Modeling of unbalanced three-phase driving-point impedance with application to control of grid-connected power converters

Summary The dq transformation is widely used in the analysis and control of three-phase symmetrical and balanced systems. The transformation is the real counterpart of the complex transformations derived from the symmetrical component theory. The widespread distributed generation and dynamically connected unbalanced loads in a three-phase system inherently create unbalanced voltages to the point of common coupling. The unbalanced voltages will always be transformed as coupled positive-sequence and negative-sequence components with double-frequency ripples that can be removed by some filtering algorithms in the dq frame. However, a technique for modeling unbalanced three-phase impedance between voltages and currents of same sequences or of opposite sequences is still missing. We propose an effective method for modeling unbalanced three-phase impedance using a decoupled zero-sequence impedance and two interacting positive-sequence and negative-sequence balanced impedances in the dq frame. The proposed method can decompose a system with unbalanced resistance, inductance, or capacitance into a combination of independent reciprocal bases (IRB). Each IRB basis belongs to one of the positive-sequence, negative-sequence, or zero-sequence system components to facilitate further analysis. The effectiveness of this approach is verified with a case study of an unbalanced load and another case study of an unbalanced voltage compensator in a microgrid application. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  Luowei Zhou,et al.  Filter‐based perturbation control of low‐frequency oscillation in voltage‐mode H‐bridge DC–AC inverter , 2015, Int. J. Circuit Theory Appl..

[2]  Benjamin Kroposki,et al.  Evaluation of VAR control and voltage regulation functionalities in a single-phase utility-connected inverter for distributed energy applications , 2009, 2009 IEEE Energy Conversion Congress and Exposition.

[3]  G. C. Paap,et al.  Symmetrical components in the time domain and their application to power network calculations , 2000 .

[4]  Francisco Jurado,et al.  Harmonic modelling of PV systems for probabilistic harmonic load flow studies , 2015, Int. J. Circuit Theory Appl..

[5]  Hong-Seok Song,et al.  Dual current control scheme for PWM converter under unbalanced input voltage conditions , 1999, IEEE Trans. Ind. Electron..

[6]  Jacquelien M. A. Scherpen,et al.  A cyclodissipativity characterization of power factor compensation of nonlinear loads under nonsinusoidal conditions , 2012, Int. J. Circuit Theory Appl..

[7]  Reza Iravani,et al.  Unbalanced Model and Power-Flow Analysis of Microgrids and Active Distribution Systems , 2010, IEEE Transactions on Power Delivery.

[8]  Kit Po Wong,et al.  Oscillatory Stability and Eigenvalue Sensitivity Analysis of A DFIG Wind Turbine System , 2011, IEEE Transactions on Energy Conversion.

[9]  C. K. Michael Tse,et al.  Bifurcation in Wind Energy Generation Systems , 2010, Int. J. Bifurc. Chaos.

[10]  Wolfgang A. Halang,et al.  Cascading failures of power grids caused by line breakdown , 2015, Int. J. Circuit Theory Appl..

[11]  Mehdi Savaghebi,et al.  Secondary Control Scheme for Voltage Unbalance Compensation in an Islanded Droop-Controlled Microgrid , 2012, IEEE Transactions on Smart Grid.

[12]  Mohsen Hamzeh,et al.  A New Control Strategy for a Multi-Bus MV Microgrid Under Unbalanced Conditions , 2012, IEEE Transactions on Power Systems.

[13]  C. L. Fortescue,et al.  Method of symmetrical co-ordinates applied to the solution of polyphase networks , 1918, Proceedings of the American Institute of Electrical Engineers.

[14]  Lie Xu,et al.  Coordinated Control of DFIG and FSIG-Based Wind Farms Under Unbalanced Grid Conditions , 2010, IEEE Transactions on Power Delivery.

[15]  Hidetoshi Ito,et al.  Enhancement of continuous operation performance of HVDC with self-commutated converter , 2000 .

