Control of Grid Integrated Voltage Source Converters under Unbalanced Conditions

Jon Are Suul Control of Grid Integrated Voltage Source Converters under Unbalanced Conditions Develoment of an On-line Frequency-adative Virtual Flux-based Aroach Thesis for the degree of Philosohiae Doctor Trondheim, March Norwegian University of Science and Technology Faculty of Information Technology, Mathematics and Electrical Engineering Deartment of Electric Power Engineering

NTNU Norwegian University of Science and Technology Thesis for the degree of Philosohiae Doctor Faculty of Information Technology, Mathematics and Electrical Engineering Deartment of Electric Power Engineering Jon Are Suul ISBN 978-8-47-3455-9 (rinted ver.) ISBN 978-8-47-3457-3 (electronic ver.) ISSN 53-88 Doctoral theses at NTNU, :9 Printed by NTNU-trykk

Abstract Three-Phase Voltage Source Converters (VSCs) are finding widesread alications in grid integrated ower conversion systems. The control systems of such VSCs are in an increasing number of these alications required to oerate during voltage disturbances and unbalanced conditions. Control systems designed for grid side voltagesensor-less oeration are at the same time becoming attractive due to the continuous drive for cost reduction and increased reliability of VSCs, but are not commonly alied for oeration during unbalanced conditions. Methods for voltage-sensor-less grid synchronization and control of VSCs under unbalanced grid voltage conditions will therefore be the main focus of this Thesis. Estimation methods based on the concet of Virtual Flux, considering the integral of the converter voltage in analogy to the flux of an electric machine, are among the simlest and most well known techniques for achieving voltage-sensor-less grid synchronization. Most of the established techniques for Virtual Flux estimation are, however, either sensitive to grid frequency variations or they are not easily adatable for oeration under unbalanced grid voltage conditions. This Thesis addresses both these issues by roosing a simle aroach for Virtual Flux estimation by utilizing a frequency-adative filter based on a Second Order Generalized Integrator (SOGI). The roosed aroach can be used to achieve on-line frequency-adative varieties of conventional strategies for Virtual Flux estimation. The main advantage is, however, that the SOGI-based Virtual Flux estimation can be arranged in a structure that achieves inherent symmetrical comonent sequence searation under unbalanced conditions. The roosed method for Virtual Flux estimation can be used as a general basis for voltage-sensor-less grid synchronization and control during unbalanced conditions. In this Thesis, the estimated Virtual Flux signals are used to develo a flexible strategy for control of active and reactive ower flow, formulated as generalized equations for current reference calculation. A simle, but general, imlementation is therefore achieved, where the control objective and the ower flow characteristics can be selected according to the requirements of any articular alication. Thus, the same control structure can be used to achieve for instance balanced sinusoidal currents or elimination of double frequency active ower oscillations during unbalanced conditions. In case of voltage sags, current references corresonding to a secified active or reactive ower flow might exceed the current caability of the converter. The limits for active and reactive ower transfer during unbalanced conditions have therefore been analyzed, and generalized strategies for current reference calculation when oerating under current limitations have been derived. The secified objectives for active and reactive ower flow characteristics can therefore be maintained during unbalanced grid conditions, while the average active and reactive ower flow is limited to kee the current references within safe values. All concets and techniques roosed in this Thesis have been verified by simulations and laboratory exeriments. The SOGI-based method for Virtual Flux estimation and the strategies for active and reactive ower control with current limitation can also be easily adated for a wide range of alications and can be combined with various tyes of inner loo control structures. Therefore, the roosed aroach can otentially be used as a general basis for Virtual Flux-based voltage-sensor-less oeration of VSCs under unbalanced grid voltage conditions. Jon Are Suul i

Keywords: Grid Synchronization, Voltage-sensor-less Oeration, Virtual Flux Estimation, Unbalanced Grid Voltage Conditions, Grid Frequency Variations, Active and Reactive Power Control, Current Limitation ii NTNU

Preface This Thesis resents the main results from my time as a PhD student at the Deartment of Electric Power Engineering at NTNU, funded by an oen grant from the Faculty of Information Technology, Mathematics and Electrical Engineering. I am grateful to NTNU for roviding such an oortunity to freely ursue technical and academic toics. My suervisor at the Deartment of Electric Power Engineering during the grant eriod has been Professor Tore Undeland. During these years of studies, I have enjoyed technical discussions and cooeration with fellow students and researchers, both at the Deartment and other institutions, which have been the source of valuable learning and interesting exeriences both in life and science. Esecially Professor Marta Molinas, who was a ost doc. researcher at the Deartment when we first worked together, has been a continuous insiration in striving for academic and scientific ideals. She has been always resent to give hel and advices, and to oint me in a good direction when facing critical moments. My closest family and friends have also been a continuous suort. During my studies, I have been working on several toics and considered several lines of research. Some of the attemted efforts have shown interesting imlications, and have been documented by ublications. In most cases, the ossibilities for achieving relevant and significant results in the context of this Thesis have, however, been out of reach within the timeframe of my studies. The breakthrough with resect to rearing this Thesis came after I was invited by Professor Pedro Rodríguez to visit his research grou on Renewable Electrical Energy Systems (REES) at the Technical University of Catalonia (UPC) in Terrassa, Sain. This invitation resulted in two short stays in Terrassa during, where the basis for the concets and ideas resented in this Thesis were develoed. While staying in Terrassa, I also received suort by the researchers and PhD students of the REES grou for working in their laboratories, making it ossible to test some of the develoed concets in short time. Thus, all exerimental results resented in this Thesis are originating from my visits to Terrassa. The suort from Professor Rodríguez and the members of his research grou is therefore highly valued, and has been crucial for the comletion of this work in its current form. Trondheim, January Jon Are Suul Jon Are Suul iii

