Coordinate transformation-based induction motor stator resistance identification method

Abstract

The invention discloses an induction motor stator resistance identification method based on coordinate transformation, and solves the problems of flux linkage and resistance parameter coupling and complex calculation in a traditional method. A resistance equation is constructed through the orthogonal relation between the stator flux linkage and the induced voltage, and the stator resistance is directly calculated by using the constraint condition that the inner product of the flux linkage and the voltage is zero in a steady state; the orthogonal relation is converted to a stator current synchronous rotating coordinate system, a flux linkage amplitude calculation module is designed in combination with instantaneous reactive power, the flux linkage amplitude is correlated through a reactive component of the current coordinate system, and resistance interference is avoided; and calculating a resistance estimation value based on the ratio of the voltage to the flux linkage component under the current coordinate system, and suppressing noise in combination with low-pass filtering. According to the method, through coordinate transformation and orthogonal decoupling, the coupling error of the flux linkage and the resistor is remarkably reduced, the calculation process is simplified, the dynamic response speed and the parameter robustness are improved, and a high-precision and low-complexity solution is provided for parameter identification of the induction motor.

Description

Technical Field

[0001] The present invention relates to the technical field of motor drive control, and in particular to a method for identifying the stator resistance of an induction motor based on coordinate transformation. Background Art

[0002] To meet the system requirements for online identification of induction motor parameters, traditional stator resistance identification methods typically rely on steady-state motor operating conditions or the injection of high-frequency signals for excitation. These methods suffer from poor real-time performance and identification accuracy that is significantly affected by temperature and magnetic saturation effects. Especially under dynamic operating conditions, changes in stator resistance can directly affect the decoupling performance of field-oriented control, leading to torque fluctuations and reduced efficiency. Existing methods often use adaptive observers or model-referenced adaptive schemes, but these algorithms are highly complex and sensitive to other motor parameters (such as inductance and rotor resistance), which can easily lead to parameter coupling errors and restrict the reliability of practical engineering applications.

[0003] The stator resistance identification method based on coordinate transformation constructs a mathematical model of the motor in a rotating coordinate system, transforming the time-varying resistance identification into a real-time solution of the voltage-current equation. This avoids the need for additional hardware sensors and reduces system costs. However, while improving integration, this method faces two key challenges: First, the coordinate transformation process requires accurate stator flux observations as input. The accuracy of the flux observer is affected by the positive feedback of the stator resistance error, resulting in convergence stability issues in the identification system. Second, the difference in parameter sensitivity between the voltage and current models under dynamic conditions introduces cross-coupling errors, causing significant fluctuations in the stator resistance identification results when subjected to sudden load changes or rapid speed changes, making it difficult to meet real-time tracking requirements.

[0004] Traditional online stator resistance identification schemes typically use DC injection or least-squares parameter estimation. The former induces additional copper loss and torque ripple, while the latter requires a continuous excitation signal and is computationally intensive. Particularly under low-speed and light-load conditions, the reduced signal-to-noise ratio of the stator current leads to insufficient observation noise tolerance for traditional methods, severely impacting identification accuracy. Furthermore, resistance drift caused by temperature changes typically exhibits slow, time-varying characteristics, making it difficult for traditional dynamic identification algorithms to distinguish resistance changes from measurement noise, resulting in delayed or even divergent parameter updates.

[0005] Research on stator resistance identification methods based on coordinate transformation not only enables sensorless online resistance monitoring, effectively eliminating the cost and volume limitations of hardware testing, but also allows for deep integration with vector control systems. By designing a novel error decoupling observer and adaptive compensation mechanism, closed-loop identification of resistance parameters can be achieved while maintaining flux observation accuracy. This has important engineering value for improving the efficiency optimization capabilities and fault tolerance of induction motor drive systems, especially in applications requiring high reliability and robustness, such as electric vehicles and industrial servos. Summary of the Invention

[0006] The present invention addresses the shortcomings of the prior art and provides a coordinate transformation-based method for identifying the stator resistance of an induction motor. This method avoids the effects of coupling with flux calculation during the identification process, improves the dynamic performance of the drive system, reduces computational complexity, and enhances the parameter robustness of the system.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] In a first aspect, the present invention provides a method for identifying the stator resistance of an induction motor based on coordinate transformation, the method comprising the following steps:

[0009] S1: The stator resistance calculation equation is constructed using the orthogonal relationship between the stator flux vector and the induced voltage.

