WARSAW UNIVERSITY OF TECHNOLOGY · Inverter”, industrial project for Liebherr-Aerospace Toulouse...

Politechnika Warszawska

Warsaw University of Technology

http://repo.pw.edu.pl

Rodzaj dyplomu / Diploma type Rozprawa doktorska / PhD thesisAutor / Author Bobrowska-Rafał Małgorzata

Tytuł / Title

Synchronizacja i sterowanie trójpoziomowych przekształtników sieciowych PWM na bazie teorii składowych symetrycznych w warunkach zapadów napięcia / Grid Synchronization and Control of Three-level Three-phase Grid-Connected Converters based on Symmetrical Components Extraction during Voltage Dips

Rok powstania / Year of creationPromotor / Supervisor Kaźmierkowski MarianJednostka dyplomująca / Certifying unit Wydział Elektryczny / Faculty of Electrical EngineeringAdres publikacji w Repozytorium URL / Publication address in Repository http://repo.pw.edu.pl/info/phd/WUT251f9d992bde4fec8b76573e571bd5b8/

WARSAW UNIVERSITY

OF TECHNOLOGY

Faculty of Electrical Engineering

Ph.D. THESIS

Małgorzata Bobrowska-Rafał, M.Sc.

Grid Synchronization and Control of Three-Level Three-Phase Grid-Connected Converters based on Symmetrical Components

Extraction during Voltage Dips

Supervisor

Professor Marian P. Kazmierkowski, Ph.D., D.Sc.

Warsaw, 2013

Pobrano z http://repo.pw.edu.pl / Downloaded from Repository of Warsaw University of Technology 2021-04-11

Abstract

The dissertation presents solutions of control algorithms dedicated for Grid Connected

Converter (GCC) operating under unbalanced voltage conditions, especially under voltage dips.

Presented control algorithms concern synchronization, current and power flow control and are

directly based on the instantaneous symmetrical component theory. The intention of usage of the

theory is elimination of negative voltage component influence appearing during unbalanced voltage

dips.

The dissertation presents analysis of Polish Grid Code in terms of definition of

requirements for GCC interfacing with wind farm and the analysis of the symmetrical components

theory in different coordinate transformations. Also the analysis of voltage dip in the power system

is given. Furthermore, the synchronization, current and power flow control algorithms are

presented and verified theoretically and in simulation and experimental validation.

Streszczenie

Niniejsza rozprawa doktorska prezentuje rozwiązania algorytmów sterowania

dedykowanych dla przekształtników sieciowych pracujących w warunkach niesymetrycznego

napięcia, a zwłaszcza zapadów napięcia. W rozprawie zaprezentowano algorytmy synchronizacji,

sterowania prądami i przepływem mocy, które bezpośrednio opierają się na teorii składowych

symetrycznych. Celem zastosowania teorii w algorytmach sterowania przekształtnikiem sieciowym

jest wyeliminowanie negatywnego wpływu składowej przeciwnej napięcia pojawiającej się

podczas niesymetrycznych zapadów.

W pracy przedstawiono analizę polskiego kodeksu sieciowego w świetle określenia

wymagań dotyczących współpracy przekształtnika sieciowego z elektrownią wiatrową przyłączoną

do sieci elektroenergetycznej. Zaprezentowano również analizę teorii składowych symetrycznych

w różnych układach współrzędnych oraz analizę zagadnienia zapadów napięcia pojawiających się

w sieci elektroenergetycznej. Zaprezentowane algorytmy synchronizacji i sterowania prądami oraz

przepływem mocy są zweryfikowane w procesie symulacji i eksperymentalnie.


Preface

The research work presented in the Thesis has been carried out during my Ph.D.

studies at the Institute of Control and Industrial Electronics, Warsaw University of

Technology in the years 2008-2013.

The significant part of the Thesis was carried out by the National Science Center of

Poland. Parts of the work were performed in cooperation with industrial companies:

REpower Systems Polska and Transmission System Operator PSE S.A. During the

research work, Author has participated in the realization of the following projects:

"Research of control algorithms dedicated to grid converters cooperating with

renewable energy sources under grid voltage distortions", research project sponsored

by the National Science Center of Poland, 2012-2013

“Grid Code Analysis for Connection Wind Farms to Polish Power System”,

industrial project for REpower Systems Polska, 2012

“Project of installation for elimination voltage dips in industrial areas and

customers with improved power quality requirements”, industrial project for PSE

Operator S.A., 2010-2011

“Development of AC-DC power electronics converter series (5-400kVA) for

distributed energy sources with improved immunity for disturbances in the grid and

reduced negative impact on the grid”, development project for National Center of

Research and Development, 2010-2011

“Research and analysis of AC-DC-AC converter connected to utility grid under

voltage dips and outage”, research project for National Center of Research and

Development,2010-2011

“Projecting and Vaildation of Modulation of Three Phase Parallel Multilevel

Inverter”, industrial project for Liebherr-Aerospace Toulouse and Airbus France,

2009-2010

"Development and validation of technical and economic feasibility of a MW

Wave Dragon offshore wave energy converter", EU research project, 2009.

During the PhD studies, based on the research work, series of articles in journals

from JCR has also been published (1 article in IEEE Transactions on Industrial

Electronics, 2 articles in the Bulletin of the Polish Academy of Sciences: Technical

Sciences, 5 articles in Przegląd Elektrotechniczny, an article in Electricity - present day


and development-magazine of polish transmission grid operator PSE S.A., 13 papers at

foreign and domestic conferences). The list of publications is presented in the Appendix of

the Thesis. Actually, author’s publications were cited 54 times, h-index of cited

publications is equal to 4 (according to Google Scholar).

Acknowledgement

Here, I would like to thank people without whom this research work would not

meet with success.

First of all I would like to extent my sincere gratitude to my mentor and supervisor

professor Marian P. Kaźmierkowski. His support and role model he delineated guided me

thorough the research work and will direct me through the lifetime.

Here, I would also like to thank with all my heart to my best research associate and

partner, to my husband Krzysztof. Common life we have chosen drove us not only through

Ph.D. studies but I do believe it tied us up inseparably.

I would like to express my appreciation to my colleagues from the Intelligent

Control Group (ICG). Especially, I would like to thank to Ph.D. Marek T. Jasiński and

D.Sc. Mariusz Malinowski for their support and professional advices.

I would like to thank to my family for their unswerving hope placed in me.

Finally, I would like to thank to my friends: Kasia, Olga and Marta for their

patience and support they showed me during the time I was working on this Thesis.


Content

1. Introduction .............................................................................................................. 1

2. Polish Grid Code ...................................................................................................... 6

2.1 Power System in Poland .............................................................................. 7

2.2 Nominal Grid Conditions .......................................................................... 10

2.3 Polish Grid Code ....................................................................................... 12

2.3.1. Steady-State Operations ...................................................................... 14

2.3.2. Active Power Control .......................................................................... 15

2.3.3. Reactive Power Control....................................................................... 15

2.3.4. Operation during Transient States ....................................................... 17

2.3.5. Voltage Dips (Fault Right Through FRT) ........................................... 18

2.3.6. Overvoltage ......................................................................................... 19

2.3.7. Frequency Deviations .......................................................................... 19

2.3.8. Flickers ................................................................................................ 21

2.3.9. Higher Harmonics ............................................................................... 21

2.4 Summary and Conclusions ........................................................................ 21

3. Voltage Dips in the Power System ........................................................................ 24

3.1. Introduction to Voltage Dips ..................................................................... 26

3.1.1. Amplitude of Voltage Dips ................................................................. 27

3.1.2. Duration of Voltage Dips .................................................................... 29

3.2. Voltage Dips Classification ....................................................................... 30

3.3. Influence of Voltage Dip on Power System .............................................. 33

3.4. Conclusions ............................................................................................... 34

4. Basics of Symmetrical Components Theory .......................................................... 36

4.1. Voltage and Current Phasors ..................................................................... 36

4.2. Symmetrical Components Theory ............................................................. 38

4.3. Symmetrical Components for Instantaneous Values ................................. 40

4.4. Symmetrical Components in Stationary Frame ......................................... 44

4.5. Symmetrical Components in Synchronous Rotating Frame ...................... 48

4.6. Conclusions ............................................................................................... 52

5. Grid Synchronization under Unbalanced Conditions ............................................ 53

5.1. Introduction ............................................................................................... 53


5.2. Short Review of PLL algorithms ............................................................... 54

5.3. Synchronous Reference Frame PLL .......................................................... 57

5.4. PLL in Stationary Reference Frame for Unbalanced Conditions .............. 60

5.5. PLL in Synchronous Reference Frame for Unbalanced Conditions ......... 64

5.6 Comparative analysis of grid synchronization methods ............................ 67

5.6.1. Balanced dips ...................................................................................... 69

5.6.2. Unbalanced dips .................................................................................. 71

5.6.3. Phase jumps ......................................................................................... 72

5.6.4. Frequency steps ................................................................................... 74

5.6.5. Attenuation of Distortion..................................................................... 76

5.7 Summary and Conclusion .......................................................................... 78

6. Converter Control Methods based on Symmetrical Components.......................... 81

6.1. Current Control under Unbalanced Conditions ......................................... 83

6.1.1. Conventional Control Methods ........................................................... 83

6.1.2. Voltage Oriented Control with Resonant Controller ........................... 88

6.1.3. Dual Synchronous Reference Frame Control Algorithms .................. 89

6.2. Power Control under Unbalanced Conditions ........................................... 92

6.2.1. Basics of Instantaneous Power Theory under Unbalanced Conditions 92

6.2.2. Current Reference Calculation Strategies ........................................... 95

6.2.3. Elimination Of Active Power Oscillations (Pconst) .............................. 96

6.2.4. Elimination Of Reactive Power Oscillations (Qconst) .......................... 98

6.2.5. Symmetrical Currents (Ibal).................................................................. 99

6.3. Grid Support under Unbalanced Conditions ............................................. 99

6.4. Summary .................................................................................................. 100

7. Simulation and Experimental Results .................................................................. 102

7.1. Current Control Methods ......................................................................... 103

7.1.1. Step Response.................................................................................... 103

7.1.2. Disturbance Rejection ....................................................................... 106

7.1.3. Influence of PLL ............................................................................... 109

7.2. Instantaneous Power Control ................................................................... 111

7.3. Grid Support ............................................................................................ 113

7.4. Summary .................................................................................................. 117

8. Summary and Final Conclusions ......................................................................... 119

Bibliography ............................................................................................................... 124


List of Author’s Publications during Ph.D. Study ...................................................... 130

Appendix .................................................................................................................... 132

A. Experimental Setup.................................................................................. 132

B. Simulation Setup...................................................................................... 135

List of Important Symbols .......................................................................................... 138

List of Abbreviations .................................................................................................. 140


1

1. Introduction

Background

Reduction of fossil fuels consumption, combat with global warming and also

mitigation of the European Union’s dependence on foreign energy imports have

established UE countries as global leaders in the development and application of

Renewable Energy Sources (RES). Therefore, in 2008 the climate and energy package was

singed as binding legislation ensuring the European Union setting three key objectives for

2020 (known as 3x20%):

20% reduction in EU greenhouse gas emissions from 1990 levels,

Raising the share of EU energy consumption produced from renewable

resources to 20%

A 20% improvement in the EU's energy efficiency.

To fulfill these ambitious requirements of the EU community, each country is

obliged to interpose legal and financial instruments smoothing the path of RES

investments. According to growing profitability of RES, more and more of such generation

units are being connected to the power system, creating part of distributed generation

system, being an essential introduction to the smart power system.

Unfortunately, such intensified environmental care caused by RES penetration, has

also disadvantages, like constantly increasing problem of power quality deterioration in the

power system. RES, especially wind power stations, are characterized by intermittent

generation, strictly depending on wind conditions. Wind units, connected to transmission

or distribution lines, generate serious distortions transferring through the power system to

consumers. Moreover, RES require constant energy back-up performed by conventional

power generation units, which can start generation during rapidly changing wind

conditions or wind farm breakdown.

However, the most serious issue of RES operation in the power system is their

sensitivity to grid voltage distortions, especially to voltage dips. Voltage dip is the most

serious variation occurring in the power system, which cause destabilization of the power

system and the majority of financial losses among voltage distortions. Sudden and often

short-liven voltage drop with phase jump can cause disconnection of wind farm from the


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power system. The disconnection lead to power generation loss seen from the power

system and voltage amplitude reduction. The consequences are amplification of distortion

and serious power system destabilization (domino scenario).

To avoid such effects, European transmission and distribution system operators

effectuate grid codes. A national grid code is a document regulating operation of RES,

especially wind farms, in the power system. It defines in details operation of RES in steady

and transient states. Especially, it names behavior of wind farms under grid voltage

distortions, like voltage dips, frequency and phase changes, higher harmonics existence,

etc. Moreover, in national grid codes more and more often appears the requirement of

supporting the power system by RES during voltage distortions, realized by additional

active or reactive power generation.

Units responsible for connection all RES to the power system are power converters,

in this applications called Grid Connected Converters (GCC). GCCs are devices converting

parameters of energy generated by RES into energy of parameters acceptable by system

operators, which can be delivered to users. It is GCC, which is exactly responsible for

energy adaptation to strict requirements of grid codes. The most important part of GCC

from point of view of power quality, is the control system. The control system defines the

parameters of generated energy, and what is even more important, is responsible for

uninterrupted operation of RES during voltage distortions like dips.

Motivation

Conventional control methods of GCC converters are not suitable to operate under

voltage distortions occurring in the power system. Devices cooperating with GCC under

unbalanced voltage conditions are just disconnected from the power system, what

nowadays is unacceptable in the light of national grid codes. Hence, more sophisticated

control methods have been employed by wind stations manufacturers due to growing

system operators requirements. Nonetheless, as more and more RES are connected to the

power system, the strictest requirements should be fulfilled. In order to meet system

operators demands and improve the quality of energy in the power system, more advanced

control method should be proposed.

The motivation of the Thesis was such elaboration of a control system dedicated to

GCC to adjust it to proper and uninterrupted operation during the most serious voltage

distortion, which are voltage dips. Hence, firstly the voltage dips issue was analyzed.


3

For better understanding the problem, conditions in which GCC cooperating with

RES, especially wind farms, were analyzed. The Polish Grid Code was studied to acquaint

to system operator requirements for GCC operation.

Then, actually existing synchronization and control methods dedicated for GCC

operating under unbalanced voltage conditions were analyzed. After the analysis, author

concluded, that for proper operation of any GCC under unbalanced conditions, the

independent control of positive and negative current component is indispensable. Hence,

the powerful instrument was applied in the GCC control system to adjust it to operation

under unbalanced voltage conditions. It was the instantaneous symmetrical component

theory.

Hence, the proposed control system, based on the instantaneous symmetrical

components theory, allows to:

Uninterrupted connection and proper operation of GCC during voltage dips,

Grid support and power flow control under unbalanced voltage conditions,

Synchronization to grid voltage during any voltage variations.

Thesis

Hence, the following thesis has been formulated:

“Application of control methods based on the instantaneous symmetrical

components theory to GCC control allows proper synchronization, current and power flow

control and guarantees better quality of generated power under unbalanced grid voltage

conditions than conventional vector control methods”.

Methodology

In order to prove the Thesis, author has conducted research including following

steps:

Analysis of requirements for wind farms connected to the Polish power system,

Theoretical analysis of actual literature describing problem of voltage dips in the

power system, application of the instantaneous symmetrical components theory,

newest achievements in the field of synchronization and control of GCC,

Computer simulation for developing synchronization and control algorithm of

GCC,

Laboratory experiment for practical validation.


4

Assumptions

During the research process following assumptions and limitations were adopted:

Proposed synchronization and control algorithm is dedicated for the power

converter cooperating with RES operating as a generator. Hence, only grid-

connected AC-DC part of the converter is considered, known as a Grid Connected

Converter (GCC),

The GCC is modulated with Pulse Width Modulation (PWM) method with constant

switching frequency,

The GCC is connected to three-phase three-wired model of power system line,

For analysis of grid voltage distortions the instantaneous symmetrical components

theory is employed.

Contribution

In the author’s opinion, the following achievements are author’s original

contribution to the research field:

Analysis of the instantaneous symmetrical components theory in the context of

synchronization and control of GCC;

Analysis of Polish Grid Code in terms of requirements definition for GCC

interfaced with RES;

Thorough analysis and selection of control methods for GCC based on the

instantaneous symmetrical component theory;

Analysis and selection of grid support method based on the instantaneous power

control;

Development of simulation model GCC operating under unbalanced grid voltage

conditions in Matlab/Simulink environment;

Laboratory verification of simulation results.

Outline

The Thesis is organized as follows:

In Chapter 2 the Grid Code for wind farms, established by Polish system operators,

is described. Firstly, the actual situation of the Polish power system is shortly presented.

The nominal grid conditions in transmission and distribution grids, according to Polish

standards and directives, are described. Then, the Polish Grid Code requirements of wind


5

farm operation are divided into steady- and transient-state requirements. The steady-state

requirements concerns active and reactive control of wind energy generation according to

operators demands. The transient-state requirements describes behavior and supporting the

grid by wind farm during grid voltage variations.

The Chapter 3 concerns problem of voltage dips in the power system. Firstly, dips

parameters are described. Then, dips classification is presented, and finally, the influence

of voltage dips on the power system is discussed.

The Chapter 4 describes the powerful tool – the instantaneous symmetrical

components theory. Firstly, the basic definitions used in the theory are presented. Then,

the symmetrical component theory of Fortesque for steady-state values is analyzed. The

instantaneous symmetrical theory is a base for analysis of voltage unbalance in stationary

and synchronous rotating frame.

The Chapter 5 describes synchronization methods based on the instantaneous

symmetrical components theory dedicated for GCC operating under unbalanced voltage

conditions. Firstly, the basic synchronization tool – Synchronous Reference Frame PLL

(SRF-PLL) and its tuning methods are presented. Finally, two algorithms, strictly based on

the instantaneous symmetrical components theory, operating in stationary and synchronous

reference frames are described and compared in the simulation study.

The Chapter 6 describes power control of GCC under unbalanced grid voltage

conditions. Firstly, the instantaneous power theory under grid voltage variations is

reminded. Then, according to the instantaneous symmetrical components theory, reference

currents are calculated. The reference currents are used in three proposed control strategies

concerning active and reactive power flow and balanced currents. Finally, grid support

methods are presented.

In Chapter 7 results of simulation and experimental verification are given. Tests

concern operation of current control methods under step response and grid voltage

disturbances. Also, the influence of employed PLL algorithm is analyzed. Then, proposed

instantaneous power control methods are verified under unbalanced grid voltage

conditions. Finally, the grid support method, based on the instantaneous symmetrical

components theory is executed.

In Chapter 8 the summary and final conclusions of the Thesis are presented.


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2. Polish Grid Code

Every year the penetration of wind farm to the power grid system rapidly growths.

Hence, in countries, where wind farms constitute an important part of the power system,

the Transmission System Operators (TSOs) set up technical requirements, which are called

the Grid Codes (GCs). Grid codes of the European Union countries (EU) introduce

regulations, which oblige wind farms to support the power system by controlling

parameters of generated power, like level of active and reactive power flow or voltage

amplitude, etc. [Tsi]. Moreover, wind power farms should hold out the appearance of

voltage variations in grid and uninterruptedly supply users in the electric power [Pse1].

The Grid Code (GC) is a technical specification defining parameters and methods

of cooperation units connected to the power system, especially which ensure security and

economic functioning of it. Increasing penetration of Renewable Energy Sources (RES)

leads to an elaboration of specific technical requirements for connection large wind farms

to the power system. Requirements of GC typically refer to large wind farms connected to

the transmission system rather than to smaller stations connected to the distribution

network [Ryn]. According to wind farms, GCs require not only a proper cooperation with

the power system but also supporting the system by power, voltage and frequency control.

Converters of wind power plants play the most important part in helping the wind turbine

meets grid codes requirements.

The main message of GCs for RES, especially for wind farms, is to behave as much

as conventional power plants in steady and in transient states. Typical requirements

concern:

Steady-state operations - when level of generated active and reactive power

changes due to wind conditions and demands of specific operator,

Transient states operations - behavior under grid voltage disturbances: Low

Voltage Right Through (LVRT) and Fault Right Through (FRT)

capabilities, reactive current junction, resuming active power, operating

during dips, frequency changes, etc.

It should be noted that GCs contain not only specific regulations for wind farms’

installations but also several important decisions concerning connection and usage of the

power grid system, cooperation between grid operators and detailed operation of the grid

system as whole.


7

In the most of developed EU countries, Grid Codes are announced by transmission

and distribution system operators. From 1st of January 2012 the new Polish Grid Code is in

force, titled: “Transmission Grid Code – Conditions for use, traffic management, operation

and development planning” [Ire]. It was established by the sole Polish TSO: PSE Operator

and introduces new decisions about an operation of wind farms in the Polish power system.

The aim of the Chapter is explanation of specified regulations contained in the

Polish GC dedicated to wind farms, concerning parameters of generated power, supporting

power system and operation under grid voltage distortions. Requirements of the Polish

energy law are presented and analyzed.

2.1 Power System in Poland

In this section is a short description of the Polish power system. The power system

consists of three main parts:

Generation system containing conventional and renewable energy power

plants;

Transmission system containing stations and high voltage power lines (400

kV and 220 kV);

Distribution system containing stations and power lines of voltage 110 kV,

medium voltage (mostly 15kV) and low voltage (0,4 kV).

The power system does not regularly cover the surface of Poland. The Southern and

the Central parts are most developed. Here, most of conventional power plants are located:

currently there are 19 conventional power plants [Ryn], where energy is generated from

stone and brown coal. Also, the majority of transmission lines are located in those regions.

The Northern and the Eastern parts of Poland are in worse conditions. There are significant

lacks of conventional power stations and transmission lines. The grid system is weak. The

HVDC connection of voltage 450 kV to the Swedish power system was supposed to be the

important stabilizing element of the Northern grid. According to attitude of PSE Operator,

it operates only in range of 10% of the nominal power and leads serious power oscillations.

Probably, problems are result of the improper design of the AC-DC converter.

In Poland, as well as in the rest of the European countries, principal requirements of

generated power quality in conventional plants and in RES are determined by TSO. In

Poland there is one TSO – PSE Operator S.A. [Pse1], which is responsible for systems of

voltage 400kV, 220kV and indirectly for system of 110kV. The decisions concerning the


8

GC are made by the TSO without cooperation of the Polish government. The GC, on the

behalf of Polish government, is acknowledged by superior Office of Power Regulations

[Ure].

It is worth to mention, that from 1995 the Polish transmission system has been

synchronously connected to the European power system. Hence, the Polish grid became a

part of the synchronous systems of the Union for the Coordination of Transmission of

Electricity (UCTE), nowadays known as European Network of Transmission Systems

Operators of Electricity (ENTSO-E) [Ent].

The map of transmission lines in Poland is presented in Fig.2.1. With dotted lines a

planned transmission lines are marked. Nowadays, the construction of energetic connection

(400 kV) between Poland and Lithuania is the most important project of the PSE Operator.

Starting of connection is planned in 2015.

