Countercurrent braking - class.ece.uw.edu

3/3/2012

1

Chapter 10: Braking of IMDynamic Braking

Dynamic braking

Ib

Ib

Vbraking

a c

b

n

Stator Circuit

b1

bdc I

R5.1VI

Rotor Circuit

Rb

Rotorterminals

Rotorwindings

Q1

Q2

Q3

Q4

Q5

Q6

a b cVdc

o

Example• An induction motor is driven by a six-step converter.

The voltage at the dc link is 200 V. At normal full load operation, the motor current is 25 A. The stator resistance is 0.5 . The FWM technique is used during the dynamic braking. Calculate the duty ratio of the FWM.

3/3/2012

2

1

bb R5.1

VI

5.05.1V75 b

dcb VdV

dc

b

VVd

Error in bookThe duty ratio iscorrectly computed here

Counter Current Braking

Countercurrent braking

ABC

ACB

nsns

65

Tl

4

Torque

Speed

12

3

ABC Sequence

ACB Sequence

Tl

12

s

s

s

s

nnn

nnns

s

s

s

s

s

s

nnn

nnn

nnns

)(4

0)(6

s

s

s

s

nnn

nnns

11

s

s

nnns

13 s

s

nns

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3

Operatingpoint

MotorSpeed

Fieldspeed

Slip Approximationmethod

Motor Torque MotorCurrent

1 n ns s1 < 1 Small slip'2s

12

RsV

'2

1RsV

2 n - nss2 > 1 Large slip

2eqs2

'2

2

X)(sRV

eqXV

3 0 - nss3 = 1 Large slip

2eqs3

'2

2

X)(sRV

eqXV

4 - n - nss4 < 1 Small slip

'2s

42

R)(sV

'2

4RsV

5 - ns - nss5 = 0 Small slip 0 0

6n ns6

- nss6 < 0 Small slip

'2s

62

R)(sV

'2

6RsV

Regenerative Braking

Basic Relationships

f: Frequency of the sourcepp: Number of pole pairsp: Number of poless: Slipn: Speed in rpm: Speed in rad/sec

nsn

rpm12060pf

ppfns

s

s

s

s

nnns

60n2

2eq

2'2

1s

'2

2d

Xs

RRs

RVT

s

sn

nns

Torque

Speed

S=0

S > 0

S < 0Motor

Generator

3/3/2012

4

1

Torque

Speed

T1T2

2

Regenerative brakingMotor Model

2

2

12

'2 N

NRR

2

2

12

'2 N

NXX

1

2r

'2 N

NII

I2’I1

X2’ R2

’

Xm

Im

Rm V )s1(

sR'

2

S>0,positiveResistance

X1 R1

Generator Model

2

2

12

'2 N

NRR

2

2

12

'2 N

NXX

1

2r

'2 N

NII

I2’I1

X2’ R2

’

Xm

Im

Rm V )s1(

sR'

2

S<0,negativeResistance

X1 R1

'2X X1

Vs

R1 '2R

)s1(s

R'2

'2I

Active Power Flow

Xm

Im

Rm

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5

Power Flow Input Power (Pm)

Rotor Copper Losses (Pcu 2)

Airgap Power (Pg)

Output Power (Pe) Stator Losses: Copper losses (Pcu 1) Core losses (Piron)

)1()('22'

2 ss

RIPP dm

11 cosIVPe m

iron

cu

RVP

RIP2

12

11

'2

2'22 )( RIPcu s

RIPPP cumg

'22'

22 )(

TPm

sm TP

Simplified Generator Model

'21eq

'21eq

XXX

RRR

I2’

I1

Xeq Req

Xm

Im

Rm V )s1(

sR'

2

NegativeResistance

Applications of Regenerative Braking

• Induction machines are heavily used in wind energy systems

• If the wind power drives the induction machines above its synchronous speed, the induction machine operates in its regenerative braking mode– The induction machine is a generator that delivers real

power to the grid.– The induction machine doesn’t produce reactive power

• Reactive power must be supplied by the grid or locally.

