EP3758031A1 - Electrical transformer with controlled distribution of leakage inductance - Google Patents

Abstract

The present invention relates to an electrical transformer comprising a magnetic core and a primary winding, forming a primary circuit, and a secondary winding, forming a secondary circuit, an electrical transformer configured so that: a first value L _1so inductance measured at the primary circuit with the secondary circuit open, a second value L _1ss of inductance measured at the primary circuit with the secondary circuit short-circuited, and a third value L <sub> 2po </ sub> inductance measured at the secondary circuit with the primary circuit open, are such that: L2PO − 1n2LM <A.L1SO − LM with LM = L1SO − L1SS × L1SO.N2 where A is a real number greater than 10.

Description

TECHNICAL FIELD OF THE INVENTION

The present invention relates to the field of electrical transformers, for example integrated into resonant voltage converters or any other type of power converters.

The present invention aims in particular to make it possible to control the distribution of the leakage inductance in an electric transformer.

STATE OF THE ART

An electrical transformer allows the transfer of electrical energy from a primary circuit to a secondary circuit.

As is known, in an electric transformer, a magnetic core and coils are used in which an electric current flows which generates a magnetic field allowing the transfer of electric energy from the primary circuit to the secondary circuit. More precisely, in an electrical transformer, in particular in a magnetizing inductor converter or in a resonant converter, there is a primary winding and a secondary winding, formed by windings around a magnetic core, between which is transferred the electric energy.

Any electrical transformer has a leakage inductance, which results in a loss of efficiency because part of the magnetic flux created in the primary circuit is not picked up by the windings of the secondary circuit. Additional losses may also appear on the windings. In the case of non-resonant voltage converters, overvoltages can also occur. The geometry of the windings of an electrical transformer, as well as the choice of the magnetic materials used for the magnetic core, or even the geometry of said magnetic core, in particular, are configured to meet electrical and magnetic criteria. One objective of the sizing of an electric transformer resides in particular in controlling the value of the leakage inductance of the electric transformer.

It is also well known that, in an electrical transformer, at the primary circuit, a resonant inductor can be connected in series with the primary winding.

Whatever the envisaged applications, the resonance inductor is in particular sized like a discrete component, which operates with an electrical transformer itself dimensioned like a discrete component. However, such an electric transformer can be configured either to minimize magnetic flux leakage, or so that the resonant inductor is integrated with said electric transformer as a leakage inductor, so as to eliminate a power electronic component. discrete and thus reduce the cost and size of the corresponding circuit.

A technical problem thus arises from the choice to integrate the resonance inductance in the electric transformer by exploiting its leakage inductance; this in fact presupposes controlling the distribution of the value of the leakage inductance of the electric transformer between the primary circuit and the secondary circuit.

By way of illustration, the figure 1 shows an equivalent _circuit diagram of a perfect LLC resonant converter, with an input voltage V _SqFHA , an output voltage V _OutFHA and an output resistor R _FHA . The resonant capacitor Cs and the resonant inductance Ls are in series and the magnetizing inductor Lp is in parallel with the output of the resonant converter LLC. In general, in an LLC resonant converter, it is desirable to place the resonant inductor Ls at the primary circuit.

On the figure 2 , there is shown an equivalent electrical diagram of a resonant converter LLC2, according to a model of an imperfect electrical transformer, n being the transformation ratio of the resonant converter LLC2, with a non-negligible leakage inductance in the secondary circuit.

The resonance inductance is here integrated into the resonant converter LLC2, in the sense that there is no discrete electronic component Ls. The leakage inductance of the electric transformer performs the function of resonance inductance and comprises a component in the primary circuit L _LK1 and a component in the secondary circuit L _LK2 .