Fig.2.1. Map of transmission lines in Poland [Pse2].


9

Energy from the transmission system is delivered to consumers by the Distribution

System Operators (DSOs). The main tasks of DSOs, beside distribution of energy, is

maintaining the grid traffic, repairs and development of a distribution system, management

of generation units (to nominal power more than 50 MW), etc. In Poland there are four

main DSOs: ENERGA, ENEA, TAURON and PGE. Fig.2.2 illustrates the geographic

location of DSOs in Poland.

Fig.2.2. Disposal zones of four main DSOs in Poland [Ure2].

In Poland the penetration of wind farms to the power system rapidly growths.

Nowadays, wind power plants are the most popular of RES in Poland. In the end of 2012

the power generated by wind turbines was equal to 2,6 GW. According to the policy of

Polish government, in 2020 the participation of energy from Renewable Sources will be

equal to 20% (currently about 10%) [Mgg1], [Mgg2]. The majority of this power is

supposed to be generated by wind power plants.

Nowadays, Polish DSOs are executing modernization programs of about half of

existing power lines (from LV to 110 kV). The aim of the modernization is an

improvement of connection conditions for existing wind farms, and for those which have

obtained connection agreements. Moreover, the DSO ENERGA, which geographic

location includes sea, does not concern connecting new off-shore wind farms, expect those

with given connection agreements (2,2 GW for PGE Operator and Kulczyk Holding). For

the same reasons, the TSO, PSE Operator does not give any new permissions for

connection new wind farms. It is worth to remember that there is huge number of given


10

connection permissions, which can be bought on the market from private investors. Even if

building the atomic power plant will be regulated, still in the power system there is a lack

of conventional power plants. It’s worth to mention that there are some plans of building

several gas power stations by private investors.

The bright plans of rapid growth of wind farms can be stopped. In the author’s

opinion the grow of the wind power plants’ penetration could be stopped due to three

significant barriers, like:

Weak grid (lack of conventional plants and transmission lines) in areas of

the best winds’ conditions in Poland: the Northern and the Eastern,

Finite energy flow capacity in the transmission and distribution systems,

Limited possibilities of the energy storage systems.

The solution can be passing by limited capacity of power system by installing an

energy compensator. Basing on previous research [Bob1], author claims that - the best

solution for big wind farms is installing a static synchronous compensator (STATCOM)

and dynamic voltage restorer (DVR) for smaller farms. Those compensators significantly

increase transmission capabilities of power system, improve power quality, facilitates

management, etc. There is possibility to install common compensator for the group of wind

farms to minimize costs.

The hint for increasing wind farms penetration gives plan of the new Polish Energy

Law [Act]. The idea is to connect wind turbines with energy storages.

2.2 Nominal Grid Conditions

In Poland the energy generation and distribution as well as energy market are

regulated by specified acts, whose main aim is safe and uninterrupted supply of electricity

and heat for every consumer. In Polish law there are three most important documents

determining and regulating power quality in electric power system:

The Act: Energy Law [Act],

Standard PN-EN:50160 [Pst1], which is implementation of European Standard

EN:50-160 [Est1],

Standard PN-IEC 60038 [Pst2], which determines the basic standards for voltage in

AC grids and DC traction grids.


11

The purpose of the Act: Energy Law is to ensure the safety of energy supply,

balancing the interests of energy operators and customers. The Act inter alia determines

requirements of delivered power quality. Interesting is the article relieving energy

companies of responsibility for side effects of poor power quality in case of energy

security of Poland, health or life hazard and risk of serious financial losses.

The parameters of power quality in Polish electrical networks are determined in two

documents. First one is the standard PN-EN:50160, which defines parameters of voltage in

medium and low voltage grids. The second one is the Decree of Minister of Economy

called “Decree of Connection” [Dme1], concerning power quality in all kinds of grids,

especially, in high voltages systems. The Decree determines six groups of units connected

to grid:

1st group – units connected directly to transmission system (400 kV and 220 kV);

2nd

group – units connected to distribution system of voltage 110 kV;

3rd

, 4th

and 5th

groups – units supplied with voltage below 110 kV;

6th

group – temporal units.

The most important requirements of power quality according to the PN-EN:50160

and the Decree of connection are listed below:

Amplitude of voltage:

o For 1st group: in every week 95% of mean RMS voltage values (measured in 10

minutes time frames) should not exceed +5%/-10% of the nominal voltage

o For other groups variations of voltage should not exceed 10%

Frequency:

o For 1st and 2

nd group: in every week 95% of measured mean values of

frequency should not exceed of the nominal 50 Hz. Moreover, 100% of

measurements should not cross limits +4%/-6%.

o For other groups : in every week 95% of measured mean values of frequency

should not exceed of the nominal 50Hz. In lower voltage grids for 99,5%

of measurements should not cross limits +4%/-6%.

Voltage fluctuations:

o For 1st and 2

nd groups: in every week for 95% of week the rate of voltage

fluctuation index (defined in [Pst1]) should be less than 0.8

o For other groups: index should be less than 1.


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Content of negative component of voltage:

o For 1st and 2

nd groups: in every week for 95% of measured voltage should

contain less than 1% of negative component

o For other groups the acceptable contain is less than 2%

Content of higher harmonics [Act]:

o For 1st and 2

nd groups, the total THD should be less than 3%. Acceptable values

of particular harmonics are given in [Act],

o For other groups the acceptable THD is less than 8%. Content of particular

harmonics is given in [Dme1].

Power factor (measured as tg ):

o For every group should not exceed value 0,4.

These requirements are summarized in Tab.2.1. Using tg instead of is

motivated by history of Polish energy market. The tg is used for calculating permitted

generation of reactive power.

Tab.2.1. Requirements of power quality in the light of polish energy law.

Parameters 1st and 2

nd groups

3rd

,4th

and 5th

groups

95% of 10-minutes time frames measuring mean RMS values of voltage contains

in range of nominal value:

Voltage

110kV

220kV 10%

110%

400kV +5%/-10%

Negative component <1% < 2%

( ) <0.4

Frequency for 100% : for 99,5% : for 95%: +4%-6% for 95%: +4%-6%

THD <3% <8%

The detailed operation’s condition of Polish electrical system are given in [Mgg2].

The requirements described above concern only parameters of energy delivered to

receivers and do not consider requirements of power generated by energy producers like

conventional power plants or RES.

2.3 Polish Grid Code

As the installed capacity of wind power plants increases, the share of renewable

energy introduced to the power grid system also grows [Ewe]. To control the mounting up

impact of renewable energy delivered to grid system, developed countries are elaborating


13

regional grid codes, which requirements of each wind power plant should meet [Tsi]. The

European Network of Transmission Systems Operators of Electricity (ENTSO-E) leaded

determinants of GCs’ requirements for European countries [Ent]:

Network Code for Requirements for Grid Connection applicable to all

Generators,

Balancing Network Code,

Network Code on Operational Security,

Network Code on Operational Planning and Scheduling,

Network Code on Load Frequency Control and Reserves,

Demand Connection Code,

Network Code for Capacity Allocation and Congestion Management.

Actually, the new grid code of Poland, established by the TSO in 2012 is in force,

titled: “Transmission Grid Code – Conditions for use, traffic management, operation and

development planning [Ire]. The GC concerns detailed requirements for wind farms in

basic issues, according to:

Connection of wind farms to the power system,

Operation during the nominal grid voltage conditions,

Supporting the power system during voltage variations.

Also requirements concerning a connection of a wind farm to the power system are

described. The process is long and complicated, a several administration requirements

must be fulfilled. It could take even several years. According to the installed power in an

ambient grid system, the kind of grid, where the wind farm is connected, different

conditions are made. The most important is obtaining environmental, development and

grid connection permissions. For every installation of the nominal power greater than 2

MW, the particular system operator executes an expertise of the wind farm’s influence has

on the power system. Additionally, two months before planned connection of a wind farm,

with the nominal power greater than 2 MW, an technical manual, prepared by investor,

must be delivered to the system operator. The manual should contains [Con1]:

Procedures of remote control and voice communication with the wind farm,

Procedures of turning on/off the wind farm, especially procedures of the

operation during renewed connection to the grid after emergency turning off

wind farm,


14

Procedures of informing the proper grid operator about an energy production

forecasts, based on weather forecasts.

The strictest conditions are demanded from installations of power higher than 5

MW connected to 110 kV line or higher. Here, the procedure is complicated and require

authorization from the particular DSO and the TSO.

Moreover, every wind installation of the nominal power greater than 2 MW should

be equipped with a remote and a voice communication with the appropriate operator. The

communication is realized by on-line system SCADA (remote) or rarely by phone line.

The automatic control of wind power stations realized by grid connected converter (GCC)

is basic level of three-stage control, presented in Fig.2.3.

Automatic Control

Remote Control

Voice Instructions

Ist Stage2nd Stage3rd Stage

AC-DC-AC

Fig.2.3. Three-stage control of wind power station.

Requirements of the Polish GC, concerning wind power plants, in whole realized

by grid connected converter (GCC), are grouped in following points:

Steady-state operations:

o Active Power Control,

o Reactive Power Control,

Transient-state operations:

o Frequency and Voltage Deviations,

o Low Voltage Ride Trough (LVRT).

2.3.1. Steady-State Operations

The most important role in the steady-state operations plays the remote control. The

change physically is carried-out by the GCC, which adapts a power generation to an actual

wind conditions. During steady-state operations, the operator exercises superior power

above the wind installation. The aim of the remote control realized during steady-states is

to support the power system by specified operation modes:

Control of active power generation,


15

Control of reactive power generation in three modes:

o Power factor cos(φ),

o Direct reactive power control,

o Voltage control,

Remote connection or disconnection of wind power plant in case of power

fluctuations in grid.

Two of Polish DSO – ENERGA Operator and TAURON Operator require on-line

changing in control concept of wind farm. Probably, this requirement concern all Polish

Operators but interestingly only ENERGA requires it formally in its GC. Other Operators

do not mention about on-line mode changing, but according to my personal appointments

with Operators agents, the on-line changing the control concept is required. Hence, each

wind farm should be equipped with procedure of on-line switching between above

mentioned modes.

2.3.2. Active Power Control

The active power control enables operation without any superior limitations

depending on wind conditions. It is realized automatically by the GCC. The most

important from operators’ point of view is remote control, permitting to impose upper

limitations. The requirements according speed of changes of active power generation are

presented in Tab.2.2.

Tab.2.2. Requirements according speed of change of active power generation.

Operation without

superior limitations

Change of active power does not exceed 10% of Pn per one

minute.

Operation with superior

limitations

20%<Pn<100% Change of active power does not exceed

2% of Pn per one second.

Pn<20% Change of active power does not exceed

10% of Pn per one minute.

The accuracy of requested level of the active power generation must be at least

±5% of the nominal power of wind farm.

2.3.3. Reactive Power Control

In the Polish GC, the control of the reactive power generation and the voltage level

is considered in grid-connected and stand-alone modes:


16

Grid-Connected Mode

In the grid-connected mode the control of the reactive power is remote. The system

operator sends to farm required value of the reactive power production due to level of the

grid voltage. It is realized only for wind farms connected to 1st and 2

nd connection groups

(from 400 kV to 110 kV). It is worth to signalize, that in the nearest future the requirement

will be demanded also for smaller installations connected to grid of voltage under 100 kV.

The Polish GC requires the on-line reactive power control. Moreover, during grid

voltage disturbances, the wind farm should be able to perform reactive power control and

actively assist the power system.

A wind power installation, operating at the nominal conditions, should be able to

produce a reactive power in range of power factor from (inductive) to

(capacitive) in the PCC. A wind power installation operating under nominal

voltage conditions, should produce a reactive power in the full accessible range in

accordance with technical abilities of the particular installation. Detailed requirements

concerning technical abilities of farms are not depicted.

Stand-alone mode

During stand-alone mode the wind farm must be able to generate a proper level of

reactive power due to voltage level in the allocated grid system. Control of the reactive

power must be consistent according to the characteristic presented in Fig.2.4.

U[kV]

Q [MVAr]

Umin Uth1

Uth2

Umax

Qmax_gen

Qmax_dr

Ur

inductive

capacitive

Fig.2.4. Characteristic of reactive power control according to level of voltage.


17

Each wind farm must be able to individual parameterization of thresholds due to

size of farm, nominal grid voltage and location. The characteristic are explained in Tab.2.3.

The important rule is that, the reactive power should not change, when cosφ =1.

Tab.2.3. Required generation of the reactive power due to changes of voltage.

Symbol Unit Description Range

110 220 400

Qmax_dr [Mvar] Maximum level of drawn by wind farm

reactive power not applicable

Qmax_ge

n [Mvar]

Maximum level of generated by wind farm

reactive power not applicable

Umin [kV] Minimum level of voltage in PCC, when

reactive power is generated 99÷110 200÷220 360÷400

Umax [kV] Minimum level of voltage in PCC, when

reactive power is drawn 110÷123 220÷245 400÷420

Uth1 [kV] Threshold value of voltage under which

generation of reactive power is required 99÷110 200÷220 360÷400

Uth2 [kV] Threshold value of voltage above which

drawn of reactive power is required 110÷123 220÷245 400÷420

Ur [kV] Range of reference voltage in PCC 99÷120 200÷245 360÷420

Note, that characteristic presented in GC between Uth1 and Uth2 has “insensivity

zone”. According to requirements of the Polish GC, the generation of the reactive power in

this range should not change. In the insensivity zone, the cosφ should not change. In the

author’s opinion this requirement is not profitable for systems operators and is result of

ignorance of current abilities of GCC cooperating with wind farms. Better solution is linear

control, permitting for an instantaneous reaction on any voltage fluctuations.

2.3.4. Operation during Transient States

A wind power plant should be able to operate continuously and support the power

system during selected grid voltage variations. Here, the control is automatic and almost

immediate. It is realized by the grid connected converter (GCC).

Automatic control of wind power plant, according to the Polish GC, during grid

variations should concern:

Uninterrupted operation during voltage dips,

Uninterrupted operation during frequency changes,

Wind plant connection and disconnection,


18

Providing the quality of the generated power.

The wind farms with nominal power greater than 50 MW should have power

quality measurement and registration system. The recorders should ensure the registration

of the runs through 10 s before the disturbance and 60 s after the disturbance. When wind

farm does not fulfill the quality requirements concluded in the GC, it can be disconnect by

system operator until requirements are fulfilled.

Additional requirements according to operation of wind farm during grid voltage

variations can be specified in individual connection conditions agreement prepared by

system operator. The conditions take into account individual technical abilities of

appropriate wind installation.

2.3.5. Voltage Dips (Fault Right Through FRT)

A wind power station must provide uninterrupted operation during voltage dips.

The curve in Fig.2.5 presents the area above which wind farms experiencing dips may not

turn off. In the Polish GC there is significant lack: no specified requirements according

operation of wind farms during sequences of dips (for example 4 dips appearing one after

another). Missing is also information about operation during unsymmetrical dips.

With the meaning of current Polish GC, a wind farm is supposed to uninterrupted

operation, when sequence of voltage dip fits in the curve of Fig.2.5.

1 t[s]

U[p.u.]

-1 20 3 4 155

0,8

0,4

0,2

0,6

1

0,15

0,6

Fig.2.5. Characteristic of required operation range during voltage dips.

During the voltage dip, a wind farms must generate the demanded level of the

reactive power and actively supports grid. The level of produced reactive power depends

on technical abilities of wind farm and requirements of the system operator presented in


19

individual connection conditions agreement. Moreover, during voltage dip the wind farm

cannot draw reactive power from grid.

Any wind farm must not cause sudden step changes exceeding 3% of the nominal

voltage. When distributions lead to grid by the wind farm are repeating, the range of single

fast distortion should not exceed 2,5% of RMS voltage value, when there are no more than

10 distortions per hour. When there are no more than 100 distortions generated by wind

farm per hour, the single distortion should not exceed 1,5%. These requirements concern

standard operations, connection and disconnection of wind station.

2.3.6. Overvoltage

In the Polish GC there is no requirements for wind farms operating during

overvoltage. Customarily wind station should operate with 110% of nominal grid voltage.

2.3.7. Frequency Deviations

The active power limitations due to increase of frequency take precedence over the

automatic remote control limitation. The curve of the active power reduction due to growth

of the grid frequency is presented in Fig.2.6. Symbols are explained in Tab.2.4.

51 f[Hz]

P [%]

50 51,550,5

Pmax

fn fmin fmax

s

49,548,54847,5

90%85%80%

Fig.2.6. Characteristic of automatic reduction of active power due to frequency growth.

The Pmax signifies the value of an active power generated by the wind when

frequency exceeds 50,5 Hz. The symbol s is the relative change of frequency due to

relative change of active power and is described by the following formula:


20

(

⁄ )

( ⁄ )

(2.1)

Tab.2.4. Symbols used in reduction of active power generation due to frequency change.

Parameter Unit Description Default

value

Setting

range

fn [Hz] Nominal value of grid frequency 50 -

fmin [Hz] Minimum value of frequency, when active

power control reacts 50,5 (50÷51)

fmax [Hz] Maximum value of frequency, when

generated power is equal to zero 51,5 (51÷fbr)

fbr [Hz] Maximum value of frequency, when wind

farm must be disconnected from grid 51,5 -

The reduction of generated active power must be primarily executed by each wind

farm controller. If this is insufficient, individual turbines may disconnect from the power

system. Additionally, when the wind farm produces from 40% to 100% of its nominal

power Pn, each turbine should be able to reduce its generated active power with rate not

lower than 5% of Pn per second. The dependence between level of generated power and

connection time of the wind farm to grid during frequency variations is depicted in

Tab.2.5.

Tab.2.5. Allowed active power generation ranges due to frequency variations.

Frequency

Range [Hz] Description of wind farm operation

(47,5÷48) Wind farm should be able to work with active power greater than 80%

at least for 10 minutes.

(48÷48,5) Wind farm should be able to work with active power greater than 85%


(48,5÷49,5) Wind farm should be able to work with active power greater than 90%


(49,5÷50,5) Wind farm operates in normal conditions, generation of power

depends on wind.

(50,5÷51,5) Wind farm operates uninterruptedly during growth of frequency

according to characteristic presented in Fig.2.6.

(f>51,5)

When frequency exceeds 51,5Hz (measured by protection relay with

time lack), wind farm must be disconnected from grid in not longer than

0,3 s.


21

2.3.8. Flickers

Voltage fluctuations generated by wind plant, according to the Polish GC,

described as short-term (Pst) and long-term (Plt) fluctuation coefficients should not exceed:

Pst<0,35 for 110 kV grid and Pst<0,30 for grid where voltage is 220 kV and

higher,

Plt<0,25 for 110 kV grid and Plt<0,20 for grid where voltage is 220 kV and

higher.

2.3.9. Higher Harmonics

For 99% of week wind power plants connected to 220 kV grid, and higher, should

not produce harmonic from range 2 to 50 exceeding 1% (with reference to the fundamental

harmonic). The Total Harmonic Distortion THD in the PCC point should not exceed 1,5%.

However, wind power plants connected to 110 kV grid, and lower, should not

produce harmonic from range 2 to 50 exceeding 1,5% (with reference to the fundamental

harmonic). The Total Harmonic Distortion THD in the PCC point should not exceed 2,5%.

2.4 Summary and Conclusions

According to rapidly growing wind farms penetration, in developed countries the

demand for regulation their operations have appeared. Regulations, called national Grid

Codes (GC) are detailed instructions describing operation of wind farms in the power

system. GCs usually concern:

quality of generated power,

active presence and supporting the power system,

technical requirements of connection to the power system.

The sole Polish Transmission System Operator (TSO): PSE Operator S.A. revealed

in the beginning of 2012 the Polish Grid Code describing requirements for wind farms

connected to the Polish power system. In fact the Polish GC is the instruction of

cooperation and communication between wind farms and the proper operator. Four main

Polish Distribution System Operators (DSOs): ENERGA, ENEA, PGE and TAURON

head the GC created by the TSO.

In the Polish GC there are two main groups of requirements for wind farms

concerning operation during steady- and transient-states.


22

In steady state, on demand of the operator, every wind farm connected to lines of

voltage 110kV-400kV must provide active and reactive power control. It is not required for

lower voltage systems, but for sure, will be a new operators’ demand in future. Transient

state requirements describe the wind farm behavior during grid voltage variations, like:

dips, short interruptions, frequency distortions, higher harmonics, flicker, etc. The division

of requirements is presented in Fig.2.7.

Active Power Control

Steady State

Wind Farm’s Operations

Reactive Power Control

Grid Connected Mode

Stand Alone Mode

Transient State:operations during faults

Dips Frequency deviations Flickers Higher harmonics Short interruptions etc.

Fig.2.7. Division of Polish Grid Code requirements for wind farms operation in the power system.

Notwithstanding, the Polish GC revealed by TSO is still incomplete. There is

significant lack of specifications concerning:

Detailed communication between wind farms and operators,

Description of wind farm operation during voltage dips,

The active power generation during frequency reduction,

No requirements for off-shore wind farms.

According to swiftly growing wind market, increasing installed power of wind

farms and development of off-shore farms, the TSO is included in continuous adapting

process of the GC.

It is worth to know, that rapidly increasing wind penetration in Poland is mainly

driven by political goals of the government and investments’ interest and surely will not be

stopped.

Nonetheless, the grow is carried out without compromising the security of the

power system. Nowadays, the power system operators struggle with lot of problems. The

huge modernization and development of the power system is carried out to face up wind

penetration. On the other hand, the process of energy connection Poland to Eastern


23

neighbors’ grid has been conducted. Additionally, Poland is obliged to turn off some

conventional power plants to fulfill the European Union’s requirements according to CO2

emission. Hence, in such a situation, the blackouts’ danger becomes real in Polish power

system. Due to the unfavorable circumstances, the attitude of Polish TSO and DSOs to

wind farms development is cautious.

According to the actual situation of the Polish power system and future legislation

plans, it is sure that demands for power quality generated by wind farms and their support

to the power system will be restricted. The restrictions will lead on the field of wind farms’

uninterrupted generation and active support under unbalanced grid voltage conditions.

The next version of the Polish GC, due to altering situation in the Polish power

system, is expected to be revealed by the TSO in another 4 years, probably in 2017.

Subsequent changes of requirements for wind farms will be also introduced in the new

renewable energy act. The act has been announced for two years. Probable release will be

in the end of 2013.


24

3. Voltage Dips in the Power System

Since the power system has been continuously developing, the more and more

variations occur in the grid voltage. Growing penetration of wind farms, introduction of

non-linear loads and power electronics and also increasing complexity of the power system

lead to many distortions. Therefore, voltage waveforms are already not sinusoidal, what

has direct impact on power quality delivered to consumers. Among voltage distortions

following problems can be distinguished [Bag]:

Voltage magnitude variations,

Voltage frequency variations,

Voltage unbalances,

Voltage fluctuations,

Harmonic voltage distortions,

Interharmonic voltage components,

Periodic voltage notching,

Mains signaling voltage (used for information transmission),

High frequency voltage noises.

