q axis | Quadrature axis |

${Q}_{\mathrm{F}}$ | WF reactive power output |

${Q}_{k}$ | WT${}_{k}$ reactive power output |

${Q}_{\mathrm{T},k}$ | WT${}_{k}$ FEC reactive power output |

${Q}_{\mathrm{T},k}^{*}$ | WT${}_{k}$ FEC reactive power (output) reference |

R | WT FEC filter resistance |

RMS | Root mean square |

RPC | Reactive power control |

RRF | Rotating reference frame |

s | Complex frequency variable |

SM | Synchronous machine |

t | Time variable |

${T}_{\mathrm{F}}$ | WF APC active power measurement filter time constant |

${T}_{\mathrm{Op}}$ | WF APC POD phase lead compensator pole time constant |

${T}_{\mathrm{Oz}}$ | WF APC POD phase lead compensator zero time constant |

${\theta}_{k}$ | WT${}_{k}$ FEC phase angle |

${U}_{0}$ | Offshore AC network voltage set point |

${U}_{k}$ | WT${}_{k}$ terminal RMS voltage |

${U}_{\mathrm{T},k}$ | WT${}_{k}$ FEC filter capacitor voltage |

${U}_{\mathrm{Td},k}$ | WT${}_{k}$ FEC filter capacitor d axis voltage |

${U}_{\mathrm{Tq},k}$ | WT${}_{k}$ FEC filter capacitor q axis voltage |

${U}_{\mathrm{W},k}$ | WT${}_{k}$ FEC voltage |

${U}_{\mathrm{Td},k}^{*}$ | WT${}_{k}$ FEC filter capacitor d axis voltage reference |

${U}_{\mathrm{Tq},k}^{*}$ | WT${}_{k}$ FEC filter capacitor q axis voltage reference |

${U}_{\mathrm{W},k}^{*}$ | WT${}_{k}$ FEC voltage reference |

${U}_{\mathrm{Wd},k}^{*}$ | WT${}_{k}$ FEC d axis voltage reference |

${U}_{\mathrm{Wq},k}^{*}$ | WT${}_{k}$ FEC q axis voltage reference |

VC | Voltage control |

VSC | Voltage source converter |

WF | Wind farm |

WT${}_{\left[k\right]}$ | [kth] Wind turbine(s) |

${z}^{-1}$ | Delay of one simulation time step |

## Appendix A

Parameter | Value | Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|---|---|

${k}_{\mathrm{Fi}}$ | 5 pu/s ${}^{\u2020}$ | ${k}_{\mathrm{O}}$ | $7.65\times {10}^{-3}$$\mathrm{pu}$ | ${T}_{\mathrm{F}}$ | 10 ms ${}^{\u2020}$ | ${T}_{\mathrm{Op}}$ | $13.9$ ms |

${k}_{\mathrm{Fp}}$ | $1\times {10}^{-3}$$\mathrm{pu}$${}^{\u2020}$ | ${k}_{\mathrm{POD}}$ | 5$\mathrm{pu}$ | ${T}_{\mathrm{Oz}}$ | $1.82$ s | ||

Limits: $0\le {P}^{*}\le 1.1\mathrm{pu}\phantom{\rule{1.em}{0ex}},\phantom{\rule{1.em}{0ex}}-1.26pu/s\le \mathrm{d}{P}^{*}/\mathrm{d}t\le 1.26pu/s\phantom{\rule{1.em}{0ex}},\phantom{\rule{1.em}{0ex}}-0.1\mathrm{pu}\le \Delta \widehat{P}\le 0.1\mathrm{pu}$ |

^{†}Not relevant to the simulations in question.

