mariusz_cichowlas.pdf

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Warsaw University of Technology

Faculty of Electrical EngineeringInstitute of Control and Industrial Electronics

Ph.D. Thesis

M. Sc. Mariusz Cichowlas

! ! ! !

Thesis supervisor

Prof. Dr Sc. Marian P. Kamierkowski

Warsaw, Poland 2004


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The work presented in this thesis was carried out during my Ph.D. studies at the Institute of

Control and Industrial Electronics at the Warsaw University of Technology. Some parts of the

work were realized in cooperation with University of Aalborg, Denmark (International

Danfoss Professor Programme Prof. Frede Blaabjerg),

First of all, I would like to thank Prof. Marian P. Kamierkowski for continuous support, help

and friendly atmosphere. His precious advice and numerous discussions enhanced my

knowledge and scientific inspiration.

I am grateful to Prof. Stanisaw Pirg from the AGH University of Science and Technology,

Cracow and Prof. Wodzimierz Koczara from the Warsaw University of Technology for their

interest in this work and holding the post of referee.

Furthermore, I thank my colleagues from the Intelligent Control Group in Power Electronics

for their support and friendly atmosphere. Specially, to Dr. D.L. Sobczuk and Dr. M.

Malinowski for his support for my education.

Finally, I would like to thank my whole family, particularly my wife Kinga and son Kuba for

theirs love and patience.


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Table of Contents

1. Introduction 7

2. Front-end Rectifiers for Adjustable Speed AC Drives 14

2.1 Introduction 14

2.2 Adjustable Speed AC Drives 14

2.3 Drive System Configurations 15

2.4 Diode rectifiers 16

2.5 Harmonic Limitations 24

2.6 Conclusions 27

3. Basic Theory of PWM Rectifier 28

3.1 Operation of the PWM Rectifier 28

3.2 Mathematical description of PWM Rectifier 33

3.3 Block diagram of PWM rectifier 35

3.4 Operating limits 37

4. Introduction to Active Filtering 39

4.1 Basic configuration 40

4.2 Control of Shunt Active Filters 40

4.3 Types of Harmonic Sources 42

4.4 Analysis of Shunt Active Filter (SAF) Operation with Different Harmonic

Sources44

4.5 Conclusions 47

5. PWM Rectifier with Active Filtering Function 49

5.1. Introduction 49

5.2. Control Methods of PWM Rectifier 50

6. Dimensioning of Power Converters 646.1 PWM Rectifier rating 65

6.2. Shunt Active Power Filter (SAF) Rating 68

6.3. PWM Rectifier with Active Filtering Function Rating 71

6.4 Design of Passive Components 73


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6.5 Conclusions 78

7. Simulation and Experimental Results 79

7.1 Voltage Oriented Control (VOC) 81

7.2 Virtual Flux Based Direct Power Control (VF-DPC SVM) 86

7.3 Summary and Comparison of Compensating Results 90

7.4 Rectifying and Regenerative Mode of PWM Rectifier Operation 92

7.5 Typical Grid Voltage Distortion 95

7.6 Influence of Passive Components, DC-link Voltage and Converter Power

Variations100

7.7 Discussion on Digital Signal Processor Implementation 102

7.8 Conclusions 104

8. Summary and Closing Remarks 107

Appendix 109

A.1 Harmonics 143

A.2 Basic Harmonic Distortion in Power System 108

A.3 Instantaneous decomposition of powers 110

A.4 Simulations and Experimental environments 115

A.5 Review and design of Current and Power Controllers 120

References 147


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List of symbols

Symbols

- phase angle of reference vector

- power factor

- phase angle of current

- angular frequency

- phase angle

- control phase angle

cos- fundamental power factor

f frequency

i(t), i instantaneous current

kP, kI proportional control part, integral control part

t instantaneous time

v(t), v- instantaneous voltage

S virtual line flux vector

S virtual line flux vector components in the stationary , coordinates

S virtual line flux vector components in the stationary , coordinates

Sd virtual line flux vector components in the synchronous d, q coordinates

Sq virtual line flux vector components in the synchronous d, q coordinates

uS line voltage vector

uS line voltage vector components in the stationary , coordinates

uS line voltage vector components in the stationary , coordinates

uSd line voltage vector components in the synchronous d, q coordinates

uSq line voltage vector components in the synchronous d, q coordinates

iS line current vector

iS line current vector components in the stationary , coordinates

iS line current vector components in the stationary , coordinates

iSd line current vector components in the synchronous d, q coordinates

iSq line current vector components in the synchronous d, q coordinates


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uC converter voltage vector

uC converter voltage vector components in the stationary , coordinates

uC converter voltage vector components in the stationary , coordinates

uCd converter voltage vector components in the synchronous d, q coordinates

uCq converter voltage vector components in the synchronous d, q coordinates

iC converter current vector

iC converter current vector components in the stationary , coordinates

iC converter current vector components in the stationary , coordinates

iCd converter current vector components in the synchronous d, q coordinates

iCq converter current vector components in the synchronous d, q coordinates

iL nonlinear load current vector

iL nonlinear load current vector components in the stationary , coordinates

iL nonlinear load current vector components in the stationary , coordinates

iLd nonlinear load current vector components in the synchronous d, q coordinates

iLq nonlinear load current vector components in the synchronous d, q coordinates

udc DC link voltage

idc DC link current

Ldc- DC link inductor

Sa, Sb, Sc switching state of the converter

C capacitance

I root mean square value of current

L inductance

R resistance

S apparent power

T time period

P active power

Q reactive power

Z- impedance

p,q- instantaneous active and reactive power

pref, qref - reference values of instantaneous active and reactive powers

pA, qA- nonlinear load instantaneous active and reactive powers

pA, qA- alternated values of instantaneous active and reactive power


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Subscripts

..a, ..b, ..c- phases of three-phase system

..d, ..q - direct and quadrature component

..+, -, 0 - positive, negative and zero sequence component

.., .., ..0 alpha, beta components and zero sequence component

..h harmonic order of current and voltage, harmonic component

..n harmonic order

..max - maximum

..min - minimum

..LL - line to line

..Load - load

..ref - reference

..m - amplitude

..rms - root mean square value

Abbreviations

APF Active Power Filter

AFF Active Filtering Function

ANN Artificial Neural Network

ASD Adjustable Speed Drives

DPC Direct Power Control

DSP Digital Signal Processor

HPF High Pass Filter

LPF Low Pass Filter

EMI Electro-Magnetic Interference

IGBT Insulated Gate Bipolar Transistor

PCC Point Of Common Coupling

PFC Power Factor Correction

PI Proportional Integral (Controller)

PLL Phase Locked Loop

PWM Pulse-Width Modulation

REC Rectifier

SVM Space Vector Modulation

THD Total Harmonic Distortion


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UPF Unity Power Factor

VF Virtual Flux

VF-DPC Virtual Flux Based Direct Power Control

VSI Voltage Source Inverter

Basic Definitions

Harmonic Distortion

%100

1X

nX

HD=

X1 RMS value of first harmonic of voltage or current

Xn RMS value of n harmonic of voltage or current

Total Harmonic Distortion

2

1100%

1

Xn

nTHD

X

>=

X1 RMS value of first harmonic of voltage or current

Xn RMS value of n harmonic of voltage or current

Power Factor

1 cosI

PF I =

Partial Weighted Harmonic Distortion

2

14

1

100%

h

h

hI

PWHDI

==

Harmonic Constant

2 2

2

1

100%

h

h

h I

HCI

==

Remark: Please note that literature is numbered using [x,y] nomenclature, where x denotes a

topic and y number of paper


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1. Introduction

Modern electric devices are usually fed by diode or thyristors front-ends. Such equipment

generates higher harmonics into a grid. Nowdays those problems are going more and more

serious. Grids disturbances may result in malfunction or damage of electrical devices.

Therefore, currently many methods for elimination of harmonic pollution in the power system

are developed and investigated.

Restrictions on current and voltage harmonics maintained in many countries through IEEE

519-1992 in the USA and IEC 61000-3-2/IEC 61000-3-4 in Europe standards, are associated

with the popular idea of clean power.

Harmonic reduction techniques can be divided as shown in Fig. 1.1, where two main groups

can be seen:

- devices for cancellation of existing harmonics,

- grid friendly devices, which do not generate (or generate limited number) harmonics.

Fig. 1.1 Most popular current harmonic reduction techniques in three-phase networks


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The classical method of current harmonic reduction uses passive LC filters (Fig.1.2) [7, 10.5,

10.7]. They are usually constructed as capacitors and inductors series or parallel-connected to

the grid. Each harmonic (5th

, 7th

, 11th

, 13th

) requires its own passive filter (see Fig. 1.2). This

means that filters can not be designed in a general way but must be designed according to

each application. Such a solution has advantages of simplicity and low cost. However, among

disadvantages are:

A passive filters are designed for a particular application (size and placement of the

filters elements, risk of resonance problems),

high power losses as a result of high fundamental current,

passive filters are heavy and bulky.

5th 7th 11th 13th

Fig. 1.2. LC passive filters

The simpler way to harmonic reduction of diode rectifier currents are additional series

inductors used in the input or output of rectifier (typical per unit value is 1-5%) (see Chapter

2).

