ECEN 667
Power System Stability
1
Lecture 6: Transient Stability Intro,
Synchronous Machine Models
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
Texas A&M University
Announcements
• Read Chapter 3, skip 3.7 for now
• Homework 2, which is posted on the website, is due on
Thursday Sept 21
2
WSCC Case One-line
3
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 Mvar
Bus 6
90 MW
30 Mvar
1.026 pu1.025 pu
0.996 pu
1.016 pu
1.032 pu 1.025 pu
1.013 pu
1.026 pu
1.040 pu
The initial contingency
is to trip the generator
at bus 3. Select
Run Transient Stability
to get the results.
Generator Governors
• Governors are used to control the generator power
outputs, helping the maintain a desired frequency
• Covered in sections 4.4 and 4.5
• As was the case with machine models and exciters,
governors can be entered using the Generator Dialog.
• Add TGOV1 models for all three generators using the
default values.
4
Additional WSCC Case Changes
• Use the “Add Plot” button on the plot designer to insert
new plots to show 1) the generator speeds, and 2) the
generator mechanical input power.
• Change contingency to be the opening of the bus 3
generator at time t=1 second. There is no “fault” to be
cleared in this example, the only event is opening the
generator. Run case for 20 seconds.
• Case Name: WSCC_9Bus_WithGovernors
5
Generator Angles on Different
Reference Frames
6
Synchronous Reference
Frame
Average of Generator Angles
Reference Frame
Both are equally “correct”, but it is much easier
to see the rotor angle variation when using the
average of generator angles reference frame
Plot Designer with New Plots
7
Note that when new plots are added using “Add Plot”, new Folders
appear in the plot list. This will result in separate plots for each group
Gen 3 Open Contingency Results
8
The left figure shows the generator speed, while the right figure
shows the generator mechanical power inputs for the loss of
generator 3. This is a severe contingency since more than 25% of
the system generation is lost, resulting in a frequency dip of almost
one Hz. Notice frequency does not return to 60 Hz.
Mech Input_Gen Bus 2 #1gfedcb Mech Input_Gen Bus 3 #1gfedcbMech Input_Gen Bus1 #1gfedcb
Time (Seconds)20191817161514131211109876543210
Me
ch
an
ica
l P
ow
er
(MW
)
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
Speed_Gen Bus 2 #1gfedcb Speed_Gen Bus 3 #1gfedcb Speed_Gen Bus1 #1gfedcb
Time (Seconds)20191817161514131211109876543210
Sp
ee
d (
Hz)
60
59.95
59.9
59.85
59.8
59.75
59.7
59.65
59.6
59.55
59.5
59.45
59.4
59.35
59.3
59.25
59.2
59.15
59.1
59.05
WSCC Frequency Recovery
• Notice that the frequency does not recovery exactly to
60 Hz; this is because of the governor “droop”
characteristic
– Full recovery is done in
interconnected systems
using AGC
– Isochronous governors
recover to a constant
frequency for stand-
alone systems
9
Load Modeling
10
• The load model used in transient stability can have a
significant impact on the results
• By default PowerWorld uses constant impedance models
but makes it very easy to add more complex loads.
• The default (global) models are specified on the Options,
Power System Model page.
These models
are used only
when no other
models are
specified.
Load Modeling
• More detailed models are added by selecting “Stability
Case Info” from the ribbon, then Case Information,
Load Characteristics Models.
• Models can be specified for the entire case (system), or
individual areas, zones, owners, buses or loads.
• To insert a load model click right click and select insert
to display the Load Characteristic Information dialog.
11
Right click
here to get
local menu and
select insert.
