CN115528965B - Method for calculating multi-damping loop inductance of permanent magnet motor with rotor provided with damping strips - Google Patents
Method for calculating multi-damping loop inductance of permanent magnet motor with rotor provided with damping strips Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/141—Flux estimation
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/34—Arrangements for starting
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
- H02P25/03—Synchronous motors with brushless excitation
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/20—Arrangements for starting
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/34—Modelling or simulation for control purposes
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
Abstract
The invention discloses a method for calculating the inductance of a multi-damping loop of a permanent magnet motor with a rotor provided with damping strips, which comprises the steps of obtaining the magnetic potential of a rotor direct-axis damping loop and the magnetic potential of a rotor quadrature-axis damping loop of a rotor damping loop according to induced current; obtaining an air gap magnetic field of the direct-axis damping loop according to the magnetic potential of the rotor direct-axis damping loop, and obtaining an air gap magnetic field of the quadrature-axis damping loop according to the magnetic potential of the rotor quadrature-axis damping loop; obtaining self inductance and mutual inductance of a permanent magnet synchronous motor direct-axis damping loop of which the rotor is provided with a damping strip and mutual inductance between a stator winding and the direct-axis damping loop according to an air gap magnetic field of the direct-axis damping loop; obtaining self inductance and mutual inductance of a quadrature axis damping loop of the permanent magnet synchronous motor with the rotor provided with the damping strips and mutual inductance between a stator winding and the quadrature axis damping loop according to an air gap magnetic field of the quadrature axis damping loop; and optimizing the permanent magnet motor with the rotor band damping strip according to the obtained damping loop inductance, and improving the transient performance and the steady-state performance of the permanent magnet motor with the rotor band damping strip in the starting process.
Description
Technical Field
The invention relates to the technical field of permanent magnet synchronous motors, in particular to a method for calculating the inductance of a multi-damping loop of a permanent magnet motor with a rotor provided with damping strips.
Background
Energy is a very important strategic material for all countries in the world, which not only affects the development of national economy, but also affects the prosperity of national strength, so that all countries in the world regard the energy problem as a major problem affecting the prosperity and the defenceness of the country. The motor is a driving device of various industrial and agricultural production equipment and is widely applied to various fields of industrial and agricultural production. The motor energy conservation plays a significant role in realizing the double-carbon target in China, and the country supports the development of high-efficiency motors, reduces the loss of the motors, can greatly save energy, and improves and relieves the energy pressure.
The self-starting permanent magnet motor is a permanent magnet synchronous motor with a damping strip on a rotor, and is more and more concerned by people, and the main reason is that the self-starting permanent magnet motor has outstanding characteristics compared with the traditional motor: (1) The self-starting permanent magnet synchronous motor is only under the action of a permanent magnet magnetic field and a stator winding magnetic field during steady-state operation, a rotor damping winding does not cut a magnetic field any more and has no damping loss, and the rotating speed during operation is synchronous and is not influenced by a load; (2) The power factor is high, the power factor of the self-starting permanent magnet synchronous motor can be adjusted through reasonable design, the motor can operate under the condition of lagging or leading power factor, and the maximum power factor of the motor can even reach the unit power factor; (3) The motor has small volume and light weight, and the common motor can be replaced by a permanent magnet motor which is 1-2 machine seat numbers smaller than the volume and the weight of the motor; (4) The economic operation range is wide, the economic allowable range of the permanent magnet synchronous motor is 10% -140% of the rated load, the economic allowable range is obviously wider than that of a common induction motor, and the power factor of the permanent magnet synchronous motor can still reach about 0.9 even under the condition of 0.25 times of the rated load; (5) Compared with the induction motor with the same specification, the self-starting permanent magnet synchronous motor has the advantage that the rated efficiency is improved by 4-12%.
