CN112994564A - Permanent magnet synchronous motor parameter identification method based on convex optimization - Google Patents

Permanent magnet synchronous motor parameter identification method based on convex optimization Download PDF

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Publication number
CN112994564A
CN112994564A CN202110276497.XA CN202110276497A CN112994564A CN 112994564 A CN112994564 A CN 112994564A CN 202110276497 A CN202110276497 A CN 202110276497A CN 112994564 A CN112994564 A CN 112994564A
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Prior art keywords
permanent magnet
magnet synchronous
synchronous motor
convex optimization
motor
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Inventor
朱庆龙
金雷
朱天翔
王宁
胡薇
陈波波
王诚成
孔令杰
丁建强
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Hefei Hengda Jianghai Pump Co Ltd
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Hefei Hengda Jianghai Pump Co Ltd
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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
    • 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
    • H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
    • 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

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)
  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses a permanent magnet synchronous motor parameter identification method based on convex optimization, which is used for solving the problem that motor parameters change due to factors such as high temperature and the like in the long-time running process of a permanent magnet synchronous motor and improving the sensorless control effect; firstly, obtaining a discrete mathematical model by a voltage equation of the permanent magnet synchronous motor under a two-phase static coordinate system through a backward difference method; secondly, determining motor parameters needing to be identified according to the influence of the motor parameter change on the control performance of the position-sensorless sensor, and further constructing a cost function; and carrying out minimum optimization on the cost function by using a convex optimization algorithm to obtain the motor parameters needing to be identified. The invention realizes the parameter identification of the permanent magnet synchronous motor, and can feed back the identified parameters to be used for updating the motor model in the position-free algorithm so as to obtain better real-time control performance.

