Power System Stability - Roorkee College of Engineeringrceroorkee.in/pdf/pdfo/TEE601.pdf ·...

GENERATOR CONTROL AND PROTECTION

Power System Stability


Outline

• Basis for Steady-State Stability

• Transient Stability

• Effect of Excitation System on Stability

• Small Signal Stability

• Power System Stabilizers

– Speed Based

– Integral of Accelerating Power

• Case Studies


Mechanical and Electrical Torque

Applied to the Shaft

T

T

M

e

T

ω

G


Stator, Rotor, and Resultant MMFs and Torque Angle

F

A

A'

B'

B

C'

C

F

R2

1

ω


Synchronous Machine Tied to Infinite Bus

XL

X

E

E

XEE

T

+XX LE =X T

T

g

gOHV

Infinite Bus


Steady State Electrical Power

Output

PE E

Xe

g T

g

= sinδ


Phasor Diagram - Generator Tied to

Infinite Bus

IX

E

E

E IXI

g

g

T

0 E

δδδδ

j

j


Transient Stability


Rubber Band Analogy

Rubber Bands

Weights


Change in Electrical Torque

∆ ∆ ∆T T Te s D= +δ ω


Transient Stability Illustration

PP

ow

er

Power Angle-

90 °0°0

180 °

Turbine

PowerP

P

P

2

1

3

4

Unstable,

machine loses

Synchronism

Stable

Retarding

Torque

Insufficient

Retarding

Torque

MAX

M

ACCEL

DECEL

°δδδδδδδδ


Effect of Fault Clearing Time -

Equal Area Not Possible

Fault

Power

Unit pulls out of sync

P

PE

M

Breakerclears

δδδδ


Effect of Fault Clearing Time -

Equal Area Substantial Margin

Power

Fault Breakerclears faults

System returns tosteady state, system stable

Rotor decelerates due toP max exceeding mechanical power

E

Equal Areasubstantial margin

P

PE

M

δδδδ


Effect of the Excitation System

on Stability


Steady State Electrical Power

Output

PE E

Xδe

g T

g

= sin


Effect of High Initial Response

Excitation System

Power

0

Fast excitation systemMaximum field forcing

First swing, system recovers

P

B

A

P

P

P

E

E-A

E-B

MMachine will losesynchronism

δδδδ


Small Signal Stability


Change in Electrical Torque

∆ ∆ ∆T T Te s D= +δ ω


Inter-Unit Oscillations

Eg2

g1

g2

X

X

Eo

1.5 - 3 Hertz

Eg1


Local Mode Oscillations

Eg

g LX XEo

.7 - 2 HertzEg


Inter-Area Oscillations

<0.5 Hertz

Eg2

g1 g2LX XX

Eg1


Block Diagram of Generator Under

Voltage Regulator Control

VREF

+

-

Gex (s)

Exciter∆E fd

-

+

K3

1+sT3

1

1+sTR

K4

K2

K6

++∆E

∆v

t

1

+

12Hs +K

D

ω0

s

∆Te

∆T

∆ω ∆δ

M

+- r

K5

K1

+∆Ψfd

Σ Σ Σ

Σ

Σ

Voltage transducer

Field circuit


Power System Stabilizers


The "Swing Equation"

2

0

2

2

H d

dtT T Km e D rω

δω= − − ∆


Small Signal Version of "Swing

Equation"

∆ ∆ ∆T T Te s D= +δ ω


Response of Speed and Angle

to Small Disturbances

0

0

∆δ

∆δ

∆δ

∆ω

∆ω

∆T

∆T

∆T

∆T

∆T

∆T

D

D

e

e

s

s∆δ

D

s

Stable

Positive • T

• Positive T

D

s

OscillatoryInstability

Positive • T

T• Negative


PSS with AVR, Exciter and

Generator

VREF

++

-

Gex (s)

Exciter

∆Efd

-

+

K3

1+sT3

1

1+sTR

K4

K2

K6

++∆E

∆v

∆v

t

1

s

+

12Hs +K

D

ω 0

s

∆Te

∆T

∆ω

∆ω

∆δ

∆δ

M

+-

r

r

K5

K1

+∆Ψfd

GP S(s)

Σ Σ Σ

Σ

Σ

Voltage transducer

Field circuit



PSS Theory of Operation

Speed Based Stabilizers


Speed-Based Stabilizer

Speed

s T5

1 + s T5

1

1 + s T6

1

1 + A1 s + A2 sKs1

1 + s T1

1 + s T2

1 + s T3

1 + s T4

Vstmax

Vstmin

Output

High-Pass Filter Stabilizer Gain & Phase Lead Limits

2

Torsional Filter


PSS Theory of Operation

Dual Input Stabilizers


Small Signal Version of "Swing

Equation"

∆ ∆ ∆T T Te s D= +δ ω


Speed Deviation from Net

Accelerating Power

d

dt HT T Kr m e D r

∆ ∆ω ω= − −1

2( )


Accelerating Power Based on

Integral of Mechanical and

Electrical Power

T ]∆ ∆ ∆ω = − ∫[∫1

2HTm e


Block Diagram of Dual-Input

Power System Stabilizer

Freq

Power

+

+

+

-

Ramp-TrackingFilter Vstmax

Vstmin

Output

High-Pass Filters

High-Pass Filters & Integrator

Stabilizer Gain & Phase LeadLimits

ΣΣΣΣ ΣΣΣΣ1+sT8

(1+sT9)

