# Reliability and Economic Evaluation of Offshore Wind Power DC Collection Systems

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Different Collection System Options

#### 1.3. The Requirement of Reliability and Economic Assessment

## 2. Network Topologies for DC Collection Systems

#### 2.1. DC Radial Collection Systems

#### 2.2. Series–Parallel Collection System

## 3. Methodology

#### 3.1. Clustering of Wind Turbine Power Output

_{w}(v

_{w}) is the power generated at wind speed v

_{w}(m/s), v

_{ci}is the cut-in wind speed, and v

_{co}is the cut-out wind speed. P

_{r}is the rated power of the wind turbine, and v

_{r}is the rated wind speed. It can be seen from Equation (1) that the relationship between the instantaneous wind speed and instantaneous power output of WT is non-linear.

_{i}is the ith data point, $\overline{z}$ is the average value of the data set, SDCM (Sum of Squared Deviations about Class Mean) is the sum of the variances when data are divided into K categories, N

_{j}is the number of data in the jth category, z

_{ij}is the ith data in the jth category, and $\overline{z}$ is the average value of the jth category. SDCM is related to the value of K. SDCM decreases with an increase in K. When K = n, SDCM = 0 and GVF = 1. The larger the GVF, the better the classification effect.

#### 3.2. Reliability Modelling

#### 3.2.1. Failure Rate Calculation of dcWT

_{i}and μ

_{i}are the failure and repair rates of the dcWT ith sub-system, which has r number of total sub-systems. The availability A

_{WT}of the whole system, i.e., the probability of being in the working state can be calculated as Equation (7), and the unavailability level U

_{WT}is defined as Equation (8):

#### 3.2.2. The Universal Generating Function

_{1}, G

_{2}, G

_{3}, …, G

_{n}, where the probability distribution of G

_{i}can be represented by two vectors g

_{i}and p

_{i}. The vector g

_{i}represents the possible value of G

_{i}and the vector p

_{i}represents the probability corresponding to the value of G

_{i}:

_{i}, the polynomial form of its z-transformation is defined as:

_{i,j}represents the value of the variable, and the coefficient p

_{i,j}represents the probability when the variable value is q

_{i,j}. Therefore, the z- transformation for the system consisting of n random variables can be represented as:

_{1}and q

_{2}) of system variables under the governing constraints. Similarly, for a system with two components in parallel, the UGF can be represented as Equation (14), where the combination operator is the addition of (q

_{1}and q

_{2}).

#### **UGF Model for Radial Topology**

_{x}MW or failed state, i.e., 0 MW with corresponding state probabilities p

_{1}and p

_{2}(=1 − p

_{1}), respectively. For the time being, assume that the probability of power output level P

_{x}is p

_{x}= 1. The UGF of the ith WT U

_{i}(z, x) can then be represented by:

_{Fk}is represented by:

_{c}

_{1}and failure as p

_{c}

_{2}by:

_{k}(k = 1,2, … k, …, m) with corresponding state probabilities of perfect functioning as p

_{cf}

_{1}and failure as p

_{cf}

_{2}is defined as:

- Radial-1 Topology

_{r1}, which has n × m number of WTs can be defined as:

_{x}power, which corresponds to cluster x with the state probability of p

_{wt_x}can be obtained as:

_{c}

_{l}WT power output clusters, the UGF of the Radial-1 topology is given by:

- Radial-2 Topology

- Radial-3 Topology

- Determine the UGF (U
_{CFk}) of each feeder DC/DC converter as in Equation (18) - Obtain the UGF of all m feeders (k = 1,2,…,m)$$\begin{array}{ll}{U}_{CF}(z,x)\hfill & =\underset{\oplus}{\otimes}({U}_{CF1}(z),{U}_{CF2}(z),\cdots ,{U}_{CFk}(z),\cdots ,{U}_{CFm}(z))\hfill \\ & =({\displaystyle \prod _{k=1}^{m}{({p}_{cf1}{z}^{n{P}_{x}}+{p}_{cf2}{z}^{0})}^{k}}\hfill \\ & ={f}_{0}{z}^{0}+{f}_{1}{z}^{n{P}_{x}}+{f}_{2}{z}^{2n{P}_{x}}+\cdots +{f}_{k-1}{z}^{(k-1)n{P}_{x}}+{f}_{k}{z}^{kn{P}_{x}}+\cdots +{f}_{m}{z}^{mn{P}_{x}}\hfill \end{array}$$
- Define the value of k
_{min}, i.e., the minimum number of centralized DC/DC converters required for a successful operation of the OWF collection system. - Obtain the new UGF by replacing all z
^{knPx}with z^{0}for k < k_{min}in Equation (25)$$\begin{array}{ll}{{U}^{\prime}}_{CF}(z,x)\hfill & ={f}_{0}{z}^{0}+{f}_{1}{z}^{0}+{f}_{2}{z}^{0}+\cdots +{f}_{k-1}{z}^{0}+{f}_{k}{z}^{kn{P}_{x}}+\cdots +{f}_{m}{z}^{mn{P}_{x}}\hfill \\ & =({f}_{0}+{f}_{1}+{f}_{2}+\cdots +{f}_{k-1}){z}^{0}+{f}_{k}{z}^{kn{P}_{x}}+\cdots +{f}_{m}{z}^{mn{P}_{x}}\hfill \end{array}$$ - Finally, combine Equation (26) with the UGF of the OWF collection system U
_{r1}, which comprises m-feeders and n-WTs per feeder, as defined in Equation (19).$$\begin{array}{ll}{U}_{r3}(z,x)\hfill & =\underset{\mathrm{min}}{\otimes}({{U}^{\prime}}_{CF}(z,x),{U}_{r1}(z,x))\hfill \\ & =(({f}_{0}+{f}_{1}+{f}_{2}+\cdots +{f}_{k-1}){z}^{0}+{f}_{k}{z}^{kn{P}_{x}}+\cdots +{f}_{m}{z}^{mn{P}_{x}})\times \hfill \\ & ({b}_{0}{z}^{0}+{b}_{1}{z}^{{P}_{x}}+{b}_{2}{z}^{2{P}_{x}}+\cdots +{b}_{ik}{z}^{ik{P}_{x}}+\cdots +{b}_{nm}{z}^{nm{P}_{x}})\hfill \\ & ={g}_{0}{z}^{0}+{g}_{1}{z}^{{P}_{x}}+{g}_{2}{z}^{2{P}_{x}}+\cdots +{g}_{ik}{z}^{ik{P}_{x}}+\cdots +{g}_{nm}{z}^{nm{P}_{x}}\hfill \end{array}$$ - The final UGF for n
_{cl}states can be obtained by referring to Equations (21) and (22).

#### **UGF Model for Series-Parallel Structure**

_{cl}clusters, the UGF of the feeder at the xth state can be represented as:

_{wt_x}is the probability of P

_{x}being in the xth state. Finally, considering all n

_{cl}cluster states, the UGF of SP topology can be obtained as follows.

#### 3.2.3. Reliability Indices

_{i}is the probability that the whole system is in the ith power output state, P

_{OWFmax}is the rated capacity of the OWF, P

_{OWFi}is the power output of the whole system in the ith state. The total number of states N is the product of the number of WTs n

_{wt}and the number of WT power output clusters n

_{cl}.

_{x}= [a

_{0}, a

_{1}, a

_{2},..., a

_{nm}] is a row matrix with a

_{0}, a

_{1}, a

_{2},..., a

_{nm}that denotes the corresponding state probabilities of the respective collection system and remains in a certain power output level P

_{x}. GRA(GRc) represents the ratio of power generation availability under the condition of at least i working wind turbines:

#### 3.3. Lifetime Cost Estimation

#### 3.3.1. Capital Investment

- WT Cost

- DC/DC Converter Costs

- DC Cable Cost

_{n}is the rated power of the cable (W), U

_{n}is the rated pole-to-pole DC voltage of the cable (V), and I

_{n}is the rated current of the cable (A). The term Rate is the exchange rate of Swedish krona to the British pound, l

_{cable}is the cable section length (km), and A and B are coefficients shown in Table 2.