Other technique, based on mixing single and three-phase (Fig. 1.3a) non-linear loads [7.7,

10.2], gives a reduced THD because the 5th

and 7th

harmonic current of a single-phase diode

rectifier often are in counter-phase with the 5th

and 7th

harmonic current of a three-phase diode

rectifier. Simulated input current waveform is presented in Fig. 1.3 b.


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Fig. 1.3. Mixed single and three-phase nonlinear loads and typical line current waveforms

The multipulse rectifier [3] gives another possibility to decrease current harmonics content.

Although it is easy to implement, it possess several disadvantages such as: bulky and heavy

transformer, higher voltage drop, and higher harmonic currents at non-symmetrical load or

line voltage conditions.

Y Y

12-pulse rectifier6-pulse rectifier

YY

YY

24-pulse rectifier

Y Y

Fig. 1.4. Basic schemes and typical line current waveforms of multipulse rectifiers

A modern alternative to the passive filter is application of the Shunt Active Filters (SAF) [5,

7, 8], which, thanks to used closed feedback loops, gives better dynamics and control of

harmonic as well as fundamental currents. Active filters are generally divided into two


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groups: the active shunt filter (current filtering) (Fig. 1.5) and the active series filter (voltage

filtering).

Non-linear

load

iC

iL

iS

L

APF

uS

Fig. 1.5. Three-phase shunt active filter together with non-linear load

The three-phase (two-level) shunt SAF consists of voltage source bridge converter. This

topology is identical to the PWM inverter. SAF represents a controlled current source iC

which added to the load current iLyields sinusoidal line current iSand provide:

harmonic compensation (much effectives than passive filters).

compensation of fundamental reactive components of load current,

load symetrization (from grid point of view),

Parallely to excellent performance, SAF possess few disadvantages as: complex control

strategy, switching losses and EMC problems. Therefore, inclusion of a small LC or LCL

passive filter between the grid and theSAF

is necessary.

Load

uS

Fig.1.6 PWM Rectifier

The other possible reduction technique of current harmonic is application of PWMRectifier

(Fig. 1.6). Two types of PWMconverters, with a voltage source output [4] (Fig. 1.7a) and a

current source output (Fig. 1.7b) can be used. First of them called a boostrectifier (increases

the voltage) operates at fixed DC voltage polarity, and the second, called a buck rectifier

(reduces the voltage) operates with fixed DC current flow.


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a) b)

C

Udc

iload

ia

ib

ic

3xL

uLa

uLb

uLc

Ui

3xL

uLa

uLb

uLc

ia

ib

ic

iload

Ldc

Udc

3xC

Fig. 1.7 Basic topology of PWM rectifier a) boostwith voltage output, b) buck with current output

Among the main features of PWM rectifiers are:

bi-directional power flow,

nearly sinusoidal input current, regulation of input power factor to unity,

low harmonic distortion of line current (THDbelow 5%),

adjustment and stabilization of DC-link voltage (or current),

reduced capacitor (or inductor) size due to the continues current.

Furthermore, it can be properly operated under line voltage distortion and notching, and line

voltage frequency variations.

This thesis is devoted to investigation of two different control strategies for boost type of

three-phase bridge PWM rectifiers. A well-known method based on current vector orientation

with respect to the line voltage vector (Voltage Oriented Control - VOC) is compared with

control strategy based on instantaneous direct active and reactive power control based on

virtual flux estimation called Virtual Flux based Direct Power Control (VF-DPC).

Additionally, in both control strategies an Active Filtering Function is applied.

Therefore, the following thesis can be formulated:

Application of Active Filtering Function to PWM Rectifier control strategy provides

more efficient utilization of power electronics equipment and leads to neutralization of

harmonics generated by other nonlinear loads. Thus, it improves the line current and

voltage at the point of common coupling (PCC).


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In order to prove the above thesis, the author used an analytical and simulation based

approach, as well as experimental verification on the laboratory setup with a 5kVA IGBT

converter. In the analytical approach mathematical description based on space vector are

applied. The following simplifications were assumed when formulated simulation models:

power transistors were considered as ideal switches, however, the voltage drop has

been taken into account,

power diodes were idealized,

models of passive components included inductance with resistance and capacitance

with resistance.

The thesis deals with analysis and comparative study of different control strategies for PWM

Rectifiers having Active Filtering Function (AFF). At legating a general information

regarding diode rectifiers, to well understand and recognition of harmonics problems

generated by them are presented and discussed. Two different control schemes for PWM

Rectifiers and three different methods for elimination of current harmonics are presented.

Additionally, information concerning design of current and power controllers, selection of

passive components and power converter rating calculation are considered. The PhD thesis

consists of 8 chapters

The first Chapter Introduction gives short overview of harmonic reduction techniques and

formulates main goals of the thesis. The second one Front-end Rectifiers for Adjustable

Speed Drivesdeals with requirements for diode rectifier, which are most common used in

inverter fed adjustable speed drives. Several models of diode rectifiers with different AC and

DC side filters are presented, as well as information about current harmonics generated by

such a rectifiers. Additionally, requirements for passive elements of diode rectifiers are

presented. Finally, international norms devoted to harmonics pollution in the grid are

included. The third chapter titled Basic Theory of PWM Rectifier consists of theoretical

information, mathematical models, basic requirements and limitations for PWM rectifiers.

The fourth chapter Introduction to Active Filtering describes basic principles of parallel

active power filters, principles of shunt active filters for current and voltage harmonics

sources. The fifth chapter PWM Rectifier with Active Filtering Function presents and

investigates, an interesting opportunity for PWM rectifier filtering function. It is a result of

conjunction a PWM rectifier and Active Power Filter. Both of them has the same power

circuit, as well as a control strategies are very similar, therefore such equipment can be

interesting alternative for expensive active filtering units. Two different control strategies are

described: VOC (Voltage Oriented Control) with two different methods of compensation


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higher current harmonics and VF-DPC (Virtual Flux based Direct Power Control). Very

important chapter sixth Dimensioning of Power Converters deals with dimensioning of

power converter, taking into account a parameters like: demanded active power of DC load,

input filter inductance, reactive and harmonics power intended to compensation. Additionally,

requirements for passive elements of power converters are presented. The chapter sevenths

entitled Simulation and Experimental Results presents simulation models developed in

thesis and selected waveforms which show operation of investigated control algorithms. Also,

comparative study of Voltage Oriented Control (VOC) versus Direct Power Control (DPC) is

presented. The last chapter eight Summary and Closing Conclusions gives general

overview and final conclusions on discussed topic. Several information, devoted to harmonic

distortion in power system, instantaneous decomposition of powers according to different

authors like: Peng, Akagi, etc. are presented in Appendix A.2. Additionally, general

information concerning simulation models, used simulation packages (SABER,

MATLAB/SIMULINK, PLECS) and laboratory setup are given in Appendix A.4. Also,

Appendix A.5 presents design algorithms for current (for VOC) and power (for VF-DPC), PI

type regulators. An Artificial Neural Network based, resonant current controllers as well as

delta modulation and hysteresies controllers are presented.

In the authors opinion the following parts of the thesis represent his original

contributions:

elaboration of Virtual Flux based Direct Power Control for PWM rectifiers with Active

Filtering Function control strategy (Chapter 5),

elaboration of methodology for converter power ratio calculations depending on

application PWM Rectifier, Active Power Filter, PWM Rectifier with Active Filtering

Function (Chapter 6),

development of two simulation algorithms in Matlab/Simulink and SABER with control

algorithm in C language for investigation of proposed solutions (Appendix A.4),

implementation and investigation of various closed-loop control strategies for PWM

rectifiers: Virtual Flux Based Direct Power Control (VF -DPC), Voltage Oriented

Control (VOC), as well as open loop and closed loop control strategies for PWM Rectifier

with Active Filtering Function ,

practical verification on the experimental setup based on a mixed RISC/DSP (PowerPC

604/TMS320F240) digital controller.


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2. Front-end Rectifiers for Adjustable Speed AC Drives

2.1 Introduction

Voltage source inverters (VSI) fed adjustable speed drives (ASD) are frequently used in

industry, especially in energy saving applications. In the conventional solution the inverter is

fed by a diode or thyristor rectifier [7.8] with a large DC link capacitor. Such a rectifier takes

a high distorted AC-grid current. Frequent use of such rectifiers as ASD front-ends has

resulted in serious utility problems like current and voltage harmonics, reactive power,

voltage notches, etc. Voltage harmonics due to current harmonics becomes the main problem

for utility.

A usual way to reduce high current harmonics is application of a DC or AC-side inductors.

Compared to DC-sided smoothing inductor, an AC-side inductor creates an electrical distance

between grid and a drive. However, the AC-inductor is a source of additional losses, has a

meaningful dimension and determines an additional cost. Fig. 2.1 shows scheme of utility

interface for converter-fed drives [7.1]. These solutions do not provide recommended IEEE

519 harmonic standards, which require voltage distortion limitation at utility-customer point

of common coupling (PCC). IEEE 519 is a justification for using of power quality

compensators.