In the permanent magnet synchronous motor with the damping strips on the rotor, the analytical calculation method of the damping strip inductance is very important for analytical calculation of the running performance of the permanent magnet synchronous motor with the damping strips on the rotor by applying a multi-damping loop model. In fact, the existing method generally adopts a rotor inductance calculation method of an electrically excited synchronous motor to be directly transplanted into a damping loop of a permanent magnet motor to calculate the rotor inductance, and at present, no accurate analytic calculation method for calculating the related inductances of a direct-axis damping loop and a quadrature-axis damping loop exists.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for calculating the inductance of a multi-damping loop of a permanent magnet motor with a rotor provided with damping strips, which comprises the following steps:
the method comprises the steps of obtaining induction current of a damping strip on a rotor in the starting process of a permanent magnet synchronous motor with the damping strip on the rotor, and obtaining the magnetic potential of a rotor direct-axis damping loop and the magnetic potential of a rotor quadrature-axis damping loop of a rotor damping loop according to the induction current; obtaining an air-gap magnetic field of the direct-axis damping loop according to the magnetic potential of the rotor direct-axis damping loop, and obtaining an air-gap magnetic field of the quadrature-axis damping loop according to the magnetic potential of the rotor quadrature-axis damping loop;
respectively obtaining the self inductance of the direct-axis damping loop and the mutual inductance of the direct-axis damping loop according to the air gap magnetic field of the direct-axis damping loop; respectively obtaining self inductance of the quadrature axis damping loop and mutual inductance of the quadrature axis damping loop according to the air gap magnetic field of the quadrature axis damping loop;
obtaining mutual inductance between a stator winding of the permanent magnet synchronous motor with the rotor provided with the damping strips and the direct-axis damping loop according to an air-gap magnetic field of the direct-axis damping loop; obtaining mutual inductance between a stator winding of the permanent magnet synchronous motor with the rotor provided with the damping strips and the quadrature axis damping loop according to an air gap magnetic field of the quadrature axis damping loop;
according to the obtained self-inductance of the direct-axis damping loop, the mutual inductance of the direct-axis damping loop, the self-inductance of the quadrature-axis damping loop, the mutual inductance between the stator winding and the direct-axis damping loop and the mutual inductance between the stator winding and the quadrature-axis damping loop, the permanent magnet motor with the rotor band damping strip is optimized, and the transient performance and the steady-state performance of the permanent magnet motor with the rotor band damping strip in the starting process are improved.
Further, the obtaining of the magnetic potential of the rotor direct axis damping loop and the magnetic potential of the rotor quadrature axis damping loop of the rotor damping loop according to the induced current includes the following steps:
when the current of the damping loop isIThen, the magnetic potential distribution of the rotor straight shaft damping loop is shown as follows:
the magnetic potential distribution of the rotor quadrature axis damping loop is shown as follows:
Further, the obtaining of the air-gap magnetic field of the direct-axis damping loop according to the magnetic potential of the rotor direct-axis damping loop includes:
straight shaft damping loop
Generating an air-gap magnetic field of
In the above formula, j represents the imaginary part of the complex number,
are respectively d 1 、d 2 、d 3 The resulting radial flux density of the direct axis damping loop,
are respectively d 1 、d 2 、d 3 The resulting tangential magnetic flux density of the direct axis damping loop,
the magnetic permeability of the air is such that,σthe magnetic flux leakage coefficient is obtained by the following steps,h m is half the thickness of the permanent magnet,b m is the width of the permanent magnet or magnets,
is the minimum air gap length and is,
is the distance between the poles of the magnetic field,
the straight-axis basic air gap field can be obtained by the following formula:
wherein the content of the first and second substances,R s is the inner radius of the stator and,R q is to solve the radius of the air gap flux density,
is coefficient of polar arcpIs the number of the pole pairs,
is the air gap length at the position of the Q point in the air gap,
is machineThe mechanical angle of the rotating shaft is changed into the angle,
representing the arctan function.
Further, the obtaining of the air-gap magnetic field of the quadrature axis damping loop according to the rotor quadrature axis damping loop magnetic potential includes:
quadrature damping circuit
The air gap magnetic field generated is:
in the above formula, the first and second carbon atoms are,
are each q 1 、q 2 、q 3 The radial magnetic density generated by the quadrature axis damping loop,
are each q 1 、q 2 、q 3 Generating tangential magnetic flux density of the quadrature axis damping loop;
the quadrature axis basic air gap field can be obtained by the following formula:
wherein the content of the first and second substances,b j is the distance between the adjacent magnetic poles,
is the intermediate variable(s) of the variable,
。
further, the obtaining of the self inductance of the direct axis damping loop and the mutual inductance of the direct axis damping loop according to the air gap magnetic field of the direct axis damping loop respectively includes:
in the above formula, the first and second carbon atoms are,
the permanent magnet synchronous motor with the damping strips for the rotor has the axial effective length,
are respectively d 1 、d 2 、d 3 Self-flux linkage generated by the direct-axis damping loop;
therein
The mutual flux linkage between the d1 and d2 direct-axis damping loops, the mutual flux linkage between the d1 and d3 direct-axis damping loops, and the mutual flux linkage between the d2 and d3 direct-axis damping loops are respectively.