[0010] S2: Convert the orthogonal relationship into a coordinate system that rotates synchronously with the stator current vector to perform coordinate transformation.

[0011] S3: Construct a stator flux amplitude calculation module including instantaneous reactive power.

[0012] S4: Calculate the estimated value of the stator resistance by the ratio of the voltage component and the flux component in the current coordinate system.

[0013] Furthermore, in step S1, the stator resistance calculation equation is constructed using the orthogonal relationship between the stator flux vector and the induced voltage:

[0014] First, the stator voltage equation of the induction motor in the αβ coordinate system is:

[0015]

[0016] where u s =[u sα ,u sβ ] T is the stator voltage vector, i s =[i sα ,i sβ ] T is the stator current vector, ψ s=[ψ sα ,ψ sβ ] T is the stator flux vector, r s is the stator resistance.

[0017] Rewriting the equation into the relationship between flux linkage and voltage is:

[0018]

[0019] Among them, the induced voltage vector is u i =u s -r s i s , reflecting the electromotive force generated by the change of magnetic field.

[0020] Under steady-state conditions, the stator flux vector moves at a synchronous angular velocity ω s Rotation, its expression is:

[0021]

[0022] where ψ sm is the flux amplitude, and θ0 is the initial phase angle.

[0023] Taking the derivative of the above equation with respect to time, we get the induced voltage equation:

[0024]

[0025] According to the steady-state expression, the expanded equation is:

[0026] u iα =-ω s ψ sβ

[0027] u iβ =ω s ψ sα

[0028] Calculate the inner product of magnetic flux and induced voltage:

[0029]

[0030] It can be seen from this that in steady state u i With ψ s Orthogonal (the inner product of the two is 0), where u i is ψ s The derivative of , whose direction leads the flux vector by 90° (determined by the complex factor j).

[0031] In the stationary coordinate system, u i =u s -r s i sSubstituting the orthogonality condition, we can obtain:

[0032]

[0033] After expansion, the stator resistance expression can be obtained as:

[0034]

[0035] Furthermore, in step S2, the orthogonal relationship is converted into a coordinate system that rotates synchronously with the stator current vector to perform coordinate transformation:

[0036] First, establish the stator current vector synchronously rotating xy coordinate system, which has the following characteristics:

[0037] 1) With the stator current vector i s The real-time phase angle γ is the reference axis

[0038] 2) Define the x-axis and i s The vector directions coincide, and the y-axis is perpendicular to the x-axis to form an orthogonal coordinate system.

[0039] Secondly, coordinate transformation operation is performed, and the coordinate system conversion is realized using the rotation transformation matrix:

[0040]

[0041] Where f represents the voltage, current or flux vector, and αβ are the components of the stationary coordinate system.

[0042] Finally, the voltage equation in the xy coordinate system can be obtained as:

[0043]

[0044] The current equation is:

[0045]

[0046] Among them, the stator current vector satisfies i in the xy coordinate system sy =0,i sx =|i s |.

[0047] The magnetic flux equation is:

[0048]

[0049] The original orthogonal relationship is converted to the xy coordinate system equation:

[0050]

[0051] Furthermore, in step S3, a stator flux amplitude calculation module including instantaneous reactive power is constructed:

[0052] First, construct the dynamic equation of the motor as:

[0053]

[0054] Among them, r sr =r s +k r r r ,τ′ sr =σl s / (r s +k r r r ).

[0055] By multiplying the above formula by vector i s , and multiply both sides of the equation by r sr The influence of stator resistance on the calculation results can be eliminated, and the equation is:

[0056]

[0057] By calculating the above formula, take the z component of all terms and assume that the magnetic field direction ψ sd =|ψ s |,ψ sq =0, the stator flux calculation equation can be obtained by calculation:

[0058]

[0059] Furthermore, in step S4, the estimated value of the stator resistance is calculated by the ratio of the voltage component to the flux component in the current coordinate system:

[0060] First, in the current xy coordinate system, project all components onto the x-axis direction of the current coordinate system, and the calculation equation of the stator resistance can be obtained as:

[0061]

[0062] The stator flux equation is:

[0063]

[0064] The voltage component equation is:

[0065]

[0066] The induced voltage calculation equation is:

[0067]

[0068] Finally, the calculation equation of the induction motor stator resistance can be obtained as:

[0069]

[0070] Through this formula, the identification result is filtered by a low-pass filter, and the stator flux is calculated in a way that is independent of the stator resistance, so that the parameter value of the induction motor stator resistance can be accurately obtained.

