TWI402527B - Estimation of Transformer Leakage Value - Google Patents

Description

Method for estimating transformer leakage inductance value

The invention relates to a method for estimating the leakage inductance value of a transformer, in particular to a method for separately estimating the leakage inductance value of the primary side of the transformer and the leakage inductance value of the secondary side.

In the past, the calculation of transformer parameters was very difficult for the designer to analyze its exact value, because the magnetizing inductance and leakage inductance in the transformer parameters depend on various factors, such as the geometry of the iron oxide core, and the material. And winding methods.

Referring to FIG. 1 and FIG. 2, the estimation of the leakage inductance of the conventional transformer is often obtained by equivalently reducing the leakage inductance on the secondary side of the transformer to the primary side or the primary side leakage inductance to the secondary side, as shown in FIG. The conventional equivalent circuit of the transformer 9, L _{l 1} and L _{l 2} are the leakage inductance value of the primary side 91 and the leakage inductance value of the secondary side 92, respectively, L _m is the magnitude of the magnetizing inductance, and N ₁ and N ₂ are respectively The number of turns of the side 91 and the secondary side 92; short-circuiting the two ends of the secondary side 92 can be equivalent to the circuit diagram shown in FIG. 2, which is seen from the primary side 91, and the original leakage inductance L _{l 2 is} reflected to the primary side. 91, the leakage side of the secondary side 92 that is seen by the primary side 91 is Since the L _m phase is much higher than L _{l 2} , it can be neglected. Finally, the total leakage inductance of the transformer 9 seen from the primary side 91 can be estimated. .

This method can only estimate the total leakage inductance value of the primary and secondary sides 91 and 92 of the transformer, and cannot obtain the respective leakage inductance values L _{l 1} and L _{l 2 of} the transformer first and secondary sides 91 and 92, so that the transformer The influence of the leakage inductance on the primary side or the secondary side cannot be displayed when the model is established.

In recent years, although many scholars have made in-depth research on the parameter estimation and model establishment of transformers, most of them need to be deduced and explained by large-scale mathematical principles, which makes the transformer modeling process very complicated.

Accordingly, it is an object of the present invention to provide a method for obtaining respective leakage inductance values of the primary and secondary sides of a transformer.

Therefore, the present invention estimates a transformer leakage inductance value, the transformer has a primary side with a coil number N ₁ and a secondary side with a coil number N ₂ , the method comprising the following steps: (A) Obtaining the self-inductance amount L _{1 of} the primary side, and obtaining the self-inductance amount L _{2 of} the secondary side; (B) obtaining a mutual inductance M of the transformer; and (C) according to the primary side and the secondary side coil The ratio of the turns, the primary side self-inductance L ₁ , the secondary side self-inductance L ₂ , and the mutual inductance M , and the leakage inductance L _{l 1} of the primary side and the leakage inductance of the secondary side are obtained. L _{l 2} . Preferably, in the step (C), according to the second calculation formula The leakage inductance L _{l 1 on} the primary side and the leakage inductance L _{l 2 on} the secondary side are obtained.

The effect of the present invention lies in the calculation of two calculations using a transformer model. The ratio of the primary side to the secondary side turns, the primary side self-inductance L ₁ , the secondary side self-inductance L ₂ , and the mutual inductance M can be determined by a conventional technique. The respective leakage inductance values L _{l 1} , L _{l 2 of the} primary and secondary sides of the transformer.

The above and other technical contents, features and advantages of the present invention will be apparent from the following detailed description of FIG.

In the first embodiment, the following derivation process is used to explain how to calculate the inductance value parameters of each transformer to obtain the calculation formula of the individual leakage inductance values of the primary side and the secondary side.

Figure 3 shows a schematic diagram of a conventional transformer 7. In the figure, M is the mutual inductance of the two windings, and L ₁ and L ₂ are the self-inductance of the primary side 71 of the transformer 7 and the self-inductance of the secondary side 72, respectively. We can also use an ideal transformer model to equivalent transformer 7, as shown in Figure 4. Where L _{l 1} , L _{l 2} and L _m are the leakage inductance value of the primary side 71 of the transformer 7, the leakage inductance value of the secondary side 72, and the magnetizing inductance value, respectively, and N ₁ and N ₂ are the coils of the primary side 71 of the transformer 7 respectively. The number of turns and the number of turns of the secondary side 72, v ₁ and v ₂ are the cross-pressure of the primary side 71 of the transformer 7 and the cross-pressure of the secondary side 72, respectively. Then, the voltage across the magnetizing inductance 712, i ₁ is the leakage current flowing through the transformer 71 side 71, and i ₂ is the current flowing through the leakage inductance 721 of the transformer 72 7 side. Then, the current i _{2 of} the secondary side 72 is reflected to the primary side 71, that is, .

