CN115561631A - Method for detecting, diagnosing and separating turn-to-turn short circuit fault of permanent magnet synchronous motor - Google Patents

Method for detecting, diagnosing and separating turn-to-turn short circuit fault of permanent magnet synchronous motor Download PDF

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CN115561631A
CN115561631A CN202211248184.4A CN202211248184A CN115561631A CN 115561631 A CN115561631 A CN 115561631A CN 202211248184 A CN202211248184 A CN 202211248184A CN 115561631 A CN115561631 A CN 115561631A
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fault
permanent magnet
synchronous motor
magnet synchronous
turn
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高超
姚德贵
刘泽辉
张博
姚利娜
白银浩
王天
潘钰婷
康运风
伍川
马伦
张世尧
刘光辉
炊晓毅
陶亚光
陈钊
张帅
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Zhengzhou University
State Grid Henan Electric Power Co Ltd
Electric Power Research Institute of State Grid Henan Electric Power Co Ltd
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Zhengzhou University
State Grid Henan Electric Power Co Ltd
Electric Power Research Institute of State Grid Henan Electric Power Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/34—Testing dynamo-electric machines
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/34—Testing dynamo-electric machines
    • G01R31/343—Testing dynamo-electric machines in operation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/52—Testing for short-circuits, leakage current or ground faults

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Abstract

The application relates to a method for detecting, diagnosing and separating turn-to-turn short circuit faults of a permanent magnet synchronous motor, which comprises the following steps: the method comprises the following steps: establishing a mathematical model of a nonlinear networked control system with random time delay and faults according to specific parameters of the three-phase permanent magnet synchronous motor; step two: obtaining a state space model of the permanent magnet synchronous motor through transformation; step three: designing a fault detection observer; step four: designing a fault separation algorithm; step five: designing a fault diagnosis algorithm; step six: and establishing an observation error dynamic system, monitoring the stability of the system, and judging whether the permanent magnet synchronous motor has a fault according to the magnitude of the residual error signal and the fault detection threshold value. The invention can judge whether the permanent magnet synchronous motor has faults or not, and can separate unknown disturbance into two types of noise disturbance and fault signal so as to analyze the reasons of the faults.

Description

Method for detecting, diagnosing and separating turn-to-turn short circuit fault of permanent magnet synchronous motor
Technical Field
The application belongs to the technical field of permanent magnet synchronous motors, and particularly relates to a method for detecting, diagnosing and separating turn-to-turn short circuit faults of a permanent magnet synchronous motor.
Background
The permanent magnet synchronous motor is used as a key part of an electric automobile, has the advantages of high power density, high power factor, high torque ratio and the like, and is very suitable for hybrid electric vehicles and electric automobiles with compact structures. But the failure rate is relatively high due to factors such as the working principle and the working environment. Stator turn-to-turn short circuit faults are faults with high frequency in faults of a motor body and are mainly caused by insulation faults between adjacent windings of coils, and if the faults are not diagnosed in time, the insulation damage of the stator is aggravated by local overheating, and even the motor can be burnt out. Therefore, fault diagnosis and separation research are carried out on the motors under different working occasions and different running states, and the reliability and the safety of the system are guaranteed to be improved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor is provided for solving the problem that the prior art is difficult to detect the fault occurrence time and position the fault.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for detecting, diagnosing and separating turn-to-turn short circuit faults of a permanent magnet synchronous motor comprises the following steps:
the method comprises the following steps: establishing a mathematical model of a nonlinear networked control system with random time delay and faults according to specific parameters of the three-phase permanent magnet synchronous motor;
step two: obtaining a state space model of the permanent magnet synchronous motor through transformation;
step three: designing a fault detection observer according to a state space model of the permanent magnet synchronous motor; after the permanent magnet synchronous motor is detected to have short-circuit fault, providing an estimated value under the fault condition for the motor, and supposing that the permanent magnet synchronous motor can generate estimated voltage and estimated current when the permanent magnet synchronous motor has fault, so that the actual fault value is compensated by adopting the estimated value; when the estimated value is inaccurate, an under-compensated residual signal or an over-compensated residual signal exists in the observer, and a calculation formula of the residual signal is obtained;
step four: designing a fault separation algorithm; modeling by regarding the signals different from the normal condition as unknown disturbance, and separating the unknown disturbance into two types of noise disturbance and fault signals;
step five: designing a fault diagnosis algorithm; defining fault observation errors, and diagnosing faults according to whether the errors are converged or not;
step six: and establishing an observation error dynamic system, monitoring the stability of the system, and judging whether the permanent magnet synchronous motor has a fault according to the magnitude of the residual error signal and the fault detection threshold value.
