Large-scale motor magnetic-thermal coupling model modeling and rapid calculation method

Abstract

The invention provides a method for improving analysis and calculation of a temperature field of a large-scale motor. The method relates to the field of motor electromagnetic field and temperature field calculation, and is suitable for temperature rise analysis of modern large motors. In order to guarantee safe and efficient operation of a large motor under various working conditions, the electromagnetic performance, temperature rise and other performance of the motor under different working conditions need to be accurately and efficiently analyzed. The invention provides a large-scale motor magnetic-thermal coupling model modeling and rapid calculation method. According to the method, the specific structure and research problem analysis of the large motor are determined, the structure is stator and rotor iron cores and coils under a large motor shell, and the research problem analysis is electromagnetic performance and thermal performance; determining physical fields related to the problem, wherein the physical fields are an electromagnetic field and a temperature field; and establishing a dynamic magnetic network model and a thermal network model, coupling the equivalent magnetic network model and the equivalent thermal network model, and analyzing the established models. Analysis is carried out according to specific problems of research, and it is guaranteed that the performance of the motor is accurately and efficiently analyzed in different states.

Description

Technical Field

[0001] The invention belongs to the field of motor electromagnetic field and temperature field calculation, and relates to a large motor magnetic-thermal coupling model modeling and fast calculation method. Technical Background

[0002] Large induction motors are favored for their relatively simple structure, high reliability, and stable operation. Generally speaking, low-speed, large-capacity induction motors are often used to drive reciprocating compressors. Due to the changes in the number of compression stages of the compressor, the drive motor often needs to be overloaded for a short period of time. In the case of overload operation, the temperature of the motor will continue to rise because the heat generation rate exceeds the heat dissipation rate. If the temperature rise exceeds the safe temperature range of the motor, the insulation performance of the windings in the motor will decrease, the magnetic conductivity of the ferromagnetic material will decrease, the life of the motor will be shortened, and in severe cases, insulation breakdown accidents will occur, damaging the equipment. In order to ensure the safe and efficient operation of the motor under various working conditions, it is necessary to accurately and efficiently analyze the electromagnetic properties and temperature rise of the motor under different working conditions.

[0003] The current methods for analyzing the temperature distribution in induction motors are the equivalent thermal network model method and the fluid network-thermal network bidirectional coupling method. The stator and rotor loss distribution characteristics of the motor are calculated by the finite element method or numerical analysis method, and the temperature distribution is obtained by establishing an equivalent thermal network model. Summary of the invention

[0004] The purpose of the present invention is to use a fluid network-thermal network to jointly analyze the temperature rise distribution of a large motor. However, the fluid network-thermal network analysis method is suitable for steady-state analysis, while the motor is dynamic during operation. This method cannot accurately reflect the change of temperature rise over time. In view of the defects of this method, a large motor magnetic-thermal coupling model modeling and fast calculation method is proposed. This method can analyze the electromagnetic performance and temperature rise of the motor under different working conditions.

[0005] To achieve the above object, the technical solution proposed in the present invention is: a modeling and rapid calculation method based on a large motor magnetic-thermal coupling model, comprising the following steps:

[0006] Step 1: Region division: The motor magnetic network model includes three parts: stator magnetic network model, rotor magnetic network model, and air gap magnetic network model. Grid division is performed on each region respectively, and the appropriate segmentation accuracy is selected based on the magnetic field distribution of each component.

