ssr in power systems

8/13/2019 SSR in power systems

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IMPLEMENTATION STRATEGIES FOR CORRECTIVE

CONTROL OF TRANSMISSION NETWORKS

HVDC Doctoral ColloquiumPorto, June 2010

DR. CARLOS E. UGALDE-LOO


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Contents

Subsynchronous Resonance (SSR) in Power Systems

What is SSR?

IEEE First Benchmark Model (FBM) for SSR studies

Results (IEEE FBM)

A Benchmark Model adapted for the GB (BM-GB)

Modelling modifications to FBM

Results (BM-GB)

Use of Fixed-Speed Induction Generators (FSIG) to damp SSR

Modelling modifications to BM-GB

Results (FSIG)

Future Work

Assessment of possible sources of SSR in the GB network: the Quadrature Booster (QB)


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What is SSR? Definition:

is an electric power system condition where the electric networkexchanges energy with a turbine generator at one or more of the

natural frequencies of the combined system below the synchronous

frequency of the system.

Dynamic phenomenon.

Any system condition providing the opportunity for the exchange ofenergy at a subsynchronous frequency:

o Natural modes of oscillation

o Forced modes of oscillation

Why should we study the SSR?

Consequences: the Mohave Generating Station case (1970 and 1971).

It mainly occurs in series capacitor-compensated transmission systems.

The GB transmission system will consider onshore reinforcement

through fixed-capacitors.


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What is SSR? The series capacitor-compensated transmission line

Consider a simple RLC series connected branch where:

Applying the Laplace transform to the voltage and impedance

The current in the branch is given by


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What is SSR?Define:

1. The undamped natural frequency:

2. The damping ratio:

3. The damping rate:

4. The damped frequency:

The Inverse Laplace transform of the current is given by

where


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What is SSR?

In the current response, there are two different frequencies:

A sinusoidal component at the frequency of the driving voltage;

A damped sinusoidal component at a frequency depending on the

network elements (R-L-C), where

For a 3-fnetwork, phases b and c will have the two frequencies present in their responses but with

different coefficients on the transient response component.

These kind of currents flow in the stator windings of the generator. The

physical process in which they are reflected into the generator rotor can bedescribed mathematically by the Parks transformation.

o The 50Hz(or 60Hz) component appears, as viewed from the rotor, as a DC

current.

o What about the transient components at the frequencyf2?


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What is SSR? The Parks transformation matrix is defined as:

Applying it to 3-fcurrents will lead to terms such as . If qis definedin terms of the base frequency of the machine as

Thus

Currents of frequency w2 are transformed into currents of frequencies containing

both the sum and difference of the two frequencies.


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What is SSR?

The difference frequencies are called SUBSYNCHRONOUS FREQUENCIES.

Subsynchronous currents inject energy into the rotating mass of the shaft.

Produce shaft torques on the turbine-generator rotor.

Cause rotor oscillations at subsynchronous frequencies.

The presence of subsynchronous torques on the rotor causes concern

because the turbine-generator shaft itself has natural modes of oscillation(typical of a spring mass system). The shaft oscillatory modes are at

subsynchronous frequencies.

Should the induced subsynchronous torques coincide with one of the

shaft natural mechanical modes of oscillation, the shaft will oscillate at

this natural frequency, sometimes with high amplitude. This is called

shaft stress & fatigue

o SUBSYNCHRONOUS RESONANCE

failure

possible damage


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What is SSR? Types of subsynchronous oscillations in series capacitor compensation:

Induction generator effect (purely ELECTRICAL PHENOMENON)

At subsynchronous current, the rotor resistance is negative (seen from the armature), while the

network has a positive resistance to these same currents.

If the negative resistance of the generator is greater than the positive resistance of the network

at the system natural frequencies, there will be sustained subsynchronous currents, causing the

self-excitation of the electrical system electrical oscillations of intolerable level.

Torsional interaction (resulting in SSR coupling between ELECTRICAL & MECHANICAL)

The induced subsynchronous torque in the generator is close to one of the torsional naturalmodes of the turbine-generator shaft.

Rotor oscillations build up, which induces armature voltage components at sub and

supersynchronous frequencies. The induced subsynchronous frequency voltage is phased to

sustain the subsynchronous torque.

If the torque equals or exceeds the inherent mechanical damping of the rotating system, the

system will become self-excited.

Transient torques (resulting in SSR coupling between ELECTRICAL & MECHANICAL)Result from system disturbances which cause sudden changes in the network, and thus changes

in currents that will tend to oscillate at the natural frequencies of the network.

If any of those subsynchronous network frequencies coincide with one of the natural modes of a

turbine-generator shaft, there can be large peak torques (proportional to the magnitude of the

oscillating current). Currents due to short circuits can produce very large shaft torques both

when the fault is applied and when it is cleared.


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What is SSR? Induction generator effect

Iffn Rnet RLC circuitwith negative resistance.

This causes self-excitation causing electrical oscillations of intolerable levels.

SOLUTION: Increase network resistance and decrease resistance of generator

rotor circuits (damping windings)


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What is SSR? Torsional interactions

Subsynchronous currents inject energy into the rotating mass of the shaft.

If the subsynchronous component of rotor torque is close to a torsional natural

mode of the turbine-generator shaft, torsional oscillations can be excited.


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IEEE First Benchmark Model for SSR Studies

Origins

The IEEE First Benchmark Model (FBM) was created by the IEEE Working Group

on Subsynchronous Resonance in 1977 for use in computer program

comparison and development.

