ECE 576 – Power System
Dynamics and Stability
Lecture 24: Renewable Energy Modeling
Prof. Tom Overbye
University of Illinois at Urbana-Champaign
overbye@illinois.edu
1
Announcements
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Read Chapter 8
Homework 7 is due today
Homework 8 will be assigned April 29; should be
completed before final but need not be turned in
2
Global Wind Flow Visualization
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Below is an interesting visualization of the global winds
(thanks to Kenta for this link)
http://earth.nullschool.net/#current/wind/isobaric/1000h
Pa/orthographic=-39.01,24.31,333
3
Type 1 Models
•
Type 1 models are just represented by an induction
machine, with possible pitch control
– Usually represent older wind turbines
– No voltage control – just an induction generator
– Below is a one mass turbine model
Quite similar
to a synchronous generator
swing equation
4
Type 1 Models
•
Below is a pseudo-governor model, modeling the
change in the mechanical power input to the induction
machine model
Modified to add non-windup limit on Ki
5
Type 1 Model Initialization
•
The initialization of the Type 1 models in the transient
stability is very similar to what is done with induction
motors
– P, Q and terminal voltages are inputs from the power flow
– Slip is calculated, with an additional capacitor used to make
up the reactive power difference
– Slip is used to calculate the reference speed, with the slip
usually negative, and hence the speed greater than
synchronous
– Pmech is greater than Pelec because of the rotor losses
6
Type 1 Model Results
•
Wind turbine models will be demonstrated with the
nine bus WSCC case with generator 3 represented as a
wind turbine
Fault is
on the
line from
9 to 6,
right at
bus 6;
cleared by
opening the
line
7
Type 1 Model Results
•
Below graphs plot the generator 3 electrical and
mechanical power, and slip
100
95
1.03
90
1.028
85
1.026
Mechanical Power (MW)
80
75
1.024
70
1.022
65
60
1.02
55
1.018
50
45
1.016
40
1.014
35
30
1.012
25
20
1.01
15
1.008
10
1.006
5
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Time (Seconds)
b
c
d
e
f
g
Mech Input_Gen Bus 3 #1 g
b
c
d
e
f
16
17
18
19
20
0
1
2
3
4
5
b
c
d
e
f
g
6
7
8
9
10
11
12
13
14
15
16
17
18
19
States of Governor\TurbineSpeed, Gen Bus 3 #1
MW_Gen Bus 3 #1
8
20
Governor and Inertia
Response Comments
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•
•
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Type 1 and 2 wind turbines have standard inertia
response
They can always provide governor response if the
frequency is too high by increasing the blade pitch to
reduce their power output (except if the pitch angle is at
its maximum)
They cannot provide addition sustained power if they
are already at maximum power
– Similar to other types of generators
Commonly WTGs are operated at maximum power
since their "fuel" is free
9
Type 2 Wind Turbines
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•
•
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As the wind speed varies, the speed of the induction
machine wind turbines also varies
Type 2 models improve on the Type 1 design by
varying the rotor resistance to achieve output power
control
Image shows how
torque-speed curve
varies with changing
rotor resistance
Example Type 2 is a
Vestas v63
Image Source: www.uwig.org:8080/index.php?title=Modeling_of_Type_2_Wind_Turbine_Generators
10
Type 2 Rotor Resistance Control
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In the WT2E model the speed and electrical input are
used to adjust the induction machine rotor resistance
Output is Rext (i.e., the external resistance)
11
Type 2 Model Results
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Previous example is modified to represent generator 3
using a Type 2 model; same fault
Below graph shows the variation in Rext
Gen Bus 3 #1 States of Exciter\Rexternal
0.041
0.0405
0.04
Gen Bus 3 #1 States of Exciter\Rexternal
•
0.0395
0.039
0.0385
0.038
0.0375
0.037
0.0365
0.036
0.0355
0.035
0.0345
0.034
0.0335
0.033
0
1
2
3
4
5
6
7
8
9
10
Time
11
12
13
14
15
16
17
18
19
20
Gen Bus 3 #1 States of Exciter\Rexternal
12
Type 1 and 2 Two Mass Model
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Both the Type 1 and 2 models allow for a two mass
model that represents the oscillations on the shaft
between the blades and the induction generator
The two mass model is the default model for Types 1 and 2
13
Previous Type 2 Example with
Two Mass Model
Graphs show mechanical input versus power output (for
twenty seconds), and shaft mass speeds (for just the
first five seconds)
1.08
90
1.075
85
80
1.07
75
70
1.065
65
Per Unit Speed
Mechanical Power (MW)
•
60
55
50
45
40
1.06
1.055
1.05
35
1.045
30
25
1.04
20
15
1.035
10
5
0
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (Seconds)
20
Time (Seconds)
b
c
d
e
f
g
Mech Input_Gen Bus 3 #1 g
b
c
d
e
f
MW_Gen Bus 3 #1
g
b
c
d
e
f
b
c
d
e
f
g
States of Governor\TurbineSpeed, Gen Bus 3 #1
States of Governor\GenSpeed, Gen Bus 3 #1
14
Type 3: Doubly Fed Asynchronous
Generators (DFAG)
•
Doubly fed asynchronous generators (DFAG) are
usually a conventional wound rotor induction generator
with an ac-dc-ac power converter in the rotor circuit
