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Transformer state forecasting and fault forecasting are important for the stable operation of power equipment and the normal operation of power systems. Forecasting of the dissolved gas content in oil is widely conducted for transformer faults, but its accuracy is affected by data scale and data characteristics. Based on phase space reconstruction (PSR) and weighted least squares support vector machine (WLSSVM), a forecasting model of time series of dissolved gas content in transformer oil is proposed in this paper. The phase spaces of time series of the dissolved gas content sequence are reconstructed by chaos theory, and the delay time and dimension are obtained by the C-C method. The WLSSVM model is used to forecast time series of dissolved gas content, the chemical reaction optimization (CRO) algorithm is used to optimize training parameters, the bootstrap method is used to build forecasting intervals. Finally, the accuracy and generalization ability of the forecasting model are verified by the analysis of actual case and the comparison of different models.

Wind power, one of renewable energy resources, is a fluctuating source of energy that prevents its further participation in the power market. To improve the stability of the wind power injected into the power grid, a short-term wind speed predicting model is proposed in this work, named VMD-P-(ARIMA, BP)-PSOLSSVM. In this model, variational mode decomposition (VMD) is combined with phase space reconstruction (P) as data processing method to determine intrinsic mode function (IMF) and its input−output matrix in the prediction model. Then, the linear model autoregressive integrated moving average model (ARIMA) and typical nonlinear model back propagation neural network (BP) are adopted to forecast each IMF separately and get the prediction of short-term wind speed by adding up the IMFs. In the final stage, particle swarm optimization least squares support vector machine (PSOLSSVM) uses the prediction results of the two separate models from previous step for the secondary prediction. For the proposed method, the PSOLSSVM employs different mathematical principles from ARIMA and BP separately, which overcome the shortcoming of using just single models. The proposed combined optimization model has been applied to two datasets with large fluctuations from a northern China wind farm to evaluate the performance. A performance comparison is conducted by comparing the error from the proposed method to six other models using single prediction techniques. The comparison result indicates the proposed combined optimization model can deliver more accurate and robust prediction than the other models; meanwhile, it means the power grid dispatching work can benefit from implementing the proposed predicting model in the system.

With the development of the carbon market in China, research on the carbon price has received more and more attention in related fields. However, due to its nonlinearity and instability, the carbon price is undoubtedly difficult to predict using a single model. This paper proposes a new hybrid model for carbon price forecasting that combines fast ensemble empirical mode decomposition, sample entropy, phase space reconstruction, a partial autocorrelation function, and an extreme learning machine that has been improved by particle swarm optimization. The original carbon price series is decomposed using the fast ensemble empirical mode decomposition and sample entropy methods, which eliminate noise interference. Then, the phase space reconstruction and partial autocorrelation function methods are combined to determine the input and output variables in the forecasting models. An extreme learning machine optimized by particle swarm optimization was employed to forecast carbon prices. An empirical study based on carbon prices in three typical regional carbon markets in China found that this new hybrid model performed better than other comparable models.

In order to improve the accuracy of wind power prediction (WPP), we propose a WPP based on multivariate phase space reconstruction (MPSR) and multivariate linear regression (MLR). Firstly, the multivariate time series (TS) are constructed through reasonable selection of wind power and weather factors, which are closely associated with wind power. Secondly, the phase space of the multivariate time series is reconstructed based on the chaos theory and C-C method. Thirdly, an auto regression model for multivariate phase space is created by regarding phase variables as state variables, and the very-short-term wind power is predicted by using a multi-linear regression algorithm. Finally, a parallel algorithm based on map/reduce is presented to improve computing speed. A cloud computing platform, Hadoop consisting of five nodes, is established as a matter of convenience, followed by the prediction of wind power of a wind farm in the Hunan province of China. The experimental results show that the model based on MPSR and MLR is more accurate than both the continuous method and the simple approximation method, and the parallel algorithm based on map/reduce effectively accelerates the computing speed.

Accurate generation prediction at multiple time-steps is of paramount importance for reliable and economical operation of wind farms. This study proposed a novel algorithmic solution using various forms of machine learning techniques in a hybrid manner, including phase space reconstruction (PSR), input variable selection (IVS), K-means clustering and adaptive neuro-fuzzy inference system (ANFIS). The PSR technique transforms the historical time series into a set of phase-space variables combining with the numerical weather prediction (NWP) data to prepare candidate inputs. A minimal redundancy maximal relevance (mRMR) criterion based filtering approach is used to automatically select the optimal input variables for the multi-step ahead prediction. Then, the input instances are divided into a set of subsets using the K-means clustering to train the ANFIS. The ANFIS parameters are further optimized to improve the prediction performance by the use of particle swarm optimization (PSO) algorithm. The proposed solution is extensively evaluated through case studies of two realistic wind farms and the numerical results clearly confirm its effectiveness and improved prediction accuracy compared to benchmark solutions.