Content ABSTRACT... I PREFACE... III CONTENT...V LIST OF FIGURES... IX LIST OF TABLES...XII NOMENCLATURE AND ABBREVIATIONS... XIII INTRODUCTION.... OVERVIEW OF CONVENTIONAL CONTROL SYSTEMS FOR GRID CONNECTED VOLTAGE SOURCE CONVERTERS.... IDENTIFICATION OF RESEARCH QUESTION...5.3 OVERVIEW OF EARLIER CONTRIBUTIONS...7.4 CONTRIBUTIONS OF THIS THESIS...9.5 OUTLINE OF THE THESIS....6 SCIENTIFIC PUBLICATIONS....6. Publications Containing Results Defended as Parts of this Thesis....6. Other Publications Preared During the PhD-studies... STATE-OF-THE ART FOR VOLTAGE-SENSOR-LESS OPERATION AND VIRTUAL FLUX-BASED CONTROL OF VSCS...5. INTRODUCTION TO VOLTAGE-SENSOR-LESS GRID SYNCHRONIZATION AND CONTROL...5.. Motivation for Voltage-sensor-less Oeration of VSCs...6.. Review of Methods for Voltage-Sensor-less Grid Synchronization...7. INTRODUCTION TO VIRTUAL FLUX ESTIMATION FOR VOLTAGE-SENSOR-LESS GRID SYNCHRONIZATION...9.. Ideal Virtual Flux Estimation for Grid Synchronization..... Imlementation Issues Regarding Virtual Flux Estimation.....3 Practical Imlementation of Virtual Flux Estimation...3..4 Initialization and Start-u of Virtual Flux-based Grid Synchronization...6..5 Virtual Flux-based Grid Synchronization and Control in Case of LCL-filters...7..6 Parameter Sensitivity of Virtual Flux Estimation...3.3 VIRTUAL FLUX-BASED GRID SYNCHRONIZATION UNDER UNBALANCED GRID VOLTAGE CONDITIONS...3.3. Methods Based on Synchronous Reference Frames for Identification of Positive Sequence Virtual Flux Comonents...3.3. Estimation of Positive and Negative Sequence Virtual Flux Comonents in the Stationary Reference Frame...3.3.3 General Features of Available Methods for Virtual Flux-based Grid Synchronization under Unbalanced Conditions...33.4 SUMMARY OF CHAPTER...33 3 VOLTAGE-SENSOR-LESS GRID SYNCHRONIZATION BY FREQUENCY-ADAPTIVE VIRTUAL FLUX ESTIMATION...35 3. FREQUENCY-ADAPTIVE IMPLEMENTATION OF CONVENTIONAL STRATEGIES FOR VIRTUAL FLUX ESTIMATION...35 3.. The Second Order Generalized Integrator Configured as a Quadrature Signal Generator (SOGI-QSG) for On-line Frequency-adative Virtual Flux Estimation...36 3.. Definition of Frequency-scaled Virtual Flux based on SOGI-QSG...39 Jon Are Suul v

3. UTILIZATION OF SOGI-QSGS FOR ON-LINE FREQUENCY-ADAPTIVE VIRTUAL FLUX ESTIMATION AND SEQUENCE SEPARATION UNDER UNBALANCED CONDITIONS...4 3.. Sequence Searation of Estimated Virtual Flux...4 3.. Sequence Searation of Converter Outut Voltages Followed by Individual Estimation of PNS-VF Comonents...4 3.3 FREQUENCY-ADAPTIVE VIRTUAL FLUX ESTIMATION WITH INHERENT SEQUENCE SEPARATION...43 3.3. Proosed Aroach for achieving Virtual Flux Estimation with Inherent Sequence Searation...43 3.3. Simulation Studies of DSOGI-VF estimation...48 3.3.3 Exerimental Verification of the DSOGI-VF Estimation Method...53 3.4 EVALUATION AND COMPARISON OF METHODS FOR VIRTUAL FLUX ESTIMATION UNDER UNBALANCED CONDITIONS...56 3.4. Comarison of Transient Resonse based on Simulation...57 3.4. Comarative Summary of Characteristics and Imlementation Comlexity of Different Methods for Grid Synchronization...6 3.5 OTHER POSSIBLE CONFIGURATIONS AND IMPLEMENTATIONS OF DSOGI-BASED VIRTUAL FLUX ESTIMATION...6 3.5. Simlified DSOGI-VF Structure for Synchronization to Converter Terminals or Available Voltage Measurements...6 3.5. Configuration with Searate Integration of Converter Outut Voltage and Resistive Voltage Dro...64 3.5.3 Possible Extensions of the Presented Aroaches for Virtual Flux Estimation based on SOGI-QSGs and Indications of Possible Toics of Future Investigations...66 3.6 SUMMARY OF CHAPTER...67 4 VIRTUAL FLUX-BASED POWER CONTROL STRATEGIES UNDER UNBALANCED CONDITIONS...69 4. INTRODUCTION TO POWER CONTROL STRATEGIES AND CURRENT REFERENCE CALCULATION UNDER UNBALANCED CONDITIONS...69 4. ACTIVE AND REACTIVE POWER EQUATIONS BASED ON VIRTUAL FLUX...7 4.. Virtual Flux-based Power Equations under Balanced Conditions...7 4.. Active and Reactive Power Equations under Unbalanced Conditions...7 4..3 Accuracy of Power Calculations and Current Reference Calculation based on Positive and Negative Sequence Virtual Flux Comonents...74 4.3 DERIVATION OF CURRENT REFERENCES FOR ACTIVE AND REACTIVE POWER CONTROL DURING UNBALANCED GRID CONDITIONS...74 4.3. Balanced Positive Sequence Control (BPSC)...75 4.3. Positive-Negative-Sequence Comensation (PNSC)...77 4.3.3 Average Active-Reactive Control (AARC)...79 4.3.4 Synthesized Exression for Current Reference Calculation and Corresonding Power Flow Characteristics...8 4.4 EXPERIMENTAL VERIFICATION OF VIRTUAL FLUX-BASED ACTIVE AND REACTIVE POWER CONTROL STRATEGIES...8 4.4. Exerimental Configuration...83 4.4. Comments on Conditions and Limitations of Exerimental Setu...84 4.4.3 Active Power control by the BPSC Strategy...85 4.4.4 Positive Negative Sequence Comensation (PNSC)...88 4.4.5 Average-Active Reactive Control (AARC)...89 4.4.6 Reactive Power Control by the Same Range of Control Objectives...9 4.4.7 Elimination of Active Power Oscillations with Simultaneous Control of Active and Reactive Power...9 4.4.8 Elimination of Reactive Power Oscillations with Simultaneous Control of Active and Reactive ower...93 vi NTNU