In order to make the non-perfect model of the electric transformer coincide as close as possible to the equivalent circuit of the perfect LLC resonant circuit shown in figure 1 , it is essential that the value of the leakage inductance in the primary circuit L _LK1 is close to the value of the resonance inductance Ls, while minimizing the value of the leakage inductance in the secondary circuit L _LK2 , so so that the secondary circuit leakage inductance L _LK2 is negligible _compared to the primary circuit leakage inductance L _LK1 . In other words, it is sought that the value of the leakage inductance in the secondary circuit L _LK2 is lower, or even negligible compared to the value of the leakage inductance in the primary circuit L _LK1 .

Thus, in particular, the operating point of the LLC2 resonant converter, like of any electrical transformer, its switching frequency, and therefore the losses, are linked to the distribution of the value of the leakage inductance between the primary circuit and the circuit. secondary. A poor distribution of the leakage inductance can cause a significant displacement of the operating point of the electric transformer with respect to its operating point defined as optimal, which can generate a risk of overheating, or even the breakage of electronic power components of the electric transformer. .

In particular, in certain applications, controlling the distribution of the leakage inductance, between the primary circuit and the secondary circuit of an electrical transformer, is of great importance. For example, any type of resonant converter, including an LC, LLC or CLLC topology, requires a leakage inductance that is concentrated in the primary circuit. However, for certain reversible electric converter applications, such as DAB (“dual-active bridge”) type converters, it is possible that a non-negligible leakage inductance in the secondary circuit is desired.

In many cases of use, however, it is particularly advantageous that most of the value of the leakage inductance is in the primary circuit, so as to ensure the function of resonant inductance of the electric transformer in a resonant circuit. type LC, LLC or CLLC.

The present invention makes it possible in particular to determine the distribution of the value of the leakage inductance of an electric transformer between a leakage inductance in the primary circuit and a leakage inductance in the secondary circuit. The invention also makes it possible to determine the value of the magnetizing inductance of the electric transformer.

Consequently, the present invention makes it possible in particular to produce an electrical transformer having a desired leakage inductance, in particular concentrated in the primary circuit.

PRESENTATION OF THE INVENTION

• une première valeur L_1so d'inductance mesurée au circuit primaire avec le circuit secondaire ouvert,
• une deuxième valeur L_1ss d'inductance mesurée au circuit primaire avec le circuit secondaire court-circuité, et
• une troisième valeur L_2po d'inductance mesurée au circuit secondaire avec le circuit primaire ouvert,
• sont telles que : $${\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{2\mathit{PO}}-\frac{1}{n^2}{L}_M<A\mathrm{.}\left({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}-L_M\right)$$
  
  avec $$L_M=\sqrt{\left({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}-{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SS}}\right)\times {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="imgf0002.png"\; state="\{\{state\}\}">N</figure-callout>}}^2}$$
  
  où A est un nombre réel supérieur à 10.

More specifically, the invention relates to an electrical transformer comprising a magnetic core and a primary winding, forming a primary circuit, and a secondary winding, forming a secondary circuit, an electrical transformer configured so that:

• a first inductance value L _1so measured in the primary circuit with the secondary circuit open,
• a second inductance value L _1ss measured in the primary circuit with the secondary circuit short-circuited, and
• a third value L _2po of inductance measured in the secondary circuit with the primary circuit open,
• are such that: $${\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{2\mathit{PO}}-\frac{1}{{\mathrm{not}}^2}{L}_M<\mathrm{AT}\mathrm{.}\left({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}-L_M\right)$$
  
  with $$L_M=\sqrt{\left({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}-{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SS}}\right)\times {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}\mathrm{.}{\mathrm{NOT}}^2}$$
  
  where A is a real number greater than 10.

According to one embodiment, A is a real number greater than or equal to 50.

According to one embodiment, A is a real number less than or equal to 100.

