# Low Voltage Ride-Through Capability Solutions for Permanent Magnet Synchronous Wind Generators

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## Abstract

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## 1. Introduction

**Figure 1.**Ride-through fault capability (RTFC) required by Brazilian grid code [3].

**Figure 2.**Wind conversion system using the permanent magnet synchronous generator (PMSG) with full scale converter.

## 2. Full Converter Permanent Magnet Synchronous Generator Wind Energy Conversion System

#### 2.1. Permanent Magnet Synchronous Generator

_{s}is the stator resistance, L

_{d}and L

_{q}are d and q-axes inductances, ${\mathsf{\omega}}_{\mathrm{r}}$ is the electrical rotational speed, ${\mathsf{\psi}}_{\mathrm{r}}$ is the magnetic flux, P is the pole number, T

_{e}is the electromagnetic torque, T

_{turb}is the torque of the turbine, J is the sum of turbine and generator inertia and B is the friction coefficient.

#### 2.2. Grid Side

_{f}is the filter resistance, L

_{f}is the filter inductance and ${\mathsf{\omega}}_{\mathrm{g}}$ is the grid angular frequency. The active and reactive powers can be written as:

_{g}oscillations in the power (cos and sin terms). Furthermore, the direct product of negative sequence components of currents and voltages can modify the power transference mean value (${P}_{{\mathrm{g}}_{0}}$and ${Q}_{{\mathrm{g}}_{0}}$).

#### 2.3. The Classic Control Structure

**Figure 3.**Control block diagram of the (

**a**) grid side converter (GSC) and (

**b**) machine side converter (MSC). Sliding mode observer: SMO.

_{d}= L

_{q}, the transfer function of the MSC outer (power) control loop yields:

_{dc}is the DC-link capacitance. Equations (13)–(16) show that all transfer functions are first order, thus, proportional-integral (PI) controllers were employed. The gains of GSC and MSC were tuned using the modulus optimum and symmetrical optimum techniques [28] and the values are presented in the Table A1 in the Appendix. Both converters use a discontinuous PWM method in order to reduce switching losses [29].

#### 2.4. Test Bench

**Figure 4.**Diagram of the test bench representing a wind energy conversion system (WECS) with full converter PMSG (FC-PMSG) technology.

_{2}cause a voltage drop in Z

_{1}which represents a voltage sag in the terminals of the system “WT”, calculated as:

**Figure 6.**Impedance voltage sag generator [30].

**Table 1.**Specification of voltage drops recommended in the IEC 61400-21 [30].

Case | Voltage Magnitude | Positive Sequence Magnitude | Duration (s) | Shape |
---|---|---|---|---|

Three-phase | 90% ± 5% | 90% | 0.5 ± 0.05 | |

Three-phase | 50% ± 5% | 50% | 0.5 ± 0.05 | |

Three-phase | 20% ± 5% | 20% | 0.2 ± 0.05 | |

Two-phase | 90% ± 5% | 95% | 0.5 ± 0.05 | |

Two-phase | 50% ± 5% | 75% | 0.5 ± 0.05 | |

Two-phase | 20% ± 5% | 60% | 0.2 ± 0.05 |

## 3. Symmetrical Voltage Sags

#### 3.1. Experimental Results

**Figure 7.**Experimental results for 25% three-phase voltage sag with the system operating with 20% of rated power: (

**a**) grid voltages; (

**b**) grid currents; (

**c**) DC-link voltage; and (

**d**) generator currents.

**Figure 8.**Experimental results for 25% three-phase voltage sag with the system operating with 100% rated power: (

**a**) grid voltages; (

**b**) grid currents; (

**c**) DC-link voltage; and (

**d**) generator currents.

#### 3.2. Results Discussion

**Figure 9.**Chopper actuation limits during balanced voltage sags according to the converter current limits.

#### 3.3. Analysis of the Low Voltage Ride-Through Capability Control Strategies Proposed in the Literature

_{0}is the speed in the sag beginning (instant t

_{0}) and ω

_{f}is the speed when the voltage is recovered (instant t

_{f}). For the 2 MW turbine under consideration, the rated speed range is 15 rpm and the inertia is 7.985 × 10

^{6}Kg·m

^{2}(generator + turbine). The worst situation is when the system is operating with rated power, i.e., rotational speed 15 rpm and the voltage sag occurs. Using Equation (18), the speed increase is plotted as a function of the voltage sag depth and duration, as presented in Figure 10a. This graph was plotted considering the conditions that the WECS must sustain operating according to the Brazilian RTFC curve (Figure 1). Figure 10b shows the worst conditions, i.e., maximum voltage sag depth and duration. This figure also indicates the total surplus energy during the voltage sag. It is important to mention that this curve does not consider the power decrease due to the speed increasing (operation below the maximum power); thus, this scenario is slightly worse than the real one.