Real Power Flow

Real Power

Xeq Req

Xm

Im

Rm V )s1(

sR'

2

NegativeResistance

Real Power

Real Power

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6

Main Advantages of IG

• Main Advantages:– Rugged machine; requires little maintenance– The least expensive option among all other wind

systems– Self-synchronized with the power grid; no

synchronization equipment• Main disadvantages:

– Reactive power demand is high– Fluctuations in voltage– Limited control actions

Power-Speed Characteristics: Real Power

1600 1800 2000 2200 2400 2600 2800-3000

-2000

-1000

0

1000

2000

3000

Speed (rpm)

Win

d Tu

rbin

e O

utpu

t (kW

)

Generator Action

Mot

or A

ctio

n

ns

2

2'2

1

'2

23

eqs

ss

e

Xnn

RnRnn

RnVP

Reactive Power Flow

Reactive Power

Xeq Req

Xm

Im

Rm V )s1(

sR'

2

NegativeResistance

Reactive Power

Reactive Power

Power-Speed Characteristics: Reactive Power

1600 1800 2000 2200 2400 2600 28000

1000

2000

3000

4000

5000

6000

Speed (rpm)

Win

d Tu

rbin

e R

eact

ive

Pow

er In

put (

kVA

r)

Generator Action

Mot

or A

ctio

n

2

2'2

1

2 1

eq

eq

m Xs

RR

XX

VQ

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Reactive Power

• The induction machine has no field circuit– draws significant amount of reactive power from

the grid– the magnitude of the reactive power imported from

the grid could exceed the magnitude of the generated real power

– The reactive power is dependent on the speed of the turbine, so it is continuously changing

– The voltage at the wind farm could sag and flicker

Voltage Variations

SCIG

GridVs=1pu

Xline

Load Vload=?

ConnectionPoint

Trunk Line

Speed

Rea

ctiv

e po

wer

sn

minQ

Generation range

2

2'2

1

2 1

eq

eq

m Xs

RR

XX

VQ

Q

VTime

Time

Vr

n

Time

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Voltage Fluctuations: Strong Trunk Line (Small Xline)

0 10 20 30 40 50 60 70 80 90 10018001810182018301840185018601870188018901900

TimeGen

erat

or S

peed

(rpm

)

0 10 20 30 40 50 60 70 80 90 1000.975

0.98

0.985

0.99

0.995

1

1.005

Time

Load

Vol

tage

(pu)

Voltage Fluctuations: Weak Trunk Line (Large Xline)

0 10 20 30 40 50 60 70 80 90 10018001810182018301840185018601870188018901900

Time

Gen

erat

or S

peed

(rpm

)

0 10 20 30 40 50 60 70 80 90 1000.75

0.8

0.85

0.9

0.95

1

Time

Load

Vol

tage

(pu)

Correlation of Voltage & Reactive Power

0 10 20 30 40 50 60 70 80 90 1000.75

0.8

0.85

0.9

0.95

1

Time

Load

Vol

tage

(pu)

0 10 20 30 40 50 60 70 80 90 100-5

0

5

10

15

20

25

30

Time

Gen

erat

or R

eact

ive

Pow

er (p

u)

Q

TimeQ

P

IM

Time

QcQc

Reactive power controller

P

Qs

Adaptive VAR Compensator (AVC)

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AVC Main Switching CircuitPower Line

50kvar

100kvar

200kvar

Switching at zero crossing of line voltage to eliminate switching transients

Tehachapi Data

Time (Hour)

-1

.

1.

