Semi-physical piecewise affine representation for governors in hydropower system generation

Abstract This paper presents a nonlinear model for a hydraulic amplifier, a component of the governor in the speed control loop of hydroelectric power plants. The amplifier transforms the electrical signal of the controller into mechanical movement of the turbine components, including the switching characteristics. This model is used to propose, on the one hand, a Piecewise Affine (PWA) representation for the hydraulic amplifier, and, on the other hand, a methodology for estimating the model parameters using field measurements, which facilitates its practical implementation. This representation is referred to as semi-physical because the model parameters are closely related with the physical construction of the hydraulic amplifier components. Among the advantages of this PWA representation are the appropriate structuring for use in system identification methods, for estimating its parameters, and the existence of advanced control techniques that use this structure in controller design, thereby improving the load-frequency control performance. The paper concludes with a description of the results, including the parameters that were estimated by using the hydraulic amplifier model with PWA structure.

[1]  Borut Zupančič,et al.  A New Technique for Translating Discrete Hybrid Automata into Piecewise Affine Systems , 2004 .

[2]  Eduardo Sontag.  Nonlinear regulation: The piecewise linear approach , 1981 .

[3]  Xin-hua Yu,et al.  Simulation Model of Hydraulic Turbine Speed Control System and Its Parameters Identification Based on Resilient Adaptive Particle Swarm Optimization Algorithm , 2010, 2010 Asia-Pacific Power and Energy Engineering Conference.

[4]  D. I. Jones,et al.  Modelling and Controlling Hydropower Plants , 2012 .

[5]  S. C. Tripathy,et al.  Optimisation of load-frequency control parameters for power systems with reheat steam turbines and governor deadband nonlinearity , 1982 .

[6]  Takashi Hiyama,et al.  Artificial neural network based modeling of governor-turbine system , 1999, IEEE Power Engineering Society. 1999 Winter Meeting (Cat. No.99CH36233).

[7]  Hui He,et al.  Identification of hydraulic turbine governor system parameters based on Bacterial Foraging Optimization Algorithm , 2010, 2010 Sixth International Conference on Natural Computation.

[8]  C. Taylor,et al.  Automatic Generation Control Analysis With Governor Deadband Effects , 1979, IEEE Transactions on Power Apparatus and Systems.

[9]  Tain-Sou Tsay.  Load–frequency control of interconnected power system with governor backlash nonlinearities , 2011 .

[10]  Alberto Bemporad,et al.  Identification of piecewise affine systems via mixed-integer programming , 2004, Autom..

[11]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[12]  Felix F. Wu,et al.  Describing-function analysis of automatic generation control system with governor deadband , 1978 .

[13]  M. Verhaegen,et al.  Subspace identification of piecewise linear systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  Wpmh Maurice Heemels,et al.  Introduction to hybrid systems , 2009 .

[15]  Jiang Chang,et al.  Nonlinear simulation of hydroturbine governing system based on neural network , 1996, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929).

[16]  S. Yokokawa,et al.  Idenntification of Parameters for Power System Stability Analysis Using Kalman Filter , 1981, IEEE Transactions on Power Apparatus and Systems.

[17]  Wei Li,et al.  Application of Recursive Least Squares Method for Parameter Identification of DEH Governing System , 2007 .

[18]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[19]  L. N. Hannett,et al.  Field tests to validate hydro turbine-governor model structure and parameters , 1994 .

[20]  P. Kundur,et al.  A study of early valve actuation using detailed prime mover and power system simulation , 1975, IEEE Transactions on Power Apparatus and Systems.

[21]  Sven Leyffer,et al.  Numerical Experience with Lower Bounds for MIQP Branch-And-Bound , 1998, SIAM J. Optim..

[22]  René Vidal,et al.  Identification of Hybrid Systems: A Tutorial , 2007, Eur. J. Control.

[23]  Hugo N. Villegas Pico,et al.  Modeling and analysis of speed controls in hydro-turbines for frequency performance , 2011, 2011 North American Power Symposium.

[24]  P. Pucar,et al.  On the Hinge-Finding Algorithm for Hinging Hyperplanes , 1998, IEEE Trans. Inf. Theory.

[25]  Ieee Report,et al.  Dynamic Models for Steam and Hydro Turbines in Power System Studies , 1973 .

[26]  C. T. Pan,et al.  Limit cycle analysis of a hydroelectric system: A new approach , 1986 .

[27]  D. Pantalone,et al.  Limit Cycle Analysis of Hydroelectric Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[28]  Z. Vukic,et al.  Speed and active power control of hydro turbine unit , 2005, IEEE Transactions on Energy Conversion.

[29]  James D. McCalley,et al.  Analysis of Hydro-Coupled Power Plants and Design of Robust Control to Damp Oscillatory Modes , 2015 .

[30]  D. G. Ramey,et al.  Detailed Hydrogovernor Representation for System Stability Studies , 1970 .

[31]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[32]  Thomas F. Coleman,et al.  On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds , 1994, Math. Program..

[33]  K. Natarajan,et al.  Robust PID controller design for hydroturbines , 2005, IEEE Transactions on Energy Conversion.

[34]  Mato Baotic,et al.  Hybrid Systems Modeling and Control , 2003, Eur. J. Control.

[35]  S. Billings.  Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains , 2013 .

[36]  N.D. Hatziargyriou,et al.  A Genetic Algorithm Solution to the Governor-Turbine Dynamic Model Identification in Multi-Machine Power Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.