Week 7

Basic characteristics of induction and synchronous generators connected to the infinite bus.

Week 8

The basic inverter and interfacing, real and reactive power control.

Week 9

Transmission lines, AC versus DC transmission.

Professor Faz RahmanRoom EE133

f.rahman@unsw.edu.auTel: 9385 4893

1

A typical power generation, transmission and distribution network (unidirectional power flow)

2

Transformer Transformer Transformer Transformer

250kVgrid

Transformer

Transformer

33kV

3.3kV

Transformer

415VIndustrial

loads

L

L

N

OtherLoad

Centers

Cont.

3

With renewable distributed generation and energy storage, power flowis bidirectional and can be rather fast, unlike in a conventional powersystem network.

Wind turbine evolvement

4

5

6

Global annual and cumulative installed wind power capacity

7

Wind energy harnessing growth

Offshore wind energy harnessing growth in Europe

8

9

Comparison between offshore and on-land wind turbines

10

Cost of wind energy harnessing

Installation of 160MW offshore substation

11

12

An example of wind farm and grid

13

14

Induction and Synchronous Generators driven by wind turbines

312 pP C AV W

15

312wP AV WPower in wind,

Wind power delivered to generator,

= air density in kg/m3; A = swept area in m2 of blades; V = wind speed in m/sec; Cp = rotor efficiency. 

16

Cp - Power Conversion efficiency,, depends on wind speed, turbine rotor speed, number of blades and blade geometry.

Cut-in speed – Wind-speed below which, the generator produces less than the power consumed by the rotating system.

Rated power – The maximum power which the turbine and generator can produce continuously without undue stress on any part

Rated wind-speed – The speed at which the turbine and generator produces the maximum power for which they are designed to produce continuously.

Cut-out speed – The wind speed beyond which turbine-generator are severely overloaded.

Below cut-in and above cut-out speeds, the turbine blades are stopped; Blades are profiled, or mechanically/hydraulically actuated to stop rotating.

17

Vd/V = 1/3 yields maximum  blade (turbine) efficiency of 0.5926.

Tip Speed Ratio

18

TipSpeed Ratio RTSRV

= turbine blade speed in rad/secR = blade length in mV = wind speed in m/sec

TSR is in the range of 4 – 6 for good efficiency. Thus, the turbine blade speedshould change with wind speed. The generator speed will also vary, producingvariable generator output frequency and voltage.

Variable‐speed options: Pole changing, variable gearbox, variable‐slip inductiongenerator, and power electronic converter between generator and grid.

Blade efficiency versus tip speed ratio

19

Turbine blade efficiency

20

21

Fixed and Variable-Speed Generators

Fixed‐speed Induction Generators• Usually for stand‐alone operation; for low power installations driving loads 

with rising torque characteristics with speed, e.g., fans, compressors, etc.• Self‐excited.

• An induction generator will self‐excite depending on the speed of the windturbine shaft, the machine parameters and the capacitance values C. Thecapacitors often have back‐back series thyristors in order to control theexcitation and power flow when connected with the AC bus. C is alsosometimes variable by use of contactors.

22

Fixed and Variable-speed Generators

Variable‐speed generators

• Power Electronic Converters (PEC) allow variable‐speed operation. The control of power (active and reactive) from generator to the to the grid can be made variable through the use of PEC (AC‐DC, DC‐AC and AC‐AC converters).

23

24

Generators commonly used with wind turbines

25

Singly‐excited induction generator

Doubly excited induction generator

Synchronous generator (PM excited)

Characteristics of a singly-fed induction generator connected to an infinite bus

26

Note: stator currents are constrained to be at the infinite bus frequency, so agear box and some adjustment to rotor speed is necessary. A rectifier +inverter connected to the stator windings offers some freedom from thisconstraint and other constraints such as pitch control, available speed rangeand many other.

Induction Generators

27

An induction generator is an AC machine with three-phase windings in the stator. For larger applications, the machines also has 3-phase windings in the rotor. The frequency fs of currents in the stator windings determine the synchronous speed syn, which is given by

ssyn

2 fp s

syn60 fN

p

in rev/minin rad/sec

Where p is the number of pairs of electromagnetic poles (always an even number of north and south magnetic poles) rotating at the synchronous speed in the air gap between the stator and the rotor.

The difference between the rotor speed (Nrot) of an induction machine defines a ratio called Slip or s, given by

syn rot syn rot

syn syn

N Ns

N

For 0 < s < 1, the machine acts as a motor, for s < 0, the machine acts as a generator. Note that for s < 0, the rotor speed is higher than the synchronous speed.