Preferably, in the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor, in the first step, a calculation formula of a three-phase voltage of the permanent magnet synchronous motor is as follows:
Figure BDA0003886852200000021
wherein u is a ,u b ,u c Is a three-phase stator voltage;
i a ,i b ,i c the three-phase stator current under normal conditions;
r is a stator resistor;
ψ a ,ψ b ,ψ c the three-phase stator flux linkage is under the normal condition;
ψ f a permanent magnet flux linkage under normal conditions;
L aa ,L bb ,L cc the self-inductance coefficient of the stator winding is obtained;
M ab ,M ac ,M ba ,M bc ,M ca ,M cb the mutual inductance coefficient between the stator windings is used;
θ e is the included angle between the rotor and the a-phase axis;
the normal condition refers to a working state when the permanent magnet synchronous motor can be in a state of not generating any fault and providing electric energy output within a reasonable range for a power system;
the flux linkage equation of the permanent magnet synchronous motor is
Figure BDA0003886852200000031
And theta is the position of the magnetic pole of the motor rotor, namely the included angle between the d axis and the A phase axis in the d-q coordinate system.
When a short-circuit fault occurs in a circuit, the current of the permanent magnet synchronous motor changes as follows
Figure BDA0003886852200000032
Wherein the content of the first and second substances,
Figure BDA0003886852200000033
three-phase stator current after short-circuit current is superposed when the circuit has short-circuit fault,
i fa ,i fb ,i fc the three-phase short-circuit current is generated when the short-circuit fault occurs in the circuit.
Preferably, in the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor, in the second step, the mathematical model of the three-phase static coordinate system in the first step is converted into a voltage equation under a d-q two-phase synchronous rotating coordinate system through Clark conversion and Park conversion;
obtaining a state space equation of the permanent magnet synchronous motor at the time t as
Figure BDA0003886852200000034
Wherein the content of the first and second substances,
Figure BDA0003886852200000035
Figure BDA0003886852200000041
‖d(t)‖≤Δ d an unknown bounded external perturbation is represented.
Preferably, in the method for detecting, diagnosing and separating turn-to-turn short circuit faults of the permanent magnet synchronous motor, the fault observer can be designed as
Figure BDA0003886852200000042
Wherein the content of the first and second substances,
Figure BDA0003886852200000043
is an estimate of x (t),
in addition, assuming that LC is a reasonable fault gain matrix, e (t) is a residual signal;
the residual signal is calculated by
Figure BDA0003886852200000044
Wherein, the fault detection threshold value lambda is determined according to 1 Whether the permanent magnet synchronous motor has a fault is judged, and the judgment logic is as follows
Figure BDA0003886852200000045
Where | e (t) | is the norm of the residual signal.
Preferably, according to the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor, when the stability of the fault observation error system is judged through the function in the sixth step, the adopted function is as follows
Figure BDA0003886852200000046
λ min (Q 1 ) Refers to the matrix Q 1 Is determined by the minimum characteristic value of (c),
condition
Figure BDA0003886852200000051
When it is established, have
Figure BDA0003886852200000052
It is true that the system state is stable at this time.
Preferably, the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor comprises the fourth step of calculating an unknown disturbance signal according to the formula
Figure BDA0003886852200000053
D (t) is noise disturbance generated by the system when the system normally operates or fails;
Figure BDA0003886852200000054
the short-circuit fault signal needing to be separated is removed under the condition that the permanent magnet synchronous motor has the short-circuit fault
Figure BDA0003886852200000055
The fault signal remaining thereafter.
Preferably, the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor comprises the fourth step of decomposing a state space model into two subsystems; the first subsystem comprises only normal signals and fault signals, in particular
Figure BDA0003886852200000056
Wherein the content of the first and second substances,
Figure BDA0003886852200000057
is a fault signal requiring separation, w 1 (t) is the output of the state space equation for the first subsystem;
the second subsystem comprises normal signals and fault signals and random noise and interference of a system, and the state equation is
Figure BDA0003886852200000058
After obtaining the two subsystems, designing the observers of the two subsystems as
Figure BDA0003886852200000059
And
Figure BDA0003886852200000061
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003886852200000062
is a subsystem state vector z 1 ,z 2 Is determined by the estimated value of (c),
Figure BDA0003886852200000063
output w for subsystem 1 (t),w 2 (ii) an estimate of the value of (t),
Figure BDA0003886852200000064
is an estimate of the fault vector, L 1 ,L 2 Is the observer gain matrix, ε, to be determined 1 (t),ε 2 (t) is the residual signal of the two subsystems, where ε 2 (t) random noise interference including systematic
Figure BDA0003886852200000065
Obtaining two residual signals epsilon according to the difference between the state equation and the observer 1 (t) and ε 2 (t) two residual signals are calculated by
Figure BDA0003886852200000066
And
Figure BDA0003886852200000067
preferably, in the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor, in the fifth step, the calculation formula of the fault observation error is
Figure BDA0003886852200000068
System for obtaining observation error dynamic state
Figure BDA0003886852200000069
Preferably, the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor comprises a fifth step of adopting a fault diagnosis algorithm
Figure BDA00038868522000000610
Wherein gamma is 1 ,Γ 2 Is a fault diagnosis gain matrix, Γ, to be determined 1 ,Γ 2 The value of (d) can be determined by solving the linear matrix inequality in the stability certification.