4.5 FURTHER APPLICATION EXAMPLES OF THE DEVELOPED STRATEGIES FOR VIRTUAL FLUX- BASED ACTIVE AND REACTIVE POWER CONTROL...94 4.5. Reduction of DC-link Voltage Oscillations during Unbalanced Conditions by Utilizing Virtual Flux Estimation at the Converter Terminals...95 4.5. Control of Active and Reactive Power at a Remote Location...98 4.6 GENERAL CONSIDERATIONS REGARDING VIRTUAL FLUX-BASED POWER CONTROL STRATEGIES UNDER UNBALANCED CONDITIONS... 4.7 SUMMARY OF CHAPTER... 5 VIRTUAL FLUX-BASED POWER CONTROL STRATEGIES OPERATING UNDER CURRENT LIMITATION...3 5. INTRODUCTION TO CURRENT LIMITATION STRATEGIES FOR VOLTAGE SOURCE CONVERTERS UNDER UNBALANCED CONDITIONS...4 5. CONSIDERATIONS REGARDING CURRENT VECTOR AMPLITUDE LIMITATION VERSUS PHASE CURRENT LIMITATION...5 5.3 POWER CONTROL STRATEGIES UNDER PHASE CURRENT LIMITATION...7 5.3. Active Power Control with Limitation of the Active Current Comonent...7 5.3. Reactive Power Control with Limitation of the Reactive Current Comonent...3 5.4 SIMULATION OF POWER CONTROL STRATEGIES OPERATED WITH PHASE CURRENT LIMITATION UNDER SINGLE-PHASE FAULT CONDITIONS...6 5.4. Converter Oeration in Resonse to Changes in the Grid Fault Phase Angle...7 5.4. Converter Oeration in Resonse to Changes in the Active Power Control Objective...9 5.4.3 General Comment Regarding Strategies for Phase Current Limitation... 5.5 SIMPLIFIED CURRENT REFERENCE CALCULATION FOR OPERATION UNDER CURRENT VECTOR AMPLITUDE LIMITATION... 5.5. Active Power Control with Current Vector Amlitude Limitation...3 5.5. Reactive Power Control with Current Vector Amlitude Limitation...4 5.6 EXPERIMENTAL RESULTS OF ACTIVE AND REACTIVE POWER CONTROL STRATEGIES WITH CURRENT VECTOR AMPLITUDE LIMITATION...4 5.6. Descrition of Laboratory Setu and Control System Imlementation...4 5.6. Active Power Control with Current Vector Amlitude Limitation...5 5.6.3 Reactive Power Control with Current Vector Amlitude Limitation...3 5.7 MAXIMUM CURRENT AND CURRENT LIMITATION STRATEGIES WITH SIMULTANEOUS CONTROL OF ACTIVE AND REACTIVE POWER...34 5.7. Calculation of Total Current Amlitude in Case of Simultaneous Control of Active and Reactive Power Flow...35 5.7. Current Limitation with Priority of either Active or Reactive Current...36 5.8 SUMMARY OF CHAPTER...36 6 CONCLUSION AND SUGGESTIONS FOR FURTHER RESEARCH...39 6. SUMMARY OF MAIN RESULTS AND CONTRIBUTIONS...39 6. OUTLINE OF RELEVANT TOPICS FOR FURTHER RESEARCH...4 6.. General Toics Related to Power System Integration and Stability of VSCs with Virtual Flux-based Grid Synchronization and Control...4 6.. Relevant Toics for Further Investigation of Control Systems for VSCs based on the Proosed Aroach for Virtual Flux Estimation and Power Control...4 6.3 CLOSING REMARKS...43 7 REFERENCES...45 APPENDIX A CONVENTIONS FOR REFERENCE FRAME TRANSFORMATIONS AND PER UNIT SCALING...67 A. BASE VALUES FOR PER UNIT SYSTEMS...67 A. TWO-PHASE REPRESENTATION OF THREE-PHASE VARIABLES IN THE STATIONARY REFERENCE FRAME...68 A.3 TRANSFORMATION TO THE SYNCHRONOUS REFERENCE FRAME...69 A.4 SPACE VECTOR REPRESENTATION OF THREE-PHASE VARIABLES...7 Jon Are Suul vii