[0007] Step 2: Establish an equivalent magnetic network model: According to the structural characteristics and magnetic distribution gradient of the large motor, the magnetic network model of the motor stator, rotor and air gap is constructed, and the models are connected according to the coupling relationship of each part to establish an equivalent magnetic network model;

[0008] Step 3: Write the magnetomotive force equations according to the equivalent magnetic network model and calculate the magnetic density distribution of nodes in each region;

[0009] Step 4: Calculate the iron loss of each area according to the magnetic density distribution of nodes in each area;

[0010] Step 5: Use numerical analysis methods to calculate the copper loss in each area;

[0011] Step 6: Divide the thermal nodes according to the thermal gradient distribution in the motor, calculate the thermal resistance of each area, and establish a thermal network model to solve the temperature rise of each node;

[0012] Step 7: Magnetic-thermal coupling calculation: Substitute the core loss calculated using the magnetic network model and the copper loss calculated using the numerical analysis method as heat sources into the thermal network model to calculate the temperature rise of each node. If the temperature does not converge, recalculate the copper loss based on the impact of the temperature rise on the impedance. Repeat the above steps until the temperature meets the set convergence accuracy. This temperature can be considered to be the target temperature.

[0013] Furthermore, in step 2, when establishing the transient equivalent magnetic network model, due to the normal operation of the motor, the magnetic flux path at the air gap changes due to the change in the relative position of the stator and rotor, thereby affecting the magnitude of the permeance value at the air gap, and the air gap permeance matrix changes with the rotor position. In combination with the characteristics of the induction motor under study, the present invention only needs to consider the spatial angle between the center lines of the two tooth tops and solve it according to the air gap permeance formula for the air gap permeance between the stator and the rotor at any time, and the air gap permeance between any stator tooth and any rotor tooth at any time and any rotor position can be obtained, and the transient equivalent magnetic network model can be established.

[0014] Furthermore, in step 4, the iron loss of each region is calculated according to the magnetic flux density distribution of each region node, and the internal magnetic field distribution gradient of the motor is also taken into account when calculating the iron loss.

[0015] Furthermore, in step 5, the influence of skin effect and proximity effect on winding copper loss should be considered; the skin effect is equivalent to reducing the area of ​​the current flowing through the conductor, indirectly increasing the resistance of the conductor, thereby increasing the loss of the conductor, reducing the motor efficiency, and increasing the temperature; when the distance between two conductors is close, alternating current is passed through adjacent conductors, and the adjacent conductors will be in each other's alternating magnetic field. At this time, the electric density distribution of each conductor will be affected by itself and the adjacent conductors, resulting in its electric density distribution being different from the electric density distribution formed when alternating current is passed through it alone.

[0016] Furthermore, in step 1 and step 6, the stator magnetic network model area division is mainly divided into the stator yoke, stator tooth, slot body leakage magnetic part and stator winding part, and the rotor magnetic network model area division is mainly divided into the rotor yoke, tooth, slot body leakage magnetic part and rotor winding part. When dividing the thermal network model, considering the magnetic-thermal distribution gradient in the motor, a common region method is adopted to divide multiple thermal regions, such as the stator core thermal zone, the rotor core thermal zone, the winding thermal zone, the air gap thermal zone, etc. Each thermal zone has its own thermal characteristics, such as heat capacity, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flow chart of an embodiment of the present invention;

[0018] Figure 2 It is a magnetic network model and some local schematic diagrams of an embodiment of the present invention;

[0019] Figure 3 It is a thermal network model and some local schematic diagrams of an embodiment of the present invention; DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solution and advantages of the present invention more clear, the technical solution in the embodiment of the present invention is clearly and comprehensively described below in combination with the embodiments of the present invention and the accompanying drawings.

[0021] According to the structural characteristics of large motors and the magnetic-thermal distribution gradient, the present invention adopts the common region method to establish a motor magnetic-thermal dynamic coupling network model, taking into account the influence of transient electromagnetic processes on motor heating. Based on the interactive relationship between the magnetic-thermal physical field in the motor, the model coupling solution parameters are determined. The analytical method is used to quickly solve the coupling model, and the electromagnetic and thermal transient characteristic data of the motor under different working conditions are stored in the host computer, so as to accurately and efficiently analyze the electromagnetic performance and temperature rise of the motor.

