masters of engineering small signal stability aaron cowan electrical engineering power
Post on 19-Dec-2015
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![Page 1: Masters of Engineering Small Signal Stability Aaron Cowan Electrical Engineering Power](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d2e5503460f94a04f9a/html5/thumbnails/1.jpg)
Masters of Engineering
Small Signal Stability
Aaron CowanElectrical Engineering
Power
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Small Signal Stability
• Exciter– Field current– Terminal voltage
• Power System Stabilizer– Enhance stability– Rotor angle
• Equal Area Criterion (Fig 13.5, Kundur)– Aa < Ad
– Aa > Ad
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SMIB Example
delta _wr
delta _deltadelta _Tedelta _Psi_fd
v_s
v_1
delta _E_t
V_refw_0/s
Voltage Transducer
1
T_R.s+1
1
2*Hs+K_D
PSS
delta_wrv _s
K_6
K_5
K_4
K_2
K_1
1s
Field Circuit
K_3
T_3.s+1Exciter
K_AV_ref
delta _Tm
Problem details in section 12.3 of Power System Stability and Control, Kundur
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Results
Matlabωd = 1.21Hzξ = 0.1447KS = 1.1062KD = 15.6306
Kundurωd = 1.05Hzξ = 0.15KS = 0.829KD = 14.08
State Matrix and eigenvalues agree
[0 −0.109 −0.123 0 0 0
376.99 0 0 0 0 00 −0.193 −0.4229 −27.317 0 27.3170 −7.312 20.839 −50 0 00 −1.037 −1.173 0 −0.714 00 −4.840 −5.477 0 26.969 −30.303
][Δ𝜔𝑟Δ𝛿Δ𝜓 𝑓𝑑Δ𝜈1Δ𝜈2Δ𝜈𝑠
]A =
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Power World Transient Stability
slack
Bus1
72 MW 27 Mvar
Bus 4
Bus 5
125 MW 50 Mvar
Bus 2
163 MW 7 Mvar
Bus 7 Bus 8 Bus 9 Bus 3
85 MW -11 Mvar
100 MW
35 MvarBus 6
90 MW
30 Mvar
1.026 pu1.025 pu
0.996 pu
1.016 pu1.032 pu 1.025 pu
1.013 pu
1.026 pu
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
• Equivalent SMIB• State Matrix• Eigenvalues{
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Power World Transient Stability
slack
Bus1
72 MW 27 Mvar
Bus 4
Bus 5
125 MW 50 Mvar
Bus 2
163 MW 7 Mvar
Bus 7 Bus 8 Bus 9 Bus 3
85 MW -11 Mvar
100 MW
35 MvarBus 6
90 MW
30 Mvar
1.026 pu1.025 pu
0.996 pu
1.016 pu1.032 pu 1.025 pu
1.013 pu
1.026 pu
1.040 pu
WECC equivalent in Power World
![Page 13: Masters of Engineering Small Signal Stability Aaron Cowan Electrical Engineering Power](https://reader036.vdocument.in/reader036/viewer/2022062421/56649d2e5503460f94a04f9a/html5/thumbnails/13.jpg)
Stability Simulation
• Default values used– 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 7-5– Both breakers open– Cleared in 0.07 sec
• 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 1
MW Terminal_Gen '1' '1'gfedcb
2520151050-5-10-15-20-25-30-35-40
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
MW vs. Rotor Angle Generator 1
MW Terminal_Gen '1' '1'gfedcb
20151050-5-10-15-20-25-30-35-40
240
220
200
180
160
140
120
100
80
60
40
20
0
-20
𝑀𝑊 0=71.6 𝛿0=3.5° 𝑀𝑊 𝑐𝑙𝑒𝑎𝑟=70.6 𝛿𝑐𝑙𝑒𝑎𝑟=−5.3 °
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Generator 2
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Generator 2: ESDC1A
MW vs. Rotor Angle Generator 2
