1. 1539pk SUBSYNCHRONOUS OSCILLATIONS Copyright © P. Kundur This material should not be used without the author's consent

2. 1539pk SO - 1 Subsynchronous Oscillations  In power system stability studies, turbine-generator rotor is assumed to be made up of a single mass  Accounts for oscillation of entire rotor  Frequency in the range of 0.2 to 2.0 Hz  In reality, a steam turbine-generator rotor has a very complex structure consisting of several predominant masses (rotors of turbine sections, generator, and exciter) connected by shafts of finite stiffness  When perturbed, torsional oscillations result between different sections of turbine-generator rotor  Torsional oscillations in the subsynchronous range could, under certain conditions, interact with the electrical system in an adverse manner:  Subsynchronous resonance with series capacitor compensated lines  Torsional interaction with power system controls

3. 1539pk SO - 2 Example of Torsional Characteristics  Figure 15.3 shows the torsional characteristics of a 555 MVA, 3600 RPM fossil-fuel-fired generating unit with a static exciter  Since rotor has five masses, there are five modes of oscillation:  1.67 Hz mode represents oscillation of the entire rotor against the power system. All five masses participate equally in this mode. This is the mode normally considered in rotor angle stability studies.  16.3 Hz mode is the first torsional mode. Has one polarity reversal in the mode shape, with the rotors of generator and LP A oscillating against rotors of LP B, IP and HP sections.  24.1 Hz is the second torsional mode. Its mode shape has two polarity reversals.  30.3 Hz and 44.0 Hz torsional modes have three and four polarity reversals, respectively

4. 1539pk SO - 3 Figure 15.3 Rotor natural frequencies and mode shapes of a 555 MVA, 3,600 r/min steam turbine generator

5. 1539pk SO - 4 Torsional Interaction with power System Controls  Torsional oscillations are inherently lightly damped  Normally, not affected by generating unit or network controls  However, there have been several instances of instability of torsional modes due to interactions with  Generator excitation controls  Prime-mover controls  Controls of nearby HVDC converters

6. 1539pk SO - 5 Interaction with Generator Excitation Controls  Torsional mode destabilization by excitation control was first observed in 1969 while applying PSS at Lambton GS in Ontario, Canada  PSS using speed signal at generator end of shaft excited lowest torsional mode  PSS transfer function designed to provide nearly zero phase shift at system mode frequency of 1.6 Hz and produce pure damping torque  At torsional frequency of 16 Hz, PSS results in 135° phase lag and hence, negative damping  Problem solved by using torsional filter and sensing speed between the two LP turbine sections  Close to the "node" of 16 Hz torsional mode  Other torsional modes also have very low amplitude

7. 1539pk SO - 6 Example 15.2: Torsional Interaction with Power System Stabilizer  Examine effect of PSS on torsional stability of a 889 MVA, 1,800 RPM generating unit with a tandem compound turbine and static exciter  Each double flow LP turbine section is represented by two masses:  Objective is to examine the system performance with different forms of PSS Figure E15.1 Shaft system representation

8. 1539pk SO - 7 Case A  Delta-omega stabilizer with shaft speed (  ) as input signal with speed measured at  the generator end  at coupling B  coupling C  both couplings B and C  Excitation system model  Results shown in Table E15.1 Figure E15.3 Thyristor exciter with delta-omega stabilizer

9. 1539pk SO - 8  Speed signal at generator end causes instability or decreased damping of torsional modes while damping system mode  Sensing at B adversely affects 23 Hz torsional mode  Sensing at C adversely affects 9 Hz torsional mode  No single speed sensing location suitable for all torsional modes  Combination of B and C best for torsional modes  System mode is insensitive to sensing location; depends only on gain  Exciter mode is heavily damped in all cases

10. 1539pk SO - 9 Table E15.1 Effect of delta-omega stabilization without a torsional filter circuit K STAB Speed Sensing Location Torsional Modes System Mode Exciter Mode 9 Hz17 Hz23 Hz24 Hz 0.0--0.05±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2+0.23±j5.7- 9.5Generator+0.31±j57.6+0.20±j106.0+0.24±j146.4-0.06±j151.3-0.73±j5.0-13.7±j13.1 9.5Coupl-B-0.25±j55.3-0.17±j105.6-0.01±j146.2-0.19±j151.2-0.75±j5.0-16.7±13.9 19.0Coupl-B-0.47±j54.3-0.28±j105.5+0.07±j146.3-0.20±j151.2-1.20±j4.2-14.5±j19.7 9.5Coupl-C+0.06±j56.6-0.26±j105.5-0.21±j146.1-0.18±j151.2-0.74±j5.0-15.5±j13.7 19.0Coupl-C+0.20±j57.0-0.46±j105.3-0.31±j146.1-0.19 j151.2-1.20±j4.2-12.8±j18.5 9.5Both B and C-0.10±j56.0-0.22±j105.5-0.11±j146.1-0.19±j151.2-0.74±j5.0-16.1±j13.8 19.0Both B and C-0.16±j55.7-0.37±j105.4-0.12±j146.1-0.20±j151.2-1.20±j4.2-13.6±j19.1 28.5Both B and C-0.22±j55.5-0.52±j105.2-0.13±j146.1-0.21±j151.2-1.36±j3.6-11.9±j22.9

