A novel transformer with adjustable leakage inductance

Abstract

Considering the challenge that the parameter of inductor is fixed and its adjustment is difficult in traditional power electronic circuit, herein we present a newly structural transformer with adjustable leakage inductance which integrates transformer and inductor. Its leakage inductance can be adjusted online. Secondary winding of the newly structure transformer is connected in series with the inductance winding and the leakage inductance can be changed by adjusting the contact area of the transformer core and the inductor core. The structure and principle of the transformer with adjustable leakage inductance are introduced. A newly structure transformer is designed using equivalent magnetic circuit method. The transformer with leakage inductance adjustable are modeled and simulated by finite element simulation software Ansoft Maxwell. The variation of inductor inductance with the core contact area and the electromagnetic properties of the new transformer with leakage inductance adjustable are shown in this thesis. Finally, the transformer with leakage inductance adjustable is manufactured, and the experimental platform is built. The results show that the principle of the transformer with leakage inductance adjustable is reasonable and its design is feasible.

Keywords

Leakage inductance adjustable transformer finite element analysis

1. Introduction

Almost all of the power circuits are inseparable from the transformer and inductor [1, 2]. The traditional transformer and inductor are two separate electrical equipments, and the combination of them leads to the large volume and the inconvenience of inductance parameter adjustment. Several types of the transformers with adjustable parameter in papers [3, 4, 5] were all by means of changing the structure of the core or the relative position of the winding to adjust the electromagnetic parameters themselves. In paper [6], a small U magnetic circuit was added, so that the leakage inductance of the transformer can be adjusted by changing the distance between the transformer core and the U-shape core. In paper [7], the inductor and the transformer were combined, and the former participated in the voltage adjustment process of the transformer and there was a coupling relationship between the transformer and the inductance. However, the parameters of the transformer were fixed and cannot be adjusted once the structure of the transformer core was determined. This paper presents a novel transformer with adjustable leakage inductance which integrates transformer and inductor. Its leakage inductance can be adjusted online. Its electromagnetic parameters are acquired by combing with the equivalent magnetic circuit method. The FEM (finite-element method) has the advantages such as good geometric adaptable, strong power to deal with the nonlinear problem [8].

An advanced numerical calculation scheme based on finite and boundary elements as well as multigrid methods is presented. This scheme is used for the precise forecast of the dynamical behavior of piezoelectric, electrostatic and magnetomechanical devices [9]. The Finite Element Methods has become a common tool for engineering analysis and design subsequent to phenomenal increase in computing power available even on laptop and personnel computers [10]. Thus, the proposed transformer is analyzed by the finite element simulation software in the paper. Also the experimental platform has been built. The simulation and the experiment prove that the principle and design of the novel transformer are reasonable and feasible.

2. The structure and the principle of transformer with adjustable leakage inductance

2.1 The structure of transformer with adjustable leakage inductance

Newly structure of the transformer with adjustable leakage inductance is shown in Fig. 1, comprising a transformer iron core, primary winding and secondary winding of the transformer. The transformer iron core including a left-column and a right-column core, between which there is an upper-beam, a middle-beam and a lower-beam composition of a “EI” type structure. The primary and secondary winding of the transformer are twined around the middle-beam. Left lateral surface of the transformer left-column core is provided with a sliding groove, which is connected with an additional removable iron core. The additional iron core is a “C” type structure comprising an upper-beam, a lower-beam and a column and the additional winding is twined around the additional iron column. The additional winding and the secondary winding of the transformer connected in series constitute the secondary winding of the transformer with adjustable leakage inductance.

Figure 1.

Structure of new transformer with adjustable leakage inductance.

2.2 The principle of the transformer with adjustable leakage inductance

As shown in Figs 2 and 3, the structure and magnetic circuit of new transformer are symmetrical, and there is no magnetic drop between the upper-beam and the lower-beam of the additional iron core when primary winding of the transformer is excited.

Figure 2.

Magnetic field distribution of the primary winding with excitation.

Figure 3.

Magnetic field distribution of additional winding with excitation.

