Wind power curve modeling is a challenging task due to the existence of inconsistent data, in which the recorded wind power is far away from the theoretical wind power at a given wind speed. In this case, confronted with these samples, the estimated errors of wind power will become large. Thus, the estimated errors will present two properties: heteroscedasticity and error distribution with a long tail. In this paper, according to the above-mentioned error characteristics, the heteroscedastic spline regression model (HSRM) and robust spline regression model (RSRM) are proposed to obtain more accurate power curves even in the presence of the inconsistent samples. The results of power curve modeling on the real-world data show the effectiveness of HSRM and RSRM in different seasons. As HSRM and RSRM are optimized by variational Bayesian, except the deterministic power curves, probabilistic power curves, which can be used to detect the inconsistent samples, can also be obtained. Additionally, with the data processed by replacing the wind power in the detected inconsistent samples with the wind power on the estimated power curve, the forecasting results show that more accurate wind power forecasts can be obtained using the above-mentioned data processing method.