2 4 6 8 10 12 14 16 18 20 22

AVC

IG

Line

time

(a)

(b)

Flicker Control

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Tehachapi Site: Flicker Control

tim e ( s )

rms v

olta

ge (V

)

1 1 41 1 51 1 61 1 71 1 81 1 91 2 0

0 5 1 0 1 5

p h a s e A

t im e ( s )

rms v

olta

ge (V

)

1 1 71 1 81 1 91 2 01 2 11 2 21 2 3

0 2 4 6 8 1 0

p h a s e A

Main Technologies for Wind Turbine Systems

• Generator– Asynchronous Generator (Induction Machine)

• Squirrel Cage Induction Generator (SCIG)• Wound Rotor Induction generator (WRIG)

– Synchronous Generator (SG)• Controls

– No Control or fixed compensation– Internal voltage and var control– External flicker and reactive power controls– Pitch control– AGC participation– Stability and ride through fault control– … … …

Main Categories of Wind Energy Systems

Power

SpeedMotor Characteristic

Wide range of Power

Narrow range of speed

Fixed speed System

Power

SpeedMotor Characteristic

Wide range of Power

Wide range of speed

Variable speed System

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11

Fixed Speed Wind Turbine (FSWT) System• Mainly directly grid coupled squirrel cage induction generator• The rotor speed variations are very small, approximately 1 to 2 % of the

rated speed. • Advantages of FSWT are

– Does not require brushes– Rugged construction– Low cost– Low maintenance– Simple to operate

• Drawbacks of FSWT are– Because the rotor speed cannot vary, fluctuations in wind speed translate

directly into drive train torque fluctuations. This causes more stress on the mechanical system

– The speed of the FSWT is very high (above the synchronous speed)• Higher structural loads• More noise• More bird collisions

Variable Speed Wind Turbine (VSWT) System

• The main advantage of VSWT are– The power can be regulated even when the speed of the turbine

changes widely– The system can produce power at low speeds (lower than the

synchronous speed)– The speed of the generator can be adjusted to achieve higher

aerodynamic efficiency (maximize the coefficient of performance)

– Lower mechanical stress due to the reduction of the drive train torque variations.

– Noise problems are reduced because the turbine runs at low speed.

• The main drawback of VSWT are– More expensive

Main Types of WTGFixed Speed Types• Type 1: Squirrel cage induction generator directly coupled to the grid. May have pitch control

• Type 2: Wound rotor induction machine with external rotor resistance control

Variable Speed Types• Type 3:Wound rotor Doubly‐fed induction generator (Voltage injected in the rotor winding)

• Type 4: Synchronous or induction generator, the stator is connected to the grid via power converter (Full converter)

Type1: SCIG with Fixed Compensation

Grid

Trunk Line

GSUxfm

Grid ConnectionPoint

HV‐GSUPoint

Farm CollectionPoint

HV‐GSU: High Voltage side of Generation Step‐Up transformer

Gear Box

SCIG

FixedCompensation

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12

Type1: SCIG with Variable Compensation

Grid

Trunk Line

GSUxfm


HV‐GSUPoint


HV‐GSU: High Voltage side of Generation Step‐Up transformer

Gear Box

SCIG

VariableCompensation

Type 2: Wound Rotor IG


Gear Box

WRIG

Pow

er

Speedns Δn

R1R2 R3

R1<R2<R3

2

2'2

1

'2

23

eqs

ss

e

Xnn

RnRnn

RnVP Type 3: Doubly Fed Induction Generator (DFIG)

Gear Box

WRIG

AC/DC + DC/AC


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Type 3: Doubly Fed Induction Generator (DFIG)

Gear Box

WRIG

DC/ACAC/DC

Line converter Rotor converterRotor inverter

dc Link

The power rating of the converter is often about 1/3 the generator rating

Doubly Fed Induction Generator (DFIG)

