The paper proposes an adaptation of mathematical models derived from the theory of deterministic chaos to short-term power forecasts of wind turbines. The operation of wind power plants and the generated power depend mainly on the wind speed at a given location. It is a stochastic process dependent on many factors and very difficult to predict. Classical forecasting models are often unable to find the existing relationships between the factors influencing wind power output. Therefore, we decided to refer to fractal geometry. Two models based on self-similar processes (M-CO) and (M-COP) and the (M-HUR) model were built. The accuracy of these models was compared with other short-term forecasting models. The modified model of power curve adjusted to local conditions (M-PC) and Canonical Distribution of the Vector of Random Variables Model (CDVRM). Examples of applications confirm the valuable properties of the proposed approaches.

This paper presents new directions in the modeling of electric arc furnaces. This work is devoted to an overview of new approaches based on random differential equations, artificial neural networks, chaos theory, and fractional calculus. The foundation of proposed solutions consists of an instantaneous power balance equation related to the electric arc phenomenon. The emphasis is mostly placed on the conclusions that come from a novel interpretation of the equation coefficients.

This study addresses the issue of diagnosing faults in electric vehicle motors and presents a method utilizing Improved Wavelet Packet Decomposition (IWPD) combined with particle swarm optimization (PSO). Initially, the analysis focuses on common demagnetization faults, inter turn short circuit faults, and eccentricity faults of permanent magnet synchronous motors. The proposed approach involves the application of IWPD for extracting signal feature vectors, incorporating the energy spectrum scale, and extracting the feature vectors of the signal using the energy spectrum scale. Subsequently, a binary particle swarm optimization algorithm is employed to formulate strategies for updating particle velocity and position. Further optimization of the binary particle swarm algorithm using chaos theory and the simulated annealing algorithm results in the development of a motor fault diagnosis model based on the enhanced particle swarm optimization algorithm. The results demonstrate that the chaotic simulated annealing algorithm achieves the highest accuracy and recall rates, at 0.96 and 0.92, respectively. The model exhibits the highest fault accuracy rates on both the test and training sets, exceeding 98.2%, with a minimal loss function of 0.0035. Following extraction of fault signal feature vectors, the optimal fitness reaches 97.4%. In summary, the model constructed in this study demonstrates effective application in detecting faults in electric vehicle motors, holding significant implications for the advancement of the electric vehicle industry.