Preferably, the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor further comprises the following steps: and verifying the observation error dynamic system and the state space model by using a simulation experiment.
The invention has the beneficial effects that:
whether the permanent magnet synchronous motor breaks down or not can be judged, unknown disturbance can be separated into two types of noise disturbance and fault signals, and therefore the reason for the fault can be analyzed conveniently.
Drawings
The technical solution of the present application is further explained below with reference to the drawings and examples.
Fig. 1 is a flowchart illustrating steps of a method for detecting, diagnosing and separating a turn-to-turn short circuit fault of a permanent magnet synchronous motor according to an embodiment of the present application;
FIG. 2 is a diagram of a three-phase stationary coordinate system and a two-phase synchronous rotating coordinate system according to an embodiment of the present application;
FIG. 3 is a diagram of the results of fault detection in an embodiment of the present application;
FIG. 4 is a graph of the fault isolation results of an embodiment of the present application;
FIG. 5 is a d-axis fault diagnosis result diagram of an embodiment of the present application;
FIG. 6 shows the q-axis fault diagnosis result of the embodiment of the present application;
fig. 7 is a diagram of a result of fault diagnosis in the three-phase stationary coordinate system according to the embodiment of the present application.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
In the description of the present application, it is to be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in the orientation or positional relationship indicated in the drawings for convenience in describing the present application and for simplicity in description, and are not intended to indicate or imply that the referenced devices or elements must have a particular orientation, be constructed in a particular orientation, and be operated in a particular manner, and are not to be considered limiting of the scope of the present application. Furthermore, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first," "second," etc. may explicitly or implicitly include one or more of that feature. In the description of the invention, "a plurality" means two or more unless otherwise specified.
In the description of the present application, it is to be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art through specific situations. In the present embodiment, the X, Y, Z direction or the X, Y, Z axis are based on the cartesian coordinate system.
The technical solutions of the present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Examples
The embodiment provides a method for detecting, diagnosing and separating turn-to-turn short circuit faults of a permanent magnet synchronous motor, as shown in fig. 1, comprising the following steps:
the method comprises the following steps: establishing a mathematical model of a nonlinear networked control system with random time delay and faults according to specific parameters of the three-phase permanent magnet synchronous motor;
step two: obtaining a state space model of the permanent magnet synchronous motor through transformation;
step three: designing a fault detection observer according to a state space model of the permanent magnet synchronous motor; after the permanent magnet synchronous motor is detected to have short-circuit fault, providing an estimated value under the fault condition for the motor, and supposing that the permanent magnet synchronous motor can generate estimated voltage and estimated current when the permanent magnet synchronous motor has fault, so that the actual fault value is compensated by adopting the estimated value; when the estimated value is inaccurate, an under-compensated residual signal or an over-compensated residual signal exists in the observer, and a calculation formula of the residual signal is obtained;
step four: designing a fault separation algorithm; modeling by regarding the signals different from the normal condition as unknown disturbance, and separating the unknown disturbance into two types of noise disturbance and fault signals;
step five: designing a fault diagnosis algorithm; defining fault observation errors, and diagnosing faults according to whether the errors are converged or not;
step six: and establishing an observation error dynamic system, monitoring the stability of the system, and judging whether the permanent magnet synchronous motor has a fault according to the magnitude of the residual error signal and the fault detection threshold value.
Specifically, firstly, a mathematical model of a nonlinear networked control system with random time delay and faults is established, and a calculation formula for obtaining the three-phase voltage of the permanent magnet synchronous motor is as follows:
Figure BDA0003886852200000091
wherein u is a ,u b ,u c Is a three-phase stator voltage;
i a ,i b ,i c the three-phase stator current under normal conditions;
r is a stator resistor;
ψ a ,ψ b ,ψ c the three-phase stator flux linkage is under the normal condition;
ψ f a permanent magnet flux linkage under normal conditions;
L aa ,L bb ,L cc the self-inductance coefficient of the stator winding is obtained;
M ab ,M ac ,M ba ,M bc ,M ca ,M cb the mutual inductance coefficient between the stator windings is used;
θ e is the included angle between the rotor and the a-phase axis.
The normal condition refers to that the permanent magnet synchronous motor can be in a normal working state, does not have any fault, and provides electric energy output within a reasonable range for a power system.
Similarly, the flux linkage equation for a PMSM is
Figure BDA0003886852200000101
And theta is the magnetic pole position of the motor rotor, namely the included angle between the d-axis and the A-phase axis in a d-q coordinate system.