VS

Motor

AC side filter DC side filterDiode rectifier InverterPCC

Fig. 2. 1 Converter-Fed adjustable drives utility interface typical scheme

2.2 Adjustable Speed AC Drives

The ASDs input current characteristics depend on: drive type, its load, and the characteristics

of the supplying system [7.4, 7.5]. The input currents harmonic distortion can vary over a

wide range. However, for purposes of analysis it is possible to identify two basic waveform

types as bellow [11].


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TYPE 1: Discontinuous mode - High Distortion Current Waveform.

This is a representation of all ASDs that have voltage source inverters without an additional

inductor for current smoothing (Fig. 2.3a). The total harmonic current distortion can be over

80%. Actually, it can be higher for small drives but waveform of Fig. 2.3b is a good

representation for larger drives or groups of smaller drives.

TYPE 2: Continuous mode - Low Distortion Current Waveform.

This mode represents behavior of DC drives, large AC drives with current source inverters,

and smaller AC drives with voltage source inverters and added inductor for current smoothing

(Fig. 2.4a). The typical waveform of Fig. 2.4b has a THD level of 30%, which is obtained for

an AC drive with a 5% inductor.

The significant harmonic reduction is obtained for ASDs just by adding an inductor at the

rectifier input. Fig. 2.5 illustrates the effect of AC-side inductance size on input currentdistortion. It is possible to include this inductance in the DC link of the drive, providing the

same harmonic current reduction benefit.

2.3 Drive system configurations

"#$#% &'"#$#% &'"#$#% &'"#$#% &'((((

A DC-side inductor can be added to a three-phase rectifier (Fig. 2.2) for harmonic reduction.

With the dc inductor of a sufficient amount, the input current becomes a square waveform. By

adding an infinite dc inductor, a perfect square waveform can be obtained. However, a perfect

square waveform will have difficulties to meet the individual limits for higher order

harmonics.

Motor

VS

Fig. 2.2. Diode rectifier with DC side capacitor and inductor.

Input current THD=60%-130%


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"#$#" &' '"#$#" &' '"#$#" &' '"#$#" &' '((((

Another solution is to add a series AC-side inductor or passive filter to remove individual

harmonics. Fig. 2.3 shows the circuit arrangement with a LC filter in front of the rectifier

together with a DC-side inductor.Generally, such a LC filter can be tuned to the 5th

or 7th

harmonic because they are most important. Once the 5

th harmonic is cancelled, rest of

harmonics can also be reduced significantly in the same way.

Motor

VS

Fig. 2.3. Diode rectifier with DC side capacitor and inductor filter and AC side inductor. Input currentTHD=30%-40%

Fig. 2.4 compares harmonic contents for different DC-side inductors.The three-phase diode

rectifier generates about 70-percent 5th harmonic. After adding 1% and 5% DC-side inductor,

the 5th harmonic content is reduced to 35% and 25%, respectively.Therefore, an individual

harmonic filter in addition to the DC-side inductor is necessary to meet IEC 1000-3-4

standards.

5 7 9 1 1 1 3 1 5 1 7 1 9

0

2 0

4 0

6 0

8 0

HD[%]

H a r m o n i c n u m b e r

T h r e e p h a s e r e c t if ie r

1 % D C i n d u c to r

5 % D C i n d u c to r

I E C 1 0 0 0 - 3 - 4 S t a n d a r d

Fig. 2.4. Comparison between different three-phase built-in passive compensation results and IEEE

standard


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2.4 Diode rectifiers

"#)#%# * &'"#)#%# * &'"#)#%# * &'"#)#%# * &'((((

The idealized model of three-phase diode rectifier with infinite DC-side inductor is presented

in Fig. 2.5a.a) b)

L

o

a

d

LDC

uA

uB

uC

iA

1/6 5/6 2

Fig. 2.5 Ideal three phase rectifier with infinite DC-side inductor Ldcand no grid impedance (a),

Voltages and currents of idealized three phase rectifier (b).

The idealized rectifiers current assumed to be smooth on the DC-side (infinite LDC) and, for

neglected commutation effects (LS=0), occurs an ideal square. As shown o Fig. 2.5b the

current changes instantaneously from zero to a finite value. Every phase is conducting only

during 2/3 of the period. The input diode rectifier current can be described in following form:

0

0

50 6

5 1

6 6

1 1( ) 0

6 6

1 5

6 6

50

6

sa

t

I t

i t t

I t

t

< <

< <

= <


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can be used to determine the order and magnitude of the harmonic currents drawn by a six-

pulse diode rectifier:

16 = kh k = 1, 2, 3. (2.3a)

h

I

Ih /1

1

= (2.3b)

Thus, the higher harmonic orders are: 5th

, 7th

, 11th

, 13th

etc., with a 50 Hz fundamental

frequency, that corresponds to 250, 350, 550 and 650 Hz, respectively. The per unit

magnitude of the harmonics of the fundamental is the reciprocal of the harmonic order: 20%

for the 5th

, 14,3% for the 7th

, etc. Eqs. (2.1)-(2.2) are calculated from the Fourier series for

ideal square wave current (critical assumption for infinite inductance on the input of the

converter). Equation (2.1) is fairly good description of the harmonic orders generally

encountered. The magnitude of actual harmonic currents often differs from the relationship

described in (2.2). The shape of theACcurrent depends on the input inductance of converter.

The ripple current is proportional to 1/L times the integral of the DC ripple voltage and

inverse proportional to LDCinductance.

1ripple DC

i U dt L

= (2.4)

"#)#" * &'"#)#" * &'"#)#" * &'"#)#" * &'((((

A diode rectifier with DC-side smoothing capacitor is common used front-end rectifier in

industry. Its construction is very cheap and compact, however from the grid point of view it

has the worst behavior.

L

o

a

d

Fig. 2. 6. Three-phase rectifier with smoothing DC side capacitor a) circuit, b) typical waveforms

b)a)


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The idealized model of three-phase diode rectifier with DC-side capacitor is presented in Fig.

2.6a. Typical input current waveform presents Fig. 2.6b, and as shown it contains high

number of higher harmonics and the THD is over 80%.

"#)#$ * '"#)#$ * '"#)#$ * '"#)#$ * '(((( &' &' &' &'((((

The idealized model of three-phase diode rectifier with AC-side inductor and DC-side

capacitor is presented in Fig. 2.7a [10.5, 10.6, 10.8]. Typical input current waveforms are

presented in Fig. 2.7b and 2.7c with 1% and 5% AC-side inductor, respectively. It can be seen

that, an input current of Fig. 2.7c consists less higher harmonics and has lower THD

compared with current of Fig. 2.7b.

Fig. 2.7. Diode rectifier with AC-side inductors (a) and typical for 1% and 5% inductor (b).


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0 1 2 3 4 5

30

40

50

60

70

80

Input

currentTHD[%]

Choke inductance [%]

Fig. 2.8. Effect of input inductance on ASDs input current distortion

Fig. 2.8 presents effect of input inductor on input current THD. The input current THD

decrease with increasing value of input inductance. Therefore, such a solution partially solves

a harmonic problem. However, application of input inductance generates some additional

problems. One of them is the phase shift between fundamental harmonics of gridvoltage and

input current, which is very important parameter determining the reactive power level. Fig.

2.9 shows that it strongly depends and increases in case of increasing input inductance or load

power.

0 4 8 12 16 20

-25

-20

-15

-10

input inductance [mH ]

iDC

[A]Phaseshiftbetwee

nfirstharmonics

oflinevoltageandinputcurrent[deg]

Fig. 2.9. Phase shift between first harmonics of grid voltage and input current versus AC-side

inductance or load power.


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Fig. 2.10 presents simulated waveforms for diode rectifier with AC-side inductance and DC-

side capacitance for two different load conditions. The decreasing amplitude and phase shift is

present in case of increasing load conditions. That gives an additional reactive power taken by

the converter.

Fig. 2.10. Typical input current waveforms for two different DC-side currents: Idc=3A (blue),

Idc=15A (green)

Applied input inductance value has an additional effect on a diode rectifier operation [9].

Adoption of it, besides of decreasing of harmonic distortion and increasing of reactive power

determine of decreasing ofi

t

parameter.

Fig. 2.11.i

t

parameter of diode rectifier input current versus input inductance value

a) LL=10mH, b) LL=1mH


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As shown in Fig. 2.11 an input inductance value has a great influence oni

t

parameter of

diode rectifier grid current. A large value of input inductance decrease significantly ofi

t

parameter.

Additional input inductance is the simplest method to reduce grid current harmonics

generated by diode rectifiers feded adjustable speed drives (ASD) converters.

Summarizing, the input inductor has following impact on diode rectifier operation:

Significantly reduce a grid current THD,

Decrease ai

t

parameter,

Increase reactive power value taken by the converter,

A source of additional voltage drop.

"#)#) "#)#) "#)#) "#)#)

Diode rectifier with DC-side capacitance

0 200 400 600 800 1000

80

100

120

140

160

180

GridcurrentTHD[%]

DC-link capacitance [uF]

Fig. 2.12. Grid current THD versus DC-link capacitance

Fig. 2.12 shows the grid current THD versus DC-link capacitance. A large value of

capacitance provide more smooth shape of DC-link voltage, however a grid current will have

higher amplitude. That significantly increase a grid current THD.