Among voltage variations power quality events can be distinguished. The power

quality events are the phenomena, which can lead to equipments’ tripping, interruptions of

the power supply or endanger of the power system operations. The power quality events

are classified as:

Interruptions – voltage events during which the magnitude is lower than 1% of

the declared voltage [Pst2]. Voltage interruptions are caused by protections’

maltrip, broken conductors or operators’ interventions.

Undervoltages – two different types of the event can be distinguished:

o Voltage sag/dip – short duration undervoltage. The term sag is preferred

by the IEEE organization, while the term dip is used by International

Electrotechnical Comission (IEC). In the thesis the term “dip” is

preferred. Dip is a reduction of the voltage’s magnitude to a value

between 90% and 1% of the declared voltage, followed by a recovery

between 10 ms to 1 minute later.

o Undervoltage – long duration undervoltage, where the magnitude is

reduced between 90% to 1%.


25

Rapid voltage change – events caused by load switching, transformers’ tap

changers, switching in the power system. The magnitude of voltage is between

90% to 110% [Bol1].

Overvoltages – there are two types of overvoltage based on their duration:

o Transient overvoltages/voltage spikes – overvoltage of very short

duration and high magnitude.

o Overvoltage – events caused by lightings strokes, switching operations,

sudden load reductions, single-phase short circuits, nonlinearities.

Phase-angle jumps and three-phase unbalances – events often strictly related to

voltage dips.

The classification of voltage events according to voltage amplitude and duration is

presented in [Bol1].

Voltage dip

Normal operating voltage

1%

90%

110%

100%

1 min t

V

Undervoltage

OvervoltageTemporary overvoltageT

ran

sie

nt

ov

erv

olt

ag

e

Short interuption Long interuption

3 min

Fig. 3.1 Definitions of voltage events according to Std. EN:50160.

Among all power phenomena, voltage dips are considered to be the most severe

disturbance for customers and system operators [San], [Nas], [Dug], [Bol1] . In many of

cases, during voltage dip, the power equipment is disconnected, which results finance

losses or even damages of devices. Consequences of voltage dips appearance can

accumulate and lead to energy losses, increased content of higher harmonics, asymmetrical

current or even shortening of lifetime of device. Only interruptions, considered as

individual phenomena, are more severe events than voltage dips. Note, that interruptions

are much rare distortions than dips. More important, they cause less financial losses and

are rather local events comparing to global influence of dips.


26

In the Chapter the voltage dip phenomena is analyzed and discussed. Reasons of

existence, parameters and dips’ classification are presented.

3.1. Introduction to Voltage Dips

The voltage dip, according to IEEE Std. 1159 [Ist], European Std. EN 50160:2002

[Est] and its Polish implementation PN-EN: 50160 [Pst1], is defined as a decrease of

voltage amplitude between 0.9 and 0.01 per unit of the declared voltage RMS value.

Amplitude of voltage dip is described using a term of dip’s depth. The depth is a

difference between the nominal RMS value of voltage and minimal value of voltage during

a dip. It means, when there is a 30% voltage dip, the value of voltage decreased from 230V

to 161V. The amplitude of voltage dip is calculated with respect the lowest grid voltage

value. For three-phase voltage, the voltage dip means reducing at least one of phase or line

voltages.

The reasons of voltage dips appearance are related to events occurring the power

system, like [Bon]:

Short-circuits in transmission and distribution systems or in users installations,

transformers energizing,

capacitors banks switching,

start of large induction motors or other severe machines,

Changes of the power system configuration.

The significant majority of dips appears due to short-circuits. As the power system

is very expanded, voltage dips are able to spread to another parts of the grid depending on

the grid topology and participants of the system. In the most cases, short-circuits in the

power system are eliminated by activation of automatic protections isolating the fault in a

few hundred milliseconds. Then, the damaged lines are separated and customers below the

line are disconnected from the supply, receivers above short-circuit experience voltage dip.

The most important parameters characterizing voltage dips are:

Amplitude - depends on configuration of the power system and the kind of

short-circuit;

Phase-angle jump - difference between voltage’s phase before dip and phase

after a transient. Depends on the kind of short-circuit causing voltage dip and

impedance between a distortion and a measurement point [Bol1],


27

Duration – number of cycles during which the RMS value is below the declared

value. Depends almost exclusively on protections used in the power system.

The exemplary shapes of real voltage dips are presented in Fig. 3.2.

a.

b.

Fig. 3.2 Shapes of voltage dips changing in two steps (a.) and three steps (b.) [Bol1].

3.1.1. Amplitude of Voltage Dips

The amplitude of voltage dip strictly depends on detailed configuration of the

power system:

Kind of power system: public, industrial, distribution or transmission;

Voltage’s level in power system,

Location and distance from short-circuit;

Kind of short-circuit,

Kind of transformers’ connecting different power systems,

Cross-section of lines and cables,

Kind of lines (overhead or underground).

To calculate the amplitude and phase of voltage dips, the simple equivalent

electrical circuit, presented in Fig. 3.3., can be used.

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

t [cycles]

V [

pu

]

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

t [cycles]

V [

pu

]


28

EsZs

Vdip Zf

PCC

Load

Short-circuit

Fig. 3.3 Equivalent electrical circuit for calculating amplitude and phase of voltage.

The voltage in the PCC is given by equation:

(3.1)

where Zs is impedance of source Es, Zf is impedance between PCC and point of

short-circuit and Vdip is voltage during the dip.

The equation above confirms the amplitude of voltage dip depends on fault

location, since grid impedance is function of a distance between fault and place of voltage

measurement. It is worth to notice that the lower is value of Zs (grid is stiffer), the lower

amplitude of voltage dip is. It means that propagation of voltage dips is less severe in

strong grids, like transmission systems. On the contrary the negative effects of voltage dip

are stronger in weak grids, like distribution systems.

The phase of voltage during dip depends on the X/R ratio between grid and fault

impedance and can be expressed as [Bon]:

( ) (

) (

) (3.2)

The voltage amplitude during dip, as a function of fault distance and short-circuit

power is plotted in Fig. 3.4a. Analysis concerns overhead 11 kV line (cross-section of line

equals to 150 mm2). In Fig. 3.4b the relation between impedance of transformer, amplitude

of voltage during dip and distance from fault is presented. First plot depicts the amplitude

during dip in 132 kV line. The second plot presents voltage reduced by 132/33 kV

transformer. It can be easily noticed that voltage reduced by transformer is specified by

smaller voltage drop due to large impedance of the transformer.


29

a.

b.

Fig. 3.4 a. Voltage amplitude during dip, as a function of fault distance and short-circuit

power; b. Relation between impedance of transformer, amplitude of voltage during dip and

distance from fault [Bol1].

3.1.2. Duration of Voltage Dips

The duration of voltage dip depends on kind of protections used in the power

system. Voltage dips in the transmission system are detected by fast protection devices. An

affected line is disconnected faster due to usage of more sophisticated and powerful

protections. In the distribution system the overcurrent protections also play the important

role. Due to selectivity their clearance time is longer than in transmission protections.

Exceptions are systems where fast limiting fuses are installed. The duration time of dip

experienced in the power system strictly depends on the protections clearance time [Bol1].

In Fig. 3.5 the relation between amplitude and voltage dip duration, according to used

protections, is presented.

In the transmission systems the voltage dips last for fraction of seconds due to fast

fault-clearing equipment. However, even short dips occurring in transmission systems can

cause even complete exclusion in distribution lines lasting several hours [Mcg].

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance to the fault [km]

V [

pu

]

75 MVA

200 MVA

750 MVA

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance to the fault [kilometers]

V [

pu

]

Faults at 132 kV

Faults at 33 kV


30

a

b

c

d

e

f

0.1 1

50%

80%

100%

0%t[s]

V

a. Short-circuits in transmission systemb. Short-circuits in distant distribution systemc. Short-circuits in local distribution systemd. Starting large motorse. Short interruptionsf. Fuses

Fig. 3.5 Relation between the protections and amplitude and duration of voltage dip.

3.2. Voltage Dips Classification

The comprehensive analysis of voltage dip phenomena and its classification due to

different conditions of grid was proposed by M.H. Bollen. According to his publication

[Boll1], the classification of voltage dips concerns seven types, which are presented

inTab.3.1. It is based on the following assumptions:

Positive and negative components impedances are equal,

The zero component of grid voltage does not propagate down through

transformers to load or receiver, hence, it is neglected in the classification,

Load currents, before, during and after dip can be neglected.

The classification considers voltage dips caused by three-phase, phase-to-phase ,

phase-to-ground, and single-phase grid faults, influence of star and delta-connected load

and all types of transformers connection. The equations describing different kinds of

voltage dips are presented in phasor form, which is explained in the next Chapter.


31

Tab. 3.1 Classification of voltage dips’ types.

Type of dip Phasor diagram Equations

-A- three phase

symmetrical dip

Va

Vb

Vc

√

√

-B- unsymmetrical one-phase dip

Va

Vb

Vc

√

√

-C- unsymmetrical two-phase dip

(phase-to-phase)

Va

Vb

Vc

√

√

-D- unsymmetrical two-phase dip

(phase-to-phase)

Va

Vb

Vc

√

√

-E- unsymmetrical two-phase dip

(phase-to-ground)

Va

Vb

Vc

√

√

-F- unsymmetrical two-phase dip

(phase-to-ground)

Va

Vb

Vc

√

√

√

√


32

-G- unsymmetrical

three-phase dip

(phase-to-ground)

Va

Vb

Vc

√

√

Dips type A are caused by three-phase faults and the voltage drop is equal in each

phase. Dips type B contain the zero voltage component and it is hardly never transported to

load due to load and transformer’s connection. The majority of existing dips constitutes

dips type C and D. For the dip type C, the two phase voltages drop in magnitude and

change in phase shift occurs. The 3rd

phase voltage remain stable. The dip type D is

similar to type C, however, the amplitude of the 3rd

phase is significantly reduced.

Moreover, dips type D contain the negative voltage component, what is particularly

disadvantageous. The above mentioned dips are caused by single-phase and phase-to-phase

faults [Boll4]. Dips type F and G, contain the negative voltage component. They are

caused by two-phase to ground faults. For types F and G every phase voltage drops. The

dip of type E contains zero voltage component and rarely appears in the power system.

Dips’ types change with the voltage transformation to lower levels of the power

system. The change appears due to different kinds of transformers connections. The

influence of transformers connection on dips type is presented in Tab. 3.2. In Tab. 3.3. the

relation between the origin of dip and the load connection is presented.

Tab. 3.2 Dips’ type change due to transformer connection.

Transformer’s

Connection

Dip on Primary Side

Type A Type B Type C Type C Type E Type F Type G

YNn A B C D E F G

Yy, Dd, Dz A D* C D G F G

Yd, Dy, Yz A C* D C F G F

The subscript “*” indicates that dip magnitude is not equal to but equal to

Tab. 3.3 Transformation of dips in different type of load connections.

Fault type Load Connection

Star Delta

Three-phase A A

Phase-to-phase C D

Two-phase-to-ground E F

Single-phase B C


33

3.3. Influence of Voltage Dip on Power System

The main causes of voltage dips at the terminals of a wind-power installations or

other devices are short-circuits in the power system. The fault current causes a voltage

drop over a wide part of the grid. The voltage starts to recover when the protection clears

the fault or when the fault clears itself in case of a self-clearing fault [Boll5].

In Fig. 3.6 the basic scheme of a radial power system and locations of short-circuits

appearance are presented. Numbers from 1 to 5 stand for places of short-circuits, whereas

letters from A to D represent loads or receivers. According to the location of short-circuit

and type of the power system (transmission, distribution or low voltage), dips influence

loads in different way [Boll3].

Transission System

1

2

A

B

C

3

Distribution System

4

D

Low Voltage

5

Transission System

Fig. 3.6 The scheme of the power system with different short-circuits locations.


34

In Tab. 3.4 the explanation of the dip influence on loads located in different kinds

of the power system is presented.

Tab. 3.4 The influence of voltage dips on receivers located in different kinds of the power

system.

Short-

circuit

location

Kind of the

power system Influence on receiver / loads

Point 1 Transmission

system

All receivers, including low voltage, experience dip,

despite of the mitigation influence of transformer stations.

Point 2

Indirect

transmission

system

No great influence on receiver A due to impedance of

transformer station between two transmission systems.

The short-circuit no. 2 leads to significant dips suffered by

receivers B, C and D.

Point 3 Distribution

Very deep dip experienced by D leads to release of

protection system, what cut the voltage supply in whole

line. The receiver C feels deep but short dip and receiver

B notices shallow dip. The dip is not reaching the receiver

A.

Point 4 Distribution

Deep dip experiences receiver C, the shallow dip

experiences receiver D. Receivers A and B do not feel any

distortion.

Point 5 Low Voltage Deep dip experiences receiver D, the shallow is noticed

by C, whereas A and B do not feel any distortion.

From [Boll1], [Ign], [Mcg], [Bag], [Nas], [Dug] and data presented in Tab. 3.4, it

follows out that the phenomenon of voltage dips is an extremely complex distortion. It is

characterized by different propagation in various kinds of power systems. Dips occurring

due to the short-circuit in the transmission system effect the whole power system even

hundreds kilometers away. Such a dip, in most of cases leads to interruption in significant

part of power system. Dips caused by the short-circuit in the distribution system do not

penetrate transmission system due to high impedance of transformers, which effectively

reduce dip depth. Still such dip seriously effects the distribution system and sometimes

leads to disconnection of the whole line of receivers placed below the short-circuit.

3.4. Conclusions

Among grid voltage variations, the most severe to every consumer are voltage dips.

In the power system voltage dips appear more often than short interruptions and hence,


35

cause higher financial losses. The voltage dips in most of cases are caused by short-circuits

and connection or disconnection of large loads.

The voltage dip is global problem of power systems. Dips caused by short-circuit in

transmission line is experienced by load several hundred kilometers away. From the other

hand, it is worth to mention that dips caused by short-circuit in lower levels of voltage do

not penetrate higher voltage levels.

Voltage dips are classified by two main parameters: amplitude and duration. The

dips amplitude depends on several conditions like distance from fault, kind of grid and

others, when duration time depends on kind of protections installed in the power systems.

There are seven types of dips including symmetrical three-phase dips and unsymmetrical

caused by: single-phase-to ground, phase-to-phase and two-phase to ground short-circuits.

The biggest problem for power converter connected to the grid experiencing

voltage dips is existence of a negative voltage component. The negative voltage

component case significant distortions seen for example in the synchronous reference

frame, usually used for converter control, as 100 Hz oscillations. Oscillations are

particularly dangerous due to destabilization of converters control system and transporting

distortions to the power system.

It is important to that only dips types D, F and G contain negative voltage

component, what is particularly destructive for industrial devices. The dip type B and E

contain the voltage zero component and it is hardly ever transported to load due to load and

transformer’s connection. The majority of existing dips are types C and D. It is also

important to remember that type of dip is not constant issue. Dips types change their

character due to different connections of transformer or lad connection.


36

4. Basics of Symmetrical Components Theory

The theory of symmetrical components is one of the most powerful tools used in

electrical engineering, which deals with the problem of unbalanced polyphase circuits.

This method is applicable to any of polyphase system, however it places emphasis on three

phase systems.

The theory of symmetrical components was developed by Charles L. Fortesque in 1912

and presented for the first time in 1918 in [For]. It has proved that any unbalanced system,

described by n related phasors can be resolved into n systems of balanced phasors. The n

phasors of each set of components are equal in length and angles between adjacent phasors

of the set are also equal. In this case balanced phasors are called symmetrical components

of original phasors [Gra].

In the electrical engineering, the symmetrical components theory provides a practical

method for understanding and analyzing three-phase power systems during unbalanced

conditions.

So far, the symmetrical component theory has been widely applied to electrical

machines. However, it is also essential for understanding voltage dips - the most dangerous

unbalances performed in power system. The problem of voltage dips has been described in

the previous Chapter. Unbalanced states in grid can be also caused by opened phases,

impedance unbalance and combination of all these [Bol1]. The symmetrical components

theory is also used in several applications, like: classification and analysis of faults, grid

unbalance mitigation (especially voltage dips), system modeling and identification, etc

[Gho].

In this Chapter, for better understanding issues concluded in the Thesis, the idea of

phasors in power system is briefly reviewed. Then, the explanation of Fortesque’s

symmetrical component theory in steady states is presented. Also, the Lyon’s

instantaneous symmetrical theory is presented. Then, methods of instantaneous values of

symmetrical components calculation in αβ stationary frame and dq synchronous rotating

frame are presented.

4.1. Voltage and Current Phasors

For understanding the theory of symmetrical components, an explanation of phasor

notation is necessary. According to IEEE Dictionary [Bla], phasor can be defined as “the


37

absolute value (magnitude) of the complex number which corresponds to either the peak

amplitude or RMS value of the quantity, and phase (argument) to phase angle at the zero

time”. It should be emphasized that phasor can only be applied as a representation of

undistorted constant frequency sinusoidal waveforms during steady-states.

The phasor notation can significantly simplify the analysis of power system instead of

using time domain functions of sinusoidal voltages and currents. To define phasor, a

sinusoidal time function of voltage v(t) (or current i(t)) with angular frequency ω, is

assumed:

( ) ( ) (4.1)

( ) ( ) (4.2)

where: V and I are magnitudes, φV and φI are initial phase angles of voltage and

current, respectively.

The phasor, noted as , related to the sinusoidal voltage v(t) can be mathematically

represented by the several alternative forms of complex numbers, given in Tab. 4.1 [Bla],

[Aka].

Tab. 4.1. Mathematical representations of complex phasor.

Phasor Exponential form Complex form Algebraic form

( )

where x is the real value ( ) of complex phasor; y is the imaginary value ( );

| | is magnitude of phasor.

Phasors of voltage and current are presented below as complex numbers in their

algebraic, trigonometric and exponential notation:

( ) ( ) ( ) ( ) (4.3)

( ) ( ) ( ) ( ) (4.4)

A complex apparent power S, defined as geometrical sum of active power P and

reactive power Q, also can be expressed as a product of voltage and current phasors:


38

( ⏟

)

⏞

( ⏟

)

⏞

(4.5)

where is conjugate value of current phasor.

The displacement angle φ between and is equal to . The phasor

notation is also commonly used to define grid impedance in power system [Bla].

The basic relation between phasors and sinusoidal functions of current and voltage

is illustrated in Fig.4.1.

y=-sinx, x∊[0,2π]

π ωt

Φ

v(ωt)i(ωt)

Φ

Im

Re

VI

a. b.

ωt

φu φi

V

v(t)

2π

I

φv

φi

Fig.4.1. Graphical representation of voltage and current as: a. time domain

functions; b. phasors.

Phasors of voltage and current always rotate counterclockwise with grid angular

frequency. Phase sequence refers to the order in which phasors occurs during rotation. The

standard sequence according to phase voltages and currents in three-phase system is abc.

4.2. Symmetrical Components Theory

According to the symmetrical component theory, unbalanced voltage or current

phasors of three-phase system can be described as three sets of balanced phasors, named

symmetrical components (or in this thesis just “components”). Under unbalanced grid

voltage there are three kinds of components equal in magnitude, presented in Fig.4.2:

Positive sequence component, denoted with subscript “+” - three phasors

are displaced by 1200 in phase, having the same phase sequence as original

phasors (abc), rotating counterclockwise;

Negative sequence component, denoted with subscript “-” – three phasors

are displaced by 1200 in phase, having opposite phase sequence as original

phasors (acb), rotating clockwise;


39

Zero sequence component , denoted with subscript “0” – three phasors with

zero phase displacement from each other.

a. b. c.

Va+

Vc+ Vb-

Va-

Vc-Vb+

ωt ωt ωt

Va0

Vb0

Vc0

Fig.4.2. Three-phase voltage symmetrical components: a. positive; b. negative; c.

zero component.

Hence, during an unbalance each distorted phase voltage (or current) according to

the symmetrical components theory can be described as a sum of three balanced

components:

(4.6)

(4.7)

(4.8)

Due to properties of symmetrical components theory, to simplify analysis, some

variables can be neglected without losing corectness of deduction proces. To minimize

number of quantities, voltages and are formulated as a product of and function of

mathematical operator a. The product henceforward is called as . Hence, positive voltage

component is marked as , negative as and zero component as . The coefficient a

is a Fortesque’s operator and it shifts a vector by an angle of 1200 counterclockwise:

( ) (4.9)

( ) (4.10)


40

In the symmetrical components theory there are two kinds of voltage components

transformations. First one – direct transformation - is used to calculate symmetrical

components having three unbalanced voltage phasors:

[

]

[

] [

] [

] (4.11)

Second one - inverse transformation - is employed to calculate phasors containing

certain amount of symmetrical components [ Paa]:

[

] [

] [

] [

] (4.12)

Thus, the symmetrical component transformation matrixes A and A-1

are equal to:

[

] (4.13)

[

]

(4.14)

According to Fortescue’s theory in balanced system only positive components

exists. The negative and the zero components appear in the electrical system during

voltage unbalance at fundamental frequency. However, it should be noted that in any three-

phase three-wire system the sum of three instantaneous phase voltages or currents is zero.

Therefore, the zero sequence component are not present. This feature greatly simplify

analysis of three-wire converter systems. Zero sequence component appears only during

unbalance of three-phase, four-wire grounded system [Mil], [Son].

4.3. Symmetrical Components for Instantaneous Values

Generally, the Fortesque’s symmetrical component theory, formalized in phasor

therms, can only be applied in steady state conditions. The first application of the

symmetrical components in time domain was presented by Lyon [Lyo1], [Lyo2]. It is

called the instantaneous symmetrical components theory. Lyon has proved, that using the


41

same topological approach as Fortesque’s theory, it is possible to analyze faults in steady

and transient states of electrical system using real time calculations.

In the Lyons theory, the most important assumption is that, complex phasors from

the symmetrical component theory are replaced by time-dependent functions, fulfilling the

concept of instantaneous components [Lev], [Lun1]. Voltage symmetrical components in

time domain are defined as v0, v

+, v

- (while steady-state phasors are noted as , and

). Instantaneous values of positive, negative and zero components, according to Lyon’s

theory, are formulated as:

(4.15)

(4.16)

(4.17)

For simplification the zero sequence component is neglected. In this thesis the

following form of positive and negative components of voltage vector is evaluated:

[

( )

(

)

(

)]

[

( )

(

)

(

)]

(4.18)

Where V+ is amplitude of positive component of voltage and V

- is amplitude of

negative voltage component.

According to Lyon’s theory, instantaneous positive and negative components of

voltage , are equal to:

[

]

[

] [

]

[

]

(4.19)

[

]

[

] [

]

[

] (4.20)

where


42

[

] (4.21)

[

] (4.22)

The transformation from unbalanced voltages to symmetrical instantaneous

components (and the inverse transformation) is similar to Fortesque’s theory. The

difference lies in displacement operators. To calculate instantaneous values of components

time domain displacement operator α should be introduced. It translates the Fortesque’s

operator a from the complex plane to time domain. The idea is to replace phasor rotation

operator a with time domain phase shift operator α, which can be interpreted as a 120°

delay. Consequently a2 stands for 240° delay.

Real-time application of symmetrical components extraction can be realized by

simply utilizing transport delay of measured signals [Kar]. The scheme for symmetrical

components extraction in natural frame is presented in Fig.4.3.