[0071] The beneficial effects of the present invention are:

[0072] 1. The stator resistance calculation equation proposed in this invention is based on the orthogonal relationship between stator flux and induced voltage. By dynamically decoupling the flux into a synchronously rotating coordinate system through coordinate transformation, it effectively avoids the coupling problem between flux calculation and resistance parameters in traditional identification, significantly improving the identification accuracy of stator resistance and the dynamic response speed of the system.

[0073] 2. The instantaneous reactive power stator flux amplitude calculation module proposed in the present invention utilizes the direct correlation between reactive power and flux amplitude in the current coordinate system, eliminates the dependence of stator resistance on flux calculation, enhances the system's robustness to changes in motor parameters, and reduces the impact of parameter sensitivity on identification results.

[0074] 3. The voltage component to flux component ratio calculation and low-pass filtering method proposed in this invention directly solves the resistance estimation value through the projection component in the current coordinate system, which simplifies the computational complexity of the traditional iterative algorithm. At the same time, combined with filtering processing to suppress high-frequency noise interference, it further improves the stability and accuracy of stator resistance identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 1 is a vector diagram of stator resistance estimation of induction motor variables in different coordinate systems according to an embodiment of the present invention.

[0076] Figure 2 4 is a flow chart of an induction motor stator resistance estimator according to an embodiment of the present invention.

[0077] Figure 3 3 is a waveform diagram of the stator flux component in a stationary coordinate system according to an embodiment of the present invention.

[0078] Figure 4 3 is a waveform diagram of the stator flux amplitude in a stationary coordinate system according to an embodiment of the present invention.

[0079] Figure 5 1 is a diagram showing the angle of the rotating coordinate system and the angle of the stator flux vector of the stationary coordinate system according to an embodiment of the present invention.

[0080] Figure 6 4 is a waveform diagram of the stator angular frequency according to an embodiment of the present invention.

[0081] Figure 74 is a waveform diagram of stator resistance identification according to an embodiment of the present invention. Specific implementation plan

[0082] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0083] Example 1

[0084] Figure 1 It is a vector diagram of the stator resistance estimation of the induction motor variables in different coordinate systems. Figure 2 This is a flowchart of an induction motor stator resistance estimator according to an embodiment of the present invention. This embodiment proposes a method for identifying the stator resistance of an induction motor based on coordinate transformation, the method comprising the following steps:

[0085] S1: The stator resistance calculation equation is constructed using the orthogonal relationship between the stator flux vector and the induced voltage.

[0086] S2: Convert the orthogonal relationship into a coordinate system that rotates synchronously with the stator current vector to perform coordinate transformation.

[0087] S3: Construct a stator flux amplitude calculation module including instantaneous reactive power.

[0088] S4: Calculate the estimated value of the stator resistance by the ratio of the voltage component and the flux component in the current coordinate system.

[0089] 1. Use the orthogonal relationship between the stator flux vector and the induced voltage to construct the stator resistance calculation equation

[0090] First, the stator voltage equation of the induction motor in the αβ coordinate system is:

[0091]

[0092] where u s =[u sα ,u sβ ] T is the stator voltage vector, i s =[i sα ,i sβ ] T is the stator current vector, ψ s =[ψ sα ,ψ sβ ] T is the stator flux vector, r s is the stator resistance.

[0093] Rewriting the equation into the relationship between flux linkage and voltage is:

[0094]

[0095] Among them, the induced voltage vector is u i =u s -r s i s , reflecting the electromotive force generated by the change of magnetic field.

[0096] Under steady-state conditions, the stator flux vector moves at a synchronous angular velocity ω s Rotation, its expression is:

[0097]

[0098] where ψ sm is the flux amplitude, and θ0 is the initial phase angle.

