  A new theoretical approach is proposed to predict a practical upper limit to
the efficiency of a very large wind farm. The new theory suggests that the
efficiency of ideal turbines in an ideal very large wind farm depends primarily
on a non-dimensional parameter $\lambda/C_{f0}$, where $\lambda$ is the ratio
of the rotor swept area to the land area (for each turbine) and $C_{f0}$ is a
natural friction coefficient observed before constructing the farm. When
$\lambda/C_{f0}$ approaches to zero, the new theory goes back to the classical
actuator disc theory, yielding the well-known Betz limit. When $\lambda/C_{f0}$
increases to a large value, the maximum power coefficient of each turbine
reduces whilst a normalised power density of the farm increases asymptotically
to an upper limit. A CFD analysis of an infinitely large wind farm with
'aligned' and 'displaced' array configurations is also presented to validate a
key assumption used in the new theory.