APPENDIX B ANALYSIS OF METHODS FOR SYMMETRICAL COMPONENT SEQUENCE SEPARATION AND VIRTUAL FLUX ESTIMATION...73 B. SEQUENCE SEPARATION IN THE STATIONARY REFERENCE FRAME...73 B. ANALYSIS OF FILTER-BASED METHODS FOR SEQUENCE SEPARATION...74 B.. Sequence Searation by using Second-order Low-ass Filters...74 B.. Sequence Searation by using SOGI-QSGs...75 B.3 ANALYSIS OF METHODS FOR ESTIMATION OF POSITIVE AND NEGATIVE SEQUENCE VIRTUAL FLUX COMPONENTS...77 B.3. Frequency Resonse of Sequence Searation and Virtual Flux Estimation based on Second-order Low-ass Filters...78 B.3. Cascaded Methods for Sequence Searation and Virtual Flux Estimation based on SOGI- QSGs...79 APPENDIX C DISCRETE TIME IMPLEMENTATION OF SOGI AND SOGI-QSG STRUCTURES...8 C. GENERAL COMMENT ON DISCRETE TIME IMPLEMENTATION OF SOGI-BASED STRUCTURES.8 C. TWO-INTEGRATOR-BASED SCHEME FOR IMPLEMENTATION OF PR CURRENT CONTROLLERS.8 C.3 STATE-SPACE MODEL AND DIFFERENCE EQUATIONS FOR IMPLEMENTATION OF SOGI-QSGS...83 C.3. Continuous Time State-Sace Model of SOGI-QSG...83 C.3. Discrete Time State-Sace Model of SOGI-QSG...84 APPENDIX D DEFINITIONS AND DERIVATIONS RELATED TO VIRTUAL FLUX- BASED POWER CONTROL AND CURRENT LIMITATION...87 D. BASIC DEFINITION OF POSITIVE AND NEGATIVE SEQUENCE VOLTAGE AND VIRTUAL FLUX SIGNALS...87 D.. Positive and Negative Sequence Voltage Signals...87 D.. Positive and Negative Sequence Virtual Flux Signals...87 D. MAXIMUM VECTOR AMPLITUDES AND GRAPHICAL ORIENTATION OF ELLIPTIC TRAJECTORIES UNDER UNBALANCED CONDITIONS...88 D.. Phase Angle Corresonding to Peak Amlitude of the Voltage Vector...88 D.. Grahical Orientation of Ellitic Trajectories in the Stationary Reference Frame under Unbalanced Conditions...89 D..3 Detection of Phase Angles of Positive and Negative Sequence Comonents...9 D.3 SIMPLIFIED EXPRESSIONS FOR POSITIVE AND NEGATIVE SEQUENCE VOLTAGE AND VIRTUAL FLUX SIGNALS...9 D.3. Voltage Vectors and Corresonding Orthogonal Signals...9 D.3. Virtual Flux Vectors and Corresonding Orthogonal Signals...9 D.4 ACTIVE AND REACTIVE POWER OSCILLATIONS RESULTING FROM THE DIFFERENT POWER CONTROL STRATEGIES...93 D.4. Active and Reactive Power Control by BPSC...93 D.4. Active and Reactive Power Control by PNSC...95 D.4.3 Active and Reactive Power Control by AARC...96 D.5 DERIVATION OF ACTIVE POWER TRANSFER LIMITATIONS AND CURRENT REFERENCE EQUATIONS FOR OPERATION OF ACTIVE POWER CONTROL STRATEGIES UNDER PHASE CURRENT LIMITATION...98 D.5. Oeration with Reduction of Active Power Oscillations ( k )...98 D.5. Oeration with Reduction of Reactive Power Oscillations ( k )... D.6 DERIVATION OF REACTIVE POWER TRANSFER LIMITATIONS AND CURRENT REFERENCE EQUATIONS FOR OPERATION OF REACTIVE POWER CONTROL STRATEGIES UNDER PHASE CURRENT LIMITATION...4 D.6. Oeration with Reduction of Reactive Power Oscillations ( k q )...4 D.6. Oeration with Reduction of Active Power Oscillations ( k q )...6 viii NTNU

List of Figures Fig. - Overview of main elements in conventional VSC control system with cascaded control loos... 3 Fig. - Overview of control system for oeration under unbalanced grid voltage conditions with indication of the focus area of this Thesis... 7 Fig. - Grid connected VSC with inductive filter... Fig. - Basic concet of ideal Virtual Flux estimation... Fig. -3 Vector diagram showing voltage and Virtual Flux at the converter terminals and at the grid side of the filter inductor... Fig. -4 Frequency resonse of filter-based methods for Virtual Flux estimation... 4 Fig. -5 Configuration with VSC and LCL-filter... 7 Fig. -6 Estimation of Virtual Flux at grid side of LCL-filter... 8 Fig. -7 Method for estimation of Positive and Negative Sequence Virtual Flux comonents roosed by Kulka in [7]... 3 Fig. 3- Exlicitly frequency-adative Second Order Generalized Integrator configured as a Quadrature Signal Generator (SOGI-QSG) with the in-quadrature outut signal qv reresenting the scaled Virtual Flux... 36 Fig. 3- Frequency resonse of SOGI-QSG... 37 Fig. 3-3 Estimation of frequency-scaled Virtual Flux based on SOGI-QSGs... 4 Fig. 3-4 Frequency adative Virtual Flux estimation cascaded with SOGI-QSG-based Sequence Searation of the estimated Virtual Flux... 4 Fig. 3-5 Frequency-adative Sequence Searation of voltages cascaded with searate estimation of PNS-VF comonents... 43 Fig. 3-6 Frequency Adative Dual SOGI-based Virtual Flux Estimation with Inherent Sequence Searation... 45 Fig. 3-7 Frequency resonse of DSOGI-VF Estimation; a) ositive sequence Virtual Flux comonents, and b) negative sequence Virtual Flux comonents... 47 Fig. 3-8 Simulation results showing the oeration of the DSOGI-VF estimation in case of an unbalanced sag in the grid voltage... 5 Fig. 3-9 Simulation results showing the resonse of the roosed Virtual Flux estimation when a large ste in grid frequency occurs... 5 Fig. 3- Overview of laboratory setu for verification of DSOGI-VF estimation... 53 Fig. 3- Laboratory results showing measured three-hase voltages, PNS comonents of measured voltage and PNS comonents of the estimated Virtual Flux, with corresonding hase angles... 55 Fig. 3- Laboratory results showing amlitudes calculated from the PNS comonents of voltage and estimated Virtual Flux before, during and after the voltage sag... 56 Fig. 3-3 Transient resonse of PNS Virtual Flux amlitudes for different estimation methods when exosed to an unbalanced dro in grid voltage... 58 Fig. 3-4 Amlitudes of estimated PNS-VF comonents for different VF estimation methods when exosed to a ste in the grid frequency... 59 Fig. 3-5 Structure of DSOGI-based estimation of Virtual Flux at converter terminals... 63 Fig. 3-6 DSOGI-based Virtual Flux estimation with inherent sequence searation and simultaneous estimation of converter Virtual Flux and grid-side Virtual Flux... 65 Fig. 4- Conventions and orientations used for ower calculations based on voltage and Virtual Flux... 7 Jon Are Suul ix

