modulation and current/voltage control of the grid converter marco liserre [email protected]...

Marco Liserre [email protected]

Modulation and current/voltage control of the grid converter


Marco Liserre

[email protected]



Introduction Modulation and ac current control are the core of grid-connected converters

They are responsible of the safe operation of the converter and of the compliance with standards and grid codes

Ac voltage control is a standard solution in WT-system however can be adopted also in PV-system for reinforcing stability or offering ancillary services

Introduction Model of the grid converter Overview of modulation techniques Current control Voltage control

A glance at the lecture content



PI-based current control implemented in a synchronous frame is commonly used in three-phase converters

In single-phase converters the PI controller capability to track a sinusoidal reference is limited and Proportional Resonant (PR) can offer better performances

Modulation has an influence on design of the converter (dc voltage value), losses and EMC problems including leakage current

Introduction: modulation and current/voltage control



In Europe there is the standard IEC 61727 In US there is the recommendation IEEE 929 the recommendation IEEE 1547 is valid for all distributed resources technologies

with aggregate capacity of 10 MVA or less at the point of common coupling interconnected with electrical power systems at typical primary and/or secondary distribution voltages

All of them impose the following conditions regarding grid current harmonic content

The total THD of the grid current should not be higher than 5%

Introduction: harmonic limits for PV inverters



harmonic limit 5th 5-6 % 7th 3-4 % 11th 1.5-3 % 13th 1-2.5 %

In Europe the standard 61400-21 recommends to apply the standard 61000-3-6 valid for polluting loads requiring the current THD smaller than 6-8 % depending on the type of network.

in WT systems asynchronous and synchronous generators directly connected to the grid have no limitations respect to current harmonics

1

Nhi

hi i

II

in case of several WT systems

Introduction: harmonic limits for WT inverters



Model of the grid converter

AD

dcv

oi R

+-

L eA

B

AD

AT

AT

BD

BD

BT

BT

di

C

CD

CD

CT

CT

n

ac voltage equation

22( ) ( ) ( ) ( )3 a b cp t p t p t p t

converter switching function

d ( ) 1( ) ( ) ( ) ( )

d dci t

Ri t e t p t v tt L



Use of a synchronous frame

1 1 2 1 22

3 0 3 2 3 2

a

b

c

pp

pp

p

2 2cos cos cos

3 3

2 2sin sin sin

3 3

ad

bq

c

pp

pp

p

1

1

dc

dc

di tRi t e t p t v t

dt Ldi t

Ri t e t p t v tdt L

1

1

dq d d d dc

qd q q q dc

di ti t Ri t e t p t v t

dt Ldi t

i t Ri t e t p t v tdt L

-frame dq-frame

v

v

qv

dv

v

a

c

b



Overview of modulation techniques



Characteristic parameters of these strategies are: the ratio between amplitudes of modulating and carrier waves (called modulation index M) the ratio between frequencies of the same signals (called carrier index m)

These techniques differ for the modulating wave chosen with the goal to obtain a lower harmonic distortion, to shape the harmonic spectrum to guarantee a linear relation between fundamental output voltage and modulation index in a wider range

The space vector modulations are developed on the basis of the space vector representation of the converter ac side voltage

Modulation techniques



analogic or digital,

natural sampled or regular sampled

symmetric or asymmetric

Modulation techniques

1

2

Ao

d

V

V

4 .1 278

.1 0

00 .1 0

M for 15fm

.3 24

Linear

Over-modulation

Square-waveOptimization both for the

linearity and harmonic content



1

ˆAmplitude modulation ratio :

ˆ

Frequency modulation ratio :

control

tri

S

VM

V

fm

f

Output voltage averaged over one switching period:

ˆ;

2control d

Ao Ao control tritri

v VV v v V

V

Sinusoidal PWM (SPWM)



the fundamental frequency componentof the output voltage is given by:

11sin( ) 1.0

2d

Ao

Vv M t M

Assuming a sinusoidal control signal:

1ˆ sin( ),control controlv V t

1

ˆ 1.02d

Ao

VV M M

The inverter stays in its “linear range”while . 0,1M

The harmonics in the output voltage appear as sidebands of fS and its multiples

1hf jm k f

The hth harmonic corresponds to the kth sidebandof j times the frequency modulation ratio m.For even values of j only exist harmonics forodd values of k, and viceversa.

