# Power Curtailment Analysis of DC Series–Parallel Offshore Wind Farms

## Abstract

**:**

## 1. Introduction

## 2. DC Series–Parallel Collection System Configuration

#### 2.1. Effect of Voltage Tolerance Levels of MVDC Converters on Energy Curtailment

#### 2.2. Defining Upper-Voltage Tolerance Levels by Redundancy Requirements

_{max}, this would cause a string failure condition.

#### 2.3. String Voltage Limits

## 3. Calculation of Power Curtailment Losses

- The windfarm layout for the DC series–parallel collection system is defined with respect to the number of wind turbines connected in the series, the number of strings connected in parallel, and the horizontal and vertical distances between the wind turbines.
- By using the well-known wake model developed by Jensen [31], the wind speed differences among the series-connected turbines are calculated considering both single and multiple wake effects. This has been carried out for the wind speeds ranging from the cut-in wind speed to the cut-out wind speed, taking into account the different wind direction sectors.
- The wind speed of each wind turbine in the string is calculated using step 2, and the output power of each wind turbine is calculated. The power outputs are assumed to be at the rated values beyond the rated speeds.
- The output power differences of the series-connected wind turbines decides the MVDC output voltage of the series-connected wind turbines in each case. Now, considering the ‘n − 1’ redundancy requirement in Equation (4), the upper-voltage tolerance levels for the wind turbine MVDC converter are identified. This factor varies concerning the configuration of the considered wind farms, depending on the number of wind turbines connected in the series.
- The quantity of the required power curtailment in order to maintain the identified upper-voltage tolerance levels of the wind turbine MVDC converter is calculated. This has been explained in [26] with respect to the different power curtailment modes. This has been carried out for all the strings in the wind farm for each combination of the wind speed and wind direction sectors. The total power curtailment losses of the wind farm are calculated as

- 6.
- The energy curtailment losses can be estimated using the total power curtailment losses of the wind farms calculated in the previous step.

## 4. Case Study for Different Configurations of DC Series–Parallel Wind Farms

#### 4.1. Upper-Voltage Tolerance Levels for Wind Turbine MVDC Converters

_{n}= 30 kV. For example, corresponding to case 1 with 20 × 1 turbines, n = 20, V

_{n}= 30 kV, and V = 600 kV, according to Equation (4), the required $\mathsf{\alpha}$ for ${\mathrm{n}}_{\mathrm{max}}$ = 1 can be found as 5.3%.

#### 4.2. Comparision of Energy Curtailment Losses with Fixed and Redundancy-Based Upper-Voltage Tolerance Levels

_{max}in Equation (4) can be chosen as 2. With this value of n

_{max}, it is possible to build the string voltage using the wind turbine MVDC converters even with a failure of two turbines in any single string. So, this will increase the reliability of the configurations in cases 1 and 2. The AEC losses corresponding to the fixed upper-voltage tolerance levels and the redundancy-based upper-voltage tolerance levels are plotted in Figure 4.

- DC-based wind farms with a greater number of series-connected turbines and a smaller number of parallel-connected strings (cases 1 and 2) can be designed with fixed upper-voltage tolerance levels. The curtailment losses were evaluated to be similar in the comparative study by considering fixed upper-voltage tolerance levels and redundancy-based upper-voltage tolerance levels for the MVDC converters of a DC series–parallel offshore wind farm. Hence, these configurations can be designed with fixed nominal upper-voltage tolerance levels, without oversizing the MVDC converters of the DC series–parallel wind farms.
- DC-based wind farm configurations with a greater number of parallel-connected strings and a smaller number of series-connected turbines (cases 3 and 4) can be designed with redundancy-based upper-voltage tolerance levels. The curtailment losses were evaluated to be lower with redundancy-based upper-voltage tolerance levels in the comparative study between fixed upper-voltage tolerance levels and redundancy-based upper-voltage tolerance levels for the MVDC converters of a DC series–parallel offshore wind farm. Hence, these configurations need to be designed with a redundancy-based upper-voltage tolerance level, which makes it essential to oversize the MVDC converters of the DC series–parallel wind farms.

