New Mathematical Techniques Simulate Offshore Wind Farms in the Netherlands

March 18, 2013

Recent figures by CBS (Statistics Netherlands) show that 4% of the energy produced in the Netherlands comes from renewable sources. Benjamin Sanderse, PhD at Centrum Wiskunde & Informatica (CWI) has developed advanced mathematical methods that are able to produce a reliable simulation of off-shore wind farms in the Netherlands.

His research, carried out for ECN, the Energy reserach Centre of the Netherlands, can give a significant boost to energy production through wind power. Sanderse will defend his thesis on 19 March 2013 at Eindhoven University of Technology (TU/e).

Off-shore wind turbines affect each other through their wakes which can be hundreds of meters long. Wakes are highly variable turbulent wind flows consisting of numerous large and small vortices. Reliably predicting these wind flows was a large challenge in Sanderse’s research. Wakes cause a lower energy production and higher load in downstream turbines, but on the other hand cause an extra inflow of air, amplifying the amount of wind in the farm. Because of the vast number of vortices, an high amount of computing power is needed to determine the flow inside the wakes.

The mathematical methods developed by Sanderse are capable of predicting the turbulent air flow in the wakes, and simulating different designs and configurations in a ‘virtual wind farm’. This simulation allows for the efficient design of large-scale wind farms. His research also enables new research questions such as the optimal distance between wind turbines and their optimal adjustment.

Sanderse developed his mathematical methods using the famous Navier-Stokes equations. These equations describe the motion of fluids and are often used to model air and water flows around aircraft and ships. The Navier-Stokes equations are one of the hardest problems in mathematics and proofs of their existence and uniqueness are still lacking. The Navier-Stokes existence problem is one of the seven Millennium Prize Problems for which the Clay Mathematics Institute has offered a 1 million dollar prize.

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Press release, March 18, 2013; Image: Nuon