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Diode rectifier with DC-side capacitance and inductance

0 200 400 600 800 1000

37

38

39

40

41

42

43

LinecurrentT

HD[%]


10 20 30 40 50

30

32

34

36

38

GridcurrentT

HD[%]

DC-link inductance [mH]

Fig. 2.13. a) Grid current THD versus DC-link capacitance, b) Grid current THD versus DC-link

inductance

In this situation a DC-link inductance provide a continuous mode of diode rectifier operation.

Therefore, both a large value of a DC-link capacitance and inductance provide decreasing of

input current THD. However, there are the maximal values for capacitance and inductance

(500uF and 30mH, respectively), above which increasing of those parameters is not

profitable, because the grid current THD do not decrease enough.

Diode rectifier with AC-side inductance and DC-side capacitance

0 200 400 600 800 1000

31,5

32,0

32,5

33,0

33,5

34,0

GridcurrentTHD[%]


0 5 10 15 20 25

20

40

60

80

100

GridcurrentTHD[%]

AC-side inductance [mH]

Fig. 2.14. a) Grid current THD versus DC-link capacitance, b) Grid current THD versus AC-side

inductance

Here, for a grid current smoothing the AC-side inductor is applied. Similar, like in previous

situation both a large value of a AC-side inductance and DC-link capacitance provide

decreasing of input current THD. Moreover, there are also the maximal values for capacitance

a) b)

a) b)


26/154


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2.5 Harmonic Limitations

Severe current or voltage harmonics may damage or malfunction various electronic

equipment supplied from the grid. However, a level of grid distortion where those problems

can occur is not precisely defined. The main reason of harmonics in power system is

electronic equipment mainly a diode rectifiers, mostly spread power electronic AC/DC

converters. The reason of diode rectifier popularity is very simple, it is cheap, robust,

efficient, reliable and has a small size. However, a diode rectifier has one big disadvantage

significantly distorted input current. Therefore, problems related to harmonics produced in the

grid by diode rectifiers, caused necessity of define and arrange requirements for nonlinear

electronic equipment. International norm precisely define maximal harmonic content in a grid

voltage as well as in the current taken by electronic equipment. Norms divide electronic

devices depending on maximum permissible current and force an application of equipment

like passive and active filters or PWM Rectifiers.

"#+#% *,,, +%-"#+#% *,,, +%-"#+#% *,,, +%-"#+#% *,,, +%-((((%--"%--"%--"%--"

This standard sets limits for harmonic voltage and currents at the Point of Common Coupling

(PCC), therefore the focus is only on the power system. It places responsibility on large

commercial and industrial consumers.

Voltage Distortion Limits

Bus Voltage at PCC Individual voltage distortion [%]* Total voltage distortion [%]

below 69kV 3.0 5.0

69kV to 138kV 1.5 2.5

Above 138kV 1.0 1.5

* maximum for individual harmonic

Current Distortion Limits

Maximum odd harmonic current distortion in percent of ILfor general distribution systems (1.120V 69kV)

ISC/IL


28/154

- 28 -

IL- fundamental of the average (over 12 months) maximum monthly demand load current at

PCC

TDD total demand distortion, harmonic current distortion in % of maximum demand load

current (15 or 30 minute demand)

"#+#" *,' .%///"#+#" *,' .%///"#+#" *,' .%///"#+#" *,' .%///(((($$$$((((" 0*,' %///" 0*,' %///" 0*,' %///" 0*,' %///(((($$$$(((("1"1"1"1

The European standard IEC 61000 defines the current distortion limits for equipment

connected to the public supply system. The objective is to limit the voltage distortion and is

addressed to small customer equipment. Emphasis onpublic, low-voltage and household.

IEC 1000-3-2 Limits for Class D Equipment

Harmonic order Maximum permissible

harmonic current per watt

Maximum permissible

harmonic current

N mA/W A

3 3.4 2.3

5 1.9 1.14

7 1.0 0.77

9 0.5 0.40

11 0.35 0.33

13


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2.6 Conclusions

International standards impose voltage and current harmonic limits.Many solutions has been

designed to deal with these standards.

The simplest compensation method is to use an AC-side inductor or an AC-side LC filters.

However, when using these passive compensation methods some problems can occur:

- Rectifier input voltage distortion and output DC link voltage reduction by AC-side

induction.

- Rectifier input current augmentation by parallel connected filters.

The active compensation is therefore preferred in case of performance basis, but its cost and

complexity is a main problem.


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3. Basic Theory of PWM Rectifier

As shown in Chapter 2, diode rectifiers are most frequently applied converters in

AC/DC power conversion. However, because of significantly distorted input current, which is

not acceptable in respect to international standards, diode rectifiers should be replaced be

other, not polluting and line power friendly equipment. Therefore, converters which present a

low interaction on the grid are going more interested. The three phase VSC (Voltage Source

Converter) applied as a grid interface stage called Boost active rectifier, can take near

sinusoidal input current with a near unity power factor but also it can work in both rectifying

and regenerative modes. From the reliability and efficiency point of view a PWM Rectifiers

are very promise solutions [1, 4, 6.2, and 6.4].

The PWM Rectifier, by many is considered as most obvious alternative to conventional diode

rectifier. This chapter introduces and presents basics of operation of PWM Rectifier and

operation limitations. Also, mathematical models in different reference frames are presented.

The basic requirements of a PWM Rectifier can be defined as follows:

bi-directional power flow,

low harmonic distortion of line current,

regulation of input power factor to unity,

adjustment and stabilization of DC-link voltage, reduced DC filter capacitor size.

3.1 Operation of the PWM Rectifier

Fig. 3.1b shows a single-phase representation of the PWM boost Rectifier circuit presented in

Fig. 3.1a. The L and R represent the line inductor. uSis the line voltage and uC is the bridge

converter voltage controllable from the DC-side. Magnitude of uCdepends on the modulation

index of the VSC and DC voltage level.


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a)

b)

uS

uc

iCL R

RiCjLiC

Fig. 3.1. Simplified representation of three-phase PWM rectifier for bi-directional power flow

a) Main circuit b) single-phase representation of the rectifier circuit

d

q

(a) (b)

Su

jL Ci

R Ci

Cid

q

Su

jL Ci

R Ci

Ci

Cu

Cu

Fig. 3.2. Phasor diagram for the PWM rectifier a) rectification at unity power factor b) inversion at

unity power factor

Inductors L connected a input of PWM converter with a grid are integral part of the rectifier

circuit. It brings current source character of input circuit and provide boost feature of

converter. The line current iC is controlled by the voltage drop across the inductance L

interconnecting two voltage sources (grid and PWM converter). It means that the inductance

voltage uI equals the difference between the line voltages uS and the converter voltage uC.

When a phase angle and amplitude of converter voltage uC is controlled, indirectly phase

and amplitude of line current is controlled. In this way average value and sign of DC current

is controlled and is proportional to active power flowing through converter. The reactive

power can be controlled independently with shift of fundamental harmonic current iC in


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respect to voltage uS. Fig. 3.2 presents general phasor diagram for both rectification and

regeneration modes when unity power factor is required. The figure shows that the voltage

vector uC is higher during regeneration (up to 3%) then rectifier mode [6.6]. Thus, PWM

Rectifier has two operation modes:

Rectifying mode, Regenerating mode.

Naturally, in a real system the power losses are present because of:

Power transistors switching losses,

AC-side inductor losses,

Heating losses and others.

Load

VS

Plosses

Rectifying mode Pgrid

= Pload

+ Plosses

Regenerating mode Pgrid

= Pload

- Plosses

Fig. 3.3. Power flow in active PWM rectifier

A three-phase symmetric system represented in a natural coordinate system by phase

quantities like for example voltages (Fig. 3.4), can be replaced by one resultant space vector.

22( ) ( ) ( )

3A B Ck k t k t k t = + + 1 a a (3.1)

Where: ( ), ( ), ( )A B Ck t k t k t - denote arbitrary phase quantities in a system of natural

coordinates (A, B, C) satisfying the condition ( ) ( ) ( ) 0A B Ck t k t k t + + =

2, ,1 a a - Complex unit vectors,

2

3- Normalization factor


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- 33 -

Fig. 3.4. Configuration of space vector

Main circuit of bridge converter (Fig. 3.1a) consists of three legs with IGBT transistor or, in

case of high power, GTO thyristors. The bridge converter voltage can be represented with

eight possible switching states (six-active and two-zero) described by equation 3.2.

Fig. 3.5a presents converter structures for eight different switching states.

