Introduction to wind energy
Relevant to offshore wind farm design
Offshore Wind Farm Design
Michiel Zaaijer
2007-2008
1
DUWIND
Overview
•
•
•
•
•
Rotor aerodynamics
Power and load control
Energy production
Turbine technology
Multi-MW turbines turbines
2007-2008
2
Rotor aerodynamics
2007-2008
3
Determining power and loads
0. The approach
2007-2008
4
Blade element – momentum method
1. Momentum balance
Macroscopic perspective
Loads from conservation laws
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≡
2. Blade elements
Local perspective
Loads from lift and drag
5
Determining power and loads
1. Momentum balance
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6
Mass, momentum and energy flows
Mass per second through A:
Mass flow
m=ρUA
Substitute:
Momentum flow
Energy flow
2007-2008
m U = ρ U2 A
½ m U2 = ½ ρ U3 A
7
Actuator disc – represents rotor
D
At actuator disc:
Axial rotor force (thrust) D
Power extraction
P
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8
Conservation laws
Thrust ≡ change in momentum
D = m (U-Ve)
Power extracted at rotor disc
D V1 = m V1 (U- Ve)
Kinetic energy loss in flow
½ m (U2-Ve2) =
½ m (U-Ve) (U+Ve)
Power ≡ Energy loss
V1 = ½ (U+ Ve)
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9
Dimensionless induction factor
Define induction factor
(dimensionless)
a = (U-V1)/U
U
U(1-a)
U(1-2a)
Rearrange
V1= U (1-a)
Substitute on previous page
Ve = U (1-2a)
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10
Substitution with induction factor
Mass flow
m
= ρ V1 A
= ρ U (1-a) A
= m (U-Ve)
= ½ ρ U2 A 4a(1-a)
Thrust
D
Power
P
2007-2008
= ½ m (U2-Ve2)
= ½ m (U-Ve)(U+Ve) = ½ ρ U3 A 4a(1-a)2
11
Dimensionless thrust and power
Define
D
P
= ½ ρ U2 A 4a(1-a) = ½ ρ Cd U2 A
= ½ ρ U3 A 4a(1-a)2 = ½ ρ Cp U3 A
Dimensionless coefficients become
Cd = 4 a (1-a)
Cp = 4 a (1-a)2
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12
Intermezzo: Optimum power
The Betz optimum:
Cp is maximum when
1
Cd
0.8
dC p
0.6
Cp
0.4
da
Result
a
0.2
0
0
0.1
0.2
0.3
0.4
0.5
a
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=0
= 1/3
CP,max = 16/27 ≈ 0.59
Cd
= 8/9
13
Annular approach
Divide stream tube in concentric annuli, parallel to flow
Assumptions
1.
Annuli don’t interact
- Induction factor ‘a’ independent of other annuli
- No flow from one annulus to another)
2.
No tangential change within one annulus
- Induction factor ‘a’ constant over annulus
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14
Mass, thrust and power per annulus
Mass flow
m = ρ V1 A
dm = mass per annulus
= ρ U (1-a) A
= ρ U (1-a) 2πr dr
Thrust
D
dD
= m (U-Ve)
= thrust per annulus
= ½ ρ U2 4a(1-a) A
= ½ ρ U2 4a(1-a) 2πr dr
Power
P
dP
2007-2008
= ½ m (U2-Ve2)
= ½ ρ U3 4a(1-a)2 A
= power per annulus = ½ ρ U3 4a(1-a)2 2πr dr
15
Determining power and loads
2. Blade elements of a rotor
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16
Cross-section of blade
Consider cross-section of blade,
perpendicular to blade axis,
U(1-a)
with velocity vectors
U(1-a) and Ωr
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Ωr
17
Aerofoil forces and velocities
l
d
Ωr
Rotor plane
θ
U(1-a)
φ
α
Vres
Ωr
= radial velocity
U(1-a) = local wind speed
Vres
= resultant speed
2007-2008
r
θ = blade twist angle
φ = angle of inflow
α = angle of attack
l = lift ⊥ Vres
d = drag // Vres
18
Lift and drag (2-dimensional flow)
1
l = Cl ⋅ ρU 2 c
2
1
d = Cd ⋅ ρU 2 c
2
Lift coefficient
Drag coefficient
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19
Flow regimes
Attached flow
after Prandtl and Wieselsberger
Separated flow
(stalled)
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20
Thrust and power
Contribution to thrust dD per blade element dr
N = Number of blades
dD = N ( l cos(φ) + d sin(φ) ) dr
dD = N ( Cl ½ ρ Vres2 cos(φ) + Cd ½ ρ Vres2 sin(φ) ) c dr
dD = N ( Cl ½ ρ (Ωr)2 + Cd ½ ρ (U(1-a))2 ) c dr
Contribution to power dP per blade element dr
dP = N ( l sin(φ) – d cos(φ) ) Ωr dr
dP = N ( Cl ½ ρ (U(1-a))2 – Cd ½ ρ (Ωr)2 ) c Ωr dr
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21
Determining power and loads
3. Blade element – momentum method: BEM
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22
Combining two theories
l
r
Ωr
U(1-a)
φ
θ
α
d
Vres
Momentum balance
Blade elements
dD = ½ ρ U2 4a(1-a) 2πr dr
dD = N ( Cl ½ ρ (Ωr)2
+ Cd ½ ρ (U(1-a))2 ) c dr
When we assume dDmomentum balance = dDblade elements
Two equations – two unknowns: dD and a
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23
Solving induction factor with BEM
For each annulus:
Choose an initial value for ‘a’.