To be observed from FIG. 3, a measuring transformer 7 of 71 is the voltage across v _1:

It can be observed from FIG. 4, 7 of a measuring transformer 71 as the voltage across v _1:

It should be noted that in the following derivation process, for the convenience of calculation, we omit the differential symbol d and directly derive it using a general four-like operation.

will Substituting into (II), and since (I) is equal to (II), it is available;

In (III), compare The coefficient can be obtained:

L ₁ = L _{l 1} + L _m ............................................. ..............................(IV)

Similarly, by observing FIG. 3 and FIG. 4, the cross-pressure v ₂ of the second measurement 72 of the transformer 7 can be obtained:

In (VI) Can be obtained by Cossief's law:

Also for the convenience of calculation here, we omit the differential symbol d and directly derive it using a general four-order operation.

Substituting (VII) into (VI) and then comparing with (V), you can get:

In (VIII), compare The coefficient can be obtained:

Substituting (X) into (IV) gives:

Substituting (X) into (IX) gives:

Referring to Figure 5, the present invention is a method to estimate a first preferred embodiment of the transformer leakage inductance comprising the following steps: First, to obtain a 71-side self-inductance L ₁ and the secondary side 7 of the self-inductance of the transformer 72 L _2.

Step 51 - As shown in Fig. 6, the secondary side 72 of the transformer 7 is opened, and the self-inductance L _{1 of} the primary side 71 is measured; as shown in Fig. 7, the primary side 71 of the transformer 7 is opened, and the secondary side 72 is measured. Self-inductance L ₂ .

Furthermore, the mutual inductance amount M is obtained through the following steps 52, 53 and 54.

Step 52 - As shown in FIG. 8, the primary side 71 of the transformer 7 is connected in series with the secondary side 72 in an opposite polarity, and a first equivalent inductance value L _{eq 1} is measured.

Step 53 - As shown in FIG. 9, the primary side 71 of the transformer 7 and the secondary side 72 are connected in series with the same polarity, and a second equivalent inductance value L _{eq 2} is measured.

Step 54 - From the equivalent circuit diagrams of FIGS. 8 and 9, it can be known that L _{eq 1} = L ₁ + L ₂ + 2 M and L _{eq 2} = L ₁ + L ₂ - 2 M , and the above two equations can be obtained. a calculation The first equivalent inductance value L _{eq 1} and the second equivalent inductance value L _{eq 2} measured in steps 52 and 53 are substituted, and the mutual inductance M is obtained.

Finally, through the step 55, step 56, we obtain the amount of leakage inductance of the transformer primary side 7 of the 71 amount of leakage inductance _{L l 1,} 72 of the secondary side _{L l 2,} and the magnetizing inductance L _m.

Step 55 - Substituting the self-inductance amount L ₁ of the primary side 71 obtained in steps 51 and 54 and the self-inductance amount L ₂ and the mutual inductance amount M of the secondary side 72 into the two calculation formulas derived from the foregoing In the middle, the leakage inductance L _{l 1 of the} primary side 71 of the transformer 7 and the leakage inductance L _{l 2 of the} secondary side 72 can be obtained.

Step 56 - Substituting the mutual inductance M obtained in step 54 into the previously derived calculation formula Find the magnetizing inductance value L _m .

In the above steps, the calculation of the parameters of the transformer 7 does not have a certain order, except that the calculation formula must be prioritized to obtain the required parameters.

It is worth mentioning that, in this embodiment, all the inductance values are measured by using an inductance meter (RLC meter), of course, the measuring instrument is not limited thereto.

Referring to FIG. 10 and FIG. 11, in order to verify the correctness of the leakage inductance L _{l 1 of the} primary side 71 of the transformer 7 and the leakage inductance L _{l 2} and the excitation inductance value L _m of the secondary side 72, we will use the transformer. The primary side 71 of 7 is connected in parallel with the secondary side 72 in an opposite polarity to form an equivalent circuit diagram as shown in FIGS. 10 and 11.

