A wide nonlinear analysis of reactive power time series related to electric arc furnaces

► In this study we analyze the nonlinear behavior of EAF reactive power variations. ► Time delay reconstruction, surrogate date, DVV and recurrence plot methods are used. ► Some new indices are defined to quantify the nonlinear component. ► We show that the nonlinear deterministic component is small. ► There is no need to use the nonlinear models for EAF reactive power prediction. Prediction of electric arc furnace (EAF) reactive power is an appropriate solution to compensate for static VAr compensator delay and improve its performance in flicker reduction. A linear autoregressive moving average (ARMA) can only pull out the linear deterministic (LD) component of EAF reactive power time series. For the prediction to be made through both nonlinear deterministic (ND) and LD components, employing nonlinear models is necessary. However, before developing the nonlinear models for prediction, the necessity of the employing them should be verified by investigating the significance of the ND components in the process. This paper presents a novel approach for wide analysis of nonlinear behavior of EAFs reactive power time series related to eight ac EAFs installed in Mobarakeh steel industry, Isfahan, Iran to answer the question about the importance of their ND components. In the approach, a suitable linear auto regressive moving average (ARMA) model with order (4,4) is used for the time series to extract the residual time series. Then, a number of well established nonlinear analysis techniques such as time delay reconstruction, surrogate data, delay vector variance and recurrence plot methods are applied to the original and residual time series. To describe the nonlinear characteristics of the time series, some new indices are defined. They quantify the significance of the ND component in compare with LD component.