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Adaptive Power Tracking Control of
Hydrokinetic Energy Conversion Systems
A thesis submitted to the School of Graduate Studies in partial fulfillment of the requirements for the degree of Doctor of Philosophy
By
Jahangir Khan, B.Sc., M.Eng.
Supervisory Committee
Dr. Tariq Iqbal, Dr. John Quaicoe, Dr. Michael Hinchey
Faculty of Engineering & Applied Science
Memorial University, St. John’s, NL, Canada
June 1, 2010
2
Outline
� Introduction
o Hydrokinetic systems, research objective & scope
� Review & Critique
o Technology status, applied & basic Research
� Modeling & Validation
o Numerical models, test & validation initiatives
� Controller Evaluation
o Power tracking control challenges, methods & solutions
� Adaptive Controller Synthesis
o Extremum Seeking Controller design for hydrokinetic systems
� Conclusion
o Contributions, future work, acknowledgements
3
� Introduction
� Review & Critique
� Modeling & Validation
� Controller Evaluation
� Adaptive Controller Synthesis
� Conclusion
4
Introduction
Hydrokinetic Energy Conversion Systems
� Electromechanical device that generates electricity by harnessing the kinetic energy of flowing water
� Areas of application: tidal/marine current, river streams, artificial waterways, irrigation canals, dam head/tailrace etc.
� Could be built as a free-rotor or duct augmented system, and deployed as modular multi-unit arrays
� Potentially requires little or no civil work, unlike large hydro power plants
Gearing
Bearing
Generator
Control System
Power Converter
Grid Integration
Augmentation
Floatation
Mounting
Mooring
Blades
Drivetrain
Protection
Screen
5
� Identify the current state of hydrokinetic technologies
… in the context of associated control challenges
� Develop direct knowledge of a turbine's operational characteristics
… by undertaking relevant design, develop & test activities
� Identify the power tracking control challenges
… that are unique to the broader class of hydrokinetic systems
� Investigate on a set of possible alternative solutions
… through simulation & qualitative evaluation on existing methods
� Formulate an advanced power tracking algorithm
… that may suit the unique needs of hydrokinetic technologies
Introduction
Research Objectives
6
� Considerations for broader spectrum of hydrokinetic technologies
� Focus on test, modeling and experiments on a small-scale vertical axis turbine containing
o multi-pole outer rotor permanent magnet alternator
o single-phase utility grid with a power electronic (ac-dc-ac) link
� Design, development & laboratory scale testing
� Validated dynamic numerical models in Matlab-SimulinkTM
� In-depth maximum power tracking controller analysis/synthesis using the models
Introduction
Research Scope
7
� Introduction
� Review & Critique
� Modeling & Validation
� Controller Evaluation
� Adaptive Controller Synthesis
� Conclusion
8
Review & Critique
Hydrokinetic Systems: Technology Status
� Primarily a nascent technology (demonstration & pre-commercial)
� Both horizontal and vertical axis turbines can be used
� Free-flowing or ducted turbines are being investigated
� Multitude of placement options can be opted
9
� Recent work: Robust gain scheduling controller ( linear
parameter varying) [Ginter, 2009]
� Early work: PID type tips speed ratio controller (horizontal axis turbine) [Tuckey et. al., 1997]
� Other works: High-level wind oriented [Ben Elghali et. al. 2008] & applied work [Mattarolo et. al. 2006, MCT 2008]
� Supporting knowledge-base:Wind energy and solar
photovoltaic maximum power point tracking control literature [various publications]
Review & Critique
Control of Hydrokinetic Turbines
H∞
10
� Introduction
� Review & Critique
� Modeling & Validation
� Controller Evaluation
� Adaptive Controller Synthesis
� Conclusion
11
Modeling & Validation
Flow Field Representation
� To identify various flow field components affecting a hydrokinetic
system and assess their possible impacts on the overall power extraction.
� To analyze the time scale of variation reflecting the dynamics of
relevant flow field components.
� To establish the magnitude and range of various flow field
parameters that are of interest to the power tracking control problem.
12
Modeling & Validation
Flow Field Representation (cont’d)
� Power captured by a hydrokinetic turbine rotor:
� Elements of the flow field
31
2rot p w r p dp
dp aug prof skew yaw
P C A v k
k k k k k
ρ=
= × × ×
Controlled element Flow field elements
Water density (temperature, salinity, pressure)
Effective area (level of submersion, boundary layer)
Water velocity (mean, stochastic, wave induced)
Design and placement related factors
Yaw misalignment factor
Skewed flow factor
Vertical velocity profile factor
Velocity augmentation factor
Prot =12CpρwArv
3pkdp
kdp = kaug × kprof × kskew × kyaw
13
Modeling & Validation
Flow Field Representation (cont’d)