Further, the obtaining of the self-inductance of the quadrature damping loop and the mutual inductance of the quadrature damping loop according to the air-gap magnetic field of the quadrature damping loop respectively includes:
further, the obtaining of the mutual inductance between the stator winding of the permanent magnet synchronous motor with the rotor having the damping strips and the direct axis damping loop according to the air gap magnetic field of the direct axis damping loop includes:
wherein the content of the first and second substances,
the number of the branches connected in parallel is equal to that of the branch,qis the number of slots per phase per pole,
the number of turns of the winding in the slot, and P is the number of pole pairs; when the rotor is in the position of
When the utility model is used, the water is discharged,
damping the flux linkage of the air-gap field entering the A-phase winding for the direct axis, an
Wherein the content of the first and second substances,mthe number of the phases is the same as the number of the phases,
is the axial position of phase A in the rotor coordinate system,
the number of the stator slots is the number of the stator slots,
is the short-range coefficient of the signal,
is the slot pitch electrical angle;
when the rotor rotates, the stator winding and the rotorRelative motion exists between the sub-damping loops; when rotor is in electrical angle position
When the rotor is in a rotating state, the direct-axis magnetic field of the stator winding changes, the mutual inductance between the stator winding and the rotor direct-axis damping loop changes simultaneously, the magnetic fields generated by the phases A, B and C have an electrical angle difference of 120 degrees in space, and the mutual inductance between the phase B and the phase C and the direct-axis damping loop can be obtained in the same way.
Further, the mutual inductance between the stator winding of the permanent magnet synchronous motor with the rotor provided with the damping strips and the quadrature axis damping loop is obtained according to the air gap magnetic field of the quadrature axis damping loop:
the mutual inductance between the phase B and the phase C and the quadrature axis damping loop can be obtained in the same way, and when the position of the rotor is
When the temperature of the water is higher than the set temperature,
the air gap magnetic fields of the quadrature axis damping loops q1, q2 and q3 enter the flux linkage of the A phase winding,
the number of the parallel branches is the same as the number of the parallel branches,
the number of the pole pairs is the number of the pole pairs,
the current of the quadrature damping loop, q is the number of slots per phase per pole,
the number of turns of the winding in the slot,
is the radius of the point Q in the air gap,
the axial effective length of the motor is long,
the resulting radial flux densities of the q1, q2, and q3 damping loops, respectively.
Further, the leakage inductance of the damping loop is also included, and is obtained by the following formula: further, the method comprises
In the above formula, the first and second carbon atoms are,pthe number of the pole pairs is the number of the pole pairs,
is a magnetic permeability of air, and
in the above formula, the first and second carbon atoms are,b ro the width of the rotor slot is the width of the rotor slot,h ro the height of the notch of the rotor is high,R rs is the radius of the circular rotor slot, and then the leakage inductance of the damping circuit
The self-inductance of the damping loop is added,
as an arcsine function。
The beneficial effects of the invention are: the invention considers the condition of uneven air gap between the stator and the rotor, and is beneficial to better optimizing the sine of the steady-state current of the permanent magnet synchronous motor with the damping strips on the rotor. The calculation of the damping loop inductance is beneficial to fast and accurate analysis optimization and design of the permanent magnet motor with the damping strips on the rotor, the transient performance in the starting process is improved, such as reduction of starting current multiples and starting torque impact, enhancement of pull-in synchronization capacity and the like, and the steady-state performance is improved, such as enhancement of stability, improvement of efficiency and power factor, and anti-interference capacity.
Drawings
FIG. 1 is a schematic flow chart of a method for calculating the inductance of a multi-damping loop of a permanent magnet motor with a rotor having damping strips;
FIG. 2 is a structural diagram of a rotor of a permanent magnet synchronous motor with damping strips;
FIG. 3 is a schematic diagram of a damping circuit structure;
FIG. 4 is a schematic diagram of the mutual inductance between phase A and damping loop d 1;
FIG. 5 is a schematic diagram of the mutual inductance between phase A and damping loop d 2;
FIG. 6 is a schematic diagram of the mutual inductance between phase A and damping loop d 3;
FIG. 7 is a schematic diagram of the mutual inductance between phase A and the damping loop q 1;
FIG. 8 is a schematic diagram of the mutual inductance between phase A and damping loop q 2;
fig. 9 is a schematic diagram of the mutual inductance between phase a and damping loop q 3.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following descriptions.
For the purpose of making the object, technical solution and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention. It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
Furthermore, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrases "comprising a" \8230; "does not exclude the presence of additional like elements in the process, method, article, or apparatus that comprises the element.
The features and properties of the present invention are described in further detail below with reference to examples.
