SUBSYNCHRONOUS
OSCILLATIONS
Copyright © P. Kundur
This material should not be used without the author's consent
1539pk
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
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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 LPA oscillating against rotors of
LPB, 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
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Figure 15.3 Rotor natural frequencies and mode shapes of a 555 MVA,
3,600 r/min steam turbine generator
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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
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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
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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:
Figure E15.1 Shaft system representation

Objective is to examine the system performance with
different forms of PSS
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Case A

Delta-omega stabilizer with shaft speed (-a) as input
signal with speed measured at
 the generator end
 at coupling B
 coupling C
 both couplings B and C

Excitation system model
Figure E15.3 Thyristor exciter with delta-omega stabilizer

Results shown in Table E15.1
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
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
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Table E15.1 Effect of delta-omega stabilization
without a torsional filter circuit
KSTAB
Speed
Sensing
Location
9 Hz
0.0
-
-0.05±j56.2
9.5
Generator
9.5
Torsional Modes
System
Mode
Exciter Mode
-0.07±j105.7 -0.10±j146.1 -0.17±j151.2
+0.23±j5.7
-
+0.31±j57.6 +0.20±j106.0 +0.24±j146.4 -0.06±j151.3
-0.73±j5.0
-13.7±j13.1
Coupl-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
19.0
Coupl-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
9.5
Coupl-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
19.0
Coupl-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
9.5
Both 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
19.0
Both 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
28.5
Both 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
17 Hz
23 Hz
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24 Hz
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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
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Table E15.2 Effect of delta-omega stabilization
with a torsional filter
KSTAB
Speed
Sensing
Location
9 Hz
17 Hz
0.0
-
-0.05±j56.2
-0.07±j105.7
9.5
Generator
-0.06±j56.2
9.5
Coupl-B
19.0
Torsional Modes
System
Mode
Exciter
Mode
-0.10±j146.1 -0.17±j151.2
+0.23±j5.7
-
-0.07±j105.7
-0.11±j146.1 -0.17±j151.2
-0.91±j5.1
-10.4±j15.8
-0.05±j56.2
-0.07±j105.7
-0.10±j146.1 -0.17±j151.2
-0.94±j5.0
-8.1±14.1
Coupl-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
9.5
Coupl-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
19.0
Coupl-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
Both 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
19.0 Both 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
28.5 Both 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
9.5
23 Hz
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24 Hz
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Case C

Stabilizer with electrical power deviation (delta-P) as
stabilizing signal

Similar to previous one, except that an equivalent
speed (-aeq) derived from electrical power is used
instead of actual shaft speed
Figure E15.4 Thyristor exciter with delta-P stabilizer

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.
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Table E15.3 Effect of delta-P stabilization
Torsional Modes
System
Mode
Exciter
Mode
-0.07±j105.7 -0.10±j146.1 -0.17±j151.2
+0.23±j5.7
-
-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
KSTAB
9 Hz
0.0
-0.05±j56.2
9.5
17 Hz
23 Hz
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24 Hz
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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
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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 fo-ft

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
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
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
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Subsynchronous Resonance
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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
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
Natural frequency fn of the circuit inductance and
capacitance:
n 
1
LC

0
 L  C 
0
 0
0
XC
rad s
XL
or
fn  f0

XC
Hz
XL
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 fo
 necessary to avoid torsional frequencies very near
the fundamental frequency fo

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 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 a
function of the degree of compensation (with f0 = 60 Hz)
Table 15.1
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
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
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
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Self-Excitation Due to Induction Generator
Effect

Since fn < f0, slip is negative.
Depending on fn, Reff 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
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Interaction with Torsional Oscillations

If the complement of fn (i.e., f0 - fn) 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
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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 turbinegenerator 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
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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/XL) 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) PL = 166.5 MW,
QL = 0
b) PL = 0
QL = 0
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Analysis
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 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
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Table E15.4 Torsional and Network modes as a Function of the
Degree Series Compensation
With PL = 166.5 MW, QL = 0
% Comp.
Freq.
(Hz)
Torsional Mode
Participation
Factors
ζ
Δω1
Δvc
Network Mode
Freq.
(Hz)
ζ
Participation Factors
Δω1
Δvc
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 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
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Table E15.5 Comparison of the Network Mode With and
Without Multimass Representation of the Turbine-Generator
Rotor
with PL = 166.5 MW QL = 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%
0.95
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 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
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Table E15.6 Torsional and Network Modes as a Function of
the Degree Series Compensation
With PL = QL = 0
% Comp.
of line 2-3
Freq.
(Hz)
Torsional Mode
Participation
Factors
ζ
Δω1
Δvc
Network Mode
Freq.
(Hz)
ζ
Participation Factors
Δω1
Δvc
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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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 networkswitching 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
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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:
Figure 15.11 A typical fatigue characteristic showing cycle life curve for fully
reversed stress

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
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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
SO - 34
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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 lineswitching 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
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
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 SteadyState Switching Operations to Minimize Harmful Effects on Steam Turbine
Generators", IEEE Trans., Vol. PAS-99, No. 4, pp. 1519-1521, July/August
1980.
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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
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
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
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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
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