Adaptive Power Tracking Control of Hydrokinetic Energy ...tariq/mjakhanphd.pdf · 2 Outline...

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





� 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





� 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





� 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


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


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


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


Darrieus Rotor Performance Analysis (cont’d)

� Performance analysis of Darrieus rotors

� Single-disk multiple-streamtube analysis:

16



� 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



� 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


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


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



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



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



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



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



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



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


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


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



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.



Tow-tank test apparatus (turbine rotors)

30



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



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



Tow-tank test apparatus (model validation – start-up)

33



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)



dc bus/load voltage (V)

dc bus/load current (A)

c

34



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)



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





� 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


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


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


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


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


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


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



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


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



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


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



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



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)


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



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



49

� Introduction





� 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


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


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


ESC in Hydrokinetic Systems

� Hydrokinetic systems with static plant model

� Assessment of dominant nonlinear plant characteristics

54


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


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


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


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



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



ESC design steps for test hydrokinetic systems:

60



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



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



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)


Tip speed ratio


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)


Tip speed ratio


63



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 height (m)

Tip speed ratio


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 height (m)

Tip speed ratio


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)


Tip speed ratio

Water height (m)




Simulation results (stochastic variations):

65



Comparative (subjective) evaluation:

66

� Introduction





� 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

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