Singly-fed induction machine characteristics

28

R1 X1

V1

I1

Im

Xm

'2R

'2R 1 s

s

' 22

IIa

'2X

1 2E aE

A

A’

2Th

max 22 'sTh Th Th 2

V3 pT2 R R X X

max

'2

T 22 'Th Th 2

RsR X X

m 1Th

1 m

X VV ;X X

Th 1R R ;

2 'Th 2

mech 2' 2s '2Th Th 2

V3 p RT ;sRR X X

s

Torque-speed characteristic of an SFIM

29

Generating modeGenerating and motoring modes

Expressions for these characteristics, Tmax and smax machine parameters, motor voltage and frequency are treated in ELEC3105.

Characteristic of a doubly-fed induction generator connected to an infinite bus

30

sl inj

r

P Ps

P

Psl = power loss in the rotor

Pinj = power injected into rotor by the inverter

Pr = Total rotor power

Characteristic of a doubly-fed induction generator connected to an infinite bus continued.

31

• This scheme is based on the hypothesis that when the power injected into therotor windings exceeds the losses in the rotor, the motor will then run at super‐synchronous speed, meaning operation with s < 0 (i.e., generator mode ofoperation).

• The rectifier/inverter allows variable power injected power into the rotor at thefrequency of the rotor currents (which is much lower than the frequency of theinfinite bus).

• It can be shown (covered in ELEC4613) that the for low slip operation, thecounter torque developed by the DFIG can be made proportional to the DCcurrent Id supplied at the input of the inverter (equivalent to controlling theamplitude of the sinusoidal AC currents supplied to the 3‐phase rotorwindings). This in turn controls the power transferred from the generator tothe bus. (Operation and control 3‐phase inverters are covered in ELEC4614).

Synchronous Generators

32

• Generators at large power stations are invariably synchronous machines with excitation of rotor electromagnets supplied from a DC supply via slip rings.  

• With distributed generation driven by wind turbines, permanent magnets are used in the rotor. These range from a few 100 W to about 10MW (recently).

• When driven at a speed, the per‐phase representation of the machine includes a sinusoidal induced voltage E, leakage and armature demagnetization effects of stator currents represented by Xs and winding resistance R per phase.

• The machine fully covered in ELEC3105.

Cont…

33

In a synchronous machine, the rotor fields (with north and south magnetic polescreated by electro or permanent magnet excitation) and the stator fields (createdby its own currents) must rotate at the same speed at steady‐state.

The induced voltages lead the corresponding stator voltage waveforms by an angle, (the load angle) when operating as a generator. When the machine is loaded,this angle increases with the power developed.

During transient operation, the speed of the machine changes causing the angleto change transiently. For stability, this angle must not exceed 90. The magnitudeof this angle also depends on the level of rotor excitation.

When a synchronous generator is connected to an infinite bus, and generates intothe bus, the components of the current flow between the generator in phase withthe bus voltage will be determined by the power delivered. (Recall, P = VIcos,where Icos is the in‐phase component of the phase current.

The synchronous generator connected to the infinite bus

34

• When the machine is connected to an infinite bus at voltage Va, the three‐phase stator currents at the bus frequency produces a stator field which rotates at syn(see slide 27). The rotor also rotates at this speed (on average) so there is no slip.

• As the generator delivers load which primarily is determined by the power received at its shaft, the induced phase voltage Ea progressively leads Va of the corresponding bus phase voltage by a phase angle , given by

Wa a

s

3V EP sinX

Nmsyn s s

P 3p VET sinX

• With fixed input power to the shaft,  the phase angle and magnitude of the stator current changes with rotor excitation, if available, with the in‐phase current remaining constant.

Ra  0

The synchronous generator on the infinite bus contd.

35

• With variable‐speed, the frequency of the induced voltages E and the bus voltage V will not be equal, so a rectifier‐inverter PEC is required. Note also that the number of poles also determine the frequency. If a machine with a large number of poles is not used, a gear‐box is required in order to run the generator at a much higher speed than the turbine, thereby reducing the size of the machine.

Power transfer between DG and Grid

36

W/phaseP VI cos VAR / phaseQ VI sinAll quantities in RMS values.

VAS P jQ

Line parameters:

ml 1R /A A

X L

H / mo d rL ln2 r

The capacitance/m for a short line may be neglected.

37

;22 1 LZ R L tanR

s RV V 0 I Z

If R << X, Z X, = 90

s RV VI 90 90X X

s RV V 0IZ

Power,  sV s Rs I s s

V VP V I cos V cos 90 V cos 90X X

W/phases RV V sinX

VR0

jXs=jsLs I

Vs

R

38

Reactive Power,  sV s Rs I s s

V VQ V I sin V sin 90 V sin 90X X

VAR/phase2

s s RV V V cosX X

Phasor diagram for a given current delivered to the grid. 

Phasor diagram for a bidirectional power flow.