When a short-circuit fault occurs in a circuit, the current of the permanent magnet synchronous motor changes as follows
Figure BDA0003886852200000102
Wherein the content of the first and second substances,
Figure BDA0003886852200000103
three-phase stator current after short-circuit current is superposed when the circuit has short-circuit fault,
i fa ,i fb ,i fc the three-phase short-circuit current is the three-phase short-circuit current when the short-circuit fault occurs in the circuit.
As shown in fig. 2, the three-phase stationary coordinate system of the permanent magnet synchronous motor is shown by ABC axis in the figure, wherein the axis a in the three-phase stationary coordinate system may be arranged to coincide with the axis of the phase a stator winding of the permanent magnet synchronous motor. In addition, the d-q coordinate in FIG. 2 is a two-phase rotating coordinate system, with the d-axis pointing in the rotor permanent magnet flux linkage direction and coinciding with the rotor pole axis,. Psi f The magnetic linkage is in a normal condition, an included angle between the magnetic linkage and the axis of the phase A stator winding of the motor is theta, the magnetic linkage rotates with the rotor at an angular speed omega in space, and the q axis leads the d axis 90 degrees anticlockwise.
Through Clark conversion and Park conversion, a voltage equation under an ABC three-phase static coordinate system can be converted into a voltage equation under a d-q two-phase rotating coordinate system. Its transformation matrix is
Figure BDA0003886852200000111
Substituting the formulas (3) and (4) into the formula (1) to obtain the voltage equation of the permanent magnet synchronous motor when short circuit fault occurs in the circuit under the d-q coordinate system
Figure BDA0003886852200000112
Wherein R is f Is a short-circuit resistance when a short-circuit fault occurs in the circuit,
i d and i q Respectively three-phase stator current i based on normal condition a ,i b ,i c The stator current under the d-q coordinate system is calculated after the coordinate system is transformed,
i fd and i fq Three-phase short-circuit current i when short-circuit fault occurs in the circuit fa ,i fb ,i fc The fault current under the d-q coordinate system is calculated after the coordinate system is transformed,
ψ d and psi q Respectively a three-phase stator flux linkage psi under normal conditions a ,ψ b ,ψ c And transforming the coordinate system and then calculating the stator flux linkage under the d-q coordinate system.
The flux linkage equation of the permanent magnet synchronous motor is
Figure BDA0003886852200000113
Wherein L is d And L q The inductances under d-q coordinate system of the permanent magnet synchronous motor respectively have L because the difference of the surface-mounted permanent magnet synchronous motor quadrature-direct axis inductance is very small q ≈L d ≈L。
Based on the above assumptions, equation (5) can be improved to
Figure BDA0003886852200000114
Considering that in an actual engineering system, the change rate of the permanent magnet flux linkage is far smaller than the state variables such as current and the like, so that the change rate can be basically ignored, and therefore, the assumption is made that
Figure BDA0003886852200000121
Thus, a current model of the permanent magnet synchronous motor can be obtained as
Figure BDA0003886852200000122
Adding in an ideal current model of a permanent magnet synchronous motorUnknown external disturbances
Figure BDA0003886852200000123
Then, after the formula (8) is arranged, the state space equation of the permanent magnet synchronous motor at the time t can be obtained as
Figure BDA0003886852200000124
Wherein the content of the first and second substances,
Figure BDA0003886852200000125
an unknown bounded external perturbation is represented.
In the above formula, y (t) is the output of the state space equation, which can be assumed as the current x of the permanent magnet synchronous motor in the d-q coordinate system.
In the step 2, the step of mixing the raw materials,
according to the invention, the design of the fault detection observer can be realized according to the state equation of the permanent magnet synchronous motor. Specifically, df is the equation of equation (9) a The term (t) is actually caused by a short-circuit fault of a circuit, so that the term does not take a value of 0 only when the permanent magnet synchronous motor has the short-circuit fault, and the essence of the term is caused by the circuit fault.
Therefore, the fault observer in the present invention can be designed as
Figure BDA0003886852200000131
Wherein the content of the first and second substances,
Figure BDA0003886852200000132
is an estimate of x (t),
further, let LC be a reasonable fault gain matrix and e (t) be the residual signal.
Specifically, in the calculation method of the present invention, after the occurrence of a short-circuit fault in the permanent magnet synchronous motor is detected, an estimated value in the case of a fault is provided for the motor, and it is assumed that the permanent magnet synchronous motor generates an estimated voltage and an estimated current when the fault occurs, so that the estimated value is used to compensate an actual fault value. When the estimated value is not sufficiently accurate, an under-compensated or over-compensated residual signal exists in the system, and the calculation formula of the signal is
Figure BDA0003886852200000133
Wherein the system may detect the threshold value Lambda based on the fault 1 To determine whether a fault has occurred in the PMSM, e.g.
Figure BDA0003886852200000134
Where | e (t) | is the norm of the residual signal.