Dynamic Load Models
• Loads can either be static or dynamic, with dynamic
models often used to represent induction motors
• Some load models include a mixture of different types
of loads; one example is the CLOD model represents a
mixture of static and dynamic models
• Loads models/changed in PowerWorld using the Load
Characteristic Information Dialog
• Next slide shows voltage results for static versus
dynamic load models
• Case Name: WSCC_9Bus_Load
12
WSCC Case Without/With
Complex Load Models
• Below graphs compare the voltage response following a
fault with a static impedance load (left) and the CLOD
model, which includes induction motors (right)
13
V (pu)_Bus Bus 2gfedcb V (pu)_Bus Bus 3gfedcb V (pu)_Bus Bus 4gfedcbV (pu)_Bus Bus 5gfedcb V (pu)_Bus Bus 6gfedcb V (pu)_Bus Bus 7gfedcbV (pu)_Bus Bus 8gfedcb V (pu)_Bus Bus 9gfedcb V (pu)_Bus Bus1gfedcb
109876543210
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
V (pu)_Bus Bus 2gfedcb V (pu)_Bus Bus 3gfedcb V (pu)_Bus Bus 4gfedcbV (pu)_Bus Bus 5gfedcb V (pu)_Bus Bus 6gfedcb V (pu)_Bus Bus 7gfedcbV (pu)_Bus Bus 8gfedcb V (pu)_Bus Bus 9gfedcb V (pu)_Bus Bus1gfedcb
109876543210
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Under-Voltage Motor Tripping
• In the PowerWorld CLOD model, under-voltage motor
tripping may be set by the following parameters
– Vi = voltage at which trip will occur (default = 0.75 pu)
– Ti (cycles) = length of time voltage needs to be below Vi
before trip will occur (default = 60 cycles, or 1 second)
• In this example change the tripping values to 0.8 pu and
30 cycles and you will see the motors tripping out on
buses 5, 6, and 8 (the load buses) – this is especially
visible on the bus voltages plot. These trips allow the
clearing time to be a bit longer than would otherwise be
the case.
• Set Vi = 0 in this model to turn off motor tripping. 14
Composite Load Model
• General trend is towards more complex load models,
sometimes with more than 100 parameters!
15
The composite
load model
includes up to
four motors,
other loads, and
a simple
distribution
system (with
an LTC)
37 Bus System
• Next we consider a slightly larger, 9 generator, 37 bus
system. To view this system open case GOS_37Bus.
The system one-line is shown below.
16
To see summary
listings of the
transient stability
models in this case
select “Stability
Case Info” from the
ribbon, and then
either “TS Generator
Summary” or “TS
Case Summary”
slack
SLACK345
SLACK138
RAY345
RAY138
RAY69
FERNA69
A
MVA
DEMAR69
BLT69
BLT138
BOB138
BOB69
WOLEN69
SHIMKO69
ROGER69
UIUC69
PETE69
HISKY69
TIM69
TIM138
TIM345
PAI69GROSS69
HANNAH69
AMANDA69
HOMER69
LAUF69
MORO138
LAUF138
HALE69
PATTEN69
WEBER69
BUCKY138
SAVOY69
SAVOY138
JO138JO345
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.02 pu
1.02 pu
1.03 pu
1.03 pu
1.00 pu
1.00 pu
1.00 pu
1.00 pu
1.01 pu
1.01 pu
1.00 pu
1.01 pu
1.01 pu
1.01 pu1.01 pu
1.03 pu
1.01 pu
1.01 pu
1.02 pu
1.01 pu
1.00 pu
1.01 pu
1.02 pu
1.01 pu
1.01 pu
1.01 pu
1.01 pu 1.00 pu
1.01 pu
1.01 pu1.02 pu
1.02 pu 1.03 pu
A
MVA
1.02 pu
A
MVA
A
MVA
LYNN138
A
MVA
1.02 pu
A
MVA
1.00 pu
A
MVA
75 MW
49 Mvar
23 MW
7 Mvar
23 MW
6 Mvar
140 MW
45 Mvar
74 MW
27 Mvar
12 MW
5 Mvar
150 MW
-2 Mvar
56 MW
13 Mvar
15 MW
5 Mvar
38 MW
4 Mvar
23 MW
3 Mvar
58 MW
36 Mvar
36 MW
10 Mvar
10 MW
5 Mvar
22 MW
15 Mvar
60 MW
12 Mvar
150 MW
-14 Mvar
23 MW
7 Mvar
33 MW
13 Mvar 16.0 Mvar
18 MW
5 Mvar
58 MW
40 Mvar 45 MW
12 Mvar
18.2 Mvar
27 MW
3 Mvar
14 MW
3 Mvar
23 MW
6 Mvar 28 MW
6 Mvar
4.8 Mvar
7.3 Mvar
12.8 Mvar
29.1 Mvar
7.3 Mvar
0.0 Mvar
75 MW
35 Mvar
20 MW
6 Mvar
150 MW
-2 Mvar
17 MW
3 Mvar
16 MW
-14 Mvar 14 MW
4 Mvar
Transient Stability Case and Model
Summary Displays
17
Right click on a line
and select “Show
Dialog” for more
information.