� Water velocity components:
� Synthesis of the water velocity model:
vp(t) = vs + vt(t) + vw(t)
vs =
{vR, River seasonal meanvT , Tidal hourly mean
svSeasonal average velocity
(river, tidal)
, ,i ii ω ϕTurbulence
component
Kolmogorov’s –5/3
Law spectrum
iv
FT FK
White noise
generator
( )we t
tσ
siT
Shaping
filter
( )Fh t
( )tv t
Filter
constants
Standard
deviation
( )wv t
Pierson – Moskowitz
spectrum Sea state
, ,w wA T L Wave induced velocity
(Intermediate depth)
0
River
Tidal
( )pv t
14
Modeling & Validation
Darrieus Rotor Performance Analysis
� Darrieus Rotor � General principle
� Relevant terms
Phyd =12ρwArv
3up
Prot = Cop12ρwArv
3eff
Cop =
ProtPhyd
CoT =
Cop
λ
λ = ωrotRveff
Incident hydraulic power -
Captured rotor power -
Power coefficient (ideal) -
Torque coefficient (ideal) -
Tip speed ratio (TSR) -
� Performance curve0.6
0.5
0.4
0.3
0.2
0.1
654321 7 8
Ideal PropellerHigh speed Propeller
Darrieus
Dutch Four Arm
Savonius
American
Multiblade
Betz Limit (0.59)
Power Coefficient, Cpo
Tip Speed Ratio,
15
Modeling & Validation
Darrieus Rotor Performance Analysis (cont’d)
� Performance analysis of Darrieus rotors
� Single-disk multiple-streamtube analysis:
16
Modeling & Validation
Darrieus Rotor Performance Analysis (cont’d)
� Mechanical torque & torque coefficient:
o With m number of streamtubes and , the mechanical torque is
o Using the normalizing torque and solidity the torque coefficient (ideal) is
� Considerations embedded within the streamtube analysis:
o Gluert's empirical formulao Lift and drag data correction (Reynold's number, Aspect ratio, Angle of attack)
Tmec = Nb
m∑i=1
1
2ρwv2rel(CH)CtangR
m
12ρwv2effDHR σr =
NbCD
CoT = σr
m∑i=1
(vrelvup
)2
Ctang
m
Ctang = CL sinαb − CD cosαb
17
Modeling & Validation
Darrieus Rotor Performance Analysis (cont’d)
� Performance curve of a test system (NECI – 4 bladed)
� Emphasis on overall system efficiency� Estimates are particularly successful in identifying the optimumTSR point
� Divergence high on post-optimum TSR region
� Contrary to expectations, multiple performance curves (at various water speeds) can be observed
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.05
0.1
0.15
0.2
0.25
Tip Speed Ratio
Ov
eral
l sy
stem
eff
icie
ncy
1.75 m/s
1.85 m/s
1.95 m/s
2.00 m/s
2.10 m/s
2.25 m/s
2.40 m/s
2.45 m/s
2.50 m/s
2.65 m/s
2.75 m/s
Estimated curve
(b)
18
Modeling & Validation
Dynamic Modeling of Hydrokinetic System
� Large-signal non-linear model formulations
� Considerations for losses within all the subsystems� Focus on electromechanical transients (as against electromagnetic transients)
� Detailed synthesis of torque components� Permanent magnet alternator (PMA) with ac-dc-ac (grid-connected) topology
� Assessment of start-up, torque ripple, and nonlinear efficiency issues
19
Modeling & Validation
Dynamic Modeling of Hydrokinetic System (Cont’d)
Vertical axis rotor
� Total rotor torque:
� Mechanical input torque:
� Oscillating torque:
Trot = Tmec + Tosc
Tmec =12ρwArCTv
2effR
Tosc = Tosc sin θb × fh(Igr)
CT =Cp
λ
Cp = ηaswCop
Cop = fr(λ)
o Effective torque coefficient:
o Effective power coefficient:
o Ideal power coefficient:
o Peak ripple torque:
o Azimuth position:
Tosc =Tmec
koscλ
θb =∫Nbωrotdt
20
Modeling & Validation
Dynamic Modeling of Hydrokinetic System (Cont’d)
Drive-train
� Rotor torque:
� Generator torque:
� Low-speed shaft torque:
Trot = Jrotdωrot
dt+ Tlss +Brotωrot
Tgen = ηtranTlssNgen
, Ngr =ωgenωrot
(Ngr > 1)
Tlss = kspr
∫(ωrot −
ωgenNgen
)dt
Low speed shaft High speed shaftGear box
Trot
Tlss
Tgen
Jgen
Jrot Ngr
Thss
rot
gen
21
Modeling & Validation
Dynamic Modeling of Hydrokinetic System (Cont’d)
Permanent magnet alternator
� Overall torque balance:
� Cogging torque:
� Load torque:
� Loss torque:
Tgen = Jgenpωgen +Bgenωgen + Tcog + Tload + Tloss
Tcog = Tcog sin θg × fh(−Igr)
Tload =32
NP
2 λmIg
Tloss =Pnll+Pll
ωgen− Bgenωgen
22
Modeling & Validation
Dynamic Modeling of Hydrokinetic System (Cont’d)
Rectifier (with capacitive filter)
� Output voltage (before filter):
� Output voltage (after filter):
V ogr =
3√3
πVg − 2Vf
VgrV ogr= 1
LfgCfgs2+RfgCfgs+1
Vgr
Igr
vb
Ra
Rb
Rc
La
Lb
Lc
va
vc
ia
ib
ic
ea
ebec
Lca Lab
Lbc
a
b
c
Power stage(s)
and Load
Filter
(Capacitor)BLDC generator
Rectifier
(Uncontrolled)
23
Modeling & Validation
Dynamic Modeling of Hydrokinetic System (Cont’d)
Converter (zero-current-switching dc-dc architecture)
� Open circuit voltage (steady-state):
� Terminal voltage under load (steady-state):� Converter voltage regulation:
� LC filter dynamics & output voltage:
Eoco =
Vtrm2.5 Vcnom
Eco = Eoco −∆Eco
Rcvr =∆Eco
Eoco=
Eoco−Eco
Eoco
ILco =1
Lco
∫(Eco − Vco)dt
Vco =1
Cco
∫(ILco − Ic)dt
24
Modeling & Validation
Dynamic Modeling of Hydrokinetic System (Cont’d)
grdVinv
E
ioLio
R
invP
grdV
invE
iI
i ioI X
pfθpaα
pfθ
Inverter (grid-connected dc-ac architecture)
� Design power output:
� Inverter output power:
