PL426049A1 - Method for determining the parameters of fractional order models for fractional order coils and supercapacitors and system for implementing the method - Google Patents

Abstract

The method of determining the parameters of fractional-order models for fractional-order coils and supercapacitors consists in measuring two resonant frequencies signaled by a current and voltage phase shift detector (D) in a circuit containing a fractional-order coil Lβ and two switched reference capacitors C1w, C2w or a supercapacitor ( Cα) and two switched reference coils (Lw1, Lw2), and then the rms value of the voltage in the resonant circuit and the current in one of the resonant states are measured, and then based on the determined resonant frequencies ƒLr1, ƒLr2 of the system with a fractional order coil or ƒCr1, ƒCr2 system with a supercapacitor Cα and the parameters of the reference elements C1w, C2w or Lw1, RLw1, Lw2, RLw2, the parameters of the fractional order elements are calculated from the phase resonance condition in the RLC circuit, which is described by the relationship Im{Z(jω)} = 0, which means that in the resonance state, the series connection of the fractional-order coil Lβ and the capacitor C1w or C2w, or the supercapacitor (Cα) and reference coil (Lw1, Lw2) from the side of the circuit terminals can be replaced by a short circuit. The system for measuring the parameters of fractional-order coils or supercapacitors (Cα) is characterized by the fact that it consists of a sinusoidal voltage generator (G) with a tunable frequency, supplied from a low-voltage network, supplying a series resonant circuit, the tested element in the form of a fractional-order coil Lβ or supercapacitor (Cα) connected by wires to one of the two switchable capacitors C1w, C2w or standard coils (Lw1, Lw2), phase shift detector (D) between current and voltage on the resonant circuit and current RMS meter (A) connected in series to resonant circuit and an RMS voltage meter (V) connected in parallel to the resonant circuit.