A method is proposed for the calculation of current density in a long solid metallic conductor placed in an external variable magnetic field. The external magnetic field is perpendicular to the conductor and constant on straight lines parallel to the conductor. The conductor is passive, connected to neither a voltage source nor a current source. It is assumed that the external magnetic field is quasi-stationary and is not affected by the magnetic field of the currents induced in the conductor under examination. The frequency of external field does not exceed 1 MHz and the displacement current is neglected. The proposed method enables the calculation of current density not only in the steady state but also in the case that the external field has an arbitrary time-dependent course. Results are given of the calculation of current density in conductors with symmetrical and unsymmetrical cross section, with constant and non-constant resistivity in the conductor cross section, for both homogeneous and non-homogeneous external steady-state sinusoidal field, and for switching the external sinusoidal field on and off.

No abstract

The paper deals with the self-induction of two parallel infinitely long conductors of arbitrary cross section connected to an ideal sinusoidal voltage source. The conductors do not move. A quasi-stationary behavior is assumed, the displacement current is neglected and the permeability of the conductors and their surroundings equals the permeability of vacuum. The subject matter of the paper is the calculation of impedance, which in the theory of circuits with lumped elements can replace 1 m of conductors. The definition of inductance and the formulae for its calculation that form part of textbooks on physics and electromagnetism have been the same for such a long time that nobody doubts their correctness. Only the recently published method for the calculation of current density in long parallel conductors allows calculating accurately the equivalent impedance and self-inductance, and also evaluating critically the present knowledge.

The article provides a comprehensive idea of the calculating the magnetic field and forces in a pair of parallel solid conductors. The conductors are connected to a sinusoidal voltage source of a frequency that does not exceed 1 MHz. Thus the current density over the conductor cross sections is not constant. Its distribution depends on the distance of the conductors and their resistivity, on the shape of conductor cross sections, and on the voltage source frequency. The distribution of current density over the conductor cross sections affects not only the magnetic field produced by the conductors but also the forces acting on the conductors. For the acting forces, general conclusions are derived that hold for conductors of arbitrary shape of cross section. Specifically, pairs of conductors of rectangular, circular and triangular cross section are examined.

Flexibility is generally considered as the potential of a facility (generation/consumption or storage) to actively change the amount of its generation/consumption/accumulated energy based on price signals or direction. This control strategies is managed to correct deviations of the electricity grid or to ensure that the purchase/sale of electricity is profitable for the flexibility provider. This paper presents a comparison of the control of heat pump consumption to provide consumption flexibility.