As shown in fig. 1, a method for calculating inductance of a multi-damping loop of a permanent magnet motor with a damping strip on a rotor includes the following steps:
the method comprises the steps of obtaining induction current of a damping strip on a rotor in the starting process of a permanent magnet synchronous motor with the damping strip on the rotor, and obtaining the magnetic potential of a rotor direct-axis damping loop and the magnetic potential of a rotor quadrature-axis damping loop of a rotor damping loop according to the induction current; obtaining an air-gap magnetic field of the direct-axis damping loop according to the magnetic potential of the rotor direct-axis damping loop, and obtaining an air-gap magnetic field of the quadrature-axis damping loop according to the magnetic potential of the rotor quadrature-axis damping loop;
respectively obtaining the self inductance of the direct axis damping loop and the mutual inductance of the direct axis damping loop according to the air gap magnetic field of the direct axis damping loop; respectively obtaining self inductance of the quadrature axis damping loop and mutual inductance of the quadrature axis damping loop according to the air gap magnetic field of the quadrature axis damping loop;
obtaining mutual inductance between a stator winding of the permanent magnet synchronous motor with the rotor provided with the damping strips and the direct-axis damping loop according to the air gap magnetic field of the direct-axis damping loop; obtaining mutual inductance between a stator winding of the permanent magnet synchronous motor with the rotor provided with the damping strips and the quadrature axis damping loop according to an air gap magnetic field of the quadrature axis damping loop;
and optimizing the permanent magnet motor with the rotor band damping strip according to the obtained self-inductance of the direct-axis damping loop, the self-inductance of the quadrature-axis damping loop, the mutual inductance between the stator winding and the direct-axis damping loop and the mutual inductance between the stator winding and the quadrature-axis damping loop, so that the transient performance and the steady-state performance of the permanent magnet motor with the rotor band damping strip in the starting process are improved.
The method for obtaining the rotor direct axis damping loop magnetic potential and the rotor quadrature axis damping loop magnetic potential of the rotor damping loop according to the induction current comprises the following processes:
when the current of the damping loop isIThen, the magnetic potential distribution of the rotor straight shaft damping loop is shown as follows:
the magnetic potential distribution of the rotor quadrature axis damping loop is shown as follows:
The air gap magnetic field of the direct-axis damping loop is obtained according to the magnetic potential of the rotor direct-axis damping loop, and the method comprises the following steps:
straight shaft damping loop
Generating an air-gap magnetic field of
In the above formula, j represents the imaginary part of the complex number,
are respectively d 1 、d 2 、d 3 The radial magnetic density generated by the straight shaft damping loop,
are respectively d 1 、d 2 、d 3 The resulting tangential magnetic flux density of the direct axis damping loop,
the magnetic permeability of the air is such that,σthe magnetic flux leakage coefficient is obtained by the following steps,h m is half the thickness of the permanent magnet,b m is the width of the permanent magnet or magnets,
is the minimum air gap length and is,
is the distance between the poles of the magnetic field,
the straight-axis basic air gap field can be obtained by the following formula:
wherein the content of the first and second substances,R s is the inner radius of the stator and,R q is to solve the radius of the air gap flux density,
is coefficient of polar arcpIs the number of the pole pairs,
is the air gap length at the position of the Q point in the air gap,
is a mechanical angle of view of the device,
representing the arctan function.
The air gap magnetic field of the quadrature axis damping loop obtained according to the rotor quadrature axis damping loop magnetic potential comprises the following steps:
quadrature damping circuit
The air gap magnetic field generated is:
in the above formula, the first and second carbon atoms are,
are each q 1 、q 2 、q 3 The radial magnetic density generated by the quadrature axis damping loop,
are each q 1 、q 2 、q 3 Generating tangential magnetic flux density of the quadrature axis damping loop;
the quadrature axis basic air gap field can be obtained by the following formula:
wherein the content of the first and second substances,b j is the distance between the adjacent magnetic poles,
is a function of the intermediate variable(s),
。
the step of respectively obtaining the self inductance of the direct axis damping loop and the mutual inductance of the direct axis damping loop according to the air gap magnetic field of the direct axis damping loop comprises the following steps:
in the above formula, the first and second carbon atoms are,
the permanent magnet synchronous motor with the damping strips for the rotor has the axial effective length,
are respectively d 1 、d 2 、d 3 The self-flux linkage generated by the straight-axis damping loop;
therein
The mutual magnetic linkage between the d1 and d2 direct-axis damping loops, the mutual magnetic linkage between the d1 and d3 direct-axis damping loops, and the mutual magnetic linkage between the d2 and d3 direct-axis damping loops.