## References

- CIGRÉ Working Group B4.55. HVDC Connection of Offshore Wind Power Plant; Technical brochure 619; CIGRÉ: Paris, France, May 2015; Available online: https://e-cigre.org/publication/619-hvdc-connection-of-offshore-wind-power-plants (accessed on 29 August 2019).
- Bresesti, P.; Kling, W.L.; Hendriks, R.L.; Vailati, R. HVDC Connection of Offshore Wind Farms to the Transmission System. IEEE Trans. Energy Convers.
**2007**, 22, 37–43. [Google Scholar] [CrossRef] - Van Hertem, D.; Gomis-Bellmunt, O.; Liang, J. (Eds.) HVDC Grids: For Offshore and Supergrid of the Future; John Wiley & Sons: Hoboken, NJ, USA, 2016. [Google Scholar]
- ABB. HVDC Light: It’s Time to Connect; Technical report; ABB: Zurich, Switzerland, March 2013; Available online: https://new.abb.com/docs/default-source/ewea-doc/hvdc-light.pdf (accessed on 29 August 2019).
- CIGRÉ Working Group B4.37. VSC Transmission; Technical brochure 269; CIGRÉ: Paris, France, April 2005; Available online: https://cigreindia.org/CIGRE%20Lib/Tech.%20Brochure/269%20VSC%20Transmission.pdf (accessed on 29 August 2019).
- Blasco-Giménez, R.M.; Añó-Villalba, S.C.; Rodríguez-D’Derlée, J.; Morant-Anglada, F.; Bernal-Pérez, S.I. Distributed Voltage and Frequency Control of Offshore Wind Farms Connected With a Diode-Based HVdc Link. IEEE Trans. Power Electron.
**2010**, 25, 3095–3105. [Google Scholar] [CrossRef] - Blasco-Giménez, R.M.; Añó-Villalba, S.C.; Rodríguez-D’Derlée, J.; Bernal-Pérez, S.I.; Morant-Anglada, F. Diode-Based HVdc Link for the Connection of Large Offshore Wind Farms. IEEE Trans. Energy Convers.
**2011**, 26, 615–626. [Google Scholar] [CrossRef] - Bernal-Pérez, S.I.; Añó-Villalba, S.C.; Blasco-Giménez, R.M.; Rodríguez-D’Derlée, J. Efficiency and Fault Ride-Through Performance of a Diode-Rectifier- and VSC-Inverter-Based HVDC Link for Offshore Wind Farms. IEEE Trans. Ind. Electron.
**2013**, 60, 2401–2409. [Google Scholar] [CrossRef] - Christ, T.; Seman, S.; Zurowski, R. Investigation of DC Converter Nonlinear Interaction with Offshore Wind Power Park System. In Proceedings of the 2015 EWEA Offshore Conference, Copenhagen, Denmark, 10–12 March 2015. [Google Scholar]
- Menke, P.; Zurowski, R.; Christ, T.; Seman, S.; Giering, G.; Hammer, T.; Zink, W.; Hacker, F.; Imamovic, D.; Thisted, J.; et al. 2nd Generation DC Grid Access for Large Scale Offshore Wind Farms. In Proceedings of the 14th Wind Integration Workshop, Brussels, Belgium, 20–22 October 2015. [Google Scholar]
- Yu, L.; Li, R.; Xu, L. Distributed PLL-Based Control of Offshore Wind Turbines Connected with Diode-Rectifier-Based HVDC Systems. IEEE Trans. Power Deliv.
**2018**, 33, 1328–1336. [Google Scholar] [CrossRef] - Saborío-Romano, O.; Bidadfar, A.; Göksu, Ö.; Altin, M.; Cutululis, N.A.; Sørensen, P.E. Connection of OWPPs to HVDC networks using VSCs and Diode Rectifiers: an Overview. In Proceedings of the 15th Wind Integration Workshop, Vienna, Austria, 15–17 November 2016. [Google Scholar]
- PROMOTioN. Deliverable 3.1: Detailed Functional Requirements to WPPs; Project deliverable; PROMOTioN: Arnhem, The Netherlands, December 2016; Available online: https://www.onlines3.eu/wp-content/uploads/deliverables/ONLINES3_WP1%20D.1.1%20Specifications.pdf (accessed on 29 August 2019).
