# Doubly Fed Induction Machine-Based DC Voltage Generator with Reduced Oscillations of Torque and Output Voltage

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Description and Modelling

_{s}, R

_{r}—stator and rotor resistance, respectively; L

_{s}, L

_{r}

_{,}L

_{m}—stator, rotor, and magnetizing inductance, respectively; T

_{em}—electromagnetic torque; and ${p}_{p}$—number of pole pairs.

_{dc}—DC-bus capacity, i

_{L}—load current, u

_{dc}—DC voltage, and dq subscripts describe space vectors orthogonal components.

_{s}and rotor p

_{r}instantaneous power flows into the DC-bus and causes DC-bus voltage oscillations. Active power equals the average value of the p component of instantaneous power by definition. The total active power provided to the DC-bus is the active electromagnetic power (calculated as the average of electromagnetic torque and mechanical speed product) reduced by the stator and rotor power losses. Thus, the total active power responsible for energy delivery to the DC-bus can be calculated by:

_{s}and p

_{r}). It could be valid for the case of constant flux, but not in the analyzed system, in which the diode rectifier causes stator voltage disturbances and, thus, flux oscillations.

## 3. Description of the Control Methods

#### 3.1. Field Oriented Control–FOC

#### 3.2. Direct Torque and Flux Module Control–DTΨC

_{rd}component of the rotor current vector is selected as the second control variable in parallel with the torque control path. In this paper, DTΨC will be compared as the method giving the smallest torque oscillations from among all methods verified in [13]. The method is schematically presented in Figure 3. The flux module will change a little depending on the load. For no load operation, the stator voltage is pure sine, and the flux is assigned as:

_{ψq}keeping the same position of the frame as the stator flux vector position.

#### 3.3. Direct Torque and x Variable Control–DTXC

_{ψq}. The difference between classic direct torque control structure (DTΨC) and the modified one (DTXC) is marked by red blocks and signal lines in Figure 3 and Figure 4. As the range of flux and x variable are different, the gains of respective controllers are also different.

## 4. Simulation Results of a MW Range DFIG-DC System

## 5. Experimental Results

_{R}= 20) is noticeable, possible for a low-power machine. Further increase in the rotor current regulator gain (even up to k

_{R}= 50) creates lower torque oscillations but significantly higher oscillations of the DC-bus voltage. Results shown in Figure 9 for this method are a compromise between torque and DC voltage oscillations. The FFT of generated DC voltage oscillations and electromagnetic torque oscillations for the FOC method is provided in Figure 9b.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ADR | auxiliary diode rectifier, |

BSF | band stop filter, |

DFIG | doubly fed induction generator, |

DFIM | doubly fed induction machine, |

DTC | direct torque control, |

DTC-SVM | direct torque control of space vector modulation, |

DTΨC | direct torque control with flux module second control variable, |

DTXC | direct torque control with dot product of flux and current vector as the second control variable, |

FFT | fast Fourier transform |

FOC | field-oriented control, |

IM | induction motor, |

PWM | pulse width modulation, |

RC | rotor converter, |

SDR | stator-connected diode rectifier, |

${\overrightarrow{u}}_{s},{\overrightarrow{u}}_{r}$ | stator and rotor voltage vectors, |

u_{dc} | DC voltage, |

${\overrightarrow{i}}_{s},{\overrightarrow{i}}_{r}$ | stator and rotor current vectors, |

${\overrightarrow{\psi}}_{s},{\overrightarrow{\psi}}_{r}$ | stator and rotor flux vectors, |

i_{L} | load current, |

${i}_{sa\_rms}^{},{i}_{sb\_rms}^{},{i}_{sc\_rms}^{}$ | rms value of stator phase currents, |

${i}_{ra\_rms}^{},{i}_{rb\_rms}^{},{i}_{rc\_rms}^{}$ | rms value of rotor phase currents, |

R_{s}, R_{r} | stator and rotor resistance, |

L_{s}, L_{r}_{,} L_{m} | stator, rotor, and magnetizing inductance, |

C_{dc} | DC-bus capacitor, |

T_{em} | electromagnetic torque, |

${T}_{e\_avg}$ | average value of electromagnetic torque, |

${p}_{p}$ | number of pole pairs, |

p_{s}, p_{r} | stator and rotor instantaneous power real components, |

${P}_{s},{P}_{r}$ | stator and rotor active power, |

${p}_{\Delta \psi}$ | machine instantaneous power real components related to the magnetic energy changes, |

${\omega}_{s}$ | synchronous speed (rotation speed of magnetic flux), |

${\omega}_{m}$ | mechanical speed, |

${E}_{{L}_{\sigma s}},{E}_{{L}_{\sigma r}},{E}_{{L}_{m}}$ | stator and rotor leakage and magnetizing inductance stored energy, |