Use this to calculate angle of attack and from this Cl and Cd
Calculate axial aerodynamic force on blade element: dD
From dD follows a new value for ‘a’ with momentum theory
Continue until ‘a’ reaches a constant value.
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24
Solving loads and power with BEM
Once ‘a’ is known for all annuli, integrate blade elements
Thrust on rotor
R
D = ∫ 0 N ( Cl ½ ρ (Ωr)2 + Cd ½ ρ (U(1-a))2 ) c dr
Power on main shaft
P = ∫ N ( Cl ½ ρ (U(1-a))2 – Cd ½ ρ (Ωr)2 ) c Ωr dr
R
0
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25
Additions to BEM
• Tip losses / infinite number of blades
• Wake rotation (tangential forces and velocities)
Included in all state-of-the-art calculation tools
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Characterising rotor aerodynamics
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27
The CP - λ curve
+
Define tip speed ratio
λ = ΩR / U
(Low λ = low Ω or high U)
Small α
Stall region
Example
α
α
λdesign = 8
Cp,max = 0.46
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28
Cp-λ curves for different pitch
Full span pitch
θnew, local = θold, local + θpitch
Pitch to stall
(increase α)
α
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Pitch to vane
(decrease α)
α
29
Wind turbine control
Aerodynamic aspects
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Power and thrust curves
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31
“Ideal” Power and thrust curves
P
T
P = T·V = Constant
~Arotor·V2
~V-1
~V3
~Ablade·V2
V
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32
Terminology for regions of operation
P
Full load
Idle / Stand-still
Partial load
Vcut-in
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Vrated
Vcut-out
V
33
Partial load – power control
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34
Ideal power control – variable speed
P = Cp ½ ρ
λ = ΩR/U
U3 A
+
P ~ U3
Cp(λ) = Cp,max
λ = λdesign
Ω ~ U
Variable speed!
(Fixed pitch)
λdesign = 8
Cp,max = 0.46
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35
Constant speed power control
P= Cp ½ ρ U3 A
P ≤ Pvariable speed
λ = ΩR/U
Cp,max only at one
wind speed
Increasing Decreasing
wind speed wind speed
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λdesign = 8
Cp,max = 0.46
36
Power, RPM, wind speed
λ constant
Power (kW)
= Cp ½ ρ U3 A
Ω constant
Wind speed (m/s)
Determined from
Cp – λ curve
Ω (RPM) = (60 / 2π) λ U / R
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37
Power difference (partial load)
P
Variable speed: ~V3
Constant speed design point:
Ω = Ωdesign; λ = λdesign; Cp = Cp,max
Constant speed: ≤~V3
Vcut-in
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V
Full load – power control
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39
Control options (constant speed)
Passive stall:
U => Cp
Active stall/
Pitch to stall:
θ & U
=> Cp
Pitch to vane:
θ => Cp
U => Cp
Total: Cp
Ω = constant:
U => λ
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40
Passive stall control
Power (kW)
Ω constant
‘Natural’ power
limitation at high
wind speeds
Ω (RPM)
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41
Passive stall power curves
Comparison of power curves
600
Identical stall-turbines
in Bockstigen wind farm
500
Power [kW]
400
P based on WS_ST, unit=1
P based on WS_nac, unit=1
300
P based on WS_ST, unit=2
P based on WS_nac, unit=2
P based on WS_ST, unit=3
200
P based on WS_nac, unit=3
P based on WS_ST, unit=4
P based on WS_nac, unit=4
100
P based on WS_ST, unit=5
P based on WS_nac, unit=5
0
0
5
10
15
20
25
30
Wind speed in tower and nacelles [m/s]
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Pitch to vane power curve
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Full load - Loads
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Non-ideal thrust of stall control
T
Stall control:
High drag
Higher lift compensates
V
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45
Dynamic loads of pitch control
l
Pitch to vane:
U => Lift • Quick
• Slow
θ => Lift
• Slow
Total: Lift
Ωr
θ
U(1-a)
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φ
α
r
d
Rotor plane
Vres
46
Dynamics thrust of pitch control
T
Response
to gust or pitch failure
V
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47
Load alleviation: gust response
Use rotor as a flywheel
Increase speed to absorb energy
Decrease speed to release energy
Reduce torque variations & peaks
Reduce power variations
Axial loads are NOT reduced!