1/3v0vabc

-120°

va

vb

vc

-240°

-240°

-120°

v+

v-

Fig.4.3. Block scheme of symmetrical components extraction in natural abc frame.

To illustrate this method, the test signal is created by adding 1pu positive

component and 0.25pu negative component voltage components, as presented in Fig.4.12.


43

Fig.4.4. Test signal for symmetrical components extraction.

This unbalanced voltage is delivered to the input of extraction scheme shown in

Fig.4.3. Results of extraction are shown in Fig.4.5. According to the symmetrical

components theory, the estimated v+ and v

- components refer to phase a of three-phase

input signal. It is shown in Fig.4.5, that in steady state estimated components follow input

signal. During transients some errors appear due to signal delay used in calculation. Two

steps can be observed: 120° and 240° after step change of input voltage components. It can

be seen, that this method is characterized with low dynamics. Moreover, when

implemented in digital systems, it requires a lot of memory for delay buffers.

Fig.4.5. Results of symmetrical component extraction in natural frame.

Another interesting formulation of the operator α can be expressed using algebraic

complex notation of a operator:

√

(4.23)

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Positive component

Voltage [

pu]

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Negative component

Va

Vb

Vc

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Unbalanced voltage

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Negative component

Original

Estimated

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Voltage [

pu]

Positive component


44

This allows to use j operator, which can be interpreted as 90° shift. This is much

easier to implement in digital systems. Moreover, symmetrical components transformation

using this notation have much in common to Clarke’s transformation. This feature enables

easy extraction of symmetrical components in stationary frame, which is explained in the

following section.

4.4. Symmetrical Components in Stationary Frame

Nowadays, in electrical engineering (especially when control of power converters is

considered) two transformations: Park’s and Clarke’s are widely used [Rao], [Kaz1]. Both

transformations are mathematical tool used to simplify the analysis of three-phase circuits

and they performs time domain signals.

The Clarke transformation, denoted as αβ transformation, is used for conversion of

three-phase signals from the natural abc frame into two signals in stationary αβ frame. The

Clarke transformation is widely used for generation of the reference signal for space vector

modulation (SVM) control of three-phase converters [Kaz]. In the three-phase three-wire

system, where the zero component is not present, voltage transformed into stationary frame

can be represent as a sum of positive and negative components in αβ [Lev]:

(4.24)

Moreover, each of voltages and

can be separated into components:

(4.25)

(4.26)

For calculating negative component of voltage, the dependence between

components is used , where is conjugate of positive component. The

graphical representation of symmetrical components in αβ frames is presented in Fig.4.7.


45

α

β

Vα+

Vβ+ Vαβ

+

Vαβ-

Vα-

Vβ-

Fig.4.6. Positive and negative voltage components in αβ frame.

An example of positive, negative and zero components in the stationary reference

frame is presented Fig.4.8 as locus of voltage phasor. It is worth to mention, that in

stationary frame the negative component (vα+ and vα

-) also has opposite sequence of vα and

vβ signals. The phasor of the negative component also draws circular locus, however, the

direction of rotation is opposite (clockwise). The locus of sum of voltage components is

not circular but draws an elliptic shape.

Fig.4.7. Symmetrical components of unbalanced voltage in stationary reference

frame (time waveforms).

Fig.4.8. Symmetrical components of unbalanced voltage in stationary reference

frame (αβ plot).

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Voltage [

pu]

Positive component

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Negative component

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Stationary frame voltage

V

V

-1 0 1

-1

-0.5

0

0.5

1

V [pu]

Negative component

-1 0 1

-1

-0.5

0

0.5

1

V [pu]

V

[pu]

Positive component

-1 0 1

-1

-0.5

0

0.5

1

V [pu]

Voltage vector trajectory


46

The magnitude and phase of vαβ can be expressed as [Teo]:

| | √( )

√

( ⏟

( )⏟

)

(4.27)

(

) (

)

( ( )

( ))

(4.28)

Where vd and vq are voltages in synchronous rotating frame.

The above equations show that the voltage understood as a sum of positive and

negative components in stationary frame has neither constant magnitude nor phase angle,

what illustrates simulation results in Fig.4.8. The magnitude of voltage is sum of positive

and negative components, which consists of two components: constant DC and AC,

changing with doubled grid frequency. That is why, both the amplitude and phase of

positive voltage component cannot be extracted just by filtering process.

The following formulas allow to reformulate the Lyon’s transformation into αβ

frame. The Clarke transformation is equal to:

[

] [ ] [

] (4.29)

where

[ ] √

[

√

√

]

(4.30)

Hence, the positive voltage component in αβ frame is equal to:

[

] [ ]

[ ] (4.31)

In the stationary frame the component matrix can be reformulated from complex

operator a signifying 1200 delay, into q operator understand as a time delay of 90

0:


47

(4.32)

(4.33)

Multiplying voltages by operator q it gives an effect of rotating a phasor by 900

without affecting the magnitude of signal. The component matrix is described with

equation:

[

] (4.34)

where:

√

√

(4.35)

√

√

(4.36)

Basing on above equations the voltage vabc can be expressed as:

[

] ([ ] [ ])

⏟

[ ]

(4.37)

Placing above result into equation (4.31), the positive voltage component in αβ

frame can be calculated as:

[

] [ ] [ ]

[

] (4.38)

Similarly, the negative voltage components in αβ frame are equal to:

[

] [ ] [ ]

[

] (4.39)

The block scheme of symmetrical component extraction in αβ is presented in

Fig.4.9.


48

qvα

1/2

vα+

vα-

vβ+

vβ-

vαβ

-90°

vα

-90°

vβ

qvβ

Fig.4.9. Block scheme of symmetrical component extraction in αβ.

The correctness of above analysis of positive and negative components of vαβ is

proved by simulation results presented in Fig.4.10. Voltage vabc consisting of positive and

negative component presented in Fig.4.9 is transformed to the stationary αβ frame.

Calculated components from derived formulas are compered to reference values of

positive and negative signals of vαβ. Note, that the real values and derived are the same.

Fig.4.10. Symmetrical components extraction in the stationary αβ frame.

4.5. Symmetrical Components in Synchronous Rotating Frame

The Park transformation, also known as a dq transformation (direct-quadrature),

converts three AC quantities into two DC quantities in dq Synchronous Rotating Frame

(SRF). It is widely used in analysis of electrical machines and power converters.

The following formulas allow to reformulate the Lyon’s transformation into dq

synchronous reference frame rotating at frequency [Xwu]:

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

Voltage [

V]

t[s]

Positive component

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

Voltage [

V]

t[s]

Negative component

V original

V estimated

V original

V estimated


49

(4.40)

Each of voltages can be separated into dq components:

(4.41)

(4.42)

The relation between positive and negative symmetrical components in αβ and dq

frames is presented in Fig.4.11.

d+

ωt

Vq+

Vd+

q+

d -

q-

Vq-

Vd-

α

β

Vα+

Vβ+

Vαβ+

Vαβ-

Vα-

Vβ-

-ωt

Fig.4.11. Positive and negative voltage components in αβ and dq frames.

In the synchronous reference frame also appear AC and DC components. Basing on

equation (2.27) and assuming that dq reference frame rotates synchronously to the positive

voltage component (the d-axis rotates in the same direction as positive voltage component

v+ and ), the voltage vdq can be expressed as:

[ ]

⏟

[ ( )

( )]

⏟

(4.43)

The DC signals in d axes and AC in q axes during appearance of negative

component are presented in Fig.4.12. When rotating frame is synchronized with positive

voltage sequence, the DC value corresponds to amplitude of positive component. The AC

value, pulsating with doubled grid frequency is the negative component. It can be seen,


50

that during appearance of negative component in grid voltage, signals in the SRF split into

DC and AC signals. AC signals appear as oscillation elements. In a dq reference frame, the

positive component appears as DC quantity in positive frame rotating in the same direction

with angular frequency. Meanwhile, the negative component appears as double frequency

term.

Fig.4.12b shows negative reference frame, rotating in opposite direction with the

grid angular frequency. On the contrary, the positive component appears as double

frequency signal while the negative is DC quantity [Tim1]. When the rotating frame is

synchronized with unbalanced voltage, both magnitude and angle of voltage vector are

distorted. AC quantities introduced by negative sequence become non-sinusoidal and

separation of symmetrical components becomes difficult.

a.

b.

c.

Fig.4.12. Voltage in synchronous rotating frame: a. synchronized with

positive sequence, b. synchronized with negative sequence, c. synchronized

with unbalanced voltage.

0.19 0.2 0.21 0.22 0.23-0.5

0

0.5

1

1.5

Voltage [

pu]

t[s]

Positive component

0.19 0.2 0.21 0.22 0.23-0.5

0

0.5

1

1.5

t[s]

Negative component

0.19 0.2 0.21 0.22 0.23-0.5

0

0.5

1

1.5

t[s]

Rotating frame voltage

Vd

Vq

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

Voltage [

pu]

t[s]

Positive component

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]

Negative component

0.19 0.2 0.21 0.22 0.23

-1

-0.5

0

0.5

1

t[s]


Vd

Vq

0.19 0.2 0.21 0.22 0.23-0.5

0

0.5

1

1.5

Voltage [

pu]

t[s]

Positive component

0.19 0.2 0.21 0.22 0.23-0.5

0

0.5

1

1.5

t[s]

Negative component

Vd

Vq

0.19 0.2 0.21 0.22 0.23-0.5

0

0.5

1

1.5

t[s]



51

It follows from the above considerations that the appearance of negative component

leads to oscillations into grid voltage. From the point of view of power converters the

oscillations appearing in signals introduce significant variations in control algorithms. The

majority of present solutions are based on well-known different filters, which do not cancel

influence of negative component only minimizing it. The solution is to employ more

sophisticated techniques, based on component estimation, rather than applying filtering

techniques for module and phase estimation. For calculation of components in dq frame the

following identity, based on Park’s transformation [Lev], is used:

[

] [ ] [

] [

] [ ] (4.44)

[

] [ ] [

] [

] [ ] (4.45)

where Park’s transformation matrix is equal to:

[ ] [ ( ) ( )

( ) ( )]

(4.46)

In the synchronous reference frame as well as in stationary fame q is operator

understand as a time delay of 900. To prove above equations, the calculated components in

dq frame are compared to reference values of positive and negative signals of vdq in

Fig.4.13. It should be noticed, that during steady state real values and estimated are equal.

In transient states during quarter of period, when 90° delay is realized, sequence estimation

is not precise.

Fig.4.13. Positive and negative components of vdq voltage.

0.19 0.2 0.21 0.22 0.23-0.5

0

0.5

1

1.5

t[s]

Negative component

0.19 0.2 0.21 0.22 0.23-0.5

0

0.5

1

1.5

Voltage [

pu]

t[s]

Positive component

Vd original

Vd estimated

Vq original

Vq estimated


52

4.6. Conclusions

In this Chapter the theories of symmetrical components and instantaneous

symmetrical components are reviewed for the convenience of the Thesis as a tools

indispensable for analysis of unbalanced voltage phenomena. Theories are studied in the

aim of better acquaint of negative component appearance during voltage dip in the power

system.

From considerations contained in the Chapter, it follows that the appearance of

negative component in three-phase three-wire system results in many distortions in grid

voltage. The amplitude and phase of disturbed voltage yield to change and even oscillate. It

leads to inappropriate operation of almost all devices connected to the grid, especially

power converters.

Hence, the issue of mitigation the negative component in the voltage grid has great

importance. However, elimination of negative component is not easy to handle. In the

Chapter calculations of instantaneous values of components in αβ and dq frame are

presented as essential for further analysis of grid synchronization and control methods used

for control of Grid-Connected Converter (GCC).

According to oscillations in dq and αβ frames, the negative component mitigation

could not be carried out using simple and well-known filtering solutions. When unbalance

is not totally eliminated, it introduces significant distortion to converter current control.

The proper solution to deal with the problem of voltage unbalance and negative

component existence, is to employ sophisticated techniques, based on component

extraction derived from the instantaneous symmetrical component theory. These

techniques are especially essential for synchronization and current control.

However, note that practical implementation of component extraction methods

using digital signal processors can result in following disadvantages, like:

High memory requirements for shifting registers to realize delay,

Estimation errors occur, when input signal is non-sinusoidal,

Estimation errors caused by grid frequency deviation.


53

5. Grid Synchronization under Unbalanced Conditions

5.1. Introduction

The accurate information about grid voltage phase angle is crucial for proper

operation of every Grid-Connected Converter (GCC). Synchronization process has become

a indispensable part of converter control algorithm in majority of GCC applications [Yua],

listed in Tab.5.1. The exact measurement of phase angle is especially important

considering deterioration of power quality in the power system.

Tab.5.1. Power electronic devices requiring synchronization to grid [Bob2].

Type of Device Applications

FACTS Static Compensator (STATCOM), Static Var Compensator (SVC), Static

Series Synchronous Compensator (SSSC), etc.

RES Wind farm, photovoltaic plant, ocean wave energy plants, etc.

PQ Compensators Uninterruptible Power Supply (UPS), Active Power Filter (APF), Dynamic

Voltage Restorer (DVR), etc.

PWM Converters Active Front End (AFE) in Adjustable Speed Drives (ASD), Grid-

Connected Converters (GCC) with unity power factor generation, etc.

To achieve accurate grid synchronization, every power converter based device

should be equipped with synchronization algorithm [Chu], named Phase Locked Loop

(PLL). The PLL is a feedback algorithm, which automatically adjusts the phase of locally

generated signal to match the phase of an input signal. It synchronizes an output signal in

frequency as well as in phase.

The basic concept of PLL, widely used in radio communication [Hsi], is presented

in Fig.5.1. Here, the PLL consists of three units:

Voltage Controlled Oscillator called (VCO). It generates output signal,

which frequency is proportional to the input signal,

Phase Detector (PD) – part responsible for generation signal proportional to

the phase difference between input signal and the signal generated by VCO,

Loop Filter (LF) - attenuates the high-frequency components from PD

output and defines control dynamics of the system.


54

LF VCOU UPD

PDULF UVCO

Fig.5.1. The basic concept of PLL algorithm: PD – Phase Detector, LF – Loop Filter, VCO –

Voltage Controlled Oscillator.

The main PLL’s objective is generation of undisturbed phase angle signal at any

grid voltage conditions, including all voltage variations. Moreover, the synchronization is

indispensable for [Bob2]:

Current control: higher harmonics and reactive power compensation,

Active and reactive power control,

Voltage regulation, dips and flicker compensation,

Voltage parameters monitoring - estimation of grid frequency, amplitude,

unbalance, harmonic distortion, power factor calculation,

Grid monitoring: fault detection by angle/frequency detection, islanding

detection, connecting/disconnecting process control, fault ride through,

5.2. Short Review of PLL algorithms

A variety of PLL structures is described in literature. There are some clear

classifications of algorithms presented in [Hsi], [Chu], [Hof], [Yua], [Teo], [Tim2], [Ani],

[Kau], [Sil]. In the Thesis simple classification based on reference coordinates, in which

PLL operates, is proposed [Bob2]. Hence, three groups of PLL can be distinguished:

classical single- and three-phase structures in natural abc coordinates,

algorithms using αβ stationary frame,

algorithms using dq synchronous rotating frames (SRF).

The classification, presented in Fig.5.2, focuses on applications aimed for digital

implementation on DSP platform. Among different techniques of synchronization single-

phase and three-phase PLL can be distinguished. In the Thesis only three-phase method are

analyzed, as ones used in medium and high power applications.


55

in natural abc coordinates

Synchronization Algorithms

Zero Crossing

in stationary αβ coordinates

in rotating dq coordinates

Single- & Three-Phase EPLL

SOGI

Dual SOGI

Virtual Flux

Dual Virtual

Flux

Filters

Low pass,

Resonant, Band

Pass, etc.

SRF-PLL with

filters

Dual SRF-PLL

Repetitive Control

DSC,Hilbert

transform

Filters: Low Pass,

Resonantetc.

RecursiveDiscrete Fourier Trans.

Fig.5.2. Classification of PLL algorithms.

The synchronization in abc frame using Discrete Fourier Transform (DFT) and

Recursive Discrete Fourier Transform (RDFT) is carried out in frequency domain. These

methods assume constant frequency of analyzed signal, hence, during frequency variations

are not reliable. Also basic zero-crossing method and single- and three-phase Enhanced

PLL do not give satisficing result according to synchronization with grid voltage [Teo1].

Generally, the concept of traditional PLL algorithms suits to basic PLL algorithms,

when the grid voltage is not polluted. In a distorted voltage conditions, synchronization

with the electrical grid becomes a challenge. Phase detection by direct methods can lead to

significant errors due to voltage variations like higher harmonics, voltage dips, change of

phase and frequency or flickers.

Operation under distorted grid voltage conditions introduces distortions to GCC control

algorithm. Incorrect calculation or generation of distorted phase angle by PLL algorithm

significantly amplifies variations in the control algorithm. It can even lead to “domino

effect”, where one distortion causes another, and leads to serious power deterioration.

Recently, any authors have proposed different advanced models, by means of building

frequency and amplitude adaptive structures. There are variety of different pre-filtering

methods proposed to overcome above mentioned problems like unbalance, faults and

higher harmonics. Among proposed solutions there are: Low Pass Filters (LPF), resonant,

notch or band pass filters [Bob2]. Also other method for detecting phase angle of grid

voltage are arranged, like: repetitive control [Luo], Virtual Flux [Bha2] and Dual Virtual

Flux [Kul], Enhanced PLL [Ant], Delayed Signal Cancellation [Wan1], Hilbert


56

Transformation [Teo] and many others. Methods based on pre-filtering only reduce

variations occurring during voltage dips and other distortions. In these methods oscillations

are not removed entirely and finally cause distortions. Moreover, using pre-filters reduces

synchronization’s dynamics. The most critical situation for PLL is operation under

unbalanced voltage, where negative sequence component has to be filtered. Because it is a

low frequency component, filtering can significantly reduce synchronization dynamics.

Hence, synchronization using pre-filers is not considered in the thesis.

Therefore, the problem to solve appears: how to assure simultaneously fast

synchronization and accurate damping of distortion. The solution is employing advanced

PLL algorithm with positive and negative voltage component extraction.

Advanced PLL algorithms with component extraction, operating in αβ and dq

coordinates have structure presented in Fig.5.3, which consists of:

Coordinates transformation block (from abc to αβ or dq);

Filter or Component Extractor (CE) - calculates and separates positive and negative

voltage components. For further calculations, only the phase of positive voltage

component is considered. The negative component can optionally be employed in

independent synchronization loop for negative sequence control;

Phase Detector (PD) – the same functionality as in the basic scheme of PLL (see

Fig.5.1),

Voltage Controlled Oscillator (VCO) – calculates phase angle.

Usually, a Synchronous Reference Frame Phase Locked Loop (SRF-PLL) is employed

for calculation of the phase angle. The SRF-PLL is the best known and most reliable

method of calculation phase angle from grid voltage [Paa].

CE

PD

SRF-PLLvdq(αβ)+

vdq(αβ)-

vabc abcdq(αβ)

vdq(αβ) v*VCO

φ

vdq(αβ)ref

ω

Fig.5.3. Scheme of PLL operating in αβ and/or dq frame.

In author’s opinion based on previous research [Bob2], and according to many

publications [Teo], [Tim1], [Rod1], [Fan], [Lun2], the synchronization based on


57

symmetrical component extraction give the best results. These methods are not only robust

to grid voltage variations but still are fast and accurate. Moreover, the methods give

opportunity to simultaneous extraction of positive and negative voltage components.

Afterwards, these components can be employed to independent control of positive and

negative current components. According to many advantages of synchronization methods

based on symmetrical components extractions, only those algorithms are further analyzed

in the Thesis.

Among documented algorithms there are two PLLs directly using the instantaneous

symmetrical components theory: DSOGI (Dual Second Order Generalized Operator),

operates in αβ coordinated frame (see Section 5.4) and DDSRF-PLL (Decoupled Double

Synchronous Frame PLL) in dq frame (see Section 5.5). These two algorithms give the

best performance according to extraction of positive and negative voltage components

[Bob2], [Teo], [Tim1], [Tim2]. Both of them uses simple SRF-PLL algorithm for grid

phase angle calculations.

5.3. Synchronous Reference Frame PLL

The Synchronous Reference Frame PLL (SRF-PLL) is the most common technique

used for calculation phase angle from three-phase grid voltage [Hsi]. It’s popularity occurs

mainly due to usage SRF-based current control methods and its simplicity and reliability.

The block scheme of the SRF-PLL is presented in Fig.5.4. Operation of the

synchronization loop is illustrated in Fig.5.5.

SRF-PLL bases on Park’s transformation of three-phase grid voltage from natural

abc frame to synchronous rotating dq frame. The aim of PLL is to adjust generated phase

angle to align d axis of SRF with grid voltage vector. It is achievable by controlling the q

component of grid voltage vector to zero. Output of the PI controller is an angular

frequency. An integration block transforms it to value of phase angle.

vqvabc abc

dqPI

SRF-PLL

ω*1/s

vqref

φ*

Fig.5.4. Basic scheme of Synchronous Frame PLL (SRF-PLL).


58

φ

ω

Im

Re

ω*

q

d

Vq φ*

Vd

Vdq

Fig.5.5. Phasor representation of SRF-PLL.

The speed and accuracy of SRF-PLL synchronization are strictly related to the

bandwidth of the employed PI controller [Tim1]. In the literature there are many

publications describing tuning procedure of PI controller, also PI for SRF-PLL. Most of

provide not complicated method of parameters calculation guarantying fast

synchronization [His], [Tim2], [Ani], [Arr], [Sil], where provide too slow dynamic of SRF-

PLL [Fra], [Kau], [Suu].

In the Thesis a method for tuning of PI controller for SRF-PLL is described, which

bases on symmetrical optimum criterion. A block scheme of the dynamic system used for

PI tuning is presented in Fig.5.6. In the system, a digital sampling delay is taken into

consideration, where Ts is sampling time. Delay of digital control system and PWM

voltage generation is approximated by first order system with time constant equal to 1.5Ts.

Vq_ref

Kp

1/sKp/Ti

φ

GPI(s)

1/s

1/(1+s1.5Ts)

GS(s)

GF(s)

PI controler

Plant

Integrator

Fig.5.6. The block diagram representing transfer function of PI controller used for SRF-PLL,

operating in closed-loop system with transfer delay Ts.


59

The transfer function of the above presented system, operating in closed-loop, is

described with equation:

( ) ( ) ( )

( ) ( ) ( ) (5.1.)

( ) (

( ) )

( ) (5.2.)

According to the symmetrical optimum criterion [Kaz1], parameters of the PI

controller for the system characterized with the above transfer function, are given as

equations:

(5.3.)

(5.4.)

where: Tr – large time constant, in case of system with integrator Tr=1; T∑ - sum of

small time constants, for given case T∑=1.5Ts; a - coefficient responsible for bandwidth of

PI controller.

In Fig.5.7 the step response of PI controller tuned with different values of a

coefficient is presented.

Fig.5.7. Step response of PI controller for different values of a.