� Grid power injection:� Power angle control:
� Line filter dynamics:
P ∗inv = 10Vco − 250; for 24 <Vco < 48
Pinv =EinvVgrd
Xiosinαpa
P ∗inv = 0; forVco < 24 and Vco > 48
αpa = Kpinv(P∗inv − Pout) +Kiinv
∫(P ∗inv − Pout)dt
Pout = VgrdIi cos θpf
LiodIidt+RioIi = Vilf
invEgrdV
ioL ioR
coV
25
Modeling & Validation
Dynamic Modeling of Hydrokinetic System (Cont’d)
Overall model
� Implemented in Matlab-SimulinkTM
� Model strength: readily usable & numerically stable
� Disturbance inputs are: water flow & velocity variation
� Control variable is: converter trimming voltage
� Output variables are: rotational speed & electrical power
� Component validation: rotor, generator, rectifier, converter, inverter
� Part-system validation: rotor, generator, rectifier + load
Terminator
h_subh_ef f
v _s v _ef f
v _s
H
v _ef f
H
w _rot
T_mec
Lambda
Rotor
V_g
I_gr
PinRECT
V_gr
I_g
P_rec
Rectifier
P_rect
I_gr
PinRECT
P_rl
RECT loss
P_rlI_grE_g
N_gen
P_cl+P_rot
P_tot
PMA loss
T_gen
I_g
P_cl+P_rot
V_g
N_gen
E_g
PMA
V_co
PinINVC
P_inv
I_c
P*inv
I_i
Inverter
I_i
P*invPinINV
INV loss
P_inv
Lambda
P_inv
V_trm
Hv_eff
N_gen
T_mec
Lambda
N_gen
T_gen
w_rot
Drivetrain
V_gr
I_c
V_trm
PinCONV
V_co
I_gr
P_con
Converter
P_con
I_cPinCONV
CON loss
Vgr
26
Modeling & Validation
Test Apparatus and Model Validation
0 100 200 300 4000
100
200
300
400
500
600
700
Rotor speed (rpm)
1.25ohm
1.67ohm
2.50ohm
5.00ohm
Data-points: Measured
Curves/LInes: Simulated
0 5 10 15 200
10
20
30
40
50
Load current (A)
100rpm
150rpm
200rpm
250rpm
300rpm
325rpm
Data-points: Measured
Curves/LInes: Simulated
(a) (b)
Steady state
Dynamic
Permanent magnet alternator (with rectifier)
5 10 15 20 25 30 35 40 45 500
200
400
600
5 10 15 20 25 30 35 40 45 500
5
10
Time (s)
5 10 15 20 25 30 35 40 45 500
250
500500
5 10 15 20 25 30 35 40 45 500
20
40
6060
5 10 15 20 25 30 35 40 45 500
10
20
Generator speed (rpm)
Output current (A)
Output voltage (V)
Output power (watt)
Prime-mover input current (A)
Experiment Simulation
27
Modeling & Validation
Test Apparatus and Model Validation (cont’d)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 55
0
10
20
30
40
50
60
70
Time (s)
Co
nv
ert
er
ou
tpu
t v
olt
ag
e (
V)
Vco
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2
0
2
4
6
8
10
12
14
Time (s)
Co
nv
ert
er
ou
tpu
t cu
rren
t (A
)
Ic
Ch A: converter voltage
(10V/d)
Ch B: converter current (1 A/d);
Current probe setting 100 m
V/A
Steady state
Dynamic
dc-dc converter
0 2 4 6 8 100
10
20
30
40
50
60
Converter output current (A)
Co
nv
ert
er
ou
tpu
t v
olt
ag
e (
V)
Vtrm
=2.5; Vgr
~45V
Vtrm
=1.98; Vgr
~25V
Vtrm
=2.27; Vgr
~35V
(a) (b)
0 0.5 1 1.5 2 2.50
10
20
30
40
50
Trimming/controlling voltage (V)
Co
nv
ert
er
ou
tpu
t v
olt
ag
e (
V)
test data with Vgr
= 25
test data with Vgr
= 45
Design estimate
Data points: measured
Curves/lines: simulated
28
Modeling & Validation
Test Apparatus and Model Validation (cont’d)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2-8
-6
-4
-2
0
2
4
6
8
Time (s)O
utp
ut
cu
rren
t (A
)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2-80
-60
-40
-20
0
20
40
60
80
Time (s)
Inv
ert
er
inp
ut
vo
ltag
e (
V)
Ch A: input voltage (20V/d)
Ch B: inverter current (2 A/d);
Current probe setting 100 m
V/A
(a)
(b)
(c)
Steady state
Dynamic
dc-ac inverter
0 10 20 30 40 50 600
50
100
150
200
250
Input voltage (V)
Ou
tpu
t p
ow
er
(watt
)
29
� MUN 3-bladed
o NACA 63-018 blades, chord 6.25 cm, height 0.75 m,
diameter 0.75 m, solidity 25%.
o Poor start-up due to low blade count & weak structure.
� MUN 6-bladed
o NACA 0012 blades, chord 6.75 cm, height 0.4 m and
diameter 0.8 m, solidity 50%.
o Poor start-up due to heavy mass, poor efficiency.
� NECI 4-bladed
o NACA 0015 blades, chord 10.1 cm, height 0.4 m,
diameter 1 m, solidity 40%.
o Promising overall performance.
Modeling & Validation
Test Apparatus and Model Validation (cont’d)
Tow-tank test apparatus (turbine rotors)
30
Modeling & Validation
Test Apparatus and Model Validation (cont’d)
Tow-tank test apparatus (instrumentations)
� NECI 4-bladed rotor coupled to a multi-pole outer rotor PMG
� Chain-sprocket gear coupling between rotor shaft and generator
� Diode bridge at the generator output coupled to a capacitor bank
and switchable load
� Customized DAQ unit with 4 sensed signals (rotor speed, flow velocity, load voltage, load current)
`
Vertical
axis turbine
Permanent magnet
generator
Chain-sprocket
gearing Diode rectifier
Capacitor
bank
Switchabl
e resistors
Signal conditioning and
Data Acquisition Unit
Generator speed
Carriage speed
Bus voltage (dc)
Bus current (dc)
Bus (dc)
Mechanical conversion
Electrical conversionSignal flow
31
Modeling & Validation
Test Apparatus and Model Validation (cont’d)
Tow-tank test apparatus (test conditions)
� Tested at MUN OERC tow tank (~55 m length)
� Each run was limited to 15-25 seconds
� Rotor mounting required
special arrangements
� Start-up and loading
manually adjusted.