The collective set T of all the moments when the fault exists can be obtained according to the formula (12) f That is to say
Figure BDA0003886852200000135
In the formula, j represents the number of sampling time points of related parameters for observing the state of the permanent magnet synchronous motor based on a fault observer, and r represents the number of sampling time points contained in all sampling times in the method.
In the invention, the difference between the formula (9) and the formula (10) is obtained
Figure BDA0003886852200000136
Wherein the content of the first and second substances,
Figure BDA0003886852200000141
is an observed value of the residual signal.
If no fault occurs in the system, df in equation (14) a (t) has a value of 0, then
Figure BDA0003886852200000142
Therefore, taking the residual signal in the formula (15) as the system state equation, which can characterize a linear system, and therefore taking a quadratic function as the lyapunov function, one can obtain
V 1 (t)＝e T (t)P 1 e(t) (16)
The derivation of the left and right sides of the formula (16) is
Figure BDA0003886852200000143
Since in a linear system the derivative of the lyapunov function is negative definite and bounded.
A lemma is provided in the background art document 1: yu Li robust control linear matrix inequality processing method, qinghua university Press, 2002, wherein the inequality in the lemma 5.4.2 is
Figure BDA0003886852200000144
The last term 2e in equation (18) T (t)P 1 Nd (t) is substituted into equation (19) while assuming D = P 1 N, E =1, and F is an appropriate dimension matrix in the background art document 2, the matrix can be obtained
Figure BDA0003886852200000145
So that rearranging equation (17) can obtain
Figure BDA0003886852200000151
Background art document 2: a linear Matrix Inequality in a system and a Control method thereof are disclosed in Boyd, S., ghaoui, L., feron, E., balakrishnan, V.Linear Matrix Inequality in Systems and Control theory, SIAM: philadelphia, PA,1994, wherein a variation of the Lyapunov Inequality (Lyapunov Inequality) is specifically disclosed in section 2.1.1 (equation 2.6).
(A-LC) T P 1 +P 1 (A-LC)+λ 1 P 1 N(P 1 N) T +Q 1 ≤0 (21)
Wherein, A-LC, N,
Figure BDA0003886852200000152
i.e. Q and P are both positive definite symmetric matrices and have lambda 1 >0。
When the inequality (31) is substituted into the first three terms on the right side of the inequality of the formula (20), then
e T (t)[(A-LC) T P 1 +P 1 (A-LC)+λ 1 P 1 N(P 1 N) T ]e(t)<-e T (t)Q 1 e(t) (22)
In addition, let
Figure BDA0003886852200000153
Then the formula (20) has
Figure BDA0003886852200000154
λ min (Q 1 ) Refers to the matrix Q 1 The minimum eigenvalue of (c).
Condition
Figure BDA0003886852200000155
When it is established, there are
Figure BDA0003886852200000156
It is true that the system state is stable at this time.
In order to accurately acquire the occurrence condition of the faults of the permanent magnet synchronous motor and the influence of the faults on the system, in the invention, signals which are different from normal conditions are regarded as unknown disturbance for modeling. The new unknown disturbance signal obtained by the method is calculated by
Figure BDA0003886852200000161
In the formula, d (t) is noise disturbance generated by a non-fault body when the system normally operates or fails; while
Figure BDA0003886852200000162
Then the short-circuit fault signal needing to be separated is removed under the condition that the permanent magnet synchronous motor has the short-circuit fault
Figure BDA0003886852200000163
The fault signal remaining thereafter.
It should be noted that the unknown disturbance signal in the above formula is obtained by amplifying based on the state equation of the permanent magnet synchronous motor, and specifically, the formula (9) may be arranged as
Figure BDA0003886852200000164
Wherein the content of the first and second substances,
Figure BDA0003886852200000165
to be a gain matrix of the augmented noise disturbance vector,
Figure BDA0003886852200000166
the fault to be isolated is a fault that,
D J for the column vector of the fault gain to be isolated,
Figure BDA0003886852200000167
removing a fault gain vector D to be separated from a fault gain matrix D in the original system J The matrix remaining thereafter.
Therefore, the unknown disturbance can be separated into two types of noise disturbance and fault signals, so that the state of the fault signals can be accurately obtained through respective calculation, and the cause of the fault can be reasonably analyzed.
In the present invention, in order to obtain an observer of noise disturbance and an observer of fault signal separately, it is necessary to decompose the formula (25) into two subsystems.