Description

Permanent magnet synchronous motor parameter identification method based on convex optimization
Technical Field
The invention relates to the field of motor driving and control, in particular to a permanent magnet synchronous motor parameter identification method based on convex optimization.
Background
In recent years, the permanent magnet synchronous motor has the advantages of high power density, high rotational inertia, high efficiency and the like, and is widely applied to high-performance application occasions such as high-power and the like of motor cars, high-speed rails, aerospace and the like. High performance control and stable, reliable operation of permanent magnet synchronous motors does not leave rotor position information, and accurate rotor absolute position information is also required. The most common method is to mount mechanical sensors (encoders, resolvers and tachogenerators) on the rotor shaft to measure the speed and position of the motor rotor. The presence of mechanical sensors increases the complexity and cost of the control system, reduces the reliability of the system, and also limits the application of permanent magnet synchronous motors in some special situations.
The accuracy of rotor magnetic pole position estimation determines the performance of a permanent magnet synchronous motor position sensorless control system, and accurate position estimation needs to be established on the basis of accurate motor parameters. Under some circumstances, motor parameters provided by manufacturers have errors, and the motor parameters may change due to factors such as high temperature and the like in the long-time running process, so that the control effect is influenced.
Disclosure of Invention
The invention aims to solve the problem that motor parameters are changed due to factors such as high temperature and the like in the long-time running process of a permanent magnet synchronous motor, and provides a permanent magnet synchronous motor parameter identification method based on convex optimization, which can identify the motor parameters on line and ensure the control performance of a position-free sensor.
The purpose of the invention can be realized by the following technical scheme: a permanent magnet synchronous motor parameter identification method based on convex optimization comprises the following steps:
acquiring a voltage equation of the permanent magnet synchronous motor under a two-phase static coordinate system, and obtaining a discrete mathematical model through a backward difference method;
determining motor parameters needing to be identified according to the influence of the motor parameter change on the control performance of the position-sensorless control system, and further constructing a cost function;
and carrying out minimum optimization on the cost function by using a convex optimization algorithm to obtain the motor parameters needing to be identified.
Preferably, the specific process of obtaining the discrete mathematical model is as follows:
setting a voltage equation of the permanent magnet synchronous motor under an alpha-beta two-phase static coordinate system as follows:
Figure BDA0002976843770000021
wherein L isd、LqDirect axis and quadrature axis inductances of the stator windings; i.e. iα、iβStator currents of an alpha-beta axis under a two-phase static coordinate system respectively; v. ofα、vβCan pass through
Figure BDA0002976843770000022
Calculating to obtain R, wherein R is the resistance of each phase of winding of the stator; omegareIs the rotor angular velocity; thetareIs the rotor position angle;
Figure BDA0002976843770000023
is a permanent magnet flux linkage; p is a differential operator;
Figure BDA0002976843770000024
discretizing the voltage equation can obtain:
Figure BDA0002976843770000025
in the formula: t issIs the sampling time; delta thetare(k) Is the approximate position offset between two adjacent sampling intervals, i.e.:
Δθre(k)＝ωre(k-1)Ts
Tpkis a transformation matrix, expressed as:
Figure BDA0002976843770000031
defining an inductance matrix L in a stationary coordinate systemab(θre) Comprises the following steps:
Figure BDA0002976843770000032
the construction cost function takes the permanent magnetic flux linkage and the quadrature axis inductance as unknowns, and specifically comprises the following steps:
Figure BDA0002976843770000033
the specific process of the convex optimization algorithm is as follows:
carrying out numerical value minimization on the value function by adopting a Newton method, specifically comprising the following steps:
firstly, substituting initial values of rotor flux linkage and quadrature axis inductance into a mathematical model;
then, the descending direction is calculated by calculating a Jacobi matrix J and a Hessian matrix H of the cost function, the function value is minimized by a line search method by taking lambda as a search coefficient, and when each iteration is finished, a new estimation variable is updated as follows:
Figure BDA0002976843770000034
compared with the prior art, the invention has the beneficial effects that: the invention provides a permanent magnet synchronous motor parameter identification method based on convex optimization, which can overcome the defects of the existing control method, and obtains a discrete mathematical model by obtaining a voltage equation of a permanent magnet synchronous motor under a two-phase static coordinate system and then by a backward difference method; determining motor parameters needing to be identified according to the influence of the motor parameter change on the control performance of the position-sensorless control system, and further constructing a cost function; the convex optimization algorithm is used for carrying out minimum optimization on the cost function, and the motor parameters needing to be identified are obtained, so that the accurate motor parameters can be still obtained when the motor parameters are changed due to factors such as high temperature and the like in the long-time running process of the permanent magnet synchronous motor, and the control performance of the position-sensorless motor is ensured.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the following embodiments, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A permanent magnet synchronous motor parameter identification method based on convex optimization comprises the following steps:
the method comprises the following steps: obtaining a discrete mathematical model by a voltage equation of the permanent magnet synchronous motor under a two-phase static coordinate system through a backward difference method; the voltage equation of the permanent magnet synchronous motor under an alpha-beta two-phase static coordinate system is as follows:
Figure BDA0002976843770000041
wherein L isd、LqAre the direct and quadrature axis inductances of the stator windings. i.e. iα、iβStator currents of an alpha-beta axis under a two-phase static coordinate system respectively; v. ofα、vβCan pass through
Figure BDA0002976843770000042
Calculating to obtain R, wherein R is the resistance of each phase of winding of the stator; omegareIs the rotor angular velocity; thetareIs the rotor position angle;
Figure BDA0002976843770000043
is a permanent magnet flux linkage; p is a differential operator;
Figure BDA0002976843770000044
discretizing the formula (1) to obtain
Figure BDA0002976843770000045
In the formula: t issIs the sampling time; delta thetare(k) For approximate positional offset between two adjacent sampling intervals, i.e.
Δθre(k)＝ωre(k-1)Ts (3)
TpkFor transforming the matrix, can be expressed as
Figure BDA0002976843770000051
Defining an inductance matrix L in a stationary coordinate systemab(θre) Is composed of
Figure BDA0002976843770000052
Step two: determining motor parameters needing to be identified according to the influence of the motor parameter change on the control performance of the position-sensorless control system, and further constructing a cost function;
the convex optimization-based position-free control algorithm depends on the parameters of the motor: the influence of the errors of the rotor flux linkage and the quadrature axis inductance in a full speed range below a rated rotating speed on the position estimation performance of the convex optimization algorithm is far larger than the influence of the errors of the rotor flux linkage and the quadrature axis inductance in the other two parameters by researching the influence of the parameter change of the motor on the position estimation performance of the convex optimization algorithm at different rotating speeds. Constructing a value function by taking a permanent magnetic flux linkage and a quadrature axis inductance as unknowns;
Figure BDA0002976843770000053
step three: carrying out minimum optimization on the cost function by using a convex optimization algorithm to obtain motor parameters needing to be identified;
the value function shown in (6) is numerically minimized by newton's method. First, the initial values of the rotor flux linkage and the quadrature axis inductance are substituted into the mathematical model. Then, the descent direction is calculated by calculating a Jacobi matrix J (2 × 1 matrix) and a Hessian matrix H (2 × 2 matrix) of the cost function. The function value is minimized by a line search method using lambda as a search coefficient. At the end of each iteration, the new estimated variables are updated as follows:
Figure BDA0002976843770000061
the working principle is as follows: acquiring a voltage equation of the permanent magnet synchronous motor under a two-phase static coordinate system, and obtaining a discrete mathematical model through a backward difference method; determining motor parameters needing to be identified according to the influence of the motor parameter change on the control performance of the position-sensorless control system, and further constructing a cost function; the convex optimization algorithm is used for carrying out minimum optimization on the cost function, and the motor parameters needing to be identified are obtained, so that the accurate motor parameters can be still obtained when the motor parameters are changed due to factors such as high temperature and the like in the long-time running process of the permanent magnet synchronous motor, and the control performance of the position-sensorless motor is ensured.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise forms disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (4)

