Sub Synchronous Resonance Damping In Interconnected Power Systems

Subsynchronous Resonance Damping in Interconnected Power Systems Nadia Yousif, Majid Al-Dabbagh Electrical Energy and Control Systems School of Electrical and Computer Engineering RMIT University – City Campus [email protected] Abstract In this paper, the subsynchronous resonance (SSR) for IEEE second benchmark system is investigated using Matlab based on the Power System Block-set (PSB) in conjunction with Simulink. The effects of both series compensation level and fault clearing time on SSR are investigated. The results obtained verify the effect of series compensation level on the subsynchronous frequencies. These studies are confirmed using both frequency analysis and eigenvalue techniques, which are carried out based on Matlab control system toolbox. In addition, the influence of both fault clearing time and series compensation level on maximum magnitudes of the turbine-generator shaft torques have been analysed using time domain simulation technique. Introduction: Series capacitors have been extensively used as a very effective means of increasing power transfer capability of transmission system, and improving transient and steady state stability limits of a power system. This is due to partially compensating the reactance of the transmission lines. However, the application of series capacitors may lead to the phenomenon of subsynchronous resonance. Under a disturbance, series capacitors may excite subsynchronous oscillations, when electrical resonant frequency (fer) of the network is close to natural torsional mode frequency of turbine-generator shaft. Under such circumstance the shaft will oscillate at this natural frequency. This oscillation might grow to endurance limit in seconds resulting in shaft fatigue and possibly damage and failure. Therefore, there is a need to investigate and analyse subsynchronous resonance when planning inclusion of series capacitors for new or existing power system. Subsynchronous resonance is addressed in three categories, i.e., induction generator effect, torsional interaction and torque amplification. In all cases, subsynchronous resonance is due to the interaction of a series capacitor with turbine-generator [1-3]. The first two types are caused by a steady state disturbance, while the third is excited by transient disturbances. Different approaches in subsynchronous resonance analysis are presented in the literature. References 1-3 refer to three analytical methods to analyse SSR: frequency scanning, eigenvalue analysis and the time domain simulation. Frequency scanning has been used to study induction generator effects [4]. The eigenvalue analysis is used

to identify frequencies of subsynchronous oscillations as well as the damping of each frequency from state space model of the entire system [1]. This analysis has been regarded as a good measurement of the proper operation of SSR countermeasures suggested in [5]. Time domain simulation has been performed in different types of programs such as EMTP (Electromagnetic Transient Program). These studies provide important information regarding peak shaft that is to be expected when a certain level of series compensation is applied [6]. In this paper, an important application of the second benchmark system [4] and Matlab [7] is presented to study subsynchronous resonance that may occur in series compensated transmission systems – in particular, the simulation of the torque amplification and eigenvalue analysis of the electrical network. The investigation of the above phenomenon is carried out using Matlab simulation and analysis tools. The subsynchronous resonance damping under different levels of series compensation in the network, and the effect of fault clearing time on the torque amplification are investigated. System configuration: The system considered in this paper is the IEEE second benchmark model of which the single line diagram and data used in this study are shown in figure 1 [1]. A single generator of 600 MVA, 22kV is connected to infinite busbar through transformer and two transmission lines. One line is series compensated

The transient disturbance considered for torque amplification study is a three-phase to ground fault applied at t = 0.02 sec and removed after 0.0017 sec. The spring-mass system is composed of three masses the generator, low-pressure and high-pressure turbines. The model is built and simulated using Power System Blockset in conjunction with Simulink. The blockset uses the Matlab computation engine to simulate and analyse the interaction of the electrical network with the mechanical part of the system. Both the electrical network and the spring-mass system are represented in Matlab in their differential equations, linearised about an operating point (Bus1) and arranged in state space for analysis and simulation purposes [1,7]. Figure 2 shows the Matlab representation of the second benchmark system. R1=0.0074 R0=0.022