- Domínguez-García, J.L.; Gomis-Bellmunt, O.; Bianchi, F.D.; Sumper, A. Power oscillation damping supported by wind power: A review. Renew. Sustain. Energy Rev.
**2012**, 16, 4994–5006. [Google Scholar] [CrossRef] - Knüppel, T.; Nielsen, J.N.; Jensen, K.H.; Dixon, A.; Østergaard, J. Power oscillation damping capabilities of wind power plant with full converter wind turbines considering its distributed and modular characteristics. IET Renew. Power Gener.
**2013**, 7, 431–442. [Google Scholar] [CrossRef][Green Version] - Domínguez-García, J.L.; Ugalde-Loo, C.E.; Bianchi, F.D.; Gomis-Bellmunt, O. Input–output signal selection for damping of power system oscillations using wind power plants. Electr. Power Energy Syst.
**2014**, 58, 75–84. [Google Scholar] [CrossRef] - Zeni, L.; Eriksson, R.; Goumalatsos, S.; Altin, M.; Sørensen, P.; Hansen, A.D.; Kjær, P.; Hesselbæk, B. Power Oscillation Damping From VSC–HVDC Connected Offshore Wind Power Plants. IEEE Trans. Power Deliv.
**2016**, 31, 829–838. [Google Scholar] [CrossRef] - Pipelzadeh, Y.; Chaudhuri, N.R.; Chaudhuri, B.; Green, T.C. Coordinated Control of Offshore Wind Farm and Onshore HVDC Converter for Effective Power Oscillation Damping. IEEE Trans. Power Syst.
**2017**, 32, 1860–1872. [Google Scholar] [CrossRef] - PROMOTioN. Deliverable 3.5: Performance of Ancillary Services Provision from WFs Connected to DR-HVDC; Project deliverable; PROMOTioN: Arnhem, The Netherlands, January 2018; Available online: https://orbit.dtu.dk/files/163308588/D3.5_PROMOTioN_Performance_of_ancillary_services_pro_vision_from_WFs_connected_to_DR_HVDC.pdf (accessed on 29 August 2019).
- PROMOTioN. Deliverable 3.2: Specifications of the Control Strategies and the Simulation Test Cases; Project deliverable; PROMOTioN: Arnhem, The Netherlands, March 2017; Available online: https://www.promotion-offshore.net/news_events/news/detail/deliverable-32-specifications-of-the-control-strategies-and-the-simulation-test-cases/ (accessed on 29 August 2019).
- Muljadi, E.; Pasupulati, S.; Ellis, A.; Kosterov, D. Method of Equivalencing for a Large Wind Power Plant with Multiple Turbine Representation. In Proceedings of the IEEE PES 2008 General Meeting, Pittsburgh, PA, USA, 20–24 July 2008. [Google Scholar]
- National Grid. The Grid Code—Issue 5, Revision 19; Network code; National Grid: Warwick, UK, September 2016; Available online: https://www.nationalgrideso.com/document/34091/download (accessed on 29 August 2019).
- Göçmen, T.; van der Laan, P.; Réthoré, P.E.; Peña-Díaz, A.; Larsen, G.C.; Ott, S. Wind turbine wake models developed at the technical university of Denmark: A review. Renew. Sust. Energy Rev.
**2016**, 60, 752–769. [Google Scholar] [CrossRef][Green Version]