#### 3.3.2. Costs Associated with Energy Losses

- Cable Losses (Radial Topology)

_{cable}is the cable length (km), as shown in Figure 7. The distance between the wind turbines in the same feeder and adjacent feeders were set to 9D, where D denotes respective rotor diameters of WTs [47,48].

- Cable Losses (SP Topology)

- Converter Losses

- Cost of Losses

_{loss}can be obtained by:

_{loss-cable}is the time-varying losses of DC cables that changes with wind speed and t

_{s}is the corresponding sampling time, i.e., wind speed measurement interval. The term T is the total period considered (typically one year). Finally, the cost of losses during the life cycle C

_{loss}can be obtained as follows:

_{life}is the average life of an OWFs.

## 4. Case Study

#### 4.1. Obtaining Optimal Number of Wind Power Output Clusters and Other Parameters

_{f1}.

#### 4.2. Reliability of DC Collection Systems

#### 4.3. Economic Evaluation of Candidate DC Collection Systems

#### 4.4. Overall Assessment of DC Collection System Options

#### 4.5. Impact of the DC Voltage Level for the Reliability of Series–Parallel Topology

#### 4.6. Discussion of the Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- UK Becomes First Major Economy to Pass Net-Zero Emissions Law. Available online: https://www.gov.uk/government/news/uk-becomes-first-major-economy-to-pass-net-zero-emissions-law (accessed on 10 February 2021).
- European Union. Going Climate-Neutral by 2050: A Strategic Long-Term Vision for a Prosperous, Modern, Competitive and Climate-Neutral EU Economy; Technical Report; European Union: Brussels, Belgium, 2019. [Google Scholar]
- Mallapaty, S. How China could be carbon neutral by mid-century. Nature
**2020**, 586, 482–483. [Google Scholar] [CrossRef] [PubMed] - Ritchie, H.; Roser, M. How Much of Our Primary Energy Comes from Renewables? Available online: https://ourworldindata.org/renewable-energy (accessed on 15 February 2021).
- Wang, Q.; Yu, Z.; Ye, R.; Lin, Z.; Tang, Y. An Ordered Curtailment Strategy for Offshore Wind Power under Extreme Weather Conditions Considering the Resilience of the Grid. IEEE Access
**2019**, 7, 54824–54833. [Google Scholar] [CrossRef] - Global Wind Energy Council. GWEC Global Wind Report 2019; Technical Report; Global Wind Energy Council: Brussels, Belgium, 2019. [Google Scholar]
- Global Wind Energy Council. Global Offshore Wind Report 2020; Technical Report; Global Wind Energy Council: Brussels, Belgium, 2020. [Google Scholar]
- News Release from Vestas Wind Systems A/S. Vestas Launches the V236-15.0 MW to Set New Industry Benchmark and Take Next Step towards Leadership in Offshore Wind. Available online: https://www.vestas.com/en/media/company-news?n=3886820 (accessed on 16 February 2021).
- Skopljak, N. 14 MW GE Haliade-X for Third Phase of World’s Largest Offshore Wind Farm. December 2020. Available online: https://www.offshorewind.biz/2020/12/18/14-mw-ge-haliade-x-for-third-phase-of-worlds-largest-offshore-wind-farm (accessed on 20 February 2021).
- Li, X.; Abeynayake, G.; Yao, L.; Liang, J. Recent Development and Prospect of Offshore Wind Power in Europe. J. Glob. Energy Interconnect.
