How do wind farm blockage and axial induction control interact?

Wake losses significantly reduce wind farm output, but wind farm flow control (WFFC) can substantially reduce these losses, using wake steering (yawing upstream turbines) and/or axial induction control (reducing turbine power and thrust to weaken their wakes). Previous work shows that ignoring wind farm blockage in traditional wake models represents a prediction bias of similar order to the gains achievable with WFFC. Axial induction control works by changing turbine thrust, which is also the cause of blockage; this raises the question of how the two effects interact. Induction control can more than compensate for any loss due to blockage, but here we investigate the relationship further. Induction control reduces turbine thrust coefficients to reduce wake losses, but this should also reduce blockage, suggesting that induction control might achieve higher gains in practice than predicted with blockage effects ignored. An engineering model for blockage effects was added to the wind farm code LongSim, and steady-state gains calculated for a well-known offshore wind farm, with and without blockage. The results confirm that the power gains are indeed higher if blockage is modelled. These results are corroborated by comparisons against RANS (Reynolds-Averaged Navier Stokes) simulations, in which blockage effects are implicitly modelled.