PMSM stator turn-to-turn short circuit fault severity parameter decoupling identification method

Abstract

The invention relates to the technical field of fault detection of a permanent magnet synchronous motor, and discloses a PMSM stator turn-to-turn short circuit fault severity parameter decoupling identification method, which comprises the following steps: by establishing a three-phase PMSM stator turn-to-turn short circuit fault equivalent circuit, deducing a turn-to-turn short circuit fault motor model under a static natural coordinate system and a synchronous rotating coordinate system; an alpha-axis counter electromotive force residual error is determined as a stator turn-to-turn short circuit fault characteristic quantity through a fault characteristic generation mechanism and a fault severity influence factor, and an improved fault characteristic observer is designed to extract fault characteristics. And the fault severity parameter is dynamically decoupled from the extracted fault characteristic quantity by using the extended Kalman filtering algorithm for online identification, so that the accuracy of fault detection is improved.

Description

Technical Field

[0001] The invention relates to the technical field of fault identification of permanent magnet synchronous motors, and in particular to a method for decoupling and identifying fault severity parameters of a PMSM stator turn-to-turn short circuit. Background Art

[0002] Permanent Magnet Synchronous Motor (PMSM) is widely used in the fields of national production and life, aviation and national defense due to its advantages such as high reliability, high power density and high efficiency. Its working environment and operating conditions are becoming more and more complex, and the possibility of system failure is increasing. Stator winding interturn short circuit is one of the most common fault forms. The short-circuit current generated by it will cause the insulation to continue to deteriorate, and eventually develop into a more serious phase-to-phase or phase-to-ground short circuit, threatening the safety of the system and personnel.

[0003] In special scenarios where fault-tolerant operation of the motor is required, rapid and accurate identification of the severity parameters of the turn-to-turn short-circuit fault can provide key information for the fault-tolerant control system and reduce the complexity of the fault-tolerant control. However, existing methods mostly focus on fault detection and diagnosis, which have problems such as complex detection process, only being able to indicate the presence or absence of a fault, and insufficient accuracy. In addition, existing methods rarely involve the decoupling identification of fault severity parameters and cannot meet the actual needs under complex working conditions. Therefore, those skilled in the art need a method for decoupling identification of PMSM stator turn-to-turn short-circuit fault severity parameters. Summary of the invention

[0004] The purpose of the present invention is to solve the above problems and to design a PMSM stator turn-to-turn short circuit fault severity parameter decoupling identification method.

[0005] To achieve the above-mentioned purpose, the technical solution of the present invention is a method for decoupling and identifying the severity parameters of a PMSM stator turn-to-turn short-circuit fault, the method comprising the following steps:

[0006] Step 1, a mathematical model of the stator turn-to-turn short circuit fault of the permanent magnet synchronous motor in the stationary coordinate system and the synchronous rotating coordinate system is established;

[0007] Step 2: Analyze the corresponding relationship between the fault parameters in the stationary coordinate system and the fault parameters in the synchronous rotating coordinate system and the fault severity, and determine the fault characteristics in the stationary coordinate system and the synchronous rotating coordinate system respectively;

[0008] Step 3, using an improved fault feature observer based on synovial film observation to observe the fault features without distortion and extract the observation results;

[0009] Step 4: Analyze the constraint relationship between fault severity parameters, derive the decoupling constraint equation between fault severity parameters, and establish a fault motor state space model with severity parameter decoupling;

[0010] Step 5: Taking the observation results of fault characteristics as input, the Extended Kalman Filter (EKF) algorithm is introduced to perform online identification of the dynamic decoupling of fault severity parameters.

[0011] The process of constructing the mathematical model of the stator turn-to-turn short-circuit fault of the permanent magnet synchronous motor in the stationary coordinate system in step 1 is as follows:

[0012] The equivalent circuit of the stator turn-to-turn short-circuit fault of the permanent magnet synchronous motor is constructed, and the short-circuit turns ratio Δ is introduced to represent the proportion of the faulty winding in the entire faulty phase winding:

[0013]

[0014] Among them, N f and N s They are the number of turns of the short-circuited part winding and the total number of turns of the fault phase winding respectively;

[0015] Assume that the motor phase resistance in a healthy state is R s , the inductance and back electromotive force of phase a are L a and e a The mutual inductance between the three phases is M ab 、M bc 、M ca , then the resistance parameters, inductance parameters and back electromotive force of PMSM under fault condition can be expressed as:

[0016]

[0017]

[0018] Among them, R ah and R af are the resistance of the healthy part and the short-circuited part of the fault phase winding, L ah and L af are the self-inductance of the healthy part and the short-circuited part of the fault phase winding, M ahaf is the mutual inductance between the healthy part and the short-circuited part of the fault phase winding, M ahb 、M ahc are the mutual inductances between the healthy part of the fault phase winding and the b and c phase windings, M afb 、M afc are the mutual inductance between the short-circuited part of the fault phase winding and the b and c phase windings, e ah and e afare the back electromotive force of the healthy part and the short-circuited part of the fault phase winding respectively;

[0019] Assume that the leakage inductance and mutual inductance of each phase winding are L ls and L ms , then the self-inductance and mutual inductance parameters are expressed as:

[0020]

[0021] Under the condition of stator turn-to-turn short circuit fault, the magnetic field generated by the PMSM fault circuit distorts the original circular rotating magnetic field in the motor air gap, destroying the electromagnetic balance of the system. Figure 1 The equivalent circuit can be obtained as shown in equation (6), and the stator turn-to-turn short-circuit fault model of the three-phase PMSM in the stationary natural coordinate system is:

[0022]

[0023] The subscript "s" and superscript "f" represent the stationary natural coordinate system and the turn-to-turn short-circuit fault state, respectively; and the voltage vector Current vector and the magnetic linkage vector Respectively expressed as:

[0024]

[0025]

[0026] The resistance matrix in formula (6) for:

[0027]

[0028] In formula (9), the inductance matrix and the permanent magnet flux vector They are:

[0029]

[0030] Among them, λ pm is the flux generated by the rotor permanent magnet, θ e is the electrical angle between the q-axis of the synchronous rotating coordinate system (i.e., the dq coordinate system) and the a-phase;

