Research Article
Introducing MRAC-PSS-VI to Increase Small-Signal Stability of the Power System after Wind Power Integration
Table 4
The eigenvalues of the system in different tie line power conditions.
| Mode | Case | Without the controller | PSS | Dominant states | λ | f (Hz) | ξ (%) | λ | f (Hz) | ξ (%) |
| 1 | a | −0.671 ± j6.550 | 1.042 | 10.195 | −0.671 ± j6.550 | 1.043 | 10.196 | G1, G2 | b | −0.643 ± j6.542 | 1.041 | 9.790 | −0.644 ± j6.542 | 1.041 | 9.789 | c | −0.618 ± j6.502 | 1.035 | 9.465 | −0.618 ± j6.502 | 1.034 | 9.466 | 2 | a | −0.589 ± j6.404 | 1.019 | 9.154 | −0.583 ± j6.401 | 1.019 | 9.079 | G3, G4 | b | −0.637 ± j6.386 | 1.016 | 9.921 | −0.631 ± j6.383 | 1.016 | 9.839 | c | −0.704 ± j6.350 | 1.011 | 11.021 | −0.697 ± j6.348 | 1.010 | 10.920 | 3 | a | −0.295 ± j3.289 | 0.524 | 8.919 | −0.259 ± j3.293 | 0.524 | 7.827 | G1−G4 | b | −0.305 ± j3.031 | 0.482 | 10.039 | −0.386 ± j3.055 | 0.486 | 12.539 | c | −0.343 ± j2.314 | 0.368 | 14.672 | −0.432 ± j2.354 | 0.375 | 18.038 | 4 | a | −0.513 ± j3.063 | 0.488 | 16.518 | −0.513 ± j3.407 | 0.542 | 14.877 | G1−G4, DFIG | b | −0.512 ± j3.056 | 0.486 | 16.524 | −0.379 ± j3.379 | 0.538 | 11.159 | c | −0.503 ± j3.028 | 0.482 | 16.387 | −0.389 ± j3.390 | 0.540 | 11.412 |
| Mode | Case | PSS-VI | MRAC-PSS-VI | Dominant states | λ | f (Hz) | ξ (%) | λ | f (Hz) | ξ (%) |
| 1 | a | −0.671 ± j6.550 | 1.043 | 10.195 | −0.628 ± j6.355 | 1.011 | 9.827 | G1, G2 | b | −0.644 ± j6.542 | 1.041 | 9.789 | −0.679 ± j6.335 | 1.008 | 10.669 | c | −0.618 ± j6.502 | 1.035 | 9.464 | −0.746 ± j6.312 | 1.004 | 11.730 | 2 | a | −0.589 ± j6.404 | 1.019 | 9.154 | −1.059 ± j5.414 | 0.862 | 19.204 | G3, G4 | b | −0.637 ± j6.386 | 1.016 | 9.920 | −0.959 ± j5.660 | 0.901 | 16.713 | c | −0.704 ± j6.350 | 1.011 | 11.021 | −1.153 ± j6.356 | 1.011 | 17.846 | 3 | a | −0.293 ± j3.290 | 0.524 | 8.879 | −0.297 ± j3.191 | 0.508 | 9.278 | G1−G4 | b | −0.304 ± j3.034 | 0.482 | 9.970 | −0.305 ± j2.928 | 0.466 | 10.345 | c | −0.342 ± j2.321 | 0.369 | 14.589 | −0.332 ± j2.194 | 0.349 | 14.978 | 4 | a | −0.687 ± j3.489 | 0.555 | 19.319 | −1.050 ± j3.495 | 0.556 | 28.783 | G1−G4, DFIG | b | −0.689 ± j3.476 | 0.553 | 19.467 | −1.081 ± j3.496 | 0.556 | 29.563 | c | −0.689 ± j3.431 | 0.546 | 19.694 | −0.946 ± j3.281 | 0.522 | 27.713 |
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