A B C

+

-

UDC

U1k = 0

Sa

=1

Sb

=0

Sc

=0

A B C

+

-

UDC

U2k = 1

Sa

=1

Sb

=1

Sc

=0

A B C

+

-

UDC

U3k = 2

Sa

=0

Sb

=1

Sc

=0

A B C

+

-

UDC

U4k = 3

Sa

=0

Sb

=1

Sc

=1

A B C

+

-

UDC

U5k = 4

Sa

=0

Sb

=0

Sc

=1

A B C

+

-

UDC

U6k = 5

Sa

=1

Sb

=0

Sc

=1

A B C

+

-

UDC

U7

Sa

=1

Sb

=1

Sc

=1

A B C

+

-

UDC

U0

Sa

=0

Sb

=0

Sc

=0

Fig. 3.5a Possible switching states (Sa, Sb, Sc) of PWM bridge converter


34/154

- 34 -

( 1) / 32

3

0

j k

DCk

U eu

=

1...6

0,7

k

k

=

=

(3.2)

As mentioned in Fig. 3.5a eight possible states of the converter can be presented in vector

representation (Fig. 3.5b). Therefore, demanded command vector, will be constructed using

the nearest accessible vectors [2.1, 2.2].

Fig. 3.5b Representation of input voltage as a space vector

Fig. 3.5b presents of input voltage as a space vector as was mentioned in Fig. 3.5a.

Only one switch in the leg of converter (Fig. 3.1a) can be turn on in one time, if two of them

will be turn on, the short circuit of DC-link will happen. To protect the converter, a delay time

(dead time) in transistor switching signals must be applied [2.3]. The dead time effect

produces a nonlinear distortion of the average voltage trajectory. Therefore, for the proper

operation a compensation of dead time is required.


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- 35 -

3.2 Mathematical description of PWM Rectifier

2

3 DC

U

2

DCU

2

DCU

2

DCU

2

DCU

2

3 DC

U

2

DCU

2DCU

2

DCU

2

DCU

DCU

DCU

Fig. 3.6 Representation of converter output voltages: a) equivalent scheme of the converter, b)

output voltages

$#$#% 2 $#$#% 2 $#$#% 2 $#$#% 2

Three phase grid voltage and the fundamental line current are described as:

sinAN mu E t= (3.3a)

2sin( )

3BN m

u E t

= + (3.3b)

2sin( )

3CN m

u E t

= (3.3c)

sin( )AN mi I t = + (3.4a)

2sin( )

3BN mi I t

= + + (3.4b)

2sin( )3

CN mi I t = + (3.4c)

where Em (Im) and are amplitude of the phase voltage (current) and angular frequency,

respectively.

With assumption


36/154

- 36 -

0AN BN CNi i i+ + (3.5)

we can transform equations (3.3) to a stationary - system and the input voltage in -

frame are expressed by:

3

sin( )2S mu E t = (3.6)

3cos( )

2S m

u E t = (3.7)

Similarly, the input voltages in the synchronous d-q coordinates are expressed by:

2 23

200

Sd S Sm

Sq

u u uE

u

+ = =

(3.8)

$#$#" * $#$#" * $#$#" * $#$#" *

Line to line input voltages of PWM rectifier can be described as:

( )AB A B DCu S S u= (3.9a)

( )BC B C DC

u S S u= (3.9b)

( )CA C A DC

u S S u= (3.9c)

and phase voltages are equal:

AN a DCu f u= (3.10a)

BN b DCu f u= (3.10b)

CN c DC u f u= (3.10c)

where:

2 ( )

3

A B Ca

S S Sf

+= (3.11a)

2 ( )

3

B A Cb

S S Sf

+= (3.11b)

2 ( )

3

C A Bc

S S Sf

+= (3.11c)

Thefa, fb, fcare assume 0, 1/3 and 2/3.


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- 37 -

3.3 Block diagram of PWM rectifier

$#)#% $#)#% $#)#% $#)#% ((((

The voltage equations for balanced three-phase system without the neutral connection (Fig.

3.1) can be written as:

S I Cu u u= + (3.12)

C

S C C

diu Ri L u

dt= + + (3.13)

Sa Ca Ca Ca

Sb Cb Cb Cb

Sc Cc Cc Cc

u i i ud

u R i L i udt

u i i u

= + +

(3.14)

and additionally for currents

dca Ca b Cb c Cc dc

duC S i S i S i idt

= + + (3.15)

A block diagram of PWM rectifier corresponding to Eqs(3.13-14) is shown in Fig. 3.7.

sLR+

1

sLR+1

sLR+

1

3

1

sC

1+

+

+

+

+

+

+

++

+

++

+

-

-

-

-

-

-

- udc

idc

uSa

uSb

uSc

Sa

Sb

Sc

iCa

iCb

iCc

fa

fb

fc

uS

a

uS

b

uSc

Fig. 3.7. Block diagram of voltage source PWM rectifier in natural three-phase coordinates

$#)#" 0$#)#" 0$#)#" 0$#)#" 0((((31313131

Eq.3.13 after coordinate transformation will receive following form:

CdSd Cd Cq Cd

diu Ri L Li u

dt= + + (3.16a)


38/154

- 38 -

Cq

Sq Cq Cd Cq

diu Ri L Li u

dt= + + + (3.16b)

( )dc Cd d Cq q dcdu

C i S i S idt

= + (3.17)

where: tStSSd sincos += ; tStSSq sincos =

)2(6

1cba

SSSS = ; )(2

1cb

SSS =

A block diagram of PWM Rectifier in synchronous rotating d-qmodel [6.5] is presented in

Fig. 3.8.

Fig. 3.8. Block diagram of voltage source PWM rectifier in synchronous d-q coordinates

Rcan be practically neglected because voltage drop on resistance is much lower than voltage

drop on inductance, what gives simplification of Eq. 3.13.

C

S C

diu L u

dt= + (3.18)

Sa Ca Ca

Sb Cb Cb

Sc Cc Cc

u i ud

u L i udt

u i u

= +

(3.19)

CS C

S C C

uu idL

u i udt

= +

(3.20)

Therefore, Eq. 3.16a and b receive following shape:

CdSd Cq Cd

diu L Li u

dt= + (3.21a)


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- 39 -

Cq

Sq Cd Cq

diu L Li u

dt= + + (3.21b)

The active and reactive power supplied from the grid is given by

{ }*Re S C S C S C Sa C a Sb Cb Sc Ccp u i u i u i u i u i u i = = + = + + (3.22)

{ } ( )*1

Im3

S S C S C Sc Ca Sa Cb Sb Ccq u i u i u i u i u i u i = = = + + (3.23)

It gives in the synchronous d-qcoordinates:

3( )

2Sq Cq Sd Cd m m

p u i u i E I= + = (3.24)

( )Sq Cd Sd Cqq u i u i= (3.25)

For a unity power factor operation, following conditions can be obtained:

iCq = 0, uSq = 0, 32

Sd mu E= , 32

Cd mi I= , q = 0 (3.26)

3.4 Operating limits

For proper operation of PWM rectifier a minimum DC-link voltage is required [4, 6, 6.3].

Generally it can be determined by the peak value of line-to-line grid voltage. Defining the

natural DC-link voltage value, as possible to obtain in case of not operating transistors, their

freewheeling diodes becomes a standard three-phase diode bridge. Therefore, the boost nature

of the active rectifier leads to:

min ( ) ( )3 2 2,45DC S rms S rmsU u u = (3.27)

If this condition is not fulfilled, the full control of the input current is not possible. Moreover,

to keep the switching losses down, a DC-link voltage should be as low as possible. Typically,

the reference value for the controlled DC-link voltage should be chosen about 10% above the

natural DC-link voltage. If unity power factor is s required for PWM Rectifier operation, it

can be obtained in case of:

2 2 2C S Iu u u= +

(3.28)

The voltage drop across the inductor (uI) depends on reactance of the inductor at the input

frequency and on the input current. The magnitude of the switching voltage vectors depends

on the DC-link voltage level. This means that the maximum AC voltage (uS) a PWM Rectifier

can generate in the linear PWM region.

Assuming the grid side resistance equal to zero and neglecting the converter losses the active

power can be calculated as follows:


40/154

- 40 -

3 3 DCC S C S U

P u i uL

= = (3.29)

This means that high value of a DC-link voltage and small value of the input inductor,

determine a high power rating of the rectifier. The active power can be also defined using DC-

link voltage and load current as follows:2

3( )C S C C DC DC P u i Ri U I = = (3.30)

Therefore, the input current becomes:

241

2 3

S S CC

u u Pi

R R R

=

(3.31)

if the following relation is satisfied:

23

4

S

C

u

P R (3.32)

At steady state operating conditions the capacitor current is zero. Thus the converter output

power is:

C DC C P U i= (3.33)

and the maximum load current that can be delivered is obtained:

2

,max

3

4

SC

DC

ui

RU= (3.34)


41/154

- 41 -

4. Introduction to Active Filtering

4.1 Basic Configuration

The Shunt Active Filters (SAF) can be divided into two groups [5.2, 5.3, 5.4]: a shuntand

series type of APF. The first one group serve for current and the second one for voltage

compensation. Shunt Active Filters(SAF) [5.2] are most often used for compensating current

distortion produced by nonlinear loads, like diode or thyristors rectifiers fed adjustable speed

drives. General scheme and typical waveforms are shown in Fig. 4.1a and b respectively.

a)

b)

0,280 0,285 0,290 0,295 0,300

-1 5

-1 0

-5

0

5

10

15

active filter current

diode rectifier current

Line current

curr

ent

time

Fig. 4.1. a) Basic configuration of Shunt Active Filter (SAF) b)Typical waveforms for input current of

a diode rectifier compensation

The SAF current injection has a large influence on the grid current and only a small on the

nonlinear load (diode rectifier) current [5.9]. The grid voltage can be modified by SAF,

particularly when it is much distorted and as a result, it modifies the load current. The SAF

effect on the load current is small but may lead to unstable operation in some cases if the

designer has not taken its dynamics into account. If this small influence is neglected and the


42/154

- 42 -

load is considered as a current source, there is no interaction between the AF and the load

currents.

