CN114944804B - Control method for eliminating virtual signal injection error synchronous motor maximum torque current ratio - Google Patents
Control method for eliminating virtual signal injection error synchronous motor maximum torque current ratio Download PDFInfo
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Abstract
The invention discloses a synchronous motor maximum torque current ratio (MTPA) control method based on a virtual signal injection method, which comprises the following steps: based on the reconstructed virtual square wave injection method mathematical model, the relation between the error caused by the non-linear characteristic of the synchronous motor parameter and the virtual square wave amplitude is presented through a linear expression, and the partial derivative item of the motor parameter which is contained in the expression and difficult to accurately calculate is considered, so that the error elimination problem is converted into the optimization problem of the upper error bound; and solving the virtual square wave signal by using an optimization method based on a coordinate descent method, and alternately optimizing the amplitude of the virtual square wave signal and the estimation value of the partial derivative of the motor parameter, so that the error is continuously converged until the error is completely eliminated, and the optimal MTPA control of the motor is realized. The method does not depend on motor parameters, does not need complex parameter calculation, does not need to acquire the motor parameters in advance, and eliminates control errors caused by non-considered parameter nonlinearity through continuous iteration to realize accurate MTPA control.
Description
Technical Field
The invention belongs to the technical field of high-performance control of synchronous motors, and relates to a synchronous motor maximum torque current ratio (MTPA) control method based on a Virtual Signal Injection Method (VSIM).
Background
The rotor of the synchronous reluctance motor has no permanent magnet, the internal magnetic field is generated by the excitation of the stator current, and the synchronous reluctance motor has the advantages of no demagnetization risk, low cost, reliable operation, easy field weakening and speed expansion, wide speed regulation range and the like, and becomes a new research hotspot in recent years. However, the performance of synchronous reluctance machines is still lacking compared to permanent magnet synchronous machines, which limits their range of applications. Although the problem can be solved to a certain extent by optimally designing the motor body, in order to further improve the operation performance of the synchronous reluctance motor and expand the application range of the synchronous reluctance motor, a high-performance control method of the synchronous reluctance motor needs to be intensively researched.
Because the iron loss of the rotor of the synchronous reluctance motor is very small, when the motor runs below the basic speed, the copper loss is the main loss. In order to reduce the motor loss and improve the motor efficiency, the maximum torque current ratio (MTPA) control needs to be performed on the motor, that is, the current of the motor is minimized by adjusting the current angle under a given load torque. Virtual Signal Injection (VSIM) is one of the on-line search methods for implementing MTPA control, and has attracted much attention because of its advantages of simple calculation, fast response, and no introduction of extra loss and torque ripple.
The existing research on VSIM is mostly applied to the permanent magnet synchronous motor, and the traditional VSIM with the parameter nonlinearity ignored can obtain a better MTPA control effect because the nonlinear characteristic of the permanent magnet synchronous motor is not obvious. Different from a permanent magnet synchronous motor, the rotor of the synchronous reluctance motor is not provided with a permanent magnet, and the magnetic circuit saturation state of the synchronous reluctance motor is completely determined by current, so that the nonlinear change of the parameters of the synchronous reluctance motor is very obvious. The traditional VSIM does not consider the nonlinear parameter change characteristic, so that inherent errors exist in the control of the synchronous reluctance motor, and the optimal MTPA control effect cannot be realized. And because the nonlinear changing parameters are difficult to be accurately modeled, the existing method for performing parameter calculation to quantize error re-compensation still has difficulty in realizing optimal MTPA control. In order to realize the optimal MTPA control of the synchronous reluctance motor, the error caused by the nonlinear characteristic of the parameter needs to be considered, the traditional VSIM method is optimized, and the problem that the error is influenced by the nonlinear characteristic of the parameter and is difficult to accurately model is solved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a VSIM-based synchronous motor MTPA control method, which is a VSIM method which does not depend on parameters and can eliminate errors, can realize optimal MTPA control on a synchronous motor, and is particularly suitable for MTPA control of a synchronous reluctance motor.
The invention considers the error generated by the nonlinear characteristic of the synchronous reluctance motor parameter and extracts the error by a virtual square wave injection method
Is analyzed and sentThe error is linearly related to the amplitude of the injected virtual square wave signal; in addition, because the error also comprises a partial derivative item of unknown motor parameters, the error elimination problem is converted into an optimization problem, and an optimization algorithm based on coordinate reduction is provided, and the algorithm can alternately optimize the amplitude of an injection signal and an estimation value of the parameter partial derivative item according to a control effect, so that the error is gradually converged to 0, and the optimal MTPA control of the motor is realized.
The technical scheme adopted by the invention is as follows:
a method for controlling the maximum torque current ratio of a synchronous motor based on a virtual signal injection method comprises the following steps: based on a reconstructed virtual square wave injection method mathematical model, presenting the relation between MTPA control error and virtual square wave amplitude caused by not considering the nonlinear characteristic of synchronous motor parameters through a linear expression, and converting the error elimination problem into an optimization problem of an upper error bound by considering a partial derivative item of the motor parameters which are contained in the expression and difficult to accurately calculate;
and solving the virtual square wave signal by using an optimization method based on a coordinate descent method, and alternately optimizing the amplitude of the virtual square wave signal and the estimation value of the partial derivative of the motor parameter, so that the error is continuously converged until the error is completely eliminated, and the optimal MTPA control of the motor is realized.
