Inrush Current Reduction Strategy for a Three-Phase Dy Transformer Based on Pre-Magnetization of the Columns and Controlled Switching
Abstract
:1. Introduction
State of the Art
- Starting/switching phase angle of voltage;
- Residual flux in core;
- Magnitude of voltage;
- Saturation flux;
- Core material;
- Supply/source impedance;
- Load and size of transformer.
2. Model of a Three-Phase Transformer with Connection Group Dy with a Non-Linear Magnetization Curve in the No-Load State
2.1. Model Concept
2.2. Residual Magnetism
2.3. Dynamic Equations of the Unloaded Transformer Dy
3. Investigation
3.1. Definition of Supply Voltages Together with the Method That Takes into Account the Time Instant Determined (Set) in the Supply Voltage Waveform
3.2. Study of the Influence of Residual Magnetism on the Maximum Values of Inrush Currents of an Unloaded Transformer
3.3. Implementation of Calculations—Calculation Algorithm
4. Simulation Results
5. Algorithm for Selecting the Time Instant Specified in the Waveform of the Switched Supply Voltage
5.1. Method of Implementation of Pre-Magnetization of the Core Columns of the Tested Transformer
5.2. Selection of the Currents Required for Core Pre-Magnetization
5.3. The Strategy of Energizing a Three-Phase, Three-Column Transformer Where Primary Winding Is Delta-Connected and Where the Columns Are Pre-Magnetized According to (20) at Specific Time Instants in the Supply Voltage Waveforms
6. The Simplifications Implied by Using the Model Formulated in this Paper
- The initial magnetization state of the transformer core can be taken into account as residual magnetism in the form of (assignable) initial conditions for the state variables , which are essentially flux linkages and , where is the residual flux density in the different columns of the transformer core.
- The integration of the equations with the initial conditions formulated in this way leads in the first instance to a solution () located deep in the saturation region of the ferromagnetic core curve; the maximum inrush currents of the unloaded transformer determined from this solution are calculated accurately.
- Taking any initial conditions (e.g., zero) for the systems of Equations (5) and (8) as the starting point leads to a steady-state solution, which is the limit cycle of the transient state solution; the trajectories of the transition to this limit cycle have no physical interpretation in this case, since the assumed mathematical model does not take into account magnetic hysteresis (it does not track the history of core magnetization).
- The model is suitable for the study of steady-state conditions of the transformer when the resistances are determined based on the idling losses, in which eddy currents and magnetic hysteresis are taken into account.
- The completed tests have shown that there is no significant influence* of the parameter of the model on the maximum values of the inrush currents of the unloaded transformer in the first period of the transient state caused by energizing the transformer (*—lossiness values provided by the manufacturer of the transformer plates vary within wide limits).
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
e | sinusoidal supply voltage |
Ψk | flux linkage associated with the transformer’s primary coil, computed as Ψk(t) = zgΦk(t), in the column of the transformer |
ik(g) | transformer primary current |
RFe,k | equivalent resistance representing the iron core losses |
iFe,k | active component of the transformer’s idle current |
Rs | equivalent resistance of the power grid (power source) |
Ls | equivalent inductance (reactance) of the power grid (power source) |
Rg | primary winding resistance |
Lg | leakage inductance of the primary winding |
H | magnetic field strength |
Φ | main flux leakage (effective value of the flux) |
Bk | flux density |
sFe | cross-sectional area of the core of the transformer |
zg | number of turns in the primary windings |
φ0 | phase of the initial supplied voltage |
ω | pulse |
Appendix A
Quantity, Unit | Value |
---|---|
Primary voltage PRI/phase to phase, V | 6000 |
Secondary voltage SEC/phase to phase, V | 230 |
Frequency | 50 |
Rated primary current, A | 800 |
Number of primary winding turns, N | 160 |
Iron power loss (for 1.7 T), W/kg | 1.05 |
Copper power loss, kW | 50 |
Short-circuit voltage, % | 5 |
Core cross-sections, m2 | 0.110565 |
Column length, m | 2 |
Length of the yoke, m | 0.76 |
Equivalent resistance of the network, Ω | 0.1 |
Equivalent reactance of the network, Ω | 0.2 |
1 | 29.9624271037522 |
2 | −76.4912078883278 |
3 | 420.867774746849 |
4 | −1274.37623231261 |
5 | 2196.27285444425 |
6 | −2301.93260519503 |
7 | 1516.77585894405 |
8 | −630.577358829122 |
9 | 160.397849549712 |
10 | −22.7840824031901 |
11 | 1.38472183966324 |
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Variant | |||
---|---|---|---|
1 | −0.6 | 1.2 | −0.6 |
2 | −1.2 | 0.6 | 0.6 |
3 | −0.6 | −0.6 | 1.2 |
4 | 0.6 | −1.2 | 0.6 |
Type | ||||||
---|---|---|---|---|---|---|
1 | −1 | 0 | 0 | |||
2 | 1 | 0 | 0 |
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Łukaniszyn, M.; Baron, B.; Kolańska-Płuska, J.; Majka, Ł. Inrush Current Reduction Strategy for a Three-Phase Dy Transformer Based on Pre-Magnetization of the Columns and Controlled Switching. Energies 2023, 16, 5238. https://doi.org/10.3390/en16135238
Łukaniszyn M, Baron B, Kolańska-Płuska J, Majka Ł. Inrush Current Reduction Strategy for a Three-Phase Dy Transformer Based on Pre-Magnetization of the Columns and Controlled Switching. Energies. 2023; 16(13):5238. https://doi.org/10.3390/en16135238
Chicago/Turabian StyleŁukaniszyn, Marian, Bernard Baron, Joanna Kolańska-Płuska, and Łukasz Majka. 2023. "Inrush Current Reduction Strategy for a Three-Phase Dy Transformer Based on Pre-Magnetization of the Columns and Controlled Switching" Energies 16, no. 13: 5238. https://doi.org/10.3390/en16135238
APA StyleŁukaniszyn, M., Baron, B., Kolańska-Płuska, J., & Majka, Ł. (2023). Inrush Current Reduction Strategy for a Three-Phase Dy Transformer Based on Pre-Magnetization of the Columns and Controlled Switching. Energies, 16(13), 5238. https://doi.org/10.3390/en16135238