• la sélection d'une géométrie de noyau magnétique pour le transformateur électrique à réaliser ;
• la détermination d'une épaisseur d'entrefer correspondant à une valeur souhaitée d'inductance magnétisante du transformateur électrique à réaliser ;
• l'enroulement d'enroulements secondaires sur un noyau magnétique ayant la géométrie sélectionnée et l'épaisseur d'entrefer, de façon à recouvrir ledit entrefer ;
• la détermination d'une valeur de reluctance de fuite du transformateur électrique en fonction du ratio entre une valeur souhaitée d'inductance de fuite au circuit primaire du transformateur électrique à réaliser, et la valeur souhaitée de l'inductance magnétisante du transformateur électrique à réaliser ;
• la détermination d'une distance h entre des enroulements primaires, destinés à former le circuit primaire du transformateur électrique à réaliser et les enroulements secondaires, en fonction de ladite valeur de reluctance de fuite ;
• l'enroulement des enroulements primaires sur le noyau magnétique du transformateur électrique à ladite distance h des enroulements secondaires.

The invention also relates to a method of making a transformer, said electrical transformer having a magnetic core, a primary circuit and a secondary circuit, said method comprising the following steps:

• selecting a magnetic core geometry for the electrical transformer to be made;
• determining an air gap thickness corresponding to a desired value of magnetizing inductance of the electric transformer to be produced;
• winding secondary windings on a magnetic core having the selected geometry and the air gap thickness, so as to cover said air gap;
• determining a leakage reluctance value of the electric transformer as a function of the ratio between a desired value of leakage inductance in the primary circuit of the electric transformer to be achieved, and the desired value of the magnetizing inductance of the electric transformer to be achieved;
• determining a distance h between primary windings, intended to form the primary circuit of the electrical transformer to be produced and the secondary windings, as a function of said leakage reluctance value;
• winding the primary windings on the magnetic core of the electrical transformer at said distance h from the secondary windings.

According to one embodiment, the magnetic core is selected of type E or of type El.

où N1 est le nombre d'enroulements au circuit primaire, µ₀ est la perméabilité électromagnétique de l'air et S est la surface effective de section magnétique du transformateur électrique,
pour déterminer la valeur de l'épaisseur e de l'entrefer requise, correspondant à la valeur souhaitée de l'inductance magnétisante L_M.According to one embodiment, the equation $$L_M={{\mathrm{NOT}}_1}^2\ast \frac{{\mu }_{0}S}{e}$$

where N1 is the number of windings in the primary circuit, µ ₀ is the electromagnetic permeability of air and S is the effective magnetic sectional area of the electrical transformer,
to determine the value of the thickness e of the required air gap, corresponding to the desired value of the magnetizing inductance L _M.

où Rgap est la reluctance de l'entrefer du transformateur électrique, µ₀ est la perméabilité électromagnétique de l'air, e est l'épaisseur de l'entrefer du transformateur électrique et S est la surface effective de section magnétique du transformateur électrique
et $$\frac{\mathit{Rgap}}{\mathit{Rfuite}}=\frac{\mathit{Lf}1}{L_M}$$

où Rfuite est la reluctance de fuite du transformateur électrique, Lf1 est l'inductance de fuite au circuit primaire du transformateur électrique et L_M est l'inductance magnétisante du transformateur électrique,
pour déterminer la valeur de la reluctance de fuite du transformateur électrique.According to one embodiment, the equations $$\mathit{Rgap}=\frac{1}{{\mu }_0}\ast \frac{e}{S}$$

where Rgap is the reluctance of the air gap of the electric transformer, µ ₀ is the electromagnetic permeability of the air, e is the thickness of the air gap of the electric transformer and S is the effective magnetic sectional area of the electric transformer
and $$\frac{\mathit{Rgap}}{\mathit{Leak}}=\frac{\mathit{Lf}1}{L_M}$$

where R leakage is the leakage reluctance of the electric transformer, Lf1 is the leakage inductance at the primary circuit of the electric transformer and L _M is the magnetizing inductance of the electric transformer,
to determine the value of the leakage reluctance of the electric transformer.

