Model predictive control for wind power gradients

We consider the operation of a wind turbine and a connected local battery or other electrical storage device, taking into account varying wind speed, with the goal of maximizing the total energy generated while respecting limits on the time derivative (gradient) of power delivered to the grid. We use the turbine inertia as an additional energy storage device, by varying its speed over time, and coordinate the flows of energy to achieve the goal. The control variables are turbine pitch, generator torque and charge/discharge rates for the storage device, each of which can be varied over given ranges. The system dynamics are quite non-linear, and the constraints and objectives are not convex functions of the control inputs, so the resulting optimal control problem is difficult to solve globally. In this paper, we show that by a novel change of variables, which focuses on power flows, we can transform the problem to one with linear dynamics and convex constraints. Thus, the problem can be globally solved, using robust, fast solvers tailored for embedded control applications. We implement the optimal control problem in a receding horizon manner and provide extensive closed-loop tests with real wind data and modern wind forecasting methods. The simulation results using real wind data demonstrate the ability to reject the disturbances from fast changes in wind speed, ensuring certain power gradients, with an insignificant loss in energy production. Copyright © 2014 John Wiley & Sons, Ltd.

[1]  Stephen P. Boyd,et al.  A Splitting Method for Optimal Control , 2013, IEEE Transactions on Control Systems Technology.

[2]  Thomas Bak,et al.  Simple model for describing and estimating wind turbine dynamic inflow , 2013, 2013 American Control Conference.

[3]  R. Teodorescu,et al.  Short term energy storage for grid support in wind power applications , 2012, 2012 13th International Conference on Optimization of Electrical and Electronic Equipment (OPTIM).

[4]  Stig Øye.  Fast pitch step experiments in a wind tunnel and comparison with computational methods , 1996 .

[5]  M. Soltani,et al.  Aeolus Toolbox for Dynamics Wind Farm Model, Simulation and Control , 2010 .

[6]  Stephen P. Boyd,et al.  Receding Horizon Control , 2011, IEEE Control Systems.

[7]  James B. Rawlings,et al.  Optimizing Process Economic Performance Using Model Predictive Control , 2009 .

[8]  Stephen J. Wright,et al.  Application of Interior-Point Methods to Model Predictive Control , 1998 .

[9]  Stephen P. Boyd,et al.  Wind turbine pitch optimization , 2011, 2011 IEEE International Conference on Control Applications (CCA).

[10]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[11]  John Bagterp Jørgensen,et al.  Sequential Convex Programming for Power Set-point Optimization in a Wind Farm using Black-box Models, Simple Turbine Interactions, and Integer Variables , 2012 .

[12]  Poul Ejnar Sørensen,et al.  Centralised power control of wind farm with doubly fed induction generators , 2006 .

[13]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[14]  Stephen P. Boyd,et al.  Load reduction of wind turbines using receding horizon control , 2011, 2011 IEEE International Conference on Control Applications (CCA).

[15]  Stephen P. Boyd,et al.  Nonconvex model predictive control for commercial refrigeration , 2013, Int. J. Control.

[16]  Niels Kjølstad Poulsen,et al.  Economic Model Predictive Control for building climate control in a Smart Grid , 2012, 2012 IEEE PES Innovative Smart Grid Technologies (ISGT).

[17]  Peter Fogh Odgaard,et al.  Repetitive model predictive approach to individual pitch control of wind turbines , 2011, IEEE Conference on Decision and Control and European Control Conference.

[18]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[19]  H. Madsen,et al.  Ultra-short term wind speed forecasting , 2004 .

[20]  David Angeli,et al.  On Average Performance and Stability of Economic Model Predictive Control , 2012, IEEE Transactions on Automatic Control.

[21]  R. Watson,et al.  Frequency Response Capability of Full Converter Wind Turbine Generators in Comparison to Conventional Generation , 2008, IEEE Transactions on Power Systems.

[22]  Stephen P. Boyd,et al.  Convex piecewise-linear fitting , 2009 .

[23]  Stephen P. Boyd,et al.  Operation and Configuration of a Storage Portfolio via Convex Optimization , 2011 .

[24]  David Angeli,et al.  Fundamentals of economic model predictive control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[25]  Manfred Morari,et al.  Use of model predictive control and weather forecasts for energy efficient building climate control , 2012 .

