icone20-power2012 july 30 - august 3, 2012, anaheim

SUBSYNCHRONOUS RESONANCE AND TORSIONAL EFFECTS ON A STEAM TURBINE GENERATOR IN TRANSMISSION SYSTEMS WITH SERIES CAPACITOR COMPENSATION

K.R. Mutama Newmont Nevada Energy

Investments Elko, Nevada, USA

J. Seeliger Newmont Nevada Energy

Investments Elko, Nevada, USA

D.H. Baker GE Energy

Schenectady, New York, USA

R. D’Aquila GE Energy


B. Fitzgerald GE Energy


C. Wegner GE Energy


R.M. Staulters GE Energy


ABSTRACT Turbine-generators which connect to transmission systems

with series capacitor compensated lines can experience

problems with the torsional oscillations of the shaft interacting

with the electrical oscillations of the series capacitors and

transmission system inductance. This resonant interaction is

called Subsynchronous Resonance (SSR) since it involves

torsional and electrical oscillations which are below the

synchronous operating frequency of the power system. The

transmission lines near the Newmont TS Power Plant will soon

have series capacitors installed. Modeling studies based on

calculated torsional frequencies and estimated torsional

damping showed that the turbine-generator could have

instabilities of the torsional oscillations under some operating

conditions. After the modeling studies were completed, actual

tests on the steam turbine generator were conducted to measure

the frequency and mechanical damping of the torsional

oscillations. Field measurements validated modeling studies

and showed the SSR risk may be higher than originally

estimated. As a result of these investigations, a torsional stress

relay is being installed to protect the unit from subsynchronous

torsional effects of the series capacitors. The torsional stress

relay will trip the unit if damaging torsional oscillations or

torsional instabilities occur.

INTRODUCTION

Numerous high voltage transmission projects are being

planned and developed throughout all of the North American

grid. The need for many of these transmission lines is driven

by new generation projects, particularly renewable generation.

In most cases, the source of generation is remote from load

centers and requires long distance transmission lines.

Compensating the long transmission lines with series capacitors

is a very cost-effective way to increase transmission capability

and minimize the total amount of new transmission required.

A significant side effect of series capacitors is the

introduction of series-resonant conditions in the grid at

frequencies below synchronous, i.e. subsynchronous.

Conventional power generation can interact adversely with

these series resonances, often resulting in destabilization or

excessive stimulation of torsional vibrations within the turbine-

generator set. This effect has been termed ―Subsynchronous

Resonance‖ (SSR) [1].

In 1970, and again in 1971, the Mohave generator in

Nevada, USA experienced a gradually growing torsional

vibration that eventually led to a fracture of the shaft section

between the generator and the rotating exciter [2,3].

Investigations uncovered an electrical resonance coincident

with the frequency of the second torsional vibration mode of

the turbine-generator. Over the past 35 years the industry has

learned to manage SSR, with specialized analysis often

Proceedings of the 2012 20th International Conference on Nuclear Engineering collocated with the

ASME 2012 Power Conference ICONE20-POWER2012

July 30 - August 3, 2012, Anaheim, California, USA

1 Copyright © 2012 by ASME

ICONE20-POWER2012-55029

required to finalize system design and special torsional

protection equipment applied to machines with potential

exposure.

NOMENCLATURE SSR – Subsynchronous Resonance

TSR – Torsional Stress Relay

FFT – Fast Fourier Transform

kV – kiloVolts of the transmission system

HP/IP – combined High and Intermediate Pressure Turbine

LP – Low Pressure Turbine

fo – operating frequency of the power grid

fe – frequency of electrical system oscillation

fm – frequency of torsional system oscillation

NEWMONT TS POWER PLANT The Newmont TS power plant is a 200 MW plant located

in Northern Nevada. The turbine and generator were

manufactured by Toshiba. The transmission system around

Newmont is shown in Figure 1. The Newmont generator is

connected by a 120 kV transmission line to the Falcon

substation. Three other 120 kV transmission lines and one

120/345 kV transformer are connected to the Falcon 120 kV

substation. The Falcon 345 kV bus has lines to Valmy and

Gondor. A new substation (Robinson) has been constructed

between Falcon and Gondor. Robinson has a 345/500 kV

transformer and a 500 kV line going south to the Harry Allen

substation (north of Las Vegas).

