A Novel Chaotic Model Of Ac Electric Arc Furnace And Its Application

The extensive application of AC electric arc furnace (EAF) and the continuous increase of monomer capacity cause power quality problems become increasingly prominent, such as voltage fluctuation and flicker, harmonics, and three-phase imbalance. Power quality problems caused by EAF even endanger the safety of Distribution System and the normal operating of other users, which have aroused great concern of many electrical engineers. In order to solve power quality problems caused by EAF, we should solve the problem of EAF model firstly. This is not only for the simulated assessment of the adverse effects caused by EAF, but also for providing preconditions to investigate the measures to mitigate power quality problems. Therefore, studying a novel model which can accurately reflect electrical characteristics of EAF, and can be accepted by most electrical engineers has a strong theoretical significance and high value.In recent years, development of nonlinear science (such as chaos and bifurcation) provides a new way to study the electrical characteristic of EAF. As the theoretical foundation to research EAF chaotic phenomena and to establish a novel chaotic model of EAF, the associated basic chaos theory is discussed at first. The U.S. Bureau of Mines Albany Research Center's recent research results are introduced, which verified that the EAF system is of low dimensionality, and the electrical fluctuations are indicative of a chaotic system.In order to accurately simulate the asymmetric double-scroll chaotic attractor observed in EAF system, an improved Chua's circuit (EAF chaotic circuit) is presented, which contains an asymmetric nonlinear resistive element. The dynamics state equations of the EAF chaotic circuit are obtained based on Kirchhoff laws. Through a rigorous mathematical analysis, the results show that the largest Lyapunov index is positive when the parameters of the EAF chaotic circuit are chose appropriately. The results of mathematical analysis meet Shilnikov theorem, and the equilibrium points P-1 and P1 are asymmetric about P0. So it is proved that the dynamics system will generate asymmetric double-scroll chaotic attractor. Simulated study is performed in MATLAB. Varying the value of linear resistor and the initial values of system state variables in the circuit, rich variety dynamical behaviors are observed, such as DC equilibrium point, Hopf bifurcation, period-doubling bifurcation, single-scroll strange attractor, periodic windows, and asymmetric double-scroll strange attractor. The extreme sensitivity in the state trajectory with respect to the initial conditions is exhibited; the special characteristic of EAF chaotic circuit is found also. A negative resistance converter is realized using an integrated operational amplifier. Two negative resistance converters are connected in parallel, whose V-I characteristics are different. And the positive and negative voltage amplitudes of power supply resource are unequal. The hardware circuit of an EAF chaotic circuit is realized, so does the experiment. The experimental results show that the designed hardware circuit of EAF chaotic circuit has the characteristic of general Chua's circuit, and it can produce asymmetric double-scroll chaotic attractor. The EAF chaotic circuit can be used to describe the actual chaotic system more accurately.In order to estimate the adverse effects caused by EAF accurately, a novel chaotic model of EAF is presented, which is useful for power quality studies. Firstly, the static model is developed based on a piecewise linear approximation of V-I characteristic of EAF, the V-I characteristic is depended on the active power consumed by the load. It is useful for harmonics study. Secondly, the dynamic model is developed using a low-frequency chaotic signal to modulate the static electric arc voltage, the chaotic signal is generated via the EAF chaotic circuit. It is useful for voltage fluctuation and flicker study. Simulation of the static model and dynamic model are performed in MATLAB. Through comparing the simulated results with the measurement data, it is shown that the model can accurately represent the static and dynamic behaviors of EAF. The developed model is valid and easy to use, which will promote the precaution measures studies of power quality problems. Finally, an EAF main circuit experimental system is established based on dSPACE equipment, which can simulate the actual electrical characteristic of EAF system, and can be used to test the effectiveness of the flexible power supply method of EAF.The voltage fluctuation and flicker caused by EAF is analyzed based on the novel chaotic model of EAF, a simulated model of IEC flickermeter is established also, which can be used to evaluate the flicker caused by EAF. Firstly, mathematical analysis of the voltage fluctuation and flicker caused by EAF is achieved; some experiential formulas to estimate voltage fluctuation and flicker are obtained. Secondly, a simulated model of IEC flickermeter is established in MATLAB, according to the verify standard recommended by IEC, the simulated IEC flickermeter is proved to be valid. Evaluation of the flicker caused by an actual EAF is achieved, the results shows that application of emulation mode to evaluate the flicker caused by EAF is an effective way. Simulated analyses of the factors affect voltage fluctuation and flicker is performed, which validated that the flicker is direct proportion to EAF capacity, and the flicker is inverse proportion to power system capacity. The chaotic model can be used to investigate the effect on flicker compensation of the insertion of series inductors at the supply side of the furnace transformer, simulation results show that considerable reduction of S(t) is obtained at the point of common coupling by series inductor installation. Finally, different measures to mitigate the voltage fluctuation and flicker caused by EAF are analyzed.In conclusion, an improved chua's circuit (EAF chaotic circuit) is presented which can describe EAF chaotic phenomenon more accurately, and the hardware circuit of EAF chaotic circuit is established based on the integrated operational amplifier. A novel chaotic model of EAF is presented, which can be used to investigate power quality problems. An EAF main circuit experimental system is developed based on dSPACE equipment. An IEC flickermeter model is established which can be used to evaluate the flicker caused by EAF.