Power curves are commonly estimated using the binning method recommended by the International Electrotechnical Commission, which primarily incorporates wind speed information. When such power curves are used to quantify a turbine's upgrade, the results may not be accurate because many other environmental factors in addition to wind speed, such as temperature, air pressure, turbulence intensity, wind shear and humidity, all potentially affect the turbine's power output. Wind industry practitioners are aware of the need to filter out effects from environmental conditions. Toward that objective, we developed a kernel plus method that allows incorporation of multivariate environmental factors in a power curve model, thereby controlling the effects from environmental factors while comparing power outputs. We demonstrate that the kernel plus method can serve as a useful tool for quantifying a turbine's upgrade because it is sensitive to small and moderate changes caused by certain turbine upgrades. Although we demonstrate the utility of the kernel plus method in this specific application, the resulting method is a general, multivariate model that can connect other physical factors, as long as their measurements are available, with a turbine's power output, which may allow us to explore new physical properties associated with wind turbine performance. Copyright © 2014 John Wiley & Sons, Ltd.