[0031] The fault phase voltage is provided by the healthy part and the short-circuited part of phase a, which can be expressed as:

[0032] u a =u ah +u af (13)

[0033] in,

[0034] u af =i f R f (14)

[0035] Substitute equation (13) into equation (6) and sort it out to obtain a new mathematical model of three-phase PMSM turn-to-turn short-circuit fault:

[0036]

[0037] Among them, the electrical angular velocity of the motor rotor is ω e , inductance L f and the back electromotive force vector e are expressed as:

[0038] L f =L af +M ahaf (16)

[0039] The construction process of the mathematical model of the stator turn-to-turn short circuit fault of the permanent magnet synchronous motor in the synchronous rotating coordinate system in step 1 is:

[0040] The Park transformation matrix based on constant amplitude transformation can be expressed as:

[0041]

[0042] The Park transformation matrix in equation (18) is modified to be:

[0043]

[0044] Its inverse matrix is:

[0045]

[0046] By transforming equation (15) using the modified Park transformation matrices (19) and (20), we can obtain the voltage equation of the PMSM in the dq coordinate system under turn-to-turn short-circuit fault:

[0047]

[0048] Among them, u d 、u q are the d-axis voltage and q-axis voltage respectively, i d 、i q are d-axis current and q-axis current respectively;

[0049] From equations (21) and (22), it can be seen that the short-circuit circulating current can be expressed as:

[0050] if =I f1 sin(θ e +φ f1 )+I f3 sin(3θ e +φ f3 ) (twenty three)

[0051] Among them, I f1 and φ f1 are the amplitude and initial phase angle of the fundamental wave of the short-circuit circulating current respectively; I f3 and φ f3 are the amplitude and initial phase angle of the third harmonic of the short-circuit circulating current respectively;

[0052] Substituting equation (23) into equations (21) and (22) and rearranging them, we can obtain the specific fault voltage equation:

[0053]

[0054] The fault characteristics in the stationary coordinate system in step 2 are: short-circuit turns ratio Δ and short-circuit resistance R f ; The fault characteristics in the synchronous rotating coordinate system are: the second harmonic components in the q-axis current and q-axis voltage.

[0055] The improved fault feature observer based on sliding film observation in step three is obtained by using the super-twisting algorithm (STA) to suppress the jitter degree of the observation signal on the basis of the traditional sliding mode fault feature observer, and applying the hyperbolic tangent switching function to smooth the observation signal.

[0056] In step 4, the system converges to the origin along the spiral trajectory within a finite time. The basic structure of the improved fault feature observer based on synovial film observation in step 3 is expressed as:

[0057]

[0058] where x 1 and x 2 represents the state variable, k 1 and k 2 represents the super-twisted sliding mode gain, where k 1 >0 and k 2 >0,ρ 1 and ρ 2 is the disturbance term;

[0059] When δ 1 When is large enough, the disturbance term is globally bounded and satisfies the following inequality:

[0060]

[0061] If the sliding mode gain k 1 and k 2 If equation (27) is satisfied, the sliding mode system can remain stable and converge to the sliding mode surface within a finite time;

[0062]

[0063] where δ 1 Can be any constant;

[0064] By improving the basic form of the superhelix algorithm, we can obtain:

[0065]

[0066] The estimated αβ axis current is taken as the state variable and x 2 Use x 1 To express, and and Substitute x 1 , the current equation of the sliding mode observer based on the improved super spiral algorithm can be constructed as:

[0067]

[0068] A smoother tanh(x) hyperbolic tangent function is introduced. The expression of the tanh(x) hyperbolic tangent function is shown in Equation (31). The tanh(x) function is bounded by ±1 and is continuous everywhere. The function boundary layer can be adjusted by the gain parameter c.

[0069]

[0070] Comparing (30) and (29), the disturbance term can be separated from the observer equation, and the expression is shown in (32):

[0071]

[0072] Substituting equation (30) for the current estimation error equation:

[0073]

[0074] When the system converges stably on the sliding surface, the back electromotive force observation can be equivalently expressed by equation (34):

[0075]

[0076] In order to meet the requirements of adaptive control gain to meet the wide speed requirements, the parameters are designed as:

[0077]

[0078] Where f(ω)=ω+abω , (0<α, 0≤b≤1), a and b are constant parameters. According to the motor speed range, adjust the growth rate of f(ω); f(ω) 3 / 2 、f(ω) 3 are bounded, satisfying 1≤f(ω) 3 / 2 ≤(ω+a bω ) 3 / 2 and 1≤f(ω) 3 ≤(ω+a bω ) 3 ;

[0079]

[0080] The low-pass filter shown in equation (36) outputs the back electromotive force observation value after filtering.

[0081] The derivation process of the decoupling constraint equation between the fault severity parameters in step 4 is:

[0082] Assume that the voltage equation of the motor with inter-turn short-circuit fault in the two-phase stationary coordinate system is:

[0083]

[0084] Estimated value of back electromotive force when a short-turn fault occurs α It includes the actual back EMF of the motor and the additional voltage component caused by the fault, as shown in equation (38):

[0085]

[0086] The improved fault feature observer is used to separate the fault feature quantity as shown in formula (39);

[0087]

[0088] The short-circuit circuit voltage equation of the motor with turn-to-turn short-circuit fault is transformed into the form shown in equation (40):

[0089] (R f +μR s +jω e μ 2 L s )i f =μ(Z h i α -ω e λ pm cosθ e ) (40)

[0090] μR s and ω e μ 2 L sIgnore, so formula (40) is simplified to the following form:

[0091] R f i f =μ(Z h i α -ω e λ pm cosθ e ) (41)

[0092] Multiply both sides of the equation (41) by available:

[0093]

[0094] According to formula (42), we can get:

[0095]

[0096] Substituting equation (39) into equation (43), we can get the short-circuit resistance R f and the short-circuit turns ratio μ form the fault parameter decoupling constraint equation, which is expressed as follows:

[0097] R f =k f μ 2 (44)

[0098] Among them, k f The definition is as follows:

[0099]