où Rfuite est la reluctance de fuite du transformateur électrique, µ₀ est la perméabilité électromagnétique de l'air, m est la profondeur de noyau magnétique du transformateur électrique et I est la largeur d'une zone de fuite électromagnétique entre les enroulements primaires et les enroulements secondaires, correspondant à la distance séparant une jambe extérieure et une jambe centrale du noyau magnétique de type E ou de type EI,
pour déterminer la valeur de la distance h entre les enroulements primaires et les enroulements secondaires.According to one embodiment, the equation is implemented: $$\mathit{Leak}=\frac{1}{2\mu }\ast \frac{l}{h\ast m}$$

where Rleakage is the leakage reluctance of the electrical transformer, µ ₀ is the electromagnetic permeability of air, m is the magnetic core depth of the electrical transformer and I is the width of an electromagnetic leakage zone between the primary windings and the secondary windings, corresponding to the distance between an outer leg and a central leg of the E-type or EI-type magnetic core,
to determine the value of the distance h between the primary windings and the secondary windings.

PRESENTATION OF FIGURES

• Fig. 1 : la figure 1 (déjà commentée) représente le circuit électrique équivalent d'un convertisseur résonnant parfait ;
• Fig. 2 : la figure 2 (déjà commentée) représente le circuit électrique équivalent d'un convertisseur résonnant non parfait ;
• Fig. 3 : la figure 3 représente le circuit magnétique équivalent d'un transformateur électrique présentant une géométrie donnée ;
• Fig. 4 : la figure 4 montre le schéma d'un transformateur électrique selon un exemple de réalisation de l'invention ;
• Fig. 5 : la figure 5 représente un schéma-bloc montrant les étapes de mise en œuvre du procédé de réalisation d'un transformateur électrique selon un exemple de l'invention.

The invention will be better understood on reading the description which follows, given solely by way of example, and referring to the appended drawings given by way of non-example. limiting, in which identical references are given to similar objects and on which:

• Fig. 1 : the figure 1 (already commented) represents the equivalent electric circuit of a perfect resonant converter;
• Fig. 2 : the figure 2 (already commented on) represents the equivalent electric circuit of a non-perfect resonant converter;
• Fig. 3 : the figure 3 represents the equivalent magnetic circuit of an electric transformer having a given geometry;
• Fig. 4 : the figure 4 shows the diagram of an electric transformer according to an exemplary embodiment of the invention;
• Fig. 5 : the figure 5 represents a block diagram showing the steps of implementation of the method for producing an electric transformer according to an example of the invention.

It should be noted that the figures set out the invention in detail in order to implement the invention, said figures being able of course to serve to better define the invention if necessary.

DETAILED DESCRIPTION OF THE INVENTION

The present invention makes it possible to determine the value of the leakage inductances, respectively in the primary circuit and in the secondary circuit, in an electric transformer.

An induced objective resides in the adaptation of the geometry of an electric transformer so that said leakage inductances in the primary circuit and in the secondary circuit conform to desired inductance values, respectively in the primary circuit and in the secondary circuit. In particular, when the electric transformer is supplied to the primary circuit only, the magnetic fluxes, not wired to the secondary circuit, leak to the primary circuit. This scenario corresponds to the equivalent magnetic circuit represented, as an example, on the figure 3 .

In particular, as indicated above, it may be desirable for the bulk of the value of the leakage inductance of an electric transformer to be in the primary circuit. In other words, in this case, an attempt is made to minimize the value of the leakage inductance in the secondary circuit. It is then desired that the value of the leakage inductance in the secondary circuit be small compared to the value of the inductance in the primary circuit, for example at least ten times smaller, preferably 50 to 100 times smaller.

For an electrical transformer considered, having in particular its own geometry, the invention makes it possible to determine the leakage inductance in the primary circuit, the value of the leakage inductance in the secondary circuit and the value of the magnetizing inductance.

To this end, three inductance measurements are carried out on said electrical transformer.

A first inductance measurement is carried out on the primary circuit L _1so , with the secondary circuit open.

