Small Signal Stability - University of Idaho€¦ ·  · 2011-05-13Small Signal Stability Aaron Cowan Electrical Engineering ... Problem details in section 12.3 of Power System Stability

Masters of Engineering

Small Signal Stability

Aaron CowanElectrical Engineering

Power

Small Signal Stability

• ExciterField current– Field current

– Terminal voltageP S t St bili• Power System Stabilizer– Enhance stability– Rotor angle

• Equal Area Criterion (Fig 13.5, Kundur)g– Aa < Ad

– Aa > Ada d

SMIB Example

PSS

delta_wrv _s

delta _deltadelta _Tedelta _Psi_fd

v_s

1

K_4

K 21K_3

K AV ref

delta _Tm

delta _wr

v_1V_ref

w_0/s2*Hs+K_D

K_6

K_2

K_1

s

Field Circuit

T_3.s+1Exciter

K_AV_ref

delta _E_t

Voltage Transducer

1

T_R.s+1K_5

Problem details in section 12.3 of Power System Stability and Control, Kundur

Results

Matlabωd = 1.21Hz

Kundurωd = 1.05Hz dωd 1.21Hz

ξ = 0.1447KS = 1.1062K 15 6306

ωd 1.05Hzξ = 0.15KS = 0.829K 14 08

State Matrix and eigenvalues agree

KD = 15.6306KD = 14.08

A   

Power World Transient Stability

Bus 2

163 MW

Bus 7 Bus 8 Bus 9 Bus 3

85 MW1.016 pu

Bus 5

163 MW 7 Mvar

85 MW -11 Mvar

100 MW 35 Mvar

Bus 6

1.026 pu1.025 pu

0.996 pu

1.032 pu 1.025 pu

1.013 pu

Bus 4

125 MW 50 Mvar

90 MW 30 Mvar

1.026 pu

slack

Bus1

72 MW 27 Mvar

1.040 pu

WECC equivalent in Power World

Exciter Models

Exciter Models

Exciter Models

PSS Model

IEEE 421.2

SMIB – Power World

l{• Equivalent SMIB• State Matrix• Eigenvalues

{• Eigenvalues

{

Power World Transient Stability

Bus 2

163 MW

Bus 7 Bus 8 Bus 9 Bus 3

85 MW1.016 pu

Bus 5

163 MW 7 Mvar

85 MW -11 Mvar

100 MW 35 Mvar

Bus 6

1.026 pu1.025 pu

0.996 pu

1.032 pu 1.025 pu

1.013 pu

Bus 4

125 MW 50 Mvar

90 MW 30 Mvar

1.026 pu

slack

Bus1

72 MW 27 Mvar

1.040 pu

WECC equivalent in Power World

Stability Simulation

• Default values usedDid change T to 0 02 in all cases– Did change TR to 0.02 in all cases

• SEXS_GE and STAB1 ↔ Fig 17.5, Kundur• Set all generator stability models equal

– Innumerable permutations

Stability Simulation

• Fault on line 7-5Both breakers open– Both breakers open

– Cleared in 0.07 secTh f h E it• Three cases for each Exciter– Each generator

• Three cases for each Exciter+PSS– Each generator

Generator 1

Generator 1: ESAC1A

MW vs. Rotor Angle Generator 1220

200

MW vs. Rotor Angle Generator 1240

220200

180

160

140

120

100

200

180

160

140

120

10080

60

40

20

0

-20

80

60

40

20

0

-20

MW Terminal_Gen '1' '1'gfedcb

2520151050-5-10-15-20-25-30-35-40-40

MW Terminal_Gen '1' '1'gfedcb

20151050-5-10-15-20-25-30-35-40

20

Generator 2

Generator 2: ESDC1A

MW vs. Rotor Angle Generator 2210200190

MW vs. Rotor Angle Generator 2220210200190

180170160150140130120110100

200190180170160150140130120110100

9080706050403020

1101009080706050403020

MW Terminal_Gen '2' '1'gfedcb

100959085807570656055

100

MW Terminal_Gen '2' '1'gfedcb

100959085807570656055

100

Generator 3

Generator 3: SEXS_GE

MW vs. Rotor Angle Generator 3

100

MW vs. Rotor Angle Generator 3

95

95

90

85

80

75

70

90

85

80

75

7070

65

60

55

50

45

65

60

55

50

45

MW Terminal_Gen '3' '1'gfedcb

6059585756555453525150494847

45

MW Terminal_Gen '3' '1'gfedcb

5958575655545352515049

Summary

• Power World Transient StabilityBlock Diagrams– Block Diagrams

– SMIB EigenvaluesESDC1A ith t PSS• ESDC1A without PSS

• SEXS_GE with PSS• PSS stability enhancement

Small Signal Stability

Questions?

Generator 1: ESDC1A

MW vs Rotor Angle Generator 1 MW vs Rotor Angle Generator 1MW vs. Rotor Angle Generator 1170160150140130120110100

MW vs. Rotor Angle Generator 1200

180

160

140

120

9080706050403020100

100

80

60

40

20

MW Terminal_Gen '1' '1'gfedcb

151050-5-10-15-20-25-30-35-40-45

0-10-20-30

MW Terminal_Gen '1' '1'gfedcb

151050-5-10-15-20-25-30-35-40-45

0

-20

Generator 1: SEXS_GE

MW vs Rotor Angle Generator 1 MW vs Rotor Angle Generator 1MW vs. Rotor Angle Generator 1

180

160

140

120

MW vs. Rotor Angle Generator 1170160150140130120110100

100

80

60

40

20

1009080706050403020

MW Terminal_Gen '1' '1'gfedcb

20151050-5-10-15-20-25-30

0

-20

MW Terminal_Gen '1' '1'gfedcb

1614121086420-2-4-6-8-10-12-14-16-18-20-22-24-26-28-30

100

-10-20

Generator 2: ESAC1A

MW vs Rotor Angle Generator 2 MW vs Rotor Angle Generator 2MW vs. Rotor Angle Generator 2210200190180170160150140130

MW vs. Rotor Angle Generator 2220210200190180170160150140130

120110100908070605040

140130120110100908070605040

MW Terminal_Gen '2' '1'gfedcb

989694929088868482807876747270686664626058565452504846

403020100

MW Terminal_Gen '2' '1'gfedcb

95908580757065605550

403020100

Generator 2: SEXS_GE

MW vs. Rotor Angle Generator 2220210200190180170160150

MW vs. Rotor Angle Generator 2200190180170160150140

1401301201101009080706050

1301201101009080706050

MW Terminal_Gen '2' '1'gfedcb

908886848280787674727068666462605856545250

50403020100

MW Terminal_Gen '2' '1'gfedcb

90888684828078767472706866646260585654

403020100

Generator 3: ESDC1A

MW vs Rotor Angle Generator 3 MW vs Rotor Angle Generator 3MW vs. Rotor Angle Generator 3

100

95

90

85

80

MW vs. Rotor Angle Generator 3

105

100

95

90

8580

75

70

65

60

55

80

75

70

65

60

55

MW Terminal_Gen '3' '1'gfedcb

64636261605958575655545352515049

50

45

MW Terminal_Gen '3' '1'gfedcb

646362616059585756555453525150494847

50

45

Generator 3: ESAC1A

MW vs. Rotor Angle Generator 3 MW vs. Rotor Angle Generator 3100

95

90

85

80

105

100

95

90

85

8075

70

65

60

55

50

80

75

70

65

60

55

MW Terminal_Gen '3' '1'gfedcb

6160595857565554535251504948474645

50

45

MW Terminal_Gen '3' '1'gfedcb

61605958575655545352515049484746

50

45