1 15

13 17 31293327

3525454743 494139 51

Sinusoidal PWM (SPWM)



Bipolar and unipolar modulations

2dcV +

-

+

-2dcV

2C

1C

dcV

+

-

v t+ -

P

P

dcV

+

-

v t+ -

P

P

P

P

00 1

0cos2

sin2

14)(

mm

nn

cndc tntmnmMqJ

q

Vtv

10120 122cos1cos

2

18cos2)(

m ncn

dcdc tntmnmMmJ

m

VtMVtv

bipolar

unipolar



0 10 20 30 40-1.5

-1

-0.5

0

0.5

1

1.5

t [ms]

v ref, v

tri

vref

vtri

0 10 20 30 40-100

-50

0

50

100

v Ao [V

]

t [ms]

0 10 20 30 40-100

-50

0

50

100

v Bo [V

]

t [ms]

0 10 20 30 40-150

-100

-50

0

50

100

150

v AB [V

]

t [ms]

0 5 10 15 20 25 30 35 40 45 50 55 600

0.20.40.60.8

1

v Ao/V

d

h

0 10 20 30 40-1.5

-1

-0.5

0

0.5

1

1.5

t [ms]

v ref, v

tri

vref

vtri

0 10 20 30 40-100

-50

0

50

100

v Ao [V

]

t [ms]

0 10 20 30 40-100

-50

0

50

100

v Bo [V

]

t [ms]

0 10 20 30 40-150

-100

-50

0

50

100

150

v AB [V

]

t [ms]

0 5 10 15 20 25 30 35 40 45 50 55 600

0.20.40.60.8

1

v AB/V

d

h

Bipolar and unipolar modulations

Due to the unipolar PWM the odd carrier and associated sideband harmonics are completely cancelled leaving only odd sideband harmonics (2n-1) terms and even (2m) carrier groups



Three-phase modulation techniques

0 10 20 30 40-1.5

-1

-0.5

0

0.5

1

1.5

t [ms]

v ref, v

tri

vref

vtri

0 10 20 30 40-100

-50

0

50

100

v Ao [V

]

t [ms]

0 10 20 30 40-100

-50

0

50

100

v An [V

]

t [ms]

0 10 20 30 40-100

-50

0

50

100

v on [V

]

t [ms]

0 10 20 30 40-150

-100

-50

0

50

100

150

v AB [V

]

t [ms]

0 10 20 30 40-150

-100

-50

0

50

100

150

E [V

]

t [ms]

0 10 20 30 40-20

-10

0

10

20

i o [A]

t [ms]

0 10 20 30 40-20

-10

0

10

20

i d [A]

t [ms]

The basic three-phase modulation is obtained applying a bipolar modulation to each of the three legs of the converter. The modulating signals have to be 120 deg displaced. The phase-to-phase voltages are three levels PWM signals that do not contain triple harmonics. If the carrier frequency is chosen as multiple of three, the harmonics at the carrier frequency and at its multiples are absent.



Extending the linear range (m=1,1)

SPWM

SVM

64



Three-phase continuous modulation techniques

0 /2 2/3 2

vdc

/2

0

-vdc

/2

0 /2 2/3 2

vdc

/2

0

-vdc

/2

0 /2 2/3 2

vdc

/2

0

-vdc

/2

onv

DCRv

ACRv

onv

DCRv

ACRv

onv

DCRv

ACRvTHIPWM1/6 THIPWM1/4 SVPWM

Maximum linear range Minimum current harmonics Maximum linear range and almost optimal current harmonics

Triple harmonic injection 1/6 Triple harmonic injection 1/4 Space vector - Triangular 1/4

Continuous modulations

sinusoidal PWM with Third Harmonic Injected –THIPWM. If the third harmonic has amplitude 25 % of the fundamental the minimum current harmonic content is achieved; if the third harmonic is 17 % of the fundamental the maximal linear range is obtained;

suboptimum modulation (subopt). A triangular signal is added to the modulating signal. In case the amplitude of the triangular signal is 25 % of the fundamental the modulation corresponds to the Space Vector Modulation (SVPWM) with symmetrical placement of zero vectors in sampling time.



