Calculation of Leakage Inductance in Stator Windings

1 Introduction The stator leakage reactance plays an important role in the transient process of the motor, so the accurate calculation of the leakage inductance at the end of the winding has important significance for the analysis and simulation of the generator's juice setting and motor over-wave process. The power generator can provide AC and DC power at the same time.

There are multiple sets of symmetrical windings on the stator, and the set provides alternating current. Known as the helium windings, other phase windings provide direct current through the rectifier bridge. It is called as the hunger and hunger. The end of the machine is actually a multi-layered coil with different dimensions. The calculation of the leakage inductance at the end of the terminal, especially between the primary and secondary windings, has not been reported in the literature.

In the past, in the design and simulation analysis of ordinary motors, the empirical equations were used to calculate the stator end leakage. 3. With the development of electromagnetic field calculation methods, many scholars have studied the electromagnetic field at the end, mainly to analyze the end of the motor. The force and end heating groups use an equivalent current plate method to handle the symmetric current 35, taking into account the total effect of the phase winding. However, such a method can be used for the first time in the first line, which can be handled in a discrete way4. The project was supported by the National Natural Science Foundation of China 59777007 and the National Education Commission's Doctoral Key Research Fund 97,00367.

Wang Shanming was born in 1972 and is a Ph.D. student in the Department of Electrical Engineering at Tsinghua University. He currently focuses on motor analysis and control.

The concept of ferromagnetic mirroring and air gap current was used in the calculation. However, the analysis of Document 4 is obtained without considering the position of the bell end of the winding end and the lower layer of the winding, which will result in a certain error. V.

Under the condition of position, the calculation formula of the end leakage inductance of the AC-DC hybrid power generator was deduced. According to the formula, the calculation program of the end leakage inductance was compiled. The results were compared with the experimental results of the test coil on the prototype.

The end-of-end leakage inductance is calculated as the end field magnetic field is a dimensional field, and there are various media such as air and iron in the end, which needs to be simplified. First air gap current is used instead of air gap. When a hypothetical air gap current flows through the air gap, the air gap no longer exists, and the analysis asks if the edge is iron and the other side is air. Then in accordance with the concept of ferromagnetic mirroring, instead of using ferromagnetic media with mirrored currents, the magnetic field at the end is reduced to the magnetic field generated by the end-current gap currents and their mirror images in a uniform air medium.

Create a cylindrical coordinate system of 1 with 1 curtained end of the wire. 00 and Ke 7 are on cylindrical surfaces with radii and + radii. Set the coil end, 0 5, and the path is short and the current direction is reversed and can be ignored during calculation. It also draws the position of the site to be sought. The following describes the magnetic flux generated on the conical surface of each current, at the end of the cylindrical surface! The resulting magnetic flux density can be seen as a special case of magnetic flux generated on a conical surface. As long as the cone angle is taken to be zero degree, the magnetic flux density generated by the current of the straight part of the end 2.1 is the axial current source of the point on the cylindrical surface and (4) the normal magnetic field generated by the radius at the conical surface and the scale point at 1 point. dense.

The projection on the circular surface is 0, especially by Bioshavud.

6 flows through Tunliu, then the air gap current is divided into the line MllUJW4MrTt.rSk ratio, the factory is the pole logarithm, the mechanical angle of the air space across the coil space 9 air gap current and radial current also have their own mirror images. Since the radial current is 18 perpendicular to the 1 and the Yang, the 15 points are in the end surface 05, and the 18 is perpendicular to the 5th plane, so 16 is perpendicular to the 5th plane. The normal component on the cylindrical surface at the especial point is a must, =, it can be projected to the normal direction of the conical surface to obtain the normal component of the conical surface, that is, this point = if the axial coordinate is the heart point The axial coordinate is then = 2, 2, 8 =, and the extension of the linear portion of the end is also summed. One can obtain 6 points of the normal magnetic dense factory where the entire straight line will be produced at the person's point, and the straight part of the upper and lower layer of the end, they are made as mirror images of two cylindrical surfaces with different radii.

In order to obtain the linear part of the end, including the normal magnetic density generated at the point of conic blood at the end of the common-segment current, one can change the stone segment in the formula 2 into 02, and change the sky into a hole +, and The radius of the cylindrical surface where the + hole is located.

The paragraph will be replaced by 62 calls, 7, replaced by 2+5, plus a negative sign before. 1 point is replaced by a 12-end involute part of the magnetic flux produced by part of the current if the end of the inflection line part of the current 71. It is decomposed into axial circumferential and radial components, ie 2 from 6 to, summation You can also, when seeking the effect of each segment of the current, perform the corresponding transformation. 2.2.2 The magnetic flux generated by the circumferential current is the point at which the fire point is located on the round surface, such as the circumferential current from the point. The resulting 45 is perpendicular to the plane, but 18 is not perpendicular to the cylindrical surface where the defect is located. , 6 can be divided into two sub-cameras. The components in the circle are the most square, and the other is in the axial component 5 perpendicular to the cylindrical surface. Both will produce normal points on the conical surface, = the total normal component on the conical surface generated by the circumferential current is 22.1 and the magnetic flux density produced on the axial current is the same as the result of 2.1 from Chinese formula 1 7 from 6 to the sum, seeking When the current of each segment is made, the corresponding transformation is also performed. The magnetic flux produced by the 2.2.3 dipole current is the point, and the projection of the point 1 is on the circular surface where the tip point is located. For example, for Court 5, the perpendicular line from the ruler is 6, and the intersection point with 05, and the intersection point from 0 to 4 is the intersection of 0.

