A novel nonlinear time-varying grey power model and its application in wind energy

Purpose Accurately predicting the installed capacity of wind energy is essential for energy strategic planning, given the growing need for environmental protection worldwide and the quick development of renewable energy. In order to provide an unprecedented high-precision scheme for wind energy installed capacity prediction and to further become the primary driving force in the process of energy planning and decision-making, this research focuses on overcoming the limitations of conventional prediction models and creatively proposes a multi-parameter collaborative optimization GM(1,1) power model. This will help the energy field advance in a more efficient and scientific direction. Design/methodology/approach The theoretical framework of the fundamental GM(1,1) power model is thoroughly examined in this study and serves as the basis for further optimizations. To unlock the potential of each parameter optimization, single-parameter optimization investigations of the model are conducted from the viewpoints of the fractional optimization, background value optimization and grey action optimization, respectively. Conversely, an inventive multi-parameter collaborative optimization power model is built. The model is given dynamic flexibility by adding time-varying parameters. The sine function and interpolation technique are used to further optimize the background value. The model’s meaning is enhanced by the inclusion of a power exponent. Furthermore, several parameters are cooperatively tuned with the aid of the sophisticated Firefly algorithm, giving the model stronger predictive powers. A multi-dimensional and multi-regional model comparison analysis is formed by selecting the wind energy installed capacity data of North America, Italy, Japan and South Korea for in-depth empirical analysis in order to confirm the model’s validity. Findings The findings show that the multi-parameter collaborative optimization model (Model 5) has an exceptional in-sample and out-of-sample prediction effect. The relative prediction error MAPEs are 0.41% and 0.31%. It has a clear advantage over the simple GM(1,1) power model and other single optimization models in applications in North America, South Korea, Japan, and Italy. Its seven variable parameters are the reason for this. These factors help create a very accurate prediction effect through joint optimization from multiple perspectives. It is noteworthy that Model 4’s nonlinear optimization of the grey action is impressive. It performs better than background value optimization and fractional-order optimization. Furthermore, according to the model’s prognosis, North America’s installed wind energy capacity is expected to develop linearly and reach 513.214 bn kilowatts in 2035. This gives the planning for energy development in this area a vital foundation. Originality/value The novel idea of the multi-parameter collaborative optimization GM(1,1) power model and its clever integration with the firefly method to accomplish parameter optimization constitute the fundamental value of this study. The substantial benefits of multi-parameter optimization in the stability of the prediction effect have been firmly validated by a thorough comparison with the basic and single-optimization models. Like a lighthouse, this novel model illuminates a more accurate path for wind energy installed capacity prediction and offers high-value reference bases for a variety of aspects, including government energy planning, enterprise strategic layout, investor decision-making direction, fostering technological innovation, advancing academic research and developing energy transformation strategies. As a result, it becomes a significant impetus for the growth of the energy sector. Highlights (1) This study proposes a new gray prediction model. Compared with the traditional grey prediction model, the modeling mechanism of this model is optimized. (2) This study is based on multi-parameter collaborative optimization to achieve the improvement of model prediction effect. The traditional grey model is two-parameter, while the model proposed in this study is seven-parameter collaborative optimization; (3) In this study, swarm intelligence algorithm-firefly algorithm is used to optimize the hyperparameters, so as to obtain the best cooperative optimization multi-parameter values; (4) The application of the model is divided into two parts: empirical and application. In the empirical stage, 5 kinds of prediction models are used to predict, which proves that the model proposed in this paper is effective and improves the prediction accuracy. The application part uses the model to forecast the installed wind power capacity in North America, and the future development trend is linear growth, which is expected to double the installed capacity by 2035.