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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

邮发代号 80-972

2019 Impact Factor: 2.657

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Frontiers in Energy  2021, Vol. 15 Issue (2): 539-549   https://doi.org/10.1007/s11708-019-0617-z
  本期目录
Improvement to observability measures of LFO modes in power systems with DFIGs
Shenghu LI()
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China
 全文: PDF(599 KB)   HTML
Abstract：

Observation of the low-frequency oscillation (LFO) modes in power systems is important to design the damping scheme. The state equations of the power system with the doubly-fed induction generators (DFIGs) are derived to find the LFO modes related to the synchronous generator (SGs) and the DFIGs. The definition of the observability measure is improved to consider the initial output and the attenuation speed of the modes. The sensitivities of the observability measures to the control parameters are derived. The numerical results from the small and large-disturbance validate the LFO modes caused by the DFIGs, and different observability measures are compared. Adjustment of the control parameters is chosen based on the sensitivity model to improve the observability and damping ratio of the LFO mode, and the stability of the wind power system.
Key words： wind power system    low-frequency oscillation (LFO)    observability measure    sensitivity    doubly-fed induction generator (DFIG)
收稿日期: 2018-05-05      出版日期: 2021-06-18
Corresponding Author(s): Shenghu LI   
 引用本文:   
. [J]. Frontiers in Energy, 2021, 15(2): 539-549.
Shenghu LI. Improvement to observability measures of LFO modes in power systems with DFIGs. Front. Energy, 2021, 15(2): 539-549.
 链接本文:  
https://academic.hep.com.cn/fie/CN/10.1007/s11708-019-0617-z
https://academic.hep.com.cn/fie/CN/Y2021/V15/I2/539
Fig.1  
Fig.2  
Controllers kp ki (p.u.)
Pitch angle control 10.0 0.30
RSC Power loop Active power (1) 0.60 0.25
Reactive power (2) 1.50 0.65
Current loop d axis (3) 0.27 0.017
q axis (4) 0.27 0.017
GSC Power loop Active power (5) 0.012 0.0006
Reactive power (6) 1.20 0.50
Current loop d axis (7) 0.70 0.40
q axis (8) 0.70 0.40
Tab.1  
Mode li (p.u.) Related state variables
(Ignoring D for convenience)
1 0 d
2 –60.92 Ed"
3/4 –26.84±j27.01 EE2, EE3, EE4
5 –21.21 Eq", EE2, EE4, PSS3
6/7 –7.93±j0.86 Eq', Eq", dw, EE2, EE4, GG1, GG2, GG3, PSS1, PSS2, PSS3
8/9 –0.92±j2.97 Eq', dw, EE2, EE4, GG1, GG2, GG3, PSS1, PSS2
10 –0.7023 Eq', dw, EE2, EE4, GG2, GG3, PSS1, PSS2
11 –1.2528 Eq', Eq", EE2, PSS2
12 –0.1086 GG2, GG3, PSS2
13 –5.0000 PSS1
14 –0.1000 GG3, PSS2
15 –33.33 EE1
Tab.2  
Mode li (p.u.)
5/6 –0.7326±j311.93
12/13 –0.2600±j2.85
15/16 –1.4876±j15.88
17/18* –0.0858±j0.84
Tab.3  
Mode Mjia/(p.u.) Mjib/(p.u.) Mjic/(p.u.)
from P from Q from P from Q from P from Q
SG 3/4 0.0261 0.0132 0.0145 0.4931 3 × 10−14 1 × 10−12
6/7 0.3969 0.2015 0.2205 7.5098 8 × 10−5 0.0027
8/9 0.0378 0.0186 0.0210 0.6923 0.0083 0.2746
DFIG 5/6 0.4488 0.3053 0.3740 0.7633 0.1810 0.3695