0 /2 2/3 2

vdc

/2

0

-vdc

/2

0 /2 2/3 2

vdc

/2

0

-vdc

/2

onv

ACRv DPWM0=-/6

DCRv

onv

ACRv

DPWM1=0DCRv

0 /2 2/3 2

vdc

/2

0

-vdc

/2

onv

ACRv

DPWM2=/6DCRv

The discontinuous modulations formed by unmodulated 60 deg segments in order to decrease the switching losses

symmetrical flat top modulation, also called DPWM1;

asymmetrical shifted right flat top modulation, also called DPWM2;

asymmetrical shifted left flat top modulation, also called DPWM0.

Three-phase discontinuous modulation techniques



Multilevel converters and modulation techniques

alternative phase opposition (APOD) where carriers in adjacent bands are phase shifted by 180 deg;

phase opposition disposition (POD), where the carriers above the reference zero point are out of phase with those below zero by 180 deg;

phase disposition (PD), where all the carriers are in phase across all bands.

Wind turbine systems: high power -> 5 MW Alstom converter

Photovoltaic systems: many dc-links for a transformerless solution

0V 0V0V

2dcV

2dcV

A B CDifferent possibilities:



ab

cd

dcV

i L

e

Cascaded inverter

v

dcV

1 1012

0

2122cos1cos2

14

cos)(

m n

N

iicn

dc

dc

mtntmnmMmJm

V

tMNVtv

( 1)i

i

N

, 1, 2,3...m kN k

Multilevel converters and modulation techniques

•carrier shifting



Carrier shifting

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-1

0

1

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-1

0

1

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-100

0

100

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-100

0

100

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-200

0

200

h

0 10 20 30 40 50 600

0.5

1

h

A [

pu]

v ab [

V]

v cd [

V]

v ad [

V]

v ref,

Vtr

iv re

f, V

tri

t [s]

t [s]

t [s]

t [s]

t [s]



PD Modulation for NPC

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-1

0

1

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-101

t [s]

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-101

t [s]

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-2000

200

t [s]

0 10 20 30 40 50 600

0.5

1

h

A [p

u]V

an [V

]V

ref, V

tri

Vre

f, Vtr

iV

bn [V

]V

ab [V

]

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-1

0

1

Best WTHD !



Current Control

PWM current control methods

ON/OFF controllers Separated PWM

hysteresis Delta optimized

linear non-linear

fuzzypassivity

PI predictive resonant

dead-beatfeedforward



Typically PI controllers are used for the current loop in grid inverters Technical optimum design (damping 0.707 overshoot 5%)

-

+- ++

gv

v gidG ( s ) fG ( s )PIG ( s )

i

+-

e

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

10-1

100

101

102

103

104

-20

-15

-10

-5

0

Ma

gn

itud

e (

Db

)

100

101

102

103

104

-400

-300

-200

-100

0

Frequency (Hz)

Ph

ase

(D

eg

ree

)

( ) IPI P

KG s K

s

sTsG

sd 5.11

1)(

( ) 1( )

( )f

i sG s

v s R Ls

PI current control



Shortcomings of PI controller

When the current controlled inverter is connected to the grid, the phase error results in

a power factor decrement and the limited disturbance rejection capability leads to the

need of grid feed-forward compensation. However the imperfect compensation action of the feed-forward control due to the

background distortion results in high harmonic distortion of the current and

consequently non-compliance with international power quality standards.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-0.2

0

0.2

0.4

0.6

0.8

1

error (scaled)

reference

actual

time [s]

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

-1.5

-1

-0.5

0

0.5

1

error

actual

reference

0.019 0.0192 0.0194 0.0196 0.0198 0.02 0.0202 0.0204 0.0206 0.0208 0.021

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.023 0.0235 0.024 0.0245 0.025 0.0255 0.026 0.0265 0.027 0.0275

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

time [s]

steady-state magnitude and

phase error

limited disturbance

rejection capability



The current control can be performed on the

grid current or on the converter current

The voltage used for the dq-frame orientation could be measured after a dominant reactance

d

q

)(te

)(ti

qi di

0( )

