The relationship between wind speed and the power produced by a wind turbine is expressed by its power curve. Power curves are commonly used to monitor the production performance of a wind turbine by asset managers to ensure optimal production. They can also be used as a tool to detect faults occurring on a wind turbine when the fault causes a decrease in performance. However, the wide dispersion of data generally observed around the reference power curve limits the detection performance of power curve-based techniques. Fault indicators, such as residuals, which measure the difference between the actual power produced and the expected power, are largely affected by this dispersion. To increase the detection performance of power-based fault detection methods, a hybrid solution of mono-multi-turbine residual generation is proposed in this paper to reduce the influence of the power curve dispersion. A new simulation framework, modeling the effect of wind nature (turbulent/laminar) on the wind turbine performance, is also proposed. This allows us to evaluate and compare the performances of two fault detection methods in their multi-turbine implementation. The results show that the application of a multi-turbine approach to a basic residual generation method significantly improves its detection performance and makes it as efficient as a more complex method.