– Power that would have been lost in external rotor resistance is
•
now used
Electrical dynamics are
dominated by the voltagesource inverter, which
has dynamics much
faster than the transient
stability time frame
Image Source: Figure 2.1 from Modeling of GE Wind Turbine-Generators for Grid Studies,
version 4.6, March 2013, GE Energy
15
Type 3: Doubly Fed Asynchronous
Generators (DFAG)
•
Doubly fed asynchronous generators (DFAG) are
usually a conventional wound rotor induction generator
with an ac-dc-ac power converter in the rotor circuit
– Power that would have been lost in external rotor resistance is
•
now used
Electrical dynamics are
dominated by the voltagesource inverter, which
has dynamics much
faster than the transient
stability time frame
Image Source: Figure 2.1 from Modeling of GE Wind Turbine-Generators for Grid Studies,
version 4.6, March 2013, GE Energy
16
Overall Type 3 WTG Model
Transient stability
models are transitioning
Image Source: WECC Type 3 Wind Turbine Generator Model –Phase II, January 23, 2014, WECC TSS
17
Type 3 Converters
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•
A voltage source converter (VSC) takes a dc voltage,
usually held constant by a capacitor, and produces a
controlled ac output
A phase locked loop (PLL) is used to synchronize the
phase of the wind turbine with that of the ac connection
voltage
– Operates much faster than the transient stability time step, so is
•
•
often assumed to be in constant synchronism
Under normal conditions the WTG has a controllable real
power current and reactive power current
WTG voltages are not particularly high, say 600V
18
Type 3 WT3G Converter Model
Network interface
is a Norton current
in parallel with
a reactance jX"
19
Type 3 Converters
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Type 3 machines can operate at a potentially widely
varying slip
– Example, rated speed might be 120% (72 Hz for a 60 Hz
•
system) with a slip of -0.2, but with a control range of +/30%
Control systems are used to limit the real power during
faults (low voltage)
– Current ramp rate limits are used to prevent system stress
•
during current recovery
Reactive current limits are used during high voltage
conditions
20
Type 3 Voltage Control
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Type 3 WTGs have the ability to regulate their reactive
power output
They can be operated either as
– Constant power factor (so reactive power varies with real
power)
– Constant reactive power
– Constant voltage control, which is more involved than with a
single conventional synchronous generator since the reactive
power response of many individual WTGs needs to be
coordinated across the wind farm (plant)
21
Type 3 Reactive Power Control
22
Aerodynamics
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•
Type 3 and 4 models have more detailed models that
directly incorporate the blade angle, so a brief coverage
of the associated aerodynamics is useful
The power in the wind is given by
P

Avw3 C p ( ,  )
2
where ρ is the density of air, A is the area swept by the blades,
vw is the wind velocity,  is the tip to wind speed ratio.
For a given turbine with a fixed blade length,  =K b ( /v w )
Modeling of GE Wind Turbine-Generators for Grid Studies, version 4.6, March 2013, GE
Energy
23
Aerodynamics
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The Cp(,) function can be quite complex, with the GE
1.5 curves given below
If such a detailed
curve is used, the
initialization is from
the power flow P.
There are potentially
three independent
variables, vw,  and
. One approach is
to fix  at rated (e.g.,
1.2) and  at min
Source: Modeling of GE Wind Turbine-Generators for Grid Studies, version 4.6, March 2013, GE Energy
24
Simplified Aerodynamics Model
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A more simplified model is to approximate this curve as

Pmech  Pm0  K aero   0 
2

where K aero is a constant, Pm0 is set by the
initial Pmech ; 0 is the initial angle, either
set to  min (when the wind speed is below
Theta2 
1
rated), or
 1  2  with Theta2 a
0.75  vw 
constant equal to the angle at twice rated speed
25
WT3T Model (Drive Train and Aero)
26
WT3P Model (Pitch Control)
27
Type 3 Example Case
Previous WSCC case, with the same line 6 to 9 fault, is
modified so gen 3 is represented by a WT3G, WT3E,
WT3T, and WT3P
Mechanical Power (MW)
•
110
105
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Graph at left shows a
zoomed (2 second)
view of the gen 3
real power output,
with the value falling to
zero during the fault,
and then ramping
back up
Time (Seconds)
b
c
d
e
f
g
Mech Input_Gen Bus 3 #1 g
b
c
d
e
f
MW_Gen Bus 3 #1
28
Type 3 Example Case
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Below graphs show the response of the WTG speed and
blade angle
1.219
1.218
1.217
1.216
1.215
1.214
1.213
1.212
1.211
1.21
1.209
1.208
1.207
1.206
1.205
1.204
1.203
1.202
1.201
1.2
1.199
1.198
1.197
1.196
1.195
1.194
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
b
c
d
e
f
g
4
5
6
7
8
States of Governor\TurbineSpeed_Gen Bus 3 #1
9
10
0
1
2
3
b
c
d
e
f
g
4
5
6
7
8
9
10
States of Stabilizer\Pitch, Gen Bus 3 #1
29
Type 4 Converters
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•