0

ip

PI dqi

p

KK

sD sK

Ks

Use of a PI controller in a rotating frame

d

q

) ‘( te

)(te ) ‘( te

d

q

dt

diLtet'e g

g



Use of a PI controller in a rotating frame

ip

KK

s

1

3

ga a gb b gc c

gab a gbc b gca c

P v i v i v i

Q v i v i v i

dcv

dcV

P

Q

i

v

P

Q+-

+-

+ -

di

qi

Q controller

P controller

dcV controller

PQ controller

+ -

PLLgv

gv

gv

fgV

je

gdv

gqv

*v

abc

je

i

i

di

qi

+-

di

di

gdv

+-

qi Current

controller

Currentcontroller

gqv

je

v

v

ip

KK

s

ip

KK

s

ip

KK

s

ip

KK

s

L

L

i αβ

abc

αβ

αβ

abc

• active and reactive

power control can be

achieved

• vdc control can be

achieved too



Use of a PI controllers in a rotating frame in single-phase systems

ip

KK

s

dcv

dci

Qgdv

Qx

+ -

qi

dcV controller

PLLgv

gv

gv

fgV

je

gdv

gqv

ije

i

i

di

qi

+-

di

di

gdv

+-

qi Current

controller

Currentcontroller

gqv

je

v

v

MPPT

P

dcV

gqv

di

L

L

ip

KK

s

ip

KK

s

2je

2je

v

an independent Q control is

achieved

A phase delay block create the

virtual quadrature component that

allows to emulate a two-phase

system

the v component of the

command voltage is ignored for

the calculation of the duty-cycle



Use of a PI controllers in two rotating frames

++

di

++

qi

PI

PI

i

i

v

v

++

di

++

qi

PI

PI

i

i

v

v

je je

je je

Under unbalanced conditions in order

to compensate the harmonics

generated by the inverse sequence

present in the grid voltage both the

positive- and negative-sequence

reference frames are required

Obviously using this approach,

double computational effort must be

devoted



Dead-beat controller

The dead-beat controller belongs to the family of the predictive controllers

They are based on a common principle: to foresee the evolution of the controlled

quantity (the current) and on the basis of this prediction: to choose the state of the converter (ON-OFF predictive) or the average voltage produced by the converter (predictive with pulse width

modulator)

The starting point is to calculate its derivative to predict the effect of the control

action

The controller is developed on the basis of the model of the filter and of the grid,

which is used to predict the system dynamic behavior: the controller is inherently

sensitive to model and parameter mismatches




*i

i

sTONt

k 1k 2k

ONt

sT

The information on the model is used to decide the switching state of the

converter with the aim to minimize the possible commutations (ON-OFF

predictive) or the average voltage that the converter has to produce in order to null

it.

In case it is imposed that the error at the

end of the next sampling period is zero

the controller is defined as “dead-beat”. It

can be demonstrated that it is the fastest

current controller allowing nulling the

error after two sampling periods.




450 460 470 480 490 500 510 520 530 540 550-0.2

0

0.2

0.4

0.6

0.8

1

samples

450 460 470 480 490 500 510 520 530 540 550-0.2

0

0.2

0.4

0.6

0.8

1

samples

resp

on

se

resp

on

se

reference

actual

reference

actual

)1()1()1()(1

)1()1( kekekib

aki

bkvkv

)()1()(1

)1( kekekib

kvkv neglecting R !



Dead-beat controller: limits

0.04 0.045 0.05 0.055 0.06-60

-50

-40

-30

-20

-10

0

10

20

time [s]

curr

ent

[A]

0.04 0.045 0.05 0.055 0.06-60

-50

-40

-30

-20

-10

0

10

20

time [s]

curr

ent

[A]

Pole-Zero Map

Real Axis

Imag

inar

y A

xis

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.90.80.70.60.50.40.30.20.1

/T

0.9/T

0.8/T

0.7/T

0.6/T0.5/T

0.4/T

0.3/T

0.2/T

0.1/T

/T

0.9/T

0.8/T

0.7/T

0.6/T0.5/T

0.4/T

0.3/T

0.2/T

0.1/T

0.04 0.045 0.05 0.055 0.06-60

-50

-40

-30

-20

-10

0

10

20

time [s]

curr

ent

[A]

due to PWM !

due to parameter error !



Resonant control Resonant control is based on the use of Generalized Integrator (GI)

A double integrator achieves infinite gain at a certain frequency, called resonance frequency, and almost no attenuation outside this frequency

The GI will lead to zero stationary error and improved and selective disturbance rejection as compared with PI controller

101

102

103

-180

-90

0

90

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

-200

-100

0

100

200

Magnitude (

dB

)

2 2

s

s

2 2

s

s GI



Resonant control

101

102

103

0

200

400

600

800

Mag

nitu

de (

dB)

Frequency (Hz)

101

102

103

-100

-50

0

50

100

Pha

se (

deg)

Frequency (Hz)

101

102

103

0

20

40

60

80

Mag

nitu

de (

dB)