32
� Cogging in PMG directly affects start-up behavior
� Unloaded rotor self-starts at 0.65 ~ 0.75 m/s
� Test prototype with load self-starts at 1.75 ~ 1.85 m/s
� Simulations successfully exhibit similar behavior
Modeling & Validation
Test Apparatus and Model Validation (cont’d)
Tow-tank test apparatus (model validation – start-up)
33
Modeling & Validation
Test Apparatus and Model Validation (cont’d)
Tow-tank test apparatus (model validation – torque ripple)
� Torque ripple is reflected on load current
� System inertia and capacitor bank reduce low frequency
ripple
� Ripple magnitude is dominant in low TSR conditions
� Ripple frequency directly relates to rotor speed
� Exact instance of ripple
occurrence is time-shifted in
simulation.
0 5 10 15 200
300
600
0 5 10 15 200
50
100
0 5 10 15 200
10
20
0 5 10 15 200
1.5
33
Time (s)
Experiment Simulation
Generator speed (rpm)
dc bus/load voltage (V)
dc bus/load current (A)
c
34
Modeling & Validation
Test Apparatus and Model Validation (cont’d)
Tow-tank apparatus (model validation – overall performance )
� Incorporation of non-linearity directly affects representation of
overall power output and efficiency
� Subtle improvements can be made (e.g., efficiency
calculations)
� Overall peak efficiency is ~ 20%
and optimum TSR is ~ 2.15 for this system
� Simulation time is short and tests
conform to simulations.
0 5 10 15 200
250
500500
0 5 10 15 200
50
100
0 5 10 15 200
5
10
0 5 10 15 200
200
400
0 5 10 15 200
2
4
Time(s)
Experiment Simulation
Generator speed (rpm)
dc bus/load voltage (V)
dc bus/load current (A)
dc bus/load power (watt)
Carriage/water velocity (m/s)
0 5 10 15 200
0.2
0.4Overall efficieny
35
� Introduction
� Review & Critique
� Modeling & Validation
� Controller Evaluation
� Adaptive Controller Synthesis
� Conclusion
36
Controller Evaluation
Control Objectives & Regions� General objective:
To achieve acceptable steady-state and transient performance
� Specific objective:
To adjust the rotor speed such that the maximum power point can be tracked
� Control Regions:o Start-up, maximum power tracking (MPT) and speed-limiting
o Hydrokinetic systems exhibits wide MPT region
StartupMaximum Power Tracking
Water velocity (m/s)
0.5 2.5Cut-in Rated
Below-Rated
Rated Power
Speed Limiting
Rotor speed (rad/s)
Rated Speed
Rated Power
Rated water
velocity
(~2.5 m/s)
Increasing
water velocity
Power Limiting
37
Controller Evaluation
Control Objectives & Regions (cont’d)
� Technological diversity:
Which MPT method would suit horizontal/vertical, ducted/free-flowing, partial/full submersion,
if at all possible ?
� State of the technology:
How to gain confidence in a particular MPT method, given little operational experience exists ?
� Resource conditions:
How to adjust a turbine’s operational parameters against variations in water velocity, level,
density, etc. ?
� Turbine design and operation:
To what extent the Cp vs. TSR curve can be relied upon toward MPT controller synthesis
(uncertain curve profile, over-time drifts/degradation, and possible local maxima/minima)
� Underwater instrumentation:
How to avoid reliance upon flow measuring instruments in implementing a MPT controller ?
38
Controller Evaluation
Effects of Efficiency Nonlinearity
� Noticeable nonlinearity within various subsystems’ efficiency characteristics
can be observed
� In addition to achieving optimum TSR,
other control requirements are present
,p sys
C η
λ
^ ^
( , )pCλ
^ ^
( , )syssys
λ η
^ ^
,r h
N PhP
rN
V
gη
gI
^ ^
( , )g gI ηg
N
eη
eI
^ ^
( , )e eI ηeF
Secondary conversion
0 0.25 0.5 0.75 1 1.250.5
0.6
0.7
0.8
0.9
1
Rectifier current (p.u.)
Rec
tifi
er e
ffic
ien
cy
Test data
Fit to test data
0 0.25 0.5 0.75 1 1.250
0.2
0.4
0.6
0.8
1
Converter current (p.u.)
Co
nv
erte
r ef
fici
ency
Test data
Fit to test data
0 0.25 0.5 0.75 1 1.250.2
0.4
0.6
0.8
1
Inverter current (p.u.)
Inv
erte
r ef
fici
ency
Test data
Fit to test data
0 0.25 0.5 0.75 1 1.250.2
0.3
0.4
0.5
0.6
0.7
0.8
Generator current (p.u.)
Gen
erat
or
effi
cien
cy
data : 0.93 p.u.
data : 0.86 p.u.
data : 0.70 p.u.
Fit to 0.93 p.u.
Fit to 0.86 p.u.
Fit to 0.70 p.u.
Rotor Speed in p.u.
0 0.25 0.5 0.75 1 1.250
0.25
0.5
0.75
1
1.25
Rotor speed (p.u.)
Sh
aft
po
wer
(p
.u.)
2.50 m/s
2.25 m/s
2.00 m/s
1.75 m/s
1.50 m/s
1.25 m/s
1.00 m/s
Water velocity
in m/s.