Type 4 WTGs pass the entire output of the WTG
through the ac-dc-ac converter
Hence the system characteristics are essentially
independent of the type of generator
– Because of this decoupling, the generator speed can be as
variable as needed
– This allows for different generator technologies, such as
permanent magnet synchronous generators (PMSGs)
– Traditionally gearboxes have been used to change the slow
wind turbine speed (e.g., 15 rpm) to a more standard
generator speed (e.g., 1800 rpm); with Type 4 direct drive
technologies can also be used
30
Example: Siemens SWT-2.3-113
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The Siemens-2.3-113 is a 2.3 MW WTG that has a
rotor diameter of 113m. It is a gearless design based on
a compact permanent magnet generator
– No excitation power, slip rings or excitation control system
Image: www.siemens.com/press/pool/de/pressebilder/2011/renewable_energy/300dpi/soere201103-02_300dpi.jpg
31
Brief Energy Economics
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With renewable sources like wind and solar in which
the fuel is essentially free, capital costs dominate
As a minimum, the energy generated over the life of the
device must be greater than its capital costs
– Simple analysis assumes zero interest and inflation
cc  lifehr  cf  price
where
cc is the capital cost in dollars (or other currency unit) per
MW (or other unit)
lifehr is the lifetime of the device in hours
cf is the capacity factor
price is the $/MWh at which the electricity is sold
32
Brief Energy Economics
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As an example, assume a wind farm project with a
capacity factor of 40% and a lifetime of 25 years
– Capital costs are covered if the price is at least $11.4/MWh
•
per $1,000,000 per MW (or $/watt)
Other wind costs include land rental (about $5000 per
year per MW), taxes (about 400K per MW valuation in
Illinois, which would be about $10,000 per year, give or
take depending on the local tax rate), operations and
maintenance (ballpark is $30,000 per year per MW)
– Total over 25 years is roughly $1,125,000 per MW
33
Type WTG4 Model
Very similar to the WTG3, except there is no X"
34
Type 4 Reactive Power Control
Also similar to the Type 3's, as are the other models
35
Solar Photovoltaic (PV)
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•
•
Photovoltaic definition- a material or device that is
capable of converting the energy contained in photons
of light into an electrical voltage and current
Solar cells are diodes, creating dc power, which in grid
applications is converted to ac by an inverter
For terrestrial applications, the capacity factor is limited
by night, relative movement of the sun, the atmosphere,
clouds, shading, etc
– A ballpark figure for Illinois is 18%
– "One sun" is defined a 1 kw/m2,which is the maximum
insolation the reaches the surface of the earth (sun right
overhead)
36
US Annual Insolation
37
Worldwide Annual Insolation
In 2013 worldwide PV capacity was about 136 GW; by country (in GW)
the leaders are Germany (35.5), China (18.3), Italy (17.6), Japan (13.6),
US (12), Spain (5.6), France (4.6)
http://www.ren21.net/Portals/97/documents/GSR/GSR2012_low%20res_FINAL.pdf
38
US Electricity Sources, 2013
•
For 2013 the US percentage of electric energy by fuel
source is
Other is about 1%.
– Coal:
– Natural Gas:
– Nuclear:
– Hydro:
– Wind:
– Wood:
– Petroleum:
– Geothermal:
– Solar PV:
– Solar Thermal:
39.1%
27.4%
19.4%
6.63%
4.13%
0.98%
0.66%
0.40%
0.20%
0.02%
Solar PV is still quite
small, but with a very
high growth rate > 100%!
Therefore its impact
needs to be considered
moving forward; about half
of the US total is in
California, which also has
some of the highest retail
electricity prices.
Data source: EIA Electric Power Monthly, Feb 2014
39
Modeling Solar PV
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•
Since a large portion of the solar PV is distributed in
small installations in the distribution system (e.g.,
residential rooftop), solar PV modeling is divided into
two categories
– Central station, which is considered a single generation plant
– As part of the load model
The central station block diagram is
40
Central Station PV System
Modeling
•
The below block diagram shows the overall structure
Solar PV has no inertia, and in contrast to wind there
is not even the ability to mimic an inertia response since
there is no energy storage in the system
Source: "Generic Solar Photovoltaic System Dynamic Simulation Model Specification," WECC Renewable Energy
Modeling Task Force, Sept. 2012 (same source for figures on the next three slides)
41
Central Station PV System
Modeling
•
The generator model is similar to the Type 4 wind
model, which is not surprising since this is modeling
the converter operation
Source: "Generic Solar Photovoltaic System Dynamic Simulation Model Specification," WECC Renewable Energy
Modeling Task Force, Sept. 2012
42
Central Station PV System
Modeling
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Reactive current control is also similar
43
Central Station PV System
Modeling
•
Usually regulation will be down only (i.e., responding
only for over frequency) since it would be at max P
44