4.2 Control of SAF

Two main ways to cancel the grid current harmonics depending on which current is measured

can be maintained. These two ways have a different control structure and lead to different

properties.

)#"#% 4 2 )#"#% 4 2 )#"#% 4 2 )#"#% 4 2

This method is based on load current measurement and then the harmonic content is extracted

from the load current (Fig. 4.2). In this way, the SAF injects the compensating current into the

grid, without information about the grid current [5.7]. All errors in the system, like parameter

uncertainties, measurement errors or control errors, will appear in the grid current as

unfiltered harmonics. The most important advantage of open loop method is system stability,

but it is connected with extended control algorithm and enlarged number of current sensors.

a)

Motor

u SLS

LC

LLiS

iC

iL

DS P

U DC

b)

GuS

zS

iL

iS

iC

uC

Fig. 4.2. a) Open loop Shunt Active Filter (SAF), b) Equivalent circuit for open loop control of SAF

C Li G i= (4.1)


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- 43 -

1

SC

G ii

G

=

(4.2)

(1 )S Li i G= (4.3)

Full compensation can be achieved if: 1G

G is the equivalent transfer function of the SAF, including detection circuit and delay of the

control. In general, G has a function of notching for the fundamental component 0f

G = and

1h

G = for harmonics.

)#"#" ' 2 )#"#" ' 2 )#"#" ' 2 )#"#" ' 2

Another way to generate the reference current is to measure the grid current. In this way, in

addition to the inner load current control loop, there is an outer grid current loop in the

control. This method does not allow harmonic correction without phase balancing and

reactive power compensation. The control algorithm is less complicated then in open loop

method and requires minimal number of current sensors.

a)

Motor

uSLS

LC

LLiS

iC

iL

DSP

b)

GuS

zS

iL

iS

iC

uC

Fig. 4.3. a) Closed loop SAF , b) quivalent circuit for closed loop control of SAF


44/154

- 44 -

C Si G i= (4.4)

1

LC

G ii

G

=

(4.5)

1

LS

ii

G=

(4.6)

Full compensation can be achieved for G

4.3 Types of Harmonic Sources

The harmonic sources are mainly divided into two groups: current and voltage types,

depending on impedance [5.14].

)#$#% 5 ')#$#% 5 ')#$#% 5 ')#$#% 5 ' 6 6 6 6

a)

ZS

Harmonic source

Ld

AC Source

b)

uS

ZS

iL

AC SourceHarmonicCurrentSource

Fig. 4.4. Typical harmonic current source a) block scheme, b) equivalent circuit

The common sources of harmonic currents are thyristor converters (Fig. 4.5) where a

sufficient dc inductance Ldforces a constant DC current. The grid voltage and rectifier current

are presented in Fig. 4.5. Because of current contents, this behaves like a current harmonic

source. However, as a current source of harmonics can be also shown a diode rectifier with a

smoothing capacitor and additional AC or DC inductors, applied for decreasing high order

harmonics content.


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- 45 -

Fig. 4.5. Voltage and current of thyristor rectifier (commutation effect is neglected)

)#$#" 5 7 6)#$#" 5 7 6)#$#" 5 7 6)#$#" 5 7 6

a)

AC Source

ZS

Harmonic source

b)

uS

ZS

AC Source

uL

iL

HarmonicVoltageSource

Fig. 4.6. Typical Harmonic Voltage Source

A diode rectifier with smoothing capacitor (Fig. 4.6) becomes another common harmonic

source. Fig. 4.7 present its voltage and current waveforms. The rectifier current is highly

distorted, its harmonic are affected by the ac side impedance. Therefore this behaves like a

voltage harmonic source.


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- 46 -

Fig. 4.7. Voltage and current of diode rectifier

4.4 Analysis of Shunt Active Filter (SAF) Operation with Different

Harmonic Sources

A Shunt Active Filter (SAF) is a PWM inverter placed in parallel with a load (harmonic

source) to inject a harmonic current with the same amplitude as that of the load, but opposite

phase into the ac system. A pure current source of harmonic representsL

z , whereas a

pure voltage source of harmonic represents 0Lz .

)#)#% 6 5 ' 6)#)#% 6 5 ' 6)#)#% 6 5 ' 6)#)#% 6 5 ' 6

GuS

ZS

iC

iS iL

iLOZL

Fig. 4.8. Basic principle of shunt active filter with harmonic current source

Fig. 4.8 presents basic principle of SAF for harmonic current source, where the harmonic

source is presented as a Nortons equivalent circuit. ZS is source impedance, ILO is the

equivalent harmonic current source, ZL is the equivalent impedance on the load side which

may include passive filters and power factor correction capacitors. All equations in the


47/154

- 47 -

following analysis are in per unit representation. Following equation from Fig.4.8 can be

obtained:

C Li Gi= (4.7)

1 1

SLS LO

L LS S

uZi i

Z ZZ ZG G

= +

+ +

(4.8)

11

1

1 1

L

SL LO

L LS S

Z

uGi iZ ZG

Z ZG G

= ++ +

(4.9)

Focusing on harmonics

1

LS h

h

ZZ

G>>

(4.10)

which is the required operating condition for the SAF to cancel the load current harmonic.

When it is satisfied, the Eqs. (4.7)-(4.9) can be written as:

C Lhi i= (4.11)

(1 ) (1 ) 0ShSh LOh

L

ui G i G

Z + (4.12)

ShLh LOh

L

ui i

Z= + (4.13)

It is seen from the equation (4.12) that source current becomes sinusoidal because of

1 0h

G = for harmonics when (4.10) is satisfied. In the Eq. (4.10) only G can be pre-

designed and determined by the SAF, while ZSand ZLare determined by the system. Because

of pure current harmonic source, represented by a thyristor rectifier with a large dc

inductance, we have L SZ Z>> . Equations (4.8) and (4.10) can be reduced respectively:

(1 )S

LO

IG

I= (4.14)

1 1h

G > will not satisfy any more.


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- 48 -

)#)#" 6 5 7 6)#)#" 6 5 7 6)#)#" 6 5 7 6)#)#" 6 5 7 6

GuS

ZS

iC

iS iL

uL

ZL

Fig. 4.9. Basic principle of shunt active filter with harmonic voltage source

Fig. 4.9 shows the basic principle of SAF with harmonic voltage source, where the harmonic

source is represented by Thevenins equivalent circuit, a voltage source VLand impedance ZL.

From Fig.9 we can write following equations:

C Li Gi= (4.16)

1

S LS

LS

u ui

ZZ

G

=

+

(4.17)

1

1 (1 )

1

S L S LL

L S LS

u u u ui

ZG G Z Z Z

G

= =

++

(4.18)

Therefore, following equation (represents required operating condition for the SAF to cancel

the load voltage harmonic) is satisfied

11

LS

h

ZZ pu

G+ >>

(4.19)

the grid current will be sinusoidal. So, with condition (4.19), equations (4.16)-(4.18) are:

C Lhi i= (4.20)

0Shi = (4.21)

Sh LhLh

L

u ui

Z

= (4.22)

But it is difficult for SAF to satisfy equation (4.19), because harmonic voltage source

represents usually very low impedance ZL for a diode rectifier with a large smoothing

capacitor 0LZ as long no series reactor placed on the ac side of the rectifier.


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4.5 Conclusions

A Shunt Active Filters (SAF) have fast dynamic behavior, thanks to large energy storage are

not sensitive for load transients. However, injection of high order harmonics requires large

power rating of applied VSI, typically 25%-100% related to load system. From the stability

point of view, are independent of system parameters and typically not influenced by the loads,

except for capacitive loads. Generally are applied for variable fundamental reactive power

compensation, suppression of non-characteristic harmonics and unbalanced systems.

Reliability of the system is good for low voltage applications, however, over-rating is

required. SAF are proposed for low to medium power systems with highly dynamics loads.

General futures of SAF are summarized in Table 4.1.

Table 4.1 Summary of Shunt Active Filter

System configuration

Basic operation principle Operates as a current source

Adaptive loadsInductive or current-source loads or harmonic current

source, e.g. phase-controlled thyristor rectifiers of ac drives

Required operation

conditions ZL should be high and the SAF should meet 1 1hG


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5. PWM Rectifier with Active Filtering Function

5.1 Introduction

Shunt Active Power Filters (SAF) [5.18 5.20] and PWM rectifiers [4] are two typical

examples from several solutions, which are used for harmonics elimination. Both of them

have basically the same power circuit configuration and can operate based on the same

control principle. SAF are able to compensate not only current harmonics, but also a reactive

power and load unbalance. Design and control have been investigated in many papers [5.11,

5.12, and 5.13] where use ness of SAF was proved. PWM Rectifiers [4] as non-polluting

equipment with sinusoidal input currents are going to be more popular because of several

advantages like:

-Bi-directional power flow,

-Closed loop based stabilization of output DC voltage,-Low harmonic distortion of line currents,

-Regulation of input power factor to unity.