[0022] This embodiment is introduced by taking a specific large-capacity induction motor as an example. The embodiment is a 20-pole squirrel cage rotor induction motor, the stator has 180 slots, the rotor has 210 slots, and is divided into three parts: stator, rotor, and air gap. The stator includes a yoke, stator teeth, stator slots, and stator windings. The stator windings use distributed windings with a pitch of 8 and 3 slots per pole per phase. The rotor includes a rotor yoke, rotor teeth, rotor slots, and rotor windings. The rotor windings use squirrel cage rotors.

[0023] As attached Figure 1 The flowchart shown is divided into the following steps:

[0024] Step 1, regional division, based on the topological structure of the motor, the motor part is divided into 6 regions. For each region, the equivalent magnetic permeance is calculated according to its geometric shape. Region 1 is the stator yoke part, which is equivalent to a combination of 2 radial rectangular magnetic permeances and 1 tangential rectangular magnetic permeance according to the specific shape; Region 2 is the stator winding, stator slot body and winding part, which is equivalent to 1 radial magnetic permeance and 1 equivalent magnetic potential source according to the shape; the stator slot body part will have some leakage magnetic flux through the slot closure, so it is equivalent to an "I"-shaped magnetic permeance structure connected by 1 radial rectangular magnetic permeance and 4 tangential rectangular magnetic permeances; Region 3 is the stator tooth part, which is refined and equivalent to a "cross"-shaped magnetic permeance structure composed of 2 radial rectangular magnetic permeances and 2 tangential rectangular magnetic permeances; similarly, the equivalent method of magnetic permeance of region 4 rotor yoke, region 5 rotor winding and rotor slot body region 6 rotor winding is similar to that of the stator. Radial magnetic permeance G ser , Tangential magnetic permeability G set 、The calculation formula is:

[0025]

[0026] Where: u is the core magnetic permeability, l is the axial length of the motor, R 1 , R 2 are the inner and outer radii of the stator yoke, θ is the mechanical angle corresponding to one tooth slot of the stator, and w 1 、w 2 is the inner and outer chord lengths of the sector-shaped flux corresponding to a stator tooth slot, and h is the tooth height.

[0027] Compared with the traditional model, the model established in the present invention fully considers the characteristics of the internal leakage flux of the motor and the obvious tooth saturation effect.

[0028] In the present invention, the air gap of the induction motor is small, and the calculation accuracy is required to be high, so the air gap permeability model needs to be analyzed independently. A transient equivalent magnetic network model is established, that is, when the motor is operating normally, the overlapping area between the stator teeth and the rotor teeth changes, which will cause the magnetic flux path at the air gap to change due to the change in the relative position of the stator and the rotor, thereby affecting the numerical value of the air gap permeability. When the stator teeth and the rotor teeth completely overlap, the permeability value is the largest; when the two teeth are completely staggered and have no overlapping area, there is no magnetic flux flowing through the two teeth at the same time, that is, there is no magnetic path connection, and the corresponding air gap permeability is 0. The air gap permeability G between the pth tooth of the stator and the qth tooth of the rotor p,q As the angle between the center lines of the two teeth changes, the air gap permeability changes from [0,G max ] range. The air gap permeability calculation formula is:

[0029]

[0030] In the formula, γ, γ′ t , γ tThe angle variable is used to divide different intervals to determine the air gap permeability calculation formula in different intervals.

[0031]

[0032] In the formula, u 0 is the magnetic permeability of air, b st is the stator tooth tip width, b tmin is the smaller value of the stator and rotor tooth width, δ is the air gap length, b ss is the stator slot width, b rt b is the rotor tooth tip width, sr is the rotor slot width, D si is the inner diameter of the stator, D ro is the rotor outer diameter, D ag is the arithmetic mean of the stator inner diameter and the rotor outer diameter, and l is the axial length of the motor.