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48
Load alleviation: Peak shaving
P
T
Start pitch control in partial load
Stop constant λ control in partial load
Vrated goes up and is less clear
Vrated
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V
49
Energy production
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50
Wind speed distribution
De Bilt
observations
1961/1970
1971/1980
Example: Wind speed
between 6 and 7 m/s
9% of the time
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51
Weibull distribution
De Bilt
Weibull fit
V
k V k −1
f ( ) = ⋅( ) ⋅e
a
a a
V
−( ) k
a
With
k = shape factor
a = scale factor
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52
Weibull distribution: examples
k=4
k=3
k=1
k=2
a=1
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53
Shape factor vs average wind speed
a=
Vavg
With
a
= Weibull scale factor
Vavg = Annual average wind speed
Γ = Gamma function
1
Γ(1 + )
k
∞
Example
Γ(α ) = ∫ β α −1e − β dβ
0
1 
0.434 
Γ(1 + ) ≈  0.568 +

k 
k 
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1
k
1
Γ(1 + ) ≈ 0.886
k
Vavg > a
54
Wind speed vs height
Power law
 h
v(h) = v(href ) ⋅ 
h
 ref
α



Offshore α ≈ 0.08 – 0.14
Guideline α = 0.11
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Calculation of annual yield
Vco
ETurbine = T ∫ Pel (V ) ⋅ f (V ) dV
T
(hours/
(m/s))
Vci
Contribution to energy (kWh/(m/s))
x
=
Power
(kW)
v (m/s)
v (m/s)
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Total area = energy
production in one year
56
Energetic efficiency (1)
P
Ω is constant
λ is constant
E
Ideal turbine
Turbine with
pitch control
Energy content
Ω is constant
(exaggerated)
x
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V
V
Turbine with
stall control
57
Energetic efficiency (2)
Vcut-in
:
Speed control :
Pitch/stall
:
Vcut-out
:
Vrated
:
2007-2008
Hardly affects E, only interest is public perception
Some effect on E
Some effect on E
Limited effect on E, primarily determined by loads
Has largest influence on E
58
Capacity factor (1)
Yearly energy production
Vco
E = T ∫ Pel (V ) ⋅ f (V ) dV
Vci
The same yearly production would be generated in an equivalent
amount of time Tequivalent running at full power:
E = Prated Tequivalent
cf =
2007-2008
Tequivalent
Tyear
is called the capacity factor
59
Capacity factor (2)
cf ≈ 0
cf ≈ 1
2007-2008
A high capacity factor is not necessarily good!
There is an economic optimum
60
Characteristic values for cf
First generation turbines: cf ≈ 0.2
Present generation:
cf ≈ 0.25 - 0.3
Offshore wind farms:
cf ≈ 0.35 - 0.45
For comparison
The capacity factor of all the power generation ability mounted in
the Netherlands :
cf =
total electricity consumption
maximum electricity production ⋅ 8760
≈ 0.5
(8760 is the number of hours in a year)
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Energy losses
P (V )Electrical = P (V )Aero ⋅ηDrive train ⋅ηGenerator ⋅ηConversion
P-V curve of manufacturer includes these losses
Additional farm related losses:
• Availability of the turbines
• Availability of the electrical infrastructure
• Aerodynamic farm losses (wakes)
• Transformation and transmission losses
2007-2008
Sources
• Models
• Guestimates
(literature)
62
Estimating energy production (1)
Energy yield =
number of hours/year * installed power * capacity factor
e.g.: 8760 h * 108 MW * 0.35 ≈ 331 GWh / y
for offshore wind park Egmond aan Zee
(Average Dutch household: 3.2 MWh / y)
Only applicable for order of magnitude guess !!
