small signal stability - university of idaho€¦ · · 2011-05-13small signal stability aaron...
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![Page 1: 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](https://reader030.vdocuments.net/reader030/viewer/2022020315/5ae2db337f8b9a7b218c63b0/html5/thumbnails/1.jpg)
Masters of Engineering
Small Signal Stability
Aaron CowanElectrical Engineering
Power
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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
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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
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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
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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
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Exciter Models
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Exciter Models
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Exciter Models
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PSS Model
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IEEE 421.2
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SMIB – Power World
l{• Equivalent SMIB• State Matrix• Eigenvalues
{• Eigenvalues
{
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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
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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
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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
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Generator 1
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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
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Generator 2
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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
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Generator 3
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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
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Summary
• Power World Transient StabilityBlock Diagrams– Block Diagrams
– SMIB EigenvaluesESDC1A ith t PSS• ESDC1A without PSS
• SEXS_GE with PSS• PSS stability enhancement
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Small Signal Stability
Questions?
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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
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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
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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
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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
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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
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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