11. 1539pk SO - 10 Case B  Stabilizer as in Case A, but with a torsional filter having a notch at 9 Hz and substantial attenuation at the higher torsional natural frequencies.  Results shown in Table 15.2  Filter makes torsional modes insensitive to speed signal stabilization  Damping of system mode with filter is about the same as without  Filter has adverse effect on "exciter mode"  Filter characteristics increase gain in the frequency range associated with exciter mode  Stabilizer gain has to be limited to low values  limits the effectiveness of PSS in damping system mode

12. 1539pk SO - 11 Table E15.2 Effect of delta-omega stabilization with a torsional filter K STAB Speed Sensing Location Torsional Modes System Mode Exciter Mode 9 Hz17 Hz23 Hz24 Hz 0.0--0.05±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2+0.23±j5.7- 9.5Generator-0.06±j56.2-0.07±j105.7-0.11±j146.1-0.17±j151.2-0.91±j5.1-10.4±j15.8 9.5Coupl-B-0.05±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2-0.94±j5.0-8.1±14.1 19.0Coupl-B-0.05±j56.2-0.06±j105.7-0.10±j146.1-0.17±j151.2-1.42±j4.1-1.9±j20.5 9.5Coupl-C-0.06±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2-0.92±j5.0-10.5±j20.0 19.0Coupl-C-0.06±j56.2-0.06±j105.7-0.10±j146.1-0.17 j151.2-1.41±j4.2-3.2±j20.0 9.5Both B and C-0.05±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2-0.93±j5.0-9.4±j21.3 19.0Both B and C-0.05±j56.2-0.06±j105.7-0.10±j146.1-0.17±j151.2-1.42±j4.2-2.5±j20.4 28.5Both B and C-0.05±j56.2-0.06±j105.7-0.10±j146.1-0.17±j151.2-1.54±j3.5+0.5±j20.6

13. 1539pk SO - 12 Case C  Stabilizer with electrical power deviation (delta-P) as stabilizing signal  Similar to previous one, except that an equivalent speed (  eq ) derived from electrical power is used instead of actual shaft speed  Results shown in Table E15.3  PSS does not cause instability of torsional modes  Exciter well damped  High stabilizer gain can be used, resulting in a well damped system. Figure E15.4 Thyristor exciter with delta-P stabilizer

14. 1539pk SO - 13 Table E15.3 Effect of delta-P stabilization K STAB Torsional Modes System Mode Exciter Mode 9 Hz17 Hz23 Hz24 Hz 0.0-0.05±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2+0.23±j5.7- 9.5-0.05±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2-0.75±j5.0-15.6±j13.7 19.0-0.05±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2-1.20±j4.2-13.1±18.6 28.5-0.05±j56.2-0.07±j105.7-0.10±j146.1-0.17±j151.2-1.40±j3.6-11.3±j22.0

15. 1539pk SO - 14 Interaction with Nearby HVDC Converters  Problem first came to light on Square Butte HVDC system in North Dakota  Consists of 250 kV, 500 MW dc link  Rectifier station located adjacent to Milton Young GS with two units: 234 MW and 410 MW  Converters employ equidistant firing system  Normal regulator control modes are constant current control at the rectifier and constant voltage at the inverter  In addition, a supplementary "frequency sensitive power controller" (FSPC) is provided for damping system oscillations  Field tests showed that  The supplementary damping controller destabilized the first torsional mode (11.5 Hz) of 410 MW generating unit  Normal constant current control, without damping controller, could cause instability of 11.5 Hz torsional mode  Problem solved by modifying converter controls

16. 1539pk SO - 15 Interaction with HVDC Converters (cont'd) Basic Phenomenon  Torsional mode oscillations cause phase and amplitude modulation of generated voltage waveform  modulated voltage has frequency components equal to f o -f t  Modulated voltage impressed on the dc system commutating bus  With equidistant firing angle control  a shift in voltage phase due to a torsional mode causes a similar shift in firing angle  results in corresponding changes in direct current, voltage and power

