Аңдатпа
The purpose of the article is to form differential equations of a new mathematical model and a system of equations for constructing the steady-state and transient operating modes of single-phase power transformers with identical secondary windings. These transformers are widely used as furnace transformers in the ferroalloy industry and metallurgy. To protect the specified transformers from short circuits, current protection is introduced, which should be produced with regard to their operating conditions in stationary and transient activation modes. Single-phase furnace transformers with a split secondary winding are distinguished among power transformers. The splitting of the secondary winding is represented by identical single-turn insulated windings performed by a bus with a large cross section. To simulate currents in the transformer windings in an arbitrary operation mode it is reasonable to use a mathematical model the differential equations of which are composed according to the second Kirchhoff law. In this case, the number of equations in this mathematical model will be equal to the number of windings and their elements in this transformer. This will make it impossible to use iterative methods (for example, the well-known Gauss method) for calculating currents in transformer windings as the number of operations in these methods depends on the calculation error. However, the solution of the system of differential equations for a multi-winding transformer is quite a challenge. In this regard, a method of replacing all identical secondary windings with one equivalent is proposed. Taking this into account, the authors have formed differential equations of a new mathematical model, as well as a system of equations for modeling steady-state and transient operation modes. The adequacy of this model has been tested in a stationary mode by comparing simulation and experimental results.