[26]  Nicolai Fog Gade-Nielsen,et al.  Numerical Methods for Solution of the Extended Linear Quadratic Control Problem , 2012 .

[27]  Henrik Madsen,et al.  Forecasting wind speeds on the minute time-scale using up-stream information , 2004 .

[28]  Stephen P. Boyd,et al.  CVXGEN: a code generator for embedded convex optimization , 2011, Optimization and Engineering.

[29]  Thyge Knuppel,et al.  Power oscillation damping controller for wind power plant utilizing wind turbine inertia as energy storage , 2011, 2011 IEEE Power and Energy Society General Meeting.

[30]  Moritz Diehl,et al.  A Lyapunov Function for Economic Optimizing Model Predictive Control , 2011, IEEE Transactions on Automatic Control.

[31]  Frank Allgöwer,et al.  Nonlinear model predictive control : towards new challenging applications , 2009 .

[32]  J. Jonkman,et al.  Definition of a 5-MW Reference Wind Turbine for Offshore System Development , 2009 .

[33]  Niels Kjølstad Poulsen,et al.  Nonlinear Model Predictive Control of a Simplified Wind Turbine , 2011 .

[34]  A. T. Holen,et al.  Operation planning of hydrogen storage connected to wind power operating in a power market , 2006, IEEE Transactions on Energy Conversion.

[35]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

[36]  Niels Kjølstad Poulsen,et al.  A fatigue approach to wind turbine control , 2006 .

[37]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[38]  G. Strbac,et al.  Value of Bulk Energy Storage for Managing Wind Power Fluctuations , 2007, IEEE Transactions on Energy Conversion.

[39]  Niels Kjølstad Poulsen,et al.  Wind turbine control with constraint handling: a model predictive control approach , 2012 .

[40]  Willett Kempton,et al.  Cost-minimized combinations of wind power, solar power and electrochemical storage, powering the grid up to 99.9% of the time , 2013 .

[41]  Bharat Singh,et al.  Wind Power Interconnection into the Power System: A Review of Grid Code Requirements , 2009 .

[42]  Lars Grüne,et al.  Economic receding horizon control without terminal constraints , 2013, Autom..

[43]  John Bagterp Jørgensen,et al.  Moving Horizon Estimation and Control , 2004 .

[44]  Jan Pierik,et al.  Inertial response of variable speed wind turbines , 2006 .

[45]  John Bagterp Jørgensen,et al.  Model predictive control technologies for efficient and flexible power consumption in refrigeration systems , 2012 .

[46]  Stephen P. Boyd,et al.  Dynamic Network Energy Management via Proximal Message Passing , 2013, Found. Trends Optim..

[47]  Mate Jelavić,et al.  Wind Turbine Power References in Coordinated Control of Wind Farms , 2011 .

[48]  Stephen P. Boyd,et al.  MPC for wind power gradients — utilizing forecasts, rotor inertia, and central energy storage , 2013, 2013 European Control Conference (ECC).

[49]  G. C. Tarnowski.  Coordinated Frequency Control of Wind Turbines in Power Systems with High Wind Power Penetration , 2012 .

[50]  Stephen P. Boyd,et al.  Recent Advances in Learning and Control , 2008, Lecture Notes in Control and Information Sciences.

[51]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[52]  Remus Teodorescu,et al.  Lifetime investigations of a lithium iron phosphate (LFP) battery system connected to a wind turbine for forecast improvement and output power gradient reduction , 2011 .

[53]  Maryam Soleimanzadeh,et al.  An optimization framework for load and power distribution in wind farms , 2012 .

[54]  Daria Madjidian,et al.  A Stationary Turbine Interaction Model for Control of Wind Farms , 2011 .

[55]  Poul Ejnar Sørensen,et al.  A survey of interconnection requirements for wind power , 2007 .

[56]  Erich Hau,et al.  Wind Turbines: Fundamentals, Technologies, Application, Economics , 1999 .

[57]  D.Q. Dang,et al.  Model Predictive Control for maximum power capture of variable speed wind turbines , 2010, 2010 Conference Proceedings IPEC.

[58]  Niels Kjølstad Poulsen,et al.  Robust model predictive control of a wind turbine , 2012, 2012 American Control Conference (ACC).