# Coordinated Control of a DFIG-Based Wind-Power Generation System with SGSC under Distorted Grid Voltage Conditions

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^{2}

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## Abstract

**:**

## 1. Introduction

^{+}reference frame are designed to provide different operation functionalities, i.e., removing the stator or rotor current harmonics, or eliminating the oscillations at six times the grid frequency in the stator output active and reactive powers. However, due to the limited RSC control variables, the proposed method cannot eliminate the stator and rotor current harmonics and the output power pulsations in the DFIG simultaneously under network harmonic distortions. Therefore, harmonic power losses in the stator and rotor windings or the stator power oscillations and torque pulsations in the DFIG still exist, which might degrade the life time of the winding insulation materials or deteriorate the output power quality.

^{+}and harmonic (dq)

^{5−}, (dq)

^{7+}reference frames, the mathematical models of SGSC and PGSC under 5th and 7th grid voltage harmonics are developed. Besides, the control target for the SGSC and different control targets for the PGSC under the distorted voltage conditions are identified, and the reference values of the PGSC’s fundamental and harmonic currents are deduced. Furthermore, a coordinated control of the SGSC, PGSC and RSC and control schemes for SGSC and PGSC using a PI controller and a harmonic resonant regulator tuned at six times the grid frequency in the positive (dq)

^{+}reference frame are developed. Finally, numerical simulations on a 2 MW DFIG system with SGSC are presented to verify the proposed control scheme.

## 2. Modeling of DFIG System with SGSC during Network Harmonic Distortions

^{+}reference frame, the d

^{+}-axis is aligned with the positive-sequence grid voltage vector.

#### 2.1. SGSC

**u**

_{com+}is the positive-sequence voltage vector error which needs to be compensated.

#### 2.2. PGSC

#### 2.3. RSC

## 3. Coordinated Control of SGSC, PGSC and RSC

#### 3.1. SGSC

#### 3.2. PGSC

_{g_av}and Q

_{g_av}, shown in Equation (6), there are four more power oscillating terms of the 6th grid frequency can be controlled when ignoring the power pulsations of the 12th grid frequency. It is worth noting that, unlike the PGSC control during a network unbalance mentioned in [22], the simultaneous elimination of the oscillations in total active and reactive power can be realized due to the enough control variables of grid currents, which can also simplify the control target selection and system control design. Consequently, the PGSC may be controlled to achieve one of the following two control targets:

#### 3.2.1. Target 1

^{+}-axis is aligned with the positive-sequence grid voltage vector, which means ${u}_{\text{gq}+}^{+}$ = 0, the required current reference values for the PGSC to realize Target 1 can be given as Equation (10), where the oscillating terms of active and reactive power flowing through the SGSC are calculated from Equation (4). The term ${i}_{\text{gd}+}^{+*}$ and ${i}_{\text{gq}+}^{+*}$ represents the dq-axis fundamental component of grid current, respectively:

_{pu}and τ

_{iu}are the proportional and integral time parameters of the PI controller, respectively.

#### 3.2.2. Target 2

#### 3.3. RSC

#### 3.4. System Implementation Using PI-R Controllers

^{+}reference frame are developed for the SGSC voltage control and PGSC current control, respectively.

^{+}reference frame consist of two parts, i.e., the dc fundamental positive-sequence component and the ac fifth- and seventh-order harmonic components oscillating at the frequencies of ±6ω. As the resonant controller is a generalized double-side ac integrator [25], it can simultaneously eliminate the ac errors of the positive- and negative-sequence components at the frequencies of ±6ω. Therefore, a resonant compensator tuned at six times the grid frequency can be introduced to regulate the fifth- and seventh-order voltages or currents to their reference values in the positive (dq)

^{+}reference frame, while the fundamental positive-sequence voltages or currents can be controlled by using a traditional PI regulator. Consequently, the PI plus R (PI-R) controllers for the SGSC and PGSC in the rotating positive (dq)

^{+}reference frame can be designed to directly regulate both the fundamental positive-sequence component and the harmonic components without involving sequential decomposition, significantly improving the transient performance of the whole system. A detailed study on the PI-R controller has been provided in [14]. Therefore, only a brief description is given in this paper.