[0099] Taking the derivative of the above equation with respect to time, we get the induced voltage equation:

[0100]

[0101] According to the steady-state expression, the expanded equation is:

[0102] u iα =-ω s ψ sβ

[0103] u iβ =ω s ψ sα

[0104] Calculate the inner product of magnetic flux and induced voltage:

[0105]

[0106] It can be seen from this that in steady state u i With ψ s Orthogonal (the inner product of the two is 0), where u i is ψ s The derivative of , whose direction leads the flux vector by 90° (determined by the complex factor j).

[0107] In the stationary coordinate system, u i =u s -r s i s Substituting the orthogonality condition, we can obtain:

[0108]

[0109] After expansion, the stator resistance expression can be obtained as:

[0110]

[0111] After verifying the orthogonal relationship between the stator flux vector and the induced voltage, it is necessary to convert the orthogonal relationship into a coordinate system that rotates synchronously with the stator current vector for coordinate transformation.

[0112] First, establish the stator current vector synchronously rotating xy coordinate system, which has the following characteristics:

[0113] 3) With the stator current vector i s The real-time phase angle γ is the reference axis

[0114] 4) Define the x-axis and i s The vector directions coincide, and the y-axis is perpendicular to the x-axis to form an orthogonal coordinate system.

[0115] Secondly, coordinate transformation operation is performed, and the coordinate system conversion is realized using the rotation transformation matrix:

[0116]

[0117] Where f represents the voltage, current or flux vector, and αβ are the components of the stationary coordinate system.

[0118] Finally, the voltage equation in the xy coordinate system can be obtained as:

[0119]

[0120] The current equation is:

[0121]

[0122] Among them, the stator current vector satisfies i in the xy coordinate system sy =0,i sx =|i s |.

[0123] The magnetic flux equation is:

[0124]

[0125] The original orthogonal relationship is converted to the xy coordinate system equation:

[0126]

[0127] Subsequent calculations will be performed in the new coordinate system.

[0128] 2. Calculate the stator flux amplitude using instantaneous reactive power

[0129] First, construct the dynamic equation of the motor as:

[0130]

[0131] Among them, r sr=r s +k r r r ,τ′ sr =σl s / (r s +k r r r ).

[0132] By multiplying the above formula by vector i s , and multiply both sides of the equation by r sr The influence of stator resistance on the calculation results can be eliminated, and the equation is:

[0133]

[0134] By calculating the above formula, take the z component of all terms and assume that the magnetic field direction ψ sd =|ψ s |,ψ sq =0, the stator flux calculation equation can be obtained by calculation:

[0135]

[0136] Through simulation, the induction motor is set to a given speed of 100 rpm. After stable operation, the components of the flux observation in the stationary coordinate system can be obtained as follows: Figure 3 As shown, the amplitude waveform of the stator flux is as follows Figure 4 As shown, it can be seen that the magnetic flux observation effect is in line with expectations and has a very good effect.

[0137] 3. Calculate the estimated value of stator resistance by the ratio of voltage component and flux component in the current coordinate system

[0138] Under the premise of accurate stator flux, in the current xy coordinate system, projecting all components onto the x-axis direction of the current coordinate system, the calculation equation of the stator resistance can be obtained as:

[0139]

[0140] The stator flux equation is:

[0141]

[0142] The voltage component equation is:

[0143]

[0144] The induced voltage calculation equation is:

[0145]

[0146] Finally, the calculation equation of the induction motor stator resistance can be obtained as:

[0147]

[0148] Through this formula, the identification result is filtered through a low-pass filter, and the stator flux calculation method that is independent of the stator resistance is adopted to accurately obtain the parameter value of the induction motor stator resistance.

[0149] Under the above operating conditions, the rotation angle of the xy coordinate system and the angle of the stator flux vector in the stationary coordinate system can be obtained by coordinate transformation as follows: Figure 5 As shown, the stator angular frequency waveform is as follows Figure 6 As shown, they are all in line with expectations, and by changing the initial value of the resistance before operation, under the conditions of 0Ω and 5.2Ω respectively, the resistance identification waveform after operation is as follows Figure 7 As shown in the figure, it can be seen that the stator resistance can quickly converge to the actual value after operation and be identified in real time. The identification result is in line with expectations.

