# Control Strategy for Offshore Wind Farms with DC Collection System Based on Series-Connected Diode Rectifier

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## Abstract

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## 1. Introduction

## 2. System Configuration and Coupling Mechanism

_{j}and V

_{outj}, the DC voltage of the HVDC link is V

_{dci}, and I

_{dc}is the DC current of the HVDC link. With the DC collection system based on DR, DC voltage step-up can be achieved by the wind turbine terminal without additional offshore platforms.

#### 2.1. Topology

_{f}is the filter capacitor, L

_{f}is the inductance, I

_{o}is the output current of the DC/AC converter, I

_{l}is the current of filter inductance, and V

_{c}is the modulation voltage of the converter, and V

_{o}is the lower side voltage of MF.

#### 2.2. Coupling Mechanism of SCUs

_{WF}satisfies:

_{out_N}is the nominal output voltage of DR and P

_{avg}is the average power flow through the branch. It can be found that the wind speed variation would result in different DC voltages of SCUs, and the DC output voltage of SCUs with less power output is lower, making other SCUs tolerate higher DC voltage under the CDV mode.

## 3. System Control Strategy

#### 3.1. Characteristics of DR

_{out}and the AC voltage of medium frequency transformer V

_{o}and output DC current I

_{dc}is:

_{F}L

_{TR}/π, L

_{TR}is the reactance of the transformer, R

_{dc}is the equivalent resistance of HVDC link, N is the ratio of the MF transformer, B is the number of diode rectifiers, and ω

_{F}is the frequency of the MF transformer. According to Equation (4), the diode rectifier conducts only when V

_{o}is higher than threshold value V

_{oth}, which is determined by V

_{out}and is referred to as clamping characteristics. V

_{o}is linear with V

_{out}if I

_{dc}is fixed, and I

_{o}is linear with I

_{dc}.

_{ac}is:

_{o}is shown in Figure 2. In CDV mode, the operating range of V

_{o}is [V

_{dci}/a, V

_{dci}], which is very small and can be linearized as the red line. Equation (6) can be rewritten as:

_{o}is the blue line in Figure 2. For the SCU, V

_{o}can work with a wide range.

#### 3.2. Control Strategy of Receiving End Converter

_{a}is the AC voltage of phase A, v

_{dc}is the DC voltage of the FB-MMC, u

_{acm}is the common-mode voltage and is used to suppress the circulation current, v

_{ap}and v

_{an}are the output voltages of the upper and lower arms of phase A, i

_{ap}and i

_{an}are the currents of the upper and lower arms of phase A.

_{c}, 0, and +v

_{c}, the DC voltage of FB-MMC can be controlled from V

_{dc}to −V

_{dc}[26,27,28]. Therefore, with proper regulating of the v

_{dc}, FB-MMC can be a current source or a voltage source. The control strategy of MMC is shown in Figure 3.

_{dc}to its reference I

_{dcref}and generates DC voltage reference V

_{dcref}. Sub-model average voltage v

_{c}is controlled to its reference value (v

_{c_ref}) by adjusting active power current I

_{d}. Reactive power Q is regulated to its reference Q

_{ref}. Current vector control regulates AC current I

_{dq}of the MMC to its reference I

_{dqref}and generates AC voltage reference u

_{abcref}. A circulating current controller is used to optimize converter properties by set d-axis and q-axis components of common mode current i

_{dq2w}to 0 and generate common-mode voltage reference u

_{acmref}. The sum of u

_{abcref}, u

_{acmref}and V

_{dcref}generate the modulation reference U

_{ref}.

#### 3.3. Control Strategy of Wind Turbine Converters

_{oref}, and the q-axis component of the voltage is zero. The phase angle θ of voltage at the MF transformer primary side is given by the local controller θ

_{ref}, that is:

_{o}is controlled to its reference V

_{oref}, I

_{ldq}is controlled to its reference I

_{ldqref}and generates modulation voltage reference V

_{cdqref}. With controlled V

_{o}, the output voltage of the SCU can be controlled indirectly. The upper limit is adopted as 1.2V

_{oref}, and 0 is the lower limit.

_{od}. The following equation can define the active power delivered by SCUs:

_{ref}is the reference value and usually is equal to MPPT once the wind speed is larger than the cut-in speed and lower than the rated speed, P is the output active power of the wind turbine. A PI controller is introduced, K

_{p}is the proportion coefficient, and K

_{i}is the integrator coefficient. With the active power controller, V

_{o}will increase or decrease to ensure the active control transmitted.

_{dc}is fixed, I

_{o}is fixed, and V

_{out,}as well as V

_{o}will change to ensure power is transmitted with the coordinate control strategy. The characteristics of DR make the control of the whole system more flexible.

## 4. Fault Analysis and Ride-through Strategy

#### 4.1. Receiving End AC Fault

_{out}will increase, which can be easily detected by wind turbines.

_{o}will increase with V

_{out}and finally reach the power controller’s upper limiter, meaning that active power cannot transmit to the HVDC link anymore. The charging of the capacitor will stop. Considering the controller’s response time, a faster protection method by setting a modulation value of the d-axis is proposed in Equation (14).

_{cdref}of those SCUs operating at low wind speed may be small. By setting V

_{cdref}to 0, the active power of the SCU decreases to 0 faster. With the detection strategy and protection strategy shown in Equations (12) and (13), no active power injects into the HVDC link, and the DC voltage of the HVDC link will remain unchanged until the AC fault is cleared.

#### 4.2. DC Grounding Fault

_{d}

_{c}and R

_{d}

_{c}are the equivalent inductance of the HVDC link; i

_{f}is the fault current, C

_{eq}is the equivalent capacitance, including capacitance of the DC cable and capacitance of the filter DC/AC converter, S

_{DC}represents DC fault.