The flux produced by primary winding is closed in the iron core after passing the core-beam and core-column of the transformer, and it will not across additional winding (as shown in Fig. 2). There is no magnetic drop in the middle-beam of the transformer iron core when additional winding is excited. The flux produced by additional winding is closed after passing the additional core and left-beam of the transformer and it will not across primary winding (as shown in Fig. 3). So, the additional winding and the additional core are equivalent to leakage inductance of the transformer with adjustable leakage inductance.

The inductance calculation formula is as shown in Eq. (1):

$L=\mu\frac{S}{l}N^{2}=\mu\frac{N^{2}}{l}S$ (1)

The expression $\mu N^{2}/l$ keeps constant after the number of turns and the size of the inductor are determined, where $\mu$ represent magnetic permeability, $l$ is magnetic path length, $N$ is coil turns. That is to say, the leakage inductance L is in proportion to the effective cross-sectional area of core S. In the linear segment of the core magnetization curve, when the core excitation current I keeps constant, the magnetic field intensity and magnetic induction intensity B also will remain the same. Thus, the core flux $\Phi$ is mainly depending on the contact of additional core and transformer core, while the contact area is the effective cross-sectional area of the transformer. When the contact area is adjusted, it means the effective cross-sectional area of the inductor S will also change, which achieves the leakage inductance of the novel transformer adjustable.

Table 1

Parameter table of transformer with adjustable leakage inductance

Parameter	Parameter value	Parameter	Parameter value
The primary voltage	220 V	$a$	22 mm
The secondary voltage	23 V	$b$	44 mm
The primary winding turns	1059	$c$	11 mm
The secondary winding turns	121	$h$	33 mm
The additional winding turns	75	$l_{1}$	66 mm
$b_{z}$	14 mm	$l_{g}$	0.16 mm

Figure 4.

Model cross section of transformer with adjustable leakage inductance.

3. Finite element analysis of the new transformer with adjustable leakage inductance

3.1 Parameters of the newly structure transformer

A novel transformer of 25 W whose leakage inductance is 12 mH is designed using the equivalent magnetic circuit method, and the model and the main parameters are shown in Fig. 4 and Table 1, respectively.

3.2 Simulation model of the newly structure transformer

According to the design size of the new transformer, its geometric simulation model can be drawn directly in the software Ansoft Maxwell [11]. The simulation model is shown in Fig. 5. A good grid subdivision is the basis when the electromagnetic equipment is analyzed by the electromagnetic field finite element analysis software [12]. Adaptive grid subdivision technique was adopted in the paper, and the subdivision result of the model is shown in Fig. 6.

3.3 The coupling analysis

According to the principle of the novel transformer, a part of the transformer core is shared by the inductor and the transformer, but there is no magnetic coupling between primary or secondary winding and additional winding. In order to prove the viewpoint, the secondary winding and the additional winding of the transformer are made disconnected firstly, after which the induced electromotive force in additional winding is detected when a rated voltage excitation is applied to primary winding, and then the induced electromotive force in primary winding and secondary winding are both detected when a rated voltage excitation is applied to additional winding. The induced voltage waves detected in the windings of the transformer are shown in Fig. 7.

Figure 5.

Simulation model of the newly structure transformer.

Figure 6.

Adaptive grid subdivision.

Figure 7.

Induced electromotive force of each winding.

As shown in Fig. 7, the RMS value of IEMF (induced electromotive force) in additional winding is 164.8 $\mu$ V, only accounted for 1.2% of its rated voltage. The value is so small that can be neglected, which shows that the flux produced itself when the working of transformer has no influence on the additional core or winding. The RMS values of the induced electromotive force in the primary winding and secondary winding are 33.55 $\mu$ V and 3.831 $\mu$ V, respectively, compared to their rated voltages. The values are close to zero, which proves that the flux producing by additional winding makes no influence on the transformer. Accordingly, there is really no magnetic coupling between the primary or secondary winding and additional winding. This result verifies that the principle of the novel transformer is reasonable.

3.4 The analysis of leakage inductance adjustment mode

There are two ways that can adjust the leakage inductance according to the structure of the novel transformer. One is that moving along the left-column of the transformer, that is to say to change the contact area by moving along y-direction (As shown in Fig. 8). Also, the contact area can be changed by moving along z-direction perpendicular to the x-y plane.