A second inductance measurement is carried out on the primary circuit L _1ss , with the secondary circuit short-circuited,

A third inductance measurement is made on the secondary circuit L _2po , with the primary circuit open.

$$L_{1\mathit{SS}}=L_{\mathit{Lk}1}+\frac{L_M\mathrm{.}{n}^2\mathrm{.}{L}_{\mathit{Lk}2}}{L_M+n^2\mathrm{.}{L}_{\mathit{Lk}2}}$$

$$L_{2\mathit{PO}}=L_{\mathit{Lk}2}+\frac{1}{n^2}\mathrm{.}{L}_M$$

Then, we solve the following system of equations: $${\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}={\mathrm{<figure-callout\; id="1"\; label="L\; Lk"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{\mathit{Lk}}+{\mathrm{<figure-callout\; id="1"\; label="L\; M\; L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_M$$

$$L_{}$$$${}_{1\mathit{SS}}={\mathrm{<figure-callout\; id="1"\; label="L\; Lk"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{\mathit{Lk}}+\frac{L_M\mathrm{.}{\mathrm{not}}^2\mathrm{.}{L}_{\mathit{Lk}2}}{L_M+{\mathrm{not}}^2\mathrm{.}{L}_{\mathit{Lk}2}}$$

$${\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{2\mathit{PO}}={\mathrm{<figure-callout\; id="2"\; label="L\; Lk"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{\mathit{Lk}}+\frac{1}{{\mathrm{not}}^2}\mathrm{.}{L}_M$$

The value of the primary leakage inductance L _Lk1 , the value of the secondary leakage inductance L _Lk2 and the value of the magnetizing inductance L _M of the electric transformer are thus determined.

Thanks to the knowledge of the values of the leakage inductance in the primary circuit L _Lk1 , of the leakage inductance in the secondary circuit L _Lk2 and of the magnetizing inductance L _M , and taking into account the desired values of the leakage inductance to the primary circuit and from the leakage inductance to the secondary circuit, the geometry of the electric transformer is adapted so as to tend towards said desired values.

In particular, to concentrate the value of the leakage inductance of the electric transformer on the primary circuit, it is ensured that the ratio between the leakage inductance in the primary circuit and the leakage inductance in the secondary circuit is greater than 10, in particular between 10 and 100, in particular between 50 and 100.

avec $$L_M=\sqrt{\left(L_{1\mathit{SO}}-L_{1\mathit{SS}}\right)\times L_{1\mathit{SO}}\mathrm{.}{N}^2}$$

où A est un nombre réel supérieur à 10, notamment supérieur à 50, notamment inférieur ou égal à 100, et N est le rapport de transformation du transformateur électrique.In other words, according to the invention, the electrical transformer is preferably configured such that the first measurement of inductance at the primary circuit L _1so , the second measurement of inductance at the primary circuit L _1ss , and the third measurement of inductance at the primary circuit secondary circuit L _{2 ''} of inductance measured at the secondary circuit with the primary circuit open, are such that: $${\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{2\mathit{PO}}-\frac{1}{{\mathrm{not}}^2}{L}_M<\mathrm{AT}\mathrm{.}\left({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}-L_M\right)$$

with $$L_M=\sqrt{\left({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}-{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SS}}\right)\times {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}_{1\mathit{SO}}\mathrm{.}{\mathrm{NOT}}^2}$$

where A is a real number greater than 10, in particular greater than 50, in particular less than or equal to 100, and N is the transformation ratio of the electric transformer.

An objective of the invention is thus to produce an electrical transformer, by configuring the distribution of the leakage inductance of said electrical transformer as desired, in particular by concentrating said leakage inductance in the primary circuit. To this end, an equivalent magnetic circuit of the electrical transformer is produced, depending on its geometry, as shown in figure 3 . The equivalent magnetic circuit shown in figure 3 thus corresponds to a given geometry of an electric transformer supplied by a voltage V1, said electric transformer being considered, in terms of positioning of the primary and secondary windings, of transformation ratio, of the number and dimensions of the legs of the magnetic core, of the position of the air gap, etc., with values for equivalent electrical components, in particular for the equivalent reluctances R1, R2, R3, R4. These values are not easily measurable but their distribution can be influenced by modifying the geometry of the electrical transformer.