0 2 4 60
0.1
0.2
0.3
0.4
0.5
0.6
Tip Speed Ratio (TSR)
Po
wer
co
effi
cien
t
Theortical estimate
Fit to theoretical estimate
(a)
(c)
(e)(b)
(d)
(f)
39
Controller Evaluation
Effects of Efficiency Nonlinearity (cont’d)
� Method to realize the true shape of the performance
curve & power curve needs to be developed
� An iterative method using a-priori knowledge of all the
subsystems’ efficiency profile
(after normalization to a base quantity) is proposed
Start
Initialization
End
Sweeping
variables
Power Output,
Rotational speed
Next subsystem
Power input
p.u. Index
variable(s)
Efficiency
information
Power output
Sink
Next
subsystem
Y
N
Output curves
Start
Tests (experimental
or analytical)
Efficiency vs. index
variable
Efficiency vs. p.u.
variable
Next
subsystem
End
Sink
YN
Database
Pre-processing
40
Controller Evaluation
Effects of Efficiency Nonlinearity (cont’d)
0 1 2 3 4 50
0.05
0.1
0.15
0.2
0.25
0.3
X: 2.1
Y: 0.2218
Tip Speed Ratio
Sy
stem
eff
icie
ncy
System A
System B
System C
0 1 2 3 4 50
0.05
0.1
0.15
0.2
0.25
0.3
X: 2.1
Y: 0.2218
Tip Speed Ratio
Sy
stem
eff
icie
ncy
X: 2.2
Y: 0.2023
X: 1.9
Y: 0.1632
X: 2.5
Y: 0.163
System A
System B
System C
0 1 2 3 4 50
0.05
0.1
0.15
0.2
0.25
0.3
X: 2.1
Y: 0.2218
Tip Speed Ratio
Sy
stem
eff
icie
ncy X: 2.2
Y: 0.1864
X: 3.1
Y: 0.1186X: 1.8
Y: 0.1132
System A
System B
System C
(a) V=2.00 m/s
(b) V=2.25 m/s
(c) V=2.50 m/s
� System A: Typical system with nonlinearity in the
front-end (rotor performance) only
� System B: Physical system (test hardware) with
true nonlinearity in all subsystems
� System C: Fictive system with significant nonlinearity
in more than one subsystems
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.05
0.1
0.15
0.2
0.25
Tip Speed Ratio
Ov
eral
l sy
stem
eff
icie
ncy
1.75 m/s
1.85 m/s
1.95 m/s
2.00 m/s
2.10 m/s
2.25 m/s
2.40 m/s
2.45 m/s
2.50 m/s
2.65 m/s
2.75 m/s
Estimated curve
0 0.5 1 1.5 2 2.50
100
200
300
400
500
Water velocity (m/s)
Po
wer
ou
tpu
t (w
att)
Estimate with nonlinear efficiency
Estimate with constant efficiency
Experimental data points
(b)
(a)
41
Controller Evaluation
Candidate Control Methods
� Power tracking methods applied in wind & photovoltaic systems
� Three basic control methods in wind energy systems can be identified (based on parameters being measured/controlled):
o Tip speed ratio (TSR) method
o Power signal feedback (PSF) method
o Hill climbing search (HCS) method
� Other methods (such as, torque control, velocity estimation, etc.) can be shown to be variants of these methods.
42
Controller Evaluation
Candidate Control Methods (cont’d)
Tip speed ratio (TSR) method :
� Most fundamental and the most direct method
� Seldom used due to high reliance on flow measurement
� Depends entirely on the prior knowledge of the normalized performance curve
� Simulation with a P-type controller:
� Block representation:
V ∗trm= kptsr(λ− λ)
λ
rotωeff
rot
v
Rωλ =
effv
λ
43
Controller Evaluation
Candidate Control Methods (cont’d)
Power signal feedback (PSF) method:
� Needs dimensional performance curves (‘power vs. speed’ or
‘torque vs. speed’ curve)
� Simulation with a P-type controller:
� Optimum/reference speed:
where and
� Block representation:
V ∗trm= kppsf (ω
∗rot− ωrot)
ω∗rot=(
P∗
sys
knccheff
) 1
3
λ =ω∗rot
R
veffkncc = ρwR
4 Cp
λ3kcf
sysP
rotω
effh*
rotω
sysP
effh
*
rotω
44
Controller Evaluation
Candidate Control Methods (cont’d)
Hill climbing search (HCS) method:� Changes in rotor speed and variations in power output are measured
� Tracking reference is generated in an iterative manner
� Sign and magnitude of incremental tracking reference can be found by
� Rotor speed is controlled around the new tracking information
� Block representation:
ω∗rot(k + 1) = ω∗
rot(k) + ∆ω∗
rot
∆ω∗rot= sign(∆ωrot,∆Psys)×
∣∣∆ω∗rot
∣∣
∣∣∆ω∗rot
∣∣ = kphcs |∆Psys|sign(∆ωrot,∆Psys) = sign(∆ωrot)× sign(∆Psys)
V ∗trm= kphcs(ω
∗rot(k + 1)− ω∗
rot)
)1k(* +ω
sysP
rotω
*( 1)
rotkω +
45
Controller Evaluation
Candidate Control Methods (cont’d)
Implementation in Matlab-SimulinkTM:
Terminator
h_subh_ef f
v _s v _ef f
v _s
H
v _ef f
H
w _rot
T_mec
Lambda
Rotor
V_g
I_gr
PinRECT
V_gr
I_g
P_rec
Rectifier
P_rect
I_gr
PinRECT
P_rl
RECT loss
P_rlI_grE_g
N_gen
P_cl+P_rot
P_tot
PMA loss
T_gen
I_g
P_cl+P_rot
V_g
N_gen
E_g
PMA
V_co
PinINVC
P_inv
I_c
P*inv
I_i
Inverter
I_i
P*invPinINV
INV loss
P_inv
Lambda
P_inv
V_trm
Hv_eff
N_gen
T_mec
Lambda
N_gen
T_gen
w_rot
Drivetrain
V_gr
I_c
V_trm
PinCONV
V_co
I_gr
P_con
Converter
P_con
I_cPinCONV
CON loss
Vgr
1
0.95s+1tac
2.15
TSRref
PID
Kstsr
V_trmPID
Gain
N_gen
Lambda
1
0.95s+1tac
1
0.75s+1
V_trmPID
Gain
N_gen
P_inv
Hf(u)f(u)
Controller 1
0.75s+1
1
0.95s+1
tacg
1
-K-
P
NNref V_trmPID
Gain
N_gen
P_inv
1
Nref
0.15
z
1
z
1
z
1
1
0.1s+1
Transfer Fcn2
Sign
10
|u|
Abs1
2
N
1
P
Nref
46
Controller Evaluation
Candidate Control Methods (cont’d)
0 10 20 30 40 50 60 70 80 900
125
250
500500
Output power (watt)
0 10 20 30 40 50 60 70 80 900
125
250250
500
Output power (watt)
0 10 20 30 40 50 60 70 80 900.3
0.35
0.4
0 10 20 30 40 50 60 70 80 902
