Simulation of Three-Phase Transformer Operational Conditions

Volgina, E. M.; Novozhilov, A. N.; Kolesnikov, Yevgeny; Rakhimberdinova, D. M.; Novozhilov, T. A.; Andreyeva, Oxana

doi:10.32014/2019.2518-170x.122

Cited by 2 publications

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“…The mathematical model of a transformer [17], represented as a set of differential equations, is transformed into a mathematical model described by a set of linear equations, taking into account the diagram of the core (Figure 1) and the electric circuit of the transformer (Figure 2). linear equations.…”

Section: Mathematical Model Of a Transformermentioning

confidence: 99%

“…In Figure 1, uA, uB, and uC (ua, ub, and uc) are the instantaneous values of phase voltages in the primary (secondary) windings of phases A, B, and C (a, b, and c); iA, iB, and iC (ia, ib, and ic) are the instantaneous values of currents in the primary (secondary) windings of phases A, B, and C (a, b, and c); wA, wB, and wC (wa, wb, and wc) are the numbers of turns in the primary (secondary) windings of phases A, B, and C (a, b, and c), For the experimental estimation of the simulation error, an experimental 6.0 kVA TT-6-type transformer is used; its parameters are given in Table 1. If the voltages are considered sinusoidal in the mathematical model [17], then the operator of differentiation, dt d , in its equations can be changed to the expression jω with allowance given [15]. In this case, the set of equations of this mathematical model is transformed into the set For the experimental estimation of the simulation error, an experimental 6.0 kVA TT-6-type transformer is used; its parameters are given in Table 1.…”

Section: Mathematical Model Of a Transformermentioning

confidence: 99%

“…If the voltages are considered sinusoidal in the mathematical model [17], then the operator of differentiation, d/dt, in its equations can be changed to the expression jω with allowance given [15]. In this case, the set of equations of this mathematical model is transformed into the set…”

Section: Mathematical Model Of a Transformermentioning

confidence: 99%

“…According to [16], the process of energy conversion in three-phase power transformers is most fully described by a quite simple and easily understandable mathematical model with phase coordinates. In this model, the operation of a three-phase two-winding transformer is described by only four differential equations [17]. These differential equations are compiled by the loop current method [18,19] for phase-to-phase voltages.…”

Section: Introductionmentioning

confidence: 99%

“…All of these shortcomings reduce the simulation accuracy and do not enable one to sufficiently and accurately determine the response threshold of, e.g., high-sensitive turn-to-turn fault protections based on built-in inductive measuring transducers [2,6]. To get rid of these shortcomings, the mathematical model presented in [17] as a set of differential equations is transformed into a mathematical model described by a set of linear equations. When simulating steady-state load operation modes of a transformer in this model, the duration of a mode under study is divided into time intervals within which the transformer parameters are considered constant.…”

Section: Introductionmentioning

confidence: 99%

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

Kolesnikov,

Novozhilov,

Rakhimberdinova

et al. 2024

Energies

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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.

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Section: Mathematical Model Of a Transformermentioning

confidence: 99%

Section: Mathematical Model Of a Transformermentioning

confidence: 99%