_{p}, K

_{i}and K

_{r}are the proportional, integral and resonant parameters of the PI-R controller, respectively. And ω

_{c}is the cutoff frequency used to widen the resonant frequency bandwidth.

^{+}reference frame, the respective SGSC and PGSC output control voltage can be obtained as:

_{seriesαβ}and u

_{cαβ}for the SGSC and PGSC can be applied by using standard space vector pulse width modulation (SVPWM) techniques.

## 4. Evaluation Studies

Converter | K_{p} | K_{i} | K_{r} | ω_{c} (rad/s) |
---|---|---|---|---|

PGSC | 10 | 200 | 200 | 5 |

SGSC | 10 | 200 | 200 | 5 |

**Figure 5.**Simulation results of DFIG system with SGSC under distorted grid voltage condition between 1.6 and 1.7 s without harmonic control. (

**a**) grid voltage (pu); (

**b**) stator voltage (pu); (

**c**) stator current (pu); (

**d**) rotor current (pu); (

**e**) total current (pu); (

**f**) PGSC active power (pu); (

**g**) stator active power (pu); (

**h**) total active power (pu); (

**i**) PGSC reactive power (pu); (

**j**) stator reactive power (pu); (

**k**) total reactive power (pu); (

**l**) electromagnetic torque (pu); (

**m**) common dc-link voltage (V); (

**n**) PGSC positive-sequence dq-axis currents reference and response (pu); (

**o**) PGSC 5th harmonic dq-axis currents (pu); (

**p**) PGSC 7th harmonic dq-axis currents (pu); (

**q**) grid and stator positive-sequence dq-axis voltages (pu); (

**r**) grid and stator 5th harmonic d-axis voltages (pu); (

**s**) grid and stator 5th harmonic q-axis voltages (pu); (

**t**) grid and stator 7th harmonic dq-axis voltages (pu).

**Figure 6.**Simulation results of DFIG system with SGSC under distorted grid voltage condition between 1.6 and 1.7 s with proposed control scheme with Target 1. (

**a**) grid voltage (pu); (

**b**) stator voltage (pu); (

**c**) stator current (pu); (

**d**) rotor current (pu); (

**e**) total current (pu); (

**f**) PGSC active power (pu); (

**g**) stator active power (pu); (

**h**) total active power (pu); (

**i**) PGSC reactive power (pu); (

**j**) stator reactive power (pu); (

**k**) total reactive power (pu); (

**l**) electromagnetic torque (pu); (

**m**) common dc-link voltage (V); (

**n**) PGSC positive-sequence dq-axis currents reference and response (pu); (

**o**) PGSC 5th harmonic dq-axis currents reference and response (pu); (

**p**) PGSC 7th harmonic dq-axis currents reference and response (pu); (

**q**) grid and stator positive-sequence dq-axis voltages (pu); (

**r**) grid and stator 5th harmonic d-axis voltages (pu); (

**s**) grid and stator 5th harmonic q-axis voltages (pu); (

**t**) grid and stator 7th harmonic dq-axis voltages (pu).

**Figure 7.**Simulation results of DFIG system with SGSC under distorted grid voltage condition between 1.6 and 1.7 s with Proposed control scheme with Target 2. (

**a**) grid voltage (pu); (

**b**) stator voltage (pu); (

**c**) stator current (pu); (

**d**) rotor current (pu); (

**e**) total current (pu); (

**f**) PGSC active power (pu); (

**g**) stator active power (pu); (

**h**) total active power (pu); (

**i**) PGSC reactive power (pu); (

**j**) stator reactive power (pu); (

**k**) total reactive power (pu); (

**l**) electromagnetic torque (pu); (

**m**) common dc-link voltage (V); (

**n**) PGSC positive-sequence dq-axis currents reference and response (pu); (

**o**) PGSC 5th harmonic dq-axis currents reference and response (pu); (

**p**) PGSC 7th harmonic dq-axis currents reference and response (pu); (

**q**) grid and stator positive-sequence dq-axis voltages (pu); (

**r**) grid and stator 5th harmonic d-axis voltages (pu); (

**s**) grid and stator 5th harmonic q-axis voltages (pu); (

**t**) grid and stator 7th harmonic dq-axis voltages (pu).

^{+}synchronous reference frame is used for the SGSC voltage and PGSC current. As the traditional single PI controller of SGSC has limited regulating gain for the fifth- and seventh-order harmonic voltage components which are oscillating at six times the grid frequency in the positive (dq)