The air gap magnetic field according to quadrature damping return circuit obtain quadrature damping return circuit's self-inductance and quadrature damping return circuit's mutual inductance respectively, include:
according to the air gap magnetic field of the direct-axis damping loop, the mutual inductance between the stator winding of the permanent magnet synchronous motor with the rotor provided with the damping strip and the direct-axis damping loop is obtained, and the method comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,
the number of the branches connected in parallel is equal to that of the branch,qis the number of slots per phase per pole,
the number of turns of the winding in the slot is P, and the number of pole pairs is P; when the rotor is in the position of
When the temperature of the water is higher than the set temperature,
damping the flux linkage of the air-gap field entering the A-phase winding for the direct axis, an
Wherein, the first and the second end of the pipe are connected with each other,mthe number of the phases is the same as the number of the phases,
is the axial position of the phase A in the rotor coordinate system,
is the number of the stator slots, and the number of the stator slots,
is the short-range coefficient of the signal,
is the slot pitch electrical angle;
when the rotor rotates, relative motion exists between the stator winding and the rotor damping loop; when rotor is in electrical angle position
When the rotor is in a rotating state, the direct-axis magnetic field of the stator winding changes, the mutual inductance between the stator winding and the rotor direct-axis damping loop changes simultaneously, the magnetic fields generated by the phases A, B and C have an electrical angle difference of 120 degrees in space, and the mutual inductance between the phase B and the phase C and the direct-axis damping loop can be obtained in the same way.
Further, the mutual inductance between the stator winding of the permanent magnet synchronous motor with the rotor having the damping strips and the quadrature axis damping loop is obtained according to the air gap magnetic field of the quadrature axis damping loop:
the mutual inductance between the phase B and the phase C and the quadrature axis damping loop can be obtained in the same way, and when the position of the rotor is
When the utility model is used, the water is discharged,
the air gap magnetic fields of the quadrature axis damping loops q1, q2 and q3 enter the flux linkage of the A phase winding,
the number of the parallel branches is the same as the number of the parallel branches,
the number of the pole pairs is the number of the pole pairs,
the current of the quadrature axis damping loop, q is the number of slots per pole and phase,
the number of turns of the winding in the slot,
is the radius of the point Q in the air gap,
the axial effective length of the motor is long,
the resulting radial flux densities of the q1, q2, and q3 damping loops, respectively.
Also includes the leakage inductance of the damping loop, which is obtained by the following formula: further, the method comprises
In the above formula, the first and second carbon atoms are,pthe number of the pole pairs is the number of the pole pairs,
is a magnetic permeability of air, and
in the above formula, the first and second carbon atoms are,b ro the width of the rotor slot is the width of the rotor slot,h ro the height of the notch of the rotor is high,R rs radius of the circular rotor slot, and then damping the leakage inductance of the circuit
The self-inductance of the damping loop is added,
is an arcsine function.
Specifically, according to the method for analyzing and calculating the inductance of the multiple damping loops of the permanent magnet synchronous motor with the damping strips on the rotor, as shown in fig. 2, in the starting process, the damping strips generate induced current.
The rotor damping loop and the stator winding are mutually linked, mutual inductance is generated between the stator and the rotor, and self inductance and mutual inductance of the rotor are also generated by the interaction between the rotor damping loops.
The magnetic potential of the damping strip induced current is related to the number of damping strips and the slot pitch. Due to the rotation of the rotor, the relative position between the rotor and the stator changes. The damping bars are divided into direct-axis damping bars and quadrature-axis damping bars to calculate the magnetic field generated by the damping bars. The magnetic potential of the rotor damping strip is direct-axis magnetic potential and quadrature-axis magnetic potential respectively.
The number of damping strips on each pole of the rotor is 6,
in order to provide a straight-axis damping loop,
is a quadrature damping loop. The number of the rotor direct axis damping loops and the number of the quadrature axis damping loops are both 3, and fig. 3 is a structural diagram of the quadrature axis damping loops and the direct axis damping loops.
Because a solid conductor is arranged in the rotor slot, the number of turns of each damping loop of the rotor is 1, and when the current of the damping loop isIIn the meantime, the method for representing the magnetic potential distribution of the rotor direct-axis damping circuit is shown as the following formula
The magnetic potential distribution of the rotor quadrature axis damping loop is shown as the following formula:
in the above formula, the first and second carbon atoms are,
are respectively q-axis q 1 、q 2 、q 3 The magnetomotive force of the damping circuit.
The magnetomotive force in the air gap between the stator and the rotor is shaped as a square wave when current flows in the damping circuit. Then straight shaft damping loop
The air gap magnetic field is generated as
In the above-mentioned formula, the compound has the following structure,
are respectively d 1 、d 2 、d 3 The resulting radial flux density of the damping circuit.
