Effect of wind turbine response time on optimal dynamic induction control of wind farms

In this work, we extend recent research efforts on induction-based optimal control in large-eddy simulations of wind farms in the turbulent atmospheric boundary layer. More precisely, we investigate the effect of wind turbine response time to requested power setpoints on achievable power gains. We do this by including a time-filtering of the thrust coefficient setpoints in the optimal control framework. We consider simulation cases restricted to underinduction compared to the Betz limit, as well as cases that also allow overinduction. Optimization results show that, except for the most restrictive underinductive slow-response case, all cases still yield increases in energy extraction in the order of 10% and more.

[1]  Johan Meyers,et al.  Optimal Coordinated Control of Power Extraction in LES of a Wind Farm with Entrance Effects , 2016 .

[2]  Jennifer Annoni,et al.  Analysis of axial‐induction‐based wind plant control using an engineering and a high‐order wind plant model , 2016 .

[3]  Jorge Nocedal,et al.  A Limited Memory Algorithm for Bound Constrained Optimization , 1995, SIAM J. Sci. Comput..

[4]  C. Meneveau,et al.  Large Eddy Simulations of large wind-turbine arrays in the atmospheric boundary layer , 2010 .

[5]  Roger Temam,et al.  DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms , 2001, Journal of Fluid Mechanics.

[6]  C. Meneveau,et al.  Large eddy simulation study of fully developed wind-turbine array boundary layers , 2010 .

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

[8]  Johan Meyers,et al.  Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows , 2016 .

[9]  Johan Meyers,et al.  Constrained optimization of turbulent mixing-layer evolution , 2009 .

[10]  C. Meneveau,et al.  Turbulent Inflow Precursor Method with Time-Varying Direction for Large-Eddy Simulations and Applications to Wind Farms , 2015, Boundary-Layer Meteorology.

[11]  S. Vandewalle,et al.  On the efficiency of gradient based optimization algorithms for DNS- based optimal control in a turbulent channel flow , 2016 .

[12]  K. Kunisch,et al.  Instantaneous control of backward-facing step flows , 1999 .

[13]  Robert Flemming Mikkelsen,et al.  Large-eddy simulations of the Lillgrund wind farm , 2013 .

[14]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[15]  J. Meyers,et al.  Optimal control of energy extraction in wind-farm boundary layers , 2015, Journal of Fluid Mechanics.