22 kv / 500 kV R=0.0002 X=0.020

X1=0.0080 X0=0.240

Rsys=0.0014

G

Study Generator 600MVA 22 kV

R2=0.0067 R0=0.0186

Bus 1

X2=0.0739 Bus 2 X0=0.210

Infinite Busbar

Figure 1 In Scope: turbine

1 0.1/600

wref dw_5-2

t1 In

0

t

Clock Pref Tr5-2

In

wm gate

t2 In

d_theta Pm

Pm

A

A a

A

a

A

A

A

B

B b

B

b

B

B

B

C

C c

C

c

C

C

C

N

STG 1.00358

Vf

m

Vf

600MVA-22kV 60Hz-3600rpm

voltmeters 600MVA-60Hz 22kV-500kV

ctrl

d_theta wm

Pe

Pe

Timer m

dw

Machines Measurement Demux

Z1-Z0

Cs%

A

A

B

B

B

C

C

C

Fault Breaker

160

Inductivesource withneutral

20% 55% 90%

140

120

100

80

60

40

20

0

0

10

20

30

40

50

60

70

80

90

100

Frequency(Hz)

Figure 3

E.V.

Xsys=0.030

G

subsynchronous frequencies (for = fo – fer). If these frequencies are close to one of the mechanical natural frequencies of the spring-mass system, the turbine – generator shaft might experience torsional modes of oscillations that will cause possible fatigue and damage.

Im pedance(dB)

with three different levels (20%, 55% and 90%) of the transmission line reactance.

Cs% = 20%

Cs% = 55%

Cs% =90%

No.

Real part

Freq (Hz)

Real part

Freq(Hz)

1

-10989570.93

-3.15E-13

-10989570.92

2.82E-17

2

-8594446.726

-1.87E-17

-8594446.726

1.32E-18

-8594446.726

3

-315128.3472

3.15E-13

-315128.3122

-3.01E-19

-315128.2772 -2.79E-19

4

-10989570.93

-1.08E-10

-10989570.92

2.51E-11

-10989570.92 -4.56E-11

5

-315128.3472

-1.66E-12

-315128.3122

7.83E-14

-315128.2772 -2.03E-14

6

-15.9363

-14.0976

-15.9482

23.6272

-15.9509

7

-15.9363

14.0976

-15.9482

-23.6272

-15.9509

30.2944

8

-29.3275

-9.21E-17

-29.3038

-1.16E-09

-17.3074

40.9551

Real part

Freq(Hz)

-10989570.92 -1.50E-17 2.55E-17

-30.2944

9

-17.2721

-19.1535

-17.2897

31.9701

-17.3074

-40.9551

10

-17.2721

19.1535

-17.2897

-31.9701

-29.2986

-1.88E-14

11

-17.2721

-19.1535

-17.2897

-31.9701

-17.3074

-40.9551

12

-17.2721

19.1535

-17.2897

31.9701

-17.3074

40.9551

13

-7.54E-07

0

-7.54E-07

0

-7.54E-07

0

14

-0.037489

0

-0.037489

0

-0.037488

0

15

-0.037489

0

-0.037489

0

-0.037488

0

A

Table 2

3.2 Eigenvalue analysis:

Z1-Z0

Figure 2

3. SUBSYNCHRONOUS RESONANCE ANALYSIS: 3.1 Frequency analysis: The existence of the subsynchronous mode in the study system can be identified by frequency domain calculation of network impedance at bus 1. The impedance of the network as function of frequency is computed for different compensation levels. From the network’s frequency spectrum shown in figure 3, the natural frequencies (fer) due to parallel resonance are clearly identified for each level of compensation suggested. These frequencies appear to the generator rotor as modulations of the fundamental frequency of the network (60 Hz), giving

There is a need to verify subsynchronous conditions severity and the distribution of these conditions between system’s state variables. This can be accurately accomplished using eigenvalue analysis, which can be easily performed using Matlab control system toolbox. Once the state space model of the system is obtained, based on its set of linearised differential equations, the eigenvalues and eigenvectors can be rapidly calculated as Power System Blockset provides the state space model for the network and spring mass system individually. Table 1 shows eigenvalue of the electrical network for different levels of compensations, where the imaginary part indicates the frequencies of the

oscillatory modes, while the real part represents the damping factor of these modes.

fault clearing time as the maximum torque amplitude decreases to lower level at 0.04 sec.