Step Response

Time (sec)

Am

plit

ud

e

0 0.005 0.01 0.015 0.02 0.0250

0.5

1

1.5

a=2

a=4

a=8

a=16


60

In practical applications discrete controllers are used. Thus performance of

continuous and discrete PI controllers are compared in Fig.5.8. The digitalization of PI

controller is done by applying forward Euler integrator. As can be noticed, if Ts << 1, it

properly maps the dynamics of the continuous system.

Fig.5.8. Comparison of operation of continous and discrete PI controller.

5.4. PLL in Stationary Reference Frame for Unbalanced Conditions

Application of DSOGI structure (Dual Second Order Generalized Integrator),

operating as symmetrical components extractor in PLL, generates positive and negative

voltage components in αβ frame. The positive voltage component is connected to SRF-

PLL, which calculates phase angle.

The component extraction performed in αβ stationary frame bases on two structures

of band pass and low pass filters, called Second Order Generalized Integrators (SOGI).

The block scheme of the SOGI is presented in Fig.5.9.

∫ω'v

∫ω'

v’

qv’

k

Fig.5.9. Basic scheme of SOGI.

Two output signals of SOGI are defined by transfer functions equal to:

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.0160

0.2

0.4

0.6

0.8

1

1.2

1.4

Step Response

Time (sec)

Am

plit

ud

e

linear

discrete


61

( )

( )

(5.5.)

( )

( )

(5.6.)

where k is a damping factor, is resonant frequency.

One of outputs D(s) operates as band pass filter. Another, Q(s) is a low pass filter.

The Bode plot for different k values is presented in Fig.5.10. Among characteristic features

that enable the SOGI usage to filtering is unity gain and certain phase shifts for resonant

frequency: first transfer function (5.5) does not introduce phase delay, while second (5.6)

shifts signal by -900. As a result two output signals are generated: one in phase with input

and another in quadrature, both having the same amplitude as input signal.

Apart from generation of orthogonal component, SOGI provides attenuation of

voltage distortions. Similarly to SRF-PLL, attenuation depends on bandwidth of the

structure. The best dynamic performance is achieved for critical damping factor √ .

This value guarantees good stabilization time and overshoot limitation [Tim1], [Rod1],

[Fre].

-40

-30

-20

-10

0

10

Ma

gn

itu

de

(d

B)

102

103

-180

-90

0

90

Ph

ase

(d

eg

)

Bode Diagram

Frequency (rad/sec)

D(s), k=0.7

Q(s), k=0.7

D(s), k=0.1

Q(s), k=0.1


62

Fig.5.10. Bode plot of SOGI for different values of factor k.

Calculation positive and negative components in stationary reference frame is

performed by Positive-Negative Sequence Calculation block (PNSC), which strictly

derives from the instantaneous symmetrical components theory. PNSC calculates positive

voltage components and

and negative components and

.

The complete DSOGI algorithm for symmetrical components extraction, based on

two SOGI structures and PNSC block, is presented in Fig.5.11. The DSOGI structure

strictly bases on the instantaneous symmetrical components theory, where voltage

components in αβ are expressed by equations (4.38) and (4.39).

∫vα

∫

ω'

qvα’

k 1/2

1/2

∫

∫

ω'

vβ’

qvβ’

k 1/2

1/2

vβ

vαβ

SOGI (α)

SOGI (β)

Vα+

Vα-

Vβ+

Vβ-

vα’PNSC

Fig.5.11. The block scheme of component extraction based on DSOGI.

For calculating phase angle, the DSOGI is connected to SRF-PLL, which uses

positive component of voltage extracted by DSOGI as an input for frame transformation

block (from αβ to dq, as SRF-PLL operates in synchronous rotating frame). Here, tuning of

the SRF-PLL is also based on the symmetrical optimum criterion. It is worth to mention

that for tuning PI controller, an additional time constant of DSOGI should be taken into

account. Then, the time constant of the DSOGI ( ⁄ ) is added to sum of small

time constants of the SRF-PLL. Also, time constant of converter ( ) should be

added, where TS is sampling time of converter. The scheme of the DSOGI-PLL with SRF-

PLL is presented in Fig.5.12.


63

vαqvα’

vβ’

qvβ’

vβ

vαβ

SOGI (α)

SOGI (β)

vα+

vα-

vβ+

vβ-

vα’

PNSC

vd+

vq+

PI

SRF-PLLφαβ

dq vq+_ref ωFLL

1/s

ωω

ωφ

Fig.5.12. Scheme of DSOGI-PLL.

A significant disadvantage of the DSOGI-PLL is sensitivity to grid frequency

variations, due to usage of ω gain in the SOGI structure. In the basic solution the reference

value of ω is constant, equals to . To reduce influence of frequency variations on

proper synchronization and components extraction, information about instantaneous value

of grid frequency should be used. A frequency estimated by SRF-PLL can be used for this

purposes. This scheme, shown in Fig.5.12 will be further called DSOGI-PLL.

Another viable solution is application of FLL (Frequency Locked Loop), presented

in Fig.5.13. It tracks grid frequency by minimization of frequency error generated by the

DSOGI, defined as [Teo]:

(( ) ( ) )

(5.7.)

This error may be minimized by simple proportional PI controller. It can use the

same gains as SRF-PLL.

The angular frequency estimated by FLL is then used in the SOGI substituting

constant ω. Thanks to usage of FLL, the SOGI is robust to frequency variations in the grid

voltage. In this scheme there is no loop for phase angle estimation, therefore it is proposed

to use arcus tangens function of positive sequence voltages. This scheme will be further

called DSOGI-FLL (Fig.5.14).


64

1/2 - 1/s

uα

qvα

uβ

qvβ

ω*

ω'

2'2'

'

vv

k FLL

ℓ

Fig.5.13. The block scheme of Frequency Locked Loop (FLL).

vαqvα’

vβ’

qvβ’

vβ

vαβ

SOGI (α)

SOGI (β)

vα+

vα-

vβ+

vβ-

vα’

PNSC

ω

ω

FLL

Fig.5.14. Scheme of DSOGI-FLL.

5.5. PLL in Synchronous Reference Frame for Unbalanced Conditions

In the dq synchronous rotating frame, the extraction of positive and negative

voltage components, based on symmetrical component theory, is obtained with Dual

Synchronous Reference Frame (DSRF) [Teo]. Extraction of components is carried out in

two synchronous frames rotating in opposite directions. Both voltage components are

separated from each other, what allows independent control of positive and negative

component of voltage or current during grid voltage variations. The the DSRF cooperates

with SRF-PLL, which calculates phase angle from voltage in q-axis Vq+.

As it has been explained in the previous Chapter, in positive rotating frame the

negative component of voltage appears as AC signal oscillating with double grid frequency

and vice versa. This situation is described by equations of voltage components in positive

and negative frame. Following expressions give evidence that AC signals in positive frame

result from DC signals from negative frame:


65

[

] [

( ) ( )

( ) ( )] (5.8.)

[

] [

( ) ( )

( ) ( )] (5.9.)

To eliminate oscillations and separate positive and negative voltage components the

Decoupling Cell is employed. Scheme of the positive sequence Decoupling Cell is

presented In Fig.5.15. It is designed to cancel out oscillations originating from opposite

symmetrical components. The Decoupling Cell permits complete elimination of double

grid frequency oscillations and shows better results than application of filters [Teo].

Similarly, calculation of negative sequence of voltage is carried out in the negative

Decoupling Cell (negative phase is used for reference frame transformation). For

calculation positive and negative voltage component two Decoupling Cells operating in

positive and negative frame are employed, forming Dual Synchronous Reference Frame

(DSRF), shown in Fig.5.16.

+

sin cos

vd+

vq+

vd+*

vq+*

_vd- _vq-

φ

Decoupling Cell-positive-

Fig.5.15. Scheme of Decoupling Cell in positive synchronous rotating frame.


66

vd+

vq+

vd-

vq-

LPF

LPF

LPF

LPF

vd+*

vq+*

vd-*

vq-*

_vd+

_vq+

_vd-

_vq-

φ+

φ-

Decoupling Cell -positive-

Decoupling Cell -negative-

vαβ

vαβ

αβdq

αβdq

Fig.5.16. Block scheme of DSRF.

Estimated DC values of voltage: vd+, vq

+, vd

- and vq

- are further filtered by Low Pass

Filter (LPF), described with equation:

( )

(5.10.)

Again, as in DSOGI-PLL, the critical value of cut-off frequency is set as

√ , which is a trade-off between fast time response and damping of oscillations [Rod3].

Output of the DSRF are four estimated values of positive and negative components

of voltage in dq reference frame. In the DSRF-PLL application of cross-feedback

decoupling network is employed, which gives a fast and precise estimation [Bob3]. Phase

angle is calculated by the SRF-PLL from the q voltage component in positive rotating

frame. It is worth to mention that voltage vq+ used for SRF-PLL input may be filtered or

taken directly from decoupling cell. The complete block scheme DSRF-PLL is presented

in Fig.5.17.


67

Vd+

Vq+

Vd-

Vq-

LPF

LPF

LPF

LPF

Vd+*

Vq+*

Vd-*

Vq-*

_Vd+

_Vq+

_Vd-

_Vq-

φ+

φ-

Decoupling Cell -positive-

Decoupling Cell -negative-

vabc

αβdq

αβdq

PI

SRF-PLLφ

Vq+_ref ωref

1/sω

Fig.5.17. Complete block scheme of DSRF-PLL.

Tuning of the SRF-PLL in DSRF-PLL is similar as in the DSOGI-PLL. In this case

additional time constant corresponding to LPF is inserted in the feedback of the

synchronization loop.

5.6 Comparative analysis of grid synchronization methods

In this Section a comparison of synchronization techniques is conducted. Finally,

five PLLs algorithm described in this Chapter, are chosen for simulation comparison:

SRF-PLL with high controller gain (a=4),

SRF-PLL with low controller gain (a=32),

DSOGI-FLL with atan function for phase calculation,

DSOGI-PLL with SRF-PLL for phase calculation,

DSRF-PLL with filtered voltage as controller input,

DSRF-PLL with unfiltered voltage as controller input.

By default pass bands of filters in DSOGI and DSRF systems are set to half of

nominal frequency (k=0.5). Tests are performed in per unit notation. To achieve the same

performance in real system with nominal values of voltages, two methods of gain

normalization of PI controller gains can be used:

Normalization of error value (vq has to be divided by voltage magnitude),

Normalization of PI controller gains.


68

The first method assures independence from the grid voltage level, however, also

requires online calculation of voltage magnitude. The second method is simpler – requires

only proper calculation of controller gains, but operates properly only for given nominal

voltage.

The described algorithms are compared under following grid voltage situations:

Balanced and unbalanced voltage dips,

Phase angle jumps,

Frequency steps,

Higher harmonics.

In this thesis following criterions for estimating influence of step and periodic

voltage variations are assumed:

Integral of Time Multiplied by Square Error (ITSE)

Hereby, the criterion called ITSE is chosen to evaluate response of PLL algorithm

on step grid voltage variations. The ITSE criterion is the integral of the control variable

square error multiplied by the time, during variation occurs. It is given by equation:

∫

(5.11.)

This criterion is used for optimization of closed control loops. It allows to

determine the response of system to the given time function of the commanded or

disturbance variable. It gives the best results when time function is step change or single

pulse, and it is not useful when periodic distortion occurs. The ITSE criterion assumes

integration for infinite period of time. In following tests the integration is stopped, when

error of tracked signal is less than 1% of nominal value.

Total Harmonic Distortion of phase angle

For evaluation of repetitive distortions of grid voltage, like higher harmonics or

unbalance, the concept of measurement of THD content is proposed. Sine function of

phase angle estimated by PLL is calculated. Then, spectral analysis is performed and THD

factor of this sine function is calculated. This method gives information about attenuation

of grid voltage distortions.


69

5.6.1. Balanced dips

In this test the ability of PLL to track voltage magnitude during balanced voltage

dips is evaluated. A symmetrical voltage dip with 50% depth is applied. The grid voltage

waveform is presented on Fig.5.18.

The SRF-PLL does not include any filtering in voltage estimation process, therefore

magnitude tracking is instantaneous and does not depend on controller tuning (Fig.5.19a).

Other algorithms based on symmetrical component extraction are characterized with step

response similar to first order low-pass filter with time constant equal to chosen passband

( ⁄ ). In these algorithms step voltage changes propagate through sequence

decoupling cause temporary error in q-component and cause small frequency deviations.

Only in the DSOGI-FLL q-component is always zero, because the phase angle is

calculated instantaneously using arcus tangens function.

Fig.5.18. Symmetrical voltage dip with 50% depth.

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Voltage [

pu]

Time [s]

Grid voltage

Ua

Ub

Uc


70

a.

b.

c.

d.

Fig.5.19. Operation of PLL algorithms under symmetrical dip of 50% depth: a. SRF-PLL; b.

DSOGI-FLL; c. DSOGI-PLL; d. DSRF-PLL.

Dynamics of the component extraction can be designed by choice of systems

passband. Both DSOGI and DSRF are tuned with k factor, which describes relation

between filters passband and nominal frequency. Oscillations in Fig.5.20 show estimation

of voltage d-component by DSOGI and DSRF for different values of passband. Results are

compared with low pass filter with time constant ⁄ . As shown, for low values of

k, response of extraction algorithms cover exactly response of low pass filter. High values

of k result in overshoot in response. It has to be noted, that it is not worth to force values of

k higher than 1, as it results in oscillations, finally leading to instability.

It can be seen clearly, that response of DSOGI and DSRF are similar. It is a result

of applying the same methodology of the symmetrical component extraction in different

reference frames. The band-pass filter used in the SOGI to filter sinusoidal signal is a

counterpart of low-pass filter implemented in the rotating frame to filter DC signals. Some

little differences are result of different digital implementation of aforementioned filters.

0.48 0.5 0.52 0.54 0.56 0.58 0.6-0.2

0

0.2

0.4

0.6

0.8

1

SRF-PLL

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-50

0

50

[

rad/s

]

Time [s]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-0.2

0

0.2

0.4

0.6

0.8

1

DSOGI-FLL

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-50

0

50

[

rad/s

]

Time [s]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-0.2

0

0.2

0.4

0.6

0.8

1

DSOGI-PLL

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-50

0

50

[

rad/s

]

Time [s]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-0.2

0

0.2

0.4

0.6

0.8

1

DSRF-PLL

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-50

0

50

[

rad/s

]

Time [s]


71

a.

b.

Fig.5.20. Estimation of d-component of grid voltage by DSOGI-PLL and DSRF-PLL for

different values of filter passbands: a. ωf=ω’/4, b. ωf=ω’/4

5.6.2. Unbalanced dips

To observe behavior of PLL algorithms under presence of negative component in

grid voltage a single-phase voltage dip of 80% depth is applied, as shown in Fig.5.21.

Fig.5.21a,b shows simple SRF-PLL algorithm without any sequence estimation. High

values of controller gain result in high 2nd

harmonic oscillations of estimated angular

frequency and oscillations of estimated phase angle. This results in deformation of

negative sequence components from sinusoidal shape. If the PI gains are chosen to be low,

the controller response is much less intensive, resulting in smaller oscillations (note

different scale) and less deformation of estimated phase angle.

Fig.5.21. Single-phase unsymmetrical voltage dip of 80% depth.

0.48 0.5 0.52 0.54 0.56 0.58 0.60.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Voltage [

pu]

Time [s]

Estimation dynamics (k=0.25)

Low-pass

DSOGI

DSRF

0.48 0.5 0.52 0.54 0.56 0.58 0.60.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Voltage [

pu]

Time [s]

Estimation dynamics (k=1)

Low-pass

DSOGI

DSRF

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Voltage [

pu]

Time [s]

Grid voltage

Ua

Ub

Uc


72

a.

b.

c.

d.

Fig.5.22. Operation of PLL algorithms under single-phase dip with: a. fast SRF-PLL, b. slow SRF-

PLL, c. DSOGI-FLL, d. DSRF-PLL.

Fig.5.21 b,c presents negative component extraction. Response of DSOGI and

DSRF based algorithms are identical. Extraction time constant is the same, as for positive

sequence. However in this case some oscillation appear as a result of interaction between

symmetrical components in the decoupling cells.

5.6.3. Phase jumps

To verify the fundamental task of PLL – phase tracking, a phase jump test was

performed. The grid voltage phase changes stepwise by 45°, like shown in Fig.5.23.The

fast SRF-PLL algorithm responds with high estimated frequency spike (again note that

scale is different), which drives phase error to zero in less than half of period. Lower

controller gains allow to respond more smoothly, increasing regulation time.

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

SRF-PLL

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-400

-200

0

200

400

[

rad/s

]

Time [s]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

SRF-PLL

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-50

0

50

[

rad/s

]

Time [s]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

DSOGI-FLL

Voltage [

pu]

Ud neg

Uq neg

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-50

0

50

[

rad/s

]

Time [s]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

DSRF-PLL

Voltage [

pu]

Ud neg

Uq neg

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-50

0

50

[

rad/s

]

Time [s]


73

Fig.5.23. Phase jump of grid voltage (at t=0.5).

a.

b.

c.

d.

e.

f.

Fig.5.24. Operation under grid voltage phase jump, with: a. fast SRF-PLL, b. slow SRF-

PLL, c. DSOGI-FLL, d. DSOGI-FLL, e. DSRF-PLL filtered, f. DSRF-PLL unfiltered.

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Vol

tage

[pu

]

Time [s]

Grid voltage

Ua

Ub

Uc

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-3

-2

-1

0

1

2

3

SRF-PLL

[

rad]

Error

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

200

400

600

800

[

rad/s

]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-3

-2

-1

0

1

2

3

SRF-PLL

[

rad]

Error

0.48 0.5 0.52 0.54 0.56 0.58 0.6-50

0

50

100

[ra

d/s

]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-3

-2

-1

0

1

2

3

[

rad]

DSOGI-FLL

Error

0.48 0.5 0.52 0.54 0.56 0.58 0.6-50

0

50

100

[

rad/s

]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-3

-2

-1

0

1

2

3

[

rad]

DSOGI-PLL

Error

0.48 0.5 0.52 0.54 0.56 0.58 0.6-50

0

50

100

[

rad/s

]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-3

-2

-1

0

1

2

3

[

rad]

DSRF-PLL

Error

0.48 0.5 0.52 0.54 0.56 0.58 0.6-50

0

50

100

[

rad/s

]

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-3

-2

-1

0

1

2

3

[

rad]

DSRF-PLL

Error

0.48 0.5 0.52 0.54 0.56 0.58 0.6-50

0

50

100

[

rad/s

]


74

In the DSOGI-FLL phase angle is calculated from extracted positive sequence by

arcus tangens function. Therefore, its dynamics depend on the passband of SOGI

algorithm, not on SRF-PLL gains (Fig.5.24a). It is characterized by relatively fast

response, but leaves small, long-term oscillations.

Response of DSOGI-PLL and DSRF-PLL are slower due to extra PLL loop in the

system. It takes few cycles to respond for a phase jump. Faster response is not possible due

to high time constant of sequence extraction in control loop. However, in the DSRF some

improvement is possible. When using filtered vq signal, response is similar to DSOGI. But

in this case it is possible to access unfiltered uq value, directly from decoupling cell. This

allows significant increase of the response time.

5.6.4. Frequency steps

All of presented PLL algorithms are able not only to track phase angle, but also

estimate frequency of the input signal. In SRF-PLL based methods the output of PI

controller is an estimated phase signal, while the DSOGI-FLL has dedicated loop for

frequency tracking. In the DSOGI-FLL, instead of simple gain a PI controller is used for

phase tracking, as proposed in the Section 5.3.

In this test a step frequency change of 5Hz in input signal is applied (Fig.5.25).

Waveforms show angular frequency estimated by different PLL algorithms. Again, the

SRF-PLL response depends highly on controller gain.

Fig.5.25. Frequency step of grid voltage (at t=0.5).

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Voltage [

pu]

Time [s]

Grid voltage

Ua

Ub

Uc


75

a.

b.

c.

d.

e.

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-10

0

10

20

30

40

50

[

rad/s

]

SRF-PLL

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-10

0

10

20

30

40

50

[

rad/s

]

SRF-PLL

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-10

0

10

20

30

40

50

[

rad/s

]

DSOGI-FLL

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-10

0

10

20

30

40

50

[

rad/s

]

DSOGI-FLL

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-10

0

10

20

30

40

50

[

rad/s

]

DSOGI-PLL


76

f.

g.

Fig.5.26. Operation of PLL under frequency step with: a. fast SRF-PLL, b. slow SRF-PLL,

c. DSOGI-PLL with PI controller, d. DSOGI-PLL with P controller, e. DSOGI-PLL, f. DSRF-PLL

filtered, g. DSRF-PLL unfiltered.

Algorithms, that use sequence extraction are not so fast an require about 0.1s to

settle. In the DSRF-PLL similar improvement as in phase tracking can be made by using

unfiltered vq signal.

A remark has to be made on DSOGI-FLL algorithm. When equipped with PI

controller, tuned with the same parameters as SRF-PLL loops, the frequency responses of

DSOGI-FLL, DSOGI-PLL and filtered DSRF-PLL loops are the same. In this case both

frequency estimation loops are equivalent.

5.6.5. Attenuation of Distortion

To measure robustness of PLL algorithms to grid voltage distortions, the input

voltage was polluted by higher harmonics. A voltage with 5% of 5th

harmonic, 3% of 7th

harmonic and 1% of 11th

harmonic was applied, as shown in Fig.5.27. To evaluate

attenuation of higher harmonics distortions by PLL algorithms, the FFT analysis is

performed and THD factor is calculated. Results of synchronization with distorted voltage

are presented in Fig.5.28.

A simple relation can be observed: algorithms with faster phase tracking are less

resistant to grid voltage distortions. In the fast SRF-PLL output distortion is only two times

smaller than input (5.28b), while best algorithms has almost no distortions at the output

(5.28 d, f). Recapitulating, during tests of different adjustments of PI controller in the SRF-

PLL it occurs that high bandwidth causes high dynamics and sensitivity to grid voltage

distortions. With low dynamics the high robustness is achieved. Unacceptable defect is

slow dynamics, what in synchronization algorithm is the most important.

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-10

0

10

20

30

40

50

[

rad/s

]

DSRF-PLL

0.48 0.5 0.52 0.54 0.56 0.58 0.6

0

0.5

1

Time [s]

Voltage [

pu]

Ud

Uq

0.48 0.5 0.52 0.54 0.56 0.58 0.6

-2

0

2

[

rad]

0.48 0.5 0.52 0.54 0.56 0.58 0.6-10

0

10

20

30

40

50

[

rad/s

]

DSRF-PLL


77

Fig.5.27. The test voltage polluted by higher harmonics: with 5% of 5th harmonic, 3% of 7th

harmonic and 1% of 11th harmonic.

a.

b.

c.

d.

e.

f.

Fig.5.28. Distortion attenuation of PLL algorithms: a. fast SRF-PLL, b. slow SRF-PLL, c. DSOGI-

FLL, d. DSOGI-PLL, e. DSRF-PLL unfiltered, f. DSRF-PLL filtered (note different scales of amplitude).