In order to achieve the decoupling of the two subsystems, the existence of transformation matrices T and S can be designed, and the method enables
Figure BDA0003886852200000168
w (t) = Sy (t), and therefore the state equation of the permanent magnet synchronous motor can be obtained in an enlarged mode
Figure BDA0003886852200000169
At this time, in order to decouple the noise disturbance signal and the fault signal, the transformation matrix T may be designed to satisfy
Figure BDA0003886852200000171
I is an identity matrix of appropriate dimension, dimension
Figure BDA0003886852200000172
Determining if it is two-dimensional
Figure BDA0003886852200000173
Wherein the content of the first and second substances,
Figure BDA0003886852200000174
and
Figure BDA0003886852200000175
is defined as a matrix
Figure BDA0003886852200000176
Two elements of (1), otherwise transforming the matrix S into
Figure BDA0003886852200000177
According to the value of the transformation matrix T, the following definitions in the formula can be realized,
Figure BDA0003886852200000178
after the above transformation, the above system can be decomposed into two subsystems. The first subsystem comprises only normal signals and fault signals, in particular
Figure BDA0003886852200000179
Wherein the content of the first and second substances,
Figure BDA00038868522000001710
is a fault signal that needs to be separated, w 1 (t) is the output of the state space equation for the first subsystem, subsystem z 1 (t) there are only fault signals that need to be separated
Figure BDA00038868522000001711
The difficulty of fault diagnosis is simplified.
The second subsystem not only includes normal signals and fault signals, but also includes random noise and interference of the system. Therefore, its state equation is
Figure BDA00038868522000001712
After obtaining the above two subsystems, the observers of the two subsystems can be designed as
Figure BDA00038868522000001713
And
Figure BDA0003886852200000181
wherein the content of the first and second substances,
Figure BDA0003886852200000182
is a subsystem state vector z 1 ,z 2 Is determined by the estimated value of (c),
Figure BDA0003886852200000183
output w for the subsystem 1 (t),w 2 (ii) an estimate of the value of (t),
Figure BDA0003886852200000184
as an estimate of the fault vector, L 1 ,L 2 Is the observer gain matrix, ε, to be determined 1 (t),ε 2 (t) is the residual signal of the two subsystems, where ε 2 (t) random noise interference including systematic
Figure BDA0003886852200000185
According to the difference between the state equation and the observer, two residual signals e can be obtained 1 (t) and e 2 (t) of (d). Specifically, the calculation formula of the two residual signals is
Figure BDA0003886852200000186
And
Figure BDA0003886852200000187
the two residual signals can be considered as noise disturbance of the respective subsystems after the system is decoupled into the two subsystems, so that the observation deviation of the system fault is not included.
In addition, the method of the invention separately defines the system fault observation error and realizes the fault diagnosis through the convergence of the error.
The fault observation error of the invention is calculated by the formula
Figure BDA0003886852200000188
Then, an observation error dynamic system can be obtained
Figure BDA0003886852200000189
The invention designs a fault diagnosis algorithm
Figure BDA00038868522000001810
Wherein gamma is 1 ,Γ 2 Is the fault diagnosis gain matrix to be determined.
Wherein r is 1 ,Γ 2 And the values of the fault diagnosis gain matrixes can be determined by solving a linear matrix inequality in the stability certification. The stability of the observation error system is also determined by theorem 2. Theorem 2 is a proof of the stability of Lyapunov, and any modern control theory can be used as a reference.
Theorem 2: for the observers (29) and (30), if a positive definite symmetric matrix P exists 2 ,P 3 And Γ 1 ,Γ 2 ,L 1 ,L 2 ,λ 1 > 0, such that the following inequality holds, the observation error dynamics system (32) is stable.
Figure BDA0003886852200000191
Therein, II 11 ＝(A 11 -L 1 S -1 C 1 ) T P 2 +P 2 (A 11 -L 1 S -1 C 1 )+λ 2 I，η 1 ,η 2 Is a relatively small positive number.
Error dynamic stability and sufficient conditions for the presence of the fault diagnosis observer:
choosing the Lyapunov function as follows
Figure BDA0003886852200000192
The Lyapunov function is empirically selected in order to ensure the stability of the system. For the system, if a Lyapunov function can be found to satisfy V (t) ≧ 0,
Figure BDA0003886852200000193
the system is stable. Where the observed error e of the selected subsystem 1 (t),e 2 (t) and fault estimation error
Figure BDA0003886852200000194
As a constituent element of the lyapunov function.
Combined with a dynamic system (32) of observation errors, can be obtained
Figure BDA0003886852200000201
For fault vector f j (t) is as follows
Figure BDA0003886852200000202
V can be obtained by combining theory 1 2 The first derivative of (t) is
Figure BDA0003886852200000203
Wherein
Figure BDA0003886852200000211
Π 11 ＝(A 11 -L 1 S -1 C 1 ) T P 2 +P 2 (A 11 -L 1 S -1 C 1 ),
Figure BDA0003886852200000212
Known from the guiding theory of Schur supplement (reference: huang Weigong. Property of matrix Schur supplement and its application. Nanjing university of information engineering, 2008.) is that the matrix phi 1 The matrices in the sum inequality (33) are equivalent, so that when the condition Φ is satisfied 1 +λe 1 T (t)e 1 (t) < 0 is true, and the following inequality can be obtained
Figure BDA0003886852200000213
Therefore, when conditions are
Figure BDA0003886852200000214
When it is established, there are
Figure BDA0003886852200000215
Therefore, the observation error dynamics system (32) is stable.