Are respectively d 1 、d 2 、d 3 The resulting tangential magnetic flux density of the damping circuit. ,
the magnetic permeability of the air is such that,σthe magnetic flux leakage coefficient is that the magnetic flux leakage coefficient,h m is half the thickness of the permanent magnet,b m is the width of the permanent magnet or magnets,
is the minimum air gap length and is,
is the distance between the two poles of the wire,
the straight-axis basic air gap magnetic field can be obtained by the following formula.
In the above formula, the first and second carbon atoms are,R s is the inner radius of the stator and,R q is to solve the radius of the air gap flux density,
is coefficient of polar arcpIs the number of the pole pairs,
is the air gap length at the position of the Q point in the air gap,
is a mechanical angle.
Quadrature damping circuit
The air gap field generated is:
in the above formula, the first and second carbon atoms are,
are each q 1 、q 2 、q 3 The resulting radial magnetic density of the damping circuit,
are each q 1 、q 2 、q 3 The generated tangential magnetic flux density of the damping loop;
the quadrature axis basic air gap field can be obtained by the following formula.
Upper typeIn the step (1), the first step,b j is the distance between adjacent magnetic poles and is,
is the intermediate variable(s) of the variable,
。
1) Self and mutual inductance of damping loops
Since the direct-axis damping loop and the quadrature-axis damping loop are orthogonal, the mutual inductance between the direct-axis loop and the quadrature-axis loop is zero. Only the self-inductance and mutual-inductance of the direct-axis damping loop and the self-inductance and mutual-inductance of the quadrature-axis damping loop exist.
a) Self-inductance and mutual inductance of direct-axis damping loop
In the above-mentioned formula, the compound has the following structure,
the permanent magnet synchronous motor with the damping strips for the rotor has the axial effective length,
is a magnetic linkage.
b) Self-inductance and mutual-inductance of quadrature damping loop
c) Leakage inductance of damping circuit
Calculating the leakage inductance of the damping circuit by considering the leakage inductance of the slot, wherein the leakage inductance of the damping circuit can be obtained by the following formula
In the above formula, the first and second carbon atoms are,pthe number of the pole pairs is the number of the pole pairs,
is a magnetic permeability of air, and
in the above-mentioned formula, the compound has the following structure,b ro the width of the rotor slot is the width of the rotor slot,h ro the height of the notch of the rotor is high,R rs the radius of a circular rotor slot. Then, handle the resistanceLeakage inductance of damping loop
Adding damping loop self-inductance.
2) Mutual inductance between stator winding and damping circuit
The damping loop is divided into a direct-axis damping loop and a quadrature-axis damping loop. According to the damping loop air gap magnetic field of the permanent magnet synchronous motor with the rotor provided with the damping strips, at different rotor positions, the flux linkage of the interlinkage of the rotor damping loop and the stator armature winding is different, and the mutual inductance between the stator winding and the damping loop can change along with the rotor position.
a) Mutual inductance between stator winding and direct axis damping circuit
The number of the straight shaft damping loops is three,
is mutual inductance between the A-phase stator winding and the direct-axis damping loop, and can be obtained by substituting the air-gap magnetic field formula of the direct-axis damping loop into the following formula
In the above-mentioned formula, the compound has the following structure,
the number of the branches connected in parallel is,qis the number of slots per phase per pole,
the number of turns of the winding in the slot; when the rotor is in the position of
When the utility model is used, the water is discharged,
damping the flux linkage of the air-gap field entering the A-phase winding for the direct axis, an
In the above formula, the first and second carbon atoms are,mthe number of the phases is shown as,
is the axial position of phase A in the rotor coordinate system,
is the number of the stator slots, and the number of the stator slots,
is the short-range coefficient of the signal,
is the slot pitch electrical angle.
When the rotor rotates, there is relative motion between the stator windings and the rotor damping circuit. When rotor is in electrical angle position
In time, the direct axis magnetic field of the stator winding changes during rotation. The mutual inductance between the stator windings and the rotor direct axis damping circuit changes simultaneously. The mutual inductance is calculated at different rotor positions. A. The phase difference of magnetic fields generated by the B phase and the C phase in the space is 120 degrees, and the mutual inductance between the B phase or the C phase and the straight-axis damping loop can be obtained by using the same principle.
b) Mutual inductance between stator winding and quadrature damping circuit
The number of the quadrature axis damping loops is three,
is mutual inductance between the A-phase stator winding and the quadrature axis damping loop, and can be obtained by substituting the air gap magnetic field formula of the quadrature axis damping loop into the following formula
Therefore, the mutual inductance between the B phase or the C phase and the quadrature damping loop can be obtained by using the same principle.