0 0.2 0.4 0.6 0.8 1-1

0

1Selected signal: 50 cycles. FFT window (in red): 1 cycles

Time (s)

0 100 200 300 400 500 600 700 8000

1

2

3

4

5

Frequency (Hz)

Fundamental (50Hz) = 1 , THD= 5.92%

Mag

(%

of

Fun

dam

enta

l)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.5

0

0.5

Selected signal: 50 cycles. FFT window (in red): 1 cycles

Time (s)

0 100 200 300 400 500 600 700 8000

0.5

1

1.5

2

Frequency (Hz)

Fundamental (50Hz) = 0.9996 , THD= 2.89%

Mag (

% o

f F

undam

enta

l)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.5

0

0.5


Time (s)

0 100 200 300 400 500 600 700 8000

0.05

0.1

0.15

0.2

Frequency (Hz)


Mag (

% o

f F

undam

enta

l)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.5

0

0.5


Time (s)

0 100 200 300 400 500 600 700 8000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency (Hz)


Mag (

% o

f F

undam

enta

l)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.5

0

0.5


Time (s)

0 100 200 300 400 500 600 700 8000

0.005

0.01

0.015

Frequency (Hz)


Mag (

% o

f F

undam

enta

l)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.5

0

0.5


Time (s)

0 100 200 300 400 500 600 700 8000

0.05

0.1

0.15

Frequency (Hz)


Mag (

% o

f F

undam

enta

l)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-0.5

0

0.5


Time (s)

0 100 200 300 400 500 600 700 8000

0.005

0.01

0.015

Frequency (Hz)


Mag (

% o

f F

undam

enta

l)


78

5.7 Summary and Conclusion

Proper synchronization of Grid Connected Converter (GCC) requires fast and

precise detection of grid voltage phase angle – it is the task of Phase Locked Loop (PLL)

algorithm. According to latest trends in the converter control, PLL algorithms should

guarantee robustness to grid voltage distortions like balanced and unbalanced dips, phase

angle jumps, frequency variations or higher harmonics content. Above all, the proper

synchronization is especially problematic during negative voltage component existence.

Hence, some PLL algorithms provide voltage symmetrical component extraction

sufficient to mitigate the influence of voltage unbalance.

In this Chapter the short review of PLL algorithms is presented. For further analysis

two dynamic systems for component extraction, based on the symmetrical component,

namely the DSOGI and the DSRF, were chosen due to their incontrovertible ability to

proper operation under negative voltage component existence.

The SRF-PLL, base of PLL algorithms, with different PI parameters tuning and

DSOGI-FLL, DSOGI-PLL, DSRF-PLL and were evaluated in the simulation tests

performed in the Chapter. Algorithms were tested under different voltage distortions. In

every analyzed case, errors of magnitude, negative sequence, phase angle and angular

frequency are calculated, respectively. The results of simulation tests are summarized up in

Tab.5.2.

Tab.5.2. Basic properties of tested grid synchronization algorithms.

SRF-PLL

fast

SRF-PLL

slow

DSOGI-

FLL*

DSOGI-

PLL

DSRF-

PLL*

Magnitude

[ITSE] 0 0 0.132 0.130 0.126

Negative

sequence

[ITSE]

- - 0.0040 0.0040 0.0042

Phase angle

[ITSE] 0.0036 0.2428 0.1338 0.8909

0.4765

(1.2123)

Frequency

[ITSE] 3 212

431

(152) 622

413

(966)

Distortion

[THD] 2.89 0.32 0.49 0.02

0.23

(0.02)

Algorithm

complexity ++ ++ + +/- -

* with PI controller in frequency loop; value in bracket relate to P controller

** with unfitered error signal; values in brackets relate to filtered error


79

Conclusions based on theoretical analysis and simulation validation made in the

Chapter follow that:

a. The SRF-PLL’s synchronization strictly depends on bandwidth of the PI

controller:

high bandwidth yields to fast phase angle detection but does not

eliminate any grid voltage distortion,

low bandwidth guarantees high robustness to grid voltage distortions but

the speed of synchronization is rather unacceptable.

Hence, under voltage distortions the SRF-PLL is no longer sufficient

solution for converter synchronization to the grid. It has good response

under balanced conditions but its performance become insufficient in

unbalanced faulty grids. The SRF-PLL requires usage of additional structure

eliminating influence of voltage distortions.

b. The best synchronization under voltage distortion is assured by PLL

algorithms based on positive and negative component extraction. There are

two synchronization algorithms with component extraction: DSOGI-PLL,

operating in stationary reference frame, and DSRF-PLL, operating in

synchronous rotating frame. Both algorithms provide almost identical

results, due to usage of the instantaneous symmetrical component theory

and filters with the same dynamics in stationary and rotating reference

frames.

c. The difference between DSOGI-PLL and DSRF-PLL lies in phase and

frequency estimation:

DSOGI-PLL with FLL structure provides the fastest response to

phase variations and frequency tracking,

The DSRF-PLL dynamic depends on the error signal provided to

SRF-PLL: if unfiltered signal is used, its performance is better, than

DSOGI-PLL, but distortions content rises. If high attenuation of

distortion has to be achieved, the DSOGI-PLL should be preferred

due to faster response, than filtered DSRF.

The final choice of the synchronization algorithm should depend on GCC

application and requirements for grid monitoring. In practical case also algorithm


80

complexity and its execution time should be considered. The DSRF-PLL requiring

multiple transformations with trigonometric functions will require heavy computational

effort, while the DSOGI-FLL can be sufficient solution for control algorithm in stationary

frame.

Due to better dynamics and less cmputational efford, in author’s opinion, the

DSOGI-PLL with FLL extension is the best tool used for synchronization of GCC under

distorted and unbalanced grid voltage conditions.


81

6. Converter Control Methods based on Symmetrical Components

Grid voltage variations, changing shape and frequency, are main reason of failure

operation of Grid Connected Converters (GCC). Depending on the severity of a

disturbance and the robustness of a GCC, variations cause disconnection or even damage.

Voltage dips impose especially negative effect on GCC operation [Etx]. The main effects

of voltage dips appearance on power converters are:

Decrease of the maximum capability of power exchange between the

converter and the grid,

Power factor and/or current amplitude error,

DC link voltage oscillations,

Unbalance and distortions of converter currents.

Control strategies have a critical influence on the GCC behavior during voltage

disturbances. Hence, to minimize the negative effect of grid distortions, different control

structures for GCC have been proposed last years [Rio1], [Son], [Sac], [Suh1]. In

Renewable Energy Sources (RES), especially in Wind Turbines (WT), the GCC control

strategy is responsible for quality of power exchanged with the grid. Improper control

algorithm leads to deterioration of current waveforms or even to sudden disconnection of

WT, what always threatens the grid stability. The most important is the current and power

flow control algorithm. Indirect requirements for operation of GCC during voltage

variations are defined in national grid codes. In example, the Low Voltage Ride Through

control strategy (LVRT) enables the WT to resist balanced and unbalanced voltage dips.

Moreover, in case of voltage dips, the most important issue for grid operators is generation

of reactive power. Hence, additional requirements according to GCC operation under dips

are requested by Polish and other European Grid Codes concerning active support of the

power system by wind turbines.

Since the majority of voltage dips are unbalanced, the need for control of positive

and negative current components is also essential. Lack of negative component control

introduces asymmetry to the converter currents. In such case, GCC protections can be

released, what leads to disconnecting WT from the grid. Critically, overcurrent can even

lead to damage of semiconductor power devices in GCC. Moreover, during voltage

unbalance, the active power is oscillating introducing oscillations to DC-link voltage.

Control of positive and negative current components give also significant profits to power


82

system operators. Reactive power can be generated with positive and negative components,

which enables possibility of voltage symmetrization, and better stabilization of the power

system.

Hence, to operate properly during unbalanced voltage distortions the converter control

algorithm requires:

Grid voltage synchronization loop - most of algorithms are implemented in

reference frame, that rotates synchronously with grid voltage. Phase Locked Loop

(PLL) algorithm, as described in Chapter 5, is responsible for proper estimation of

grid voltage phase angle even under grid voltage disturbances. Some of PLLs also

include symmetrical component extraction algorithms;

Current control algorithm, able to operate under unbalanced conditions, equipped

with positive and negative current components control;

Power flow control algorithm, that calculates current references under unbalanced

voltage and realizes different power flow strategies;

Grid voltage monitoring and support, that assures reactive power generation and

decides about disconnection of turbine.

The general block scheme of such control algorithm is presented in Fig. 6.1. Following

sections explain in detail functions of control blocks.

AC-DC

LU

DC voltage control

PLLPWM

Current control

uDC

iabc

uabc

φ+, φ-

Power flow control

p*q*

u*u+, u-

i+*, i-*

Grid support

Grid Input Filter

Power Converter

Fig. 6.1. General block scheme of control of Grid Connected Converter (GCC).


83

6.1. Current Control under Unbalanced Conditions

6.1.1. Conventional Control Methods

During last decades different control strategies for Grid Connected Converters have

been reported in the literature. The classification of control strategies, according to [Kaz3]

is presented in Fig. 6.2. In this Section only the most commonly used linear control

methods are described to present conventional control solutions dedicated for GCC

operating under nominal, not distorted, grid voltage.

linear

PWM current control methods

ON/OFF controllers Separated PWM

non-linear

passivity fuzzy

predictivePI resonant

feedforward dead-beat

Deltahysteresis optimized

Fig. 6.2. Overview of current control methods dedicated to Grid Connected Converter

(GCC).

Generally, PWM current control methods are divided into two groups: ON/OFF

non-linear controllers and with separated PWM techniques. The ON/OFF methods are not

accepted in commercial applications due to variable switching frequency and difficulties in

digital implementation [Kaz3].

Controllers with separated PWM use dedicated modulator (carrier-based or space-

vector), that allows constant switching frequency. The second part is a current controller,

which calculates reference voltage for the modulator. Among methods with separated

PWM linear and non-linear controllers can be distinguished. Non-linear methods are

described widely in literature, however, not popular in practical applications.

The most widespread are linear PWM controllers. Predictive and deadbeat control

methods are very promising and provide excellent dynamics but they are still too sensitive

to inaccuracy of model parameters [Rod4]. The most popular linear control methods are


84

the ones based on proportional-integral controllers (PI) in synchronous frame and resonant

controllers in stationary frame [Cic].

The most popular and straightforward method applied to three-phase converters is

Voltage Oriented Control (VOC), presented in Fig. 6.3. In this method current is

transformed to Synchronous Rotating Frame (SRF), aligned with the grid voltage vector.

The VOC method, uses two PI controllers for current control in d and q axes. While grid

voltage remains balanced and PLL operates correctly, currents in these axes are

proportional to active and reactive power, respectively. Thanks to frame coordinate

transformation from abc to dq, the currents become DC values, and PI controllers reduce

the errors of the fundamental component to zero. Usually, the VOC control method is

equipped with decoupling network to cancel out cross-coupling terms existing in three-

phase converter.

The transfer function of PI controller used in synchronous frame is equal to:

( )

(6.1.)

The PI parameters (Kp – proportional gain, Ki – integral gain) are tuned using many

different methods like modulus or symmetry criterion, damping factor criterion, etc.

[Kaz2]. Thanks to well-developed tuning methods, the VOC guarantees good dynamic and

static performance.

Despite mentioned advantages, PI controllers are sensitive to any periodic voltage

disturbances like higher harmonics or negative components. The controller gain at higher

frequencies is not sufficient to eliminate current errors caused by voltage distortions.

Therefore, to eliminate these drawbacks, the VOC is often enriched with additional

harmonic compensation loops or negative component controllers. Moreover, the VOC

requires special care in PLL design. Distorted grid voltage results in phase angle

distortions, that cause deformation of waveforms during coordinate transformation

between stationary and rotating reference frames, what increases current THD and/or

unbalance.


85

a.

Vqϕ

abcdq

idq

PI

ωL

ωL

PI

dq

αβ

id

iq iq*

id*Vd

Vdqiabc Vαβ

ϕ

b.

id

Kp

1/sKp/Ti

GPI(s)

id*

ud

Fig. 6.3. a. Control scheme of synchronous control method performed in dq frame; b.

Illustration of transfer function of PI controller.

The second of the most popular linear control methods is application of

proportional-resonant (P-Res) controllers in stationary reference frame, as presented in Fig.

6.4. In stationary frame currents are sinusoidal values. Therefore, to obtain zero steady

state error, controller have to present infinite gain at the grid voltage frequency. This is

possible with use of resonant controller path instead of integral. The equivalent single

phase P-Res controller centered around AC control frequency, achieving the same DC

response as PI controller, is described as:

( )

(6.2.)

where ωs is the resonant frequency, equal to nominal grid frequency.

It is worth to mention that the resonant control method is simpler than synchronous

control methods. It does not require coordinate transformation and additional calculation of

phase angle φ by a PLL algorithm, indispensable to dq transformation. Conventional

resonant controllers are, however, applicable only under constant frequency. Operation

under frequency distortions requires online tuning of the controllers, which complicates

implementation of such control structure. Practically, resonant controller can be


86

implemented using structure similar to SOGI, described in Section 5.4. If the feedback

from the output signal is removed, this structure behaves as sinusoidal signal integrator.

Moreover, frequency adaptation can be easily achieved.

a.

abcαβ

iαβ

P-RESiα

iα*

Vαβiabc

P-RESiβ

iβ*

b.

id

Kp

Kr

GP-Res(s)

id*

ud

22

ss

s

Fig. 6.4. a. Control scheme of resonant control method performed in αβ frame; b.

Illustration of transfer function of resonant controller.

Among control methods dedicated for GCC the Direct Power Control with Space

Vector Modulation (DPC-SVM), presented in Fig. 6.5, is also important [Mal]. Here, the

control values are instantaneous active and reactive power. However, this method is

difficult to adapt for operation under unbalanced voltage. The DPC-SVM controls

instantaneous power values, that are product of unbalanced current and voltage (see

Section 6.2.1). During voltage variations the DPC gives no opportunity for direct control of

current and minimize distortions, especially during voltage unbalance. For this reasons,

this method will not be further investigated.


87

abcαβ

iαβ

PIPI

Q*

P*iabc

Vdq*

vabc vαβ

Instantaneous power

calculation

dq

αβ

Vαβ*

Fig. 6.5. General scheme of Direct Power Control.

For proper operation during unbalance, the current control method should provide:

Decoupled control of positive and negative current component control,

Unbalanced disturbance rejection (operation under unbalanced grid voltage

conditions),

High dynamics and accuracy.

All presented conventional current control methods have different characteristics

regarding operation in unbalanced conditions. The influence of voltage unbalance and

negative component existence is here explained in frequency domain. Even if P-Res

controller in stationary frame is an equivalent of PI controller in rotating frame, there is

substantial difference in control ability of negative component.

In stationary frame, the negative component occurs as component oscillating with

frequency –ω, while the positive component oscillates with the frequency ω (Fig. 6.6a).

The resonant path of the controller controls both components (–ω and ω) in the same time,

in frequency domain. Therefore, it has the same gain for component rotating with

frequency –ω and ω, allowing proper control of both current sequences.

The synchronous frame, rotating with frequency ω, is shifted in frequency domain by

with respect to stationary frame (Fig. 6.6b). Hence, the positive component is a DC

value. Steady state errors are then eliminated using integral path I in the controller. The

problem occurs due to the negative component oscillating with frequency -2ω. The PI

controller has to low gain in 2ω frequency. Therefore, the typical VOC algorithm has

significant phase and amplitude errors, when operating under unbalanced conditions.

Hence, conventional VOC method is not able to operate properly under unbalanced

voltage conditions or control negative current sequence. Application of synchronous

controllers in unbalanced system requires modification of control scheme.


88

a.

-ωn 0 ωn

Res

b.

I

-2ωn -ωn 0 ωn

e-jωt e-jωt

ω

Fig. 6.6. Symmetrical components control in: a) stationary frame, b) Synchronous Reference

Frame (SRF).

6.1.2. Voltage Oriented Control with Resonant Controller

As illustrated in Fig. 6.6b, after transformation to SRF, negative component

oscillates at -2ω frequency. A solution, that allows control of negative component in SRF

with zero steady state error, is controller with infinite gain at 2ω. The proposed approach is

usage of PI controller for control the positive current component, which in rotating frame

is a DC value, and usage of the resonant controller in synchronous frame for control of

negative component. This idea is presented in Fig.6.7, and will be further called VOC+Res

method.

I

-2ωn -ωn 0 ωn

e-jωt e-jωt

ω

Res

Fig. 6.7. Symmetrical components control in Synchronous Rotating Frame (SRF) with

additional resonant path.

The practical implementation of this method is very simple. A resonant path is

added in parallel to PI controllers implemented in SRF, as shown in Fig. 6.8. This

enhancement allows to preserve high dynamics of VOC and include control of negative

component. The disadvantage of this method is appearance of disturbances caused by


89

resonant controllers response to reference value steps or voltage disturbances, even under

balanced conditions.

Vqϕ

abcdq

idq+

PI

ωL

ωL

PI

dq

αβ

id

iq

iq*

id*

Vd

Vdqiabc Vαβ

Res2ω

Res2ω

Fig. 6.8. Voltage Oriented Control with Resonant Current Controller (VOC+Res).

6.1.3. Dual Synchronous Reference Frame Control Algorithms

One of possible adaptations of VOC scheme for unbalanced conditions is Dual

Synchronous Rotating Frame (DSRF) current control. The concept bases on splitting

unbalanced system into two reference frames, as shown in Fig. 6.9:

Positive, rotating counterclockwise with positive voltage component,

Negative, rotating counterclockwise.

The most straightforward application is parallel transformation of current into two

reference frames using phase angle φ and –φ. The scheme is presented in Fig. 6.10.

Although the method is able to control both current components, high distortions appear in

rotating frames. For example in negative rotating frame the component oscillating at 2ω

with a nominal voltage amplitude exists. Thus, the DSRF algorithm using control of

positive and negative current components has significant disadvantage: 2ω components

distorts the control process. In the literature there are many solutions of the DSRF current

algorithm employing different filtering methods [Teo]. To minimize the influence of 2ω

components, different techniques are employed:

Notch filters - tuned for filtering 2ω frequency [Lyo3] – if the damping factor is too

high, the notch filter affects the current control loop by reducing phase control

range, what declines stability margin of the system. If the damping factor is too


90

low, the setting time of controllers extends. The solution for above disadvantage is

usage of adaptive filters.

Delayed Signal Cancellation (DSC) technique [Bob3] – the main task of the filter is

to eliminate the component of 2ω frequency. The idea of DSC is adding to the

voltage in d and q frame, voltage delayed by quarter of period. The result is

filtering the negative component oscillating with 2ω frequency,

Component decoupling methods (DSOGI, DSRF or others).

Above mentioned filtering solutions are located between the frame transformation

blocks and the controllers, as shown in Fig. 6.8. Despite using different types of filtering,

the oscillations are not eliminated and still have negative impact on control process,

especially during higher harmonic existence.

The solution of this problem is employment of decoupling cells, described in

Section 5.4. Application of decoupling process for elimination influence of 2ω, called

Decoupled Dual Synchronous Reference Frame algorithm (DDSRF), gives better results

than using notch filters or DSC [Teo]. The method is presented in Fig. 6.9. Here,

components -2ω and 2ω are eliminated by decoupling process.

a.

0 ωn

e-jωt

ω -ωn 0 ω

ejωtIpos Ineg

Fig. 6.9. Symmetrical components control in Decoupled Dual Synchronous Reference

Frame (DDSRF).


91

Vq+

Positive component control

ϕ+

abcdq

idq+

PI

ωL

ωL

PI

dq

αβ

id+

iq+

iq+*

id+*

Vd+

Vdq+

Vq-

iabc

Negative component control

ϕ-

idq-

PI

ωL

ωL

PI

αβ

id-

iq-

iq-*

id-*

Vd-

Vdq-abcdq

dq

Vαβ

Filter

Filter

ϕ+

ϕ-

Fig. 6.10. Dual Synchronous Reference Frame current controller.

Thanks to decoupling networks, influence of negative component in steady state is

eliminated. However, this method presents lower dynamics, than previously presented

schemes.

Vq+

Positive component control

ϕ+

abcdq

idq+

PI

ωL

ωL

PI

dqαβ

id+

iq+

iq+*

id+*

Vd+

Vdq+

Vq-

iabc

Negative component control

ϕ-

idq-

PI

ωL

ωL

PI

αβ

id-

iq-

iq-*

id-*

Vd-

Vdq-abc

dq

dq

Vαβ

LPF

dq2ϕ-

LPF

dq2ϕ+

Decoupling Network

ϕ+

ϕ-

Fig. 6.11. Decoupled Dual Synchronous Reference Frame (DDSRF) current controller using

a decoupling network.


92

6.2. Power Control under Unbalanced Conditions

As it was presented in Section 6.1, for proper operation of the GCC under

unbalanced voltage conditions, conventional current control methods have not been

sufficient yet. The control method Direct Power Control (DPC), designed especially for

control of active and reactive power components, and its variations [Mal1, Mal2], have not

already been proper solutions in case of voltage unbalance. During negative voltage

component existence, active and reactive power terms oscillate. Hence, controlled power

signals are no longer constant values. Maintaining, at all costs, smooth and balanced active

and reactive power during unbalanced voltage conditions cause highly distorted currents.

For the other hand, oscillations cannot be eliminated, when the conventional balanced

current strategy (VOC) is employed. Therefore, the conventional power control strategies,

based on DPC, are no longer sufficient. The solution is connection of adequate current

control method, maintaining high quality of currents, with proper power control strategy.

In this Section extended control strategies based on instantaneous power theory are

presented. In strategies a real-time current symmetrical components extraction to calculate

appropriate current references is employed[Etx].

6.2.1. Basics of Instantaneous Power Theory under Unbalanced Conditions

Every year dozens of articles describing different approaches to the power theory

are published, mainly due to economic reasons: poor power quality has a great impact on

economy. The review of power quality theories is deeply analyzed in [Ben]. For better

understanding of the phenomena occurring in control of GCC during unbalanced voltage

condition, the look on instantaneous power theory [Aka], also called p-q theory, is

required.

The instantaneous power theory, presented in 1983 by Akagi and Nabae [Aka] is

currently the most popular theory in the area of power quality improvements. The p-q

theory describes physical phenomena with simple mathematical operations occurring only

in three-phase systems. The theory is based on scalar transformation from abc coordinates

to αβ stationary frame. In three-wire systems, where zero sequence is not present, and the

p-q theory is reduced to a set of simple equations.

The instantaneous complex power s in αβ stationary frame is defined as a product

of voltage vector v and conjugate of current vector i*:


93

( )( ) ( )⏟

( )⏟

(6.3.)

where p is instantaneous active power and q is instantaneous reactive power.

The p-q equations can be presented in matrix form as [Aka]:

[ ] [

] [

] (6.4.)

When unbalance occurs, the grid voltage and current in αβ and in dq frame, consist

of positive and negative components:

(6.5.)

(6.6.)

According to the instantaneous symmetrical theory, power components during

unbalanced grid voltage can be expressed by constant and oscillating components. The

active and reactive power of GCC, operating under unbalanced grid voltage, can be

expressed as:

( ) ( ) (6.7.)