[0100] The construction process of the fault motor state space model with severity parameter decoupling in step 4 is as follows:

[0101] Transforming the faulty motor model in the two-phase stationary coordinate system yields:

[0102]

[0103] Further simplifying formula (46) yields:

[0104]

[0105] In formula (47), the specific elements of matrix C and matrix G are as follows:

[0106]

[0107] In order to make the equation more in line with the needs of extended Carr filtering recursion, the differential terms in the equation are processed independently through matrix operations and obtained:

[0108]

[0109] Among them, the matrix C 3 for:

[0110]

[0111] According to formula (51), the fault parameter identification system based on EKF is constructed. Substituting the decoupling constraint (44) into the standard state space model for decoupling the fault parameters is obtained as shown in formula (52):

[0112]

[0113] in:

[0114]

[0115] Differentiating the observation equation in equation (54) yields its Jacobian matrix:

[0116]

[0117] The system state transfer matrix is ​​obtained from formula (54):

[0118]

[0119] The process of online identification of the dynamic decoupling of the fault severity parameter in step 5 is as follows:

[0120] The voltage and current are collected to obtain the real-time signal of the motor operation. The collected voltage and current data are used by the improved sliding film observer to estimate the back electromotive force parameters and calculate the fault characteristic quantity. The fault characteristic quantity is compared with the predetermined threshold value to preliminarily determine whether a fault occurs.

[0121] If it is determined that a turn-to-turn short circuit fault has occurred, the coefficient k is calculated. f , forming a short-circuit turns ratio μ and a short-circuit resistance R f When the fault characteristic value is greater than the threshold, the extended Kalman filter algorithm is started to identify the fault severity parameters; the extended Kalman filter algorithm is triggered only after the severity deterioration is detected;

[0122] Determine whether the fault parameter identified by the extended Kalman filter exceeds the allowable range. If the parameter value does not exceed the threshold, the system returns to the monitoring state, continues to update the threshold and observes the system operation status; if the parameter value exceeds the set threshold, shut down for maintenance or make the control system enter the fault-tolerant control stage.

[0123] Compared with the prior art, the present invention has the following beneficial effects:

[0124] 1. The present invention can utilize the permanent magnet synchronous motor (PMSM) stator turn-to-turn short-circuit fault severity parameter decoupling to identify the PMSM stator turn-to-turn short-circuit fault under different motor operating conditions and improve the accuracy of detection.

[0125] 2. The present invention can better monitor the state of the permanent magnet synchronous motor (PMSM) and diagnose faults, and effectively improve the operating reliability and fault-tolerant control capability of the motor system. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] Figure 1 It is an overall flow chart of a PMSM stator turn-to-turn short-circuit fault severity parameter decoupling identification method according to the present invention;

[0127] Figure 2 is an equivalent circuit diagram of a stator turn-to-turn short circuit fault of the permanent magnet synchronous motor according to the present invention;

[0128] Figure 3 300rpm half-load experimental waveform diagram of the conventional synovial observer and the improved observer, wherein (a) is the conventional synovial observer experimental waveform, and (b) is the improved observer experimental waveform;

[0129] Figure 4 It is the observation result of the turn-to-turn short-circuit fault characteristic by the improved fault characteristic observer under 300rpm half load of the present invention;

[0130] Figure 5 300rpm half-load steady-state fault severity parameter identification result diagram of the present invention, wherein (a) is the short-circuit turns ratio μ identification result, (b) is the short-circuit resistance R f Identification results;

[0131] Figure 6 300rpm half-load dynamic change fault severity parameter identification result diagram of the present invention, wherein (a) is the short-circuit turns ratio μ identification result, (b) is the short-circuit resistance Rf identification result. DETAILED DESCRIPTION

[0132] The present invention will be described in detail below in conjunction with the accompanying drawings. Figure 1-6 As shown;

[0133] The equivalent circuit of a three-phase PMSM under stator turn-to-turn short-circuit fault is as follows: Figure 2 As shown. Each phase of the motor contains resistance R, self-inductance L, mutual inductance M and back electromotive force e. f is the short-circuit resistance, which reflects the degree of deterioration of the winding insulation. Taking the fault of phase A as an example, the short-circuit resistance short-circuits part of the winding of phase A to form a fault circuit, and phase A is divided into healthy winding a h and the fault winding a fTwo parts, the current i flowing through the short-circuit resistor f It is called short circuit current.

[0134] The short-circuit turns ratio Δ is introduced to indicate the proportion of the faulty winding in the entire faulty phase winding:

[0135]

[0136] Among them, N f and N s They are the number of turns of the short-circuited part winding and the total number of turns of the faulty phase winding respectively.

[0137] The motor phase resistance in a healthy state is R s , the inductance and back electromotive force of phase a are L a and e a The mutual inductance between the three phases is M ab 、M bc 、M ca , Figure 1 The PMSM resistance parameters, inductance parameters and back electromotive force under the medium fault state can be expressed as:

[0138]

[0139] Among them, R ah and R af are the resistance of the healthy part and the short-circuited part of the fault phase winding, L ah and L af are the self-inductance of the healthy part and the short-circuited part of the fault phase winding, M ahaf is the mutual inductance between the healthy part and the short-circuited part of the fault phase winding, M ahb 、M ahc are the mutual inductances between the healthy part of the fault phase winding and the b and c phase windings, M afb 、M afc are the mutual inductance between the short-circuited part of the fault phase winding and the b and c phase windings, e ah and e af They are the back electromotive force of the healthy part and the short-circuited part of the fault phase winding respectively.

[0140] For the surface-mount PMSM studied in this invention, the leakage inductance of each phase winding and the mutual inductance of each phase winding are L ls and L ms , the self-inductance and mutual inductance parameters can be further expressed as:

[0141]

[0142] Under the condition of stator turn-to-turn short circuit fault, the magnetic field generated by the PMSM fault circuit distorts the original circular rotating magnetic field in the motor air gap, destroying the electromagnetic balance of the system. Figure 1 The equivalent circuit can be obtained as shown in equation (6) for the three-phase PMSM stator turn-to-turn short-circuit fault model in a stationary natural coordinate system:

[0143]

[0144] The subscript "s" and superscript "f" represent the stationary natural coordinate system and the turn-to-turn short-circuit fault state, respectively. Current vector and magnetic linkage vector Respectively expressed as:

[0145]

[0146] The resistance matrix in formula (6) for:

[0147]

[0148] In formula (9), the inductance matrix and the permanent magnet flux vector They are:

[0149]

[0150] Among them, λ pm is the flux generated by the rotor permanent magnet, θ e It is the electrical angle between the q-axis of the synchronous rotating coordinate system (ie, the dq coordinate system) and the a-phase.