**Figure 4.**Wind farm active power control; parameter values given in Table A1.

**Figure 5.**Open-loop response at low wind speed; $\Delta {\widehat{P}}_{\mathrm{OL}}=\left(0.1\mathrm{pu}\right)cos\left[2\pi \left(0.3\mathrm{Hz}\right)t\right]$.

**Figure 6.**Open-loop response at medium-low wind speed; $\Delta {\widehat{P}}_{\mathrm{OL}}=\left(0.1\mathrm{pu}\right)cos\left[2\pi \left(0.3\mathrm{Hz}\right)t\right]$.

**Figure 7.**Open-loop response at high wind speed; $\Delta {\widehat{P}}_{\mathrm{OL}}=\left(0.1\mathrm{pu}\right)cos\left[2\pi \left(0.3\mathrm{Hz}\right)t\right]$.

**Figure 8.**Open-loop response at low wind speed; $\Delta {\widehat{P}}_{\mathrm{OL}}=\left(0.1\mathrm{pu}\right)cos\left[2\pi \left(2\mathrm{Hz}\right)t\right]$.

**Figure 9.**Open-loop response at medium-low wind speed; $\Delta {\widehat{P}}_{\mathrm{OL}}=\left(0.1\mathrm{pu}\right)cos\left[2\pi \left(2\mathrm{Hz}\right)t\right]$.

**Figure 10.**Open-loop response at high wind speed; $\Delta {\widehat{P}}_{\mathrm{OL}}=\left(0.1\mathrm{pu}\right)cos\left[2\pi \left(2\mathrm{Hz}\right)t\right]$.

**Figure 12.**Wind farm response to onshore (active) power oscillations at medium-low and low wind speeds.

**Figure 13.**WT${}_{k}$ response to onshore (active) power oscillations at medium-low and low wind speeds; solid: $k=1$, dashed: $k=9$.

Wind | Aerodynamic Power Available from the Wind [pu] | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Speed | ${\mathit{P}}_{\mathbf{ava}}$ | ${\mathit{P}}_{\mathbf{ava},1}$ | ${\mathit{P}}_{\mathbf{ava},2}$ | ${\mathit{P}}_{\mathbf{ava},3}$ | ${\mathit{P}}_{\mathbf{ava},4}$ | ${\mathit{P}}_{\mathbf{ava},5}$ | ${\mathit{P}}_{\mathbf{ava},6}$ | ${\mathit{P}}_{\mathbf{ava},7}$ | ${\mathit{P}}_{\mathbf{ava},8}$ | ${\mathit{P}}_{\mathbf{ava},9}$ | ${\mathit{P}}_{\mathbf{ava},10-18}$ | ${\mathit{P}}_{\mathbf{ava},19-50}$ |

Low | 0.100 | 0.232 | 0.086 | 0.105 | 0.092 | 0.086 | 0.080 | 0.075 | 0.072 | 0.072 | 0.100 | 0.100 |

Med.-Low | 0.400 | 0.930 | 0.345 | 0.421 | 0.366 | 0.344 | 0.318 | 0.299 | 0.289 | 0.289 | 0.400 | 0.400 |

Medium | 0.600 | 0.987 | 0.564 | 0.644 | 0.586 | 0.562 | 0.535 | 0.515 | 0.504 | 0.504 | 0.600 | 0.600 |

High | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

© 2019 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**

Saborío-Romano, O.; Bidadfar, A.; Göksu, Ö.; Zeni, L.; Cutululis, N.A. Power Oscillation Damping from Offshore Wind Farms Connected to HVDC via Diode Rectifiers. *Energies* **2019**, *12*, 3387.
https://doi.org/10.3390/en12173387

**AMA Style**

Saborío-Romano O, Bidadfar A, Göksu Ö, Zeni L, Cutululis NA. Power Oscillation Damping from Offshore Wind Farms Connected to HVDC via Diode Rectifiers. *Energies*. 2019; 12(17):3387.
https://doi.org/10.3390/en12173387

**Chicago/Turabian Style**

Saborío-Romano, Oscar, Ali Bidadfar, Ömer Göksu, Lorenzo Zeni, and Nicolaos A. Cutululis. 2019. "Power Oscillation Damping from Offshore Wind Farms Connected to HVDC via Diode Rectifiers" *Energies* 12, no. 17: 3387.
https://doi.org/10.3390/en12173387