subsynchronous oscillations

5/21/2018 Subsynchronous Oscillations

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Copyright P. Kundur

This material should not be used without the author's consent


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In power system stability studies, turbine-generatorrotor 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 verycomplex structure consisting of several predominant

masses (rotors of turbine sections, generator, and

exciter) connected by shafts of finite stiffness

! When perturbed, torsional oscillations resultbetween different sections of turbine-generator rotor

Torsional oscillations in the subsynchronous rangecould, under certain conditions, interact with the

electrical system in an adverse manner:

! Subsynchronous resonance with series capacitorcompensated lines

! Torsional interaction with power system controls


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Figure 15.3 shows the torsional characteristics of a555 MVA, 3600 RPM fossil-fuel-fired generating unit

with a static exciter

Since rotor has five masses, there are five modes ofoscillation:

! 1.67 Hz mode represents oscillation of the entirerotor 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 onepolarity reversal in the mode shape, with the rotors

of generator and LPAoscillating against rotors ofLPB, IP and HP sections.

! 24.1 Hz is the second torsional mode. Its modeshape has two polarity reversals.

! 30.3 Hz and 44.0 Hz torsional modes have three andfour polarity reversals, respectively


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Figure 15.3Rotor natural frequencies and mode shapes of a 555 MVA,

3,600 r/min steam turbine generator


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Torsional oscillations are inherently lightly damped

Normally, not affected by generating unit or networkcontrols

However, there have been several instances ofinstability of torsional modes due to interactions with

! Generator excitation controls! Prime-mover controls! Controls of nearby HVDC converters


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Torsional mode destabilization by excitation control was firstobserved in 1969 while applying PSS at Lambton GS in Ontario,Canada

! PSS using speed signal at generator end of shaft excitedlowest torsional mode

! PSS transfer function designed to provide nearly zero phaseshift at system mode frequency of 1.6 Hz and produce puredamping torque

! At torsional frequency of 16 Hz, PSS results in 135 phase lagand hence, negative damping

Problem solved by using torsional filter and sensing speedbetween the two LP turbine sections! Close to the "node" of 16 Hz torsional mode! Other torsional modes also have very low amplitude


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Examine effect of PSS on torsional stability of a 889MVA, 1,800 RPM generating unit with a tandem

compound turbine and static exciter

Each double flow LP turbine section is represented bytwo masses:

Objective is to examine the system performance withdifferent forms of PSS

Figure E15.1 Shaft system representation


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Delta-omega stabilizer with shaft speed (-a) as inputsignal with speed measured at

! the generator end! at coupling B! coupling C! both couplings B and C

Excitation system model

Results shown in Table E15.1Figure E15.3 Thyristor exciter with delta-omega stabilizer


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Speed signal at generator end causes instability ordecreased 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


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KSTAB

Speed

Sensing

Location

Torsional Modes System

ModeExciter Mode

9 Hz 17 Hz 23 Hz 24 Hz

0.0 - -0.05j56.2 -0.07j105.7 -0.10j146.1 -0.17j151.2 +0.23j5.7 -

9.5 Generator +0.31j57.6 +0.20j106.0 +0.24j146.4 -0.06j151.3 -0.73j5.0 -13.7j13.1

9.5 Coupl-B -0.25j55.3 -0.17j105.6 -0.01j146.2 -0.19j151.2 -0.75j5.0 -16.713.9

19.0 Coupl-B -0.47j54.3 -0.28j105.5 +0.07j146.3 -0.20j151.2 -1.20j4.2 -14.5j19.7

9.5 Coupl-C +0.06j56.6 -0.26j105.5 -0.21j146.1 -0.18j151.2 -0.74j5.0 -15.5j13.7

19.0 Coupl-C +0.20j57.0 -0.46j105.3 -0.31j146.1 -0.19 j151.2 -1.20j4.2 -12.8j18.5

9.5 Both B and C -0.10j56.0 -0.22j105.5 -0.11j146.1 -0.19j151.2 -0.74j5.0 -16.1j13.8




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Stabilizer as in Case A, but with a torsional filterhaving 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 sameas 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