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) DC series–parallel collection system. (

**b**) Generators and power conversion components in an individual wind turbine.

**Figure 2.**Representation of one string of DC series–parallel offshore wind farms (it is assumed that ${P}_{1}$ ≥ ${P}_{2}$ ≥ ⋯ ≥ ${P}_{n}$ ).

**Figure 3.**Configuration of the wind farms considered for the case study with DC series–parallel collection systems. (

**a**) 20 × 1 turbines (pure DC series wind farm with a single string and 20 turbines connected in a series, HVDC voltage: 600 kV) (

**b**) 10 × 2 turbines (DC series–parallel wind farm with 2 strings and each string with 10 series-connected turbines, HVDC voltage: 300 kV) (

**c**) 5 × 4 turbines (DC series–parallel wind farm with 4 strings and each string with 5 series-connected turbines, HVDC voltage: 150 kV) (

**d**) 4 × 5 turbines (DC series–parallel wind farm with 5 strings and each string with 4 series-connected turbines, HVDC voltage: 120 kV). (

**e**) Generators and power conversion components in an individual wind turbine.

**Figure 4.**Comparison of AEC losses with fixed and redundancy-based upper-voltage tolerance levels for different wind farm configurations.

Parameter | 10 MW DTU Wind Turbine [32,33,34] |
---|---|

Cut-in wind speed | 4 m/s |

Rated wind speed | 11.4 m/s |

Cut-out wind speed | 25 m/s |

Rotor diameter | 178.3 m |

Rated power | 10 MW |

Cases | 20 × 1 V = 600 kV | 10 × 2 V = 300 kV | 5 × 4 V = 150 kV | 4 × 5 V = 120 kV |
---|---|---|---|---|

Upper-voltage tolerance levels of wind turbine MVDC converters V_{n} (1 + α) | 31.6 kV | 33.3 kV | 37.5 kV | 40 kV |

α | 5.3% | 11% | 25% | 33.3% |

Annual Energy Production for a 200 MW DC Wind Farm: 960.02 GWh. | ||||
---|---|---|---|---|

Losses in GWh (%) | ||||

20 × 1 V = 600 kV | 10 × 2 V = 300 kV | 5 × 4 V = 150 kV | 4 × 5 V = 120 kV | |

AEC losses with a fixed upper-voltage tolerance level (10%) for wind turbine MVDC converters | 2.7154 (0.28%) | 4.8695 (0.51%) | 16.9492 (1.77%) | 18.7045 (1.95%) |

AEC losses with redundancy-based upper-voltage tolerance levels for wind turbine MVDC converters | 2.8662 (0.30%) | 4.8089 (0.50%) | 10.5349 (1.10%) | 10.1851 (1.07%) |

Annual Energy Production for a 200 MW DC Wind Farm: 960.02 GWh. | ||||
---|---|---|---|---|

Losses in GWh (%) | ||||

20 × 1 V = 600 kV | 10 × 2 V = 300 kV | 5 × 4 V = 150 kV | 4 × 5 V = 120 kV | |

AEC losses with a fixed upper-voltage tolerance level (10%) for wind turbine MVDC converters | 1.8977 (0.20%) | 3.1880 (0.33%) | 5.4676 (0.57%) | 5.9247 (0.62%) |

AEC losses with redundancy-based upper-voltage tolerance levels for wind turbine MVDC converters | 2.0557 (0.21%) | 3.1307 (0.33%) | 3.3706 (0.35%) | 2.6947 (0.28%) |

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**MDPI and ACS Style**

Lakshmanan, P.
Power Curtailment Analysis of DC Series–Parallel Offshore Wind Farms. *Wind* **2022**, *2*, 466-478.
https://doi.org/10.3390/wind2030025

**AMA Style**

Lakshmanan P.
Power Curtailment Analysis of DC Series–Parallel Offshore Wind Farms. *Wind*. 2022; 2(3):466-478.
https://doi.org/10.3390/wind2030025

**Chicago/Turabian Style**

Lakshmanan, Padmavathi.
2022. "Power Curtailment Analysis of DC Series–Parallel Offshore Wind Farms" *Wind* 2, no. 3: 466-478.
https://doi.org/10.3390/wind2030025