### Abstract

The relevance of the work. When producing, transporting and processing geo assets it is necessary to use various electrical equipment, the transformers are the main electricity distributors in this case. In some cases it is necessary to route the local electric network to recharge elec- tric power devices for processing geo assets, the transformers are the main units of network as well. The efficiency of electric networks depends on the state of distribution devices - transformers, especially on the condition of the transformer windings. Therefore, the in- vestigation and modeling of the transformer windings are the important tasks. When presenting the transformer windings as a distribu- ted system we need to know the values of the equivalent circuit elements. In the presence of high-frequency currents in the circuit, the skin effect - the dependence of current on frequency - influences the value of equivalent circuit elements. The relevance of the research is caused by the fact that the pulse of nanosecond duration, which spectrum is filled with high frequencies, is used as the probe pulse for the transformer. The high frequency of the probe pulse provokes the skin effect, which, in its turn, contributes the frequency de- pendence to the value of the equivalent circuit parameters. The aim of the research is to introduce the probe nanosecond pulse as a superposition of harmonics with different frequencies; to cal- culate inductance and resistance for the transformer equivalent circuit for each harmonic with fixed frequency, which forms the pulse; to determine the values of inductance and capacitance using the calculation of electromagnet field and taking into account the skin ef- fect as well. The energy of the calculated electromagnetic field allows retrieving the inductance and resistance values of the investigated system at the fixed frequency. To get the resulting equivalent circuit, which consists of combined circuits, obtained for each frequency separately, using superposition principle; to obtain voltage and currents of equivalent circuit of transformer windings and compare them with the experimental data. Method of investigation is based on superposition principle, which means the expansion of arbitrary functions to the Fourier series. The authors use as well the numerical solution of partial differential equations - Helmholtz equation using the finite element method. To implement the method of finite elements the mathematical package COMSOL Multyhpisics was used. Results. The authors carried out frequency decomposition of nanosecond pulse and use it as a probe signal for transformer diagnosis. Ba- sed on the solution of Maxwell's equations the spatial distribution pattern of the magnetic vector potential was obtained. To extract the information on the inductance and resistance of the equivalent circuit of transformer winding the vector magnetic potential was used. The authors obtained the graphs of inductance and resistance of equivalent circuit for the transformer winding as a function of frequency. Graphical dependences are given for a variety of cross-sections of the transformer windings: round and rectangular shapes. Based on the obtained graphical dependencies the equivalent circuits of the transformer windings with the possible influence of the skin effect were built. The paper introduces the calculations of voltage and current of transformer windings using the equivalent circuit, as well as the results of comparison of theoretical calculations with the experimental ones.

Original language | English |
---|---|

Pages (from-to) | 47-55 |

Number of pages | 9 |

Journal | Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering |

Volume | 326 |

Issue number | 9 |

Publication status | Published - 2015 |

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### Keywords

- Distributed parameters
- Frequency spectrum
- Helmholtz equation
- Probe pulse
- Skin effect
- State-space equation
- Transformer winding

### ASJC Scopus subject areas

- Economic Geology
- Geotechnical Engineering and Engineering Geology
- Fuel Technology
- Management, Monitoring, Policy and Law
- Waste Management and Disposal
- Materials Science (miscellaneous)

### Cite this

**Calculation of equivalent distributed circuit parameters of transformer winding under the influence of skin effect.** / Isaev, Yusup N.; Startseva, Elena V.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Calculation of equivalent distributed circuit parameters of transformer winding under the influence of skin effect

AU - Isaev, Yusup N.

AU - Startseva, Elena V.