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KSTAB

Speed

Sensing

Location

Torsional Modes System

Mode

Exciter

Mode9 Hz 17 Hz 23 Hz 24 Hz

0.0 - -0.05j56.2 -0.07j105.7 -0.10j146.1 -0.17j151.2 +0.23j5.7 -

9.5 Generator -0.06j56.2 -0.07j105.7 -0.11j146.1 -0.17j151.2 -0.91j5.1 -10.4j15.8

9.5 Coupl-B -0.05j56.2 -0.07j105.7 -0.10j146.1 -0.17j151.2 -0.94j5.0 -8.114.1

19.0 Coupl-B -0.05j56.2 -0.06j105.7 -0.10j146.1 -0.17j151.2 -1.42j4.1 -1.9j20.5

9.5 Coupl-C -0.06j56.2 -0.07j105.7 -0.10j146.1 -0.17j151.2 -0.92j5.0 -10.5j20.0

19.0 Coupl-C -0.06j56.2 -0.06j105.7 -0.10j146.1 -0.17 j151.2 -1.41j4.2 -3.2j20.0



28.5 Both B and C -0.05j56.2 -0.06j105.7 -0.10j146.1 -0.17j151.2 -1.54j3.5 +0.5j20.6


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Stabilizer with electrical power deviation (delta-P) asstabilizing signal

Similar to previous one, except that an equivalentspeed (-aeq) 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


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KSTABTorsional Modes System

ModeExciterMode9 Hz 17 Hz 23 Hz 24 Hz

0.0 -0.05j56.2 -0.07j105.7 -0.10j146.1 -0.17j151.2 +0.23j5.7 -

9.5 -0.05j56.2 -0.07j105.7 -0.10j146.1 -0.17j151.2 -0.75j5.0 -15.6j13.7

19.0 -0.05j56.2 -0.07j105.7 -0.10j146.1 -0.17j151.2 -1.20j4.2 -13.118.6

28.5 -0.05j56.2 -0.07j105.7 -0.10j146.1 -0.17j151.2 -1.40j3.6 -11.3j22.0


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Problem first came to light on Square Butte HVDCsystem 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 sensitivepower 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 dampingcontroller, could cause instability of 11.5 Hztorsional mode

Problem solved by modifying converter controls


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Basic Phenomenon

Torsional mode oscillations cause phase andamplitude modulation of generated voltage waveform

! modulated voltage has frequency components equalto fo-ft

Modulated voltage impressed on the dc systemcommutating 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


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Closed-loop current control responds to correct thesechanges

! 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


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Occurs mainly in series capacitor compensatedtransmission systems

First experienced in 1970 resulting in shaft failure ofunits at Mohave Plant in Southern California

Not until the second failure in 1971 was the real causeof failure recognized as SSR

Consider a simple radial system:

Figure 15.9 Radial series compensated system


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Natural frequency fnof the circuit inductance andcapacitance:

or

In an uncompensated transmission system, faults andother disturbances result in dc offset components in

generator stator windings:

! result in a component of air-gap torque at slipfrequency equal to fo

! necessary to avoid torsional frequencies very nearthe fundamental frequency fo

In a series capacitor compensated system, instead ofthe dc component, the offset transient current is an

alternating current of frequency equal to the natural

frequency fn

! induce rotor currents and torques of slip frequency(fo-fn) Hz


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Table 15.1 shows the natural and slip frequencies as afunction of the degree of compensation (with f0 = 60 Hz)

Percent Compensation

(XC/XL) x 100 (%)

Natural Frequency

fn(Hz)

Slip Frequency

60-fn(Hz)

10 18 42

25 30 30

30 32.6 27.4

40 38 22

50 42.4 17.6

Table 15.1


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Here we have considered a simple radial system. For acomplex 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 ornegatively 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 supersynchronousrange

! Subsynchronous oscillations normally do not posea problem

! Exceptions are situations involving very long linesand a high degree of shunt compensation


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Since fn< f0, slip is negative.Depending on fn, Reff can be negative

At high degrees of compensation, the apparentnegative resistance of the generator may exceed thetransmission network resistance,

! Effectively results in an RLC circuit with negativeresistance

Will result in self-excitation causing electricaloscillations of intolerable levels

Purely electrical phenomenon; not dependent on shafttorsionals


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If the complement of fn(i.e., f0 - fn) is close to one of thetorsional frequencies, torsional oscillations are excited

! Results in a strong "coupling" between electrical andmechanical 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 itenhances rotor oscillations

Consequences of SSR can be dangerous! If oscillations build up, shaft will break!