[0151] The fault phase voltage is provided by the healthy part and the short-circuited part of phase a, which can be expressed as:

[0152] u a =u ah +u af (13)

[0153] in,

[0154] u af =i f R f (14)

[0155] Substitute equation (13) into equation (6) and sort it out to obtain a new mathematical model of three-phase PMSM turn-to-turn short-circuit fault:

[0156]

[0157] Among them, the electrical angular velocity of the motor rotor is ω e , inductance L f and the back electromotive force vector e are expressed as:

[0158] Lf =L af +M ahaf (16)

[0159] From formula (15), it can be seen that the PMSM can still run for a period of time and have a certain torque output capacity under the inter-turn short-circuit fault. The magnitude of its short-circuit circulating current is related to the short-circuit turn ratio (Δ), short-circuit resistance (R f ) is closely related to the motor operating conditions.

[0160] The synchronous rotating coordinate system used in the present invention is as follows: Figure 3 As shown, the motor rotor is at zero position (i.e., electrical angle θ e =0), the q axis coincides with the a phase coordinate axis.

[0161] The Park transformation matrix based on constant amplitude transformation can be expressed as:

[0162]

[0163] It can be seen from equation (15) that the voltage equation related to the short-circuit circulating current is added to the PMSM turn-to-turn short-circuit fault model. Therefore, it is necessary to improve the Park transformation matrix in equation (18) to meet the requirements of coordinate transformation under fault conditions. The modified Park transformation matrix is:

[0164]

[0165] Its inverse matrix is:

[0166]

[0167] Take the surface mounted PMSM studied in this invention as an example (L d =L q =L s ), using the modified Park transformation matrix (19) and (20) to transform equation (15), the voltage equation of the PMSM in the dq coordinate system under turn-to-turn short-circuit fault can be obtained:

[0168]

[0169] Among them, u d 、u q are the d-axis voltage and q-axis voltage respectively, i d 、i q are the d-axis current and the q-axis current, respectively. From equations (21) and (22), we can see that compared with the motor dq voltage equation in the healthy state, the voltage equation under the turn-to-turn short-circuit fault has a new addition related to the short-circuit circulating current i fRelated coupling terms. Since the three-phase winding structure of the motor is no longer symmetrical under the inter-turn short-circuit fault, there are obvious third harmonics in the reverse electromotive force of each phase abc, which in turn causes the third harmonics in the short-circuit circulating current. Ignoring the higher harmonics with smaller amplitudes, the short-circuit circulating current can be expressed as:

[0170] i f =I f1 sin(θ e +φ f1 )+I f3 sin(3θ e +φ f3 ) (twenty three)

[0171] Among them, I f1 and φ f1 are the amplitude and initial phase angle of the fundamental wave of the short-circuit circulating current respectively; I f3 and φ f3 are the amplitude and initial phase angle of the third harmonic of the short-circuit circulating current respectively. Substituting equation (23) into equations (21) and (22) and rearranging them, a more specific fault voltage equation can be obtained:

[0172]

[0173] From equations (24) and (25), it can be seen that after the turn-to-turn short circuit fault occurs, additional fault information appears in the motor dq voltage, including DC components and second and fourth harmonics. f The fundamental component affects the amplitude of the second and fourth harmonics in the dq voltage. f The fundamental component and the third harmonic component have a common influence. The fault information introduced by the inter-turn short circuit in the dq voltage is not only related to the motor speed (ω e ) and the motor's own parameters (L s and R af ) and is also affected by the severity of the turn-to-turn short-circuit fault (Δ, I f1 ,I f3 ,φ f1 and φ f3 ). When the fault severity is low, the DC component offset in the dq voltage is not obvious, while the second harmonic component is obtained by Park change of the fundamental voltage negative sequence component and the third harmonic voltage positive sequence component, and its change is more obvious. It is more reliable to use the second harmonic of the dq voltage for fault diagnosis.

[0174] The research object of the present invention is to use i d=0 controlled surface-mount PMSM, the second harmonic component in the q-axis current and q-axis voltage is selected as the turn-to-turn short-circuit fault characteristic. However, the harmonic content in the current and voltage is not only affected by the turn-to-turn short-circuit fault, but also by the motor operating conditions. The moment the operating conditions change, accompanied by the closed-loop control adjustment process, the harmonic content in the current and voltage (including the turn-to-turn short-circuit fault characteristic harmonics) will change irregularly, affecting the diagnosis of the turn-to-turn short-circuit fault.

[0175] In order to solve the problem that the fault feature observation accuracy of traditional sliding mode observers is often reduced due to output signal jitter in applications, the present invention combines the superhelical algorithm and the hyperbolic tangent nonlinear saturation function to improve the observer. The superhelical algorithm significantly weakens the high-frequency ripple component caused by jitter by introducing high-order dynamic compensation, while the hyperbolic tangent saturation function can achieve smoother and more accurate fault feature observation. In order to ensure the stability of the improved sliding mode observer, the convergence of the observer is theoretically proved based on the Lyapunov stability theory, verifying its stability and reliability in dynamic observation.

[0176] The core of sliding mode variable structure control is to switch the system structure dynamically over time. In sliding mode control, the switching function drives the system state to change between different control units to achieve nonlinear control.

[0177] The state variable u is affected by the sliding surface function s(x). + (x) and u - (x) changes alternately, reflecting the dynamic adjustment characteristics of the system structure. The design process of sliding mode control usually includes the following steps: first, construct the sliding surface according to the reference state equation; then, design a sliding mode control law that meets the system performance requirements, so that the system state can enter the sliding surface within a finite time, and finally converge to the target point along the sliding surface trajectory, achieving stable and robust control of the system.