2.25
2.52.5
Time (sec)
Water height (m)
Water veloicty (m/s)
0 10 20 30 40 50 60 70 80 900
125
250
500500
Output power (watt)
Simulation results:
0 10 20 30 40 50 60 70 80 900
125
250250
500
Output power (watt)
0 10 20 30 40 50 60 70 80 900.3
0.35
0.4
0 10 20 30 40 50 60 70 80 902
2.25
2.52.5
Time (sec)
Water height (m)
Water veloicty (m/s)
0 10 20 30 40 50 60 70 80 900
125
250
500500
Output power (watt)
0 10 20 30 40 50 60 70 80 900
125
250
500500
Output power (watt)
47
� Tip speed ratio (TSR) method:
+ Superior steady-state and dynamic characteristics
+ Conceptually simple
−−−− Absolute reliance on a-priori knowledge of the optimum operating point
− Velocity measurement is required, which is prone to reliability and accuracy issues
� Power signal feedback (PSF) method:
+Moderate steady-state and dynamic characteristics
+ Conceptually simple & less dependent on a-priori knowledge
−−−− Possibilities of sub-optimal operation
−−−− Controller design process is often subject to device specific parameter tuning
−−−− Water level measurement is required, which is prone to reliability and accuracy issues
� Hill climbing search (HCS) method:
+Model/device independent and exhibits adaptive performance
+ Can be implemented without using underwater sensors
−−−− System output can be oscillatory in nature and no guarantee of system stability
−−−− Step size needs to be properly tuned considering the turbine dynamics and settling time
Controller Evaluation
Candidate Control Methods (cont’d)
48
Attributes of a more suitable power tracking controller for hydrokinetic systems:
� Adaptive
... adapts to variations in internal and external parameters & disturbances
� Sensorless
... does not require underwater instrumentation (i.e, flow/speed sensors)
� Model independent
… can be tuned without relying on the performance curve & model details
Controller Evaluation
Candidate Control Methods (cont’d)
49
� Introduction
� Review & Critique
� Modeling & Validation
� Controller Evaluation
� Adaptive Controller Synthesis
� Conclusion
50
Adaptive Controller Synthesis
Extremum Seeking Control (ESC)
� A special class of non-linear adaptive control method
� Model-independent and self-regulating to an unknown setpoint
� Particularly suitable where a single maximum or minimum
characterizes the non-linearity
� Primary difference with mainstream adaptive control methods:
ESC is capable of working under unknown reference
� Early research dates back to 1922, significant work done during 1940-1970 through Soviet-era activities
� Series of fundamental works by Krsti´c et. al. has caused a noticeable resurgence
� Application in wind, solar photovoltaic & fuel-cell systems being
reported
51
Adaptive Controller Synthesis
Extremum Seeking Control (cont’d)Principles of ESC, plants with static nonlinearity:
� Plant model:
� Unknown setpoint (maxima):
� Plant input:
� Estimate of the setpoint:
� Estimation error:
� By entering
in the plant model, it can be shown that
(after reductions):
� With , , it is guaranteed that estimation
error will always approach zero
� Frequencies of interest ( ):
o Fastest: Plant dynamics,
o Medium: Perturbation signal frequency,
o Slowest:Washout filter cut-off frequency,
fx(θx) = f∗x +12f
′′x (θx − θ∗x)
2
θ∗x
θx = ax sin(ωxt) + θx
θx
θx = θ∗x − θx
θx − θ∗x = ax sin(ωxt)− θx
.
θx≈ 1
2kxaxbxf′′
x θx
f ′′x < 0 kxaxbx > 0 sign(.
θx) = sign(θx)
ωpa
ωx
ωhx
ωhx < ωx < ωpa
52
Adaptive Controller Synthesis
Extremum Seeking Control (cont’d)Considerations for ESC in plants with nonlinear dynamics:
� Use of Wiener-Hammerstein model
� Setpoint may drift during prolonged operation or may be unknown due to
modeling uncertainty
� Internal and external noise may impact the success of convergence
� Average linearized relationship between error in estimated & actual optimum
point:
� Average linearized relationship between output error & system noise:
θxθ∗x= 1
1+Lx(s)
ΥxFox(s)[f∗x ]+ϑx
= − Mx(s)1+Mx(s)
53
Adaptive Controller Synthesis
ESC in Hydrokinetic Systems
� Hydrokinetic systems with static plant model
� Assessment of dominant nonlinear plant characteristics
54
Adaptive Controller Synthesis
ESC in Hydrokinetic Systems (cont’d)
� Hydrokinetic systems with dynamic plant model studied with
o Compensator:
o Input & output dynamics:
� Frequency domain analysis with multiple cases having variations in controller parameters
Cx(s) = 1 + dxs
Fix(s) = Fox(s) =1
0.5s+1
55
Adaptive Controller Synthesis
ESC in Hydrokinetic Systems (cont’d)
� Favorable features:
o Model independence
o Robustness against drift
o Stabilization near maxima
� Challenge areas:
o High number of parameters to be tuned
o Heuristic method of parameter tuning
56
Adaptive Controller Synthesis
ESC Synthesis & Implementation� On a hierarchical viewpoint, there are two levels of control within the ESC design
exercise:
o Internal speed controller design (and development of input dynamics model)
o Extremum seeking controller parameter selection (and development of output dynamics
model).