**2019**, 2, 116–126. [Google Scholar] - Pérez-Rúa, J.-A.; Cutululis, N.A. Electrical Cable Optimization in Offshore Wind Farms—A Review. IEEE Access
**2019**, 7, 85796–85811. [Google Scholar] [CrossRef] - Amaral, L.; Castro, R. Offshore wind farm layout optimization regarding wake effects and electrical losses. Eng. Appl. Artif. Intell.
**2017**, 60, 26–34. [Google Scholar] [CrossRef] - Banzo, M.; Ramos, A. Stochastic optimization model for electric power system planning of offshore wind farms. IEEE Trans. Power Syst.
**2011**, 26, 1338–1348. [Google Scholar] [CrossRef] - Cerveira, A.; de Sousa, A.; Pires, E.J.S.; Baptista, J. Optimal cable design of wind farms: The infrastructure and losses cost minimization case. IEEE Trans. Power Syst.
**2016**, 31, 4319–4329. [Google Scholar] [CrossRef] - Fischetti, M.; Pisinger, D. Optimizing wind farm cable routing considering power losses. Eur. J. Oper. Res.
**2018**, 270, 917–930. [Google Scholar] [CrossRef] [Green Version] - Pérez-Rúa, J.A.; Lumbreras, S.; Ramos, A.; Cutululis, N.A. Closed-loop two-stage stochastic optimization of offshore wind farm collection system. J. Phys. Conf. Ser.
**2020**, 1618, 042031. [Google Scholar] [CrossRef] - De Prada Gil, M.; Domínguez-García, J.L.; Díaz-González, F.; Aragüés-Peñalba, M.; Gomis-Bellmunt, O. Feasibility analysis of offshore wind power plants with dc collection grid. Renew. Energy
**2015**, 78, 467–477. [Google Scholar] [CrossRef] [Green Version] - Lakshmanan, P.; Liang, J.; Jenkins, N. Assessment of collection systems for HVDC connected offshore wind farms. Electr. Power Syst. Res.
**2015**, 129, 75–82. [Google Scholar] [CrossRef] [Green Version] - Abeynayake, G.; Li, G.; Liang, J.; Cutululis, N.A. A Review on MVdc Collection Systems for High-Power Offshore Wind Farms. In Proceedings of the 2019 14th Conference on Industrial and Information Systems (ICIIS), Kandy, Sri Lanka, 18–20 December 2019; pp. 407–412. [Google Scholar]
- Musasa, K.; Nwulu, N.I.; Gitau, M.N.; Bansal, R.C. Review on DC collection grids for offshore wind farms with high-voltage DC transmission system. Iet Power Electron.
**2017**, 10, 2104–2115. [Google Scholar] [CrossRef] - Wei, S.; Feng, Y.; Liu, K.; Fu, Y. Optimization of Power Collector System for Large-scale Offshore Wind Farm Based on Topological Redundancy Assessment. E3S Web Conf.
**2020**, 194, 03025. [Google Scholar] - Dahmani, O.; Bourguet, S.; Machmoum, M.; Guerin, P.; Rhein, P.; Josse, L. Optimization and Reliability Evaluation of an Offshore Wind Farm Architecture. IEEE Trans. Sustain. Energy
**2017**, 8, 542–550. [Google Scholar] [CrossRef] - Shin, J.; Kim, J. Optimal Design for Offshore Wind Farm considering Inner Grid Layout and Offshore Substation Location. IEEE Trans. Power Syst.
**2017**, 32, 2041–2048. [Google Scholar] [CrossRef] - Holtsmark, N.; Bahirat, H.J.; Molinas, M.; Mork, B.A.; Hoidalen, H.K. An All-DC Offshore Wind Farm with Series-Connected Turbines: An Alternative to the Classical Parallel AC Model? IEEE Trans. Ind. Electron.
**2013**, 60, 2420–2428. [Google Scholar] [CrossRef] - Bahirat, H.J.; Kjølle, G.H.; Mork, B.A.; Høidalen, H.K. Reliability assessment of DC wind farms. In Proceedings of the 2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 22–26 July 2012; pp. 1–7. [Google Scholar]
- Abeynayake, G.; Li, G.; Joseph, T.; Ming, W.; Liang, J.; Moon, A.; Smith, K.; Yu, J. Reliability Evaluation of Voltage Source Converters for MVDC Applications. In Proceedings of the 2019 IEEE Innovative Smart Grid Technologies—Asia (ISGT Asia), Chengdu, China, 21–24 May 2019; pp. 2566–2570. [Google Scholar]