37 Bus Case Solution
18
Speed_Gen WEBER69 #1gfedcb Speed_Gen JO345 #1gfedcbSpeed_Gen JO345 #2gfedcb Speed_Gen SLACK345 #1gfedcbSpeed_Gen LAUF69 #1gfedcb Speed_Gen BOB69 #1gfedcbSpeed_Gen ROGER69 #1gfedcb Speed_Gen BLT138 #1gfedcbSpeed_Gen BLT69 #1gfedcb
20191817161514131211109876543210
60
59.98
59.96
59.94
59.92
59.9
59.88
59.86
59.84
59.82
59.8
59.78
59.76
59.74
59.72
59.7
59.68
59.66
59.64
59.62
59.6
Graph
shows the
generator
frequency
response
following
the loss
of one
generator
Stepping Through a Solution
• Simulator provides functionality to make it easy to see
what is occurring during a solution. This functionality
is accessed on the States/Manual Control Page
19
Run a Specified Number of Timesteps or Run
Until a Specified Time, then Pause.
See detailed results
at the Paused Time
Transfer results
to Power Flow
to view using
standard
PowerWorld
displays and
one-lines
Synchronous Machine Modeling
• Electric machines are used to convert mechanical
energy into electrical energy (generators) and from
electrical energy into mechanical energy (motors)
– Many devices can operate in either mode, but are usually
customized for one or the other
• Vast majority of electricity is generated using
synchronous generators and some is consumed using
synchronous motors, so that is where we'll start
• Much literature on subject, and sometimes overly
confusing with the use of different conventions and
nominclature
20
3 bal. windings (a,b,c) – stator
Field winding (fd) on rotor
Damper in “d” axis
(1d) on rotor
2 dampers in “q” axis
(1q, 2q) on rotor
21
Synchronous Machine Modeling
Two Main Types of Synchronous
Machines
• Round Rotor
– Air-gap is constant, used with higher speed machines
• Salient Rotor (often called Salient Pole)
– Air-gap varies circumferentially
– Used with many pole, slower machines such as hydro
– Narrowest part of gap in the d-axis and the widest along the
q-axis
22
Rotating Magnetic Field Demo
23
Dq0 Reference Frame
• Stator is stationary, rotor is rotating at synchronous
speed
• Rotor values need to be transformed to fixed reference
frame for analysis
• Done using Park's transformation into what is known as
the dq0 reference frame (direct, quadrature, zero)
– Parks’ 1929 paper voted 2nd most important power paper of
20th century (1st was Fortescue’s sym. components paper)
• Convention used here is the q-axis leads the d-axis
(which is the IEEE standard)
– Others (such as Anderson and Fouad) use a q-axis lagging
convention 24
11 1 1
11 1 1
22 2 2
fdfd fd fd
dd d d
qq q q
qq q q
dv i r
dt
dv i r
dt
dv i r
dt
dv i r
dt
Kirchhoff’s Voltage Law, Ohm’s Law, Faraday’s
Law, Newton’s Second Law
aa a s
bb b s
cc c s
dv i r
dt
dv i r
dt
dv i r
dt
shaft 2
2m e f
d
dt P
dJ T T T
P dt
Stator Rotor Shaft
25
Fundamental Laws
