The analytical model of steady-state of three-phase circuit with nonlinear load

Abstract

Higher harmonics are particularly important among disturbances of the power quality. Their primary source are nonlinear loads which process the energy of fundamental harmonic on the higher harmonics energy. Such load can be used in the stiffness test of the supply network. An arc furnace is one of more often met industrial nonlinear load. The paper deals with the balanced three-phase circuit of the arc furnace in which arcs voltages are proportional to the sign of arcs currents. The equation of fundamental harmonic and equations of higher harmonic phasic currents were determined. Next the higher harmonics of currents and further fundamental harmonic of currents were designated analytically. On its base equivalent diagrams of nonlinearities were described. The analyzed load has the univalent characteristics (without hysteresis) and also does not cumulate the energy. During the work the circuit of the furnace on terminals of the power source it is observed greater inductances than during short circuit tests. This difference arise of the equivalent inductance of the electric arc, calculated for first of harmonic. The total reactive power of the nonlinearity being with the sum of all harmonics reactive powers, computed as proportional to the product of the voltages and the time derivative of the current is equal to the zero. All that concerns the circuit with the countable number of the zero crossing of currents. Equations of the considered circuit describe also other nonlinear receiver, less burdensome for the environment and the modelling than the three-phase electric arcs.