[0178] Assume that the state equation of the nonlinear control system is:

[0179]

[0180] In formula (58), x is the system state variable, x∈R n ; u is the control input variable, u∈R n .

[0181] Assume that there is a sliding membrane surface in the state space as defined in equation (59):

[0182] s(x)=s(x 1 ,x 2 ,x 3 …x n-1 ,x n )=0 (59)

[0183] The sliding surface divides the motion forms of the state variables in the state space into three typical cases: a normal point (such as point A), a starting point (such as point B), and an end point (such as point C).

[0184] Usually, the point and the starting point will cause the system state to deviate from the sliding surface, making it difficult to converge. Only the end point can ensure that the system state gradually approaches and eventually converges to the sliding surface. If all points in a certain area meet the conditions of the end point, the system state will eventually enter the sliding surface. This area is called the "sliding zone", and the system state can reach the sliding surface within a limited time in this area and maintain "sliding motion".

[0185] The system is switched up and down on the sliding surface through the control function, that is:

[0186]

[0187] Where u + (x, t) ≠ u - (x, t), and they are all continuous functions.

[0188] In order to ensure that the moving point of the system can reach and remain on the sliding surface, the accessibility condition and stability condition of the sliding mode need to be met. When s(x)>0, the system state moves in the negative direction to approach the sliding surface; and when s(x)<0, the system state moves in the positive direction to approach the sliding surface. Its mathematical expression can be described as:

[0189]

[0190] Formula (61) is the necessary and sufficient condition for the existence of sliding mode state, which can be simplified as: It aims to ensure that the system gradually stabilizes at the equilibrium point after reaching the sliding surface, thereby achieving the expected dynamic control goal.

[0191] Stability: In sliding mode control, in order to ensure that the system state can slide stably on the sliding surface, the stability condition needs to be met. When the system state point moves along the sliding surface, the sliding mode of the system is required to have asymptotic stability. The Lyapunov function shown in equation (62) is constructed for verification.

[0192]

[0193] After differentiating equation (62), we can get:

[0194]

[0195] Combined with the accessibility condition, when it meets When , the Lyapunov function decreases monotonically, indicating that the sliding mode motion of the system gradually approaches the equilibrium point and finally converges to the sliding surface, which further indicates that the motion behavior of the system on the sliding surface depends only on the sliding surface parameters and has nothing to do with the dynamic characteristics of the original system. This characteristic gives the sliding mode control strong robustness to system parameter perturbations and external disturbances.

[0196] Based on the shortcomings of the traditional sliding mode fault feature observer, this paper proposes an improved fault feature observer, which uses the Super-Twisting Algorithm (STA) to suppress the jitter of the observation signal, and applies the hyperbolic tangent switching function to further smooth the observation signal and improve the accuracy and robustness of fault feature extraction. Through these optimization methods, the present invention aims to build a more efficient and stable fault feature observer, providing reliable support for the subsequent fault severity parameter decoupling identification.

[0197] The present invention adopts the super spiral algorithm to construct a second-order sliding mode observer, which is used to further improve the anti-interference ability of the system and the accuracy of fault feature extraction. The super spiral algorithm avoids the discontinuity caused by high-frequency switching in the first-order sliding mode by introducing a second-order control term into the dynamic characteristics of the sliding mode surface, and can suppress the sliding mode chattering without sacrificing the system's responsiveness. The system converges to the origin along the spiral trajectory in a finite time, and the basic structure can be expressed as:

[0198]

[0199] where x 1 and x 2 represents the state variable, k 1 and k 2 represents the super-twisted sliding mode gain, where k 1 >0 and k 2 >0,ρ 1 and ρ 2 is the disturbance term. 1 When is large enough, the disturbance term is globally bounded and satisfies the following inequality:

[0200]

[0201] If the sliding mode gain k 1 and k 2 If equation (28) is satisfied, the sliding mode system can remain stable and converge to the sliding surface within a finite time.

[0202]

[0203] where δ 1 Can be any constant.

[0204] Although the traditional superhelical algorithm can suppress chattering, it may not be able to quickly return to the sliding surface when the system deviates from the sliding surface due to disturbance. In order to solve this problem, additional linear terms and adaptive laws are introduced on the basis of the traditional algorithm. The basic form of the improved superhelical algorithm can be expressed as:

[0205]

[0206] The improved superhelical algorithm is applied to PMSM, and the estimated αβ axis current is used as the state variable with reference to the traditional SMO design. 2 Use x 1 To express, and and Substitute x 1 , the current equation of the sliding mode observer based on the improved super spiral algorithm can be constructed as:

[0207]

[0208] The traditional sign(x) function is prone to aggravate high-frequency jittering phenomenon and affect observation accuracy in practical applications due to its non-smooth switching characteristics. It is also insufficient in processing external noise and system disturbances, and is prone to amplify high-frequency noise and increase the instability of system signals. In order to overcome these problems, the present invention introduces a smoother tanh(x) hyperbolic tangent function to further enhance the observer's ability to suppress jittering. The expression of the tanh(x) hyperbolic tangent function is shown in formula (31). The tanh(x) function is bounded by ±1 and is continuous everywhere. The function boundary layer can be adjusted by the gain parameter c.

[0209]

[0210] The disturbance term can be separated from the observer equation as shown in (32):

[0211]

[0212] The current estimation error equation is obtained by subtracting the observer equation from the PMSM stator current equation:

[0213]

[0214] When the system converges stably on the sliding surface, the back EMF observable can be equivalently expressed by equation (34).

[0215]

[0216] The back-EMF observable output by the improved observer consists of three parts. The first term is similar to the traditional sliding film, which is related to the switching function and decreases as the system converges to the sliding film surface. The last two terms are the linear term and the continuous integral term related to the current error, respectively.

[0217] In addition, an adaptive control gain is proposed to meet the wide speed requirement. The parameters are designed as:

[0218]

[0219] Where f(ω)=ω+a bω , (0<a, 0≤b≤1), a and b are constant parameters. According to the motor speed range, adjust the growth rate of f(ω). f(ω) 3 / 2 、f(ω) 3 are bounded, satisfying 1≤f(ω) 3 / 2 ≤(ω+a bω ) 3 / 2 and 1≤f(ω) 3 ≤(ω+a bω ) 3 .

