Research on a Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power
Abstract
:1. Introduction
2. An Interconnected Power System with Large-Scale Wind Power and Its Model
2.1. Interconnected Power System with Large-Scale Wind Power and Its Typical Characteristics
2.2. Equivalence of Large-Scale Wind Power Base
2.3. Model of Interconnected Power System with Large-Scale Wind Power
3. Traditional Analysis Method of Small Signal Stability Region Boundary and Its Disadvantage
4. Catastrophe Theory
Catastrophe model | Potential functions |
---|---|
Fold | V(x) = x3 + vx |
Cusp | V(x) = x4 + μx2 + vx |
Swallowtail | V(x) = x5 + μx3 + vx2 + ωx |
Butterfly | V(x) = x6 + tx4 + μx3 + vx2 + ωx |
Elliptic | V(x, y) = x3 − xy2 + w(x2 + y2) + μx + υy |
Hyperbolic | V(x, y) = x3 + y3 + ωxy + μx + υy |
Parabolic | V(x, y) = y4 + x2y + wx2 + ty2 + μx + υy |
5. Eigenvalue Catastrophe Indications
6. Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power
6.1. Small Signal Stability Region Boundary Model in Two-Dimensional Power Injection Space
6.2. Small Signal Stability Region Boundary Model in Multidimensional Power Injection Space
7. Simulation Verification
7.1. Example 1
7.1.1. Test of the Two-Dimensional Boundary Model
7.1.2. Verification of the Multidimensional Boundary Model
7.1.3. Time-Domain Simulation Verification
7.2. Example 2
Transformer | Rated voltage (kV) | Rated power (MVA) | Short-Circuit voltage Uk (%) | No-Load current I0 (%) | Connection type |
---|---|---|---|---|---|
Tw1, Tw2 | 20/0.69 | 166.65 | 5 | 3 | YN/yn0 |
8. Conclusions
- (1)
- The small signal stability region boundary model in two-dimensional power injection space is a straight line. When the other injected power doesn’t change, the power from the two power sources influencing the dominant oscillation mode shows a linear relation between them.
- (2)
- The small signal stability region boundary model in multidimensional power injection space is a hyper-plane. When the other injected power doesn’t change, the power from sources influencing the dominant oscillation mode forms a hyper-plane.
- (3)
- Compared with the conventional system, large-scale wind power integration doesn’t change the form of the small signal stability region boundary model but only the dimensions of the hyper-plane and the values of the parameters.
Acknowledgments
Author Contributions
Appendices
Appendix A: A typical catastrophe mechanism explaining the basic principle of catastrophe theory, (Figure A1)
Appendix B
Appendix B1: DFIG Parameters
Pn (MW) | Us (V) | Rs (p.u) | Xs (p.u) | Xm (p.u) | Rr (p.u) | Xr (p.u) | Hw (s) | Hg (s) | K |
---|---|---|---|---|---|---|---|---|---|
2 | 690 | 0.01 | 0.1 | 3.5 | 0.01 | 0.1 | 4.02 | 0.47 | 80.27 |
Appendix B2: Generator Parameters
Generator | Capacity (WVA) | Voltage (KV) | xd (p.u) | xq (p.u) | ||||
---|---|---|---|---|---|---|---|---|
G1 | 300 | 18 | 1.72 | 1.66 | 0.23 | 0.378 | 0.8 | 0.12 |
Appendix B3: Excitation Parameters
τR | τA1 | KA | τA2 | VRmax | VRmin | τE | KE | KF | τF | E1 | Se1 | E2 | Se2 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.001 | 0.05 | 400 | 0.01 | 3 | −3 | 0.95 | −0.17 | 0.04 | 1 | 3.66 | 0.03 | 4.89 | 0.1 |
Appendix B4: Line Parameters
Appendix C
P1 (MW) | P2 (MW) | Real part | Imaginary part |
---|---|---|---|
160 | 192.95 | −0.00002 | 7.371781 |
170 | 180.84 | 0.00001 | 7.42214 |
180 | 168.34 | −0.00004 | 7.473076 |
190 | 155.49 | 0.00001 | 7.518541 |
200 | 142.43 | −0.00003 | 7.544407 |
210 | 128.98 | 0 | 7.568171 |
220 | 115.07 | 0 | 7.593426 |
230 | 100.64 | −0.00004 | 7.62154 |
240 | 85.64 | 0.00001 | 7.65214 |
250 | 69.94 | 0.00002 | 7.689427 |
P1 (MW) | P2 (MW) | Error (%) |
---|---|---|
160 | 192.95 | 0.557664 |
170 | 180.84 | 0.204026 |
180 | 168.34 | 0.062567 |
190 | 155.49 | 0.247486 |
200 | 142.43 | 0.381506 |
210 | 128.98 | 0.419963 |
220 | 115.07 | 0.346774 |