Wind speed distribution (based on data) indispensable
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63
Estimating energy production (2a)
Estimate power curve
P
P = ⅛ ρ Cp V3 π D2
use
D and estimate of Cp
or
Prated and
Vrated ≈ 10-12 m/s
Prated
Vcut-in
≈ 3-5
2007-2008
Vrated
≈ 10-12
Vcut-out
V (m/s)
≈ 25-30
64
Estimating energy production (2b)
Estimate wind speed distribution
Data at reference height
Weibull scale
Average wind speed Weibull shape factor
at reference height
Gamma function
at reference height
Power law
at reference height
Equal
(simple model)
Weibull scale factor Average wind speed Weibull shape factor
at hub height
2007-2008
at hub height
at hub height
65
Turbine technology
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66
Blades
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67
Blades
Composite
One-piece
Flexible
Skin / spar
T-bolts
Picture source: LM
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68
Large blades: pre-bending in mould
Blade pitched 90º
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Overview of the drive train
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70
Drive train (with gearbox)
rotor bearing
hub
main shaft
generator shaft
with coupling
brake
gearbox
generator
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71
yaw ring
yaw gear
Drive train without gear: direct drive
Zephyros 2 MW turbine
2007-2008
72
Compact drive train
1-stage gearbox,
medium speed
generator, direct hubgear-generator
connections
Multibrid
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73
Gearbox & generator
Clipper Liberty
2.5 MW
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74
Hub
2007-2008
75
Hub
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76
Hub and cover
Composite
aerodynamic cover
Cast-iron hub for rotor loads
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77
Main shaft and bearings
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78
Double and single bearings
Direct connection to hub
Rotating main shaft
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79
Bearings on fixed axle pin
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80
Gearbox
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81
type of transmission
Parallel
Planetary
Simple
Compact for high power
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82
Gearbox – planetary & parallel stages
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83
Generator
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84
Doubly fed generator
Partly variable speed
Fed rotor
Inverters needed
5 MW-class from ABB
1:n
ASM
ac
dc
dc
2007-2008
ac
85
Direct drive (synchronous) generator
ENERCON 4.5 – 6 MW
Full variable speed
Rotor windings for magnetic field
Inverters needed
Low speed:
(Very) big diameters needed
SM
2007-2008
dc
dc
dc
ac
86
Permanent magnet generator
Full variable speed
No rotor windings
Inverters needed
SM
2007-2008
dc
dc
dc
ac
87
Brakes
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88
Location of (fail-safe) brakes
• brake located on slow shaft
(rotor shaft has double bearings)
• brake located on fast shaft
Brakes are actively released (hydraulics)
and passively clamped (springs)
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89
Aerodynamic brake
- Each blade can pitch individually to brake
- Only mechanical parking brake
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90
Bedplate / Main frame
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91
Traditional bedplate
Cast-iron mainframe
for rotor loads
Welded frame to carry
other components
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92
Compact frames
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93
Yaw system
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94
Yaw system
Bearing
Engines
Gearboxes
Yaw brakes
2007-2008
Cable twist counter &
pull switch (redundancy)
95
Control
State of the art
• Variable speed (restricted in US through patent)
• Pitch control
Future advances
• Individual pitch
• Smart rotors
2007-2008
96
Multi-MW turbines in the market
≥ 5MW (prototypes)
GE 3.6 – 3.6s
Enercon E-112
REpower 5M
Multibrid M5000
Siemens SWT-3.6-107
2007-2008
97
GE 3.6 – 3.6s (3.6 MW)
First prototype: April 2002
Rotor:
104 m
Gearbox:
3-stage (PPE)
Generator:
Asynchronous
Doubly-fed
Inverter:
2007-2008
Partial (30%)
98
Enercon E-112 (4.5 MW)
First prototype: August 2002
Rotor:
114 m
Gearbox:
No
Generator:
Synchronous
Wound rotor
Inverter:
2007-2008
Full (100%)
99
REpower 5M (5 MW)
First prototype: November 2004
Rotor:
126 m
Gearbox:
3-stage (PPE)
Generator:
Asynchronous
Doubly-fed
Inverter:
2007-2008
Partial (30%)
100
Multibrid M5000 (5MW)
First prototype: December 2004
Rotor:
116 m
Gearbox:
1-stage (Planet)
Generator:
Synchronous
Permanent Magnet
Inverter:
2007-2008
Full (100%)
101
Siemens SWT-3.6-107 (3.6 MW)
First prototype: December 2004
Rotor:
107 m
Gearbox:
3-stage (PPE)
Generator:
Asynchronous
Squirrel cage
Inverter:
2007-2008
Full (100%)
102
Future developments
• Announced by leading manufacturers
• Vestas V120 (4.5 MW)
• Upgrade Enercon E-112 E-126 (?? MW)
• Developers involvement
• Bard Engineering – Bard VM (5 MW)
• Econcern – DarwinD (4.5 MW)
• No end to scale and concept evolution
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103