Fig. 4- Overview of laboratory setu... 83 Fig. 4-3 Overview of control structure imlemented in laboratory setu... 84 Fig. 4-4 Results from exeriment with. u active ower reference and reference current calculation by BPSC (k = )... 86 Fig. 4-5 Virtual Flux and current trajectories with active ower control by BPSC... 87 Fig. 4-6 Exerimental results with =. u and ower control by PNSC (k = )... 88 Fig. 4-7 Virtual Flux and current trajectories with active ower control by PNSC... 89 Fig. 4-8 Exerimental results with =. u and ower control by AARC (k = )... 9 Fig. 4-9 Virtual Flux and current trajectories with active ower control by AARC... 9 Fig. 4- Fig. 4- Fig. 4- Fig. 4-3 Fig. 4-4 Fig. 4-5 Fig. 5-. Fig. 5-. Fig. 5-3. Fig. 5-4. Fig. 5-5. Fig. 5-6 Fig. 5-7 Fig. 5-8 Exerimental results with =. u and q =. u, with active current reference calculation by PNSC (k = ) and reactive current reference calculation by AARC (k q = ) for elimination of active ower oscillations... 9 Virtual Flux and current trajectories with active and reactive ower control for elimination of active ower oscillations... 9 Exerimental results with =. u and q =. u, with active current reference calculation by AARC (k = ) and reactive current reference calculation by PNSC (k q = ) for elimination of reactive ower oscillations... 93 Virtual Flux and current trajectories with active and reactive ower control for elimination of reactive ower oscillations... 94 Exerimental results with =. u, Virtual Flux estimation at the converter terminals and active current reference calculation by PNSC (k = ) for elimination of active ower oscillations... 97 Exerimental results illustrating generic oeration with Virtual Flux estimation at a remote oint with =. u, q =. u and oeration for elimination of double frequency oscillations in active ower flow (k =, k q = )... 99 Illustration of the difference between hase current limitation and current vector amlitude limitation... 6 Virtual Flux and current trajectories in the case of ower control with elimination of double frequency active ower oscillations... 9 Profile of maximum current vector amlitude as function of the fault angle and the level of unbalance... Virtual Flux and current trajectories in case of active ower control with elimination of double frequency reactive ower oscillations... Profile of maximum current vector amlitude as function of the fault angle and the level of unbalance... 3 Simulation results for control by AARC with hase current limitation under unbalanced conditions with χ + = χ =.5 u when the hase angle δ between ositive and negative sequence comonents is swet from to 9... 8 Simulated trajectories of Virtual Flux and current for control by AARC with hase current limitation under unbalanced conditions with χ + = χ =.5 u when the hase angle δ between ositive and negative sequence comonents is swet from to 9... 9 Simulation results for active ower control with hase current limitation under unbalanced conditions with χ + = χ =.5 u when the control arameter k is swet from (AARC) to (PNSC)... x NTNU

Fig. 5-9 Simulated trajectories of Virtual Flux and current for active ower control with χ + = χ =.5 u when k is swet from (AARC) to (PNSC)... Fig. 5- Overview of control configuration oerated on the dspace latform... 5 Fig. 5- Current Reference Calculation with Vector Amlitude Limitation... 6 Fig. 5- Active ower control by PNSC with the amlitude of the active current vector reference i limited to.8 u... 7 Fig. 5-3 Trajectory of estimated Virtual Flux and calculated current reference for ower control by PNSC with current vector amlitude limitation... 8 Fig. 5-4 Active ower control by BPSC with the active current reference i limited to.8 u... 9 Fig. 5-5 Active ower control by AARC with the amlitude of the active current vector reference i limited to.8 u... 3 Fig. 5-6 Reactive ower control by PNSC with the amlitude of the reactive current vector reference i q limited to.8 u... 3 Fig. 5-7 Trajectory of estimated Virtual Flux and calculated current reference for current limited reactive ower control by PNSC... 3 Fig. 5-8 Reactive ower control by BPSC with the vector amlitude of the reactive current reference i q limited to.8 u... 33 Fig. 5-9 Reactive ower control by AARC with the vector amlitude of the reactive current reference i q limited to.8 u... 34 Fig. A- Sace vector diagram showing the rojection of the current sace vector into the different reference frames... 7 Fig. B- Frequency resonse of sequence searation based on nd order low-ass filters.. 74 Fig. B- Frequency resonse of Sequence Searation based on SOGI-QSGs... 76 Fig. B-3 Frequency resonse of Sequence Searation based on unfiltered inut signals and in-quadrature signals from SOGI-QSGs... 77 Fig. B-4 Frequency resonse of Sequence Searation cascaded with PNS VF estimation based on Second Order Low-ass Filters... 78 Fig. B-5 Frequency resonse of Sequence Searation cascaded with PNS VF estimation based on SOGI-QSGs... 79 Fig. C- Structure of Second Order Generalized Integrator in the continuous time domain... 8 Fig. C- Structure of Second Order Generalized Integrator imlemented by a two-integrator scheme in the discrete time domain... 83 Fig. C-3 Structure of SOGI-QSG for establishing state sace model... 84 Fig. D- Grahical orientation of ellitic voltage trajectory under unbalanced conditions 9 Jon Are Suul xi

List of Tables Table 3- Parameters for simulation study... 48 Table 3- Details of Laboratory Setu... 53 Table 3-3 Summary of Performance Characteristics and Imlementation Comlexity for Different Synchronization Methods... 6 Table 4- Details of Laboratory Setu... 83 Table D- Orientation of Virtual Flux trajectories and influence on equations for hase current limitation when k... Table D- Orientation of Virtual Flux trajectories and influence on equations for hase current limitation when k... 4 xii NTNU