� External extremum-seeking controller adaptively generates the speed reference
� Internal controller adjusts the set point of the power electronic stage such that the
speed reference (as generated by the extremum-seeking controller) can be tracked
� Two measured parameters (rotational speed & output power) and one control
variable (power converter settings)
57
Adaptive Controller Synthesis
ESC Synthesis & Implementation (cont’d)
Internal speed controller design:
� Represented using a reduced order linear averaged model
� Plant-actuator transfer function:
where , ,
and ,
� Speed sensor transfer function:
� Speed controller (minimal overshoot & sufficiently damped):
� Overall transfer function (input dynamics block):
Gpa(s) =kpa
τpas+1
kpa =Ngr
ktsc ktsc = −12ρwArveffR
2C′TO C ′TO =∂CT (λ)
∂λ
∣∣∣λsys
τpa =NgrJerg
ktscJerg = Jgen +
1N2grJrot
Gs(s) =Ngen
Ngr= 1
τ1s+1
Gω(s) = kpω +kiωs
inτ
Fix(s) =kpa(kpωτ1s
2+(kpωτ1+kpω)s+kiω)τpaτ1s3+(τpa+τ1)s2+kpakpωs+kpakiω
≈ 1τins+1
58
Adaptive Controller Synthesis
ESC Synthesis & Implementation (cont’d)
ESC parameter tuning considerations:
� Each parameter affects the performance (in various degrees) in
terms of
o convergence, overshoot, limit cycle amplitude,
o sensitivity to noise, capability to override local maxima,
o structural stress & overall stability
� Modulating and demodulating signal:
� Controller gain:
� Modulating signal frequency:
� Washout filter cut-off frequency using:
� Dynamic compensator:
� Output dynamic block:
ax = bx < 1% of Nbgen
kx ≈Pbinv
Nbgen
ωpa = 2π1
τin
ωpa ≥ ωx ≥ ωhx > ωv
dx ≈ τin
Fox(s) =1
τouts+1
59
Controller Evaluation
ESC Synthesis & Implementation (cont’d)
ESC design steps for test hydrokinetic systems:
60
Adaptive Controller Synthesis
ESC Synthesis & Implementation (cont’d)
Test of stability, tracking capability & sensitivity to noise:
Drift in setpoint Sensitivity to noise
-50
0
50
Magnitude (
dB
)
10-2
10-1
100
101
0
45
90
Phase (
deg)
Bode Diagram
Frequency (rad/sec)
0 10 20 30 40 500
0.2
0.4
0.6
0.8
1Step Response
Time (sec)
Am
plit
ude
-200
0
200
Magnitude (
dB
)
10-2
100
102
0
180
360
Phase (
deg)
Bode Diagram
Frequency (rad/sec)
0 10 20 30 40 50-0.5
0
0.5Step Response
Time (sec)
Am
plit
ude
61
Adaptive Controller Synthesis
ESC Synthesis & Implementation (cont’d)
Implementation in simulation model:
Terminator
h_subh_ef f
v _s v _ef f
v _s
H
v _ef f
H
w _rot
T_mec
Lambda
Rotor
V_g
I_gr
PinRECT
V_gr
I_g
P_rec
Rectifier
P_rect
I_gr
PinRECT
P_rl
RECT loss
P_rlI_grE_g
N_gen
P_cl+P_rot
P_tot
PMA loss
T_gen
I_g
P_cl+P_rot
V_g
N_gen
E_g
PMA
V_co
PinINVC
P_inv
I_c
P*inv
I_i
Inverter
I_i
P*invPinINV
INV loss
P_inv
Lambda
P_inv
V_trm
Hv_eff
N_gen
T_mec
Lambda
N_gen
T_gen
w_rot
Drivetrain
V_gr
I_c
V_trm
PinCONV
V_co
I_gr
P_con
Converter
P_con
I_cPinCONV
CON loss
Vgr
w=2pi
1.15
k_x
-K-a_x
1
0.75s+1
Wattmeter
s
s+pi
Washout fi l ter
1
0.95s+1
Speed sensor
PID
Speed controller
Modulation
V_trm
P_inv
P_invN_gen
Lambda
v_eff
N_gen
Demodulation
0.8s+1
s
C_x(s)
XiN*_gen
62
Adaptive Controller Synthesis
ESC Synthesis & Implementation (cont’d)
0 5 10 15 20 25 300
100
200
0 5 10 15 20 25 300
250
500500
0 5 10 15 20 25 300
1
2
3
0 5 10 15 20 25 300
1
2
3
Time (sec)
Output power (watt)
Generator speed (rpm)
Tip speed ratio
Water veloicty (m/s)
Simulation results (single-step & dual-ramp variations):
0 5 10 15 20 25 300
100
200
0 5 10 15 20 25 300
200
400
0 5 10 15 20 25 300
1
2
3
0 5 10 15 20 25 302
2.25
2.52.5
Time (sec)
Output power (watt)
Generator speed (rpm)
Tip speed ratio
Water veloicty (m/s)
63
Adaptive Controller Synthesis
ESC Synthesis & Implementation (cont’d)
0 10 20 30 40 50 60 70 80 900
125
250
0 10 20 30 40 50 60 70 80 900
250
500500
0 10 20 30 40 50 60 70 80 900
2
4
0 10 20 30 40 50 60 70 80 900.3
0.35
0.40.4
0 10 20 30 40 50 60 70 80 902
2.25
2.52.5
Time (sec)
Output power (watt)
Water veloicty (m/s)
Water height (m)
Tip speed ratio
Generator speed (rpm)
Simulation results (multiple-step & stochastic variations):
0 10 20 30 40 50 60 70 80 900
125
250
0 10 20 30 40 50 60 70 80 900
250
500500
0 10 20 30 40 50 60 70 80 900
2
4
0 10 20 30 40 50 60 70 80 900.3
0.35
0.40.4
0 10 20 30 40 50 60 70 80 902
2.25
2.52.5
Time (sec)
Output power (watt)
Water veloicty (m/s)
Water height (m)
Tip speed ratio
Generator speed (rpm)
64
0 50 100 150 200 250 3000
125
250
0 50 100 150 200 250 3000
250
500500
0 50 100 150 200 250 3000
1
2
3
0 50 100 150 200 250 3000.25
0.3
0.35
0 50 100 150 200 250 3002
2.25
2.52.5
Time (sec)
Output power (watt)
Generator speed (rpm)
Tip speed ratio
Water height (m)
Water veloicty (m/s)
Adaptive Controller Synthesis
ESC Synthesis & Implementation (cont’d)