- Lisnianski, A.; Frenkel, I.; Ding, Y. Multi-State System Reliability Analysis and Optimization for Engineers and Industrial Managers; Springer: London, UK, 2010. [Google Scholar]
- Chuangpishit, S.; Tabesh, A.; Moradi-Shahrbabak, Z.; Saeedifard, M. Topology Design for Collector Systems of Offshore Wind Farms with Pure DC Power Systems. IEEE Trans. Ind. Electron.
**2014**, 61, 320–328. [Google Scholar] [CrossRef] - Liu, H.; Dahidah, M.S.A.; Yu, J.; Naayagi, R.T.; Armstrong, M. Design and Control of Unidirectional DC-DC Modular Multilevel Converter for Offshore DC Collection Point: Theoretical Analysis and Experimental Validation. IEEE Trans. Power Electron.
**2019**, 34, 5191–5208. [Google Scholar] [CrossRef] - Engel, S.P.; Stieneker, M.; Soltau, N.; Rabiee, S.; Stagge, H.; De Doncker, R.W. Comparison of the Modular Multilevel DC Converter and the Dual-Active Bridge Converter for Power Conversion in HVDC and MVDC Grids. IEEE Trans. Power Electron.
**2015**, 30, 124–137. [Google Scholar] [CrossRef] - Meyer, C. Key Components for Future Offshore Dc Grids. Ph.D. Thesis, Institution of Power Generation and Storage Systems, RWTH Aachen University, Aachen, Germany, 2007. [Google Scholar]
- Lakshmanan, P.; Guo, J.; Liang, J. Energy curtailment of DC series-parallel connected offshore wind farms. IET Renew. Power Gener.
**2018**, 12, 576–584. [Google Scholar] [CrossRef] - Dahmani, O.; Bourguet, S.; Machmoum, M.; Guerin, P.; Rhein, P. Reliability analysis of the collection system of an offshore wind farm. In Proceedings of the 2014 Ninth International Conference on Ecological Vehicles and Renewable Energies (EVER), Monte-Carlo, Monaco, 25–27 March 2014; pp. 1–6. [Google Scholar]
- Huang, L.; Fu, Y.; Mi, Y.; Cao, J.; Wang, P. A Markov-Chain-Based Availability Model of Offshore Wind Turbine Considering Accessibility Problems. IEEE Trans. Sustain. Energy
**2017**, 8, 1592–1600. [Google Scholar] [CrossRef] - Ramezanzadeh, S.P.; Mirzaie, M.; Shahabi, M. Reliability assessment of different HVDC transmission system configurations considering transmission lines capacity restrictions and the effect of load level. Int. J. Electr. Power Energy Syst.
**2021**, 128, 106754. [Google Scholar] [CrossRef] - MacIver, C.; Bell, K.R.W.; Nedić, D.P. A Reliability Evaluation of Offshore HVDC Grid Configuration Options. IEEE Trans. Power Deliv.
**2016**, 31, 810–819. [Google Scholar] [CrossRef] [Green Version] - Chao, H.; Hu, B.; Xie, K.; Tai, H.; Yan, J.; Li, Y. A Sequential MCMC Model for Reliability Evaluation of Offshore Wind Farms Considering Severe Weather Conditions. IEEE Access
**2019**, 7, 132552–132562. [Google Scholar] [CrossRef] - Leite, J.B.; Mantovani, J.R.S.; Dokic, T.; Yan, Q.; Chen, P.; Kezunovic, M. Resiliency Assessment in Distribution Networks Using GIS-Based Predictive Risk Analytics. IEEE Trans. Power Syst.
**2019**, 34, 4249–4257. [Google Scholar] [CrossRef] - Abeynayake, G.; Van Acker, T.; Van Hertem, D.; Liang, J. Analytical Model for Availability Assessment of Large-Scale Offshore Wind Farms including their Collector System. IEEE Trans. Sustain. Energy
**2021**. [Google Scholar] [CrossRef] - Sulaeman, S.; Benidris, M.; Mitra, J.; Singh, C. A wind farm reliability model considering both wind variability and turbine forced outages. IEEE Trans. Sustain. Energy
**2017**, 8, 629–637. [Google Scholar] [CrossRef] - Zhao, M.; Chen, Z.; Blaabjerg, F. Generation Ratio Availability Assessment of Electrical Systems for Offshore Wind Farms. IEEE Trans. Energy Convers.