Nomenclature and Abbreviations Symbols In general, uercase symbols are exressing hysical, un-scaled, variables or arameters, while lowercase symbols are exressing er unit variables or arameters. There are a few excetions from this rule, corresonding to well-established nomenclature in relevant literature. In these cases, er unit variables are denoted with u as subscrit. Bold symbols are reresenting vector quantities corresonding to voltages, currents and Virtual Flux signals. V,v Voltage [V, u] Ψ, ψ Flux [Wb, u] Χ, χ Virtual Flux scaled with grid frequency [Wb/s, u] = [V, u] I,i Current [A, u] Charge, corresonding to integral of current [u] S Aarent ower [VA] (Only used in the definition of er unit systems) ω f δ Angular frequency [rad/s] Grid frequency [Hz] Fault angle, describing the grahical orientation of the voltage or Virtual Flux trajectory in the stationary reference frame under unbalanced conditions [rad] Phase angle of ositive or negative sequence voltage comonents [rad] P, Q,q t T L/l R/r C/c a b g h m Active ower [W, u] Reactive ower [VAr, u] Time [s] Period-time of eriodic signal [s] Inductance [H, u] Resistance [Ω, u] Caacitance [F, u] Reresentation of hase shift of on comlex form Susetance (used for both voltage and Virtual Flux-based susetance) Conductance (used for both voltage and Virtual Flux-based conductance) Denotes a generic transfer function Modulation index for PWM algorithm Jon Are Suul xiii

q θ γ τ Subscrits abc αβ c DC b N Phase shifting oerator corresonding to 9 hase shift Phase angle of voltage Phase angle of estimated Virtual Flux Time constant [s] Three-hase quantities in the natural reference frame Quantities in the stationary αβ reference frame Variables at converter outut Variable associated with the DC-link of the converter Base value for er unit system Nominal value C Caacitor values in case of LCL filter configuration f Variables at the grid side of the filter inductor g Variables at connection oint to a grid equivalent source Parameters of filter inductor connected to converter terminals Parameters of grid side filter inductor in LCL filter configuration ω q d-t sw th r BP LP LP ref sam Indicates active or reactive ower comonent oscillating at twice the grid frequency Indicates active current comonents or oscillating active or reactive ower comonents originating from average active ower flow Indicates reactive current comonent, or oscillating active or reactive ower comonent originating from average reactive ower flow Dead-time Semiconductor switch Semiconductor threshold voltage Resistance Band-Pass filter Low-Pass filter Second Order Low-Pass filter Reference signal for PWM Samling in case of digital control system imlementation xiv NTNU

tot h lim max Total used in case of equivalent aramters for resistance and inductance Phase variables Limitation secified for eack value of active or reactive hase current or current vector comonent Maximum values of current vector amlitude or active or reactive ower flow associated with an imosed current limitation Suerscrits + Positive Sequence quantity Negative Sequence quantity Zero Sequence quantity Values estimated by SOGI and/or FLL Denotes average values of active and reactive ower comonents ~ Denotes active and reactive ower comonents oscillating at twice the grid frequency Defines estimated values during start-u rocedures Reference value for currents or ower comonents ^ Peak values Indicate inut and outut variables from Virtual Flux estimation,ideal Denotes ideal integration Abbreviations AARC Average-Active-Reactive Control BPSC Balanced Positive Sequence Control DPC Direct Power Control DSC Delayed Signal Cancellation DSOGI Dual Second Order Generalized Integrator DSOGI-VF Dual Second Order Generalized Integrator-based Virtual Flux EMI Electro-Magnetic Interference FLL Frequency-Locked Loo PLL Phase-Locked Loo PNS Positive and Negative Sequence PNSC Positive-Negative-Sequence Comensation QSG Quadrature Signal Generator RMS Root Mean Square SOGI Second Order Generalized Integrator THD Total Harmonic Distortion VF Virtual Flux Jon Are Suul xv

Introduction The utilization of ower electronic technology in ower system alications has been steadily increasing during the last decades. The continuous imrovement of semiconductor device technology and the availability of digital control systems with continuously increasing erformance have reinforced this develoment. Power electronic converter technology has also been an imortant enabling factor for the recent develoments in distributed generation and renewable energy systems, esecially with resect to wind ower and hotovoltaic systems. A large variety of controllable ower electronic converter toologies are currently being utilized in grid connected alications. The range of well known alications san from large thyristor-based line-commutated converters for classical high-voltage DC (HVDC) transmission systems, to small single-hase ower-factor-correction circuits used for low ower domestic loads. In between these examles, a wide range of toologies have been develoed and otimized for various alications. However, only a few of the available three-hase toologies have reached widesread deloyment and mass roduction. During the last coule of decades, the Voltage Source Converter (VSC) has emerged as the dominant toology for actively controlled three-hase alications. This develoment has been suorted by the widesread use of VSCs in variable seed electric drive systems. VSCs oerating as active rectifiers have also become a relevant otion for relacing diode rectifiers or line-commutated converters due to the Pulse Width Modulated (PWM) oeration, which ensures limited current distortion and reduced harmonic filter requirements together with the ability to control ower factor and DC-link voltage []-[3]. Thus, almost identical VSC modules connected in a backto-back configurations have become the most common solution for regenerative motor drives and variable seed generator systems [], [4]-[6]. Various configurations based on three-hase VSCs are also used for distributed energy resources like hotovoltaic s and fuel cell systems which naturally rovide a DC outut and deend on ower electronic converters for integration to the AC grid [4], [6]-[8]. Other well-known alications of grid integrated VSCs include oeration as grid interfaces of energy storage systems, reactive ower comensation when configured as a Static Synchronous Comensators (STATCOM), and active filter systems [4], [6], [7], [9]-[3]. Large scale deloyment of VSCs has until now been most common in low voltage AC systems (below kv), based on the two-level VSC toology. The ower ratings of such converter units are usually limited to about 5 MW, due to the high currents. However, multi-level VSC toologies are currently finding numerous alications in the medium voltage (kv) range, and are commercially available with ower ratings u to about 5 MW [4]-[7]. Medium-voltage grid integrated multi-level VSCs have until now Jon Are Suul

