# Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review
## 4 Forecasting of Chaotic Time Series in Various Applications
### Power and Energy
#### 4.1.3 Other Power Systems  
Under certain circumstances, chaos in an electrical power system can show abnormal oscillations, threatening the electrical grid's reliability and stability. Because of the nonlinearities of electricity networks, chaos theory is a high priority. Hence, the application of chaos theory and several forecasting approaches to improve the accuracy and reliability of load forecasting. The proposed forecasting approaches for predicting the electrical daily peak load of the power systems, such as South Korea Electric Power Corporation, Daqing oilfield company in China, New South Wales in Australia, and North China city, are as follows:  
* ANN [26];
* Bee evolution modifying PSO tuned chaotic neural network [71];
* Adding-weighted LLE [72];
* Dynamic recurrent FNN [76];
* Chaotic RBFNN [84];
* Chaotic local weighted linear forecast algorithm based on angle cosine [88].  
The self-adaptive chaotic BPNN and parallel chaos algorithm reported in [128], and [118], respectively, are used for forecasting the short-term electrical power load in the China network. The limitations of the proposed approaches are eliminated with the application of hybridized chaotic RBFNN-quantile regression model for forecasting the weather, seasons, wind power, and electricity price. The hybrid forecasting approaches developed for predicting the dynamic characteristics of electricity are the wavelet decomposition methodology [120], variational mode decomposition-maximum relevance minimum redundancy based BPNN-LS-SVM [156], and short- and medium-term load in the Xi'an power grid corporation, China.  
Short-term electricity price forecasting has become crucial in the power markets, as it allows for the foundation for market participants' profit maximization. The proposed methods for forecasting the short-term electricity spot market prices and the marginal price at the New England and California electricity markets in the USA are as follows:* Nonlinear auto-correlated chaotic model-based WNN [38];
* RNN [40];
* LS-SVM algorithm [60];
* Add-weighted one-rank multi-steps prediction model [63].  
The generation companies can decide on scheduling generators and provide high-quality power services to customers. Thus, the validation algorithm presented in [93] is based on the voltage sensor applied to a DC zonal shipboard electric power system, using decentralized polynomial chaos theory for the sensor validation decentralized state prediction. In addition, it is to be reported that the presented conventional algorithms were improved using artificial intelligence techniques. The independent component analysis method reported in [94] for predicting the amplitude and frequency of highly chaotic distorted power system signals is presented based on duffing oscillator solutions. The proposed approach can be used for the real-time control and measurement of the fundamental frequency of a power system while focusing mainly on chaotic disturbances. The maximum velocity criterion method, sinusoidal wave frequency modulation, and chaotic control algorithm are for forecasting the chaos and suppressing the predicted chaos to increase the security for cyber-physical power systems [112]. The modified BPNN, chaos-search GA, and SA algorithms are applied to predict a smart grid's short-term electrical energy demand in New South Wales, Australian grid [115]. The proposed approach can also lower the system's total operational costs and ensure the next-generation power grids' effective and reliable functioning. The polynomial chaos expansion-based Langevin Markov chain Monte Carlo and multi fidelity-surrogate-based Bayesian inference via adaptive importance sampling predict decentralized dynamic parameters, such as inertia, exciter gains, damping ratio, and the droop of the synchronous generator in New England, USA [138; 151].