dynamic grid equivalent with rei method
TRANSCRIPT
Dynamic grid equivalent with REI method
Josef Stadler
Sep 4th 2012
Overview
2
Motivation
Ward vs. REI Method
REI Method on “Kundur’s Two Area System”
Outlook
Dynamic grid equivalent with REI method
Motivation
3
Power systems increase in size and complexity
For research: Small area of interest
Internal or study system
Remaining part o External system
o Frontier or border buses
Static network reduction Ward
REI (Radial, Equivalent, Independent)
Dynamic network reduction Heuristic approach
Modal analysis approach
Coherency approach o REI
Dynamic grid equivalent with REI method
Ward vs. REI
4 Dynamic grid equivalent with REI method
Ward
Reduced generators and loads are located at the border buses
Reduced generators and loads represent certain load status
No way to keep single machine characteristics
REI (Radial, equivalent, Independent)
Transform external system into a passive network:
Insert a lossless REI Network
Radial, fictitious lines
Loads and generation are aggregated on a new bus
Characteristic of single machine can be preserved
Kundur‘s „two area system“ Source: P. Kundur, Power System Stability and Control
5 Dynamic grid equivalent with REI method
G1 – G2: S = 900 MVA; Xd = 1.8; Xd‘ = 0.3; D = 15; H = 6.5
G3 – G4: S = 900 MVA; Xd = 1.8; Xd‘ = 0.3; D = 15; H = 6.175
Loads: Bus 7: PL7 = 967 MW; QL7 = 100 MVar; QC7 = 200 MVar;
Bus 9: PL9 = 1767 MW; QL9 = 100 MVar; QC9 = 350MVar;
Transformer: 20 kV / 230 kV; S = 900 MVA; Z = 0 + j0.15
Lines: (0.0001 + j0.001) pu/km
REI Method on Kundur‘s „Two Area System"
6 Dynamic grid equivalent with REI method
1 5 6 7 8 9 10 11 3
2 4
internal buses
border bus
external buses
REI Method on Kundur‘s „Two Area System"
7 Dynamic grid equivalent with REI method
1 5 6 7 8 9 10 11 3
2 4 G
R
~
Reduced network
8 Dynamic grid equivalent with REI method
1 3 4 5 6 7 8 R
2
Comparison load flow results
9 Dynamic grid equivalent with REI method
bus Original network Reduced network
|Un| in pu Ang(Un) in ° |Un| in pu Ang(Un) in °
1 1,030 0,00 1,030 0,00
2 1,010 -9,84 1,010 -9,92
3 1,030 -28,00
4 1,010 -38,23
5 1,004 -6,49 1,003 -6,52
6 0,973 -16,66 0,970 -16,76
7 0,952 -25,18 0,946 -25,36
8 0,931 -39,44 0,918 -39,93
9 0,962 -53,52 0,950 -54,44
10 0,978 -45,01 0,968 -45,74
11 1,006 -34,64
R 1,021 -33,70
Parameter for the equivalent generator
10 Dynamic grid equivalent with REI method
Distribution participation factor:
𝑃𝐹𝑖 = 𝑅𝑒𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑝𝑒𝑟 𝑟𝑎𝑑𝑖𝑎𝑙 𝑓𝑖𝑐𝑡𝑖𝑡𝑜𝑢𝑠 𝑙𝑖𝑛𝑒 𝑖
𝑡𝑜𝑡𝑎𝑙 𝑎𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑤𝑒𝑟 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟 𝑖
Power base
𝑆𝑁𝑔 = 𝑃𝐹𝑖 ∙ 𝑆𝑁𝑖𝑖
Inertia
𝐻𝑔 =1
𝑆𝑁𝑔 𝑃𝐹𝑖 ∙ 𝐻𝑖 ∙ 𝑆𝑁𝑖𝑖
Synchronous reactance
𝑋𝑑𝑔 =1
𝐻𝑔 𝐻𝑖 ∙ 𝑋𝑑𝑖𝑖
Source: F. Milano, K. Srivastava, Dynamic REI equivalents for short circuit and transient stability analyses
Dynamic simulation
11 Dynamic grid equivalent with REI method
Only motion equations of synchronous generators
No AVR
No PSS
𝜔𝐸
𝜗𝐸 =
−𝐷
𝑇−
𝐾
𝑇
𝜔𝑛 0∙𝜔𝐸
𝜗𝐸 Δ𝑃𝐸 = 𝐾 ∙ 𝜗𝐸
𝐾 calculated with DC load flow
Numerical integration with second-order Runge-Kutta method
Comparison: unreduced generators
12 Dynamic grid equivalent with REI method
0 1 2 3 4 5 6 7 8 9 10-34
-32
-30
-28
-26
-24
-22
-20
-18
-16
original: generator 1
t in s
an
gle
in
de
gre
es
0 1 2 3 4 5 6 7 8 9 10-34
-32
-30
-28
-26
-24
-22
-20
-18
-16
reduced: generator 1
t in s
an
gle
in
de
gre
es
0 1 2 3 4 5 6 7 8 9 10-42
-41
-40
-39
-38
-37
-36
-35
-34
-33
-32
original: generator 2
t in s
an
gle
in
de
gre
es
0 1 2 3 4 5 6 7 8 9 10-43
-42
-41
-40
-39
-38
-37
-36
-35
-34
-33
reduced: generator 2
t in s
an
gle
in
de
gre
es
Modal analysis
13 Dynamic grid equivalent with REI method
Original:
Reduced:
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
mode shape: 0.96156 Hz
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
mode shape: 0.93936 Hz
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
mode shape: 0.62045 Hz
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
mode shape: 0.61608 Hz
0.5
1
30
210
60
240
90
270
120
300
150
330
180 0
mode shape: 1.0136 Hz
1
2
3
1
2
3
4
Comparison: reduced generators with equivalent generator
14 Dynamic grid equivalent with REI method
0 1 2 3 4 5 6 7 8 9 10-56
-54
-52
-50
-48
-46
-44
original: generator 3
t in s
an
gle
in
de
gre
es
0 1 2 3 4 5 6 7 8 9 10-62
-60
-58
-56
-54
-52
-50
reduced: equivalent generator
t in s
an
gle
in
de
gre
es
0 1 2 3 4 5 6 7 8 9 10-70
-68
-66
-64
-62
-60
-58
-56
-54
-52
original: generator 4
t in s
an
gle
in
de
gre
es
Outlook
15 Dynamic grid equivalent with REI method
Appliance on a major grid
> 1 REI networks
> 1 equivalent machine
E.g. UK Matlab model derived from public data by Herwig
Reduction with retaining one or more important machines
parameterization with WAMS data
Including dynamic loads
Reduction including control units of the machines
AVR
PSS