**Figure 10.**Speed increase for different voltage sags, considering the Brazilian RTFC curve and the 2 MW WECS: (

**a**) speed as a function of voltage sag amplitude and duration and (

**b**) maximum speed considering the worst conditions (maximum sag depth and duration).

^{°}/s.

## 4. Asymmetric Voltage Sags

#### 4.1. Experimental Results

**Figure 11.**Experimental results for 50% phase-to-phase voltage sag with the system operating at 100% of rated power: (

**a**) grid voltage; (

**b**) grid currents; (

**c**) DC-link voltage; (

**d**) generator currents; and (

**e**) direct grid current (sag beginning and recovery instants).

#### 4.2. Results Discussion and Low Voltage Ride-through Capability Control Strategies Proposed in the Literature

## 5. Resonant Control

#### 5.1. The Control Strategy

_{p}, K

_{i}and K

_{r}are respectively the proportional, integral and resonant gains, ω

_{c}is the controller bandwidth and ω

_{0}is the resonant frequency. As seen previously, the negative sequence current components in the positive synchronous reference frame appear as oscillations with twice the grid frequency (120 Hz). Therefore, ω

_{0}is set to 2×π×120 rad/s.

_{r}and ω

_{c}. The K

_{r}gain value is directly related with the resonant peak and the bandwidth around the selected frequency, ω

_{0}. An increase of the bandwidth ω

_{c}affects the controller selectivity which can be helpful for reducing sensitivity, for example, toward frequency deviations. The K

_{r}and ω

_{c}adjustment is a balance between fast response and selectivity. The K

_{p}and K

_{i}are kept equal to the classical case, since generally its bandwidth is not affected by the resonant parcel.

_{g}oscillation on the dq-axes grid current, i.e., the negative sequence component is canceled. It is also possible to set a reference for the negative sequence component in order to, for example, reduce the power oscillations [14,24]. In this work, this strategy is not used, since the main objective is to limit the grid current during the voltage sag.

#### 5.2. Experimental Results

**Figure 13.**Experimental results for 20% phase-to-phase voltage sag with the system operating at 100% of rated power using RC: (

**a**) grid currents; (

**b**) grid currents zoom; (

**c**) DC-link voltage; and (

**d**) direct and quadrature grid currents (sag beginning and recovery instants).

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix

Machine Side Converter | ||||

Control | Proportional (K_{p}) | Integral (K_{i}) | ||

Current control loop | 2 | 20 | ||

Power loop | 0.05 | 1 | ||

Grid Side Converter | ||||

Control | Proportional (K_{p}) | Integral (K_{i}) | Resonant (K_{r}) | |

Current control loop | 2 | 100 | 50 | |

DC-Link control loop | 0.6 | 10 | - |

Generator | |

Rated power | 34 kW |

Frequency | 60 Hz |

Pole pair number | 24 |

Rated speed | 150 rpm |

Rated current | 76 A |

Rated voltage | 365 V |

Motor (turbine simulator) | |

Rated power | 37 kW |

Frequency | 60 Hz |

Number of poles | 8 |

Rated current | 83 A |

Rated voltage | 380 V |

Converter | |

Rated power | 42 kVA |

Grid voltage | 380 V |

Switching frequency | 6 kHz |

DC-link voltage | 640 V |

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**MDPI and ACS Style**

Mendes, V.F.; Matos, F.F.; Liu, S.Y.; Cupertino, A.F.; Pereira, H.A.; De Sousa, C.V.
Low Voltage Ride-Through Capability Solutions for Permanent Magnet Synchronous Wind Generators. *Energies* **2016**, *9*, 59.
https://doi.org/10.3390/en9010059

**AMA Style**

Mendes VF, Matos FF, Liu SY, Cupertino AF, Pereira HA, De Sousa CV.
Low Voltage Ride-Through Capability Solutions for Permanent Magnet Synchronous Wind Generators. *Energies*. 2016; 9(1):59.
https://doi.org/10.3390/en9010059

**Chicago/Turabian Style**

Mendes, Victor F., Frederico F. Matos, Silas Y. Liu, Allan F. Cupertino, Heverton A. Pereira, and Clodualdo V. De Sousa.
2016. "Low Voltage Ride-Through Capability Solutions for Permanent Magnet Synchronous Wind Generators" *Energies* 9, no. 1: 59.
https://doi.org/10.3390/en9010059