Figure 8.

Adjustment mode of transformer with adjustable leakage inductance.

The two adjustment modes both can adjust leakage inductance by changing the contact area of the additional core and the left-column of the transformer. In order to compare their advantages and disadvantages, the two methods of adjusting the leakage inductance are modeled and simulated respectively in the paper. The contact area of two adjustment modes are both set at half of total area in the simulation, and the results are shown in Figs 9 and 10.

Figure 9.

Induced electromotive force in primary winding under y-direction regulation modes.

Figure 10.

Induced electromotive force in primary winding under z-direction regulation modes.

In Figs 9 and 10, because of the different regulation modes, the RMS values of the induced electromotive force in the primary winding are 5.6502 mV and 6.7999 $\mu$ V respectively when the rated voltage is applied to additional winding, and the results show that the differences are obvious. The reason is that the magnetic circuit becomes asymmetric under y-direction regulation modes, and a few of the flux produced by the additional winding will pass through the core-beam where the primary and secondary windings wrapped, so that there is electromotive force induced in the windings. After comparing the two adjustment modes, the contact area is changed by moving along z-direction to adjust leakage inductance of the transformer in this paper. The chosen adjustment mode does not change the symmetry of the magnetic circuit in the process of adjustment. The coupling coefficient of the primary or secondary winding and the additional winding is nearly to the zero.

3.5 The leakage inductance measurement

The inductance matrix is set to calculate the value of leakage inductance when the current excitations is applied to all the windings of the novel transformer respectively, and the relationship curve acquired is shown in Fig. 11.

Figure 11.

Relationship between leakage inductance and relative contact area.

Figure 12.

Magnetic density vector distribution of additional core when the relative contact area is 1.

As shown in Fig. 11, leakage inductance of the novel transformer reaches the maximum when the relative contact of the core is the largest, while leakage inductance linearly decrease according to the reduction of the relative contact area. The flux density distribution in the additional core is about 0.5 T when the relative contact area is 1 (Fig. 12), while the flux density distribution is about 0.3 T when the relative contact area is 0.3 (Fig. 13). The flux density in additional core decreases with the reduction of relative contact area. The simulation result agrees well with theoretical analysis.

4. Experiment research on new transformer with adjustable leakage inductance

4.1 Design and manufacture of the newly structure transformer

In order to verify the rationality and feasibility of the principle of new transformer with adjustable leakage inductance, the new transformer was manufactured according to the simulation parameters obtained before, as showed in Fig. 14. The core adopts the silicon steel material of 50W600 produced by the WISCO, whose width is 0.5 mm. The numbers of turns of the primary winding and secondary winding are 1059 and 121, respectively, while the turns of the additional winding is 74. The additional core is remade by the E-shape silicon steel directly.

4.2 Coupling experiment of the new transformer

According to the novel transformer manufactured before, the following experiment research is focused on the coupling relationship between primary or secondary winding and additional winding, and the measurement of leakage inductance. To verify the coupling relationship mentioned, the secondary winding and the additional winding of the transformer are made disconnected firstly. The connection of winding and the transformer in the experiment is shown as Figs 15 and 16.

In the experiment, the values of induced voltage of other windings are detected as shown in Tables 2–4 when only the primary winding, secondary winding or additional winding is excited.

Table 2
Induced electromotive force when the primary winding is excited

The primary voltage(v)	The secondary winding IEMF(v)	The additional winding IEMF(v)
217.8	24.82	0

Table 3

Induced electromotive force when the secondary winding is excited

The primary winding IEMF(v)	The secondary voltage(v)	The additional winding IEMF(v)
201.2	23.14	0

Figure 13.

Magnetic density vector distribution of additional core when the relative contact area is 0.3.

Table 4

Induced electromotive force when the additional winding is excited

Relative contact area	The primary winding	The secondary winding	The additional winding
	IEMF (mV)	IEMF (mV)	voltage (V)
1	85.9	10.3	4.016
0.7	0	0	3.329
0.2	0	0	1.018

Figure 14.

Physical figure of transformer with adjustable leakage inductance.

Figure 15.

