# Connection System for Small and Medium-Size Wind Generators through the Integration in an MMC and NLC Modulation

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## Abstract

**:**

## 1. Introduction

## 2. Fundamentals of Modular Multilevel Converters (MMC) and Near Level Control (NLC)

#### 2.1. Fundamentals of MMC

#### 2.2. Fundamentals of NLC

## 3. Proposed Wind Farm Topology with NLC Modulation

#### 3.1. Topology

- (1).
- Fewer semiconductors. The classic configuration uses for each wind generator two three-phase DC/AC converters, i.e., 12 IGBT/MOSFETs, while the developed configuration uses one three-phase DC/AC converter and one HB, in total 8 IGBT/MOSFETs.
- (2).
- Lower switching losses. The classical configuration uses high-frequency modulation because it uses two-level converters; the configuration presented in this paper generates an output voltage with many phase-to-neutral voltage levels (e.g., 11 voltage levels for 10 PM per arm), so it is not necessary to use high-frequency modulation but it is more appropriate to use low-frequency modulation such as NLC. Thus, switching power losses are greatly reduced.
- (3).
- Lower filtering requirements. The classic setup has a filter between the output converter and the grid to filter the two-level voltage of the converter; it uses one filter per generator. The proposed configuration generates the output voltage with a large number of steps so that the filtering requirements are very low or even eliminated, also, only one filter would be needed since there is only one converter connected to the grid.

#### 3.2. Control Schemes

## 4. Power Transfer between Phases and between Arms

#### 4.1. Balanced Generation

#### 4.2. Imbalance between Phases

#### 4.3. Imbalance between Arms

#### 4.4. Imbalance between Phases and Arms

## 5. Analysis of a Case for Different Generation Scenarios

- Discrete simulation.
- Fixed-step. The sample time was set at ${T}_{S}=10\mathsf{\mu}\mathrm{s}$.
- Solver: Bogacki–Shampine.

#### 5.1. Balanced Generation

#### 5.1.1. Balanced Generation and Medium Power

#### 5.1.2. Balanced Generation and Full Power

#### 5.2. Imbalance between Phases

#### 5.2.1. Medium Imbalance between Phases

#### 5.2.2. Large Imbalance between Phases

#### 5.3. Imbalance between Arms

#### 5.3.1. Medium Imbalance between Arms

#### 5.3.2. Large Imbalance between Arms

#### 5.4. Conclusions of the Case Study

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**Top**) Topology of a modular multilevel converter (MMC) connected to the grid by means of an inductance. (

**Bottom**) Switching modules (SM): (

**a**) half-bridge (HB), and (

**b**) full-bridge (FB) [21].

**Figure 2.**(

**Top**) Reference voltage and near level control (NLC) voltage graphs when the switching period is fixed. (

**Bottom**) Reference voltage and near level control (NLC) voltage graphs when the switching period is variable [21].

**Figure 3.**Proposed MMC for wind power generation, where the details of a power module (PM) including the wind generator, the generator-side converter, and the HB-SM can be seen.

**Figure 4.**Control scheme of the new topology that integrates the wind generators into the structure of an MMC and uses an NLC modulator.

**Figure 5.**Vector diagram of the variables involved in power transmission from the arms. All of them are 50 Hz variables (harmonic 1).

**Figure 7.**Simulation graphs when the power is medium and the generation is balanced. (

**a**) Output voltages. (

**b**) Output currents. (

**c**) Power transferred between phases. (

**d**) Power delivered by each phase. (

**e**) Voltage on the DC link. (

**f**) Circulating currents. (

**g**) Capacitor voltages.

**Figure 8.**Simulation graphics when the generation is balanced and the power is full. (

**a**) Output currents. (

**b**) Power transferred between phases. (

**c**) Power delivered by each phase. (

**d**) Voltage on the DC link. (

**e**) Capacitor voltages.

**Figure 9.**Simulation graphs when the generation has a medium phase imbalance. (

**a**) Output currents. (

**b**) Power transferred between phases. (

**c**) Power delivered by each phase. (

**d**) Voltage on the DC link. (

**e**) Capacitor voltages.

**Figure 10.**Simulation graphs when the generation has a large imbalance between phases. (

**a**) Output currents. (

**b**) Power transferred between phases. (

**c**) Power delivered by each phase. (

**d**) Voltage on the DC link. (

**e**) Capacitor voltages.

**Figure 11.**Simulation plots when the generation has an intermediate imbalance between arms. (

**a**) Output currents. (

**b**) Power of the upper and lower arms. (

**c**) Power delivered by each phase. (

**d**) Voltage on the DC link. (

**e**) Capacitor voltages.

**Figure 12.**Vector diagram of the variables involved in the transmission of power from the arms when the generation has a medium imbalance between arms. All of them are 50 Hz variables (harmonic 1).

**Figure 13.**Simulation plots when the generation has a large imbalance between arms. (

**a**) Output currents. (

**b**) Power of the upper and lower arms. (

**c**) Power delivered by each phase. (

**d**) Voltage on the DC link. (

**e**) Capacitor voltages.

**Figure 14.**Vector diagram of the variables involved in the transmission of power from the arms when the generation has a large imbalance between arms. All of them are 50 Hz variables (harmonic 1).