C

c

ba

vdc

Rotor Converter

vs

vs vs

Line Converter

50El-Sharkawi@University of Washington

El-Sharkawi@University of Washington

51

DC/AC

dc Link

AC

To rotor

AC/DCC AC

From Line

dci VdV32

)30(cos56.1

)30(cos1.1 max

rmsi

i

VdV

VdV2

maxVVrms

)30(cos6542.1 max VVdc

Example• Compute the duty ratio for an injected voltage

of 10V. The stator voltage is 690V. The triggering angle of the AC/DC converter is 50o

• Solution

32

2

10*9.2)80(cos*690*56.1

10

)3050(cos56.1

)30(cos56.1

d

VVd

VdV

rms

i

rmsi

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Rotor Injection X1

I2

Vi Vs

I1

s X2 R1 R2 N1 : N2

s E2

Frequency of Vi is the frequency of the rotor

srotor fsf

Rotor Injection X1

I2

Vi /sVs

I1

X2 R1 R2 /s N1 : N2

E2

I2’

I1

R2’/sXeq R1

Xm

Im

Rm Vs Vi

’/s

Rotor Injection

2'

21

'

'2 I

Xjs

RR

Vs

V

I

eq

si

I2’

I1

R2’/sXeq R1

Xm

Im

Rm Vs Vi

’/s

Both I2 and are functions of generator speed and injected voltage

Rotor Injection

Since I2 and are functions of the generator speed and injected voltage, P and Q are also functions of the generator speed and injected voltage

I2’

I1

R2’/sXeq R1

Xm

Im

Rm Vs Vi

’/s

m

sss

m

sss

XVIVQ

RVIVP

2

2

2

2

sin

cos

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Injected Voltage; Effect on Real Power

1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880-3000

-2000

-1000

0

1000

2000

3000

4000

Speed (rpm)

Win

d Tu

rbin

e po

wer

(kW

)Vi=0Vi>0Vi<o

Injected Voltage: Effect on Reactive Power

1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880-500

0

500

1000

1500

2000

2500

3000

Speed (rpm)

Win

d Tu

rbin

e R

eact

iev

Pow

er (k

VAr)

Vi=0Vi>0Vi<o

Constant Complex Power Operation

0 10 20 30 40 50 60 70 80 90 1001800

1820

1840

1860

1880

1900

Time

Spee

d (r

pm)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.5

0

0.5

1

1.5Complex Power Command

Real Power (MW)

Rea

ctiv

e Po

wer

(MVA

r)

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

Time

Inje

ctio

n Vo

ltage

(V)

0 10 20 30 40 50 60 70 80 90 100-200

-150

-100

-50

0

50

100

150

200

Time

Angl

e of

Inje

ctio

n Vo

ltage

Type 3: Basic Control of DFIG

Gear Box

WRIG

DC/ACAC/DC dc Link

El-Sharkawi@University of Washington 60

Power Control

InjectionControl

Target power

Actual power

Desired rotor current

Actual rotor current

Control signals

Controlled injected voltage

PWM

Referencesignal

Bus voltagesignal

VrVgc

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Type 3: Common Control for DFIG

Gear Box

WRIG

AC/DC + DC/AC

Controller

1. Power Command

Injected voltages

Pitch angle

3. Limits on Current, Voltage and speed2. Speed Command


Vr

Vgc

Type 3: Advanced Control with AGC

Gear Box

WRIG

AC/DC + DC/AC

AGCGrid Conditions and

requirements

Injected voltage

Pitch angle

Wind Conditions Plant objectives and limits


Type 4: SG with AGC (Full Converter)

AC/DC + DC/AC

Excitation


AGCGrid Conditions and

requirements

Excitation voltage

Pitch angle

Wind Conditions Plant objectives and limits

Performance Comparison

Type1 & 2 Type 3 Type 4

Voltage Control Poor Better Best

Flicker Control Poor Better Best

Low Voltage Ride-Through Poor Better Best

Stability Control Poor Better Best

AGC Control Poor Better Best

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Wind Turbine

Generator

High speed shaft

Low speed shaft

Rotating bladesGear box

Tower

Housing

Yaw

Tip speed ratio (TSR)

w: wind speedvtip: tip velocity of blade: angular speed of blade in rad/sn: blade speed is rps

rnrvtip 2

r

vtip

Blade

wvtip

Coefficient of Performance

The blades of the wind turbine only capture part of the available wind energy.