Even if oscillations not unstable, system disturbancescan 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


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Illustrates the two forms of instability ofsubsynchronous 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 torsionalcharacteristics of the generating unit are as shown in

Figure 15.3


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Power flow condition is as follows:

Pt= 519.5 MW Et= 1.08 EB= 1.0

Degrees of compensation (i.e., XC/X

L) is varied and the

reactive power output of the generator varies

accordingly

Focus is on the interaction between the lowesttorsional (16 Hz) mode and the subsynchronous

natural frequency oscillation of the network for the

following values of load at the HV bus:

a) PL= 166.5 MW, QL= 0

b) PL= 0 QL= 0


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Case (a): With PL= 166.5 MW, QL= 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 dampingratios of lowest torsional mode and network mode

Participation factors associated with generator speeddeviation and voltage across the series capacitor are also

given

! help identify extent of interaction between the twomodes

Network is in dqreference frame (rotates at generatorspeed)

! frequency of network mode is the complement of thenetwork natural frequency

With no compensation, torsional mode has frequency of16.29 Hz and small positive damping

With 25% compensation, frequency and dampingincrease slightly

! little interaction between modes


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% Comp.

Torsional Mode Network Mode

Freq.(Hz)

!

ParticipationFactors Freq.

(Hz)!

Participation Factors

"#1 "vc "#1 "vc

0.0 16.29 0.0004 0.90 - - - - -

25.0 16.32 0.0006 0.90 0.002 35.20 0.0130 0.03 1.00

50.0 16.41 0.0010 0.90 0.01 24.75 0.0288 0.02 0.99

60.0 16.50 0.0012 0.90 0.04 21.80 0.0231 0.01 1.00

65.0 16.61 0.0010 0.91 0.09 20.09 0.0230 0.05 1.00

70.0 16.90 -0.0027 0.91 0.31 18.27 0.0273 0.26 1.00

75.0 16.85 -0.0468 0.93 0.77 16.88 0.0721 0.65 0.95

80.0 16.28 -0.0590 0.93 0.75 16.05 0.0858 0.63 0.95


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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 unstableand noticeable interaction between torsional and

network modes

Further increase in compensation strengthens"coupling"

! pulls modes together in frequency but apart indamping

At 75% to 80% compensation, coupling is strongestand frequencies are nearly equal

Effect of "interaction" of torsional and network modeon characteristics of network mode can be seen in

Table E15.5

! provides frequency and damping of network modewith and without multimass representation


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% Comp. ofline 2-3

Network mode withmultimass representation of

the turbine-generator rotor

Network mode with singlelumped mass representation

of the turbine-generator rotor

Freq. (Hz) Damp. Freq. (Hz) Damp.

0.0% 0.95 0.0280 0.95 0.0244

25.0% 35.20 0.0130 35.32 0.0133

50.0% 24.75 0.0288 25.13 0.0185

60.0% 21.80 0.0231 21.82 0.0205

65.0% 20.09 0.0230 20.27 0.0215

66.0% 19.74 0.0230 19.96 0.0217

68.0% 19.04 0.0241 19.37 0.0221

70.0% 18.27 0.0273 18.78 0.0224

71.3% 17.70 0.0376 18.39 0.0227

72.0% 17.49 0.0460 18.20 0.0228

74.0% 17.06 0.0658 17.63 0.0231

75.0% 16.88 0.0721 17.35 0.0233

77.0% 16.51 0.0814 16.74 0.0237

78.0% 16.23 0.0850 16.27 0.0239

80.0% 16.05 0.0858 15.96 0.0241


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Case (b): With PL= QL= 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 tothe induction

motor effect

As the frequency of the network mode approaches thetorsional mode frequency, the coupling between the

two modes increases

! The effect of the interaction is to increase thedamping of the torsional mode and to decrease the

damping of the network mode


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% Comp.of line 2-3

Torsional Mode Network Mode

Freq.(Hz)

!

