Power regulation of horizontal-axis grid-connected up-wind constant-speed pitch-regulated wind turbines presents a demanding control problem with the plant, actuation system and control objectives all strongly nonlinear. In this paper, a novel nonlinear control strategy is devised which, in some sense, optimises performance across the operating envelope. In comparison with linear control, the nonlinear strategy achieves a substantial improvement in performance. The realisation adopted is crucial in attaining the required performance. An extended local linear equivalence condition is introduced which provides a basis for the selection of an appropriate realisation. This is an important, and general, issue in the design of gainscheduled systems and generic realisations, which satsify the extended local linear equivalence condition, are derived for SISO systems scheduled upon an internal plant or controller variable. For the wind turbine nonlinear controller, realisations which satisfy the extended local linear equivalence condition provide a substantial improvement in performance in comparison to linear control and realisations which do not satisfy this condition.