Modeling and Stability Analysis of Weak-Grid Tied Multi-DFIGs in DC-Link Voltage Control Timescale
Abstract
:1. Introduction
2. Dynamic Interactions for Multi-DFIGs in DC-Link Voltage Control Timescale
2.1. DC-Link Voltage Control Timescale Dynamics of DFIGs
2.2. DC-Link Voltage Control Timescale Interactions of Multi DFIGs in Weak Grid Condition
3. Modeling of Multi DFIGs Connected to Grid
- (1)
- Both the stator and rotor windings of the generator adopt the motor convention. The fast flux dynamics are ignored, and an algebraic generator model is utilized;
- (2)
- The fast dynamic processes of the RSC and GSC’s inner current loops are neglected;
- (3)
- As the mechanical rotor speed control of wind turbines is much slower than the converter control dynamics, its output power reference (see Figure 1) is assumed to be constant;
- (4)
- The system is lossless.
4. Stability Analysis of Multi DFIGs Connected to Weak Grids
4.1. Eigenvalue and Participation Factor Analysis
4.2. Effect of Grid Strengths
4.3. Effect of Operating Points
4.4. Effect of PLL Bandwidths
5. Simulation Validations
6. Conclusions
- For a relatively strong grid, the system’s dominant mode is highly participated in by the DVC, and this mode is hardly affected by other controls and grid strength variations. However, in very weak grids, the PLL-related mode becomes dominant, and has the risk of instability;
- The damping of the dominant mode for a multi-DFIG system under weak grid condition is reduced with the decline of the grid’s strength or the increase of the DFIG’s power outputs.
- In ultra-weak grid conditions, the stability of a two-DFIG system gets worse when the bandwidths of the PLLs of the two DFIGs are close, reaching a condition of near modal resonance. In contrast, to improve system stability, the bandwidths of the PLLs in different wind generators should be separated.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Pe | Active power output of a DFIG |
DVC | DC-link voltage control |
APC, TVC | Active power control, terminal voltage control |
RSC, GSC | Rotor side converter and grid side converter |
Pr, Pc | DFIG RSC and GSC active power outputs |
Uc, θc | VSC internal voltage (the voltage behind the filter) magnitude and phase |
Ut, θt | DFIG terminal voltage magnitude and phase angle |
Mechanical rotor angular frequency | |
ωr, ω1 | Electrical rotor angular frequency, synchronous angular frequency |
sr | =(ω1 − ωr)/ω1, Slip ratio |
Ug | Infinite bus voltage magnitude |
Ic | Current of the gird side converter |
Is, Ir | Stator current and rotor current |
θpll | PLL output angle |
Udc | DC-link voltage |
C | DC-link capacitance |
Xg | Transmission line impedance |
Xs, Xr, Xm | The equivalent reactance of stator winding and rotor winding and their mutual inductance |
, | Proportion coefficient and integral coefficient of DC-link voltage controller |
, | Proportion coefficient and integral coefficient of PLL |
, | Proportion coefficient and integral coefficient of terminal voltage controller |
, | Proportion coefficient and integral coefficient of active power controller |
Subscripts: | |
* | Reference value |
pm | Phase-locked loop coordinate system for the m-th DFIG |
sm | Synchronous rotating coordinate system for the m-th DFIG |
Subscripts: | |
d, q | Rotating reference frame d-axis and q-axis components |
n | The total number of wind turbines |
m | The sequence number of DFIGs |
Appendix A
Pbase = 2 MW | Ubase = Ustator_base = 690 V (Line to line rms value) | ||
ωbase = 2 πfbase | fbase = 50 Hz | Rs = 0.022 p.u. | Rr = 0.009 p.u. |
Lls = 0.171 p.u. | Llr = 0.156 p.u. | Lm = 3.9 p.u. | Lc = 0.3 p.u. |
Udcref = 1200 V | C = 0.047 F | Ug = 1 p.u. | Rg = 0.1 ω1 Lg |
RSC active power control | ||
RSC terminal voltage control | ||
DC-link voltage control | ||
Phase-locked loop |
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Wang, D.; Chen, H.; Huang, Y.; Deng, X.; Zhu, G. Modeling and Stability Analysis of Weak-Grid Tied Multi-DFIGs in DC-Link Voltage Control Timescale. Energies 2020, 13, 3689. https://doi.org/10.3390/en13143689
Wang D, Chen H, Huang Y, Deng X, Zhu G. Modeling and Stability Analysis of Weak-Grid Tied Multi-DFIGs in DC-Link Voltage Control Timescale. Energies. 2020; 13(14):3689. https://doi.org/10.3390/en13143689
Chicago/Turabian StyleWang, Dong, Houquan Chen, Yunhui Huang, Xiangtian Deng, and Guorong Zhu. 2020. "Modeling and Stability Analysis of Weak-Grid Tied Multi-DFIGs in DC-Link Voltage Control Timescale" Energies 13, no. 14: 3689. https://doi.org/10.3390/en13143689