Introduction mainly been used in regenerative motor drives, but similar converter units are also exected to be utilized for wind ower alications aroaching MW [5], [6]. High voltage, high ower VSC toologies have also been develoed for High Voltage DC (HVDC) transmission systems and for ower system alications within the Flexible AC Transmission System (FACTS) concet [8]-[]. The largest VSC HVDC converters currently in oeration are in the range of 4 MW, but systems reaching MW with ± 3 kv DC voltage are considered within the reach of available technology. Two- or three-level VSC toologies imlemented by series connection of a large number of high voltage semiconductors has been used for most of the existing VSC HVDC systems, illustrating that the same toology as for low voltage alications can be used even in the high voltage range. This brief overview demonstrates how the three-hase VSC is a very flexible toology that can be designed and imlemented for a wide range of alications and voltage levels, sanning the ower range from a few kw to hundreds of MWs. The main difference between the basic two-level toology comared to the varieties of multi-level converters will be the PWM technique used to control the oeration of the individual switches. Therefore, the main rinciles of oeration as well as the general structure and functionality of the control system are usually the same for most alications of grid connected VSCs. Thus, the further discussions will be limited to the basic three-hase, three-wire two-level VSC toology.. Overview of Conventional Control Systems for Grid Connected Voltage Source Converters There has been an intense research effort on develoment and analysis of control systems for grid connected VSCs during the last coule of decades. A large variety of techniques and methods for grid synchronization and control have therefore been roosed and analyzed. The main rinciles of oeration for VSCs in grid integrated alications are, however, similar to what has been well known for control of VSCbased electric drives. Many of the control techniques and traditions develoed for imlementation of machine drive systems have therefore been successfully adated to oeration of grid connected VSCs. When oerated in grid integrated alications, the VSC will be exosed to disturbances, transients and interrutions that roagate through the electric ower system. A large share of such disturbances and transients are likely to introduce temorary unbalanced grid voltage conditions [3]-[5]. In an increasing number of grid connected alications, the VSC is also required to oerate during such voltage disturbances and grid voltage unbalance, while the conventional aroach has been to disconnect from the ower system to rotect the converter [6]-[34]. Such requirements have become well known under the general term of Low-Voltage Ride-Through (LVRT) for wind ower systems, and are becoming increasingly relevant for other distributed generation systems as well as for comensation systems, regenerative loads and energy storage alications. Safe oeration during severe voltage transients and grid voltage unbalance will usually require added functionality and increased comlexity of the control system, since the erformance of conventional control strategies insired by electrical drives systems will deteriorate under unbalanced conditions [35]-[38]. Research and develoment related to VSC control systems for NTNU

. Overview of Conventional Control Systems for Grid Connected Voltage Source Converters Main elements of VSC Control System V s, ab Outer Loo Control Grid information Grid Synchronization V s, ab I cab, L V DC V AC Power Balance Control Reactive Power Control Active current/ower reference Reactive current/ower reference Inner Loo Control & Modulation Icab, Synchronizing signal VDC g 6 C DC Fig. - Overview of main elements in conventional VSC control system with cascaded control loos oeration during unbalanced conditions have therefore received significant attention during the last few years. Although there is a wide range of ossible control techniques that can be alied to a grid connected VSC, most of the available roosals share a general structure, with three main elements as indicated in Fig. -. Assuming a VSC converter that will always be connected to an external grid without the need for stand-alone oeration, these three elements can be listed and briefly described as:. Grid Synchronization: Information about the hase angle, amlitude and/or frequency of the grid voltage is of vital imortance for the converter control system to be able to accurately control the flow of active and reactive ower. The main urose of the grid synchronization technique is therefore to identify the information needed by the rest of the control system. Although a wide range of synchronization methods have been roosed, the most common and well known synchronization technique for three-hase VSCs is the Synchronous Reference Frame (SRF) Phase Locked Loo (PLL) [39]- [44]. In case of oeration during unbalanced grid voltage conditions, the grid synchronization method is usually required to identify the hase angle and amlitude of the ositive sequence (and sometimes also the negative sequence) comonent of the grid voltage. Adding functionality to the conventional SRF PLL, or imlementing techniques for symmetrical comonent sequence searation in the stationary reference frame are among the most common strategies for grid synchronization under unbalanced conditions [6], [8], [45]-[57]. V DC Jon Are Suul 3

Introduction The grid synchronization is usually based on voltage measurements, but voltage-sensor-less techniques for grid synchronization are gaining interest due to otential cost reduction and imrovement of reliability [58]-[65]. Voltage-sensor-less grid synchronization based on the concet of Virtual Flux, where the integral of the converter outut voltage is considered in analogy to the flux of an electrical machine, has for instance become relatively well known [66]-[68]. However, voltagesensor-less control systems are not yet commonly alied for converters required to have the caability for oerating under unbalanced conditions.. Inner loo control and modulation: The inner control loos of the converter control system must be fast and accurate, since they will control the PWM switching oeration of the converter and determine the erformance limits for the outer loos [69]. Traditionally, the inner control loos are controlling the currents in the filter inductor L indicated in Fig. - [69]-[79]. The inner control loos can also be designed to control the active and reactive ower flow directly, according to the concet known as Direct Power Control (DPC) [59], [6], [66], [67], [8]. Deending on the tye of controller, the inner control loo control can directly rovide the switching signals controlling the VSC oeration, or the switching signals can be rovided by a searate PWM mechanism. Inner control loos acting directly on the switching states of the converter are usually associated with nonlinear control and variable switching frequency, while PWM mechanisms with a voltage reference inut will be oerating at fixed switching frequency. In case of fixed frequency PWM, the inner loo current or ower controllers are therefore roviding a voltage reference, or a modulation index, which corresonds to the desired average outut voltage of the converter within one switching eriod [69], [8]. For three-hase three-wire VSCs, the fixed frequency PWM mechanisms must be secifically adated for maximizing the utilization of the available DC-link voltage [8]-[84], while this is usually inherently achieved with nonlinear control loos acting directly on the switching signals. The erformance of traditional Proortional-Integral (PI) current control loos imlemented in the Synchronous Reference Frame, as well known from vector oriented control of electric drives, will usually deteriorate during unbalanced conditions. This roblem is usually solved by either dulicating the current controller imlementation in both the ositive and negative sequence SRFs, or by utilizing controllers which are caable of achieving negligible steady state errors when oerating with sinusoidal reference values [3], [34], [75]-[79], [85]-[9]. 3. Outer loo control: In a traditional cascaded control structure as indicated in Fig. -, there are usually a set of outer loo controllers roviding the reference values to the inner control loos. 4 NTNU