[0033] Step 2: According to the structural characteristics and magnetic distribution gradient of large motors, the magnetic network model of the motor stator, rotor and air gap is constructed, and the model is connected according to the coupling relationship of each part. Figure 2 As shown, the nodes represent the magnetic potential of different regions, and the branches represent the magnetic circuits, whose magnetic resistance is related to the equivalent magnetic permeance. The nodes and magnetic permeance branches are numbered according to the order of the stator magnetic network, the rotor magnetic network and the air gap magnetic network. The motor has a total of 2940 nodes, as shown in the appendix. Figure 2 As shown, nodes 1 and 2 are the node numbers of the stator yoke, node 3 is the node number of the stator tooth, node 4 is the node number of the stator tooth tip, nodes 5 and 6 are the node numbers of the stator slot body, and nodes 1-1080 are the node numbers of the stator magnetic network model; node 2551 represents the first stator tooth, and nodes 2551-2730 are the node numbers of the stator teeth; nodes 1081 and 1082 are the node numbers of the rotor yoke, node 1083 is the node number of the rotor tooth, nodes 1084 and 1085 are the node numbers of the rotor tooth tip, nodes 1086 and 1087 are the node numbers of the rotor slot body, and nodes 1081-2550 are the node numbers of the rotor magnetic network model. Node 2731 is the first rotor tooth, and nodes 2731-2940 are the node numbers of the rotor teeth; on this basis, the initial permeability matrix G can be written.

[0034] Step 3, write the magnetic potential source F in the dynamic magnetic network according to the current and winding turns of the stator and rotor. In Ampere's circuit law, the difference in magnetomotive force between adjacent tooth slots is equal to the number of ampere-turns of the total current between the slots. The magnetic potential source of the stator and rotor is calculated to obtain the magnetic potential source matrix F s :

[0035] F s =[F D1 … F DnF Z1 … F Zn ]

[0036] In the formula, F Dn is the magnetic potential source on the nth stator tooth, F Zn The magnetic potential source on the nth tooth of the rotor.

[0037] The node magnetomotive force equations of the dynamic magnetic network are established, and the node equations are as follows:

[0038]

[0039] Where G(i, j) is the magnetic permeance between nodes, U(i) is the magnetomotive force of node i, and φ(i) is the magnetic flux of node i.

[0040] Calculate and solve the magnetic flux density B(i, j) of the magnetic permeance between nodes. The formula is as follows:

[0041]

[0042] B(i, j) is the magnetic flux density between nodes i and j, G(i, j) is the branch permeance between nodes i and j, U n (i) U n (j) is the node magnetic potential, and S is the area of ​​the region.

[0043] At different transient time points, according to the equivalent magnetic network model and the magnetomotive force equations, the non-threaded matrix equations are solved by the successive super-relaxation iteration method to calculate the magnetic density distribution of nodes in each region. In each time step, the parameters such as magnetic permeability are updated, and the calculation is repeated until the set transient time range is reached to obtain the magnetic density under different time states. The magnetic density data of different regions at different transient times obtained in the equivalent magnetic network calculation are sorted and brought into the formula, and the core loss of each region is solved by calculation.

[0044] Step 4: According to the mechanism of core loss, core loss is divided into hysteresis loss, eddy current loss and abnormal loss. For yoke core loss, substitute the magnetic flux density data of the yoke into the corresponding formula for calculation; for tooth core loss, substitute the magnetic flux density data of the tooth for calculation. The formula for core loss calculation is as follows:

[0045] P Fe =P h +P c +P e

[0046] Where P h is the hysteresis loss, P c is the eddy current loss, P e Abnormal loss.

[0047] The calculated core losses of various parts, such as the core losses of the stator and rotor yokes and the core losses of the teeth, are used as heat sources in the corresponding areas divided by the equivalent thermal network model.