As can be observed from Fig. 10, a third equivalent inductance value L _{eq 3} is:

To be observed from FIG. 11, measured across the transformer primary voltage of 7 v 71 ₁ is:

(XIV), For the secondary side 72 of the transformer 7, the current i _{2 is} reflected to the primary side 71, ie . It can also be observed from Fig. 11 that the cross-over voltage v ₂ of the secondary measurement 72 of the transformer 7 is:

For the primary side 71, the voltage across the magnetizing inductance 712, (XV) Can be obtained by Cossief's law:

Also for the convenience of calculation here, we omit the differential symbol d and directly derive it using a general four-order operation.

Substituting the formula (XVI) into the formula (XV), and since the primary side 71 is connected in parallel with both ends of the secondary side 72, v ₁ = v ₂ , which yields:

Because the input current i = i ₁ + i ₂ , you can get:

From the primary side 71, the voltage across the magnetizing inductance 712 is equal to the voltage across the secondary side 72 looking at the magnetizing inductance 712, so After finishing, you can get:

Bring (XVII) into (XIX)

Then bring (XVIII) into (XX), you can get:

It can be observed from Fig. 10 and Fig. 11, , substituting (XIX), you can get:

We transformer obtain 56 Step 55 Step 7 primary leakage inductance weight side 71 of the _{L l 1,} the secondary leakage inductance weight side 72 of the _{L l 2} and the magnetizing inductance L _m is substituted into formula (XXII) to give a Estimating the third equivalent inductance value L _{eq 3} , comparing the value to the third equivalent inductance value L _{eq 3} measured by using the inductance measuring instrument, and confirming the estimated L _{l 1} , L _{l 2} and L _m correctness.

Here, the results of an experimental data are used as an aid. The core used in this experiment is a ring core produced by micrometals. The specifications of T130-52 are shown in Table 1.

The T130-52 is used as the core of the transformer, the primary side is 20 匝, and the secondary side is 40 匝. The concentrated winding is used. According to the steps of the first preferred embodiment of the present invention, the LC meter model is used for measuring the KC-605. The test frequency is 100 kHz, and the obtained measured value, estimated value and verified result are shown in Table 2.

It can be seen from Table 2 that the estimated third equivalent inductance value L _{eq 3} =4.37μH is very close to the actual measured value 4.21μH, so the leakage inductance estimation of the proposed transformer can be separated from the traditional estimation method. The measured side leakage inductance value and the secondary side leakage inductance value are also relatively accurate when the model is established.

Referring to FIG. 12, it is a second preferred embodiment of the method for estimating the leakage inductance of the transformer according to the present invention. The steps are substantially the same as those of the first preferred embodiment. The manner in which the mutual inductance M is obtained is different. This embodiment includes The following steps: First, the primary side 71 self-inductance L _{1 of the} transformer 7 and the secondary side 72 self-inductance L _{2 are obtained} .

Step 121- 6, 7 of the secondary side of the transformer 72 is open, the measured primary side 71 of the self-inductance L _1; 7, 71 open the primary side of the transformer 7, the measured secondary-side 72 Self-inductance L ₂ .

Furthermore, the mutual inductance amount M is obtained through the following steps 122 and 123.

Step 122 - As shown in FIG. 8, the primary side 71 of the transformer 7 is connected in series with the secondary side 72 in an opposite polarity, and a first equivalent inductance value L _{eq 1} is measured.

Step 123- the equivalent circuit diagram of FIG 8, it is possible that _{L eq 1 = L 1 + L} 2 +2 M, step 121 and step 122 a first measured value of the equivalent inductance L _{eq 1} is substituted, seek The mutual inductance is M.

Finally, through the step 55, step 56, we obtain the amount of leakage inductance of the transformer primary side 7 of the 71 amount of leakage inductance _{L l 1,} 72 of the secondary side _{L l 2,} and the magnetizing inductance L _m.

Step 124- Step 121 and step 123 in the self-inductance of the primary side 71 of the acquired L _1, the secondary side 72 of the self-inductance L ₂ and the mutual inductance M, substituting the two previously deduced calculation formula The leakage inductance L _{l 1 of the} primary side 71 of the transformer 7 and the leakage inductance L _{l 2 of the} secondary side 72 are obtained.

Step 125 - Substituting the mutual inductance M obtained in step 123 into a calculation formula Find the magnetizing inductance value L _m .

The present embodiment changes only the method of obtaining the mutual inductance M, the leakage inductance of the amount of amount of leakage inductance on the primary side 71 of the _{L l} according to the present invention finally obtained _a secondary side 72 of the _{L l 2} and the magnetizing inductance L _m does not affect, Compared with the first preferred embodiment, the present embodiment eliminates the step of measuring the second equivalent inductance value L _{eq 2} .