To increase the power transfer capability of the 345 kV

transmission line between Falcon and Robinson, series

capacitors are being installed at each end of the line. At 60 Hz,

these series capacitors have a reactance that is a negative 70%

of the reactance of the transmission line inductance at 60 Hz.

The result is the line only appears to have 30% of its original 60

Hz reactance. This lower effective reactance allows a larger

power flow along the line without reducing the transient

stability of the power system.

Newmont Generator

Falcon 120

Falcon 345 kV Robinson 345

Robinson 500

Gondor 345

Valmy 345

Harry Allen 500

Figure 1 Transmission System Around Newmont

The Newmont TS Power Plant turbine is composed of a

combined High and Intermediate Pressure (HP/IP) turbine and

a single Low Pressures (LP) turbine. The generator and a

rotating exciter complete the shaft system. These four elements

have rotating inertia and the shafts connecting them have

torsional stiffness. This results in torsional modes of oscillation

for the shaft system. The rotor inertias and shaft torsional

stiffnesses of the torsional system are given in Table 1. This

data was supplied by the turbine-generator manufacturer.

The four inertias and three shaft stiffnesses of the torsional

system result in calculated torsional modes of oscillation at the

frequencies given in Table 2. There are two frequencies (24.0

and 34.3 Hz) below the 60 Hz operating frequency of the unit

and these are called subsynchronous frequencies. The third

torsional mode at 78.5 Hz is above the operating frequency.

Mode shapes for the torsional oscillations are also given in

Table 2 and shown graphically in Figure 2. The mode shapes

show relative motion of each turbine-generator section and are

normalized on the section with the highest motion. For

example, the exciter has the greatest motion for torsional mode

1. The HP/IP turbine will oscillate at 72% of the magnitude of

oscillation of the exciter but in the opposite direction. This

results in a slight twisting of the shaft from one end to the other

at mode 1 torsional frequency (24 Hz). For mode 2, the 34.3

Hz oscillations would result in the most motion of the HP/IP

turbine with the exciter moving at 13% of the magnitude and in

the same direction, but the LP turbine would be moving in the

opposite direction at 18% of the magnitude. Mode 3 at 78.5 Hz

has motion mostly in the exciter inertia.

Table 1 Rotor Inertias and Torsional Stiffnesses (Metric Units)

Inertia Name Inertia Constant WR

2 (J)

kg-m2

Spring Constant (K)

kg m/rad

HP/IP 1275 (J1)

5.12×106

(K12)

LP 9425 (J2)

7.26×106

(K23)

Generator 4050 (J3)

3.00×106

(K34)

Exciter 125 (J4)

Table 2 Torsional Mode Frequencies and Mode Shapes

Mode 1 2 3

Frequency (Hz) 24.0 34.3 78.5

Location Mode Shape (Normalized Amplitude)

HP/IP -0.7191 1.0000 -0.0002

LP -0.3042 -0.1816 0.0011

Generator 0.9035 0.1038 -0.0333

Exciter 1.0000 0.1294 1.0000


SUBSYNCHRONOUS RESONANCE With no series capacitors, unit torsional oscillations are

dormant or have little or no magnitude. Torsional oscillations

can be excited by operations in the transmission grid such as

line switching or faults. The mechanical damping, though

small, results in these oscillations being damped in five to 10

seconds. Mechanical damping is higher at rated load in

torsional modes which have significant motion in the turbine

elements. This is due to steam flow for steam turbines (or gas

flow for gas turbines).

Figure 2 Newmont Torsional Mode Shapes

Unless repeated transmission grid events occur close together

(such as high speed reclosing of transmission lines following

faults) the torsional oscillations do not reach an amplitude that

results in shaft fatigue.