Fig. 4-9 illustrate the mutual inductance between the a-phase winding and the damping loop. As can be seen from FIGS. 4-9, the magnetic field calculated by the analytic method and the finite element method has good goodness of fit, and the correctness of the analytic method adopted by the invention is proved. The method for calculating the inductance of the damping loop of the permanent magnet synchronous motor with the rotor provided with the damping strip can further carry out accurate analytic simulation calculation on the starting performance of the permanent magnet synchronous motor with the rotor provided with the damping strip
The foregoing is illustrative of the preferred embodiments of the present invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and is not to be construed as limited to the exclusion of other embodiments, and that various other combinations, modifications, and environments may be used and modifications may be made within the scope of the concepts described herein, either by the above teachings or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. A method for calculating the inductance of a permanent magnet motor with a damping strip on a rotor and multiple damping loops is characterized by comprising the following steps:
the method comprises the steps of obtaining induction current of a damping strip on a rotor in the starting process of a permanent magnet synchronous motor with the damping strip on the rotor, and obtaining the magnetic potential of a rotor direct-axis damping loop and the magnetic potential of a rotor quadrature-axis damping loop of a rotor damping loop according to the induction current; obtaining an air-gap magnetic field of the direct-axis damping loop according to the magnetic potential of the rotor direct-axis damping loop, and obtaining an air-gap magnetic field of the quadrature-axis damping loop according to the magnetic potential of the rotor quadrature-axis damping loop;
respectively obtaining the self inductance of the direct-axis damping loop and the mutual inductance of the direct-axis damping loop according to the air gap magnetic field of the direct-axis damping loop; respectively obtaining self inductance of the quadrature axis damping loop and mutual inductance of the quadrature axis damping loop according to the air gap magnetic field of the quadrature axis damping loop;
obtaining mutual inductance between a stator winding of the permanent magnet synchronous motor with the rotor provided with the damping strips and the direct-axis damping loop according to the air gap magnetic field of the direct-axis damping loop; obtaining mutual inductance between a stator winding of the permanent magnet synchronous motor with the rotor provided with the damping strips and the quadrature axis damping loop according to an air gap magnetic field of the quadrature axis damping loop;
according to the obtained self-inductance of the direct-axis damping loop, the mutual inductance of the direct-axis damping loop, the self-inductance of the quadrature-axis damping loop, the mutual inductance between the stator winding and the direct-axis damping loop and the mutual inductance between the stator winding and the quadrature-axis damping loop, the permanent magnet motor with the rotor band damping strip is optimized, and the transient performance and the steady-state performance of the permanent magnet motor with the rotor band damping strip in the starting process are improved.
2. The method for calculating the inductance of the multiple damping loops of the permanent magnet motor with the damping strips on the rotor according to the claim 1, wherein the method for obtaining the magnetic potential of the direct-axis damping loop and the magnetic potential of the quadrature-axis damping loop of the rotor of the damping loop according to the induced current comprises the following steps:
when the current of the damping loop isIThen, the magnetic potential distribution of the rotor straight shaft damping loop is shown as follows:
the magnetic potential distribution of the rotor quadrature axis damping loop is shown as follows:
3. The method for calculating the inductance of the multiple damping loops of the permanent magnet motor with the rotor provided with the damping strips according to the claim 2, wherein the step of obtaining the air-gap magnetic field of the direct-axis damping loop according to the magnetic potential of the direct-axis damping loop of the rotor comprises the following steps:
straight shaft damping loop
Generating an air-gap magnetic field of
In the above formula, j represents the imaginary part of the complex number,
are respectively d 1 、d 2 、d 3 The resulting radial flux density of the direct axis damping loop,
are respectively d 1 、d 2 、d 3 The resulting tangential magnetic flux density of the direct axis damping loop,
the magnetic permeability of the air is such that,σthe magnetic flux leakage coefficient is obtained by the following steps,h m is half the thickness of the permanent magnet and,b m is the width of the permanent magnet or magnets,
is the minimum air gap length and is,
is the distance between the two poles of the wire,
the straight-axis basic air gap field can be obtained by the following formula:
wherein the content of the first and second substances,R s is the inner radius of the stator and,R q is to solve the radius of the air gap flux density,
is the coefficient of the polar arc,pis the number of the pole pairs,
is the air gap length at the position of the Q point in the air gap,
is a mechanical angle of view of the device,
representing the arctan function.