wind

bladep P

PC ,

Cp

Cp max

ideal

For fixed pitch angle, when wind speed changes, Cp changes

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18

Variable Pitch Angle

wind

bladep P

PC ,

For variable speed wind turbine, when wind speed changes, the pitch angle is changed to keep close to maximum

Cp

1

3

2

3 > 2 > 1

Betz Limit

• Not all of the energy present in a stream of moving air can be extracted– Building a wall would stop the air and no more

energy can be obtained• The maximum Theoretical energy that can be

extracted from a stream is 59%– This is known as Albert Betz maximu

• Most modern wind turbines are in the 35–45% range

Rotor Solidity

Solidity is the ratio of total rotorarea to total swept area

Low solidity (0.10) = high speed, low torqueHigh solidity (>0.80) = low speed, high torque

A

Ra

2

33SolidityRa

Aa

1.5 MW Turbine

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Basic Wind Turbine Specifications (2MW)

Rotor Diameter = 80 metersSwept Area = 5,026 m2

Blade Rotation = 15.5-16.5 rpmGenerator Voltage = 690 VoltsCapacity = 1,800-2,000 kWNacelle (housing) Weight = 77 tonsRotor Weight = 41 tonsTower Weight = 105 tonsTotal Weight = 223 tons

GE 3.6MW

Typical Blade lengthBlade length (m) Power Rating (kW)

27 22527-33 30033-40 50040-44 60044-48 75048-54 100054-64 150064-72 200072-80 2500

Can We Exceed 100m?• Wind speed increases with height above

ground• 100m diameter can produce 3-5MW• Can we go higher than 100m?

– Introduces transportation constraints in most highways

• Max trailer dimension is 4.1m (H) X 2.6m (W)– Requires large cranes that are not readily available– Produces a new set of technical and environmental

problems (impact on grid, wake, etc.)

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VESTAS 1.8MW

Off-Shore Wind System

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21

Orientation

Vertical Axis Horizontal Axis

Vertical Axis TurbinesAdvantages• Omnidirectional (accepts wind from any angle)• Can theoretically use less materials to capture the same

amount of windDisadvantages• Rotors generally near ground where wind speed is low• Centrifugal force stresses blades• Requires support at top of turbine rotor• Overall poor performance and reliability• Have never been commercially successful

Two Blades Turbines• Advantages:

– Runs at fast speed to improve Cp; gearbox ratio reduced

– Blades easier to assembled on ground• Disadvantages:

– For the same wind speed, the two-blade system captures less power then the three-blade system

– Creates gyroscopic imbalances (tower wind shade)

– Higher speed means more noise, visual, and wildlife impact

– Higher rate of bird collisions– Noisy

Three-Blade Turbine• Advantages:

– Slow rotation– three blades capture more energy than

two blades for the same wind speed– Gyroscopic forces are better balanced– More aesthetic, less noise, fewer bird

collisions• Disadvantages:

– Slower rotation increases gearbox costs– Rotor cannot fully assembled on the

ground

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22

Bending Moments (2-blade)• When one blade is at the top, it is

receiving the maximum force of the wind

• The bottom blade is in the shadow of the tower; thus receiving less force

• The forces are not balanced at hub– Torque on the hub is pulsating, thus

stressing the hub gears

Wind Force

Wind Force

Bending Moments (3-blade)• The bottom blade in the

shadow of the tower receives less than the maximum force

• The other two blades are not in the vertical position, so they also receive less than the maximum force

• The forces are balanced at the hub

Why not 5 or 7 Blades?• More expensive• Increase wind wall effect

– Reduction of wind speed in front of the blades, thus reducing the amount of energy that can be captured by the blade