[0220]

[0221] Equation (34) outputs the back electromotive force observation value after filtering by a low-pass filter. Under the inter-turn short-circuit fault state, the two back electromotive force observation results are calculated by the formula (36) to extract the fault characteristic observation quantity composed of the short-circuit turn ratio and the short-circuit current, which provides the input quantity containing fault information for the subsequent fault severity parameter identification.

[0222] The present invention derives the decoupling constraint equations between parameters by analyzing the constraint relationship between fault severity parameters, providing a theoretical basis for solving the parameter coupling problem. In order to further improve the identification accuracy, the fault feature observation results are used as the input of the model, and a dynamic decoupling online identification method is constructed in combination with the extended Kalman filter algorithm. The EKF algorithm can not only effectively filter out noise interference through recursive estimation of system state variables, but also dynamically correct and accurately decouple fault severity parameters, providing reliable protection for real-time fault diagnosis of the system.

[0223] According to mathematical modeling, the voltage equation of the motor with stator interturn short circuit fault in the two-phase stationary coordinate system is:

[0224]

[0225] From the analysis of formula (37), it can be seen that the short-turn fault will occur at V α The additional fault component is introduced, and V β There is no additional component introduced by the fault. Compared with the healthy state, the short-turn fault causes E α Decreases, while E βunchanged, so this additional component is the key to the decoupling identification of severity parameters. As shown in formula (38), the estimated back electromotive force value E when a short-turn fault occurs is α Contains the actual back EMF of the motor and additional voltage components caused by faults.

[0226]

[0227] The improved fault feature observer is used to separate the fault feature quantity as shown in formula (39).

[0228]

[0229] The short-circuit circuit voltage equation of the motor with turn-to-turn short-circuit fault is transformed into the form shown in equation (40):

[0230] (R f +μR s +jω e μ 2 L s )i f =μ(Z h i α -ω e λ pm cosθ e ) (40)

[0231] The stator turn-to-turn short-circuit fault of a permanent magnet synchronous motor is a gradual fault, which is often developed from the deterioration of the turn-to-turn insulation. Therefore, in the early stage of the fault, the short-circuit turn ratio μ is small and the short-circuit resistance R f In actual engineering situations, the motor electrical angular velocity ω e Usually in the lower range, and the motor stator inductance is usually several orders of magnitude lower than the resistance, so it is similar to R f In comparison, μR s and ω e μ 2 L s Ignore it, so simplify it to the following form:

[0232] R f i f =μ(Z h i α -ω e λ pm cosθ e ) (41)

[0233] Multiply both sides of the equation (41) by available:

[0234]

[0235] According to formula (42), we can get:

[0236]

[0237] Substituting equation (39) into equation (43), we can get the short-circuit resistance R f and the short-circuit turns ratio μ form the fault parameter decoupling constraint equation, which is expressed as follows:

[0238] R f =k f μ 2 (44)

[0239] Among them, k f The definition is as follows:

[0240]

[0241] In the research of parameter decoupling identification algorithm for turn-to-turn short-circuit fault, constructing a reasonable state space model is a key link. The state space model needs to contain the parameters to be estimated, but the existing mathematical model of the faulty motor does not decouple and separate them, and cannot be directly applied to the extended Kalman parameter identification algorithm. Therefore, it is necessary to establish a state space model that can adapt to the recursive framework of the extended Kalman filter. Transforming the faulty motor model in the two-phase stationary coordinate system yields:

[0242]

[0243] Further simplifying formula (46) yields:

[0244]

[0245] In formula (47), the specific elements of matrix C and matrix G are as follows:

[0246]

[0247] In order to make the equation more consistent with the requirements of extended Carr filtering recursion, as shown in equation (50), the differential terms in the equation are processed independently through matrix operations:

[0248]

[0249] Among them, the matrix C 3 for:

[0250]

[0251] According to formula (51), the EKF-based fault parameter identification system is constructed. Substituting the decoupling constraint (44) into the standard state space model for decoupling the fault parameters as shown in formula (52), the state variables are defined as follows:.

[0252]

[0253] in:

[0254]

[0255] In formula (52), in order to independently identify the fault parameter μ, the state space model of the original system is expanded and reconstructed using system enhancement technology. At the same time, in order to avoid the coupling terms that are difficult to separate in the model by directly taking the short-circuit turns ratio μ as the state variable, It is incorporated into the system state space model as an additional state variable and recursive estimation is achieved with the help of Kalman filter.

[0256] Differentiating the observation equation in equation (52) yields its Jacobian matrix:

[0257]

[0258] The system state transfer matrix is ​​obtained from formula (54):

[0259]

[0260] Based on equations (52) to (57), the Kalman filter algorithm is applied to embed the parameters to be identified into the state space model, and the prediction results are continuously corrected by using the recursive time update and measurement update process combined with real-time measurement data to achieve dynamic decoupling online identification of fault parameters. The above process makes full use of the robustness of the extended Kalman filter algorithm to noise and the adaptability of the dynamic system, and can effectively deal with the nonlinear characteristics and noise interference in parameter identification.

[0261] The present invention acquires real-time signals of motor operation by collecting voltage and current to provide basic data for subsequent calculations. The collected voltage and current data are used to estimate the back electromotive force parameters and calculate the fault characteristic quantity through the improved sliding film observer, which contains important information required for subsequent fault parameter identification. Then, the fault characteristic quantity is compared with the predetermined threshold to preliminarily determine whether a fault has occurred. If it is determined that a turn-to-turn short circuit fault has occurred, the coefficient k is further calculated. f , forming a short-circuit turns ratio μ and a short-circuit resistance R f Through the decoupling constraint, the two fault parameters form a parameter bundle, one of which can be calculated from the other parameter in combination with the decoupling constraint. Based on this, the state space equation is equivalent to containing only one parameter to be estimated, and the fault parameter is regarded as a newly added state variable for estimation through system enhancement technology.

