Analysis of Subsynchronous Resonance Characteristics and Influence Factors in a Series Compensated Transmission System
Abstract
:1. Introduction
2. Eigenvalue Analysis and System Modeling
2.1. Eigenvalue Analysis
 A detailed mathematical model is established for various components of the SSR system and the power network, and the differential equations describing the transient process is obtained.
 By linearizing the differential equations near stable values and writing out the standard form $\dot{\mathit{X}}=\mathit{A}\mathit{X}$, the statespace representation is acquired, which is suitable for eigenvalue analysis.
 The initial values of the studied system under stable operation are calculated.
 The eigenvalues of characteristic equations are solved, and the stability and damping characteristics of the system are analyzed based on the results.
2.2. System Modeling
2.2.1. Turbine Speed Governing System
2.2.2. Turbine Prime Mover Model
3. Case Analysis
3.1. Model Parameters
3.2. Eigenvalue Calculation Results
4. Analysis of Influence Factors of SSR
4.1. Influence of Compensation Level
4.2. Influence of Synchronous Generator Parameters
4.3. Influence of Speed Governing System Parameters
4.3.1. With or Without Speed Governing System
4.3.2. Influence of Speed Governing System Parameters
4.4. Influence of Excitation System Parameters
5. Conclusions
 The series compensation level ${k}_{C}$ has the greatest influence on the torsional mode damping of the system. With the increase of ${k}_{C}$, one or more torsional mode damping will appear negative, indicating that the system may have a single mode or multimode SSR, and the greater ${k}_{C}$ is, the lower the torsional mode frequency is, but the change of ${k}_{C}$ does not affect total damping of the system, that is, the total damping of the system is conserved.
 The parameters of the synchronous generator will not affect torsional mode frequencies of the turbogenerator shaft, and the reactance parameters of generators have a certain influence on torsional mode damping of the system. The variation of the reactance parameters may lead to instability of the torsional mode when ${f}_{SUB}$ and ${f}_{TMx}$ become close. However, the damping of adjacent torsional modes will be increased, which is beneficial to its stability. In addition, the resistance parameters of synchronous generator have little effect on the damping of each torsional mode, which can be ignored.
 Speed governing system parameters ${K}_{G}$, ${T}_{SR}$ and ${T}_{SM}$ have a great influence on TM0 damping, and slightly affect other torsional modes damping. Excitation system parameter ${K}_{A}$ significantly affects TM0 damping, and has little effect on other torsional modes damping.
Author Contributions
Funding
Conflicts of Interest
References
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SSR Analysis Methods  Features  Advantages  Disadvantages 

Eigenvalue analysis  It is also called statespace analysis method, which is a quantitative analysis method based on the small disturbance linearization model and obtains SSRrelated information by solving eigenvalues. 
 Higher order model parameters are required for the entire system, which is difficult to analyze. 
Electromagnetic transient analysis  Using a stepbystep numerical integration method, a set of differential equations of the system are solved. The mathematical model can be linear or nonlinear. 
 Only time domain response results can be given. It is difficult to directly give SSR reasons and the mechanism of instability. 
Complex torque coefficient analysis  Frequency scanning of the mechanical and electrical complex torque coefficients of the shaft system in the subsynchronous frequency range to determine whether the system will undergo subsynchronous oscillation. 


Frequency scanning  It is an approximate linear method to calculate the equivalent impedance for a specific frequency and filter out the system conditions with potential SSR. 


Mass Block  Inertia Constant, ${\mathit{T}}_{\mathit{J}}$ (s)  Shaft Segment  Elastic Constant, K (p.u.) 