Claims

1. A method for identifying the stator resistance of an induction motor based on coordinate transformation, comprising the following steps: S1: The stator resistance calculation equation is constructed using the orthogonal relationship between the stator flux vector and the induced voltage. S2: Convert the orthogonal relationship into a coordinate system that rotates synchronously with the stator current vector to perform coordinate transformation. S3: Construct a stator flux amplitude calculation module including instantaneous reactive power. S4: Calculate the estimated value of the stator resistance by the ratio of the voltage component and the flux component in the current coordinate system.

2. The control method according to claim 1, characterized in that: In step S1, the stator resistance calculation equation is constructed using the orthogonal relationship between the stator flux vector and the induced voltage: First, the stator voltage equation of the induction motor in the αβ coordinate system is: where u s =[u sα ,u sβ ] T is the stator voltage vector, i s =[i sα ,i sβ ] T is the stator current vector, ψ s =[ψ sα ,ψ sβ ] T is the stator flux vector, r s is the stator resistance. Rewriting the equation into the relationship between flux linkage and voltage is: Among them, the induced voltage vector is u i =u s -r s i s , reflecting the electromotive force generated by the change of magnetic field. Under steady-state conditions, the stator flux vector moves at a synchronous angular velocity ω s Rotation, its expression is: where ψ sm is the flux amplitude, and θ0 is the initial phase angle. Taking the derivative of the above equation with respect to time, we get the induced voltage equation: According to the steady-state expression, the expanded equation is: you iα =-ω s ψ sβ you iβ =ω s ψ sα Calculate the inner product of magnetic flux and induced voltage: It can be seen from this that in steady state u i With ψ s Orthogonal (the inner product of the two is 0), where u i is ψ s The derivative of , whose direction leads the flux vector by 90° (determined by the complex factor j). In the stationary coordinate system, u i =u s -r s i s Substituting the orthogonality condition, we can obtain: After expansion, the stator resistance expression can be obtained as:

3. The control method according to claim 1, wherein: In step S2, the orthogonal relationship is converted into a coordinate system that rotates synchronously with the stator current vector to perform coordinate transformation: First, establish the stator current vector synchronously rotating xy coordinate system, which has the following characteristics: 1) With the stator current vector i s The real-time phase angle γ is the reference axis 2) Define the x-axis and i s The vector directions coincide, and the y-axis is perpendicular to the x-axis to form an orthogonal coordinate system. Secondly, coordinate transformation operation is performed, and the coordinate system conversion is realized using the rotation transformation matrix: Where f represents the voltage, current or flux vector, and αβ are the components of the stationary coordinate system. Finally, the voltage equation in the xy coordinate system can be obtained as: The current equation is: Among them, the stator current vector satisfies i in the xy coordinate system sy =0,i sx =|i s |. The magnetic flux equation is: The original orthogonal relationship is converted to the xy coordinate system equation:

4. The control method according to claim 1, wherein: In step S3, a stator flux amplitude calculation module including instantaneous reactive power is constructed: First, construct the dynamic equation of the motor as: among them,r sr =r s +k r r r ,t′ sr =σl s / (r s +k r r r )。 By multiplying the above formula by vector i s , and multiply both sides of the equation by r sr The influence of stator resistance on the calculation results can be eliminated, and the equation is: By calculating the above formula, take the z component of all terms and assume that the magnetic field direction ψ sd =|ψ s |,ψ sq =0, the stator flux calculation equation can be obtained by calculation:

5. The control method according to claim 1, characterized in that: In step S4, the estimated value of the stator resistance is calculated by the ratio of the voltage component and the flux component in the current coordinate system: First, in the current xy coordinate system, project all components onto the x-axis direction of the current coordinate system, and the calculation equation of the stator resistance can be obtained as: The stator flux equation is: The voltage component equation is: The induced voltage calculation equation is: Finally, the calculation equation of the induction motor stator resistance can be obtained as: Through this formula, the identification result is filtered by a low-pass filter, and the stator flux is calculated in a way that is independent of the stator resistance, so that the parameter value of the induction motor stator resistance can be accurately obtained.

Images