Simulation results (stochastic variations):
65
Adaptive Controller Synthesis
ESC Synthesis & Implementation (cont’d)
Comparative (subjective) evaluation:
66
� Introduction
� Review & Critique
� Modeling & Validation
� Controller Evaluation
� Adaptive Controller Synthesis
� Conclusion
67
Conclusion
Summary
� Due emphasis given on identifying the problem of maximum power point tracking for hydrokinetic systems
� Efforts given to develop sufficient operational experience and multiple design, testing & performance evaluation activities
undertaken
� Detailed modeling of systems/subsystems conducted and validated
� Comparative evaluation of various candidate power tracking
methods conducted
� Suitability of extremum seeking control method investigated & systematic parameter tuning method developed
� The ESC method has been found to be of good promise
68
Conclusion
Future Work
� Open-ended initiative where further design & development activities are indispensable
� Future work along this topic needs to be directly linked to real-world trials
� Device sizes (physical dimensions as well as power ratings) need
to be sufficiently large
� Considerations for economic aspects, environmental impacts,
practical usage & sustainability factors need also be given
� Significant test & development program underway
69
Conclusion
Contributions
� M.J. Khan, M.T. Iqbal, J.E. Quaicoe; Dynamics of a Vertical Axis Hydrokinetic
Energy Conversion System with a Rectifier Coupled Multi-pole Permanent Magnet
Generator; IET Renewable Power Generation, Vol. 4, Iss. 2, pp. 116–1272010,
2010
� M. J. Khan, M. T. Iqbal and J. E. Quaicoe, Tow tank testing and performance
evaluation of a permanent magnet generator based small vertical axis hydrokinetic turbine,
Journal of Ocean Technology, Vol,. 4, No. 1, pp. 66-84, 2009.
� M.J. Khan, G. Bhuyan, M.T. Iqbal, J.E. Quaicoe; Hydrokinetic energy conversion
systems and assessment of horizontal and vertical axis turbines for river and tidal
applications: A technology status review; Applied Energy, Volume 86, Issue 10,
October 2009, Pages 1823-1835
� M.J. Khan, M.T. Iqbal, J.E. Quaicoe; River current energy conversion systems:
Progress, prospects and challenges; Renewable and Sustainable Energy Reviews; 12 (2008)
2177–2193
70
Conclusion
Contributions (cont’d)� Jahangir Khan, Tariq Iqbal and John Quaicoe; Effects of Nonlinear Efficiency Characteristics on the Power-
Tracking Control: A Case Study of Hydrokinetic Energy Conversion System, Presented at IEEE Energy Conversion Congress and Exposition (ECCE), San Jose, California, USA, September 20-24, 2009
� Jahangir Khan, Ali Moshref, Gouri Bhuyan; A Generic Outline for Dynamic Modeling of Ocean Wave and Tidal Current Energy Conversion Systems; Presented at IEEE PES General Meeting, 26-30 July, 2009, Calgary, Alberta, Canada
� M. J. Khan, M.T. Iqbal, J.E. Quaicoe; Tow Tank Testing and Performance Evaluation of a Permanent Magnet Generator Based Small Vertical Axis Hydrokinetic Turbine; NAPS 2008; September 2008; Calgary; Canada
� Jahangir Khan, Gouri Bhuyan, Ali Moshref, Kip Morison, John H. Pease Jr., and Jim Gurney, ‘Ocean Wave and Tidal Current Conversion Technologies and their Interaction with Electrical Networks’, IEEE PES General Meeting, 20-24 July 2008, Pittsburgh, PA, USA
� M.J. Khan, M.T. Iqbal, J.E. Quaicoe; Dynamics of a Vertical Axis Hydrokinetic Energy Conversion System with Rectifier Coupled Multi-pole Permanent Magnet Generator, NECEC 2008; St. John s, NL, Canada; November 2008
� M. J. A. Khan, M. T. Iqbal, Simplified modeling of rectifier coupled brush-less DC generators, Presented at IEEE 4th international conference on electrical and computer engineering conference, Dhaka Bangladesh, December 18-21, 2006.
� M. J. A. Khan, M. T. Iqbal, and J. E. Quaicoe, Design Considerations of a Straight Bladed Darrieus Rotor for River Current Turbines, Presented at IEEE International Symposium on Industrial Electronics ISIE06, Montreal, Canada, July 9-13, 2006.
� M. J. A. Khan, M. T. Iqbal, and J. E. Quaicoe, A technology review and simulation based performance analysis ofriver current turbine, CCECE 2006: Canadian Conference on Electrical and Computer Engineering Ottawa 7-10 May, 2006.
71
Conclusion
Acknowledgement
� Supervisory Committee, Examination Committee
� NSERC, AIF
� Dr. Gouri Bhuyan, Dr. Ali Moshref & Powertech Labs Inc., BC
� Clayton Bear, Vince Ginter and Justin Boal from New Energy Corp Inc. (NECI), AB
� Jim Gosse, Razzaqul Ahsan, Dr. Brian Veitch, Paul Bishop, Jerry Smith, Billy Bidgood, MUN
� Faculty of Engineering & Applied Science, MUN
� School of Graduate Studies, MUN
� Technical Services, MUN
Thank You