A 2-level rectifier/inverter circuit

39

Diodes D1‐D6 form a rectifier. IGBTsswitches T1 – T6 have pulse‐widthmodulated (PWM) on‐off duty cyclessynchronized with vsa – vsc, whichforces sinusoidal in‐phase currents tobe drawn from the generator. Itoperates as a boost converter with Vdc> Vl-lmax.

T1D1 – T6D6 form an inverter,converting Vdc into 3‐phase AC outputsat the grid frequency and synchronizedwith v’sa – v’sc. On‐off duty cycles of T1– T6 are also PWM. It operates as abuck converter with Vdc < Vl-lmax. Theinverter supplies AC currents to thegrid with specified phase angles.

Inverter interfacings

40

41

3‐phase PWM converter

3‐phase PWM rectifier / inverter circuitshave been used in this part in order toillustrate the operation of DG systems.There are many other types of convertercircuits that may suit particularapplications and performancerequirements. Some of these circuits arecovered in the Power Electronics courseELEC4614.

In inverter mode, Vdc is the input and 3‐phase sinusoidal voltages of arbitraryamplitude and frequency are the outputs. In this mode, the switching of theinverter must be synchronised with the grid voltages.

In rectifier mode, the 3‐phase AC voltages are the inputs, while the Vdc is theoutput. In this mode, the switching of the converter must be synchronised withthe AC voltages.

42

control

tri

v̂mv̂

1

sf

fmf

The Depth of Modulation,

The Carrier Ratio,

where fs and f1 are the frequencies of the carrier and fundamental (desired) output. respectively.

43

A sinewave reference and a sawtooth carrier are compared to produce a logiclevel out put of 1 and 0 of variable duty cycle. The carrier frequency is muchhigher than the sinewave frequency. If the output signals are used to turn onand off the two switches in an inverter leg, the resulting pole voltage at A (orB or C) will replicate the sinewave .The amplitude of the average pole voltage will be proportional to theamplitude of the reference sinewave and it will be of the same phase and thereference sinewave. It can be shown that the output pole phase voltage isgiven by

dcAn

Vv̂ m2

Operation of a PWM inverter

44

D6T2T4

T3T1 D3

D4

D1

Vd

D2

D5

T6

T5

CA B

A B C

ia ib ic 0V

+Vd/2

Vd/2

idP

N

dAn,1

VV m

2 2 0 354. m Vd

dAB,1 d

3VV m 0.612m V

2 2

m is the depth of modulation

45

V1

mfmf + 2

3mf2mf + 2 3mf + 2

2mf

Harmonics vl-l

mn

0.2 0.4 0.6 0.8 1.0

1 0.122 0.245 0.367 0.490 0.612mf 2

mf 4

0.010 0.037 0.080 0.135

0.005

0.195

0.0112mf  1

2mf 5

0.116 0.200 0.227 0.192

0.008

0.111

0.0203mf 2

3mf 4

0.027 0.085

0.007

0.124

0.029

0.108

0.064

0.038

0.0964mf 1

4mf 5

4mf 7

0.100 0.096 0.005

0.021

0.064

0.051

0.010

0.042

0.073

0.030

Wind generator controls

46

47

Using the sensed AC voltages, the angle  between E and V (or Vs and VR) can be determined.Controller 1 transfers the generator output power to DC link capacitor. Controller 2 transfers this power to the infinite bus.

48

Control of the generator side converter (rectifier)

49

Note that for small , sin and cos 1. Vs and VR are voltage to the left and right sides of Xgen, respectively. Only VR can be measured.

This controller is based on the steady‐state equivalent circuit of the synchronous generator; so the control action is not very fast and can become easily unstable.

Control of the grid-side converter (inverter)

50

Power input to the DC link capacitor is the difference between the generator output power and the power transferred to the grid.

C gen grid DC c

2DC DC

DC

P P P V I

dV dV1V C Cdt 2 dt

2DC C

DC gen grid

2V P dtC

2V P P dtC

If controller 2 maintains the VDC to a reference value, and Ic = 0, all of Pgentransfers to the grid. This control implies that Pgen = Pgrid.

51

Control in the synchronously rotating frame

52

The controllers of the foregoing slides are based on the steady‐state equivalentcircuit and they control the inverter/rectifier output voltages. These do not addressthe dynamics of the system. Fast controllers that are able to respond to thedynamics with fast control of power, voltage and frequency, require vector controlwhich also impart control actions via regulation of currents rather than voltages.Currents that are regulated are transformed into a quadrature dq‐axes whichrotate synchronously with the stator supplies of the generator or the grid.Controlling the current in the q‐ and d‐axes in this reference frame allowsindependent control of the active and reactive power supplied by the generator orthe inverter. Vector control principles are covered in Electric Drives course(ELEC4613).

53

Real and reactive power control in the dq reference frame

Real and reactive power control in the dq reference frame

54