Large-scale offshore wind farms are integrated with onshore ac grids through the voltage source converter based high voltage direct current (VSC-HVDC) transmission system. The impact on the stability of the ac grids will be significant. The small signal model of a wind farm connected with voltage source converter based dc transmission system is studied in this paper. A suitable model for small signal stability analysis is presented. The control system of wind generator and the HVDC system has also been modeled in this model for small signal stability analysis. The impact of the control parameters on the network stability is investigated.
Due to the advantages in speed control, and four-quadrant active and reactive power regular capabilities, the large offshore wind farms based on doubly fed induction generator (DFIG) have been planned around worldwide [
VSC-HVDC transmission system was employed in [
The dynamic behavior of the DFIG has been investigated by many researchers [
In this paper, the DFIG-based wind farm via VSC-HVDC transmission system connected to the grid is studied. The single-machine infinite-bus (SMIB) structure is followed. The paper is organized as follows. In Section
The study system is shown in Figure
The study system.
The one-phase equivalent electric circuit of the DFIG rotor and stator is shown in Figure
The equivalent electric circuit of the DFIG.
The circuit of rotor and stator
Equivalent circuit
For stability analysis, the generators are modeled as an equivalent voltage source based on transient impedance. The dynamic model of DFIG is shown as
The purpose of the rotor side converter controller is to control the active power so as to track the maxim power
The VSC-HVDC system is employed to transfer wind energy from offshore to onshore. As shown in Figure
Converter circuit diagram.
As shown in Figure
The dynamic model in “
In ideal condition, the dynamic of the dc side transmission system is shown in
The wind farm side converter (WFVSC) should keep the wind farm side ac bus working at constant frequency and voltage. So, the controller of wind farm side converter should maintain the ac bus frequency and voltage as a constant. After that, the primary requirement of the WFVSC is to transfer energy collected from the wind farm. The output power form DFIG is controlled by power electronic converters and MPPT system and the network frequency variations when little influence is on the power generation. The main task for the WFVSC is to collect energy from the wind farm and to control the ac voltage and frequency of the local wind farm network. Therefore, the control strategy adopted on the WFVSC is to control the wind farm side converter as an infinite voltage source with constant frequency, voltage amplitude, and phase angle. The control block diagram for the WFVSC is shown in Figure
Control block diagram of the wind farm side converter.
Consider the voltage measurement devise delay; the measurement unit can be modeled as a first-order process,
Thus, the control strategy makes the wind farm be connected to an infinite ac system; the power generated by the wind farm is automatically absorbed by the source resembled by the wind farm side converters and then transmitted to the grid via the DC lines.
The WSVSC collects energy from wind farm and then transmits it to the power grid via the dc transmission and grid side converter (GSVSC) (Figure
Control block diagram of the grid side converter.
The control system of the grid side converter.
The current control loop is designed as
For small signal model, four middle variables named
Combine (
The complete state-space representation of the test system is obtained by combining all the linearized models. As shown in Figure
The combined small signal model for whole system.
The small signal stability can be observed by eigenvalue analysis of the whole system linearized model. In this case, the “small signal” disturbances are considered sufficiently small to permit the equations representing the system to be linearized and expressed in state-space form. The model of a power system can be expressed as a set of DAE. The linearized model of the test system can be expressed in state-space form as in
The purpose to model the small signal model of the system is to study the small signal stability and for the further study to investigate the controller parameters design to enhance the small signal stability. The control parameters employed in this study are shown in Table
Controller parameters.
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0.45 | 0.5 | 0.025 | 0.005 | 0.01 | 0.25 | 15 | 1 | 1 | 10 | 0.01 |
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0.25 | 0.45 | 0.2 | 0.15 | 0.25 | 0.15 | 20 | 8 | 8 | 200 | 300 |
The eigenvalue analysis of the small signal model is show in Table
Eigenvalues.
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Damping ratio |
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1218.7 | 0.183 |
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215.8 | 0.21 |
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45.06 | 0.053 |
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33.76 | 0.026 |
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82.96 | 0.086 |
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13.58 | 0.091 |
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34.97 | 0.128 |
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1.31 | 0.753 |
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0.9 | 0.302 |
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0.69 | 0.009 |
A linearized mathematical model for small signal stability analysis of VSC-HVDC transmission system collected with a DFIG-based wind farm has been presented in this paper. The linearized model is based on the state-space models. The state matrix is employed to investigate the small signal stability performance of the studied system through the eigenvalue analysis. It was validated that, using the small signal stability model, it was possible to design improved controllers for the VSCs of the dc network, which ensure stable network operation and enhanced dynamic performance.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National High Technology Research and Development Program (no. 2012AA050208).