[0262] When the fault characteristic value is greater than the threshold, the extended Kalman filter algorithm is started to identify the fault severity parameters. In addition, a threshold update link is set up to trigger the estimation process again whenever the fault develops to a higher severity. In the entire identification process, only the fault characteristic quantity observation process runs continuously, and the Kalman filter link with higher computational requirements is triggered only after the severity deterioration is detected, which effectively reduces the computing pressure of the processor.

[0263] Next, the system will determine whether the fault parameter identified by the extended Kalman filter exceeds the allowable range. If the parameter value does not exceed the threshold, the system returns to the monitoring state, continues to update the threshold and observes the system operation status; if the parameter value exceeds the set threshold, the system will be shut down for maintenance or the control system will enter the fault-tolerant control stage. Fault-tolerant control is the last step of the entire process. By adjusting the operating strategy (such as reducing the load, changing the control parameters, etc.), the normal operation of the motor is protected to prevent the fault from further deteriorating.

[0264] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that may be made to certain parts thereof by technicians in this technical field all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A PMSM stator turn-to-turn short-circuit fault severity parameter decoupling identification method, characterized in that: The method comprises the following steps: Step 1, a mathematical model of the stator turn-to-turn short circuit fault of the permanent magnet synchronous motor in the stationary coordinate system and the synchronous rotating coordinate system is established; Step 2: Analyze the corresponding relationship between the fault parameters in the stationary coordinate system and the fault parameters in the synchronous rotating coordinate system and the fault severity, and determine the fault characteristics in the stationary coordinate system and the synchronous rotating coordinate system respectively; Step 3, using an improved fault feature observer based on synovial film observation to observe the fault features without distortion and extract the observation results; Step 4: Analyze the constraint relationship between fault severity parameters, derive the decoupling constraint equation between fault severity parameters, and establish a fault motor state space model with severity parameter decoupling; Step 5: Taking the observation results of fault characteristics as input, the extended Kalman filter algorithm is introduced to perform online identification of the dynamic decoupling of fault severity parameters.

2. A PMSM stator turn-to-turn short-circuit fault severity parameter decoupling identification method according to claim 1, characterized in that: The process of constructing the mathematical model of the stator turn-to-turn short-circuit fault of the permanent magnet synchronous motor in the stationary coordinate system in step 1 is as follows: The equivalent circuit of the stator turn-to-turn short-circuit fault of the permanent magnet synchronous motor is constructed, and the short-circuit turns ratio Δ is introduced to represent the proportion of the faulty winding in the entire faulty phase winding: Among them, N f and N s They are the number of turns of the short-circuited part winding and the total number of turns of the fault phase winding respectively; Assume that the motor phase resistance in a healthy state is R s , the inductance and back electromotive force of phase a are L a and e a The mutual inductance between the three phases is M ab 、M bc 、M ca , then the resistance parameters, inductance parameters and back electromotive force of PMSM under fault condition can be expressed as: Among them, R ah and R af are the resistance of the healthy part and the short-circuited part of the fault phase winding, L ah and L af are the self-inductance of the healthy part and the short-circuited part of the fault phase winding, M ahaf is the mutual inductance between the healthy part and the short-circuited part of the fault phase winding, M ahb 、M ahc are the mutual inductances between the healthy part of the fault phase winding and the b and c phase windings, M afb 、M afc are the mutual inductance between the short-circuited part of the fault phase winding and the b and c phase windings, e ah and e af are the back electromotive force of the healthy part and the short-circuited part of the fault phase winding respectively; Assume that the leakage inductance and mutual inductance of each phase winding are L ls and L ms , then the self-inductance and mutual inductance parameters are expressed as: Under the stator turn-to-turn short-circuit fault state, the magnetic field generated by the PMSM fault circuit distorts the original circular rotating magnetic field in the motor air gap, destroying the electromagnetic balance of the system. By analyzing the equivalent circuit in Figure 1, we can obtain the equation (6), and the three-phase PMSM stator turn-to-turn short-circuit fault model in the stationary natural coordinate system is: The subscript "s" and superscript "f" represent the stationary natural coordinate system and the turn-to-turn short-circuit fault state, respectively; and the voltage vector Current vector and magnetic linkage vector Respectively expressed as: The resistance matrix in formula (6) for: In formula (9), the inductance matrix and the permanent magnet flux vector They are: Among them, λ pm is the flux generated by the rotor permanent magnet, θ e is the electrical angle between the q-axis of the synchronous rotating coordinate system (i.e., the dq coordinate system) and the a-phase; The fault phase voltage is provided by the healthy part and the short-circuited part of phase a, which can be expressed as: in a =in ah +in af (13) in, u af =i f R f (14) Substitute equation (13) into equation (6) and sort it out to obtain a new mathematical model of three-phase PMSM turn-to-turn short-circuit fault: Among them, the electrical angular velocity of the motor rotor is ω e , inductance L f and the back electromotive force vector e are expressed as: L f =L af +M ahaf (16) 3. The method for decoupling and identifying the severity parameters of a PMSM stator turn-to-turn short-circuit fault according to claim 1 is characterized in that: The construction process of the mathematical model of the stator turn-to-turn short-circuit fault of the permanent magnet synchronous motor in the synchronous rotating coordinate system in step 1 is: The Park transformation matrix based on constant amplitude transformation can be expressed as: The Park transformation matrix in equation (18) is modified to be: Its inverse matrix is: By transforming equation (15) using the modified Park transformation matrices (19) and (20), we can obtain the voltage equation of the PMSM in the dq coordinate system under turn-to-turn short-circuit fault: Among them, u d 、u q are the d-axis voltage and q-axis voltage respectively, i d 、i q are d-axis current and q-axis current respectively; From equations (21) and (22), it can be seen that the short-circuit circulating current can be expressed as: I f =I f1 sin(θ e +φ f1 )+I f3 sin(3θ e +φ f3 ) (23) Among them, I f1 and φ f1 are the amplitude and initial phase angle of the fundamental wave of the short-circuit circulating current respectively; I f3 and φ f3 are the amplitude and initial phase angle of the third harmonic of the short-circuit circulating current respectively; Substituting equation (23) into equations (21) and (22) and rearranging them, we can obtain the specific fault voltage equation:

4. The method for decoupling and identifying the severity parameters of a PMSM stator turn-to-turn short-circuit fault according to claim 1, characterized in that: The fault characteristics in the stationary coordinate system in step 2 are: short-circuit turns ratio Δ and short-circuit resistance R f ; The fault characteristics in the synchronous rotating coordinate system are: the second harmonic components in the q-axis current and q-axis voltage.

