power system stability

Power System Stability

GENERATOR CONTROL AND PROTECTION

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 Te

T

G T

M

ω


Stator, Stator, Rotor, Rotor, and and Resultant Resultant MMFs MMFs and Torque Torque Angle Angle R

F

2

A

B'

C'

C

B

F

1

A' GENERATOR CONTROL AND PROTECTION

ω

Synchronous Machine Tied to Infinite Bus ET

E HV

EO

Xg

Infinite Bus XL XT

Eg

X E =X T +X L


Steady State Electrical Power Output

Pe =

EgE T X g

sinδ


Phaso Phasorr Diag Diagram ram - Gene Generat rator or Tie Tied d to Infinite Bus

Eg jIXg δ

I

ET E0 IXE j


Transient Stability


Rubber Band Analogy Rubber Bands

Weights GENERATOR CONTROL AND PROTECTION

Change in Electrical Torque

∆Te = Ts∆δ + T D∆ω


Transient Stability Illustration PMAX

3 4 P DECEL

PM

Insufficient Retarding Torque

Stable

1

Retarding Torque

r e w o P

P ACCEL

2 0

0°

δ°

90 ° Power Angle- δ


Turbine Power Unstable, machine loses Synchronism

180 °

Effect of Fault Clearing Time Equal Area Not Possible P E

PM

Power

Unit pulls out of sync Breaker clears

Fault

δ


Effect of Fault Clearing Time Equal Area Substantial Margin Rotor decelerates due to PE max exceeding mechanical power

P E

System returns to steady state, system stable

Power

PM

Breaker clears faults

Fault

δ GENERATOR CONTROL AND PROTECTION

Equal Area substantial margin

Effect of the Excitation System on Stability


Steady State Electrical Power Output Pe =

EgE T X g

sin δ


Effect of High Initial Response Excitation System P E

B P E-A

A

Power

P E-B

Fast excitation system Maximum field forcing First swing, system recovers PM

Machine will lose synchronism

0

δ


Small Signal Stability


Change in Electrical Torque

∆Te = Ts∆δ + T D∆ω


Inter-Unit Oscillations Xg1 Eo

Eg1

1.5 - 3 He Hertz Xg2

Eg2


Local Mode Oscillations Xg

XL

Eg


Eo

.7 - 2 He Hertz

Inter-Area Oscillations <0.5 Hertz Xg1

XL

Eg1


Xg2

Eg2

Block Diagram of Generator Under Voltage Regulator Control K4

VREF

∆TM

+

Σ

Exciter

∆ E fd

G ex (s) +

-

Σ

K3

∆Ψfd

+ K2

1+sT3

∆Te -

Σ

+

Σ

+

1 2Hs +KD

Field circuit ∆v 1

K1 K6

+ 1

∆E t

1+sTR

Σ

+ K5

Voltage transducer


∆ωr

ω

∆δ 0

s

Power System Stabilizers


The "Swing Equation" 2

2 H d δ 2

ω 0 dt

= Tm − Te − K D ∆ω r


Small Signal Version of "Swing Equation"

∆Te = Ts ∆δ + T D ∆ω


Response of Speed and Angle to Small Disturbances ∆δ

Stable • PositiveT s • PositiveT D

∆ω ∆ T D

∆δ ∆ T s

0 ∆δ

∆ T e

Oscillatory ∆ω Instability • PositiveT s • NegativeT D ∆ T D

0


∆ T s

∆ T e

∆δ

PSS with AVR, Exciter and Generator ∆ωr

G P S(s) (s)

∆δ

K4 ∆vs

+ VREF

∆TM

-

+

Σ

∆ E fd

G ex (s) (s) -

+

Σ

Exciter

K3

∆Ψfd

K2

1+sT3

+

∆Te -

Σ

+

Σ

+

1 2Hs +KD ∆ω r

Field circuit

∆v 1

K1 K6

+ 1

∆E t

1+sTR

Σ

+ K5

Voltage transducer


ω0

s

∆δ


PSS Theory of Operation Speed Based Stabilizers


Speed-Based Stabilizer High-Pass Filter

Torsional Filter

Stabilizer Gain & Phase Lead

Limits Vstmax

Speed

1 1 + s T6 T6

s T5 1+sT5

1 1 + A 1 s + A2 s

2

Ks1

1 + s T1 T1 1+sT2

1 + s T3

Output

1+sT4

Vstmin


PSS Theory of Operation Dual Input Stabilizers


Small Signal Version of "Swing Equation"

∆Te = Ts ∆δ + T D ∆ω


Speed Deviation from Net Accelerating Power

d dt

∆ω r =

1

(Tm − Te − K D ∆ω r ) 2 H


Accelerating Power Based on Integral of Mechanical and Electrical Power

∆ω =

1 2 H

[∫ ∆ T m − ∫ ∆ Te ]


Block Diagram of Dual-Input Power System Stabilizer Ramp-Tracking Filter

High-Pass Filters sTw1 Freq

1 + sTw1

sTw2 1 + s Tw2

+

Σ +

N

1+sT8

+

M

(1+sT9 )

Stabilizer Gain & Phase Lead

Limits Vstmax

Σ

Ks1

1+ sT1 1+ s T2

1+sT3

Output

1+sT4

Vstmin

High-Pass Filters & Integrator Power

sTw3 1+sTw3

Ks2 1+s T7


Speed Derived from VT and CT Signals Generator

EI

I

jXqI t t

Et

d-axis

ω GENERATOR CONTROL AND PROTECTION

q-axis

Accelerating-Power Design (Speed Input) High-Pass Filters Compensated Frequency Equivalent to Rotor Speed

s Tw1 Tw1

s Tw Tw 2

1 + s Tw1

1 + s Tw Tw 2

Generator Speed Deviation Signal (i.e. no steady state component)