_{f}is:

#### 4.3. Open DC Line Fault

_{i}and cable capacity S

_{i}[30]:

_{rate}will be lost, although only two SCUs stop working. According to the economy and power loss during a fault, topology two would be a better choice.

## 5. Simulation

#### 5.1. Start-Up

#### 5.2. Wind Speed Growth Scenario

#### 5.3. AC Fault of Receiving End

_{o}will increase with V

_{out}until it reaches the upper limiter of the power controller shown in Figure 4, making the SCU blocked, and active power cannot transmit to the HVDC link anymore according to Equation (5), as shown in Figure 10e. However, the DC voltage of the HVDC link reaches 1.3 times its nominal voltage because of the controller’s response time.

#### 5.4. DC Grounding Fault U

## 6. Conclusions

- (1)
- With the coupling mechanism analysis, it is pointed out that the CDC mode is suitable for SCUs to eliminate energy curtailment without an auxiliary control strategy or equipment during unequal wind speed. Characteristics of DR are analyzed, and the linear relationship among active power, AC voltage of the MF transformer, output DC voltage, and output DC current of SCUs is researched first. Combining DR characteristics and CDC mode, a coordinate control strategy for the DC wind farm is proposed, where the receiving end converter operates as a DC current source with the DC current controller and the offshore wind turbine operates as a DC voltage source with a triple loop mediate AC voltage control strategy. Under the coordinate control strategy, the SCUs can track its MPPT without energy curtailment or overvoltage issues.
- (2)
- The fault isolation problems caused by SCUs are analyzed. Benefiting from the unidirectional conduction characteristics of DR, the healthy SCUs can keep operating without special equipment after a grounding DC fault occurs and the AC current of fault ones is smaller than 1.2 pu without destruction of SCUs. Considering the power loss and economy, reconfiguration switches are proposed, and only 40% active power is lost before the broken DC line is repaired. In addition, the characteristics of an AC fault located at the onshore grid are analyzed. A detecting and protection strategy is proposed for onshore AC fault without communication to protect the MMC from destruction quickly with sub-module voltage smaller than 1.12 pu.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Equivalent circuit of DC grounding fault, (

**a**) topology, (

**b**) fault current path, (

**c**) equivalent circuit.

**Figure 6.**Reconfiguration with switches when open DC line fault occurs, (

**a**) reconfiguration topology one, (

**b**) equivalent circuit of reconfiguration one after a fault occurs, (

**c**) reconfiguration topology two, (

**d**) equivalent circuit of reconfiguration two after a fault occurs, (

**e**) reconfiguration topology three, (

**f**) equivalent circuit of reconfiguration three after a fault occurs.

**Figure 7.**Startup of the offshore wind farm, (

**a**) Active power of SCU, (

**b**) Output voltage of SCU, (

**c**) DC voltage of HVDC link, (

**d**) DC current of HVDC link.

**Figure 8.**Waveforms of MMC during start-up, (

**a**) Arm voltage of upper arm, (

**b**) Average capacitor voltage of sub-model.

**Figure 9.**Output power of DC wind farm during unequal wind speed (

**a**) Active power of SCU, (

**b**) Output voltage of SCU, (

**c**) DC voltage of HVDC link, (

**d**) DC current of HVDC link, (

**e**) Capacitor voltage of sub-model.

**Figure 10.**Output power of DC wind farm during onshore fault (

**a**) DC voltage of HVDC link, (

**b**) DC current of HVDC link (

**c**) Capacitor voltage of sub-model of MMC, (

**d**) Output power of MMC, (

**e**) Active power of SCU.

**Figure 11.**Waveforms of DC wind farm during DC fault (

**a**) DC voltage of HVDC link and SCU, (

**b**) DC current of HVDC link and SCU (

**c**) current of SCU, (

**d**) Output power of MMC, (

**e**) Active power of SCU.

Topology One | Topology Two | Topology Three | |
---|---|---|---|

Length of DC cable | 14d | 10d | 10d |

Number of switches | 3 | 2 | 5 |

Economy (k/EUR) | 2084 | 2400 | 3720 |

Estimated power loss | 3P_{rate} | 3P_{rate} | 1P_{rate} |

Onshore MMC | Rated power | 160 MW |

DC voltage | 320 kV | |

DC current | 0.5 kA | |

Onshore grid voltage | 400 kV | |

Offshore Wind Farm | Number of SCUs in a string | 8 |

Rated power of PMSG | 20 MW | |

Rated frequency | 12 Hz | |

Rated voltage | 3.6 kV | |

The output voltage of the AC/DC rectifier | 6 kV | |

The output voltage of DR converter | 40 kV | |

Output DC current of DR converter | 0.5 kA | |

Isolation transformer of SCUs | 250 Hz, Y/∆, 3.3/66, leakage inductance, 1% |

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## Share and Cite

**MDPI and ACS Style**

Xie, L.; Cheng, F.; Wu, J.
Control Strategy for Offshore Wind Farms with DC Collection System Based on Series-Connected Diode Rectifier. *Sustainability* **2022**, *14*, 7860.
https://doi.org/10.3390/su14137860

**AMA Style**

Xie L, Cheng F, Wu J.
Control Strategy for Offshore Wind Farms with DC Collection System Based on Series-Connected Diode Rectifier. *Sustainability*. 2022; 14(13):7860.
https://doi.org/10.3390/su14137860

**Chicago/Turabian Style**

Xie, Lijun, Fan Cheng, and Jing Wu.
2022. "Control Strategy for Offshore Wind Farms with DC Collection System Based on Series-Connected Diode Rectifier" *Sustainability* 14, no. 13: 7860.
https://doi.org/10.3390/su14137860