PY - 2015

Y1 - 2015

N2 - The relevance of the work. When producing, transporting and processing geo assets it is necessary to use various electrical equipment, the transformers are the main electricity distributors in this case. In some cases it is necessary to route the local electric network to recharge elec- tric power devices for processing geo assets, the transformers are the main units of network as well. The efficiency of electric networks depends on the state of distribution devices - transformers, especially on the condition of the transformer windings. Therefore, the in- vestigation and modeling of the transformer windings are the important tasks. When presenting the transformer windings as a distribu- ted system we need to know the values of the equivalent circuit elements. In the presence of high-frequency currents in the circuit, the skin effect - the dependence of current on frequency - influences the value of equivalent circuit elements. The relevance of the research is caused by the fact that the pulse of nanosecond duration, which spectrum is filled with high frequencies, is used as the probe pulse for the transformer. The high frequency of the probe pulse provokes the skin effect, which, in its turn, contributes the frequency de- pendence to the value of the equivalent circuit parameters. The aim of the research is to introduce the probe nanosecond pulse as a superposition of harmonics with different frequencies; to cal- culate inductance and resistance for the transformer equivalent circuit for each harmonic with fixed frequency, which forms the pulse; to determine the values of inductance and capacitance using the calculation of electromagnet field and taking into account the skin ef- fect as well. The energy of the calculated electromagnetic field allows retrieving the inductance and resistance values of the investigated system at the fixed frequency. To get the resulting equivalent circuit, which consists of combined circuits, obtained for each frequency separately, using superposition principle; to obtain voltage and currents of equivalent circuit of transformer windings and compare them with the experimental data. Method of investigation is based on superposition principle, which means the expansion of arbitrary functions to the Fourier series. The authors use as well the numerical solution of partial differential equations - Helmholtz equation using the finite element method. To implement the method of finite elements the mathematical package COMSOL Multyhpisics was used. Results. The authors carried out frequency decomposition of nanosecond pulse and use it as a probe signal for transformer diagnosis. Ba- sed on the solution of Maxwell's equations the spatial distribution pattern of the magnetic vector potential was obtained. To extract the information on the inductance and resistance of the equivalent circuit of transformer winding the vector magnetic potential was used. The authors obtained the graphs of inductance and resistance of equivalent circuit for the transformer winding as a function of frequency. Graphical dependences are given for a variety of cross-sections of the transformer windings: round and rectangular shapes. Based on the obtained graphical dependencies the equivalent circuits of the transformer windings with the possible influence of the skin effect were built. The paper introduces the calculations of voltage and current of transformer windings using the equivalent circuit, as well as the results of comparison of theoretical calculations with the experimental ones.

AB - The relevance of the work. When producing, transporting and processing geo assets it is necessary to use various electrical equipment, the transformers are the main electricity distributors in this case. In some cases it is necessary to route the local electric network to recharge elec- tric power devices for processing geo assets, the transformers are the main units of network as well. The efficiency of electric networks depends on the state of distribution devices - transformers, especially on the condition of the transformer windings. Therefore, the in- vestigation and modeling of the transformer windings are the important tasks. When presenting the transformer windings as a distribu- ted system we need to know the values of the equivalent circuit elements. In the presence of high-frequency currents in the circuit, the skin effect - the dependence of current on frequency - influences the value of equivalent circuit elements. The relevance of the research is caused by the fact that the pulse of nanosecond duration, which spectrum is filled with high frequencies, is used as the probe pulse for the transformer. The high frequency of the probe pulse provokes the skin effect, which, in its turn, contributes the frequency de- pendence to the value of the equivalent circuit parameters. The aim of the research is to introduce the probe nanosecond pulse as a superposition of harmonics with different frequencies; to cal- culate inductance and resistance for the transformer equivalent circuit for each harmonic with fixed frequency, which forms the pulse; to determine the values of inductance and capacitance using the calculation of electromagnet field and taking into account the skin ef- fect as well. The energy of the calculated electromagnetic field allows retrieving the inductance and resistance values of the investigated system at the fixed frequency. To get the resulting equivalent circuit, which consists of combined circuits, obtained for each frequency separately, using superposition principle; to obtain voltage and currents of equivalent circuit of transformer windings and compare them with the experimental data. Method of investigation is based on superposition principle, which means the expansion of arbitrary functions to the Fourier series. The authors use as well the numerical solution of partial differential equations - Helmholtz equation using the finite element method. To implement the method of finite elements the mathematical package COMSOL Multyhpisics was used. Results. The authors carried out frequency decomposition of nanosecond pulse and use it as a probe signal for transformer diagnosis. Ba- sed on the solution of Maxwell's equations the spatial distribution pattern of the magnetic vector potential was obtained. To extract the information on the inductance and resistance of the equivalent circuit of transformer winding the vector magnetic potential was used. The authors obtained the graphs of inductance and resistance of equivalent circuit for the transformer winding as a function of frequency. Graphical dependences are given for a variety of cross-sections of the transformer windings: round and rectangular shapes. Based on the obtained graphical dependencies the equivalent circuits of the transformer windings with the possible influence of the skin effect were built. The paper introduces the calculations of voltage and current of transformer windings using the equivalent circuit, as well as the results of comparison of theoretical calculations with the experimental ones.

KW - Distributed parameters

KW - Frequency spectrum

KW - Helmholtz equation

KW - Probe pulse

KW - Skin effect

KW - State-space equation

KW - Transformer winding

UR - http://www.scopus.com/inward/record.url?scp=85019173183&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019173183&partnerID=8YFLogxK

M3 - Article

VL - 326

SP - 47

EP - 55

JO - Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering

JF - Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering

SN - 2500-1019

IS - 9

ER -