[0048] In step 5, the copper loss is calculated using a numerical analysis method. The copper loss is mainly generated by the rotor winding and the stator winding, and the influence of the skin effect and the proximity effect on the copper loss of the induction motor winding is considered. In the calculation process, the current excitation of the winding is first applied to calculate the copper loss at that time. According to the temperature rise, the winding resistance is updated, the copper loss is recalculated, and it is brought into the thermal network as a new heat source for calculation until the temperature change of the thermal network is less than the preset threshold and the iteration is terminated, otherwise the iteration continues.

[0049] The copper loss calculation formula is:

[0050] P cu =mI 2 R

[0051] Where: m is the number of phases, I is the effective value of the phase current, and R is the resistance of each phase winding.

[0052] The copper loss of the stator and rotor windings is obtained through numerical calculation, and its power value at different transient times is recorded as the heat source in the winding area, which participates in the subsequent thermal analysis together with the core loss heat source.

[0053] Step 6: Based on the motor structure characteristics and heat distribution gradient, the thermal network model is constructed by comprehensively considering the regional coupling relationship with the magnetic network model, as shown in the Appendix Figure 3 As shown, the node represents the temperature of the hot zone, and the branch represents the thermal resistance. Node 1 is the node number of the stator core hot zone; Node 2 is the node number of the stator winding hot zone; Node 3 is the node number of the stator slot wedge hot zone. Each area contains heat capacity; different areas have different heat sources, such as the stator winding part of node 2 uses copper loss as the heat source, and the stator core hot zone of node 1 uses core loss as the heat source; nodes 1-1080 are stator hot zones, representing 1-180 stator teeth. Nodes 1081-1920 are rotor hot zones, representing 210 rotor teeth; among them, node 1081 is the node number of the rotor bar hot zone, node 1082 is the node number of the rotor core hot zone, and 1921-2130 are air gap nodes.

[0054] Construct equivalent thermal network models for each part, set the initial temperature distribution of thermal analysis, and substitute the heat source power value into the thermal network model according to the characteristics of each region; for example, the magnetic loss of nodes 1 and 2 in the magnetic network model corresponds to the regional heat source in the node 1 region in the thermal network model, and the temperature rise at node 1 of the thermal network model is solved; the loss of the remaining parts is calculated in this way, and the loss is brought into the corresponding region of the thermal network model as the heat source; at the same time, the influence of the heat capacity of each region must also be considered to store transient temperature rise data.

[0055] For each area inside the motor, write the heat balance equation according to Fourier's law of heat conduction. Use differential methods (such as finite difference method, finite element method, etc.) to perform numerical solutions and calculate the temperature changes of each heat area at different transient times; in each time step, update the heat source power (because the change of resistance with temperature causes the change of copper loss, and the core loss may also change with temperature to a certain extent), repeat the calculation until the set transient time range is reached, and obtain the temperature change curve with time.

[0056] Under different working conditions, the temperature rise of the motor is dynamic and the dynamic component heat capacity should be considered.

[0057] Heat capacity C refers to the amount of heat absorbed when the temperature of an object rises by 1°C, reflecting the dynamic rise of the object's temperature. The formula is as follows:

[0058] C D =cvp

[0059] C D is the equivalent heat capacity of each partition, c is the specific heat capacity of the sub-region, v is the volume of the sub-region, and p is the density of the sub-region.

[0060] Under different conditions, the temperature rise of the motor is dynamic. The dynamic component heat capacity should be considered to construct the dynamic heat balance equation as follows:

[0061]

[0062] G is the thermal resistance matrix, T(t) is the node temperature rise matrix, C is the heat capacity matrix, and P(t) is the heat source matrix.

[0063] Step 7, magnetic-thermal coupling calculation: Substitute the core loss calculated using the magnetic network model and the copper loss calculated using the numerical analysis method as heat sources into the thermal network model to calculate the temperature rise T of each node i If the temperature does not converge, recalculate the copper loss based on the impact of temperature rise on impedance and repeat the above steps until the temperature meets the set convergence accuracy, as shown in the following formula:

[0064]

[0065] T i+1 is the temperature obtained in the i+1th iteration, T i is the temperature obtained in the ith iteration, and ε is the convergence accuracy. If the convergence accuracy is met, this temperature can be considered to be the target temperature.