17. 1539pk SO - 16  Closed-loop current control responds to correct these changes  reflected as a change in the generator power  If the net phase lag between the variation in shaft speed at the torsional frequency and the resulting change in electrical torque of the generator exceeds 90°,  torsional oscillations become unstable

18. 1539pk SO - 17 Subsynchronous Resonance

19. 1539pk SO - 18 Subsynchronous Resonance (SSR)  Occurs mainly in series capacitor compensated transmission systems  First experienced in 1970 resulting in shaft failure of units at Mohave Plant in Southern California Not until the second failure in 1971 was the real cause of failure recognized as SSR  Consider a simple radial system: Figure 15.9 Radial series compensated system

20. 1539pk SO - 19  Natural frequency f n of the circuit inductance and capacitance: or  In an uncompensated transmission system, faults and other disturbances result in dc offset components in generator stator windings:  result in a component of air-gap torque at slip frequency equal to f o  necessary to avoid torsional frequencies very near the fundamental frequency f o  In a series capacitor compensated system, instead of the dc component, the offset transient current is an alternating current of frequency equal to the natural frequency f n  induce rotor currents and torques of slip frequency (f o -f n ) Hz

21. 1539pk SO - 20  Table 15.1 shows the natural and slip frequencies as a function of the degree of compensation (with f 0 = 60 Hz) Percent Compensation (X C /X L ) x 100 (%) Natural Frequency f n (Hz) Slip Frequency 60-f n (Hz) 101842 2530 32.627.4 403822 5042.417.6 Table 15.1

22. 1539pk SO - 21  Here we have considered a simple radial system. For a complex network, the frequency-dependent characteristic of the effective impedance seen by a generator may be determined by a frequency scanning program  A series compensated network can cause sustained or negatively damped subsynchronous oscillations by two distinctive mechanisms: a)Self-excitation due to induction generator effect b)Interactions with torsional oscillations (SSR)  A shunt compensated transmission system normally has natural frequencies in the supersynchronous range  Subsynchronous oscillations normally do not pose a problem  Exceptions are situations involving very long lines and a high degree of shunt compensation

23. 1539pk SO - 22 Self-Excitation Due to Induction Generator Effect  Since f n < f 0, slip is negative. Depending on f n, R eff can be negative  At high degrees of compensation, the apparent negative resistance of the generator may exceed the transmission network resistance,  Effectively results in an RLC circuit with negative resistance  Will result in self-excitation causing electrical oscillations of intolerable levels  Purely electrical phenomenon; not dependent on shaft torsionals

24. 1539pk SO - 23 Interaction with Torsional Oscillations  If the complement of f n (i.e., f 0 - f n ) is close to one of the torsional frequencies, torsional oscillations are excited  Results in a strong "coupling" between electrical and mechanical systems  Condition referred to as "subsynchronous resonance"  A small voltage induced by rotor oscillations can result in large subsynchronous currents  Will produce torque whose phase is such that it enhances rotor oscillations  Consequences of SSR can be dangerous  If oscillations build up, shaft will break  Even if oscillations not unstable, system disturbances can cause shaft torques of high magnitude and loss of shaft fatigue life  Countermeasures to SSR:  Static filter  Dynamic filter  Dynamic stabilizer  Excitation system damper  Protective relays  NGH scheme

25. 1539pk SO - 24 Example 15.3 Instability of Subsynchronous Oscillations  Illustrates the two forms of instability of subsynchronous oscillations associated with series capacitor compensated systems  SSR and self-excitation  Test system considered is shown below  consists of a 555 MVA, 24 kV, 3,600 RPM turbine- generator feeding power through a series capacitor compensated transmission system to an infinite bus  Shaft system parameters and the torsional characteristics of the generating unit are as shown in Figure 15.3

26. 1539pk SO - 25  Power flow condition is as follows: P t = 519.5 MWE t = 1.08E B = 1.0  Degrees of compensation (i.e., X C /X L ) is varied and the reactive power output of the generator varies accordingly  Focus is on the interaction between the lowest torsional (16 Hz) mode and the subsynchronous natural frequency oscillation of the network for the following values of load at the HV bus: a)P L = 166.5 MW,Q L = 0 b)P L = 0Q L = 0