Referring to FIG. 13, FIG. 13 is a third preferred embodiment of the method for estimating the leakage inductance of the transformer according to the present invention. The steps are substantially the same as those of the first preferred embodiment. The manner in which the mutual inductance M is obtained is different. This embodiment includes the following steps: first, to obtain a 71-side self-inductance L ₁ and the secondary side 7 of the self-inductance of the transformer 72 L _2.

Step 131 - As shown in Fig. 6, the secondary side 72 of the transformer 7 is opened, and the self-inductance L _{1 of} the primary side 71 is measured; as shown in Fig. 7, the primary side 71 of the transformer 7 is opened, and the secondary side 72 is measured. Self-inductance L ₂ .

Furthermore, the mutual inductance amount M is obtained through the following steps 132 and 133.

Step 132 - As shown in FIG. 9, the primary side 71 of the transformer 7 and the secondary side 72 are connected in series with the same polarity, and a second equivalent inductance value L _{eq 2} is measured.

Step 133- the equivalent circuit diagram of FIG 8, it is possible that _{L eq 2 = L 1 + L} 2 -2 M, the equivalent inductance value of the second measured in step 132 and step 131 are substituted into L _{eq 2,} seek The mutual inductance is M.

Finally, through the step 55, step 56, we obtain the amount of leakage inductance of the transformer primary side 7 of the 71 amount of leakage inductance _{L l 1,} 72 of the secondary side _{L l 2,} and the magnetizing inductance L _m.

Step 134- Step 131 and step 133 in the self-inductance of the primary side 71 of the acquired L _1, the secondary side 72 of the self-inductance L ₂ and the mutual inductance M, substituting the two previously deduced calculation formula The leakage inductance L _{l 1 of the} primary side 71 of the transformer 7 and the leakage inductance L _{l 2 of the} secondary side 72 are obtained.

Step 135 - Substituting the mutual inductance M obtained in step 133 into the previously derived calculation formula Find the magnetizing inductance value L _m .

In this embodiment and the second preferred embodiment, only the method of changing the mutual inductance M is changed with respect to the first preferred embodiment, and the result is not affected, and the first equivalent inductance value L _{eq is} omitted in the embodiment. ₁ step.

In summary, the effect of the present invention lies in the three calculations derived from the transformer model. And obtaining the ratio of the measured primary side to the secondary side coil turns, the primary side self-inductance L ₁ , the secondary side self-inductance L ₂ , and the mutual inductance M , and obtaining a conventional estimation method The leakage inductance values L _{l 1} , L _{l 2} and the magnetizing inductance value L _{m of the} primary and secondary sides of the transformer that cannot be disassembled can be more conducive to the discussion of the soft switching circuit that needs to resonate by the leakage inductance of the transformer. Establish a more accurate transformer model to facilitate the simulation of the system.

The above is only the preferred embodiment of the present invention, and the scope of the invention is not limited thereto, that is, the simple equivalent changes and modifications made by the scope of the invention and the description of the invention are All remain within the scope of the invention patent.

7. . . transformer

71. . . Primary side

72. . . Secondary side

51~56. . . step

121~125. . . step

131~135. . . step

Figure 1 is a circuit diagram illustrating a conventional equivalent circuit of a transformer;

2 is a circuit diagram showing that in the past, only the secondary side of the transformer can be short-circuited to measure the leakage inductance value of the overall transformer;

Figure 3 is a circuit diagram illustrating a conventional transformer;

Figure 4 is a circuit diagram showing the ideal model of the transformer ignoring iron loss;

FIG 5 is a flow diagram illustrating a first preferred embodiment of the method of the present invention estimates values of the sense transformer leakage how to obtain the amount of leakage inductance of the transformer primary side of this _{L l 1,} amount of the secondary side of the leakage inductance _{L l 2} and Excitation inductance value L _m ;

Figure 6 is a circuit diagram showing how the self-inductance L _{1 of the} primary side is measured;

Figure 7 is a circuit diagram showing how the self-inductance L _{2 of the} secondary side is measured;

Figure 8 is a circuit diagram showing how to measure the first equivalent inductance value L _{eq 1} ;

Figure 9 is a circuit diagram showing how to measure the second equivalent inductance value L _{eq 2} ;