For stable conditions all eigenvalues must be at the left of imaginary axis. If the locus of a particular eigenvalue approach or cross the imaginary axis, then a critical conditions is identified that requires the application of one or more countermeasure.

State variables of the electrical network Right hand eigenvector for Right hand eigenvector for Eigenvector No. 8 Eigenvector No. 10 Uc_Cs 55%/Cs = 55%/Series RLC Branch1 Uc_Cs 55%/Cs = 55%/Series RLC Branch 2 Uc_Cs 55%/Cs = 55%/Series RLC Branch 3

In addition, the state variables that have important role to contribute to a given mode of oscillation are identified using eigenvectors. This often tells the engineer exactly those variables that need to be controlled in order to damp a subsynchronous oscillation.

0.22199+0.77801i

-0.79864-0.20136i

0.22199+0.77801i

0.39905+0.10054i

0.22199+0.77801i

0.3996+0.10082i

IL_winding1 Z1-Z0/Mutual Inductance

0.00015687+0.00054979i

0.0006424-0.0039527i

IL_winding2 Z1-Z0/Mutual Inductance

0.00015687+0.00054979i

-0.00032063+0.0019749i

IL_winding3 Z1-Z0/Mutual Inductance

0.00015687+0.00054979i

-0.00032177+0.0019777i

IL_winding1 Z1-Z0/Mutual Inductance

-0.038773-0.13589i

-0.00064347+0.0039488i

IL_winding2 Z1-Z0/Mutual Inductance

-0.038773-0.13589i

0.00032116-0.001973i

IL_winding3 Z1-Z0/Mutual Inductance

-0.038773-0.13589i

0.00032231-0.0019758i

0.038616+0.13534i

6.8498e-007+3.8137e-006i

IL_600MVA-60 Hz 22 kV-500 kV

Every eigenvalue has its own right-hand eigenvector that determines the distribution of the mode of response through the state variable. Table 2 shows the right-hand eigenvectors for eigenvalues No. 8 and 10 for 55% level of compensation, where U_Cs% is the voltage across the series capacitor and IL is the current through an inductor.

IL_600MVA-60 Hz 22 kV-500 kV

-1.3037e-008-4.5693e-008i -1.5145e-005+4.3989e-005i

IL_600MVA-60 Hz 22 kV-500 kV IL_600MVA-60 Hz 22 kV-500 kV

0.038616+0.13534i

IL_600MVA-60 Hz 22 kV-500 kV IL_600MVA-60 Hz 22 kV-500 kV

-3.4256e-007-1.9054e-006i

-1.3037e-008-4.5693e-008i 7.5633e-006-2.1979e-005i 0.038616+0.13534i

-3.4241e-007-1.9083e-006i

-1.3037e-008-4.5693e-008i 7.582e-006-2.2009e-005i

Table 2

3.3 Time domain simulation using PSB:

The fault clearing time has significant effect on the magnitudes of torque’s oscillation. Figure 6 shows the oscillation of the torques, the percentage speed deviation and the voltage across the capacitor when the fault clearing time is 0.05 sec for 55% level of compensation. Table 3 shows the results of four Matlab time domain simulation cases for different fault clearing times and for 55% series compensation. The worst torque amplification is observed at 0.017

Fault clearing time 0.017 0.03 0.05 0.06

Peak torque (p.u.) Gen-LP 4.05 3.00 1.44 3.00

LP-HP 1.91 1.20 1.18 1.29

Speed deviation % Gen 1.51 1.27 0.79 1.2

LP 0.7 0.5 0.25 0.4

HP 2.42 1.62 1.1 1.8

Table 3 4 LP-HP Gen-LP

Torque(p.u.)