( ) ( ) (6.8.)

Where and are the average values of the instantaneous active and reactive

powers, and , , and are magnitudes of oscillating terms [Teo]. The oscillating

terms are signals of twice frequency of fundamental input, appearing during unbalanced

voltage. They are result of multiplying positive and negative components of voltages and

currents.

In αβ frame the active power’s magnitudes of components are expressed as:

(

)

(6.9.)

(

)

(6.10.)


94

(

)

(6.11.)

Similary, the reactive power’s magnitudes are defined as:

(

)

(6.12.)

(

)

(6.13.)

(

)

(6.14.)

In dq synchronous frame the active power’s magnitude of components are equal to:

(

)

(6.15.)

(

)

(6.16.)

(

)

(6.17.)

While the reactive power’s magnitudes are defined as:

(

)

(6.18.)

(

)

(6.19.)

(

)

(6.20.)

The average represents the energy flowing per time unity in one direction only.

The represents the oscillating energy flow per time unity, producing zero value,

representing an amount of additional power flow in the system without effective

contribution to the energy transfer. The average value of reactive power corresponds to

conventional reactive power and does not contribute to energy transfer. The oscillating

value corresponds to power being exchanged among three phases without transferring


95

any energy between source and load [Aka]. Two oscillating terms and results from

interaction of voltage and current components with different frequencies or sequences

[Teo].

6.2.2. Current Reference Calculation Strategies

In literature there are many current and power control strategies during voltage

unbalance. However, only strategies based on the instantaneous symmetrical component

theory give the most promising results under voltage unbalance. These strategies depend

on assumptions made in the control system of GCC.

Generally, to realize defined p and q power transfer, current components should be

calculated as:

[

]

[

] [

]

(6.21.)

However, as it is proved in Chapter 7, during unbalanced voltage conditions,

conventional control of instantaneous active and reactive power results in very high current

distortion. To maintain sinusoidal currents a strategy based on symmetrical components

has to be introduced.

The idea of currents’ set calculation in dq frame, proposed by [Rio1], is presented

in Fig. 6.12. The most important here is the reference current generator based on equations

(6.29-6.32). The equations are Multiply and Accumulate (MAC) operations, that could be

easily implemented in fixed point DSP platform [Roi2].

Basing on calculated components of active and reactive powers, currents can be

defined. In currents’ calculation four degrees of freedom exist, namely [

]. Four

of six power magnitudes [ ] can be controlled for given four voltage

components [

]. Hence, the current and power control can be defined in

various ways depending on chosen control strategy.

On the base of described control method, maintaining constant DC voltage and

attenuating active power oscillations [Yin], [Etx], [Suh2], [Lxu], [Rod5], [Wan2] several

studies proposed various control objectives, like:

control of the instantaneous active and reactive powers,

cancellation of active and reactive powers oscillation,


96

injection of sinusoidal balanced currents into the grid

The calculation of the currents’ set can be performed in αβ or dq frame.

PIUDC

UDC_ref

P0in

kpf

Synchronization and component

extraction

vd+, vq+, vd-, vq-

id+, iq+ Reference current

generator

Current Controller

Vαβvd

vq

id-, iq-

dqαβ

Fig. 6.12. The principle of reference currents calculation in dq frame.

6.2.3. Elimination Of Active Power Oscillations (Pconst)

The most popular strategy is providing constant instantaneous active power at the

converter output and avoiding higher harmonics in the converter current [Teo], called Pconst

strategy. Oscillations of active power can cause significant variations in converter DC-link

capacitor voltage. Therefore, form the converter point of view, it is desired to maintain

constant active power.

To achieve this goal, the proper set of current should be chosen and controlled.

There are only four degrees of freedom in controlling current components. Hence, from

among six power components, only four can be taken into consideration. In the control

algorithm providing constant active power, four power components are taken into

consideration: . The constrains and = 0 are necessary to eliminate

the oscillating components of the instantaneous active power and obtain stable DC-link

voltage [Roi1].

Two extant values are not used in reference current calculation. These

components are treated as power compensation components, which are injected to the

original power references to obtain smooth active power and sinusoidal currents.

Components and are related to the average active and reactive power regulation and

are controlled according to the original constant power references.


97

The power terms for keeping constant DC voltage are collected in following matrix

M1:

[

]

[

]

⏟

[

]

(6.22.)

Sum of the two components is denoted as P0. Q0 is the average input reactive power

exchanged with the grid [Roi3].

The currents’ set, based on certain values of active and reactive powers, is

calculated by inverting matrix M1 and following equations:

[

]

( )

[

]

⏟

[

]

(6.23.)

To solve above equation, signed minors of matrix M1 are determined as:

(

)

(

) (

) (6.24.)

(

)

(

) (

) (6.25.)

(

)

(

) (

) (6.26.)

(

)

(

) (

) (6.27.)

Basing on signed minors, a determinant of the matrix M1 is equal to:

( )

(6.28.)

Then, assuming that reference oscillatory terms are set to zero, the reference current

components are expressed as:


98

( )

(6.29.)

( )

(6.30.)

( )

(6.31.)

( )

(6.32.)

6.2.4. Elimination Of Reactive Power Oscillations (Qconst)

Similar approach presents the strategy of elimination of reactive power oscillations.

Here, the condition should be fulfill.

The power terms for eliminating reactive power oscillations are expressed as:

[

]

[

]

⏟

[

]

(6.33.)

Despite of noticeable difference between matrix M1 and M2, the calculated

determinant and signed minors are the same.

Reference current components in elimination of reactive power oscillations strategy

are expressed as:

( )

(6.34.)

( )

(6.35.)

( )

(6.36.)


99

( )

(6.37.)

6.2.5. Symmetrical Currents (Ibal)

Elimination of negative current components is the third approach to control of

instantaneous current components during unbalanced voltage conditions. In this strategy

the negative oscillating current components and

are eliminated. Hence, the reference

current components are equal to:

( )

(6.38.)

( )

(6.39.)

(6.40.)

(6.41.)

6.3. Grid Support under Unbalanced Conditions

As described in national grid coder (see Section 2.1.2), generation units connected

to the grid should generate reactive power, depending on the voltage level. The main

objective of this requirement is to support the grid with capacitive reactive power during

voltage dips. However, none of grid operators defines voltage level and reactive power in

terms of symmetrical components. It is assumed, that positive component reactive power

should be generated. Moreover, method of three-phase voltage amplitude measurement is

not defined. Considering, that majority of dips are unbalanced, it is a very important aspect

of generation unit operation.

The grid support mechanism is based on a fact, that in most cases grid impedance

has inductive character. Reactive component of the current is thus responsible for

regulation of voltage amplitude. In the scope of symmetrical components it can be noticed,

that both components of reactive current can be used:

Positive reactive power component for amplitude control,

Negative reactive power component for voltage symmetrization.


100

To fulfill grid code requirements, the generation of positive reactive power component

can be controlled by setting reference of power Q. In this way average reactive power over

a period will be maintained. However, with different instantaneous power control

strategies, different current sequences will be generated:

Balanced currents – the effect will be the same, as setting manually reference

value of iq+ current,

Constant active power – unbalanced currents and reactive power will appear at

a cost of keeping instantaneous active power constant,

Constant reactive power – reference reactive power will be tracked perfectly,

although unbalanced currents and high active power oscillations will appear.

Performance of these strategies is evaluated in the next Chapter.

6.4. Summary

This Chapter has presented control methods for GCC operating under unbalanced

voltage conditions.

Firstly, current control methods suitable to deal with negative component are

presented. Among conventional methods the best solution for current components control

in stationary frame is usage of a robust solution - proportional-resonant controllers (P-Res).

P-RES can simultaneously control both current components without additional

modifications. On the contrary, methods based solely on PI controllers (VOC) are not

suitable for operation under unbalanced conditions. Therefore, two modifications of this

method are proposed.

One of solutions to extend VOC operation to unbalanced conditions is enhancement

of PI controller with resonant path (VOC+Res), that eliminates steady state error of 2ω

component (Fig. 6.8). The second option is use of decoupled SRFs: one for positive

component and one for negative component (DDSRF) – Fig. 6.11.

Also, instantaneous power theory is combined with symmetrical components

decomposition to explain power flow under unbalanced voltage conditions. While voltage

is unbalanced, it is impossible to maintain instantaneous active and reactive power

components constant without severe distortion of current shape. Therefore, three current

reference generation strategies are presented, that maintain sinusoidal currents under

unbalanced conditions:


101

Elimination of active power oscillations (Pconst),

Elimination of reactive power oscillations (Qconst),

Balanced currents (Ibal).

These methods are also considered for reactive power generation under grid faults.

The results of simulation and experimental validation are presented in Chapter 7,

where also conclusions of the current control methods are presented.


102

7. Simulation and Experimental Results

This Chapter presents simulation and experimental results of proposed

synchronization and control methods for Grid Connected Converter (GCC) operating under

unbalanced and distorted grid voltage conditions.

The simulation and experimental verification process is divided into three parts. In

the first part of verification, current control methods are investigated. For verification

following control methods are chosen:

Synchronous reference frame - PI control (VOC),

Stationary reference frame - resonant control (P-Res),

Synchronous reference frame control with negative component controller

(VOC-Res),

Decoupled Dual Synchronous Reference Frame PI control (DDSRF).

The dynamic behavior of current control method is illustrated with step responses

to positive and negative components of current references. The disturbance rejection

capability is tested under balanced and unbalanced voltage dips.

In the second part of laboratory verification following instantaneous power control

methods are tested under unbalanced and distorted grid voltage:

Symmetrical currents strategy (Ibal),

Constant active power strategy (Pconst),

Constant reactive power strategy (Qconst).

The third part of experimental verification focuses on the grid support possibilities

of GCC under unbalanced grid voltage.

The simulation tests were carried out in Matlab Simulink environment. The

simulation conditions and parameters are described in Appendix.A.

The experimental verification was conducted in the laboratory equipped with setup

based on 15kVA NPC converter. The laboratory setup is described in Appendix B.

Note, that every test is performed with active power flowing from the converter to

the grid. It is to simulate converter-based energy sources such as wind or PV power plant.


103

During tests, PI controllers are tuned using modulus optimum criterion. Resonant

controllers are tuned to achieve the same gain as PI integral gain. Hence, the performance

of PI and Res controllers are equivalent.

7.1. Current Control Methods

7.1.1. Step Response

Step responses of positive and negative voltage components are used for

comparison of dynamic behavior of different current control methods.

In Fig.7.1, an amplitude of positive current component (10A) step is presented.

Note, that current step is always imposed in the same phase of grid voltage. Here,

experimental results of current control methods are compared to simulation results.

In this Section, all of the presented results present correct operation under balanced

voltages and currents and provide elimination of steady state error.

The best dynamic response is obtained with the VOC algorithm. It provides the

fastest response with the smallest overshoot. The P-Res current control method presents

slightly lower dynamics and higher error in both d and q current axes. It is a consequence

of lack of decoupling network in this control scheme. When the VOC-Res control scheme

is used, the overshoot is increased. It is a result of adding extra parallel resonant path,

increasing response of the controller for the step signal.

The DDSRF control method presents the slowest response among tested

controllers. A delay is introduced by a decoupling network in the feedback loop.

Improvement in DDSRF dynamics can be obtained with additional feedback from error

signals, described in [Teo].

It is also desired, that current controller minimizes a negative current component.

Therefore, tests for negative component step was also performed. Results are shown in

Fig.7.2.

The VOC presents fast response for the reference signal step, however, significant

phase and magnitude errors are observed in steady state. Very good results are obtained

using P-Res, as well as VOC-Res controllers. Both provide fast response and elimination

of steady state errors. The DDSRF provides the same dynamics for negative and positive

sequences and is the slowest of all controllers.


104

a

a.

b

b.

c

b.

d

c.

e

d.

Fig.7.1. Positive sequence step response of current controllers, left - experimental, right -

simulation : a) voltage waveform, b) VOC, c) P-Res, d) VOC-Res, e) DDSRF.

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068

-300

-200

-100

0

100

200

300

Phase v

oltages [

V]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-5

0

5

10

15

t[s]S

RF

curr

ents

[A

]

Iq

Id

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-5

0

5

10

15

t[s]

SR

F c

urr

ents

[A

]

Iq

Id

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-5

0

5

10

15

t[s]

SR

F c

urr

ents

[A

]

Iq

Id

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-5

0

5

10

15

t[s]

SR

F c

urr

ents

[A

]

Iq

Id


105

a

a.

b

b.

c

c.

d

d.

e

e.

Fig.7.2. Negative sequence step response of current controllers, left - experimental, right -

simulation: a) voltage waveform, b) VOC, c) P-Res, d) VOC-Res, e) DDSRF.

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068

-300

-200

-100

0

100

200

300

Phase v

oltages [

V]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068

-10

0

10

t[s]S

RF

curr

ents

[A

]

Iq

Id

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068

-10

0

10

t[s]

SR

F c

urr

ents

[A

]

Iq

Id

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.036 0.04 0.044 0.048 0.052 0.056 0.06 0.064 0.068

-10

0

10

t[s]

SR

F c

urr

ents

[A

]

Iq

Id

0.056 0.06 0.064 0.068 0.072 0.076 0.08 0.084 0.088-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.056 0.06 0.064 0.068 0.072 0.076 0.08 0.084 0.088

-10

0

10

t[s]

SR

F c

urr

ents

[A

]

Iq

Id


106

7.1.2. Disturbance Rejection

Converter current controllers must be able to operate properly under disturbed

voltage conditions. The most critical situations is voltage dips appearance, when voltage

magnitude changes suddenly. Thus, presented controllers are verified for the case of

balanced and unbalanced voltage dips. In the experiment, controllers are supposed to

maintain 10A magnitude positive component current under voltage distortions.

First test is a response to 80% symmetrical voltage dip. Due to laboratory

equipment limitations, voltage dips appear in different point of voltage waveform. This,

however does not influence dynamics of the controllers and SRF current waveforms. The

representative experimental voltage waveform is presented in Fig.7.3a. Respective

simulation results, that are conducted in repeatable conditions, present high convergence

with experiment.

Again, VOC presents the best dynamics of disturbance rejection. The response is

characteristic for PI controller. The behavior of P-Res and VOC-Res controllers is similar

– after fast rejection of current overshoot, some error remains during half of period. In the

DDSRF current error also remains for a longer period, however, a current overshot is the

smallest among tested control schemes.

Next test illustrates response of controllers to unbalanced voltage dip with a

negative voltage component. A single phase 60% voltage dip is imposed, as shown in

Fig.7.4a. It is seen, that voltage measured in the experiment presents amplitude reduction

in all phases. It is caused by measurement method, where neutral point of the grid is not

connected with neutral point of the voltage measurement circuit.

Under unbalanced conditions, the VOC behavior is not satisfactory. PI controller is

not able to achieve zero error in steady state under unbalanced voltage. It results in highly

unbalanced currents.

All of other controllers are able to compensate for voltage unbalance. Again P-Res

and VOC-Res controllers present similar dynamics with fast rejection of first overshoot

and long “tail”. The DSRF compared to these methods provides better attenuation of first

overshoot, resulting in fastest rejection of voltage disturbance.


107

a

a.

b

b.

c

c.

d

d.

e

e.

Fig.7.3. Balanced voltage dip response of current controllers, left - experimental, right -

simulation: a) voltage waveform, b) VOC, c) P-Res, d) VOC-Res, e) DDSRF

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108

-300

-200

-100

0

100

200

300

Phase v

oltages [

V]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-10

0

10

20

t[s]S

RF

curr

ents

[A

]

Iq

Id

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-10

0

10

20

t[s]

SR

F c

urr

ents

[A

]

Iq

Id

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-10

0

10

20

t[s]

SR

F c

urr

ents

[A

]

Iq

Id

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-10

0

10

20

t[s]

SR

F c

urr

ents

[A

]

Iq

Id


108

a

a.

b

b.

c

c.

d

d.

e

e.

Fig.7.4. Unbalanced voltage dip response of current controllers, left - experimental, right -

simulation: a) voltage waveform, b) VOC, c) P-Res, d) VOC-Res, e) DDSRF.

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108

-300

-200

-100

0

100

200

300

Phase v

oltages [

V]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-10

0

10

20

t[s]S

RF

curr

ents

[A

]

Iq

Id

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-10

0

10

20

t[s]

SR

F c

urr

ents

[A

]

Iq

Id

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-10

0

10

20

t[s]

SR

F c

urr

ents

[A

]

Iq

Id

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.076 0.08 0.084 0.088 0.092 0.096 0.1 0.104 0.108-10

0

10

20

t[s]

SR

F c

urr

ents

[A

]

Iq

Id


109

7.1.3. Influence of PLL

All of the results presented above are conducted with the DSOGI-PLL algorithm

synchronizing to positive component of the grid voltage. In this way active and reactive

current components are controlled properly and no distortions appear during voltage dips,

as it was presented in Chapter 5. To illustrate influence of PLL on current controller, tests

are performed with different synchronization algorithms.

Fig.7.5 presents performance of the VOC-Res algorithm with applied different PLL

algorithms. In the test, constant current reference of 10A magnitude is set.

In PLL algorithms the intensity of distortion in generated phase angle depends on

PI controller gains. When distortion is carried from grid voltage to generated phase angle,

the current unbalance and deterioration of waveform appear even if particular current

controller is capable to operate under unbalance.

Based on tests, it can be noticed, that SRF-PLL algorithms cause high distortions of

phase angle during voltage dips. Slowing down the PI controller, reduces distortion

significantly, although distortion is still clearly noticed. Both PLL algorithms with

component extraction – DSOGI and DSRF – provide appropriate synchronization with

positive component. They both generate stable phase angle, that does not introduce

distortions to current control algorithm.


110

a.

b.

c.

d.

e.

Fig.7.5. Unbalanced voltage dip response of current controllers: a) voltage waveform, b)

SRF-PLL fast, c) SRF-PLL slow, d) DSOGI-FLL, e) DSRF-PLL.

0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-400

-300

-200

-100

0

100

200

300

400

Phase v

oltages [

V]

0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-4

-2

0

2

4

Phase a

ngle

[ra

d]

0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-4

-2

0

2

4

Phase a

ngle

[ra

d]

0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-4

-2

0

2

4

Phase a

ngle

[ra

d]

0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12-4

-2

0

2

4

Phase a

ngle

[ra

d]


111

7.2. Instantaneous Power Control

Current reference generation methods, presented in Section 6.2, allow realization of

different control strategies under unbalanced conditions. Here, in this Section three

presented methods are compared under unbalanced voltage dips.

Fig.7.5 presents results of power control strategy during 60% single-phase voltage

dip, and Fig.7.6 presents 70% two-phase voltage dip. During both dips the negative

voltage component appears.

For the tests the DDSRF current controller was used. The GCC is operated at unity

power factor with a goal to maintain average active power at a constant level (Pconst).

In symmetrical balanced currents strategy (Ibal), currents are symmetrical even

under voltage unbalance (Fig.7.5a, Fig.7.6a), oscillating term at 2ω appears in both active

and reactive power. Note, to maintain the same power under reduced voltage, current

magnitude must be increased.

The Pconst strategy enables elimination of active power oscillations. To do so,

negative current component is generated in such way, that current magnitude in faulted

phases is increased. In this case instantaneous reactive power oscillations are increased.

However, it has no negative impact on the system in a physical way.

In the Qconst strategy, reactive power oscillations are eliminated. In contrary to

previous method it increases oscillations of active power. This is disadvantageous for

converter, because it induces high oscillations in DC-link voltage. With Qconst strategy,

currents in faulted phases are reduced.

Due to existence of negative voltage component, current magnitudes are increased

in particular phases. This requires special care in order not to damage converter’s

semiconductor switches and can cause problems with automatic protection devices.

Therefore, converter control algorithm should be equipped with functions, that monitor and

limit maximal current amplitude [Teo]. Appearance of unbalanced currents during grid

faults should be also considered in switchgear design.


112

a

a.

b

b.

c

c.

d

d.

Fig.7.6. Power control under single-phase voltage dip: a) voltage waveform, b)

symmetrical, c) constant P, d) constant Q.

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-400

-300

-200

-100

0

100

200

300

400

Phase v

oltages [

V]

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-5000

0

5000

10000

t[s]

Insta

nta

neous p

ow

er

Q

P

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-5000

0

5000

10000

t[s]

Insta

nta

neous p

ow

er

Q

P

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-5000

0

5000

10000

t[s]

Insta

nta

neous p

ow

er

Q

P


113

a

a.

b

b.

c

c.

d

d.

Fig.7.7. Power control under two-phase voltage dip: a) voltage waveform, b) symmetrical,

c) constant P, d) constant Q.

7.3. Grid Support

Reactive power generation is one of the most important tasks required by system

operators during voltage dips. Therefore, tests were performed to verify influence of GCC

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-400

-300

-200

-100

0

100

200

300

400

Phase v

oltages [

V]

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-5000

0

5000

10000

t[s]

Insta

nta

neous p

ow

er

Q

P

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-5000

0

5000

10000

t[s]

Insta

nta

neous p

ow

er

Q

P

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-15

-10

-5

0

5

10

15

Phase c

urr

ents

[A

]

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115-5000

0

5000

10000

t[s]

Insta

nta

neous p

ow

er

Q

P


114

instantaneous power control strategies on the grid voltage during fault. For these test the

grid impedance was set to 5mH, to be able to observe influence of reactive power on the

grid voltage. During test the reference of reactive power is set to 5kVA capacitive. Results

of the simulation for single- and two-phase voltage dips are presented in Fig.7.8 and

Fig.7.9. In the tests, three instantaneous power control strategies are consequently switched

on:

Constant active power Pconst (0.04 – 0.08s);

Symmetrical currents Ibal (0.08 – 0.12s),

Constant reactive power Qconst (0.012 – 0.016s).

In Fig.7.8 and Fig.7.9. the influence of control strategies on grid voltage can be

seen. Note, that all of the strategies have similar influence on modulus of grid voltage

positive component. However, different influence on voltage unbalance of modulus of

negative voltage component |U-| can be observed. With reference to the symmetrical

current generation, the constant active power strategy Pconst has property of decreasing

negative component, while constant reactive power strategy Qconst increases negative

component.

These results were confirmed experimentally with use of a power quality analyzer,

described in Appendix B. Results of measurement are presented in Fig.7.10. Conditions in

the experiment were different, than simulation. Grid inductance was 2mH and reactive

power was set at 3kVA. Conclusions drawn from simulation are confirmed in the

laboratory test. With respect to symmetrical current generation:

Pconst strategy decreases voltage unbalance,

Qconst strategy increases voltage unbalance.

It is a consequence of current reference generation strategies. In constant active

power strategy Pconst, current is increased in faulted phases. Therefore, reactive current in

faulted phase is increased, providing stronger support for the faulted phase. Constant

reactive power strategy Qconst does the opposite – current is reduced in faulted phases.


115

Fig.7.8. Grid support during 80% single-phase voltage dip.

Fig.7.9. Grid support during 50% two-phase voltage dip.