Figure 10 is a circuit diagram in which the primary side and the secondary side of the transformer are connected in parallel to verify the results of the first preferred embodiment;

Figure 11 is a circuit diagram in which the primary side and the secondary side of the transformer of Figure 4 are connected in parallel with each other;

FIG 12 is a flowchart illustrating a second preferred embodiment of the method of the present invention estimates values of the sense transformer leakage how to obtain the amount of leakage inductance of the transformer primary side of this _{L l 1,} amount of the secondary side of the leakage inductance _{L l 2} and Excitation inductance value L _m ;

FIG 13 is a flowchart illustrating a second preferred embodiment of the method of the present invention estimates values of the sense transformer leakage how to obtain the amount of leakage inductance of the transformer primary side of this _{L l 1,} amount of the secondary side of the leakage inductance _{L l 2} and The magnetizing inductance value L _m .

51~56. . . step

Claims (14)

A method for estimating a leakage inductance value of a transformer having a primary side with a coil number N ₁ and a secondary side with a coil number N ₂ , the method comprising: (A) obtaining the primary side Sensing L ₁ and obtaining the self-inductance L _{2 of} the secondary side; (B) obtaining a mutual inductance M of the transformer; and (C) determining the ratio of the primary side to the secondary side turns The side self-inductance L ₁ , the secondary side self-inductance L ₂ , and the mutual inductance M are obtained, and a leakage inductance L _{l 1 on} the primary side and a leakage inductance L _{l 2 on} the secondary side are obtained. According to the method for estimating the leakage inductance value of the transformer according to claim 1 of the patent application, before the step (B), a step (D) is further included, and the primary side and the secondary side are connected in opposite polarity, and the measurement is performed. A first equivalent inductance value L _{eq 1} . According to the method for estimating the leakage inductance value of the transformer according to the second aspect of the patent application, in the step (B), the primary side self-inductance L ₁ , the secondary side self-inductance L ₂ , and the first An equivalent inductance value L _{eq 1 is} obtained to obtain the mutual inductance M. According to the method for estimating the leakage inductance value of the transformer according to item 3 of the patent application scope, in the step (B), the mutual inductance is obtained according to a calculation formula L _{eq 1} = L ₁ + L ₂ + 2 M M. According to the method for estimating the leakage inductance value of the transformer according to claim 1 of the patent application, before the step (B), a step (E) is further included, and the primary side and the secondary side are connected in series with the same polarity, and the measurement is performed. A second equivalent inductance value L _{eq 2} . According to the method for estimating the leakage inductance value of the transformer according to the fifth aspect of the patent application, in the step (B), the primary side self-inductance amount L ₁ , the secondary side self-inductance amount L ₂ , and the first The equivalent inductance value L _{eq 2 is} obtained, and the mutual inductance M is obtained. According to the method for estimating the leakage inductance value of the transformer described in claim 6 of the patent application, in the step (B), the mutual inductance is obtained according to a calculation formula L _{eq 2} = L ₁ + L ₂ -2 M M. According to the method for estimating the leakage inductance value of the transformer according to the second aspect of the patent application, before the step (B), a step (E) is further included, and the primary side and the secondary side are connected in series with the same polarity, and the measurement is performed. The second equivalent inductance value L _{eq 2} . According to the method for estimating the leakage inductance value of the transformer according to claim 8 of the patent application, in the step (B), according to the first equivalent inductance value L _{eq 1} and the second equivalent inductance value L _{eq 2} , Find the mutual inductance M. The method for estimating the leakage inductance value of the transformer according to claim 9 of the patent application scope, in the step (B), according to a calculation formula Find the mutual inductance M. The method for estimating the leakage inductance value of the transformer according to the claims 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 of the patent application, in the step (C), based on the second calculation formula The leakage inductance L _{l 1 on} the primary side and the leakage inductance L _{l 2 on} the secondary side are obtained. According to the method for estimating the leakage inductance value of the transformer according to claim 11 of the patent application, the step (B) further comprises a step (F), and a magneto-inductance value L _{m is} obtained according to the known mutual inductance M. . The method for estimating the leakage inductance value of the transformer according to claim 12 of the patent application scope, in the step (C), according to a calculation formula The magnetizing inductance value L _{m is obtained} . According to the method for estimating the leakage inductance value of the transformer according to claim 11 of the patent application, in the step (A), the secondary side is opened and the self-inductance L _{1 of} the primary side is measured, and the first time is made. The side is opened and the self-inductance L _{2 of} the secondary side is measured.