2 0 -2 -4 0

0.1

0.2

0.3

0.4

0.5

Speed Deviation%

0.02 HP LP Gen

0.01 0 -0.01 -0.02 0

0.1

0.2

0.3

0.4

0.5

200 Ph C Ph B Ph A

100

VCs (kV)

This program uses step-by-step numerical integration to solve set of differential equations representing the overall system under study. Power System Blockset allows detailed modelling of machines and network as well as circuit breakers action and transient faults. Time simulation is most useful to study torque amplification, where maximum turbine-generator shaft stress for predicting fatigue life expenditure of the shaft and the risk of dynamic conditions can be determined. Figures 4 and 5 show the effect of series compensation level on the magnitude of the torque oscillation between generator and low-pressure turbine and between low pressure and high-pressure turbine. For every case of compensation the fault clearing time is 0.017 sec. The increase in maximum magnitude of the torques of the two shaft segments Gen-LP and LPHP is evidenced when the compensation level is changed from 20% to 55%.

0 -100 -200 0

0.1

0.2

0.3

Time (s)

Figure 4

0.4

0.5

4. CONCLUSION From the results presented in this paper, it is clearly seen that the network frequencies depend on series compensation level. Further, the fault clearing time has a significant role in the dynamic behaviour of the system. From such investigation as in this paper, planners will be able to establish acceptable series compensation levels and switching arrangements for a specific stage of system design and development taking into account power quality and system’s reliability. The existence of subsynchronous conditions and their severity can be verified using Matlab and PSB as a simulation and analytical tool. The cases investigated in the paper provide comparison between the analytical techniques corresponding to different types of subsynchronous resonance and the evaluation of appropriate countermeasure.

5. REERENCES: 1.

Anderson, P.M, Agrwal, B.L., Van Ness, J.E., ‘Subsynchronous Resonance in Power System’, IEEE Press, 1990, New York.

2.

Farmer, R.G., Agrawal, B.L., ‘ Power System Dynamic Interaction with TurbineGenerators’, The Electric Power Engineering Handbook, 1990.

3.

Subsynchronous Resonance Working Group of the System Dynamic Performance Subcommitee, ‘ Reader Guide to Subsynchronous Resonance’, IEEE Transaction on Power System, Vol. 7, No. 1, February 1992.

4.

Subsynchronous Resonance Working Group of the System Dynamic Performance Subcommitee, ‘ Second Benchmark Model for Computer Simulation of Subsynchronous Resonance’, IEEE Transaction on Power apparatus and Systems, Vol PAS-104, No. 5, May 1985.

5.

Hossiani, S.H., Mirshekar, O., ‘ Optimal Control of SVC for Subsynchronous Resonance Stability in Typical Power System’, IEEE Transaction on Power Apparatus and Systems, 2001.

6.

Lie, X., Jaing, D., Yang, Y.T., ‘ Analysing Subsynchronous Resonance Using a Simulation Program’, IEEE Transaction on Power Apparatus and Systems, 2000.

7.

MathWorks, Matlab, version 6.1.0.450, release 12.1, May 2001.

7

Torque(p.u.)

LP-HP Gen-LP

0

-7

0

0.1

0.2

0.3

0.4

0.5

0.06

Speed Deviation%

HP LP Gen

0

-0.06

0

0.1

0.2

0.3

0.4

0.5

500

V Cs (kV)

Ph C Ph B Ph A

0

-500

0

0.1

0.2

0.3

0.4

0.5

Time (s)

Figure 5 4 LP-HP Gen-LP

Torque(p.u.)

2 0 -2 -4

0

0.1

0.2

0.3

0.4

0.5

Speed Deviation%

0.025 HP LP Gen

0

-0.025

0

0.1

0.2

0.3

0.4

0.5

500

VCs (kV)

Ph C Ph B Ph A

0

-500

0

0.1

0.2

0.3

Time (s)

Figure 6

0.4

0.5