However, the presence of series capacitors in the

transmission lines will result in an electrical system resonance.

For a simple radial system the resonance would be at an

electrical frequency corresponding to 𝑓𝑒 = √𝑋

𝑋 , where XC is

the 60 Hz reactance of the capacitor and XLT is the 60 Hz

reactance of the total series inductance of the generators,

transformers, and transmissions lines. Since XC would be less

than XL of just the transmission line, the electrical frequency

would be less that 60 Hz or the system operating frequency, fo.

Subsynchronous currents at frequency fe, flowing in the

generator stator windings will produce an electrical torque

component at frequencies fo-fe and fo+fe since electrical torque

is produced by flux times current and the stator flux is changing

at frequency fo. Conversely, a torsional oscillation at frequency

fm will produce stator voltage components at fo-fm and fo+fm

since stator voltage is the product of speed times the stator flux.

If fe is close to fo-fm, an interaction occurs where the stator

voltages produce stator currents and the stator currents produce

electrical torque and the electrical torque produces speed

variations which then produce stator voltages. This feedback

process can produce unstable oscillations. This is a resonant

condition of the interaction of two closely corresponding

system modes of oscillation. Since these are frequencies below

synchronous operating frequency, the process has been given

the name Subsynchronous Resonance [1] or SSR. The

interplay between the electrical and torsional systems that

produce unstable oscillations has been further identified as

torsional interaction in the definitions. Since the unstable

oscillations are most evident in the shaft torsional system, they

are often referred to as unstable torsional oscillations.

Another aspect of SSR is shaft torque amplification where

the torsional oscillations following a system disturbance are

larger in the series compensated system even if they are still

stable.

TORSIONAL TESTS AT NEWMONT Initial SSR analysis of the Newmont TS plant was

performed using the calculated torsional frequencies listed in

Table 2, and estimated torsional damping. This analysis

showed a potential for unstable SSR conditions.

Analytical torsional frequency estimates can have an

uncertainty of up to a few Hz and mechanical damping cannot

be calculated. The authors experience has shown that calculated

torsional frequencies are within 1 Hz of measured for a large

percentage of tested units. However, errors in calculated

frequency of 2 Hz or more have been observed. Therefore,

when analysis indicates that SSR may be a potential concern,

field testing may be performed to confirm the findings. Testing

of the torsional frequencies and torsional damping at Newmont

was performed during April 2011.

The speed of the turbine generator was measured from a

front standard toothed wheel. The torsional frequencies can be

measured during normal operation of the unit by sampling a

long time period and performing a fast Fourier transform (FFT)

of the change in speed as shown in Figure 3. The

subsynchronous torsional frequencies were measured at

Newmont operating at full load as 24.3 and 33.5 Hz. This is

0.3 and 0.2 Hz higher than the calculated frequencies.

Torsional damping was measured by stimulating the

torsional oscillations via transmission line switching (out and

then back in), unit tripping at low load and unit

synchronization.

The results of a synchronizing event are shown in Figure 4.

The TWIB2 signal is the raw measurement of unit speed

deviation (0 corresponds to synchronized speed). The bottom


trace shows the TWIB signal filtered to torsional mode 1 at

24.3 Hz.

The damping is measured by performing an FFT of the

speed signal as shown in Figure 5. The top trace shows the

magnitude of a 24.3 Hz signal versus time and the bottom trace

the log of the magnitude versus time. The slope of the line

fitting the log magnitude corresponds to damping. The on line

damping constant (σ) and damping ratio () measured is σ = -

0.107 sec-1

(=0.00070).

Figure 3 FFT Measurement of Torsional Oscillations

Figure 4 Mode 1 Response to Unit Synchronization

Unit synchronization immediately followed by a reopening

the generator breaker but keeping the turbine operating allowed

the no load mechanical damping to be measured. These values

are:

Mode 1 σNo Load = -0.009 sec-1

(=0.000059)

Mode 2 σNo Load = -0.014 sec-1

(=0.000067)

Figure 5 Measurement of Torsional Damping

Testing when synchronizing and remaining on line gives a

combined mechanical and electrical damping effect on the

torsional oscillations. Taking the difference from on line to off

line gives the electrical contribution. This is then subtracted

from the full load damping measurements to get the full load

mechanical damping. These values are:


Mode 1 σFull Load = -0.045 sec-1

(=0.00029)

Mode 2 σFull Lload = -0.221 sec-1

(=0.00105)

These values are used in the plots of electrical damping in

the following section.