0.04 0.06 0.08 0.1 0.12 0.14 0.16-400

-200

0

200

400

Phase v

oltages [

V]

0.04 0.06 0.08 0.1 0.12 0.14 0.16-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.04 0.06 0.08 0.1 0.12 0.14 0.1650

100

150

200

250

300

t[s]

Voltage c

om

ponents

[V

]

|U+|

|U-|

0.04 0.06 0.08 0.1 0.12 0.14 0.16-5000

0

5000

10000

t[s]

Insta

nta

neous p

ow

er

Q

P

0.04 0.06 0.08 0.1 0.12 0.14 0.16-400

-200

0

200

400

Phase v

oltages [

V]

0.04 0.06 0.08 0.1 0.12 0.14 0.16-20

-10

0

10

20

Phase c

urr

ents

[A

]

0.04 0.06 0.08 0.1 0.12 0.14 0.16

50

100

150

200

250

t[s]

Voltage c

om

ponents

[V

]

|U+|

|U-|

0.04 0.06 0.08 0.1 0.12 0.14 0.16

-2000

0

2000

4000

6000

8000

t[s]

Insta

nta

neous p

ow

er

Q

P


116

a.

b.

c.

d.

Fig.7.10. Grid support during 80% single phase dip: a) no reactive power, b) symmetrical

currents, c) P const, d) Q const.


117

7.4. Summary

In this Chapter several Grid Connected Converter (GCC) control algorithms based

on the symmetrical components theory are verified in simulation and in the laboratory

model.

Current controllers were evaluated and compared in various scenarios. Results are

summarized in Tab.7.1. Among tested algorithms only conventional VOC was not able to

operate properly under unbalanced conditions. Both algorithms equipped with resonant

controllers (P-Res and VOC-Res) tend to have very similar dynamic behavior. The

DDSRF is characterized with slowest response to reference value steps, but the fastest

rejection of grid voltage disturbances. However, it was reported in [Teo], that the DDSRF

dynamics can be improved with feedforward of current error.

Tab.7.1. Comparison of current controllers.

Positive

component

step

Negative

component

step

Balanced

voltage dip

Unbalanced

voltage dip

Complexity

VOC ++ - + -- ++

P-Res + + + + +

VOC-Res + + + + +

DDSRF - - ++ ++ -

Also strong influence of PLL on controllers performance is observed. Algorithms

implemented in SRF require undisturbed phase angle to generate high quality current.

During voltage dips only algorithms with component extraction can provide proper

synchronization.

Instantaneous power control strategies were verified, and proved correctness of

current reference generation methods. Pconst and Qconst methods allow to eliminate

oscillations of chosen power component at cost of unbalanced currents. If the current

unbalance is not acceptable, it is possible to use Ibal strategy at a cost of active and reactive

power oscillations.

In author opinion Pconst strategy is the best solution for converter control because of

following observations:

Pconst maintains constant instantaneous active power. It is advantageous for power

converter, because DC-link voltage oscillations caused by unbalanced grid voltage

are eliminated, allowing for reduction of DC-link capacitance,


118

In the strategy maintains sinusoidal currents,

If grid support by reactive power strategy Qconst is performed, negative component

reactive power is injected to maintain constant active power. This fact increases

reactive current magnitude in faulted phases, which constitutes to grid voltage

balancing.

The performance of different instantaneous power control strategies is summed up

in Tab.7.2. Hence, it can be concluded, that constant active power strategy is advantageous

both from grid and converter point of view. It assures stabilization of converter DC-link

voltage and provides grid support with a property of voltage balancing.

Tab.7.2. Comparison of instantaneous power control methods.

DC voltage

variations

Grid

support

Overcurrent Complexity

Ibal - + + +

Pconst + ++ - -

Qconst -- - - -

Finally, choice of the current control algorithm and PLL depends on selected

reference frame. It is natural to combine DSOGI-FLL with P-Res controller in stationary

frame and DSRF-PLL with VOC-Res or DDSRF controllers in rotating frame. It has to be

noted, that implementation of control in stationary reference frame requires less

computational effort. This application does not require coordinate transformation,

therefore, even calculation of phase angle is not necessary.

In low power applications, where fault ride through and grid support is not critical

and DC-link capacitance is relatively big, resonant controllers with balanced current

strategy might be sufficient solutions.

However, in applications with significant power, mainly in converter based

renewable sources, control strategies under unbalanced conditions become critical. The

computational effort for full implementation of control methods based on symmetrical

components is very high, when compared to conventional methods. However, it can bring

many advantages for converter, as well as for the grid system. Since cost of

microcontroller computational power is becoming lower, it is worth to invest in advanced

instantaneous power control algorithms.


119

8. Summary and Final Conclusions

The Thesis presents comprehensive analysis of solutions dedicated for

synchronization and control of Grid Connected Converter (GCC) operating under

unbalanced grid voltage. The issue was undertaken due to rapidly growing penetration of

RES, especially wind farms, into the power system and power system operators

requirements of uninterrupted operation of RES during grid voltage variations.

Conventional synchronization and linear current control solutions dedicated for

GCC struggle with improper operation during unbalanced voltage dips. The biggest

problem for proper GCC operation is appearance of oscillations at double grid frequency,

which are particularly dangerous due to destabilization of control system and, as

consequence, transporting of distortions to the power system.

To solve the problem, the instantaneous symmetrical component theory was

employed. Furthermore, for power flow control, the instantaneous power theory was used.

Based on mathematical equations derived from the theories synchronization, current and

power control strategies are presented for improvement of GCC operation with unbalanced

voltage. The aim of the Thesis was to verify that only application of control methods based

on the instantaneous symmetrical components theory guarantees proper operation of GCC

during unbalanced voltage dips.

The author contribution into development of GCC control under unbalanced

voltage conditions concern:

Analysis of the instantaneous symmetrical components theory in the context of

synchronization and control of GCC (Chapter 4);

Analysis of Polish Grid Code in terms of requirements definition for GCC

interfaced with RES (Chapter 2.3);

Thorough analysis, selection and experimental verification of control methods for

GCC based on the instantaneous symmetrical component theory (Chapters 6.2, 7);

Analysis and mathematical calculation of power control strategies based on the

instantaneous power theory and instantaneous symmetrical component theory

(Chapter 6.2) ;

Development of simulation model GCC operating under unbalanced grid voltage

conditions in Matlab/Simulink environment (Chapters 5, 6);

Laboratory verification of simulation results (Chapter 7).


120

Author defined three areas of GCC control algorithm, which are the most sensitive

to negative sequence voltage component:

Synchronization algorithm,

Current control algorithm,

Power control algorithm.

To solve the problem author formulated thesis, that GCC algorithm should be

equipped with instruments based on the symmetrical component theory to improve GCC

operation during negative component existence.

Proper GCC synchronization, realized by Phase Locked Loop algorithms, is

especially problematic during voltage unbalance. Author claims that PLL should provide

voltage symmetrical component extraction to mitigate the influence of voltage unbalance

by synchronizing with positive component component. In the Thesis two types of

synchronization algorithms, directly based on the instantaneous symmetrical component

theory, were chosen for analysis and verification:

DSOGI, operating in stationary reference frame;

DSRF, operating in synchronous rotating frame.

As shown in Section 5.6, both algorithms provide almost identical results, due to

application of the same theory in different reference frames. When compared to

conventional SRF-PLL, phase angle during unbalance is almost free of disturbance. During

verification, a strong influence of PLL on controllers performance was observed (Fig. 7.5).

In conventional SRF-PLL structure the negative voltage component introduces oscillations

that significantly increase current unbalance and deteriorate its waveform. Proposed

algorithms, that extract symmetrical components and synchronize with positive component

do not introduce such distortions.

Symmetrical components theory should also be applied to GCC current control. As

author proved in Chapter 7, conventional current control methods based solely on PI

controllers (VOC) are not suitable for operation under unbalanced conditions. Therefore,

two modifications of the VOC method are described and verified. One of solutions to

extend VOC operation to unbalanced conditions is enhancement of PI controller with

resonant path (VOC+Res), that controls negative component in SRF. The second option is

use of decoupled SRFs: one for positive component and one for negative component.

Among conventional control methods the best solution for positive and negative current


121

components control in stationary frame is usage of a robust solution: proportional-resonant

controllers (P-Res). The P-RES can simultaneously control both current components

without additional modifications. Different current control methods were compared in Tab.

7.1. Here, the best performance under voltage unbalance is guaranteed by DDSRF control

algorithm (Fig. 7.4).

Negative voltage components is also highly problematic for power flow control.

Voltage unbalance causes oscillations to instantaneous active and reactive power. While

voltage is unbalanced, it is impossible to maintain instantaneous active and reactive power

at a constant level without severe distortion of current shape. To solve this issue, equations

calculated from theories (6.22-6.41) were employed for current reference generation, used

in three proposed power flow control strategies designed to operate under unbalance:

Elimination of active power oscillations (Pconst),

Elimination of reactive power oscillations (Qconst),

Balanced currents (Ibal).

Instantaneous power control strategies were verified (see Tab. 7.2), and correctness

of current reference generation methods was proved. In author’s opinion, the best solution

for GCC control is Pconst strategy because of following observations:

Pconst maintains constant instantaneous active power. It is advantageous for power

converter, because DC-link voltage oscillations caused by unbalanced grid voltage

are eliminated, allowing for reduction of DC-link capacitance,

The strategy maintains sinusoidal currents,

If grid support by reactive power strategy with Pconst is performed, a negative

current component is injected to maintain constant active power. This fact increases

reactive current magnitude in faulted phases, which constitutes to grid voltage

balancing.

Hence, it can be concluded, that constant active power strategy is advantageous

both from grid and converter point of view. The strategies are not applied in actual

industrial GCC solutions and comprise vision of future requirements, which in author

opinion will be demanded by transmission and distribution system operators.


122

In author’s opinion the thesis formulated in Chapter 1 has been proven and

verified in simulation and experimental validation. Synchronization and control

methods based on symmetrical components provide superior performance to

conventional control methods. Based on conducted research author claims that:

PLL methods based on symmetrical components can provide

synchronization with unbalanced voltage, assuring high dynamics and

very good rejection of disturbance,

DDSRF current control method with independent control of both

current component provides the best disturbance rejection among

tested algorithms,

Instantaneous power control methods based on symmetrical

components are able to eliminate oscillating components of active or

reactive power.

Combination of abovementioned algorithms can provide sinusoidal currents

during unbalanced conditions and at the same time realize chosen power flow control

strategy.

The final choice of the current control algorithm and PLL should depend on

preferred reference frame. It is natural to combine DSOGI-FLL with P-Res controller in

stationary frame and DSRF-PLL with VOC-Res or DDSRF controllers in synchronous

rotating frame. Implementation of control in stationary reference frame requires less

computational effort than in SRF. This application does not require coordinates

transformation, therefore, even calculation of phase angle is not necessary and can be

successfully applied to every GCC.

It has to be noted, that presented symmetrical component extraction algorithms

(DSOGI or DSRF) are essential for calculation of current reference in instantaneous power

control strategies. On the contrary, current control method can be freely chosen by the

system designer, as long as its dynamics are sufficient to control negative component.

The disadvantage of presented algorithms is higher computational effort, when

compared to conventional methods. However in applications with significant power,

mainly in converter based RES, control strategies under unbalanced conditions become

critical, even if computational effort for full implementation of control methods based on

symmetrical components is very high, when compared to conventional methods. Since cost


123

of microcontroller computational power is becoming lower, it is worth to invest in

advanced instantaneous power control algorithms. Implementation of advanced control

methods based on symmetrical components can bring many advantages for converter, as

well as for the grid.

One has to keep in mind, that proposed constant power methods result in

unbalanced currents. It can cause some problems with the protection devices. If current

unbalance is not acceptable, it is possible to use Ibal strategy at a cost of active and reactive

power oscillations.

The Polish Grid Code (GC) contains definition of requirements for GCC interfacing

with wind turbine concerning operation under voltage dips and grid support. However, in

author opinion the Polish GC is still incomplete. There is significant lack of specification

concerning wind turbine operation during unbalanced voltage. Especially, the grid support

during unbalanced dips is not defined. According to the current situation of the Polish

power system and future legislation plans, it is sure that demands for power quality

generated by wind farms and their support to the power system will be restricted, what is

associated with next requirements for GCC. In author opinion, next requirements will

concern different control strategies of active grid support during voltage variations,

especially unbalance. Hence, the contribution of the Thesis is sort of indication of future

solution, which should be applied to GCC interfacing RES to fulfill grid operator

requirements.


124

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List of Author’s Publications during Ph.D. Study

[1] M. Bobrowska-Rafał, K. Rafał i M. P. Kaźmierkowski, „Zapady napięcia – kompensacja przy zastosowaniu

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2012

[2] M. Bobrowska-Rafał, K. Rafał, M. Jasiński, M.P. Kaźmierkowski, “Grid Synchronization and Symmetrical

Components Extraction with PLL Algorithm for Grid Connected Power Electronic Converters – A Review”,

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[3] K. Rafał, M. Bobrowska-Rafał, M. Jasiński, „Sterowanie przekształtnikiem AC-DC-AC elektrowni wiatrowej z

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[7] B. Cougo, G. Gateu, T. Meynard, M. Bobrowska-Rafal, M. Cousineau, “PD Modulation Scheme for Three-

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[8] M. Bobrowska-Rafał, K. Rafał, S. Piasecki, M. Jasiński, „Resonant Controller for Higher Harmonics

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[10] P. Zielonka, M. Jasiński, M. Bobrowska-Rafał, A. Sikorski, „Sterowanie przekształtnika sieciowego AC-DC

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[11] G. Wrona, M. Jasiński, M. Kaźmierkowski, M. Bobrowska-Rafał, M. Korzeniowski, „Procesory

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[12] Krzysztof Rafał, Małgorzata Bobrowska-Rafał, „Synchronization of Three-Phase PWM Rectifiers with

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PWM Rectifiers with Unbalanced and Distorted Grid Voltage”, PhD Students and Young Scientists

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[15] Marek Jasinski, Marian P. Kazmierkowski, Malgorzata Bobrowska-Rafal, "AC-DC-AC Converter with Grid

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132

Appendix

A. Experimental Setup

The laboratory studies were carried out in laboratory of Control and Industrial

Electronics at Warsaw University of Technology. In experimental verification was used the

laboratory setup, built and improved by Ph.D. Sebastian Synski and M.Sc. Krzysztof

Rafal, in details described in Ph.D thesis [Sty], [Raf].

The scheme of laboratory setup, presented in Fig. A.1, which consists of:

NPC grid-connected converter with LCL filter,

Programmable voltage source,

Separation transformer,

Resistive load.

Programmable Source

LCL filter

Grid Side Converter

Resistance

Transformer

PCC

Measurements Energy storage

DC link

Fig. A.1. Scheme of laboratory setup.

The system is controlled by a dSPACE based control circuit. Measurements

equipment is connected at the PCC.

In tests a multilevel NPC converter (15kVA) was used, based on using 2MBI75S-

120 IGBT modules delivered by Fuji Electric. The converter, presented in Fig. A.2.a, is

connected to grid via LCL filter. The converter parameters are presented in Tab.A.1.


133

Tab.A.1. Parameters of three-level NPC converter.

Parameter Symbol Value

Rated voltage Un 3x400V

Rated power Sn 15kVA

Switching frequency fs 5kHz

Deadtime td 2μs

Grid filter Lg/C/Lc 2,2mH / 6μF / 2,8mH

DC-link capacitance Cdc 2200μF

a.

b.

Fig. A.2. View of a. Three-level NPC converter experimental stage; b. Programmable voltage source and

separating transformer.

To simulate grid voltage distortions, a California Instruments 15003ix, three-phase

programmable voltage source is employed. The source, presented in Fig.A.2b, composed

of three independent modules (5001ix), which generate three-phase voltage of desired

waveform. Parameters of the programmable source are presented in Tab.A.2.

During tests, the bidirectional power flow was ordered. Hence, to the DC link a DC

energy storage was connected. As energy storage a supercapacitor was employed (75V,


134

96F). To the source a resistance bank was connected to overcome problem of

unidirectional power flow of the source. To the resistive load of 7.5kW, active power can

be controlled by conditioner in ±7.5kW range. For safety reasons, the programmable

source is connected to the converter via 1:1 separation transformer (Yy). Ratings of the

transformer are given in Tab.A.3.

Tab.A.2. Parameters of programmable source.


Voltage range Un 0-400V

Rated current In 18.5A

Resistance range Rk 0,016-1Ω

Inductance range Lk 0,084-1mH

Tab.A.3. Parameters of separation transformer.

Parameter Symbol Primary

value

Secondary

value

Rated voltage Un 3x400V 3x400V

Rated current In 14.4A 14.4A

Winding resistance Rt 0,43Ω 0,51Ω

Leakage inductance Lt 0,87mH 0,91mH

The system is controlled by a dSPACE DS1005 modular system based PowerPC

750GX processor running at 1GHz. Peripheral devices include:

• DS2003 Multi-Channel A/D Board for analog to digital conversion,

• DS2101 D/A Board for control of external equipment and view of control signals,

• DS5101 Digital Waveform Output Board for outputting PWM signals.

The dSPACE control system is controlled from a PC using ControlDesk

application. Control algorithms are written in C++ code and downloaded to the processor

using dSPACE compiler.

Currents and voltages in the power circuit are measured using sensors:

LEM LV25 for all voltages,


135

LEM LA55 for converter currents,

LEM LA200 for supercapacitor current.

Measured values are given to the A/D board via Burr Brown ISO124P isolating

amplifiers. Current control loop uses measurement at a grid side of the filter.

For measuremen, following equipement was used:

Fluke 434 Power Quality Analyzer

Tektronix TDS3034B Digital Phosphor Oscilloscopes

Tektronix A622 current probes

o AC-DC measuring range from 50mA to 100A;

o AC-DC measuring frequency: up to 100kHz;

Elditest GE8100 Differential voltage probes

o AC-DC measuring range x200: 700V;

o AC-DC measuring range x20: 70V.

B. Simulation Setup

The simulation tests was carried out in Matlab/Simulink environment.

For the verification two different simulation models were created for the purpose of

verification of described algorithms.

The first model is designed to test and compare different PLL algorithms. It is

equipped with programmable voltage source able to simulate various voltage distortions

including amplitude, frequency and phase angle steps and others. Presented PLL

algorithms are implemented in a function block as a C code executed with fixed frequency

of 5kHz. Estimated values of voltage symmetrical components and phase angle are

compared on the scopes. The model is implemented in per unit notation (nominal

amplitude is equal to 1).


136

Fig. A.3.Simulation model for PLL algorithms testing.

Second model is built to verify control structures f converter, presented in Fig.A.4.

It contains three-level Neutral Point Clamped converter connected to the grid through an

LCL filter. Basic parameters of the model are presented in Tab.A.4. DC-link of the

converter is connected to the DC voltage source. This model is also equipped with

programmable voltage source used to generate unbalanced voltage dips.

Converter switches are controlled with Space Vector Modulation technique.

Current and power controllers are implemented in function block as a C code. This

technique is very convenient, because tested code can be later easily transferred to a DSP

controller used in the laboratory setup.

Tab.A.4. Parameters of separation transformer.


Rated voltage Un 3x400V

Rated power Sn 15kVA

Switching frequency fs 5kHz

Grid filter Lg/C/Lc 2,2mH / 6μF / 2,8mH


137

Fig. A.4. Simulation model of GCC for control algorithms testing.


138

List of Important Symbols

[A] Symmetrical component transformation matrix

[S] Symmetrical component transformation matrix for instantaneous values

[Tdq] Park’s transformation matrix

[Tαβ] Clark’s transformation matrix

a Fortesque’s operator

Es Source voltage

fbr Maximum value of frequency, when a wind farm must be disconnected

from the grid system

fmax Maximum value of frequency, when generated wind power is equal to zero

fmin Minimum value of frequency, when wind active power control reacts

fn Nominal value of grid frequency

I Current magnitude

i(t) Sinusoidal time function of current

j Complex number

k Damping factor of SOGI filter

Kp Proportional gain of PI controller

P Active power

Plt Long-term fluctuation coefficient

Pst Short-term fluctuation coefficient

Q Reactive power

q Time delay operator of 900

Qmax_dr Maximum level of drawn by wind farm reactive power

Qmax_gen Maximum level of generated by wind farm reactive power

s Relative change of frequency due to relative change of wind active power

S Apparent power

T∑ Sum of small time constants of PI controller

Tc Time constant of converter

Ti Integral gain of PI controller

Tp Time constant of DSOGI filter

Tr Large time constant of PI controller

Ts Sampling time of converter

uf Average frequency error of DSOGI filter

Umax Minimum level of voltage in PCC, when reactive power is drawn


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Umin Minimum level of voltage in PCC, when reactive power is generated

Ur Range of reference voltage in PCC

Uth1 Threshold value of voltage under which generation of reactive power is

required

Uth2 Threshold value of voltage above which drawn of reactive power is

required

V Voltage magnitude

v Voltage in time domain

v(t) sinusoidal time function of voltage

Vdip voltage during the dip

Phasor of voltage

Zf Impedance between PCC and point of short-circuit

Zs Impedance of source Es

α Lyon’s operator

φ The displacement angle between and

φ Phase angle of grid voltage

φI Initial phase angle of current

φV Initial phase angle of voltage

Phase angle during voltage dip

ω angular frequency

ω' Resonant frequency of SOGI filter


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List of Abbreviations

APF Active Power Filter

ASD Adjustable Speed Drive

CE Component Extraction

CUPS Custom Power System

DC Decoupling Cell

DDSRF Decoupled Dual Synchronous Reference Frame

DPC Direct Power Control

DSO Distribution System Operators

DSOGI Dual Second Order Generalized Operator

DSRF Dual Synchronous Reference Frame

DVR Dynamic Voltage Restorer

ENTSO-E European Network Of Transmission Systems Operators Of

Electricity

FACTS Flexible AC transmission System

FLL Frequency Locked Loop

FRT Fault Right Through

GC Grid Code

GCC Grid Connected Converter

IEC International Electrotechnical Commission

IEEE Institute of Electrical and Electronics Engineers

ITSE Integral of time multiplied by square error

LF Loop Filter

LPF Low Pass Filter

LVRT Low Voltage Ride Through

PCC Point Of Common Coupling

PD Phase Detector

PLL Phase Locked Loop

PNSC Positive-Negative Sequence Extraction

PWM Pulse Width Modulation

RES Renewable Energy Sources

SOGI Second Order Generalized Operator

SRF Synchronous Rotating Frame

SSSC Static Series Synchronous Compensator


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STATCOM Static Synchronous Compensator

SVM Space Vector Modulation

THD Total Harmonic Distortion

TSO Transmission System Operator

UCTE Union For The Coordination Of Transmission Of Electricity

UPS Uninterruptible Power Supply

VCO Voltage Controlled Oscillator

VOC Voltage Oriented Control


WARSAW UNIVERSITY OF TECHNOLOGY · Inverter”, industrial project for Liebherr-Aerospace Toulouse...

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Transcript of WARSAW UNIVERSITY OF TECHNOLOGY · Inverter”, industrial project for Liebherr-Aerospace Toulouse...