12/13 0.0684 1 × 10−15 0.0570 3 × 10−15 0.0439 2 × 10−15
15/16 0.0017 1 × 10−13 0.0014 4 × 10−13 3 × 10−4 8 × 10−14
17/18 0.0063 5 × 10−14 0.0053 1 × 10−13 0.0048 1 × 10−13
Tab.4  
Mode l/(p.u.) w/Hz x r Relation
162/163* –0.0373±j0.26 0.041 0.1432 0.0427
50/51 –1.40±j13.08 2.0819 0.1062 21.78 SG
54/55 –1.30±j11.94 1.8997 0.1085 16.85
56/57 –0.82±j11.48 1.8267 0.0715 106.33
58/59 –0.89±j10.82 1.7226 0.0815 98.27
60/61 –0.99±j9.85 1.5670 0.0998 13.15
62/63 –0.49±j9.62 1.5307 0.0509 25.20
86/87 –0.85±j8.11 1.2909 0.1043 13.58
88/89 –0.52±j7.69 1.2245 0.0673 26.09
143/144 –0.086±j0.84 0.1332 0.1021 >103** DFIG
Tab.5  
Output Observability measure/(p.u.)
Mjia Mjib Mji*a Mji*b
V SG 1 0.043419 0.026595 0.041351 0.025329
DFIG 0.023040 0.014112 0.022116 0.013547
P SG 1 0.790767 0.484362 0.439315 0.269090
DFIG 0.007527 0.004611 0.006273 0.003842
Q SG 1 0.043253 0.026494 1.612400 0.987630
DFIG 0.000033 0.000020 0.000083 0.000051
d DFIG 0.046680 0.028593 0.040740 0.024954
Tab.6  
Output Observability measure/(p.u.)
Mjia Mjib Mji*a Mji*b
V SG 1 0.000379 0.000348 0.000361 0.000331
DFIG 0.001586 0.001455 0.001522 0.001397
P SG 1 0.004329 0.003973 0.002405 0.002207
DFIG 0.072576 0.066600 0.060480 0.055500
Q SG 1 0.000381 0.000350 0.014210 0.013040
DFIG 0.000000 0.000000 0.000001 0.000001
d DFIG 0.045303 0.041573 0.039537 0.036282
Tab.7  
Fig.3  
Fig.4  
Fig.5  
Fig.6  
t ∂λ/∂τ(p.u.) ∂ξ/∂ τ(p.u.)
kp1 (–3.75±0.37i) × 10−3 4.46 × 10−3
ki1 0.0043±1.4084i –0.1752
kp2 (1.26±0.057i) × 10−6 –1.49 × 10−6
ki2 (–0.27±4.70i) × 10−4 8.86 × 10−5
ki3 (–1.65±1.41i) × 10−8 1.77 × 10−8
kp4 (–0.43±3.64i) × 10−8 7 × 10−10
ki4 (1.37±0.02i) × 10−5 –1.61 × 10−5
kp6 (–6.36±3.59i) × 10−4 7.91 × 10−4
ki6 –0.1091±0.2498i 9.82 × 10−2
ki7 (1.74±2.10i) × 10−8 –2.30 × 10−8
ki8 (–3.46±2.18i) × 10−8 4.33 × 10−8
Tab.8  
Observation from Mjia/(p.u.) Sen. to kp1 Sen. to ki1 Sen. to ki6
SG 1 0.004329 1 × 10−5 –0.021 8.1
DFIG 0.072576 3 × 10−5 –0.367 134.3
Observation from Mjib/(p.u.) Sen. to kp1 Sen. to ki1 Sen. to ki6
SG 1 0.003973 –1 × 10−5 0 –1 × 10−5
DFIG 0.066600 –2.2 × 10−4 2 × 10−5 –1.8 × 10−4
Observation from Mji*a/(p.u.) Sen. to kp1 Sen. to ki1 Sen. to ki6
SG 1 0.002405 –0.021 –0.012 –0.012
DFIG 0.060480 –0.361 –0.306 –0.301
Observation from Mji*b/(p.u.) Sen. to kp1 Sen. to ki1 Sen. to ki6
SG 1 0.002207 7.2 4.5 4.0
DFIG 0.055500 120.7 111.9 100.6
Tab.9  
Mode l/(p.u.) w/Hz Relation
161/162* –0.0421±0.25i 0.0399
50/51 –1.3814±13.13i 2.0899 SG
54/55 –1.2984±11.94i 1.8999
56/57 –0.8232±11.49i 1.8295
58/59 –0.8831±10.84i 1.7258
60/61 –0.9791±9.87i 1.5712
62/63 –0.4884±9.64i 1.5337
86/87 –0.8527±8.11i 1.2913
88/89 –0.5178±7.70i 1.2256
143/144** –0.086±0.84i 0.1332 DFIG
Tab.10  
Output Observability measure/(p.u.)
Mjia Mjib Mji*a Mji*b
V SG 1 0.000392 0.000359 0.000373 0.000342
DFIG 0.001609 0.001476 0.001525 0.001399
P SG 1 0.004385 0.004023 0.002436 0.002235
DFIG 0.073572 0.067489 0.061310 0.056241
Q SG 1 0.000343 0.000315 –0.024200 –0.022199
DFIG 0.000000 0.000000 0.000001 0.000001
d DFIG 0.045838 0.042048 0.039998 0.036691
Tab.11  
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