4. The method for calculating the inductance of the multiple damping loops of the permanent magnet motor with the rotor provided with the damping strips according to the claim 3, wherein the step of obtaining the air-gap magnetic field of the quadrature damping loop according to the rotor quadrature damping loop magnetic potential comprises the following steps:
quadrature damping circuit
The air gap magnetic field generated is:
in the above formula, the first and second carbon atoms are,
are each q 1 、q 2 、q 3 The resulting radial magnetic density of the damping circuit,
are each q 1 、q 2 、q 3 The resulting tangential flux density of the damping circuit;
the quadrature axis basic air gap field can be obtained by the following formula:
wherein, the first and the second end of the pipe are connected with each other,b j is the distance between adjacent magnetic poles and is,
is the intermediate variable(s) of the variable,
。
5. the method for calculating the inductance of the multiple damping loops of the permanent magnet motor with the damping strips on the rotor according to the claim 4, wherein the step of respectively obtaining the self inductance of the direct-axis damping loop and the mutual inductance of the direct-axis damping loop according to the air-gap magnetic field of the direct-axis damping loop comprises the following steps:
in the above formula, the first and second carbon atoms are,
the permanent magnet synchronous motor with the rotor provided with the damping strips has the axial effective length,
are respectively d 1 、d 2 、d 3 The self-flux linkage generated by the straight-axis damping loop;
therein are
，
And
the mutual magnetic linkage between the d1 and d2 direct-axis damping loops, the mutual magnetic linkage between the d1 and d3 direct-axis damping loops, and the mutual magnetic linkage between the d2 and d3 direct-axis damping loops.
6. The method for calculating the inductance of the multiple damping loops of the permanent magnet motor with the damping strips on the rotor according to the claim 5, wherein the self inductance of the quadrature damping loop and the mutual inductance of the quadrature damping loop are respectively obtained according to the air-gap magnetic field of the quadrature damping loop, and the method comprises the following steps:
7. the method for calculating the inductance of the multiple damping loops of the permanent magnet motor with the rotor damping strips according to the claim 6, wherein the step of obtaining the mutual inductance between the stator winding of the permanent magnet synchronous motor with the rotor damping strips and the direct-axis damping loops according to the air-gap magnetic field of the direct-axis damping loops comprises the following steps:
wherein the content of the first and second substances,
the number of the branches connected in parallel is,qis the number of slots per pole per phase,
the number of turns of the winding in the slot is P, and the number of pole pairs is P; when the rotor is in the position of
When the temperature of the water is higher than the set temperature,
damping the flux linkage of the air-gap field entering the A-phase winding for the direct axis, an
Wherein, the first and the second end of the pipe are connected with each other,mthe number of the phases is the same as the number of the phases,
is the axial position of phase A in the rotor coordinate system,
the number of the stator slots is the number of the stator slots,
is the short-range coefficient of the signal,
is the slot pitch electrical angle;
when the rotor rotates, relative motion exists between the stator winding and the rotor damping loop; when the rotor is in electrical angle position
When the rotor is rotated, the direct-axis magnetic field of the stator winding changes in the rotating process, the mutual inductance between the stator winding and the rotor direct-axis damping loop changes simultaneously, the magnetic fields generated by the A phase, the B phase and the C phase have an electrical angle difference of 120 degrees in space, and the mutual inductance between the B phase and the C phase and the direct-axis damping loop can be obtained in the same way.
8. The method for calculating the inductance of the multiple damping loops of the permanent magnet motor with the rotor damping strips as claimed in claim 7, wherein the mutual inductance between the stator winding of the permanent magnet synchronous motor with the rotor damping strips and the quadrature damping loops is obtained according to the air-gap field of the quadrature damping loops:
in the same way, the mutual inductance between the B phase and the C phase and the quadrature axis damping loop can be obtained when the rotor is positioned
When the utility model is used, the water is discharged,
the air gap magnetic fields of the quadrature axis damping loops q1, q2 and q3 enter the flux linkage of the A phase winding,
the number of the parallel branches is the same as the number of the parallel branches,
the number of the pole pairs is the number of the pole pairs,
the current of the quadrature axis damping loop, q is the number of slots per pole and phase,
the number of turns of the winding in the slot,
is to solve for the radius of the air gap flux density,
the axial effective length of the motor is long,
the resulting radial flux densities of the q1, q2, q3 damping loops, respectively.
9. The method for calculating the inductance of the multiple damping loops of the permanent magnet motor with the damping strips on the rotor according to claim 8, further comprising the leakage inductance of the damping loops, which is obtained by the following formula:
in the above-mentioned formula, the compound has the following structure,pthe number of the pole pairs is the number of the pole pairs,
is a magnetic permeability of air, and
in the above formula, the first and second carbon atoms are,b ro the width of the rotor slot is the width of the rotor slot,h ro the height of the notch of the rotor is high,R rs radius of the circular rotor slot, and then damping the leakage inductance of the circuit
The self-inductance of the damping loop is added,
is an arcsine function.
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