With reference to the figure 3 , there is thus represented a total magnetic flux flux_total of which a flux_sec portion is transferred to the secondary circuit while two other portions flux_leak1, flux_leak2 correspond to the magnetic fluxes leaking to the primary circuit.

Starting from the equivalent magnetic diagram of the figure 3 , it is possible, thanks to the knowledge of the desired values of the magnetizing inductance and of the leakage inductances in the primary circuit L _LK1 and in the secondary circuit L _LK2 , in particular determined in accordance with the invention and corresponding to the electrical transformer considered or to be produced , because of its type of geometry, to determine the geometric criteria of the electrical transformer, including in particular the thickness of the air gap and the relative positioning of the primary and secondary windings.

Other geometric criteria can be taken into account in the context of the implementation of the method for producing an electrical transformer according to an example of the invention, including the position of the air gap, the number and dimensions of the legs. of the magnetic core, for example, to influence the distribution of the equivalent reluctances R1, R2, R3, so as to obtain a desired distribution of the value of the leakage inductances in the electric transformer. For example, we can analyze the equivalent magnetic circuit of the figure 3 in correspondence with the electrical transformer diagram of the figure 4 . Therefore, on the equivalent magnetic circuit of the figure 3 , the reluctances R1 and R3 represent the leakage reluctances corresponding to the leakage zones S1, S2 on the figure 4 . Reluctance R2 represents the reluctance of the air gap G, covered by the secondary winding 2 on the figure 4 . Thus, by reducing the value of the leakage reluctances R1 and R3, compared to the reluctance R2, the magnetic flux which passes through the separation zone of the primary and secondary windings is increased and, thus, the value of the inductance of leak in the primary circuit. This reduction in the value of the leakage reluctances R1, R2 can in particular be achieved by moving the primary and secondary windings away.

A magnetic core geometry must be chosen such that the air gap is framed, on both sides, by a winding belonging to the secondary winding, in order to minimize the leakage inductance in the secondary circuit L _LK2 . By analyzing the equivalent magnetic circuit of the figure 3 , in the "reverse" direction and by moving the voltage source V1 to the side of the secondary flux dry flux, the reluctances R1 and R3, 100 times greater than the reluctance R4 of the magnetic circuit, block the passage of any magnetic flux of leak. Therefore, all the magnetic flux will pass through the primary flux flux_pri with minimized leakage flux.

With reference to figures 4 and 5 , there will now be detailed a method of making an electric transformer based on the use of the equations and principles proposed above, relating to the distribution of the leakage inductance of an electric transformer between the primary circuit and the secondary circuit .

The example detailed below relates more particularly to the production of an electric transformer with integrated leakage inductance concentrated in the primary circuit, having a magnetic core F of type E or type EI.

avec :

• N1 est le nombre d'enroulements primaires ;
• µ₀ est la perméabilité de l'air ;
• S est la surface effective de section magnétique du transformateur électrique ;
• e est l'épaisseur de l'entrefer G du transformateur électrique.

$$\mathit{Rgap}=\frac{1}{{\mu }_0}\ast \frac{e}{S}$$

avec R_gap est la reluctance de l'entrefer G. $$\frac{\mathit{Rgap}}{\mathit{Rfuite}}=\frac{\mathit{Lf}1}{L_M}$$

avec :

• Rfuite est la reluctance de fuite du transformateur électrique ;
• Lf1 est la valeur souhaitée de l'inductance de fuite du transformateur électrique au circuit primaire ;
• L_M est la valeur souhaitée de l'inductance magnétisante du transformateur électrique.

To produce an electric transformer with a desired magnetizing inductance L _M value and the desired leakage inductance value concentrated in the primary circuit, the equations developed below are used. $$L_M={{\mathrm{NOT}}_1}^2\ast \frac{{\mu }_{0}S}{e}$$

with:

• N1 is the number of primary windings;
• µ ₀ is the permeability of air;
• S is the effective magnetic sectional area of the electric transformer;
• e is the thickness of the air gap G of the electrical transformer.

$$\mathit{Rgap}=\frac{1}{{\mu }_0}\ast \frac{e}{S}$$

with R _gap is the reluctance of the gap G. $$\frac{\mathit{Rgap}}{\mathit{Leak}}=\frac{\mathit{Lf}1}{L_M}$$

with:

• Rleakage is the leakage reluctance of the electric transformer;
• Lf1 is the desired value of the leakage inductance of the electric transformer in the primary circuit;
• L _M is the desired value of the magnetizing inductance of the electric transformer.