SSR ANALYSIS FOR NEWMONT One way of analyzing SSR stability is to calculate the

damping torque. This is the real part of the transfer function

from rotor speed to electrical torque modeling the electrical

portion of the generator and the transmission system to which it

is connected. This analysis includes the integral of rotor speed

to rotor angle with respect to the rest of the electrical system.

This calculation can be made by eigenvalue analysis and

transfer function calculation. Methods have also been

developed to calculate damping torque by combining frequency

scans at the two complementary frequencies of fo-fm and fo+fm

[4,5].

A torsional mode of oscillation can be modeled by the

―modal oscillator‖ as shown in Figure 6. The generator speed

(g) and rotor angle (g) are the sum of the modal speeds and

angles (including a rigid body mode) with a factor (QGi) for the

generator location of the mode shape factor for the ―i‖th

torsional mode. Through the electrical system calculations

speed (and angle) produce the electrical torque. The electrical

torque is applied back to the modal oscillator with the same

factor (QGi). Parameters of the modal oscillator are the modal

inertia (Jni), the modal frequency (fni), and the mechanical

damping (mi), all for the ―i‖th torsional mode.

Modulating speed (and hence angle) as a function of

frequency produces ―damping torque‖ (De(f)) as the real part of

the transfer function and ―synchronizing torque‖ as the

imaginary part. The mode shape factor squared times the

damping torque at the torsional frequency is a damping

contribution. The value of (QGi)2

*De(fni) gives the electrical

system damping contribution and 2*mi gives mechanical

damping contribution. When the electrical damping

contribution is negative and its magnitude exceeds the

mechanical damping contribution, instability occurs.

1

Jni

QXi

QTi

1s

2mi

1s

(2fni

)2

QGi

QGi

Te

Tex

Tm

ni

QGi

G

Other

Modes

Other

Modes

G

+--

-

Te

G(f) = D

e(f) -j

Ke(f)

2f

-

Figure 6 Modal Oscillator Representation of Torsional

Vibration Mode

The damping torque calculated for Newmont is shown in

Figure 7. Sixteen cases are plotted for all combinations of lines

in and out for the three 120 kV lines out of the Falcon

substation and the 345 kV line to Valmy from Falcon. Two ―I-

bars‖ are also plotted which show the subsynchronous torsional

frequencies. The top of the ―I-bar‖ corresponds to no load

mechanical damping and the bottom of the ―I-bar‖ to full load

mechanical damping. The cases generally fall into two groups

depending upon whether the line from Falcon to Valmy is in or

out of service. With the Falcon to Valmy line in service, there

is a negative dip in the damping torque around mode 1 torsional

frequency (24.3 Hz). With the Falcon to Valmy line out of

service, there is a much larger dip in damping torque around the

mode 2 torsional frequency (33.5 Hz).

Mode 1 would be unstable for all load conditions with the

Falcon to Valmy line in service since the negative damping

torque exceeds the mechanical damping.

Reducing the series compensation to 60% of the line

impedance would solve the SSR problems as shown in Figure 8

except for possibly at very light load conditions following

synchronization with multiple lines out of service. Torsional

protection of the unit for these conditions was considered

necessary.

Figure 7 Damping Torque for 70% Compensation

TORSIONAL STRESS RELAY If a turbine-generator has torsional problems due to SSR

(or interactions with nearby large power electronic converters,

steel mill arc furnaces, etc.) then torsional protection should be

considered to trip the unit during SSR events before significant

damage occurs. GE's protection offering is called the Torsional


Stress Relay (TSR). Newmont's SSR problems are severe

enough to justify a TSR and one will be installed in the spring

of 2012.