This chapter explores another task of PWM rectifier - active filtering function, which adds

Motor

VS

Motor

LS

LC

LL

iS

iC

iL

DSP

UDC

Motor

VS

Motor

LS

LC

LL

iS

iC

iL

DSP

a)

b)

Fig. 5.1. Control strategy a) open loop with 4 current sensors and b) closed loop with 2 current sensors


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- 51 -

advantages of SAF and PWM Rectifiers. So, the PWM rectifier supplies its load and at the

same time compensates AC grid current. This concept was at first introduced in works [4.1 -

4.4 and 14].

The open loop control strategy illustrated in Fig. 5.1a requires additional control functions

and measurement of nonlinear load current (iL). In contrast the closed loop control strategy

presented in Fig. 5.1b is based on PWM Rectifier operation and do not require additional

current sensors or any modifications in control algorithm. The difference results from location

of line current sensors. Compared to open loop control strategy, where current harmonic

content and power factor improvement can be controlled independently, such a system

performs both of these functions simultaneously.

5.2 Control Methods of PWM Rectifier

The dynamic and static performance of PWM Rectifier depends strongly on adopted control

methods. Therefore, in the next section some basic control strategies used for PWM Rectifiers

will be presented.

+#"#%# 7 4 ' 074'1+#"#%# 7 4 ' 074'1+#"#%# 7 4 ' 074'1+#"#%# 7 4 ' 074'1

Voltage Oriented Control (VOC) is based on coordinate transformations between stationary

and synchronous rotating dq reference system. It guarantees fast transient response and

high performance in steady state. Because of VOC uses an internal current control loops final

performance of the system strongly depends on applied current control techniques [1.2]

mentioned in Appendix.The conventional VOC system (Fig. 5.3) uses synchronous current control in rotating

reference coordinates, as shown in Fig. 5.2. A meaningful feature for this type of current

controller is signal processing in two coordinate systems. The first is stationary -and the

second is synchronously rotating d-q coordinate system. Three phase measured values are

converted to equivalent two-phase system -and then are transformed to rotating coordinate

system in a block -/d-q:

cos sin

sin cos

d US US

q US US

k k

k k

=

(5.1a)

Thanks to the above transformation the control values are DC signals. An inverse

transformation d-q/-is used on the output of control system and it gives a result on rectifier

reference signals in stationary coordinate:

cos sin

sin cos

dUS US

qUS US

k k

k k

=

(5.1b)


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The angle of the voltage vector USis defined as:

( ) ( )22

sin / US S S S u u u = + (5.2a)

( ) ( )22

cos / US S S S u u u = + (5.2b)

In voltage oriented d-qcoordinates, the AC line current vector iCis split into two rectangular

components iC=

[iCd, iCq](Fig. 5.2).The component iCddeterminates active power, where iCq

decides about reactive power flow. Thus the active and the reactive power can be controlled

independently via active and reactive components of line current vector iC. The UPF

condition is met when the line current vector, iC,is aligned with the line voltage vector, uS. By

placing the d-axis of the rotating coordinates on the line voltage vector uS a simplified

dynamic model can be obtained.

axis(fixed)

axis

d-axis

(rotating)

q-axisiS

iCd

iCq

uS= u

Sd

US

=t

iC

iC

uS

uS

Fig. 5.2. Vector diagram of VOC. Coordinate transformation of line current, line voltage and rectifier

input voltage from stationary coordinates to rotating d-qcoordinates

The grid voltage equations in the d-qsynchronous reference frame are as follows:

CdSd Cd Cd Cq

diu R i L u L i

dt= + + (5.3)

Cq

Sq Cq Cq Cd

diu R i L u L i

dt= + + + (5.4)

According to Fig. 5.3, the q-axis current is set to zero in all condition for unity power factorcontrol while the reference current iCdis set by the DC-link voltage controller and adjust the

active power flow between the grid and the DC-link. ForR 0equations (5.3), (5.4) can be

reduced to:

Cd

Sd Cd Cq

diu L u L i

dt= + (5.5)


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- 53 -

0Cq

Cq Cd

diL u L i

dt= + + (5.6)

With the q-axis current regulated to zero, the following equations (5.5 and 5.6) becomes

C

Sd Cd

diu L u

dt= + (5.7)

0 Cq Cd u L i= + (5.8)

As current controller, the PI-type can is used. However, the PI current controller has no

satisfactory performance, because of the coupled system described by Eqs. (5.5), (5.6).

Therefore, for high performance application with accuracy current tracking at dynamic state

the decoupled controller should be applied. The output signals from PI controllers after dq/

transformation (Eq. (5.1b)) are delivered to a Space Vector Modulator (SVM) which

generates switching signals for power transistors.

-

udc_ref udc id_ref

PI

PI

PIica

icc

icb

PWM

PI

abc

dq

dq

iq

id -

-

-

-

ud

uq

us

id_err

iq_err us

udc

+

+

ul ul

iq_ref

= 0

Fig. 5.3. Baseic block of VOC scheme

+#"#" +#"#" +#"#" +#"#"

5.2.2.1 VOC with active filtering function: total harmonic compensation method

As an active filter, PWM rectifier is able to compensate higher harmonics in a grid current

taken by the whole load. In order to compensate higher harmonics additional control block

(AFF) has to be added to standard VOC strategy (Fig. 5.4).A PWM Rectifier part of control is the same like described in previous chapter. The distorted

currents ila, ilb, ilc are delivered to the abc/dq transformation, where a fundamental (50 Hz)

harmonic becomes a DC quantity and other harmonics are non-DC values. Next those signals

are delivered to the High Pass Filter (HPF), which provides the higher harmonics signals

extraction. Then higher harmonics compensating signals id_fr, iq_frare added with an opposite


54/154

- 54 -

sign to the standard VOC reference signals iCd, iCqand in the same provide higher harmonics

compensation.

_ _ _

_ _ _

d err Cd ref Cd d f

q err Cq ref Cq q f

i i i i r

i i i i r

=

= (4.9)

-

udc_ref udc iCd_refPI

PI

PIica

icc

icb

ilc

ilb

ila

HPF

PWM

PI

abc

dq

abc

dq

dq

ab

idl

iCq

iql

iCd -

-

-

-

ud

uq

us aid_err

iq_err usb

udc

HPFid_fr

iq _ fr

+

+

ul

ul

ul

iCq_ref= 0

AFF

Fig. 5.4. Block diagram of VOC scheme with Active Filtering Function (AFF) block based on total

harmonic compensation

The compensating signals are high frequency components, added to the DC values reference

signal produce non-DC reference signals passed to a PI controllers. These give non ideal

conditions for PI controllers operation and produce an additional phase shift between

reference and actual current.


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- 55 -

5.2.2.2 VOC with active filtering function: selective harmonic compensation method

7 harm

id_fr iq_fr

-

udc_ref udc iCd_ref

PI

PI

PIica

icc

icb

PWM

PI

abc

dq

dq

iCq

iCd -

-

-

-

ud

uq

us

id_err

iq_err

us

udc

+

+

ul ul

iCq_ref

= 0

ul

dq

ilc

ilb

ila

LPF

abc

dq

idl_7h

iql_7h

LPFid_7h

iq_7h

ul

dq

ul 7*7*

+ +

+ +

5 harm

ilc

ilb

ila

LPF

abc

dq

idl_5h

iql_5h

LPFid_5h

iq_5h

ul

dq

ul-5* -5*

11 harm 13 harm+ +

Fig. 5.5. Block diagram of VOC with Active Filtering Function (AFF) scheme based on selective

harmonic compensation

In scheme of Fig. 5.5 active filtering function operates independently on few different main

current harmonics, like 5th

, 7th

, 11th

and 13th

in harmonic synchronous coordinates [5.5, 5.15,

5.17]. Moreover, nonlinear load currents ila, i lb, i lcare transformed to dq frame using suitably

angle ul for each harmonic intended to compensation. Then the distorted currents ila, ilb, ilcare

delivered to the Low Pass Filter (LPF), which provides the higher harmonics signals

extraction. Next after back transformation dq/ these signals idfr and iqfrare added with an

opposite sign to the standard VOC reference signals iCdand iCqgiving final commands id_err,

iq_err delivered to PI current controllers. The same procedure is used for all specified

harmonics.


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- 56 -

+#"#$ +#"#$ +#"#$ +#"#$

-

udc_ref udc id_ref

PI

PI

PIisa

isc

isb

PWM

PI

abc

dq

dq

abciq

id -

-

-

-

ud

uq

us

id_err

iq_err

us

udc

+

+

ul ul

iq_ref

= 0

Fig. 5.6. VOC closed loop control strategy

Closed loop control strategy of Fig. 5.6 operates like conventional VOC with the only change

on current sensor location instead PWM rectifier input currents iLa, iLb, iLc, the source

currents iSa, iSb, iScare measured and controlled.