The leakage reluctance Rleak between the primary 1 and secondary 2 windings takes into account the areas S1, S2 between the primary windings 1 and the secondary windings 2.

où h est la distance séparant les enroulements primaire 1 et secondaire 2 et I la largeur des zones S1, S2, comme indiqué sur la figure 4. La largeur I correspond ainsi à la largeur d'une zone de fuite électromagnétique entre les enroulements primaires 1 et les enroulement secondaires 2, correspondant à la distance séparant une jambe extérieure et une jambe centrale du noyau magnétique F de type E ou de type EITherefore, for an electric transformer having a magnetic core F of type E or of type EI, with a depth of magnetic core denoted by m, the leakage reluctance Rleak can be estimated by means of the following equation: $$\mathit{Leak}=\frac{1}{2{\mu }_0}\ast \frac{l}{h\ast m}$$

where h is the distance separating the primary 1 and secondary 2 windings and I the width of the zones S1, S2, as indicated on the figure 4 . The width I thus corresponds to the width of an electromagnetic leakage zone between the primary windings 1 and the secondary windings 2, corresponding to the distance separating an outer leg and a central leg of the magnetic core F of type E or of type EI

Certain electrical transformers, in particular having a magnetic core of the PQ type, have a magnetic core depth having a non-constant value. In this case, an estimated effective value of the depth of the magnetic core can be used to implement the method of making an electrical transformer according to an example of the invention.

For another geometry of an electrical transformer according to which the windings of the primary circuit are distributed over two upper and lower portions, on either side of the secondary windings, the calculated distance h can be calculated as corresponding to the sum of the two respective distances between each portion of windings of the primary circuit and the windings of the secondary circuit, distributed symmetrically.

Known simulation tools can also be used to analyze the value of the leakage reluctance Rleak of the electrical transformer to be produced.

In order to design and produce an electric transformer, in accordance with the invention, in particular an electric transformer in which the value of the leakage inductance is concentrated in the primary circuit, it is therefore necessary to implement the steps below, with reference to to the figure 5 .

First, we define (step E1) the desired value of the leakage inductance Lf1 and that of the magnetizing inductance L _M of the electric transformer to be produced. Then, it is necessary to choose (step E2) a geometry of the magnetic core, for example, according to the example of figure 4 , a type E magnetic core, for the electrical transformer to be produced. Therefore, we apply the equation [Math. 12] (step E3) above to calculate the thickness e of the required air gap G, corresponding to the desired value of the magnetizing inductance L _M. The secondary windings 2 are then wound (step E4) on the magnetic core F corresponding to the chosen geometry and to the calculated air gap thickness G, so as to cover said air gap G entirely by the secondary windings 2. Thanks to the equations [Math. 13] and [Math. 14], the value of the leakage reluctance Rleakage is calculated (step E5) as a function of the ratio between the value desired of the leakage inductance Lf1 to the primary circuit, which preferably concentrates the leakage inductance of the electric transformer, and the desired value of the magnetizing inductance L _M of the electric transformer. Thanks to the equation [Math. 15], the value of the distance h between the primary windings 1 and the secondary windings 2 is calculated (step E6). The primary windings 1 are then wound (step E7) on the magnetic core of the electric transformer in order to respect said distance h .

If necessary, adjustments to the arrangement of the primary 1 and / or secondary 2 windings can be made as a function of actual measurements of the leakage inductances and of the magnetizing inductance on the electrical transformer thus produced. These additional measurements make it possible to finely adjust the distance h to reach the desired value of primary leakage inductance even more precisely.