NAVAJO PROJECT (US):ARIZONA, NEVADA & CALIFORNIA

892.4MVA generators

500 kVtransmission line

60Hzfrequency

Navajo-McCullough line

parameters radial circuit.

Series capacitor-compensated

transmission line connecting asynchronous generator to a

large system.

Only one interaction between

the machine and the network.

SIMPLICITY!


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IEEE First Benchmark Model for SSR Studies The turbine-generator shaft model

The network model T

Shaft inertias and spring in p.u. on the generator

base (892.4 MVA)

Inertia Inertia

constant H[s]

Shaft

section

Spring constant

K [p.u. T/rad]HP turbine 0.092897

HPIP 19.303

IP turbine 0.155589

IPLPA 34.929

LPA turbine 0.858670

LPALPB 52.038

LPB turbine 0.884215

LPBGEN 70.858

Generator 0.868495

GENEXC 2.82

Exciter 0.0342165

Network impedances in p.u. on

the generator base (892.4 MVA)

Parameter Positive seq. Zero seq.

R 0.02 0.50

XT 0.14 0.14

XL 0.50 1.56

XSYS 0.06 0.06


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IEEE First Benchmark Model for SSR Studies The generator (non-reduced order) model

Two damper windings in the q-axis and one in the d-axis are included in the

rotor. A field winding is considered in thed-axis.

T

Synchronous machine parameters (base 892.4 MVA)

Parameter Units [ p.u.] Parameter Units [ p.u.] Parameter Units [ p.u.]

Xd 1.79 d0 4.3 s Xmd, Xmq 1.666, 1.58

Xq 1.71 q0 0.032 s Rfd, Xfd 0.011, 1.7

Ra 0.0015 d0 0.850 s Rkd 0.0037

Xd 0.169 q0 0.050 s Xkd 1.666

Xq 0.228 d 0.40598 Rkq1 0.0053

Xd 0.135 q 0.02556 Xkq1 0.695

Xq 0.2 d 0.11333 Rkq2 0.0182

Xl 0.13 q 0.04386 Xkq2 1.825


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IEEE First Benchmark Model for SSR Studies Some calculations

The Navajo McCullough line considers a 70% of series compensation. This provides

a total impedance of

where 0.35p.u. corresponds to a 70% compensation of the 0.50p.u. inductive

reactance of the transmission line. The undamped natural frequency is given by

This will be reflected in the following supersynchronous and subsynchronous

frequencies:


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Some calculations

The state-space representation of the linearised system (shaft, generator and

network model), has the form

The eigenvalueslare defined as the

solution of the matrix equation

The system is of 20th order with 10

eigenvalues having frequencies in

the subsynchronous range and close

to the imaginary axis. The system is

unstable.Notice that the predicted network

resonance frequency (110 rad/s) is

near that of two pair of unstable

eigenvalues.

IEEE First Benchmark Model for SSR Studies

Eigenvalues of the IEEE FBM

Eigenvalue

number

Real part

[s1]

Imaginary

part [rad/s]

Imaginary

part [Hz]

1, 2 +0.0785 127.1556 20.2374

3, 4 +0.0782 99.7088 15.8692

5, 6 +0.0409 160.3899 25.5268

7, 8 +0.0023 202.8631 32.2867

9, 10 0.0000005 298.1767 47.4563

11 0.7758

12 0.9480

13, 14 1.2180 10.5951 96.6162

15, 16 5.5411 136.9774 21.8006

17, 18 6.8096 616.5325 98.1228

19 25.4112

20 41.2955


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Results (IEEE FBM) PSCAD Implementation


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Results (IEEE FBM)

PSCAD Implementation: 70% series compensation


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Results (IEEE FBM)

PSCAD Implementation: no series compensation


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A Benchmark Model adapted for the GB (BM-GB)

Modelling modifications to FBM

Key parameters are modified to make the system relevant to that of GB. The

main purpose is to be able to reproduce the SSR phenomenon.

2800MVA generators


50Hzfrequency


transmission line connecting a

synchronous generator to a

large system.

Only one interaction between

the machine and the network.

SIMPLICITY!


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Results (BM-GB)

PSCAD Implementation


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Results (BM-GB)

PSCAD Implementation: 70% series compensation


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Results (BM-GB)

PSCAD Implementation: no series compensation


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Use of Fixed-Speed Induction Generators to damp SSR

Modelling modifications to BM-GB

A fixed-speed induction generator (FSIG) based wind farm is added to the

network to assess the its ability to damp subsynchronous oscillations

2.5MVA induction generator

units


50Hzfrequency


transmission line connecting a

synchronous generator to a

large system. Induction generators connected

to simulate the effects on the

system of a wind farm.


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Results (FSIG) PSCAD Implementation


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Results (FSIG)


1 FSIG unit (70% comp.)70% compensationNo compensation


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Results (FSIG)


100 FSIG units (70% comp.)10 FSIG unit (70% comp.) 300 FSIG units (70% comp.)


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Future Work

Assessment of possible sources of SSR in the GB network: the Quadrature

Booster (QB)

The QB consists of two transformers: one in shunt and one in series. The shuntunit provides a variable voltage from a fully tapped secondary winding to the

primary winding of a transformer, which secondary is connected in series with

the line. The connection causes the 90 degree phase shift.

It injects a voltage into the network to cause a circulating current. This

increases the power flow in some lines and reduces it in others, allowing the

operator to balance flows.


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Questions?

ssr in power systems

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