ParticipationFactors Freq.

(Hz)!

Participation Factors

"#1 "vc "#1 "vc

0.0 16.28 0.0003 0.896 - - - - -

25.0 16.32 0.0004 0.898 0.002 35.20 0.0088 0.03 1.00

70.0 16.94 0.0050 0.909 0.34 18.25 -0.0058 0.33 1.00

75.0 16.79 0.0570 0.940 0.88 16.94 -0.0611 0.78 1.00

80.0 16.14 0.0681 0.930 0.88 16.20 -0.0758 0.78 1.00

85.0 15.53 0.0500 0.871 0.83 15.46 -0.0639 0.71 1.00

93.7 15.80 0.0013 0.870 0.13 12.9 -0.0241 0.07 1.00


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A generating unit encounters multitude of switchingduties 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 aportion 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, andgeneral recommendations made to industry

concerning:

a) steady-state switching

b) successive network switching


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Fatigue is a cumulative process in which additional events addto previous life expenditure

Observable defects such as cracks will not be formed until allthe fatigue life is consumed

Typical fatigue characteristics:

High-cycle fatigue limit (HCFL) is the limiting value of cyclicstress to which shaft can be subjected such that nocumulative fatigue damage occurs

Figure 15.11 A typical fatigue characteristic showing cycle life curve for fullyreversed stress


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Most severe switching operation, with the networkinitially under steady state, is the reclosing of lines

across a large breaker angle

! Depending on network impedances, the resultingsudden increase in generator torque of a nearbygenerator could be very large

! If resulting torques are high, this may result in lossof shaft fatigue life

For planned switching operations, such as a simpleline 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 bepreserved to withstand impact of unplanned and

unavoidable disturbances, such as faults


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A detailed investigation, involving assessment of shafttorques and loss of fatigue life, for all possible line-

switching duties would be impractical

Reference 32 prepared by an IEEE Working Groupprovides general guidelines to permit utilities toscreen 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 severityof a switching operation

! circuit impedances play a major role Therefore, severity is measured in terms of the sudden

change in the generator power ("P), as computed by a

conventional transient stability program


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A rule-of-thumb limit for "P is:! 0.5 pu of generator MVA rating

A line-switching case resulting in "P of less than 0.5pu considered safe

! no contribution to loss of fatigue life Switching operations resulting in "P greater than the

0.5 pu limit have to be studied in detail to assess theshaft duty

Reference 32: IEEE WG Report, "IEEE Screening Guide for Planned Steady-State Switching Operations to Minimize Harmful Effects on Steam TurbineGenerators", IEEE Trans., Vol. PAS-99, No. 4, pp. 1519-1521, July/August1980.


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Successive network disturbances, such as automatichigh-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 impactsmay reinforce the initial oscillations

! risk of amplifying torsional oscillations to damaginglevels is a function of the type of disturbance and

the timing of subsequent switching operations

Reference 33 prepared by the IEEE Working Groupgives a summary of the predicted range of fatigue life

expenditure for various types of disturbances:

! different type faults, fault clearing, successfulreclosing, unsuccessful reclosing

cont'd


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Automatic high speed reclosing of multiple faultedlines near thermal generating plants pose significant

risks of shaft fatigue life expenditure

! where contemplated, a study of shaft fatigue dutyrecommended

The following are possible alternative reclosingstrategies with reduced risk of shaft damage:

! Delayed reclosing, with a delay of 10 seconds ormore

! Sequential reclosing: automatic reclosing from theremote end, followed by synchro-check reclosing of

the plant end

! Selective reclosing: limiting high-speed reclosing toL-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


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Rotor of a hydraulic generating unit consists of aturbine runner and a generator rotor

! If unit has a shaft-driven exciter, there is anadditional 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 withelectrical network

Principal reasons for absence of adverse interaction:

a) High generator rotor inertia relative to turbine runner

" effectively shields the rotor mechanical systemfrom the electrical network

b) Viscous waterwheel damping" torsional oscillations inherently highly damped

subsynchronous oscillations

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