. Identification of Research Question The reference signal influencing the active ower flow of the converter is usually rovided by a control loo oerating on the ower balance of the converter. Usually, this control loo is a PI-controller oerating on the DC-link voltage or the energy stored in the DC-link caacitor, but also more advanced methods for controller designs are used [9]-[93]. The reference signal influencing the reactive ower flow of the converter usually originates from a control loo designed to follow a reference for either the reactive ower flow, the ower factor of the converter or the voltage in the AC grid [39], [94]-[97]. Under unbalanced conditions, the active and reactive ower flow in the converter will be characterized by an average value and an oscillating comonent at twice the grid frequency [89], [96], [98], [99]. The outer loo controllers in a cascaded control system must however be slower than the inner loos, and are usually controlling only the average values of the active and reactive ower flow. Therefore, an intermediate level between the outer and inner control loos is usually required for oeration under unbalanced conditions, where the intended characteristics of active and reactive ower flow of the converter should be secified. The tye and urose of the outer loo controllers, as well as the relevant methods for design and analysis of these control loos will deend on the alication. The outer loo controllers will therefore not be further investigated.. Identification of Research Question Grid synchronization and control of VSCs, as briefly outlined in the revious section, have received significant attention during the last decades, and most issues related to conventional control of VSCs during both balanced and unbalanced conditions have therefore been thoroughly addressed. Voltage-sensor-less oeration during unbalanced conditions is, however, a relatively new toic, and the studies available in the scientific literature have been mainly focused on achieving articular, alication secific objectives. The resented techniques and methods have therefore not yet converged towards a generally valid aroach for voltage-sensor-less grid synchronization and control of the active and reactive ower flow during unbalanced conditions. One of the main goals for this Thesis has therefore been to address these issues in a way that should be valid for a wide range of alications, control objectives and oerating conditions. The desired features that should be fulfilled for control and oeration of a grid connected VSC considered in this Thesis can be summarized by the following oints: Ability to oerate in voltage-sensor-less mode: The method for grid synchronization should still be relatively simle and easily understandable. The concet of Virtual Flux-based grid synchronization and control has therefore been considered as a suitable starting oint, since it can be easily understood in analogy to the flux of an electrical machine. Jon Are Suul 5

Introduction The alied method for voltage-sensor-less grid synchronization should be generally valid for unbalanced grid voltage conditions. The accuracy and dynamic resonse of the grid synchronization method should not be significantly influenced by variations in the grid frequency. The converter control system should be able to control both average active and average reactive ower flow, as well as the double frequency oscillating comonents of the active and reactive ower flow during unbalanced conditions. The control strategy should be generally valid for both balanced and unbalanced conditions, and it should be ossible to determine the active and reactive ower flow characteristics in a flexible manner. The converter control system should be able to limit the current references during balanced and unbalanced disturbances in the grid voltage to safe values, while still maintaining the requested ower flow characteristics From the few examles given in the revious sections it can be seen that current controllers for VSCs have been exhaustively studied in the available literature, both for oeration under balanced and unbalanced conditions. The design, oeration and erformance of the current controllers can also to some extent be considered indeendently from to the grid synchronization method. Current controllers for VSCs will therefore not be further investigated. Similarly, the outer loo controllers for maintaining the active and reactive ower balance of the converter are usually not deending on the imlementation of the inner loo controllers or the grid synchronization method. The focus of this Thesis will therefore be limited to two main arts of a general control system of a current controlled VSC intended for oeration under unbalanced conditions, as illustrated in Fig. -. First, synchronization methods with otential for voltage-sensor-less oeration will be investigated, starting from the concet of Virtual Flux. Secondly, the issue of current reference calculation will be addressed with the urose of achieving generalized strategies for voltage-sensor-less control of active and reactive ower flow and ower flow characteristics under voltage-sensor-less oeration. The general research question behind the results and analysis that will be resented in this Thesis can therefore be defined as: How to develo and analyze a general aroach for Virtual Flux-based voltage-sensor-less grid synchronization and control of a grid integrated threehase Voltage Source Converter? It is taken as a condition that the VSC control system should be able to fulfil all the desired features listed above when oerating in voltage-sensorless mode. It should also be ossible to easily adat the control system to oeration based on available voltage measurements. 6 NTNU

.3 Overview of Earlier Contributions Main elements of VSC Control System with inner loo current controllers Focus of this Thesis V s, ab Grid information Voltage-sensor-less Grid Synchronization I cab, V DC L V DC V AC Power Balance Control Reactive Power Control P Q Current Reference Calculation I Current Control & Modulation Icab, Synchronizing signals VDC g 6 I cab, C DC Fig. - Overview of control system for oeration under unbalanced grid voltage conditions with indication of the focus area of this Thesis V DC.3 Overview of Earlier Contributions From the revious discussions, it can be noted that a wide range of literature is available on various asects of grid connected voltage source converters. This section is intended to give a brief outline of the revious contributions that constitute the main basis for the results achieved in this Thesis. The methods for voltage-sensor-less grid synchronization that will be discussed in this Thesis are based on the concet of Virtual Flux. The most imortant revious contributions that have been used as basis for develoing this concet are listed in the following: The fist examle of flux-based control for a three-hase grid connected VSC was resented by Weinhold in 99 []. Another examle of flux-based control was resented by Chandorkar et al. later in the same year [], and a filter-based method for imlementation of the flux estimation was subsequently discussed by Bhattacharya et al. in 995 []. The concet of flux-based control, and the benefits of using the flux instead of the grid voltage to establish a Synchronous Reference Frame for vector oriented control of grid connected VSCs, was discussed in a general way by Duarte et al. in 999 [3]. Voltage-sensor-less control based on the converter flux was first exlicitly discussed by Manninen in 995, in combination with a modulation method based on the Direct Torque Control for controlling the active and reactive ower flow of a VSC [4]. Jon Are Suul 7