Wind Force

Wind Force

Pitch, Yaw and Feather Control• Most turbines operate at wind speed of 12 – 30 mph• Pitch Control

– To maximize Cp– Reduce Cp when wind speed produces power higher

than the rating of the turbine– Regulate the output power of the turbine as part of grid

control action• Yaw Control

– To align the rotor to face the wind• Feathering

– To lock the blades at high wind speeds (>50mph)

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23

Typical Power-Speed Characteristics

Ramp down

Cut-in speedWind Speed

Pow

er

Cut-out speed

Wind power

Output PowerRatedPower

Ramp up

Rated speed

Wind Turbine PerformanceVestas V80 Power Curve

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 10 20 30 40 50 60

Windspeed MPH

Pow

er k

W

Typical On-Shore System

WPS

Grid

Trunk Line

GSUxfm On-Shore

Wind PowerSystem


HV-GSUPoint


HV-GSU: High Voltage side of Generation Step-Up transformer

Typical Off-Shore System

WPS

Grid

Trunk CableMarine Cable

GSUxfm Off-Shore

Wind PowerSystem


HV-GSUPoint


3/3/2012

24

Off-Shore Offshore Wind Energy

• A good match between generation and demand– 28 states in the USA have costal lines– These states consumes 78% of the national

electric energy• 900 MW offshore capacity installed in

Europe• 10 offshore system, 2.4GW capacity are

considered in the USA

Offshore Wind Energy• Normally between 2-5MW• 80-126m in blade length• Transportation restriction is less than on-shore systems• Mostly at relatively shallow water, depth of up to 30m• Marine cables are used to connect the systems to the

shore stations– Cable capacitance is much higher than that for overhead

lines– This may result in leading power factor at the shore station– Inductive compensation may be needed to prevent the

overvoltage at the shore stataion

Challenges to Offshore Systems

• High cost of installation– Transportation, construction, foundations,

anchors, and moorings• High cost of maintenance• Technology is limited for deep waters• Wind specific safety standards

– offshore oil and gas standards

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25

Challenges to Off-Shore Wind

• Prediction of the dynamic forces and motions acting on off-shore turbines are needed

• Offshore winds are much more difficult to characterize than winds over land

• Marine life– Foundations can act as artificial reefs– fish population increases– bird population increases– bird collisions increases

Challenges to Off-Shore Wind

• Interference with – commercial shipping and fishing– recreational boating.

• Could affect maritime radar systems • Visual impacts for systems close to shores • Impacts of low frequency motion noise on

mammals is unknown

Floating Technology

3/3/2012

26

Factors Affecting Wind Generation

• Wind speed and length of wind season– Most wind turbines operate at 4 -16 m/s

• Diameter of rotating blades– The power captured by the blades is a function of the

area they sweep– The area is circular with a radius equal to the length of

one blade – The power is then proportional to the square of the

radius• a 10% increase in the blade length will result in 21% increase in the

captured power.

• Efficiency of wind turbine components


• Pitch control– With pitch control, the TSR can be adjusted to produce

power at a wide range of wind speeds. • Yaw Control

– Most wind turbines are equipped with yaw mechanism to keep the blades facing into the wind as the wind direction changes.

– Some turbines are designed to operate on downwind; these turbines don't need yaw mechanisms as the wind aligns these turbines.


• Arrangement of the turbines (array effect)– the blades of the front turbines create wakes of turbulent wind that

can reach the rare turbines. – efficiency is reduced when wind is turbulent.

• Reliability and maintenance– The cost of electricity generated by the wind farm is a function of

• Capital cost• Land use• Maintenance• Contractual arrangement.

– The early designs of wind turbines were high maintenance machines as well as cost ineffective systems. Newer designs, however, are much better with a reliability rate around 98 percent.

Documents

Countercurrent braking - class.ece.uw.edu