Nonlinear deterministic modeling of highly varying loads

Power Quality Issues of Electric Arc Furnace and their Mitigations -A Review

“…presented an arc furnace model based on V-I characteristics which is obtained by the differential equation [31] Some studies have been suggested to simulate the arc furnace which is based on deterministic [32], [33], Stochastic [34], [35] and chaotic assumptions [36], [37], [38]. The deterministic model of the arc furnace is proposed by modulating the arc radius with sinusoidal signal in form of equation (1)     The author suggests that this model of electric arc furnace is helpful in the planning stage of new arc furnace on the new distribution system.…”

EMTP Implementation and Analysis of Nonlinear Load Models

“…T he chaos-based model is implemented by an adaptive modeling process whereby deterministic chaos models are selected to yield time series with some of the same features as a given sample of highly varying load current [4]. A well-known chaotic system, the Lorenz system, proved to be useful in representing the highly varying behavior of the currents in an EAF.…”

“…Further details about this model can be found in [4]. Since the chaos-based model discussed in the previous section has certain similarities to ANN modeling, an ANN model was developed using the Matlab software environment.…”

“…Finally, the low-frequency variation of the arc current sample data is captured through a peak detector (local maxima or minima). T his variation is combined with a second chaotic signal that is used to modulate the model data [4]. T his completes the tuning phase.…”

“…T hese indices describe conditions such as icker, system losses, and interference [15]. T he largest Lyapunov exponent [4] was also calculated for the actual data and the output current from the models. T his exponent is a measure of sensitivity to initial conditions (chaos) and was used to determine how well the models preserve the chaotic dynamics of the data.…”