Embed Size (px)
Citation preview
Masters of Engineering
Small Signal Stability
Aaron CowanElectrical Engineering
Power
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
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
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 =
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
Exciter Models
Exciter Models
Exciter Models
PSS Model
IEEE 421.2
SMIB – Power World
• Equivalent SMIB• State Matrix• Eigenvalues{
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
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
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
Generator 1
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 °
Generator 2
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 °
Generator 3
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 °
Summary
• Power World Transient Stability– Block Diagrams– SMIB Eigenvalues
• ESDC1A without PSS• SEXS_GE with PSS• PSS stability enhancement
Small Signal Stability
Questions?
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
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
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
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
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
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