The circuit diagram.

Figure 16.

Experiment equipment.

In Tables 2 and 3, when only the primary winding or secondary winding is excited, there is no induced voltage in additional winding, which shows that the primary winding and the secondary winding have no impact on additional winding when working normally.

Seen from Table 4:

When the additional core and the transformer left-core contact completely, the RMS values of the induced electromotive force in the primary winding and secondary winding are 85.9 mV and 10.3 mV, respectively, with additional winding excited by a rated current. The values are so small that can be neglected comparing to the rated values.

Keeping the excitation current of additional winding for rating, the values of induced electromotive force in primary winding and secondary winding are both zero when the contact area of the additional core and the transformer left-core is changed, which indicates that additional winding has no impact on primary or secondary winding of the transformer.

The above analysis shows that the coupling relationship between primary or secondary winding and additional winding of the novel transformer does not exist.

4.3 Leakage inductance measurement of the new transformer

Traditional methods of inductance measurement mainly include the voltammetry, the LCR meter method and the resonance method [13]. The voltammetry is adopted to measure the leakage inductance of the new transformer when it is excited differently.

According to the existing laboratory equipment, the experimental connection diagram is designed as shown in Fig. 17. Closing the switch S1 means only the additional winding is excited, while closing the switch S1 and S2 means that the primary winding and additional winding are excited together.

Figure 17.

Experimental circuit diagram of voltammetry.

By the inductance calculation formula:

$\left\{{\begin{array}[]{l}Z=U/I\\ R=P/I^{2}\\ X_{L}=\sqrt{Z^{2}-R^{2}}\\ L=X_{L}/2\pi f\\ \end{array}}\right.$ (2)

Figure 18 is obtained after the experimental data is processed according to Eq. (2).

Figure 18.

Relationship of leakage inductance and contact area under different excitation conditions.

Figure 19.

Comparison of simulation results and experimental results.

Seen from the relationship curves in Fig. 18:

Whether additional winding excites alone or additional winding and primary winding excite together, the leakage inductance has a linear relationship with the contact area, which agrees well with the theoretical analysis.

After contrasting the leakage inductance under different excitation conditions, the bigger the contact area of additional core and left-column core of transformer is, the bigger the difference of the leakage inductance will be. The reason probably is that the width of left-column core of the transformer is smaller than the theory after processed, and the flux density of which increases when excited together, causing the working point nearing the saturated section of the core magnetization curve. Then the core permeability decreases and the reluctance increases, so the inductance decreases. When the contact area decreases, the magnetic flux decreases, and subsequently the working point is away from the saturation point, which causes the change of permeability decreasing, so the difference of the inductance decreases.

The results of the finite element simulation and the experiment are drawn in the same coordinate system, as shown in Fig. 19.

Seen from Fig. 19, the inductance obtained from the FEM simulation roughly has the same variation trend with the inductance measured in the experiment. Merely, the experiment result is smaller than the simulation result, but the difference is not big. The reason is that the air gap of the novel transformer is the average equivalent air gap, and the manual operation in the process of the experiment will also cause the inevitable errors. Even so, the experiment results still prove that the proposed theory about the newly structure transformer with adjustable leakage inductance is reasonable and feasible.

5. Conclusion

This paper presents a novel transformer which integrates transformer and inductor together. As the inductor becomes secondary leakage inductance of the transformer, its leakage inductance can be adjusted online according to the inductance needed. The structure and the principle of the transformer with adjustable leakage inductance are introduced in the paper, and the design parameters are also given. The new transformer proposed is simulated by FEM and the platform is also built to do the experimental research. The simulation and the experiment show that the transformer and the inductor have no magnetic coupling, and there is also no influence on the transformer itself when secondary winding of the transformer is in series with the inductor coil. As the inductor becomes leakage inductance of the transformer, its leakage inductance can be adjusted online. The result verifies that the principle and design of the new transformer are rational and feasible. Because it has a simple structure, convenient inductance adjustment to match the power supply, and also can decrease the volume and the maintenance work, the new transformer has a certain practical value.

Footnotes

Acknowledgments

This work has been supported by 2014 China Nature Science Foundation (BK20140204).

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