HP  0.185794     
IP  0.311178  HPIP  19.303 
LPA  1.717340  IPLPA  34.929 
LPB  1.768430  LPALPB  52.038 
GEN  1.736990  LPBGEN  70.858 
EXC  0.068433  GENEXC  2.822 
Eigenvalue  Torsional Mode  Real Part (1/s)  Imaginary Part (rad/s)  Frequency (Hz) 

1,2  TM0  −0.5073  ±11.66  1.86 
3,4  TM1  0.0931  ±100.28  15.96 
5,6  TM2  0.2034  ±128.08  20.38 
7,8  TM3  −0.1352  ±160.34  25.52 
9,10  TM4  −0.0404  ±202.78  32.27 
11,12  TM5  −0.1818  ±298.17  47.46 
Eigenvalue  Torsional Mode  K_{C} = 0.1  K_{C} = 0.3  K_{C} = 0.5  K_{C} = 0.7  K_{C} = 0.9 

1,2  TM0  0.0693 ± j8.46  −0.0748 ± j9.31  −0.2597 ± j10.35  −0.5073 ± j11.66  −0.8623 ± j13.41 
3,4  TM1  −0.1487 ± j99.13  −0.1422 ± j99.27  −0.1106 ± j99.52  0.0931 ± j100.28  3.9947 ± j98.05 
5,6  TM2  −0.6549 ± j127.02  −0.6525 ± j127.03  −0.6423 ± j127.07  0.2034 ± j128.08  −0.6522 ± j126.92 
7,8  TM3  −0.1627 ± j160.62  −0.1479 ± j160.69  0.4564 ± j161.08  −0.1351 ± j160.34  −0.1644 ± j160.46 
9,10  TM4  −0.0301 ± j203.01  0.3233 ± j203.43  −0.0125 ± j202.68  −0.0404 ± j202.78  −0.0449 ± j202.84 
11,12  TM5  −0.1819 ± j298.17  −0.1819 ± j298.17  −0.1819 ± j298.17  −0.1819 ± j298.17  −0.1819 ± j298.17 
13,14  SUB  −7.1191 ± j283.35  −7.1702 ± j213.94  −7.0882 ± j166.68  −6.5888 ± j128.06  −9.1422 ± j96.86 
15,16  SUPER  −7.5026 ± j470.47  −7.5806 ± j539.24  −7.6238 ± j586.55  −7.6543 ± j624.99  −7.6778 ± j658.22 
17,18  −4.6872 ± j0.6335  −4.7382 ± j0.3856  −4.8737 ± j0.2566  −4.9573 ± j0.1521  −3.4114 ± j0.5459  
19  −1.8966  −1.8446  −1.7833  −1.6996  −1.5619  
20  −24.7628  −24.7842  −24.8113  −24.8466  −24.8939  
21  −30.8793  −31.5042  −32.3627  −33.6064  −35.5306  
22  −8.5726  −8.3123  −7.9786  −7.5383  −6.9382  
23  −101.8931  −101.7953  −101.648  −101.4514  −101.1882  
24  −499.9582  −499.9821  −499.9783  −499.9742  −499.9713  
25  −2.9453  −3.1215  −3.4887  −3.4828  −3.9244  
26  −0.1417  −0.1417  −0.1418  −0.1419  −0.1419  
27  −4.6223  −4.3293  −3.6731  −3.5842  −4.1051  
sum  −696.0893  −696.1123  −696.1281  −696.0932  −696.1024 
Torsional Mode  With Speed Governing System  Without Speed Governing System  

Real Part (1/s)  Imaginary Part (rad/s)  Real Part (1/s)  Imaginary Part (rad/s)  
TM0  −0.2597  10.35  −0.3099  10.56 
TM1  −0.1818  298.17  −0.1828  298.17 
TM2  −0.0125  202.68  −0.0153  202.68 
TM3  0.4564  161.08  0.4453  161.08 
TM4  −0.6423  127.07  −0.6505  127.07 
TM5  −0.1106  99.52  −0.1224  99.52 
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He, C.; Sun, D.; Song, L.; Ma, L. Analysis of Subsynchronous Resonance Characteristics and Influence Factors in a Series Compensated Transmission System. Energies 2019, 12, 3282. https://doi.org/10.3390/en12173282
He C, Sun D, Song L, Ma L. Analysis of Subsynchronous Resonance Characteristics and Influence Factors in a Series Compensated Transmission System. Energies. 2019; 12(17):3282. https://doi.org/10.3390/en12173282
Chicago/Turabian StyleHe, Chengbing, Dakang Sun, Lei Song, and Li Ma. 2019. "Analysis of Subsynchronous Resonance Characteristics and Influence Factors in a Series Compensated Transmission System" Energies 12, no. 17: 3282. https://doi.org/10.3390/en12173282