[0066] In summary, the present invention proposes a modeling and rapid calculation method for a large motor magnetic-thermal coupling model, which ensures accurate and efficient analysis of the motor's performance under different conditions. It is well-organized and easy to operate, and effectively improves the calculation efficiency.

Claims

1. A method for modeling and rapidly calculating a large motor magnetic-thermal coupling model, comprising the following steps: Step 1: Region division: The motor magnetic network model includes the stator magnetic network model, the rotor magnetic network model, and the air gap magnetic network model. Each region is meshed separately, and the appropriate segmentation accuracy is selected based on the magnetic field distribution of each component. Step 2: Establish an equivalent magnetic network model: According to the structural characteristics and magnetic distribution gradient of the large motor, the magnetic network model of the motor stator, rotor and air gap is constructed, and the models are connected according to the coupling relationship of each part to establish an equivalent magnetic network model; Step 3: Write the magnetomotive force equations according to the equivalent magnetic network model and calculate the magnetic density distribution of nodes in each region; Step 4: Calculate the iron loss of each area according to the magnetic density distribution of nodes in each area; Step 5: Use numerical analysis methods to calculate the copper loss in each area; Step 6: Divide the thermal nodes according to the thermal gradient distribution in the motor, calculate the thermal resistance of each area, and establish a thermal network model to solve the temperature rise of each node; Step 7: Magnetic-thermal coupling calculation: Substitute the core loss calculated using the magnetic network model and the copper loss calculated using the numerical analysis method as heat sources into the thermal network model to calculate the temperature rise of each node. If the temperature does not converge, recalculate the copper loss based on the impact of the temperature rise on the impedance. Repeat the above steps until the temperature meets the set convergence accuracy. This temperature can be considered to be the target temperature.

2. According to the method for calculating the temperature rise of a large motor based on the magnetic-thermal coupling method of claim 1, the step 2 is characterized by: When establishing a transient equivalent magnetic network model, due to the normal operation of the motor, the magnetic flux path at the air gap changes due to the change in the relative position of the stator and rotor, which in turn affects the magnitude of the permeance value at the air gap. In combination with the characteristics of the motor under study, the present invention only needs to consider the spatial angle between the center lines of the two tooth tops and solve it according to the air gap permeance formula for the air gap permeance between the stator and the rotor at any time, and then the air gap permeance between any stator tooth and any rotor tooth at any time and any rotor position can be obtained, and a transient equivalent magnetic network model can be established.

3. According to the method for calculating the temperature rise of a large motor based on the magnetic-thermal coupling method of claim 1, the step 4 is characterized by: An equivalent magnetic network model is established to obtain the magnetic flux density of nodes in each region. While calculating the iron loss, the internal magnetic field distribution gradient of the motor is also taken into account.

4. According to the method for calculating the temperature rise of a large motor based on the magnetic-thermal coupling method of claim 1, the step 5 is characterized by: When calculating the stator and rotor copper loss, the influence of skin effect and proximity effect on winding copper loss is considered.

5. The method for calculating the temperature rise of a large motor based on the magnetic-thermal coupling method according to claim 1, wherein the steps 1 and 6 are characterized by: The stator magnetic network model area division is mainly divided into the stator yoke, stator teeth, slot body leakage magnetic part and stator winding part, and the rotor magnetic network model area division is mainly divided into the rotor yoke, teeth, slot body leakage magnetic part and rotor winding part. When dividing the thermal network model, considering the magnetic-thermal distribution gradient in the motor, the common region method is adopted to divide multiple thermal regions, such as the stator core thermal zone, rotor core thermal zone, winding thermal zone, air gap thermal zone, etc. Each thermal zone has its own thermal characteristics, such as heat capacity, etc.

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