**2007**, 22, 755–763. [Google Scholar] [CrossRef] - Wind Farm Costs, CATAPULT Offshore Renewable Energy, UK. Available online: https://guidetoanoffshorewindfarm.com/wind-farm-costs (accessed on 20 February 2021).
- Parker, M.A.; Anaya-Lara, O. Cost and losses associated with offshore wind farm collection networks which centralise the turbine power electronic converters. IET Renew. Power Gener.
**2013**, 7, 390–400. [Google Scholar] [CrossRef] [Green Version] - Stamatiou, G. Techno-Economical Analysis of DC Collection Grid for Offshore Wind Parks. Master’s Thesis, University of Nottingham, Nottingham, UK, 2010. [Google Scholar]
- Lundberg, S. Performance Comparison of Wind Park Configurations; Technical Report; Department of Electric Power Engineering, Chalmers University of Technology: Göteborg, Sweden, 2003. [Google Scholar]
- Bahirat, H.J.; Mork, B.A.; Høidalen, H.K. Comparison of wind farm topologies for offshore applications. In Proceedings of the 2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 22–26 July 2012; pp. 1–8. [Google Scholar]
- de Prada, M.; Igualada, L.; Corchero, C.; Gomis-Bellmunt, O.; Sumper, A. Hybrid AC-DC Offshore Wind Power Plant Topology: Optimal Design. IEEE Trans. Power Syst.
**2015**, 30, 1868–1876. [Google Scholar] [CrossRef] [Green Version] - Baring-Gould, I. Offshore Wind Plant Electrical Systems. In Proceedings of the BOEM Offshore Renewable Energy Workshop, Sacramento, CA, USA, 29–30 July 2014. [Google Scholar]
- Abeynayake, G.; Li, G.; Joseph, T.; Liang, J.; Ming, W. Reliability and Cost-oriented Analysis, Comparison and Selection of Multi-level MVdc Converters. IEEE Trans. Power Deliv.
**2021**. [Google Scholar] [CrossRef] - Ørsted Offshore Operational Data Sharing: Anholt and Westermost Rough LiDAR Data Documentation. Available online: https://orsted.com/en/our-business/offshore-wind/wind-data (accessed on 5 March 2021).
- MHI Vestas Offshore V164-9.5 MW. Available online: https://en.wind-turbine-models.com/turbines/1605-mhi-vestas-offshore-v164-9.5-mw (accessed on 10 March 2021).
- MHI Vestas Offshore V164-8.0 MW. Available online: https://en.wind-turbine-models.com/turbines/1419-mhi-vestas-offshore-v164-8.0-mw (accessed on 12 March 2021).
- Saeki, M.; Tobinaga, I.; Sugino, J.; Shiraishiet, T. Development of 5-MW offshore wind turbine and 2-MW floating offshore wind turbine technology. Hitachi Rev.
**2014**, 63, 414. [Google Scholar] - Bala, S.; Pan, J.; Das, D.; Apeldoorn, O.; Ebner, S. Lowering failure rates and improving serviceability in offshore wind conversion-collection systems. In Proceedings of the 2012 IEEE Power Electronics and Machines in Wind Applications, Denver, CO, USA, 16–18 July 2012; pp. 1–7. [Google Scholar]
- Rock, D. Guidance on the Offshore Transmission Owner Licence for Tender Round 5 (TR5); Ofgem: London, UK, 2017; pp. 1–39. [Google Scholar]
- International Renewable Energy Agency (IRENA). Renewable Power Generations Costs in 2018. Available online: https://www.irena.org/Publications (accessed on 15 March 2021).

