A novel monotonic wind turbine power-speed characteristics model

Major issues with logistic functions (LFs) in modeling wind turbine power-speed characteristics (WTPSCs) include: 1. low accuracy near cut-in and rated wind speeds due to lack of continuity; 2. difficulties in fitting their parameters because of ill-conditioning; 3. no guaranteed monotonicity; 4. no systematic way to determine upper and lower limits for their parameters. The literature also reports that six parameter LFs may sometimes provide less accurate results than five, four, and three parameter models, implying: 1. they are unsuitable for WTPSC modeling; 2. lack of systematic method to determine upper and lower limits for optimization algorithms to search in. In this paper, we propose a new six parameter LF then employ subspace trust-region (STIR) algorithm to estimate its parameters. We compare the accuracy of our six parameter model to others from the literature. With 42 on-shore and off-shore WTs database of ratings varying from 275 to 8000 kW, we the comprehensiveness of our model. The results show an average mean absolute percent error (MAPE) of 2.383 x 10-3. Furthermore, our model reduces average and median normalized root mean square error (NRMSE) by 32.3% and 38.5%, respectively.