Figure BDA0003886852200000216
Is the result of the final finishing for stability verification.
In summary, the method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor of the embodiment,
in the embodiment, the logic of verifying the detection, separation and diagnosis of the turn-to-turn short circuit fault of the permanent magnet synchronous motor and judging the stability of the system by using a simulation experiment is that when the logic is yes
Figure BDA0003886852200000217
When true, the system state is stable;
whether the space state model is in failure or not is judged through a failure detection and diagnosis algorithm, when the residual signal exceeds a threshold value, the failure is indicated (see formulas (12-13)) and the amplitude (size or severity) of the failure is determined through a failure diagnosis algorithm (see formula (31)).
In order to verify the feasibility and effectiveness of the proposed turn-to-turn short circuit fault detection, separation and diagnosis method, a MATLAB simulation experiment is used for verification, and a detailed description is given below.
TABLE 1 PMSM system parameters
Figure BDA0003886852200000221
Assuming that the number of short-circuit phase short-circuit resistance turns is 50% of the total number of turns, the short-circuit resistance is R f =10 Ω, and when a short-circuit fault occurs, a short-circuit current as follows will be generated
Figure BDA0003886852200000222
Solving parameters required for fault detection, separation and diagnosis by using MATALB tool box
Γ 1 ＝0.9921,Γ 2 ＝-16.4881,
Figure BDA0003886852200000223
And detecting, separating and diagnosing the turn-to-turn faults of the permanent magnet synchronous motor by using the obtained parameters, and obtaining results shown in the figures 3 to 7. It can be seen from fig. 3 that a short-circuit fault occurs at 50s, and the designed residual signal can accurately and quickly detect the fault; and the fault separation result in the dq coordinate system in fig. 4 can also accurately separate the fault; 5-6, it can be seen that the designed fault diagnosis algorithm can accurately estimate the occurrence size of the fault; after the inverse Park transform, it can be seen from fig. 7 that only phase a fails and that phases B and C do not fail.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (10)

1. A method for detecting, diagnosing and separating turn-to-turn short circuit faults of a permanent magnet synchronous motor is characterized by comprising the following steps:
the method comprises the following steps: establishing a mathematical model of a nonlinear networked control system with random time delay and faults according to specific parameters of the three-phase permanent magnet synchronous motor;
step two: obtaining a state space model of the permanent magnet synchronous motor through transformation;
step three: designing a fault detection observer according to a state space model of the permanent magnet synchronous motor; after the permanent magnet synchronous motor is detected to have short-circuit fault, providing an estimated value under the fault condition for the motor, and supposing that the permanent magnet synchronous motor can generate estimated voltage and estimated current when the permanent magnet synchronous motor has fault, so that the actual fault value is compensated by adopting the estimated value; when the estimated value is inaccurate, an under-compensated residual signal or an over-compensated residual signal exists in the observer, and a calculation formula of the residual signal is obtained;
step four: designing a fault separation algorithm; modeling by regarding the signals different from the normal condition as unknown disturbance, and separating the unknown disturbance into two types of noise disturbance and fault signals;
step five: designing a fault diagnosis algorithm; defining fault observation errors, and diagnosing faults according to whether the errors are converged or not;
step six: and establishing an observation error dynamic system, monitoring the stability of the system, and judging whether the permanent magnet synchronous motor has a fault according to the magnitude of the residual error signal and the fault detection threshold value.
2. The method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor according to claim 1, wherein in the step one, a calculation formula of a three-phase voltage of the permanent magnet synchronous motor is as follows:
Figure FDA0003886852190000011
wherein u is a ,u b ,u c Is a three-phase stator voltage;
i a ,i b ,i c the three-phase stator current under normal conditions;
r is a stator resistor;
ψ a ,ψ b ,ψ c the three-phase stator flux linkage is under the normal condition;
ψ f a permanent magnet flux linkage under normal conditions;
L aa ,L bb ,L cc is the self-inductance coefficient of the stator winding;
M ab ,M ac ,M ba ,M bc ,M ca ,M cb the mutual inductance coefficient between the stator windings is used;
θ e is the included angle between the rotor and the a-phase axis;
the normal condition refers to a working state when the permanent magnet synchronous motor can be in a state of not generating any fault and providing electric energy output within a reasonable range for a power system;
the flux linkage equation of the permanent magnet synchronous motor is
Figure FDA0003886852190000021
And theta is the magnetic pole position of the motor rotor, namely the included angle between the d-axis and the A-phase axis in a d-q coordinate system.