**Table 1.**Variables and states of a half-bridge (HB) switching module (SM) [21].

SM State | ${\mathbf{T}}_{1}\mathbf{State}$ | ${\mathbf{T}}_{2}\mathbf{State}$ | ${\mathit{i}}_{\mathit{S}\mathit{M}}$ | $\mathbf{\Delta}{\mathit{v}}_{\mathit{C}}$ | ${\mathit{i}}_{\mathit{S}\mathit{M}}\mathbf{Flows}\mathbf{through}$ | ${\mathit{v}}_{\mathit{S}\mathit{M}}$ |
---|---|---|---|---|---|---|

ON | ON | OFF | $>0$ | $+$ | ${\mathrm{D}}_{1}$ | ${v}_{C}$ |

ON | ON | OFF | $<0$ | $-$ | ${\mathrm{T}}_{1}$ | ${v}_{C}$ |

OFF | OFF | ON | $>0$ | $0$ | ${\mathrm{T}}_{2}$ | $0$ |

OFF | OFF | ON | $<0$ | $0$ | ${\mathrm{D}}_{2}$ | $0$ |

Number of Electric Generators = N_{EG} | Classical Topology | Proposed Topology |
---|---|---|

Electric generators | N_{EG} | N_{EG} |

DC/AC converters | 2 N_{EG} | N_{EG} |

Switching modules (SM) | 0 | N_{EG} |

IGBTs | 12 N_{EG} | 8 N_{EG} |

Switching frequency | High | Low |

Switching losses | High | Low |

Filters between converter and grid | N_{EG} | 0/1 |

Wind turbine transformers | 0/N_{EG} | 0 |

Grid coupling transformer | 0/1 | 1 |

N° | Cases |
---|---|

1 | Balanced generation: all wind generators generate the same power. |

2 | Imbalance between phases: generators of the same phase generate the same power, which is different from that generated by turbines of a different phase. |

3 | Imbalance between arms: all phases generate the same total power, but their upper and lower arms generate different power. |

4 | Imbalance between phases and arms. It is a mixture of cases 2 and 3, so it will not be studied |

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

$n$ | $10$ | ${L}_{c}$ | $15\mathrm{m}\mathrm{H}$ |

${T}_{S}$ | $10\mathsf{\mu}\mathrm{s}$ | ${i}_{q}{}^{*}$ | $0$ |

${T}_{reg}$ | $130\mathsf{\mu}\mathrm{s}$ | ${k}_{p,VDC}$ | $0.64$ |

${v}_{DC}$ | $2.4\mathrm{k}\mathrm{V}$ | ${k}_{i,VDC}$ | $1.6$ |

${v}_{ph,ph}$ | $1300{V}_{RMS}$ | ${k}_{p,id,iq}$ | $2.5$ |

$C$ | $120\mathrm{m}\mathrm{F}$ | ${k}_{i,id,iq}$ | $25$ |

${C}_{DC}$ | $40\mathsf{\mu}\mathrm{F}$ | ${k}_{p,PLL}$ | $0.2$ |

$L$ | $375\mathsf{\mu}\mathrm{H}$ | ${k}_{i,PLL}$ | $2$ |

**Table 5.**Summary of the peak values of the variables obtained in the simulation. Voltages are in volts, currents in amperes, and angles in degrees. All variables are 50 Hz except where noted.

Sub-Section | ${\mathit{i}}_{\mathit{a}}$ | ${\mathit{i}}_{\mathit{u}\mathit{a}}$ | ${\mathit{i}}_{\mathit{l}\mathit{a}}$ | ${\mathit{v}}_{\mathit{u}\mathit{a}}$ | ${\mathit{v}}_{\mathit{l}\mathit{a}}$ | ${\mathit{i}}_{\mathit{z}\mathit{a}}$ | ${\mathit{i}}_{\mathit{z}\mathit{A}\mathit{C}2\mathit{a}}$_{(100 HZ)} |
---|---|---|---|---|---|---|---|

5.1.1 | 28.47L0.0° | 14.42L-8.3° | 14.35L188.3° | 1069.99L187.2° | 1069.23L7.2° | 2.08L-89.0° | 3.64L98.3° |

5.1.2 | 56.87L-0.7° | 28.65L-1.9° | 28.23L180.6° | 1096.65L194.2° | 1096.37L14.2° | 0.64L-71.8° | 7.11L107.0° |

5.2.1 | 27.08L1.2° | 12.08L-4.5° | 15.10L185.8° | 1062.72L186.7° | 1062.30L6.7° | 1.94L219.7° | 3.16L95.0° |

5.2.2 | 28.86L-1.6° | 13.25L-5.2° | 15.65L181.4° | 1072.55L187.1° | 1072.32L7.1° | 1.45L212.8° | 3.13L101.7° |

5.3.1 | 46.16L-1.0° | 29.37L67.1° | 44.53L141.3° | 1082.10L191.5° | 1089.03L11.6° | 29.84L113.0° | 5.58L104.0° |

5.3.2 | 32.61L1.1° | 46.63L93.6° | 58.08L127.7° | 1064.22L188.0° | 1075.34L8.2° | 50.08L112.6° | 4.27L98.0° |

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**MDPI and ACS Style**

Martinez-Rodrigo, F.; Ramirez, D.; de Pablo, S.; Herrero-de Lucas, L.C.
Connection System for Small and Medium-Size Wind Generators through the Integration in an MMC and NLC Modulation. *Energies* **2021**, *14*, 2681.
https://doi.org/10.3390/en14092681

**AMA Style**

Martinez-Rodrigo F, Ramirez D, de Pablo S, Herrero-de Lucas LC.
Connection System for Small and Medium-Size Wind Generators through the Integration in an MMC and NLC Modulation. *Energies*. 2021; 14(9):2681.
https://doi.org/10.3390/en14092681

**Chicago/Turabian Style**

Martinez-Rodrigo, Fernando, Dionisio Ramirez, Santiago de Pablo, and Luis Carlos Herrero-de Lucas.
2021. "Connection System for Small and Medium-Size Wind Generators through the Integration in an MMC and NLC Modulation" *Energies* 14, no. 9: 2681.
https://doi.org/10.3390/en14092681