Frequency (Hz)

101

102

103

-100

-50

0

50

100

Pha

se (

deg)

Frequency (Hz)

22 2

2)(

ss

sKsG

c

ciAC

22

2)(

s

sKsG i

ACs

KsG i

DC )(

)(1)(

c

iDC s

KsG

)()()( jsGjsGsG DCDCAC The resonant controller can be obtained via a frequency shift

Bode plots of ideal and non-ideal PR with KP = 1, Ki = 20, = 314 rad/s c = 10 rad/s



-200

-100

0

100

200

300

400

Magnitude (

dB

)

101

102

103

-180

-90

0

90

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

-100

0

100

200

300

400

Magnitude (

dB

)

Bode Diagram

Frequency (Hz)

101

102

103

-180

-90

0

90

180P

hase (

deg)

2 2P I

sk k

s

PM

The stability of the system should be taken into consideration

The phase margin (PM) decreases as the resonant frequency approach to the crossover frequency

2 2

1P I

sk k

R Lss

Resonant control



Tuning of resonant control The gain Kp is founded by ensuring the desired bandwidth

The integral constant Ki acts to eliminate the steady-state phase error

A higher Ki will "catch" the reference faster but with higher overshoot

Another aspect is that Ki determines the bandwidth centered at the resonance frequency, in this case the grid frequency, where the attenuation is positive. Usually, the grid frequency is stiff and is only allowed to vary in a narrow range, typically ± 1%.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-6

-4

-2

0

2

4

650Hz response

Time (sec)

Am

plit

ud

e

2 2( )c P I

o

sG s K K

s

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-6

-4

-2

0

2

4

650Hz response

Time (sec)A

mp

litu

de

2 2( )c P I

o

sG s K K

s

Ki = 100 Ki = 500



Discretization of generalized integrators

2 2

2

1

1

y s u s v sy s s su s s

v s y ss

2

y u

v

GI integrator decomposed in two simple integrators

1 1 1

21

( )k k s k k

k k s k

y y T u v

v v T y

*2 2

( ) Ii p

K su s s K

s

Forward integrator for direct path and backward for feedback path

The inverter voltage reference

1 1 1

*,

21

1

1

1

k k s I k s k

i k p k k

k k s k

k k

k k

k k

y y T K T v

u K y

v v T y

y y

v v

Difference equationsi i

*

i i

i i u i*

y u

v

k p

k I

2

a w

G f ( s )

Control diagram of PR implementation

max max

max max

,

,

y y y yaw

y y y y



2 20

2 20

0

( )

0

ip

PRi

p

K sK

sD s

K sK

s

Use of P+resonant controller in stationary frame

3

2

SVM

PLL

3

2

u

ix*

iy*

idd*

i*

iiy

ix

ux*

uy*

iy*

ix*

Kp

Kp

-

+

+

+

+

+

+

+

-

6

ej

2 2

Ki s

s

2 2

Ki s

s

ixd*

)(te

)(ti

The voltage used for reference generation could be measured after a dominant reactance

The current control can be performed on the grid current or on the converter current



PI vs PR for single-phase grid inverter current control

The current loop of PV inverter with PR controller

The current loop of PV inverter with PI controller

( ) IPI P

KG s K

s

2 2( )c P I

o

sG s K K

s

No grid voltage feed-forward is required

GIs tuned to the low harmonics can be used for selective harmonic compensation by cascading the fundamental component GI

2 2

2 2

( ) 1( )

( )

LCif

i fi res

s zi sG s

u s L s s

.

1

1)(

sd sT

sG

Plant

Inverter

PRPI

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Linear controllers : from PI in a rotating-frame to P+res for each phase

each current is determined only by its voltage !



Linear controllers : results (ideal grid conditions)

current error

current error

harmonic spectrum

harmonic spectrum

PI controller in a rotating frame

P+resonant controller for each phase



Linear controllers: results (equivalence of PI in dq and P+res in )

PI controller in a rotating frame

P+resonant in stationary frame

triggering LCL-filter resonance

triggering LCL-filter resonance



Ac voltage control When it is needed to control the ac voltage because the system should operate

in stand-alone mode, in a microgrid, or there are requirements on the voltage quality a multiloop control can be adopted

The ac capacitor voltage is controlled though the ac converter current.

The current controlled converter operates as a

current source to charge/discharge the

capacitor.



