Mathematical Model of a Nonlinear Power Transformer for Needs of Relay Protection

Abstract

In this work, a mathematical model of a three-phase nonlinear transformer is suggested. The model enables simulating the transformer operation with allowance for its nonlinearity and covers needs of the relay protection. Our model has been developed on the basis of a mathematical model with phase coordinates, where differential equations are composed by the Kirchhoff’s phase-voltage law. Based on this model, we first compose a mathematical model for simulating steady-state operation modes of a transformer, taking into account the asymmetry and nonlinearity of its ferromagnetic core. In this model, the initial values of inductances and mutual inductances of loops are determined from the main phase inductance calculated by the experimentally found no-load current, and their current values are determined from the currents in windings and the magnetic fluxes in legs of the transformer core. The magnetic fluxes are calculated by the nodal-pair method. This improved mathematical model is verified through a comparison between the calculated harmonic components of the phase currents and the experimental results. The harmonic components are calculated with the use of Fourier expansion of the calculated phase currents. Their experimental values are determined with a spectrum analyzer. The calculated and experimental harmonic components of the currents of phase A during no-load and rated-load operation of the transformer are tabulated. The comparison of these results shows that the mathematical model of a three-phase transformer we suggest makes it possible to simulate currents in transformer windings under steady-state operation modes with accuracy acceptable for relay protection.

Keywords

• nonlinear transformer
• mathematical model
• electrical circuit
• magnetic circuit
• inductance
• mutual inductance