230 | 100.64 | 0.151014 |
240 | 85.64 | 0.172708 |
250 | 69.94 | 0.644714 |
P1 (MW) | P2 (MW) | P3 (MW) | Real part | Imaginary part |
---|---|---|---|---|
190 | 170.76 | 180 | 0.0001 | 7.536991 |
200 | 157.61 | 180 | 0 | 7.585456 |
210 | 144.3 | 180 | −0.00002 | 7.610067 |
220 | 130.58 | 180 | −0.00002 | 7.63315 |
230 | 116.39 | 180 | −0.00001 | 7.656929 |
190 | 163.21 | 190 | 0 | 7.52991 |
200 | 150.12 | 190 | −0.00002 | 7.565746 |
210 | 136.74 | 190 | −0.00004 | 7.590114 |
220 | 122.94 | 190 | 0.00001 | 7.613221 |
230 | 108.64 | 190 | 0.00001 | 7.638675 |
190 | 147.67 | 210 | 0.00002 | 7.49535 |
200 | 134.54 | 210 | 0 | 7.520848 |
210 | 121 | 210 | 0.00003 | 7.545433 |
220 | 106.98 | 210 | 0.00003 | 7.572346 |
230 | 92.41 | 210 | −0.00002 | 7.603393 |
190 | 139.64 | 220 | 0.00002 | 7.470371 |
200 | 126.43 | 220 | 0 | 7.496321 |
P1 (MW) | P2 (MW) | P3 (MW) | Error (%) |
---|---|---|---|
190 | 170.76 | 180 | 0.067958 |
200 | 157.61 | 180 | 0.013502 |
210 | 144.3 | 180 | 0.067639 |
220 | 130.58 | 180 | 0.051357 |
230 | 116.39 | 180 | 0.044867 |
190 | 163.21 | 190 | 0.008951 |
200 | 150.12 | 190 | 0.100204 |
210 | 136.74 | 190 | 0.141877 |
220 | 122.94 | 190 | 0.111855 |
230 | 108.64 | 190 | 0.002365 |
190 | 147.67 | 210 | 0.085745 |
200 | 134.54 | 210 | 0.16861 |
210 | 121 | 210 | 0.182398 |
220 | 106.98 | 210 | 0.116044 |
230 | 92.41 | 210 | 0.040263 |
190 | 139.64 | 220 | 0.079899 |
200 | 126.43 | 220 | 0.148584 |
210 | 112.78 | 220 | 0.144009 |
220 | 98.64 | 220 | 0.058873 |
230 | 83.92 | 220 | 0.119396 |
Appendix D
P1 (MW) | P2 (MW) | P3 (MW) | P4 (MW) | Real part | Imaginary part |
---|---|---|---|---|---|
164.25 | 130 | 90 | 130 | 0.00002 | 6.182942 |
162 | 130.11 | 93 | 130 | −0.00005 | 6.135284 |
160 | 132 | 95 | 128.23 | −0.00002 | 6.130719 |
155 | 135 | 92 | 133.33 | −0.00009 | 6.108222 |
155 | 135 | 89 | 136.1 | −0.00006 | 6.11538 |
150 | 139.94 | 90 | 135 | −0.00012 | 6.123751 |
153.94 | 140 | 90 | 130 | 0.00003 | 6.195451 |
156.63 | 130 | 100 | 130 | 0 | 6.015732 |
155.96 | 130 | 90 | 140 | 0 | 6.026069 |
151 | 135 | 108 | 123.01 | 0.00001 | 5.995063 |
154.24 | 140 | 95 | 125 | 0.00001 | 6.186703 |
142.92 | 145 | 103 | 125 | 0.00005 | 6.069223 |
143.43 | 150 | 90 | 130 | 0.00003 | 6.213094 |
147 | 135 | 100 | 134.51 | −0.00008 | 5.94512 |
152.053 | 130 | 105 | 130 | 0 | 5.92228 |
136 | 148.31 | 80 | 150 | 0.00013 | 6.061767 |
130.98 | 150 | 105 | 130 | −0.00007 | 5.96777 |
P1 (MW) | P2 (MW) | P3 (MW) | P4 (MW) | Error (%) |
---|---|---|---|---|
164.25 | 130 | 90 | 130 | 0.084283 |
162 | 130.11 | 93 | 130 | 0.019028 |
160 | 132 | 95 | 128.23 | 0.003579 |
155 | 135 | 92 | 133.33 | 0.033593 |
155 | 135 | 89 | 136.1 | 0.028496 |
150 | 139.94 | 90 | 135 | 0.040916 |
153.94 | 140 | 90 | 130 | 0.03755 |
156.63 | 130 | 100 | 130 | 0.031047 |
155.96 | 130 | 90 | 140 | 0.01475 |
151 | 135 | 108 | 123.01 | 0.042525 |
154.24 | 140 | 95 | 125 | 0.036604 |
142.92 | 145 | 103 | 125 | 0.065856 |
143.43 | 150 | 90 | 130 | 0.031106 |
147 | 135 | 100 | 134.51 | 0.050112 |
152.053 | 130 | 105 | 130 | 0.066951 |
136 | 148.31 | 80 | 150 | 0.001088 |
130.98 | 150 | 105 | 130 | 0.064887 |
Conflicts of Interest
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Liu, W.; Ge, R.; Lv, Q.; Li, H.; Ge, J. Research on a Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power. Energies 2015, 8, 2312-2336. https://doi.org/10.3390/en8042312
Liu W, Ge R, Lv Q, Li H, Ge J. Research on a Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power. Energies. 2015; 8(4):2312-2336. https://doi.org/10.3390/en8042312
Chicago/Turabian StyleLiu, Wenying, Rundong Ge, Quancheng Lv, Huiyong Li, and Jiangbei Ge. 2015. "Research on a Small Signal Stability Region Boundary Model of the Interconnected Power System with Large-Scale Wind Power" Energies 8, no. 4: 2312-2336. https://doi.org/10.3390/en8042312