Ac voltage control The repetitive controller ensures precise tracking of the selected harmonics and

it provides the reference of the PI current controller. Controlling the voltage Vc’ the PV shunt converter is improved with the function of voltage dips mitigation. In presence of a voltage dip the grid current Ig is forced by the controller to have a sinusoidal waveform which is phase shifted by almost 90° with respect to the corresponding grid voltage.

PV converter

Iload

Ic’

E Ig

PIRepetitive

control

Ic’

Vref+

- -

+

Iref

Vc’



Conclusions

The PR uses Generalized Integrators (GI) that are double integrators achieving very high gain in a narrow frequency band centered on the resonant frequency and almost null outside.

This makes the PR controller to act as a notch filter at the resonance frequency and thus it can track a sinusoidal reference without having to increase the switching frequency or adopting a high gain, as it is the case for the classical PI controller.

PI adopted in a rotating frame achieves similar results, it is equivalent to the use of three PR’s one for each phase

Also single phase use of PI in a dq frame is feasible

Dead-beat controller can compensate current error in two samples but it is affected by PWM limits and parameters mismatches



Bibliography1. D. G. Holmes and T. Lipo, Pulse Width Modulation for Power Converters, Principles and Practice. New York: IEEE Press, 2003.

2. M. Kazmierkowski, R. Krishnan, and F. Blaabjerg, Control in Power Electronics – Selected Problems. Academic Press, 2002.

3. X. Yuan, W. Merk, H. Stemmler, and J. Allmeling, “Stationary-frame generalized integrators for current control of active power filters with zero steady-state error for current harmonics of concern under unbalanced and distorted operating conditions,” IEEE Trans. on Industry Applications, vol. 38, no. 2, pp. 523–532, 2002.

4. D. Zmood and D. G. Holmes, “Stationary frame current regulation of PWM inverters with zero steady-state error,” IEEE Trans. on Power Electronics, vol. 18, no. 3, pp. 814–822, 2003.

5. M. Bojrup, P. Karlsson, M. Alaküla, L. Gertmar, ”A Multiple Rotating Integrator Controller for Active Filters”, Proc. of EPE 1999, CD-ROM.

6. R. Teodorescu, F. Blaabjerg, M. Liserre and A. Poh Chiang Loh, “Proportional-Resonant Controllers and Filters for Grid-Connected Voltage-Source Converters” IEE Proceedings on Electric Power Applications.

7. A. Timbus, M. Liserre, R. Teodorescu, P. Rodriguez, F. Blaabjerg, Evaluation of Current Controllers for Distributed Power Generation Systems, IEEE Transactions on Power Electronics, March 2009, vol. 24, no. 3, pp. 654-664.

8. R. A. Mastromauro, M. Liserre, A. Dell'Aquila, “Study of the Effects of Inductor Nonlinear Behavior on the Performance of Current Controllers for Single-Phase PV Grid Converters”, IEEE Transactions on Industrial Electronics, May 2008, vol. 55, no 5, pp. 2043 – 2052.

9. IEEE Std 1547-2003 "IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems", 2003.

10. IEEE Std 1547.1-2005 "IEEE Standard Conformance Test Procedures for Equipment Interconnecting Distribut ed Resources with Electric Power Systems", 2005.

11. IEC Standard 61727, “Characteristic of the utility interface for photovoltaic (PV) systems,”, 2002.

12. IEC Standard 61400-21 “Wind turbine generator systems Part 21: measurements and assessment of power quality characteristics of grid connected wind turbines”, 2002.

13. IEC Standard 61000-4-7, “Electromagnetic Compatibility, General Guide on Harmonics and Interharmonics Measurements and Instrumentation”, 1997.

14. IEC Standard 61000-3-6, “Electromagnetic Compatibility, Assessment of Emission Limits for Distorting Loads in MV and HV Power Systems”, 1996.



Acknowledgment

Part of the material is or was included in the present and/or past editions of the

“Industrial/Ph.D. Course in Power Electronics for Renewable Energy Systems – in theory and practice”

Speakers: R. Teodorescu, P. Rodriguez, M. Liserre, J. M. Guerrero,

Place: Aalborg University, Denmark

The course is held twice (May and November) every year

modulation and current/voltage control of the grid converter marco liserre [email protected]...

Documents

grid converter marco

currentvoltage control

introduction modulation

core of grid

ac current control

modulation index

grid codes ac voltage

grid current harmonic