1. A permanent magnet synchronous motor parameter identification method based on convex optimization is characterized by comprising the following steps:
acquiring a voltage equation of the permanent magnet synchronous motor under a two-phase static coordinate system, and obtaining a discrete mathematical model through a backward difference method;
determining motor parameters needing to be identified through the influence of the motor parameter change on the control performance of the position-sensorless control system, and further constructing a cost function;
and carrying out minimum optimization on the cost function by using a convex optimization algorithm to obtain the motor parameters needing to be identified.
2. The permanent magnet synchronous motor parameter identification method based on convex optimization according to claim 1, wherein the specific process of obtaining the discrete mathematical model is as follows:
setting a voltage equation of the permanent magnet synchronous motor under an alpha-beta two-phase static coordinate system as follows:
Figure FDA0002976843760000011
wherein L isd、LqDirect axis and quadrature axis inductances of the stator windings; i.e. iα、iβStator currents of an alpha-beta axis under a two-phase static coordinate system respectively; v. ofα、vβCan pass through
Figure FDA0002976843760000012
Calculating to obtain R, wherein R is the resistance of each phase of winding of the stator; omegareIs the rotor angular velocity; thetareIs the rotor position angle;
Figure FDA0002976843760000013
is a permanent magnet flux linkage; p is a differential operator;
Figure FDA0002976843760000014
discretizing the voltage equation can obtain:
Figure FDA0002976843760000021
in the formula: t issIs the sampling time; delta thetare(k) Is the approximate position offset between two adjacent sampling intervals, i.e.:
Δθre(k)＝ωre(k-1)Ts
Tpkis a transformation matrix, expressed as:
Figure FDA0002976843760000022
defining an inductance matrix L in a stationary coordinate systemab(θre) Comprises the following steps:
Figure FDA0002976843760000023
3. the permanent magnet synchronous motor parameter identification method based on convex optimization according to claim 1, wherein the constructed cost function takes permanent magnet flux linkage and quadrature axis inductance as unknowns, and specifically comprises:
Figure FDA0002976843760000024
4. the permanent magnet synchronous motor parameter identification method based on convex optimization according to claim 3, characterized in that the convex optimization algorithm comprises the following specific processes:
carrying out numerical value minimization on the value function by adopting a Newton method, specifically comprising the following steps:
firstly, substituting initial values of rotor flux linkage and quadrature axis inductance into a mathematical model;
then, byCalculating a Jacobi matrix J and a Hessian matrix H of the value function to calculate a descending direction, minimizing a function value by using a line search method by taking lambda as a search coefficient, and updating a new estimation variable into:
Figure FDA0002976843760000031
CN202110276497.XA 2021-03-15 2021-03-15 Permanent magnet synchronous motor parameter identification method based on convex optimization Pending CN112994564A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114374350A (en) * 2021-12-20 2022-04-19 江苏大学 Surface-mounted permanent magnet synchronous motor parameter identification method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
YINGGUANG SUN等: "Unified Wide-Speed Sensorless Scheme Using Nonlinear Optimization for IPMSM Drives", 《IEEE TRANSACTIONS ON POWER ELECTRONICS》 *
景杰: "基于凸优化的永磁同步电机无位置传感器控制策略研究", 《中国优秀硕士学位论文全文数据库（电子期刊）•工程科技Ⅱ辑》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114374350A (en) * 2021-12-20 2022-04-19 江苏大学 Surface-mounted permanent magnet synchronous motor parameter identification method
CN114374350B (en) * 2021-12-20 2023-12-15 江苏大学 Parameter identification method for surface-mounted permanent magnet synchronous motor

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Application publication date: 20210618