Energy transport through coordinated wake control in offshore wind farm clusters

Abstract

Offshore wind farms in the North Sea are built in proximity of each other. Close enough that one can block and reduce each other’s incoming wind. This thesis asks whether that coupling can be used on purpose. Curtailing an upwind farm weakens its wake, increasing the incoming wind speed at the downwind farm. The upwind farm gives up energy, and the downwind farm partly recovers it. That is what a transmission line does, but less efficiently.

Whether the trade-off is worth making depends on the wake physics and the electricity market. Efficiency and direction of the trade-off depends on wake and atmospheric physics. Whether the energy is more needed downwind depends on the energy-market conditions.

Combining them in one optimisation problem is difficult, because the wake is non-linear in exactly the quantity being optimised. The Jensen wake model is therefore linearised in two steps. First, the
power curve, the power coefficient curve and the mapping to the axial induction factor are replaced with piecewise linear fits. Second, the remaining dependence on curtailment is removed with a Taylor expansion around two reference points. The result maps a single scalar to the output of every turbine in a two-farm cluster and remains tractable for clusters of 374 turbines.

The cluster is placed in two market settings. In the first, day-ahead prices are fixed, and the operator
maximises cluster revenue. Applied to the Belgian–Dutch cluster on 6 August 2021, curtailing the Belgian farm raises revenue from 81.8 to 96.7 kEUR, an increase of 18 %. Kenis et al. report 21 % for the same hour with a Gaussian wake model and multiplicative superposition. The two studies agree on
direction and order of magnitude, and the difference follows from the wake model that the linearisation permits. Over 2021 as a whole, the control strategy increases revenue in 310 of 8688 hours and raises annual cluster revenue by 1.1 %.

In the second setting, the price is no longer an input. The cluster is embedded in a nodal model of the Dutch and Belgian electricity systems, which minimises total system cost. The question becomes whether curtailment serves the system rather than the wind farm operator. Four cases are examined; IJmuiden Ver with Hollandse Kust West shows no benefit: a detour with spare capacity always remains available, and the system prefers the cable. Borssele with the Belgian zone in the 2020 system shows none either, because neither country holds a surplus of cheap generation. Adding 10 GW of planned Dutch capacity changes that. At windy hours, the Netherlands generates more cheap wind energy than the demand and interconnectors can handle. Curtailing the upwind farm increases the downwind farm’s energy generation, which can displace energy generation from fossil gas. Over a 24 h window 2.2 GW h of gas generation is avoided. Reducing the Belgian nuclear fleet to its 2026 capacity increases the windows when curtailing is useful, because a flexible unit is left on the margin more often. Measured as power gained downwind over power given up upwind, the cluster transports at 29 to 63 % efficiency.

Cluster control is therefore not a substitute for transmission, and the conditions under which it pays are narrow. A congested border, a surplus of cheap generation in the upwind zone, a flexible generator still on the margin downwind, and a wind direction running from one to the other must all hold at the same time. Wherever a route with spare capacity exists, the system takes it instead. In the cases studied
here, those conditions were met in a small share of the year, and only after 10 GW of planned capacity was added to the system. But where they do hold, the effect is not marginal: a single eight-hour period displaced 3.1 GW h of gas generation, and the periods over which the wind allows it can last for days rather than hours.