27. 1539pk SO - 26 Analysis Case (a): With P L = 166.5 MW, Q L = 0  Eigenvalue analysis used to analyze the modal interaction  system model includes the dynamics of the transmission network and the generator stator circuits. The complete system equations are expressed in the dq reference frame  Table E15.4 gives eigenvalues, frequencies, and damping ratios of lowest torsional mode and network mode  Participation factors associated with generator speed deviation and voltage across the series capacitor are also given  help identify extent of interaction between the two modes  Network is in dq reference frame (rotates at generator speed)  frequency of network mode is the complement of the network natural frequency  With no compensation, torsional mode has frequency of 16.29 Hz and small positive damping  With 25% compensation, frequency and damping increase slightly  little interaction between modes

28. 1539pk SO - 27 Table E15.4 Torsional and Network modes as a Function of the Degree Series Compensation With P L = 166.5 MW, Q L = 0 % Comp. Torsional ModeNetwork Mode Freq. (Hz) ζ Participation Factors Freq. (Hz) ζ Participation Factors Δω 1 ΔvcΔvc ΔvcΔvc 0.016.290.00040.90----- 25.016.320.00060.900.00235.200.01300.031.00 50.016.410.00100.900.0124.750.02880.020.99 60.016.500.00120.900.0421.800.02310.011.00 65.016.610.00100.910.0920.090.02300.051.00 70.016.90-0.00270.910.3118.270.02730.261.00 75.016.85-0.04680.930.7716.880.07210.650.95 80.016.28-0.05900.930.7516.050.08580.630.95

29. 1539pk SO - 28  As compensation is increased  frequency of the torsional mode varies slightly  damping increases slightly at first, then decreases  At 70% compensation, torsional mode is just unstable and noticeable interaction between torsional and network modes  Further increase in compensation strengthens "coupling"  pulls modes together in frequency but apart in damping  At 75% to 80% compensation, coupling is strongest and frequencies are nearly equal  Effect of "interaction" of torsional and network mode on characteristics of network mode can be seen in Table E15.5  provides frequency and damping of network mode with and without multimass representation  interaction of the two modes increases the damping of the network mode

30. 1539pk SO - 29 Table E15.5 Comparison of the Network Mode With and Without Multimass Representation of the Turbine-Generator Rotor with P L = 166.5 MW Q L = 0 % Comp. of line 2-3 Network mode with multimass representation of the turbine-generator rotor Network mode with single lumped mass representation of the turbine-generator rotor Freq. (Hz)Damp.Freq. (Hz)Damp. 0.0% 0.950.02800.950.0244 25.0% 35.200.013035.320.0133 50.0% 24.750.028825.130.0185 60.0% 21.800.023121.820.0205 65.0% 20.090.023020.270.0215 66.0% 19.740.023019.960.0217 68.0% 19.040.024119.370.0221 70.0% 18.270.027318.780.0224 71.3% 17.700.037618.390.0227 72.0% 17.490.046018.200.0228 74.0% 17.060.065817.630.0231 75.0% 16.880.072117.350.0233 77.0% 16.510.081416.740.0237 78.0% 16.230.085016.270.0239 80.0% 16.050.085815.960.0241

31. 1539pk SO - 30 Case (b): With P L = Q L = 0  Results are summarized in Table E15.6  With the load removed, the effective resistance of the network is reduced significantly. Consequently, the network mode becomes unstable due to the induction motor effect  As the frequency of the network mode approaches the torsional mode frequency, the coupling between the two modes increases  The effect of the interaction is to increase the damping of the torsional mode and to decrease the damping of the network mode

32. 1539pk SO - 31 Table E15.6 Torsional and Network Modes as a Function of the Degree Series Compensation With P L = Q L = 0 % Comp. of line 2-3 Torsional ModeNetwork Mode Freq. (Hz) ζ Participation Factors Freq. (Hz) ζ Participation Factors Δω 1 ΔvcΔvc ΔvcΔvc 0.016.280.00030.896----- 25.016.320.00040.8980.00235.200.00880.031.00 70.016.940.00500.9090.3418.25-0.00580.331.00 75.016.790.05700.9400.8816.94-0.06110.781.00 80.016.140.06810.9300.8816.20-0.07580.781.00 85.015.530.05000.8710.8315.46-0.06390.711.00 93.715.800.00130.8700.1312.9-0.02410.071.00

33. 1539pk SO - 32 Impact of Network Switching Disturbances on Steam Turbine-Generators  A generating unit encounters multitude of switching duties during its lifetime  can produce high levels of oscillatory shaft torques  the resulting cyclic stress variations on the shaft may cause loss of "fatigue life"  a cumulative process with each incident using a portion of the total fatigue life  In the early 1970s, it was recognized that network- switching operations could contribute to shaft fatigue damage  Problem examined by an IEEE Working Group, and general recommendations made to industry concerning: a)steady-state switching b)successive network switching