The TSR measures the shaft speed at one or two points

along the shaft as necessary to measure all subsynchronous

torsional frequencies that are to be protected. The signals are

then processed to separate the oscillations of the different

modes and determine their magnitude. The speed measurement

of the shaft for each mode is correlated to the turbine-generator

shaft section which is most sensitive to the modal oscillations.

Figure 8 Damping Torque for 60% Compensation

Based upon shaft fatigue curves of the correlated shaft, a

cumulative time inverse curve is used to determine when to trip

the turbine-generator due to excessive torsional oscillations.

Alarms are also given for low, medium, and high level torsional

oscillations. An instability trip is also incorporated to trip the

unit sooner if instability is determined. The trip time versus

torsional amplitude for Newmont mode 1 is given in Figure 9.

In addition to the generator trip contact, a line/aux trip output

contact is provided which may be used in some special

applications.

Figure 9 Newmont TSR Protective Curve for Mode 1

CONCLUDING REMARKS Subsynchronous resonance studies were conducted at the

Newmont TS Power Plant which will soon have series

capacitors installed on nearby transmission lines. Modeling

studies based on calculated torsional frequencies and estimated

torsional damping showed that the turbine-generator could have

instabilities of the torsional oscillations under some operating

conditions. Calculated torsional frequencies were in close

agreement with the measured frequencies of 24.3 and 33.3 Hz.

Mechanical damping of the torsional oscillations were also

measured by stimulating the torsional oscillations via

transmission line switching, unit tripping at low load and unit

synchronization. As a result of these studies a torsional stress

relay is being installed to protect the unit from subsynchronous

and torsional effects of the series capacitors. The torsional

stress relay will trip the unit if damaging torsional oscillations

or torsional instabilities occur.

Turbine-generators which are connected to series

compensated transmission lines need to be evaluated for

potential subsynchronous resonance. Studies must be

performed to evaluate SSR risk and potential solutions.

Torsional testing may also be required to measure torsional

frequencies and damping. In cases like Newmont, where there

is a risk of unstable SSR conditions, protection is needed. In

addition, SSR mitigation might be needed if 70% series

compensation is installed on the Falcon-Robinson transmission

line. The SSR risk will need to be re-evaluated as changes are

made to the transmission grid.

ACKNOWLEDGMENTS The authors would like to thank Newmont Nevada Energy

Investments for their permission to publish the work. The

authors would like to acknowledge George Zielinski, Dan

Leonard and Richard Piwko of GE Energy for their

involvement in torsional testing and TSRs. The authors would

also like to thank engineers at NV Energy during the execution

of this project for their cooperation and collaboration.


REFERENCES [1] ―Proposed Terms and Definitions for Subsynchronous

Oscillation,‖ IEEE Subsynchronous Resonance Working

Group, IEEE Trans. on Power Apparatus and Systems. Vol.

PAS-99, No. 2, Mar-April 1980, pp. 506-511.

[2] ―Experience With 500-kV Subsynchronous Resonance and

Resulting Turbine Generator Shaft Damage at Mohave

Generating Station,‖ M. C. Hall, D. A, Hodges, IEEE PES

Special Publication 76 CII l066-0-PWR, pp. 22-29.

[3] ―Results of the Subsynchronous Resonance Tests at

Mohave,‖ D. N. Walker, C. E, J. Bowler, R. L. Jackson, D.

A. Hodges, IEEE Trans. on Power Apparatus and Systems.

Vol. PAS-94, No. 5, Sept/Dec. 1975, pp. 1878-89.

[4] ―Understanding Subsynchronous Resonance,‖ C. E. J.

Bowler, IEEE PES Special Publication 76CH 1066-0-

PWR, pp. 66-73.

[5] ―Use of Frequency Scanning Techniques for

Subsynchronous Resonance Analysis,‖ R. G. Farmer and

B. L. Agrawal, IEEE Power Apparatus and Systems, Vol.

PAS—98, No. 2, March—April 1979, pp. 341—348.


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