From the radial current of the point, the vertical point produces 垂 and it must be perpendicular to the box level. It is not conical. It can be decomposed into the component 1 in the circle and the axial component 14 of the cylindrical surface. Both components will be Produces a normal component on the conical surface. The total normal component on the conical surface generated by the radial current is, for example, 2 from 6 to sum. When seeking the effect of each segment of the current, a corresponding transformation is also required.

The air gap current produced by the air gap current includes mirrored common segments. The effect of the air gap current is similar to the effect of the circumferential current on the evolute secondary winding. It can be found in a similar way. The air gap current inside the coil is generated at the location where the air gap current is located, and the normal magnetic density generated by the air gap current from 02 to the outside of the coil divides the current of each part of the coil into many small currents. The source can find the normal magnetic density generated by each current source at a certain point on a cylindrical or conical surface, and sum it to obtain the total normal magnetic density produced at a certain point by the energizing coil. The magnetic flux surrounded by the non-energizing coil is obtained by summing the product of the normal flux density and the cell area on the unit between two coils, and is then multiplied by the number of turns divided by the current to obtain the mutual leakage sense at the ends. When calculating the flux leakage inductance of the coil end, the internal inductance caused by the internal flux linkage of the wire rod should also be 2. The length of the end of the coil.

3 Experimental verification According to the above method, the end leakage sensor program was programmed and verified on the prototype. The stator of the prototype has alternating sets of phases around the stator, where the sleeve is different from the rest of the sleeve and is called the main winding. The rest of the sleeve is the secondary winding sister. The set of secondary windings 1 is evenly distributed on the stator. For the convenience and accuracy of verification, the coils with the same shape and size as the end portions of the human phase are also wound around the phases of the sheathed windings. They are also referred to as the primary and secondary test coils respectively, and are tied to the corresponding ends of the stator windings. The wire test wire has an end portion, a portion within the special groove, and is energized in the phases of the main and secondary windings when the experiment is closed at the end face of the stator core, and the voltage on the test coil is measured and compared with the calculated value. The number of slots per phase for each winding of the main winding is 5,44,5; the number of windings per phase for each winding is 16; the test coils are all 40 turns. The comparison of measured and calculated values is shown as 1 and 2.

From the comparison of the data, it can be seen that the calculation of the leakage inductance at the end is close to the real ride value. When the secondary winding is energized, the number of turns and the number of turns of the subtest coil are small, and the current of the energization is small, and the induced voltage is lower than that of the energized winding. , Main test coil phase voltage, test calculation test coil test calculation test coil 2 phase voltage, test calculation test coil test calculation test coil test calculation main winding phase main winding 8 phase main winding phase winding, 1 phase secondary winding, phase secondary winding 1 phase secondary winding. 42-phase secondary winding 32-phase secondary winding 02-phase secondary winding 3-phase secondary winding 83-phase secondary winding 03 secondary winding 4-phase secondary winding 134 secondary winding 04-phase main test coil test coil current winding current A test calculation test calculation test Calculate the test calculation, and calculate the influence of the geometric dimension of the 4 terminal 4 part of the primary winding phase winding of the 1 phase secondary winding of the secondary winding of the 1 phase secondary winding of the secondary winding and the secondary winding of the secondary winding phase to the salt leakage at the end. The mutual leakage of the ends 1 of each phase winding increases as the length of the end gradually increasing the secondary line.

The relationship between the size of the end and the leakage inductance was studied by using the previously-reviewed end leakage inductance calculation method. Several possible conditions for the dimensions of the end were separately calculated and summed up as follows: 1 Without changing the end extension When the length and the angle of the bellmouth are different, each end of the phase winding has a mutual leakage sensation with the length of the linear portion of the end. When the straight portion and the total length of the end portion do not change, the ends of the respective phase windings leak from each other. The sensation will increase as the angle of the end flare increases. In the case where the straight portion of the end portion and the total length of the end portion are not changed, the mutual self-leakage sensation of the end portion of each phase winding increases and then decreases with the angle of the end flare.

5 Conclusions From the viewpoint of output voltage equivalence, the single-phase switching power factor correction device is equivalent to the team converter of the working body 01. The simplified equivalent circuit can correctly reflect the fire of the original circuit; the dynamic and steady state characteristics of No. 1 . So far. The design of the single-phase switching power factor corrector can only adopt the trial and error method and the simplified model put forward by Muwen can make the design direct and easy. Another contribution of this paper is to make the frequency domain design of the regulator possible and very easy.

1 Cai Xuan. Gong Shaowen. High frequency power electronics DC DC conversion section. Beijing: Science Press. 1993.

3 Yu Xu, Hou Zhencheng. Single-switch, power factor corrector, simplified large-signal model. 2000 China Power Supply New Technology and Application Symposium, North g, Received date 200007, then page 5 When increasing the radius of the cylindrical surface where the windings are located, the mutual self-leakage sensibility of the ends of each phase winding follows the radius of the cylindrical surface. , And reduce, mutual leakage sense between the ends of the main and secondary windings is not only related to the above factors, but also related to the relative size of the two, need to be calculated and analyzed according to the situation.

5 Conclusions The method for calculating the end-leakage inductance at the mouth and in the winding layering, and the test measurement method at the end of the stator and rotor of the stator motor, indeed, on this basis, the influence of the end geometry on the leakage inductance at the end was studied. The text 6696002 Gao Jingde, Qiu Liban, Li Fahai. AC motor and system analysis. Beijing Tsinghua University Press. 1993.

Received date 2000