Claims (8)

Electrical transformer comprising a magnetic core and a primary winding, forming a primary circuit, and a secondary winding, forming a secondary circuit, electrical transformer configured so that: a first inductance value L _1so measured in the primary circuit with the secondary circuit open, a second inductance value L _1ss measured in the primary circuit with the secondary circuit short-circuited, and a third value L _2po of inductance measured in the secondary circuit with the primary circuit open,
are such that: $$L_{2\mathit{PO}}-\frac{1}{{\mathrm{not}}^2}{L}_M<\mathrm{AT}\mathrm{.}\left(L_{1\mathit{SO}}-L_M\right)$$

with $$L_M=\sqrt{\left(L_{1\mathit{SO}}-L_{1\mathit{SS}}\right)\times L_{1\mathit{SO}}\mathrm{.}{\mathrm{NOT}}^2}$$

where A is a real number greater than 10. An electrical transformer according to claim 1, wherein A is a real number greater than or equal to 50. An electrical transformer according to claim 1 or 2, wherein A is a real number less than or equal to 100. Method for making a transformer, said electric transformer having a magnetic core (F), a primary circuit and a secondary circuit, said method comprising the following steps: selecting (E2) a magnetic core geometry (F) for the electrical transformer to be produced; determining (E3) an air gap thickness (G) corresponding to a desired value of magnetizing inductance (L _M ) of the electric transformer to be produced; winding (E4) of secondary windings (2) on a magnetic core (F) having the selected geometry and the air gap thickness (G), so as to cover said air gap (G); the determination (E5) of a leakage reluctance (Rleak) value of the electric transformer as a function of the ratio between a desired value of leakage inductance (Lf1) at the primary circuit of the electric transformer to be produced, and the desired value of l 'magnetizing inductance (L _M ) of the electric transformer to be produced; determining (E6) a distance h between primary windings (1), intended to form the primary circuit of the electrical transformer to be produced and the secondary windings (2), as a function of said leakage reluctance value (Rfuite); the winding (E7) of the primary windings (1) on the magnetic core (F) of the electric transformer at said distance h from the secondary windings (2). A method according to claim 4, wherein the magnetic core is selected of type E or type EI. Method according to claim 5, in which the equation is implemented: $$L_M={{\mathrm{NOT}}_1}^2\ast \frac{{\mu }_{0}S}{e}$$

where N ₁ is the number of windings in the primary circuit, µ ₀ is the electromagnetic permeability of air and S is the effective magnetic sectional area of the electrical transformer,
to determine the value of the thickness e of the air gap (G) required, corresponding to the desired value of the magnetizing inductance L _M. Method according to claim 5 or 6, in which the equations are implemented: $$\mathit{Rgap}=\frac{1}{{\mu }_0}\ast \frac{e}{S}$$

where R _gap is the reluctance of the air gap (G) of the electric transformer, µ ₀ is the electromagnetic permeability of the air, e is the thickness of the air gap (G) of the electric transformer and S is the effective area of magnetic section of electric transformer
and $$\frac{\mathit{Rgap}}{\mathit{Leak}}=\frac{\mathit{Lf}1}{L_M}$$

where R leakage is the leakage reluctance of the electric transformer, Lf1 is the leakage inductance at the primary circuit of the electric transformer and L _M is the magnetizing inductance of the electric transformer,
to determine (E5) the value of the leakage reluctance (Rleak) of the electric transformer. Method according to one of claims 5 to 7, in which the equation is implemented: $$\mathit{Leak}=\frac{1}{2{\mu }_0}\ast \frac{l}{h\ast m}$$

where Rleakage is the leakage reluctance of the electrical transformer, µ ₀ is the electromagnetic permeability of air, m is the magnetic core depth of the electric transformer and I is the width of an electromagnetic leakage zone (S1) between the primary windings (1) and the secondary windings (2), corresponding to the distance between an outer leg and a central leg of the magnetic core (F) type E or type EI,
to determine (E6) the value of the distance h between the primary windings (1) and the secondary windings (2).

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