N

M

sTw2

1 + sTw2

sTw1

1 + sTw1Ks1

1+sT1

1+sT2

1+ sT3

1+ sT4

sTw3

1+sTw3

Ks2

1+sT7


Speed Derived from VT and CT Signals

ω

E

E

Generator

q-axis

d-axis

jX

I

It

t

Itq


Accelerating-Power Design (Speed

Input)

Compensated FrequencyEquivalent to Rotor Speed

s Tw1

1 + s Tw1

s Tw 2

1 + s Tw2

High-Pass Filters

Generator Speed DeviationSignal (i.e. no steady state component)


Integral of Electrical Power Block

Diagram

Active Powers Tw3

1 + s Tw3

K 2

1 + s T7

High-Pass Filters & Integrator

Integral-of-PowerDeviation


Output Stage of PSS to AVR

Ks11 + s T1

1 + s T2

1 + s T3

1 + s T4

Vstmax

Vstmin

Output to AVR

S

Filtered Speed

tabilizer Gain & Phase LeadLimits


Case Studies


Case 1 - Hydro Generator without PSS

• Time (seconds)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


Case 1 - Hydro Generator with PSS

• Dual Input Stabilizer, Phase Lead=(1+0.05s)/(1+0.01s), Gain=40

• Time (seconds)1 2 3 4 5 6 7 8 9 10 11 12


Ks=6, 92MW Hydro Turbine Generator

A single input PSS measures only frequency, power or speed

Case 2 - On-line Step Response Frequency Type PSS


Ks=7.5, 92MW Hydro Turbine Generator

The PSS monitors frequency and power for superior performance

Case 2 - On-line Step Response Dual input PSS


Case 3 – Step

Response

All generators

in service,

Stabilizer OFF


Case 3 –

Step Response

All generators

in service,

Stabilizer Gain = 1


0.875

0.01

0.01

-1.5

1

0.975

WATTS

TEST OUT

PSS OUT

GEN TERM F

POSTLIM OUT

GEN TERM V

0.865

0.006

0.006

-2.5

0

0.965

0.855

0.002

0.002

-3.5

-1

0.87

0.008

0.008

-2

0.5

0.97

0.86

0.004

0.004

-3

-0.5

0.96

0.85

0

0

-4

0

0

0

0

0

0

x10-4

8

8

8

8

8

8

4

4

4

4

4

4

12

12

12

12

12

12

18

18

18

18

18

18

2

2

2

2

2

2

10

10

10

10

10

10

16

16

16

16

16

16

6

6

6

6

6

6

14

14

14

14

14

14

20

20

20

20

Time (Sec) Time (Sec)

20

20

Case 4 - 1165MW Nuclear Unit - Baseline


Case 4 - 1165MW Nuclear Unit - Final Setting0.87

0.016

2

0.98

WATTS

TEST OUT

PSS OUT

GEN TERM F

POSTLIM OUT

GEN TERM V

0.86

0.006

10

2

0

0.97

0.85

0.002

0

- 2

-2

0.865

0.008

15

4

1

0.975

0.855

0.004

5

0

-1

0.965

0.845

0

-5

- 4

0

0

0

0

0

0

x10-4

x10-3

x10-3

8

8

8

8

8

8

4

4

4

4

4

4

12

12

12

12

12

12

18

18

18

18

18

18

2

2

2

2

2

2

10

10

10

10

10

10

16

16

16

16

16

16

6

6

6

6

6

6

14

14

14

14

14

14

20

20

20

20

Time (Sec) Time (Sec)

20

200.96


Case 5 –

SCT/PPT Phase

Compensation

Requirements

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

0.1 1 10

53 MW41 MW28 MW14 MW7 MWstabilizer phase compensation

Frequency (Hz)

Pha

se

(de

gre

es)


Case 5:

On-Line Step

Test

with PSS Off

59.99

60.00

60.01

60.02

Ge

n F

req

(Hz)

0

80

160

240

Fie

ld

(Vd

c)

250

270

290

310

330

0 5 10 15

Time (seconds)

Fie

ld

(Ad

c)

51

53

55

57

Active

Po

we

r

(MW

)

-12

-8

-4

0

Re

active

Po

we

r

(MV

Ar)

13.8

13.9

14.0

14.1

14.2

Te

rmin

al V

(kV

)


Case 5:

On-Line Step

Test with PSS

On

60.00

60.01

60.02

60.03

Gen

Fre

q

(Hz)

55

56

57

58

59

60

Active

Po

we

r

(MW

)

-8

-4

0

4

8

Re

active

Po

we

r

(MV

Ar)

0

50

100

150

200

250

Fie

ld

(Vd

c)

-3

-2

-1

0

1

0 5 10 15

Time (seconds)

PS

S+

Te

st

(%)

14.0

14.1

14.2

14.3

14.4

Te

rmin

al V

(kV

)


Case 6: Off-Line Step of Reference Test


Case 6: On-Line Step of Reference Test - PSS Off


Case 6: Off-Line Step of Reference Test – PSS On


Power System Stability

– A function of fast protective relaying

– PSS is used to provide damping to prevent

power system oscillations

– Provide damping via excitation control

– PSS has little effect on first swing stability, but

restores damping lost by adding high initial

response excitation systems

– Many different stabilizing schemes exist - focus

on integral of accelerating power


QUESTIONS?

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Power System Stability - Roorkee College of Engineeringrceroorkee.in/pdf/pdfo/TEE601.pdf ·...

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