^{+}reference frame, the fifth- and seventh-order voltage harmonics in the stator still exist and the stator voltages will contain 300 Hz pulsations in the positive synchronous reference frame, as shown in Figures 5b,q–t. The harmonically polluted stator voltages will lead to badly distorted stator currents, which inevitably make the rotor currents contain both fundamental component of 15 Hz, and harmonic components of 315 Hz (300 + 15 Hz) and 285 Hz (300 – 15 Hz), respectively. Consequently, the significant oscillations at 300 Hz in the electromagnetic torque and instantaneous stator powers of DFIG could occur, as shown in Figure 5g,j,l. In the meanwhile, distorted currents and power pulsations in the PGSC will also result from the failure regulation of harmonic currents in the PGSC when a single current PI controller is used, which further degrading the operation performance of whole system, as shown in Figure 5e,f,h,i,k,n. As it can be seen from Figure 6 and Figure 7b,q–t, when the proposed control strategy for the SGSC under distorted grid voltage condition is implemented, the harmonic voltage at the DFIG’s stator terminal can be eliminated by injecting appropriate series compensation voltages of SGSC to counteract the grid voltage harmonics, although the grid voltage harmonics always exist. Compared with the conventional control method, the fundamental component of the stator voltage is controlled to be equal to the positive-sequence grid voltage, while the harmonic components of the stator voltage are effectively controlled to zero by using the proposed PI-R voltage control strategy. As analyzed in Section 2, once the stator voltage harmonics are suppressed, the stator and rotor current harmonics, electromagnetic torque and power oscillations in the DFIG will be eliminated naturally, which are nicely demonstrated in Figure 6 and Figure 7c,d,g,j,l.

^{+}reference frame can be tuned to the their references by using the resonance regulator. Consequently, it can be seen that the voltage and current feedback signals of SGSC and PGSC precisely track their corresponding reference values, which indicates that the developed PI-R controllers have excellent dynamic response performance. It is also worth noting that the function of SGSC does not need to be changed during the normal grid condition and the distorted voltage condition for the PGSC’s two control strategies, and the R regulator can eliminate the harmonic voltages or currents when the voltage distortions is cleared, which means that the developed PI-R regulator can work under both distorted grid voltage conditions and the normal conditions, without any modifications.

**Figure 8.**Harmonic spectrums. (

**a**) No harmonic control; (

**b**) Proposed control scheme with Target 1; (

**c**) Proposed control scheme with Target 2.

Measured Parameter | Conventional | Target 1 | Target 2 |
---|---|---|---|

u_{s} 5th harmonic (%) | 3.94% | 0.08% | 0.08% |

u_{s} 7th harmonic (%) | 3.09% | 0.05% | 0.05% |

i_{s} 5th harmonic (%) | 4.16% | 0.08% | 0.07% |

i_{s} 7th harmonic (%) | 2.01% | 0.05% | 0.02% |

i_{r} 19th harmonic (%) | 1.80% | 0.14% | 0.13% |

i_{r} 21st harmonic (%) | 4.09% | 0.15% | 0.14% |

i_{total} 5th harmonic (%) | 4.23% | 3.13% | 0.06% |

i_{total} 7th harmonic (%) | 2.46% | 3.12% | 0.04% |

P_{s} pulsation (pu) | 0.03 | 0.007 | 0.007 |

Q_{s} pulsation (pu) | 0.06 | 0.012 | 0.01 |

P_{total} pulsation (pu) | 0.04 | 0.01 | 0.07 |

Q_{total} pulsation (pu) | 0.13 | 0.03 | 0.12 |

T_{em} pulsation (pu) | 0.10 | 0.01 | 0.01 |

u_{dc} pulsation (V) | 4.0 | 2.0 | 2.0 |

**Figure 9.**Simulation results with PGSC’s reactive power step at 2.0 s and generator speed variations during 2.0 s to 2.7 s. (

