An accurate wind turbine power curve (WTPC) plays a vital role in wind power forecasting and wind turbine condition monitoring. There are two major shortcomings of current WTPC models that prevent more accurate WTPC estimation, limited nonlinear fitting ability and the lack of in-depth understanding of the complex characteristics of WTPC. This paper proposes two novel regression models to overcome these two disadvantages simultaneously. First, they make use of multiple spline regression models (MSRM) with different basis functions and different numbers of knots to describe the complex nonlinear relationship between wind speed and wind power. Moreover, sparse prior distributions help avoid the adverse effects of redundant mapping features and useless basis functions on the model performance. Second, they embed the heteroscedasticity of WTPC modeling into MSRM based on Gaussian and Student's t-distributions, respectively. Finally, two sparse heteroscedastic MSRM with Gaussian and Student's t-distributions will be constructed and named as SHMSRM-G and SHMSRM-T, respectively. We compare the proposed models with fifteen benchmark models, and find that they can generate more accurate WTPCs than the others in different seasons and different wind farms. Thus, it is important to consider the complex nonlinear fitting ability and heteroscedasticity together in constructing accurate WTPC models.