34. 1539pk SO - 33 Torsional Fatigue Characteristics  Fatigue is a cumulative process in which additional events add to previous life expenditure  Observable defects such as cracks will not be formed until all the fatigue life is consumed  Typical fatigue characteristics:  High-cycle fatigue limit (HCFL) is the limiting value of cyclic stress to which shaft can be subjected such that no cumulative fatigue damage occurs Figure 15.11 A typical fatigue characteristic showing cycle life curve for fully reversed stress

35. 1539pk SO - 34 Steady-State Switching  Most severe switching operation, with the network initially under steady state, is the reclosing of lines across a large breaker angle  Depending on network impedances, the resulting sudden increase in generator torque of a nearby generator could be very large  If resulting torques are high, this may result in loss of shaft fatigue life  For planned switching operations, such as a simple line restoration, IEEE Guidelines recommend that switching be conducted so that it does not contribute significantly to cumulative shaft fatigue  Magnitude of cycle shaft stress, should be kept mostly below HCFL  This way, nearly all of fatigue capability will be preserved to withstand impact of unplanned and unavoidable disturbances, such as faults

36. 1539pk SO - 35 IEEE Guidelines for Screening Acceptable Steady-State Line - Switching Duties  A detailed investigation, involving assessment of shaft torques and loss of fatigue life, for all possible line- switching duties would be impractical  Reference 32 prepared by an IEEE Working Group provides general guidelines to permit utilities to screen switching operations  assume a simple line restoration from steady state  hence, applicable only for delayed (10 seconds or more) reclosing  based on detailed studies of a number of cases  Breaker angle is not by itself useful in judging severity of a switching operation  circuit impedances play a major role  Therefore, severity is measured in terms of the sudden change in the generator power (ΔP), as computed by a conventional transient stability program

37. 1539pk SO - 36  A rule-of-thumb limit for ΔP is:  0.5 pu of generator MVA rating  A line-switching case resulting in ΔP of less than 0.5 pu considered safe  no contribution to loss of fatigue life  Switching operations resulting in ΔP greater than the 0.5 pu limit have to be studied in detail to assess the shaft duty Reference 32: IEEE WG Report, "IEEE Screening Guide for Planned Steady- State Switching Operations to Minimize Harmful Effects on Steam Turbine Generators", IEEE Trans., Vol. PAS-99, No. 4, pp. 1519-1521, July/August 1980.

38. 1539pk SO - 37 Successive Network-Switching  Successive network disturbances, such as automatic high-speed line reclosing following a fault,  can result in dangerously high torques  Concern is for the compounding effects of the different switching operations  torsional oscillations due to successive impacts may reinforce the initial oscillations  risk of amplifying torsional oscillations to damaging levels is a function of the type of disturbance and the timing of subsequent switching operations  Reference 33 prepared by the IEEE Working Group gives a summary of the predicted range of fatigue life expenditure for various types of disturbances:  different type faults, fault clearing, successful reclosing, unsuccessful reclosing cont'd

39. 1539pk SO - 38  Automatic high speed reclosing of multiple faulted lines near thermal generating plants pose significant risks of shaft fatigue life expenditure  where contemplated, a study of shaft fatigue duty recommended  The following are possible alternative reclosing strategies with reduced risk of shaft damage:  Delayed reclosing, with a delay of 10 s or more  Sequential reclosing: automatic reclosing from the remote end, followed by synchro-check reclosing of the plant end  Selective reclosing: limiting high-speed reclosing to L-G faults and L-L faults Reference 33: IEEE Working Interim Report, "Effects of Switching Network Disturbances on Turbine-Generator Shaft System", IEEE Trans., Vol. PAS-101, No. 9, pp. 3151-3157, September 1982

40. 1539pk SO - 39 Hydro Generator Torsional Characteristics  Rotor of a hydraulic generating unit consists of a turbine runner and a generator rotor  If unit has a shaft-driven exciter, there is an additional rotor mass  There are at most two torsional modes of oscillation  Inertia of generator rotor about 10 to 40 times that of turbine runner (waterwheel)  No reported cases of adverse dynamic interaction with electrical network  Principal reasons for absence of adverse interaction: a)High generator rotor inertia relative to turbine runner  effectively shields the rotor mechanical system from the electrical network b)Viscous waterwheel damping  torsional oscillations inherently highly damped