IMPLEMENTATION STRATEGIES FOR CORRECTIVE

CONTROL OF TRANSMISSION NETWORKS

HVDC Doctoral ColloquiumPorto, June 2010

DR. CARLOS E. UGALDE-LOO

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)

What is SSR? Definition:

“… is an electric power system condition where the electric network exchanges 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 of energy 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.

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

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

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-f network, 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 be described mathematically by the Park’s transformation.

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

o What about the transient components at the frequency f2?

What is SSR? The Park’s transformation matrix is defined as:

Applying it to 3-f currents will lead to terms such as . If q is defined in 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.

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

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 natural modes 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 changesin 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.

What is SSR? Induction generator effect

If fn < f0 , s < 0 rotor behaves as an induction machine running at supersynchronous speed.

Depending on fn , Reff < 0. At high compensation, │Reff│ > │Rnet│ RLC circuit with 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)

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.

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

892.4 MVA generators500 kV transmission line

60 Hz frequency

Navajo-McCullough line parameters – radial circuit. Series capacitor-compensated

transmission line connecting a synchronous generator to a large system. Only one interaction between

the machine and the network.

SIMPLICITY!

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 Inertiaconstant H [s]

Shaft section

Spring constant K [p.u. T/rad]

HP turbine 0.092897

HP–IP 19.303

IP turbine 0.155589

IP–LPA 34.929

LPA turbine 0.858670

LPA–LPB 52.038

LPB turbine 0.884215

LPB–GEN 70.858

Generator 0.868495

GEN–EXC 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

XT0.14 0.14

XL0.50 1.56

XSYS0.06 0.06

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 the d-axis.

T

Synchronous machine parameters (base 892.4 MVA)

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

Xd 1.79 t’d0 4.3 s Xmd , Xmq 1.666, 1.58

Xq 1.71 t’q0 0.032 s Rfd , Xfd 0.011, 1.7

Ra 0.0015 t”d0 0.850 s Rkd 0.0037

X’d 0.169 t”q0 0.050 s Xkd 1.666

X’q 0.228 t’d 0.40598 Rkq1 0.0053

X”d 0.135 t’q 0.02556 Xkq1 0.695

X”q 0.2 t”d 0.11333 Rkq2 0.0182

Xl 0.13 t”q 0.04386 Xkq2 1.825

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

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

This will be reflected in the following supersynchronous and subsynchronousfrequencies:

Some calculations

The state-space representation of the linearised system (shaft, generator and network model), has the form

The eigenvalues l are 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

Eigenvaluenumber

Real part[s–1]

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

Results (IEEE FBM) PSCAD Implementation

Results (IEEE FBM) PSCAD Implementation: 70% series compensation

Results (IEEE FBM) PSCAD Implementation: no series compensation

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.

2800 MVA generators400 kV transmission line50 Hz frequency

Series capacitor-compensated transmission line connecting a synchronous generator to a large system. Only one interaction between

the machine and the network.

SIMPLICITY!

Results (BM-GB) PSCAD Implementation

Results (BM-GB) PSCAD Implementation: 70% series compensation

Results (BM-GB) PSCAD Implementation: no series compensation

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

2.5 MVA induction generator units400 kV transmission line50 Hz frequency

Series capacitor-compensated transmission line connecting a synchronous generator to a large system. Induction generators connected

to simulate the effects on the system of a wind farm.

Results (FSIG) PSCAD Implementation

Results (FSIG)

PSCAD Implementation

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

Results (FSIG)

PSCAD Implementation

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

Future Work

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

The QB consists of two transformers: one in shunt and one in series. The shunt unit 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.

Questions?