Voltage Ride-Through Capability Verification of Wind Turbines With Fully-Rated Converters Using Reachability Analysis

Wind turbines are required to meet grid interconnection codes for voltage ride-through, which mandate that they should not disconnect during a specified range of grid disturbances. One of the tasks of a turbine's design verification process is to ensure that it will be able to withstand any such event. This paper sets forth a powerful computational technique for design verification of Type-4 permanent-magnet synchronous generator-based turbines with fully-rated grid-side converters. The proposed method can provide assurance as to whether the currents and voltages will remain within acceptable bounds. To this end, reachability theory is employed to find sets that enclose all possible trajectories for the system states caused by a given set of unknown-but-bounded disturbances. The computation of the reachable sets is carried out by using on-the-fly linearization of the nonlinear system dynamics, zonotopes, and interval analysis.

[1]  Reigh A. Walling,et al.  Current contributions from Type 3 and Type 4 wind turbine generators during faults , 2012, T&D 2012.

[2]  Matthias Althoff,et al.  Transient stability analysis by reachable set computation , 2012, 2012 3rd IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe).

[3]  A. Mullane,et al.  Wind-turbine fault ride-through enhancement , 2005, IEEE Transactions on Power Systems.

[4]  Scott D. Sudhoff,et al.  Analysis of Electric Machinery and Drive Systems , 1995 .

[5]  Alexandre M. Bayen,et al.  Computational techniques for the verification of hybrid systems , 2003, Proc. IEEE.

[6]  O. Stursberg,et al.  Computing Reachable Sets of Hybrid Systems Using a Combination of Zonotopes and Polytopes , 2010 .

[7]  Takashi Hikihara,et al.  A Hybrid System Approach to the Analysis and Design of Power Grid Dynamic Performance , 2012, Proceedings of the IEEE.

[8]  J. Morren,et al.  Ridethrough of wind turbines with doubly-fed induction generator during a voltage dip , 2005, IEEE Transactions on Energy Conversion.

[9]  Mohsen Rahimi,et al.  Grid-fault ride-through analysis and control of wind turbines with doubly fed induction generators , 2010 .

[10]  Eric Walter,et al.  GUARANTEED NONLINEAR STATE ESTIMATION FOR CONTINUOUS-TIME DYNAMICAL MODELS FROM DISCRETE-TIME MEASUREMENTS , 2006 .

[11]  K. Baker,et al.  Standardized notation in interval analysis , 2010 .

[12]  Paul I. Barton,et al.  Convex enclosures for the reachable sets of nonlinear parametric ordinary differential equations , 2010, 49th IEEE Conference on Decision and Control (CDC).

[13]  N. Elia,et al.  Reachability analysis based transient stability design in power systems , 2010 .

[14]  Matthias Althoff,et al.  Reachability analysis of linear systems with uncertain parameters and inputs , 2007, 2007 46th IEEE Conference on Decision and Control.

[15]  Nacim Meslem,et al.  A Hybrid Bounding Method for Computing an Over-Approximation for the Reachable Set of Uncertain Nonlinear Systems , 2009, IEEE Transactions on Automatic Control.

[16]  Matthias Althoff,et al.  Reachability analysis of nonlinear systems with uncertain parameters using conservative linearization , 2008, 2008 47th IEEE Conference on Decision and Control.

[17]  T. Hikihara,et al.  Predicting Voltage Instability of Power System via Hybrid System Reachability Analysis , 2007, 2007 American Control Conference.

[18]  B. Krogh,et al.  Computing polyhedral approximations to flow pipes for dynamic systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[19]  N. Nedialkov,et al.  Interval Tools for ODEs and DAEs , 2006, 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006).

[20]  R. Teodorescu,et al.  A Stationary Reference Frame Grid Synchronization System for Three-Phase Grid-Connected Power Converters Under Adverse Grid Conditions , 2012, IEEE Transactions on Power Electronics.

[21]  Yu Christine Chen,et al.  A Method to Study the Effect of Renewable Resource Variability on Power System Dynamics , 2012, IEEE Transactions on Power Systems.

[22]  Pravin Varaiya,et al.  Ellipsoidal Techniques for Reachability Analysis , 2000, HSCC.

[23]  Bruce H. Krogh,et al.  Computational techniques for hybrid system verification , 2003, IEEE Trans. Autom. Control..

[24]  Matthias Althoff,et al.  Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars , 2010 .

[25]  Bart De Schutter,et al.  Supervisory hybrid model predictive control for voltage stability of power networks , 2007, 2007 American Control Conference.

[26]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[27]  Bruce H. Krogh,et al.  Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations , 1999, HSCC.

[28]  Ian A. Hiskens,et al.  Power system modeling for inverse problems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Stavros A. Papathanassiou,et al.  A review of grid code technical requirements for wind farms , 2009 .

[30]  Nedialko S. Nedialkov,et al.  Validated solutions of initial value problems for ordinary differential equations , 1999, Appl. Math. Comput..

[31]  Math Bollen.  Characterisation of voltage sags experienced by three-phase adjustable-speed drives , 1997 .

[32]  Siegfried M. Rump,et al.  INTLAB - INTerval LABoratory , 1998, SCAN.

[33]  Antoine Girard,et al.  Reachability of Uncertain Linear Systems Using Zonotopes , 2005, HSCC.

[34]  N. Samaan,et al.  Characteristics of wind turbine generators for wind power plants , 2009, 2009 IEEE Power & Energy Society General Meeting.

[35]  Max b. Müller.  Über das Fundamentaltheorem in der Theorie der gewöhnlichen Differentialgleichungen , 1927 .

[36]  B. Krogh,et al.  Reachability analysis of nonlinear systems using trajectory piecewise linearized models , 2006, 2006 American Control Conference.

[37]  Wei Li,et al.  Power Electronic Converter Control Techniques for Improved Low Voltage Ride Through Performance in WTGs , 2006 .

[38]  Ian M. Mitchell,et al.  Level Set Methods for Computation in Hybrid Systems , 2000, HSCC.

[39]  Pravin Varaiya,et al.  Ellipsoidal Techniques for Reachability Analysis of Discrete-Time Linear Systems , 2007, IEEE Transactions on Automatic Control.

[40]  N. Elia,et al.  Power system transient stability design using reachability based stability-region computation , 2005, Proceedings of the 37th Annual North American Power Symposium, 2005..

[41]  Bernd Tibken,et al.  Computing Guaranteed Bounds for Uncertain Cooperative and Monotone Nonlinear Systems , 2008 .

[42]  I. Erlich,et al.  Advanced grid requirements for the integration of wind turbines into the German transmission system , 2006, 2006 IEEE Power Engineering Society General Meeting.

[43]  Martin Berz,et al.  Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models , 1998, Reliab. Comput..

[44]  B. Tibken,et al.  Guaranteed Bounds for Uncertain Systems: Methods Using Linear Lyapunov-like Functions, Differential Inequalities and a Midpoint Method , 2006, 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006).

[45]  A.G. Beccuti,et al.  A Hybrid System Approach to Power Systems Voltage Control , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.