[16]  A.M. Sharaf,et al.  Novel controllers for the 48-pulse VSC STATCOM and SSSC for voltage regulation and reactive power compensation , 2005, IEEE Transactions on Power Systems.

[17]  C. K. Michael Tse,et al.  Anti-windup dual-loop control of DFIG under unbalanced voltage conditions , 2012, 2012 IEEE International Symposium on Circuits and Systems.

[18]  Zhe Chen,et al.  Enhanced Control of a DFIG-Based Wind-Power Generation System With Series Grid-Side Converter Under Unbalanced Grid Voltage Conditions , 2013, IEEE Transactions on Power Electronics.

[19]  Aurelio Medina,et al.  Optimization‐based method for shunt hybrid filter compensation in non‐stiff systems , 2013, Int. J. Circuit Theory Appl..

[20]  M. Karimi-Ghartemani,et al.  Processing of Symmetrical Components in Time-Domain , 2007, IEEE Transactions on Power Systems.

[21]  Chen Chen,et al.  Analysis and effective controller design for the cascaded H‐bridge multilevel APF with adaptive signal processing algorithms , 2012, Int. J. Circuit Theory Appl..

[22]  Braz J. Cardoso Filho,et al.  Analysis of the operation of a D-STATCOM in unbalanced distribution systems under voltage disturbances , 2010, 2010 IEEE/PES Transmission and Distribution Conference and Exposition: Latin America (T&D-LA).

[23]  Antonio Gómez Expósito,et al.  Application of generalized phasors to eigenvector and natural response computation of LTI circuits , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Jian Sun,et al.  Impedance Modeling and Analysis of Grid-Connected Voltage-Source Converters , 2014, IEEE Transactions on Power Electronics.

[25]  Arindam Ghosh,et al.  Stability boundary analysis of the dynamic voltage restorer in weak systems with dynamic loads , 2012, Int. J. Circuit Theory Appl..

[26]  Silvia Lamonaca,et al.  Unbalanced Three-Phase Optimal Power Flow for Smart Grids , 2011, IEEE Transactions on Industrial Electronics.

[27]  Frede Blaabjerg,et al.  Overview of Control and Grid Synchronization for Distributed Power Generation Systems , 2006, IEEE Transactions on Industrial Electronics.

[28]  Fang Lin Luo,et al.  Space vector pulse-width modulation theory and solution for Z-source inverters with maximum constant boost control , 2014, Int. J. Circuit Theory Appl..

[29]  Lie Xu,et al.  Coordinated Control of DFIG's Rotor and Grid Side Converters During Network Unbalance , 2008, IEEE Transactions on Power Electronics.

[30]  Rong-Jong Wai,et al.  Grid-Connected Photovoltaic Generation System , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[31]  Mehdi Savaghebi,et al.  Autonomous Voltage Unbalance Compensation in an Islanded Droop-Controlled Microgrid , 2013, IEEE Transactions on Industrial Electronics.

[32]  Paolo Mattavelli,et al.  Reactive power and imbalance compensation using STATCOM with dissipativity-based control , 2001, IEEE Trans. Control. Syst. Technol..

[33]  Tzung-Lin Lee,et al.  A Cooperative Imbalance Compensation Method for Distributed-Generation Interface Converters , 2007 .

[34]  Jacques L. Willems,et al.  Reactive power compensation in a multi‐line system under sinusoidal unbalanced conditions , 2011, Int. J. Circuit Theory Appl..

[35]  Frede Blaabjerg,et al.  Power Controllability of a Three-Phase Converter With an Unbalanced AC Source , 2013, IEEE Transactions on Power Electronics.

[36]  Shuo Wang,et al.  DQ-Frame Modeling of an Active Power Filter Integrated With a Grid-Connected, Multifunctional Electric Vehicle Charging Station , 2013, IEEE Transactions on Power Electronics.

[37]  P. Rodriguez,et al.  Enhanced Decoupled Double Synchronous Reference Frame Current Controller for Unbalanced Grid-Voltage Conditions , 2012, IEEE Transactions on Power Electronics.