The nonlinear load current iL is not measured (see Fig. 5.1b). It is naturally created by the

converter as a result of ac-line current sensor location at point of common coupling (PCC),

where the system controls the current to be sinusoidal and may be determined by considering

the summation of currents at the PCC:

C S Li i i=

The source currents iSa, iSb, iScare measured and taken into control strategy.

+#"#) 7 8 9+#"#) 7 8 9+#"#) 7 8 9+#"#) 7 8 9 & ' 07 & ' 07 & ' 07 & ' 07((((&' 671&' 671&' 671&' 671

Basic principles of virtual flux based active and reactive power estimation is presented below.

It is economically motivated to replace the AC-line voltage sensors [3.1] with a virtual flux

(VF) estimator [4, 6.1, 12]. The principle of VF is based on assumption that the voltages

imposed by the line power in combination with the AC side inductors can be considered as

quantities related to a virtual AC motor (see Fig. 5.7). Where R and L represent the stator

resistance and leakage inductance of the virtual motor. Line to line voltages: USab, USbc, USca

can be considered as induced by a virtual flux. Hence the integration of the voltages leads to

determination of a virtual flux vector S , in stationary -coordinates presents Eq.5.11.


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- 57 -

Fig. 5.7. PWM Rectifier

With the definitions

S Su dt = (5.9)

where

11

2 2

3 30

2

S S ab

S

S Sbc

u uu

u u

= =

(5.10)

SS

S SS

u dt

u dt

= =

(5.11)

30

2 2

3 33

2

C Ca

C

C Cb

i ii

i i

= =

(5.12)

1 11

2 2 20

3 3 30

2 2

CAM

C

C CBM

C

CCM

uu

u uu

u

= =

(5.13)

Operation of PWM rectifier is based on assumption, that input current ic is controlled by the

voltage drop across the inductor L interconnecting line and converter voltage sources. It

means that the inductance voltage uIequals the difference between the line voltage uSand the

converter voltage uC

S C Iu u u= + (5.14)


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- 58 -

and similarly a virtual flux equation can be presented as:

S C I = + (5.15)

axis(fixed)

axis

d-axis(rotating)

q-axis

iC

iCd

iCq

uS= u

Sq

S

=t

iC

iC

uS

uS

S

S

S

uCuI

=j

Li L

C

I

Fig. 5.8. Reference coordinates and vectors (for fundamental component): S virtual line flux vector,

C virtual flux vector of converter, I virtual flux vector of inductor, uC converter voltage vector,

uS- line voltage vector, uI inductance voltage vector, iC input current vector

Based on the measured DC link voltage Udcand the duty cycles of SVM modulator SA, SB, SC

the virtual flux Scomponents are calculated in stationary coordinates system as follows:

2 1( ( )

3 2S dc A B C C

U S S S dt Li

= + +

(5.16a)

1( )

2S dc B C C U S S dt Li

= +

(5.16b)

The measured input converter currents ica, icb and the estimated virtual flux components S

,Sare used for estimation of the instantaneous power. The voltage equation can be written

as

( )CS C Cd

u Ri Lidt

= + + (5.17a)

In practice,Rcan be neglected, giving

C CCS C

d i d diu L L u

dt dt dt = + = + (5.17b)

Using complex notation, the instantaneous power can be calculated as follows:

Re( )S Cp u i

= (5.18a)

Im( )S Cq u i

= (5.18b)

where * denotes the conjugate line current vector. The line voltage can be expressed by the

virtual flux as


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- 59 -

( )j t j t j tSSS S Sdd d

u e e j edt dt dt

= = = + j tSS

de j

dt

= + (5.19)

where Sdenotes the space vector and S its amplitude. For the virtual flux oriented d-q

coordinates (Fig. 5.20), S=Sd, and the instantaneous active power can be calculated from

(5.10a) and (5.11) as

SdCd Sd Cq

dp i i

d t

= + (5.20)

For sinusoidal and balanced line voltages, equation (5.12) is reduced to

0Sdd

dt

= (5.21)

Sd Cqp i= (5.22)

which means that only the current components orthogonal to the flux Lvector, produce the

instantaneous active power.

Similarly, the instantaneous reactive power can be calculated as:

SdCq Sd Cd

dq i i

dt

= + (5.23)

and with (5.13) it is reduced to:

Sd Cd q i= (5.24)

As mentioned in [4] for sinusoidal and balanced line voltage the derivatives of the flux

amplitudes are zero. By simulation and experiment investigation were proofed, that even for

distorted line voltage the simplified equations for the instantaneous active and reactive powers

can be used:

( )S C S C

p i i = (5.25a)

( )S C S C q i i = + . (5.25b)

The measured line currents iCa, iCb and the estimated virtual flux components S,S are

delivered to the instantaneous power estimator block .


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- 60 -

Fig. 5.9. VF-DPC control scheme

A VF-DPC control strategy main scheme is presented in Fig. 5.9. The commanded (delivered

from the outer PI DC voltage controller) active power prefand reactive power qref(set to zero

for unity power factor) values are compared with the estimated instantaneous p and q values,

respectively. The errors are delivered to PI controllers, where the variables are DC quantities

and steady state error were eliminated. The output signals from PI controllers after

transformation (5.29) are delivered to a Space Vector Modulator (SVM).

Fig. 5.10. Power estimation block

Fig. 5.10 shows an instantaneous powers estimation block. The angle is calculated using

estimated virtual flux components Sa,Sb.


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- 61 -

+#+#+#+#""""####++++

Fig. 5.11. VF-DPC scheme with Active Filtering Function (AFF) block



62/154

- 62 -

In this scheme of Fig. 5.11 measured input converter currents ica, icb and the estimated virtual

flux components Sa,Sbare used for the power estimation Fig. 5.12. For a PWM rectifier

operation the reference active powerpref(generated by the outer PI DC voltage controller) and

reactive power qref (set to zero for unity power factor) values are compared with estimated

instantaneouspand qvalues, respectively. The errors are delivered to PI controllers, which

eliminates steady state error. The output signals from PI controllers after transformation

pq/:

sin cos

cos sin

C CpS S

C CqS S

u u

u u

=

(5.26)

where:

( ) ( )22

sin / S S S S = + (5.27a)

( ) ( )22

cos / S S S S = + . (5.27b)

are used for switching signals generation by Space Vector Modulator.

Here a modified algorithm based on virtual flux, which operates directly on instantaneous

active and reactive power components is presented [5.6]. The instantaneous active and

reactive powers are estimated using currents intended to compensate ila, ilb, ilcand virtual flux

Sa,Sbaccording to Eqs (5.11a and b) as:

( )A S l S lp i i = (5.28a)

( )A L l L l

q i i = + (5.28b)

The calculated active power (pA) and reactive power (qA) are delivered to the high pass filter

(HPF) to obtain values of the instantaneous active power ( p A) and reactive power (q A)

which finally are used as a compensating components. Adding active filtering function will

cause suitable distortion of input PWM rectifier current, which will assure almost sinusoidal

line current. It permits to use PWM rectifier as a current harmonics eliminating device.


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- 63 -

Fig. 5.13. Instantaneous power waveforms for different current shapes.

a) current in phase with voltage b) current with phase shift c) distorted current

From the top: grid voltage, grid current, active and reactive power

Fig. 5.13 presents simulated examples of active and reactive powers for different current

shapes. It is obvious that for sinusoidal voltage and in phase current an active power has a

certain value and reactive power is equal 0 (Fig. 5.13a). In case that grid current is not in

phase with grid voltage but is still sinusoidal, the active power will have the same level, but

non zero value of reactive power will appear (Fig. 5.13b). If the current become a distorted

one, in active and reactive powers a pulsation component will be visible (Fig. 5.13c).

Summarizing, for higher harmonics elimination two high pass filters are needed, one for each

power component. For higher harmonics elimination and reactive power compensation, onlyone high pass filter in active power is required (switch in Fig. 5.11).

+#"#+#"#+#"#+#"#....

Fig. 5.14. VF-DPC control block


64/154

- 64 -


The nonlinear load current iLis not measured Fig. 5.1b. It is reconstructed by the converter as

a result of AC-line current sensor location at point of common coupling (PCC), where the

system controls the current to be sinusoidal and may be determined by considering the

summation of currents at the PCC.

C S Li i i= (5.29)

The grid currents isa, isband the estimated virtual flux components Sa,Sbare used for

estimation of power components. The reference active power pref and reactive power qref

values are compared with the estimated instantaneouspand qvalues, respectively. The errors

are delivered to PI controllers. The output signals from PI controllers after transformation

pq/are used as a reference signals for Space Vector Modulator.


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- 65 -

6. Dimensioning of Power Converters

This chapter is devoted to dimensioning of power converters. This is obvious, that proper

dimensioning is very critical issue for designing and selection of PWM Rectifier. Main power

scheme of parallel connected conventional diode rectifier fed Adjustable Speed Drive (ASD)

and modern PWM rectifier/inverter fed system is shown in Fig.6.1. It is very simp

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