Integral of Electrical Power Block Diagram High-Pass Filters & Integrator

Active Power

s Tw3 1 + s Tw3

K 2 1+sT7


Integral-of-Power Deviation

Output Stage of PSS to AVR Stabilizer Gain & Phase Lea Lead Filtered Speed

Ks1 Ks1

1 + s T1 1 + s T2

Limits Vstmax

1 + s T3 1 + s T4

Output to AVR

Vstmin


Case Studies


Case Case 1 - Hydro Hydro Gene Generato ratorr witho without ut PSS

1

2

3

4

5

6

•

7

8

9

10

11

12 13 14 15

Time (seconds)


Case Case 1 - Hydr Hydro o Gen Gener erato atorr with with PSS PSS

1

2

3

4

5

•

6

7

8

9

10

11

12

Time (seconds)

• Dual Dual Input Input Stabil Stabilize izer, r, Phase Phase Lead=( Lead=(1+0 1+0.05 .05s)/ s)/(1+ (1+0.0 0.01s) 1s),, Gain=4 Gain=40 0 GENERATOR CONTROL AND PROTECTION

Case 2 - On-line On-line Step Step Respons Responsee Frequency Frequency Type PSS PSS Ks=6, 92MW Hydro Turbine Generator

A single input PSS measures only frequency, power or speed


Case 2 - On-line On-line Step Response Response Dual Dual input PSS Ks=7.5, 92MW Hydro Turbine Generator

The PSS monitors frequency and power for superior performance


Case 3 – Step Response All generators in service, Stabilizer OFF


Case 3 – Step Response All generators in service, Stabilizer Gain = 1


Case Case 4 - 1165 1165MW MW Nuc Nucle lear ar Unit Unit - Base Baseli line ne WATTS

0.875

POSTLIM OUT

1

0.87

0.5

0.865 0 0.86 -0.5

0.855 0.85 0

2

4

6

8

10

12

14

16

18

20

GEN TERM V

0.975

-1

0

2

4

6

8

10

12

14

16

18

20

14

16

18

20

14

16

18

20

PSS OUT

0.01 0.008

0.97

0.006 0.004

0.965

0.002 0.96 0 -1.5

2

4

6

8

10

12

14

16

18

20

GEN TERM F

x10-4

0 0

0.008

-2.5

0.006

-3

0.004

-3.5

0.002

-4 2

4

6

8

10 12 Time (Sec)

4

6

14

16

18

20

8

10

12

TEST OUT

0.01

-2

0

2

0 0

2

4

6

8


10 12 Time (Sec)

Case Case 4 - 1165 1165MW MW Nucl Nuclea earr Uni Unitt - Final Final Se Sett ttin ing g -3

WATTS

0.87

2

0.865

POSTLIM OUT

x10

1

0.86 0 0.855 -1

0.85 0.845 0

2

4

6

8

10

12

14

16

18

20

-2 0

10

0.97

5

0.965

0

6

0

2

4

6

x10-4

8

10

12

14

16

18

20

0

2

4

6

2

0.006

0

0.004

-2

0.002 4

6

8

10 12 Time (Sec)

14

16

18

20

12

14

16

18

20

8

10

12

14

16

18

20

14

16

18

20

TEST OUT

0.01

2

10

PSS OUT

GEN TERM F 0.008

0

8

-5

4

-4

6

15

0.975

0.96

4

x10-3

GEN TERM V

0.98

2

0 0

2

4

6

8

10 12 Time (Sec)


Case 5 – SCT/PPT Phase Compensation Requirements

300 30 0 280 28 0 260 26 0

53 MW 41 MW 28 MW 14 MW 7 MW stabilizer phase compensation

240 24 0 220 22 0 200 20 0 180 18 0 ) s e e r 16 0 g 160 e d ( e 14 0 s 140 a h P 120 12 0 100 10 0 80 60 40 20 0 0.1

1 Frequency (Hz)


10

Case 5: On-Line Step Test with PSS Off

14.2 V 14.1 l a ) n V i k 14.0 m r ( e 13.9 T

13.8 57 r e w ) 55 o P W e M v ( 53 i t c A 51 r 0 e w o ) r -4 P A e V v i t M -8 c ( a e R -12

60.02 q e ) 60.01 r F z H n ( e 60.00 G

59.99 240 160 d ) c l e d i V F ( 80 0 330 310 d ) c l e d 290 i A F ( 270 250

0

5

10 Time (seconds)


15

Case 5: On-Line Step Test with PSS On

14.4 V 14.3 l a ) n V 14.2 i k m r ( e 14.1 T 14.0 r e w ) o P W e ( v M i t c A

60 59 58 57 56 55

r 8 e w 4 o ) r P A e V 0 v i t M c ( -4 a e R -8

60.03 q e ) 60.02 r F z H n ( e 60.01 G

60.00 250 200 d ) c 150 l e d i V 100 F ( 50 0 1 t s 0 e T ) + % -1 S ( S -2 P -3

0

5

10 Time (seconds)


15

Case 6: Off-Line Step of Reference Test


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


Case 6: Off-Lin Off-Linee Step Step of Refer Reference ence Test Test – PSS On On


Power System Stability – A funct function ion of of fast fast protec protectiv tivee relayi relaying ng – PSS is used used to provide provide damping damping to to preve prevent nt power system oscillations – Provi Provide de dampi damping ng via via excita excitatio tion n contr control ol – PSS has has little little effect effect on first first swing swing stabilit stability, y, but but restores damping lost by adding high initial response excitation systems – Many Many differ different ent stabil stabilizi izing ng schem schemes es exist exist - focus focus on integral of accelerating power


QUESTIONS?


power system stability

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