WT Capacity (MW) | Cost per WT (£) |
---|---|

10 | 1,366,674 |

8 | 1,149,339 |

5 | 823,337 |

Voltage Levels (kV) | A (×10^{6}) | B |
---|---|---|

±10.0 | −0.32 | 0.0850 |

±12.5 | −0.32 | 0.0850 |

±20.0 | −0.314 | 0.0618 |

±25.0 | −0.314 | 0.0618 |

±40.0 | 0 | 0.0280 |

±100.0 | 0.079 | 0.0120 |

Capacity (MW) | Model | Rated Wind Speed (m/s) | Cut-In Speed (m/s) | Cut-Out Speed (m/s) | Rotor Diameter (m) |
---|---|---|---|---|---|

10 (S1) | V164-9.5 [51] | 14 | 3.5 | 25 | 164 |

8 (S2) | V164-8.0 [52] | 13 | 4.0 | 25 | 164 |

5 (S3) | HTW5.0-126 [53] | 13 | 4.0 | 25 | 126 |

Cluster Number | Cluster Center (MW) | State Probability |
---|---|---|

1 | 0.000 | 0.0700773 |

2 | 0.474 | 0.0422715 |

3 | 1.572 | 0.0756075 |

4 | 2.796 | 0.0811175 |

5 | 3.967 | 0.0929224 |

6 | 5.113 | 0.0934911 |

7 | 6.267 | 0.0968191 |

8 | 7.390 | 0.0924218 |

9 | 8.506 | 0.0869786 |

10 | 9.540 | 0.0664654 |

11 | 10.000 | 0.2018278 |

WT Component | Failure Rate (occ/yr) | Repair Time (h) |
---|---|---|

Generator | 0.1000 | 240 |

Transformer | 0.0131 | |

AC breaker | 0.0250 | |

DC breaker | 0.0250 | |

Full power converter | 0.2000 | |

AC/DC converter | 0.1000 | |

DC/DC converter | 0.6132 |

Rated Power (MW) | Converter Type and Scenario | Input and Output Voltage Levels (kV) | Percentage Losses |
---|---|---|---|

40 | R-3 (C_{f1}); S2 | ±10/±20 | 1.79% |

40 | R-2 (C_{f1}); S2 | ±10/±40 | 1.88% |

50 | R-3 (C_{f1}); S3 | ±10/±12.5 | 1.53% |

50 | R-3 (C_{f1}); S1 | ±10/±25 | 1.68% |

50 | R-2 (C_{f1}); S2 | ±10/±40 | 1.65% |

400 | R-2 (C1); S1, S2, S3 | ±40/±100 | 1.31% |

400 | R-1 (C1); S1, S2, S3 | ±10/±100 | 1.44% |

WT Capacity | Terminal Voltage (kV) | WTs per Feeder | EENS (MWhr/yr) |
---|---|---|---|

10 MW | ±2.5 | 40 | 1.4980 × 10^{6} |

±5.0 | 20 | 1.5015 × 10^{6} | |

±10.0 | 10 | 1.5496 × 10^{6} | |

±12.5 | 8 | 1.5292 × 10^{6} | |

±20.0 | 5 | 1.7179 × 10^{6} | |

±25.0 | 4 | 1.6653 × 10^{6} |

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## Share and Cite

**MDPI and ACS Style**

Sun, R.; Abeynayake, G.; Liang, J.; Wang, K.
Reliability and Economic Evaluation of Offshore Wind Power DC Collection Systems. *Energies* **2021**, *14*, 2922.
https://doi.org/10.3390/en14102922

**AMA Style**

Sun R, Abeynayake G, Liang J, Wang K.
Reliability and Economic Evaluation of Offshore Wind Power DC Collection Systems. *Energies*. 2021; 14(10):2922.
https://doi.org/10.3390/en14102922

**Chicago/Turabian Style**

Sun, Ruijuan, Gayan Abeynayake, Jun Liang, and Kewen Wang.
2021. "Reliability and Economic Evaluation of Offshore Wind Power DC Collection Systems" *Energies* 14, no. 10: 2922.
https://doi.org/10.3390/en14102922