1539pk

SUBSYNCHRONOUS SUBSYNCHRONOUS OSCILLATIONSOSCILLATIONS

Copyright © P. KundurThis material should not be used without the author's consent

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Subsynchronous OscillationsSubsynchronous 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 CharacteristicsExample 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 Torsional Interaction with power System ControlsControls

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 Interaction with Generator Excitation ControlsControls

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: Example 15.2: Torsional Interaction with Power System Torsional Interaction with Power System StabilizerStabilizer

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

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Case ACase 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

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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 Table E15.1 Effect of delta-omega stabilization Effect of delta-omega stabilization without a torsional filter circuitwithout a torsional filter circuit

KSTAB

Speed Sensing Location

Torsional ModesSystem Mode

Exciter Mode9 Hz 17 Hz 23 Hz 24 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 Generator +0.31±j57.6 +0.20±j106.0 +0.24±j146.4 -0.06±j151.3 -0.73±j5.0 -13.7±j13.1

9.5 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

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Case BCase 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 Table E15.2 Effect of delta-omega stabilization Effect of delta-omega stabilization with a torsional filterwith a torsional filter

KSTAB

Speed Sensing Location

Torsional ModesSystem Mode

Exciter Mode9 Hz 17 Hz 23 Hz 24 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 Generator -0.06±j56.2 -0.07±j105.7 -0.11±j146.1 -0.17±j151.2 -0.91±j5.1 -10.4±j15.8

9.5 Coupl-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

19.0 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

9.5 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

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Case CCase 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

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Table E15.3Table E15.3 Effect of delta-P stabilization Effect of delta-P stabilization

KSTAB

Torsional ModesSystem Mode

Exciter Mode9 Hz 17 Hz 23 Hz 24 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

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Interaction with Nearby HVDC ConvertersInteraction 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 Interaction with HVDC Converters (cont'd)(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 ResonanceSubsynchronous Resonance

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Subsynchronous Resonance (SSR)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:

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 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

srad

X

X

CLLC

1

L

C0

00

0n

HzX

Xff

L

C0n

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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)

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 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 Self-Excitation Due to Induction Generator EffectEffect

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 OscillationsInteraction 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 Example 15.3 Instability of Subsynchronous OscillationsInstability 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

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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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AnalysisAnalysis

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 E15.4Table E15.4 Torsional and Network modes as a Function of Torsional and Network modes as a Function of the Degree Series Compensationthe Degree Series Compensation

With With PP LL = 166.5 MW, = 166.5 MW, QQ LL = 0 = 0

% Comp.

Torsional Mode Network Mode

Freq. (Hz)

ζ

Participation Factors Freq.

(Hz)ζ

Participation Factors

Δω1 Δvc 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 Table E15.5 Comparison of the Network Mode With and Comparison of the Network Mode With and Without Multimass Representation of the Turbine-Generator Without Multimass Representation of the Turbine-Generator

RotorRotor

with with PPL L = 166.5 MW = 166.5 MW QQL L = 0= 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 E15.6Table E15.6 Torsional and Network Modes as a Function of Torsional and Network Modes as a Function of the Degree Series Compensationthe Degree Series Compensation

With With PPLL = = QQLL = 0 = 0

% Comp. of line 2-3

Torsional Mode Network Mode

Freq. (Hz)

ζ

Participation Factors Freq.

(Hz)ζ

Participation Factors

Δω1 Δvc 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 Impact of Network Switching Disturbances on Steam Turbine-Generatorson 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

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Torsional Fatigue CharacteristicsTorsional 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

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Steady-State SwitchingSteady-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

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IEEE Guidelines for Screening Acceptable IEEE Guidelines for Screening Acceptable Steady-State Line - Switching DutiesSteady-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

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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 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.

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Successive Network-SwitchingSuccessive 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 CharacteristicsHydro 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