When a short-circuit fault occurs in a circuit, the current of the permanent magnet synchronous motor changes as follows
Figure FDA0003886852190000022
Wherein the content of the first and second substances,
Figure FDA0003886852190000023
superimposing short-circuit current for short-circuit fault of circuitThe latter three-phase stator current is then,
i fa ,i fb ,i fc the three-phase short-circuit current is the three-phase short-circuit current when the short-circuit fault occurs in the circuit.
3. The method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor according to claim 2, wherein in the second step, a mathematical model of a three-phase static coordinate system in the first step is converted into a voltage equation under a d-q two-phase synchronous rotating coordinate system through Clark conversion and Park conversion;
the state space equation of the permanent magnet synchronous motor at the moment t is obtained as
Figure FDA0003886852190000031
Wherein the content of the first and second substances,
Figure FDA0003886852190000032
Figure FDA0003886852190000033
‖d(t)‖≤Δ d an unknown bounded external disturbance is represented.
4. The PMSM turn-to-turn short circuit fault detection, diagnosis and separation method according to claim 3, wherein in step three, the fault observer can be designed as a fault observer
Figure FDA0003886852190000034
Wherein the content of the first and second substances,
Figure FDA0003886852190000035
is an estimate of x (t),
in addition, assuming that LC is a reasonable fault gain matrix, e (t) is a residual signal;
the residual signal is calculated by
Figure FDA0003886852190000036
Wherein, the fault detection threshold value lambda is determined according to 1 Whether the permanent magnet synchronous motor has a fault is judged, and the judgment logic is as follows
Figure FDA0003886852190000037
Where | e (t) | is the norm of the residual signal.
5. The method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor according to claim 4, wherein when the stability of the fault observation error system is judged through the function in the sixth step, the function is adopted as follows
Figure FDA0003886852190000041
λ min (Q 1 ) Refers to the matrix Q 1 Is determined by the minimum characteristic value of (c),
condition
Figure FDA0003886852190000042
When it is established, there are
Figure FDA0003886852190000043
It holds that the system state is stable.
6. The method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor according to claim 5, wherein in the fourth step, the calculation formula of the unknown disturbance signal is
Figure FDA0003886852190000044
D (t) is noise disturbance generated by the system when the system normally operates or fails;
Figure FDA0003886852190000045
then the short-circuit fault signal needing to be separated is removed under the condition that the permanent magnet synchronous motor has the short-circuit fault
Figure FDA0003886852190000046
The fault signal remaining thereafter.
7. The method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor according to claim 6, wherein in the fourth step, the state space model is decomposed into two subsystems; the first subsystem comprises only normal signals and fault signals, in particular
Figure FDA0003886852190000047
Wherein the content of the first and second substances,
Figure FDA0003886852190000048
is a fault signal that needs to be separated, w 1 (t) is the output of the state space equation for the first subsystem;
the second subsystem comprises normal signals and fault signals and random noise and interference of a system, and the state equation is
Figure FDA0003886852190000051
After obtaining the two subsystems, designing the observers of the two subsystems as
Figure FDA0003886852190000052
And
Figure FDA0003886852190000053
wherein the content of the first and second substances,
Figure FDA0003886852190000054
is a subsystem state vector z 1 ,z 2 Is determined by the estimated value of (c),
Figure FDA0003886852190000055
output w for subsystem 1 (t),w 2 (ii) an estimate of the value of (t),
Figure FDA0003886852190000056
as an estimate of the fault vector, L 1 ,L 2 Is the observer gain matrix that needs to be determined,
ε 1 (t),ε 2 (t) is the residual signal of the two subsystems, where ε 2 (t) random noise interference including systematic
Figure FDA0003886852190000057
Obtaining two residual signals epsilon according to the difference between the state equation and the observer 1 (t) and ε 2 (t) two residual signals are calculated by
Figure FDA0003886852190000058
And
Figure FDA0003886852190000059
8. the PMSM turn-to-turn short circuit fault detection, diagnosis and separation method according to claim 7, wherein in step five, a calculation formula of fault observation error is
Figure FDA00038868521900000510
System for obtaining observation error dynamic state
Figure FDA00038868521900000511
9. The PMSM turn-to-turn short circuit fault detection, diagnosis and separation method according to claim 8, wherein in step five, the fault diagnosis algorithm
Figure FDA0003886852190000061
Wherein gamma is 1 ,Γ 2 Is a fault diagnosis gain matrix, Γ, to be determined 1 ,Γ 2 The value of (d) can be determined by solving the linear matrix inequality in the stability certification.
10. The method for detecting, diagnosing and separating the turn-to-turn short circuit fault of the permanent magnet synchronous motor according to any one of claims 1 to 9, further comprising the step of seven: and verifying the observation error dynamic system and the state space model by using a simulation experiment.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117852476A (en) * 2024-03-08 2024-04-09 中科鉴芯(北京)科技有限责任公司 Method and device for simulating based on incomplete algorithm

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