${q}_{s},{q}_{m},{q}_{r}^{s}$ | stator, magnetizing, and rotor instantaneous power imaginary components seen from the stator side, |

dq | subscripts describing two-dimensional rotating space. |

## Appendix A

Parameter | Value (2 MW) | Value (7.5 kW) |
---|---|---|

Rated power | 2 MW | 7.5 kW |

Stator voltage (L-L) | 690 V | 182 V |

Rotor voltage (L-L) | 2 kV | 380 V |

Number of pole pairs | 2 | 2 |

L_{m} (magnetizing inductance) | 2.5 mH | 27.52 mH |

L_{s} (stator inductance) | 2.587 mH | 29.82 mH |

L_{r} (rotor inductance) | 2.587 mH | 29.82 mH |

R_{s} (stator resistance) | 2.6 mΩ | 0.16 Ω |

R_{r} (rotor resistance) | 2.6 mΩ | 0.1 Ω |

f_{s} (sampling frequency) | 4 kHz | 4 kHz |

C_{dc} (DC-bus capacity) | 10 mF | 1 mF |

u_{dc}^{ref} (reference DC-bus voltage) | 970 V | 250 V |

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**Figure 3.**Stand-alone DFIG-DC voltage generator controlled with direct torque and flux module control DTΨC.

**Figure 4.**Stand-alone DFIG-DC voltage generator controlled with the direct torque and x variable control DTXC.

**Figure 5.**Simulation results of a 2 MW DFIG-DC system at 1200 rpm for field-oriented control FOC (

**a**), direct torque and flux module control DTΨC (

**b**), and the proposed direct torque and x variable control DTXC (

**c**) with unlimited rotor voltage at the steady state.

**Figure 6.**Simulation results of a 2 MW DFIG-DC system at 1200 rpm for field-oriented control FOC (

**a**), direct torque and flux module control DTΨC (

**b**), and the proposed direct torque and x variable control DTXC (

**c**) with limited rotor voltage at the steady state.

**Figure 7.**Simulation results of a 2 MW DFIG-DC system at 1200 rpm for field-oriented control FOC (

**a**), direct torque and flux module control DTΨC (

**b**), and the proposed direct torque and x variable control DTXC (

**c**) with limited rotor voltage during transient.

**Figure 9.**Experimental results of a small-power DFIG-DC system for field-oriented control FOC (

**a**) and the FFT results of DC-bus voltage and torque oscillations for this method (

**b**).

**Figure 10.**Experimental results of a small-power DFIG-DC system for the classic direct torque control DTΨC (

**a**) and the FFT results of DC-bus voltage and torque oscillations for this method (

**b**).

**Figure 11.**Experimental results of a small-power DFIG-DC system for the proposed direct torque control DTXC (

**a**) and the FFT results of DC-bus voltage and torque oscillations for this method (

**b**).

Experiment/Simulation | |||
---|---|---|---|

FOC | DTΨC | DTXC | |

Torque pulsations peak to peak, (Nm) (for dominating harmonic) | 6/3.4 k | 4/2.2 k | 4/2.5 k |

Ratio of torque pulsations to average, (%) (for dominating harmonic) | 35/23 | 24/15 | 24/16 |

DC voltage pulsations peak to peak, (V) (for dominating harmonic) | 3.8/30 | 2.5/18 | 1.6/3 |

Ratio of DC voltage pulsation to average, (%) (for dominating harmonic) | 1.5/3 | 1/2 | 0.6/0.3 |

DC voltage swell during 50% unloading, (V) | -/250 | -/140 | -/60 |

Ratio of the DC voltage swell to steady state during 50% unloading, (V) | -/26 | -/14 | -/6 |

Stator current THD, (%) | 16.3/13.5 | 16.7/14.7 | 17/15 |

Rotor current THD, (%) | 10.9/11.8 | 9.5/16.4 | 8.4/12.8 |

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**MDPI and ACS Style**

Iwański, G.; Piwek, M.; Dauksha, G.
Doubly Fed Induction Machine-Based DC Voltage Generator with Reduced Oscillations of Torque and Output Voltage. *Energies* **2023**, *16*, 814.
https://doi.org/10.3390/en16020814

**AMA Style**

Iwański G, Piwek M, Dauksha G.
Doubly Fed Induction Machine-Based DC Voltage Generator with Reduced Oscillations of Torque and Output Voltage. *Energies*. 2023; 16(2):814.
https://doi.org/10.3390/en16020814

**Chicago/Turabian Style**

Iwański, Grzegorz, Mateusz Piwek, and Gennadiy Dauksha.
2023. "Doubly Fed Induction Machine-Based DC Voltage Generator with Reduced Oscillations of Torque and Output Voltage" *Energies* 16, no. 2: 814.
https://doi.org/10.3390/en16020814