MW Terminal_Gen '2' '1'gfedcb
100959085807570656055
210
200
190
180170
160
150
140
130120
110
100
90
8070
60
50
40
3020
10
0
MW vs. Rotor Angle Generator 2
MW Terminal_Gen '2' '1'gfedcb
100959085807570656055
220210200190180170160
1501401301201101009080706050403020100
𝑀𝑊 0=163 𝛿0=61.1° 𝑀𝑊 𝑐𝑙𝑒𝑎𝑟=163 𝛿𝑐𝑙𝑒𝑎𝑟=70.7 °
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Generator 3
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Generator 3: SEXS_GE
MW vs. Rotor Angle Generator 3
MW Terminal_Gen '3' '1'gfedcb
6059585756555453525150494847
100
95
90
85
80
75
70
65
60
55
50
45
MW vs. Rotor Angle Generator 3
MW Terminal_Gen '3' '1'gfedcb
5958575655545352515049
95
90
85
80
75
70
65
60
55
50
45
𝑀𝑊 0=85 𝛿0=54.1 ° 𝑀𝑊 𝑐𝑙𝑒𝑎𝑟=85 𝛿𝑐𝑙𝑒𝑎𝑟=51.9 °
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Summary
• Power World Transient Stability– Block Diagrams– SMIB Eigenvalues
• 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 Terminal_Gen '1' '1'gfedcb
151050-5-10-15-20-25-30-35-40-45
170
160
150
140
130
120
110
100
90
80
70
6050
40
30
20
10
0
-10
-20
-30
MW vs. Rotor Angle Generator 1
MW Terminal_Gen '1' '1'gfedcb
151050-5-10-15-20-25-30-35-40-45
200
180
160
140
120
100
80
60
40
20
0
-20
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Generator 1: SEXS_GE
MW vs. Rotor Angle Generator 1
MW Terminal_Gen '1' '1'gfedcb
20151050-5-10-15-20-25-30
180
160
140
120
100
80
60
40
20
0
-20
MW vs. Rotor Angle Generator 1
MW Terminal_Gen '1' '1'gfedcb
1614121086420-2-4-6-8-10-12-14-16-18-20-22-24-26-28-30
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
-10
-20
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Generator 2: ESAC1A
MW vs. Rotor Angle Generator 2
MW Terminal_Gen '2' '1'gfedcb
989694929088868482807876747270686664626058565452504846
210
200
190180
170
160
150140
130
120
110100
90
80
7060
50
40
3020
10
0
MW vs. Rotor Angle Generator 2
MW Terminal_Gen '2' '1'gfedcb
95908580757065605550
2202102001901801701601501401301201101009080706050403020100
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Generator 2: SEXS_GE
MW vs. Rotor Angle Generator 2
MW Terminal_Gen '2' '1'gfedcb
908886848280787674727068666462605856545250
220
210200
190180
170160
150140
130120
110100
9080
7060
5040
3020
100
MW vs. Rotor Angle Generator 2
MW Terminal_Gen '2' '1'gfedcb
90888684828078767472706866646260585654
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
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Generator 3: ESDC1A
MW vs. Rotor Angle Generator 3
MW Terminal_Gen '3' '1'gfedcb
64636261605958575655545352515049
100
95
90
85
80
75
70
65
60
55
50
45
MW vs. Rotor Angle Generator 3
MW Terminal_Gen '3' '1'gfedcb
646362616059585756555453525150494847
105
100
95
90
85
80
75
70
65
60
55
50
45
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Generator 3: ESAC1A
MW vs. Rotor Angle Generator 3
MW Terminal_Gen '3' '1'gfedcb
6160595857565554535251504948474645
100
95
90
85
80
75
70
65
60
55
50
45
MW vs. Rotor Angle Generator 3
MW Terminal_Gen '3' '1'gfedcb
61605958575655545352515049484746
105
100
95
90
85
80
75
70
65
60
55
50
45