**a**) Reactive power step with Target 1; (

**b**) Reactive power step with Target 2; (

**c**) Variable rotor speed with Target 1; (

**d**) Variable rotor speed with Target 2.

## 5. Conclusions

## Nomenclature

u_{s} and u_{g} | Stator and grid voltage vectors. |

u_{seires} | Series injected voltage vector of SGSC referred to stator-side. |

i_{s}, i_{r} | Stator and rotor current vectors. |

i_{series} | SGSC current vector referred to stator-side. |

i_{total} | Total current vector of the DFIG system. |

P_{s} and Q_{s} | Stator output active and reactive powers. |

P_{r} and Q_{r} | Rotor output active and reactive powers. |

P_{g} and Q_{g} | PGSC output active and reactive powers. |

P_{series} and Q_{series} | Active and reactive powers through SGSC. |

P_{total} and Q_{total} | Total output active and reactive powers of the DFIG system with SGSC. |

T_{e} | Electromagnetic torque. |

u_{dc} | Common dc-link voltage. |

ω | Synchronous angular speed. |

θ_{g} | Grid voltage angle. |

s | Slip. |

C | Common dc-link capacitance. |

## Subscripts

α,β | Stationary α- and β-axis. |

av | Average component. |

sin and cos | Sine and cosine oscillating components. |

abc | Stationary abc-axis. |

dq | Synchronous dq-axis. |

s and r | Stator and rotor. |

g and series | PGSC and SGSC. |

+, 5– and 7+ | Fundamental, fifth-order and seventh-order components. |

## Superscripts

+, 5– and 7+ | Positive (dq) ^{+}, harmonic (dq)^{5−} and (dq)^{7+}reference frames |

* | Reference value |

^ | Conjugate complex |

## Acknowledgments

## Conflict of Interest

## Appendix A: Simulation System Parameters

DFIG parameters | Value | DFIG parameters | Value |
---|---|---|---|

Rated generator power | 2 MW | Rotor resistance | 0.00549 pu |

Rated generator voltage | 690 V | Rotor leakage inductance | 0.1493 pu |

Frequency | 50 Hz | Magnetizing inductance | 3.9527 pu |

Stator resistance | 0.00488 pu | Stator/rotor turns ratio | 0.45 |

Stator leakage inductance | 0.1386 pu | Inertia constant H | 3.5 s |

Step-up transformer parameters | Value | Series transformer parameters | Value |
---|---|---|---|

Rated capacity | 2.5 MVA | Rated capacity | 200 kVA |

Frequency | 50 Hz | Frequency | 50 Hz |

Primary windings | 20 kV-Yg | Stator to SGSC side transformer turns ratio | 1:7 |

Secondary windings | 690 V-Δ | Sum of transformer and choke resistance | 0.006 pu |

Short circuit impedance | 0.0098 + j0.09241 pu | Sum of transformer and choke inductance | 0.03 pu |

Grid-side converter parameters | Value | Grid-side converter parameters | Value |
---|---|---|---|

Reactor resistance | 6 mΩ | Common dc-link capacitor | 38,000 μF |

Reactor inductance | 0.6 mH | Common dc-link voltage reference value | 1,200 V |

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## Share and Cite

**MDPI and ACS Style**

Yao, J.; Li, Q.; Chen, Z.; Liu, A.
Coordinated Control of a DFIG-Based Wind-Power Generation System with SGSC under Distorted Grid Voltage Conditions. *Energies* **2013**, *6*, 2541-2561.
https://doi.org/10.3390/en6052541

**AMA Style**

Yao J, Li Q, Chen Z, Liu A.
Coordinated Control of a DFIG-Based Wind-Power Generation System with SGSC under Distorted Grid Voltage Conditions. *Energies*. 2013; 6(5):2541-2561.
https://doi.org/10.3390/en6052541

**Chicago/Turabian Style**

Yao, Jun, Qing Li, Zhe Chen, and Aolin Liu.
2013. "Coordinated Control of a DFIG-Based Wind-Power Generation System with SGSC under Distorted Grid Voltage Conditions" *Energies* 6, no. 5: 2541-2561.
https://doi.org/10.3390/en6052541