5. The method for decoupling and identifying the severity parameters of a PMSM stator turn-to-turn short-circuit fault according to claim 1, characterized in that: The improved fault feature observer based on sliding film observation in step three is obtained by using a super spiral algorithm to suppress the chattering degree of the observation signal on the basis of the traditional sliding mode fault feature observer, and applying a hyperbolic tangent switching function to smooth the observation signal.

6. A PMSM stator turn-to-turn short-circuit fault severity parameter decoupling identification method according to claim 1, characterized in that: In step 4, the system converges to the origin along the spiral trajectory within a finite time. The basic structure of the improved fault feature observer based on synovial film observation in step 3 is expressed as: Where x1 and x2 represent state variables, k1 and k2 represent super-twisted sliding mode gains, where k1>0 and k2>0, ρ1 and ρ2 are disturbance terms; When δ1 is large enough, the disturbance term is globally bounded and satisfies the following inequality: If the sliding mode gains k1 and k2 satisfy equation (28), the sliding mode system can remain stable and converge to the sliding mode surface in a finite time; Where δ1 can be any constant; By improving the basic form of the superhelix algorithm, we can obtain: The estimated αβ axis current is used as the state variable, x2 is expressed as x1, and and Substituting x1, the current equation of the sliding mode observer based on the improved super-helical algorithm can be constructed as: A smoother tanh(x) hyperbolic tangent function is introduced. The expression of the tanh(x) hyperbolic tangent function is shown in Equation (31). The tanh(x) function is bounded by ±1 and is continuous everywhere. The function boundary layer can be adjusted by the gain parameter c. Comparing (30) and (29), the disturbance term can be separated from the observer equation, and the expression is shown in (32): The current estimation error equation is obtained from equation (30): When the system converges stably on the sliding surface, the back electromotive force observation can be equivalently expressed by equation (34): In order to meet the requirements of adaptive control gain to meet the wide speed requirements, the parameters are designed as: Where f(ω)=ω+a bω , (0<a, 0≤b≤1), a and b are constant parameters. According to the motor speed range, adjust the growth rate of f(ω); f(ω) 3 / 2 、f(ω) 3 are bounded, satisfying 1≤f(ω) 3 / 2 ≤(ω+a bω ) 3 / 2 and 1≤f(ω) 3 ≤(ω+a bω ) 3 ; Equation (34) outputs the back electromotive force observation value after being filtered by a low-pass filter.

7. A PMSM stator turn-to-turn short-circuit fault severity parameter decoupling identification method according to claim 1, characterized in that: The derivation process of the decoupling constraint equation between the fault severity parameters in step 4 is: The voltage equation of the motor with a short-circuit fault between sub-turns in a two-phase stationary coordinate system is assumed to be: Estimated value of back electromotive force when a short-turn fault occurs α It includes the actual back EMF of the motor and the additional voltage component caused by the fault, as shown in equation (38): The improved fault feature observer is used to separate the fault feature quantity as shown in formula (39); The short-circuit circuit voltage equation of the motor with turn-to-turn short-circuit fault is transformed into the form shown in equation (40): (R f +μR s +jω e m 2 L s )i f =μ(Z h I α -oh e l pm cosθ e ) (40) μR s and ω e μ 2 L s Ignore, so (41) is simplified to the following form: R f I f =μ(Z h I α -oh e l pm cosθ e ) (41) Multiply both sides of the equation (41) by available: According to formula (42), we can get: Substituting equation (39) into equation (43), we can get the short-circuit resistance R f and the short-circuit turns ratio μ form the fault parameter decoupling constraint equation, which is expressed as follows: R f =k f m 2 (44) Among them, k f The definition is as follows:

8. The method for decoupling and identifying the severity parameters of a PMSM stator turn-to-turn short-circuit fault according to claim 1, characterized in that: The construction process of the fault motor state space model with severity parameter decoupling in step 4 is as follows: Transforming the faulty motor model in the two-phase stationary coordinate system yields: Further simplifying formula (46) yields: In formula (49), the specific elements of matrix C and matrix G are as follows: In order to make the equation more in line with the needs of extended Carr filtering recursion, the differential terms in the equation are processed independently through matrix operations and obtained: Among them, the matrix C3 is: According to formula (51), the fault parameter identification system based on EKF is constructed. Substituting the decoupling constraint (44) into the standard state space model for decoupling the fault parameters is obtained as shown in formula (52): in: Differentiating the observation equation in equation (52) yields its Jacobian matrix: The system state transfer matrix is ​​obtained from formula (52):

9. A PMSM stator turn-to-turn short-circuit fault severity parameter decoupling identification method according to claim 1, characterized in that: The process of online identification of the dynamic decoupling of the fault severity parameter in step 5 is as follows: The voltage and current are collected to obtain the real-time signal of the motor operation. The collected voltage and current data are used by the improved sliding film observer to estimate the back electromotive force parameters and calculate the fault characteristic quantity. The fault characteristic quantity is compared with the predetermined threshold value to preliminarily determine whether a fault occurs. If it is determined that a turn-to-turn short circuit fault has occurred, the coefficient k is calculated. f , forming a short-circuit turns ratio μ and a short-circuit resistance R f When the fault characteristic value is greater than the threshold, the extended Kalman filter algorithm is started to identify the fault severity parameters; the extended Kalman filter algorithm is triggered only after the severity deterioration is detected; Determine whether the fault parameter identified by the extended Kalman filter exceeds the allowable range. If the parameter value does not exceed the threshold, the system returns to the monitoring state, continues to update the threshold and observes the system operation status; if the parameter value exceeds the set threshold, shut down for maintenance or make the control system enter the fault-tolerant control stage.

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