In the above technical solution, further, based on the reconstructed virtual square wave injection mathematical model, the relationship between the MTPA control error and the virtual square wave amplitude, which is caused by not considering the nonlinear characteristic of the synchronous motor parameter, is represented by a linear expression, as follows:
the error ε is expressed as:
r＝Aδ+B
wherein
Where δ is the virtual square of the injectionAmplitude of the wave signal, P representing the number of pole pairs of the motor, L d ,L q D and q axis inductance parameters of the motor, i d ,i q D, q-axis currents, I, of the motor m Representing the amplitude of the current vector, wherein beta is an included angle between the current vector and the q axis;
the partial derivative of the motor inductance parameter contained in B is difficult to calculate accurately, so the parameter gamma is introduced to estimate B, which is expressed as
|ε|＝|Aδ+B|≤|Aδ+γ|+|B-γ|.
Then epsilon can be eliminated by optimizing the upper bound of error, which is used
And (3) expressing, converting the error elimination problem into an optimization problem of an upper error bound:
further, delta and gamma are alternately and iteratively updated by using a coordinate descent method, so that
And at minimum, updating delta according to delta = root (A delta + gamma) according to gamma updated in each iteration, generating a virtual square wave signal, controlling the synchronous motor based on VSIM, and extracting
When it is gradually close to 0, the MTPA control is implemented, otherwise the next iteration is performed.
Further, the iterative process is as follows:
δ (k) ＝root(Aδ (k) +γ (k-1) )，
γ (k) ＝min|B-γ( k) |.
wherein k is the number of iterations in the coordinate descent method;
in each iteration, the basis of a line search method is adopted
Updating gamma to make gamma gradually approach B; wherein:
c 1 、K i two parameters are introduced to overcome the problem of system delay.
Further, K i The first arrow in the middle subscripts I = ↓ ↓, ↓ ↓ ↓, and I represents I m The trend of change, the second arrow shows the current trend of gamma, and K is present ↑↑ ＞K ↑↓ ,K ↓↑ ＜K ↓↓ ，c 1 Taking a positive integer as the threshold value.
The invention has the beneficial effects that:
unlike the traditional MTPA control method which does not consider the inherent error caused by the nonlinear change of the parameters, the invention can realize the optimal MTPA control on the synchronous motor by a VSIM method based on a coordinate descent method, which considers and eliminates the error. Compared with other MTPA control methods by compensating errors, the method provided by the invention does not depend on motor parameters, does not need complex calculation, and can eliminate errors caused by parameter nonlinearity through continuous iteration to realize accurate MTPA control.
Drawings
FIG. 1 is a flow chart of the method of the present invention
FIG. 2 is a schematic diagram of generating a virtual square wave signal
FIG. 3 is an overall block diagram of a VSIM-based synchronous reluctance motor control system
FIG. 4 is a waveform illustrating the magnitude of the motor current according to an embodiment
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings and specific examples.
The invention provides an algorithm independent of parameters, solves the problems of inaccurate error quantification and high difficulty in the prior art, eliminates errors and provides an efficient and accurate MTPA control method based on VSIM, aiming at the problem that the traditional VSIM has inherent error in controlling a synchronous reluctance motor.
The method considers that a new error expression related to the amplitude of the square wave signal is obtained through the re-modeling of the virtual square wave signal injection method in the traditional VSIM control process, and provides a new idea of eliminating the error through adjusting the amplitude of the square wave. Considering that the error expression contains the partial derivative items of the motor parameters which are difficult to accurately calculate, in order to avoid complex parameter calculation and realize control without parameter dependence, an optimization algorithm based on coordinate descent is provided, the amplitude of the square wave signal and the estimation value of the partial derivative items of the motor parameters are alternately optimized, so that the error is continuously converged until completely eliminated, and the optimal MTPA control of the motor is realized. The method flow is shown in fig. 1, and mainly comprises the steps of re-modeling a virtual square wave injection method, estimating parameter partial derivatives based on line search, eliminating errors by a coordinate descent method and the like.
According to a specific example of the present invention, the method comprises the following:
step 1: conventional VSIMs fail to account for errors due to non-linear changes in parameters and therefore require re-modeling of existing virtual square wave injection methods.
The virtual square wave signal injection method carries out Taylor expansion on the electromagnetic torque after the virtual signal is injected to obtain MTPA judgment information
The extraction formula of (1) is as follows:
wherein, T e For the torque before the injection of the virtual signal,
torque after injection of the virtual signal, delta is the amplitude of the injected virtual square wave signal, P represents the number of pole pairs of the motor, L d ，L q D and q axis inductance parameters of the motor respectively，i d ，i q The d-axis current and the q-axis current of the motor are respectively.
However, taking into account the non-linear behavior of the motor parameters, it is true
Expressed as:
therefore, the MTPA control of the motor by adopting a virtual square wave signal injection method has inherent errors:
for more convenient analysis, the error ε may be rewritten as:
ε＝Aδ+B
wherein
I m Representing the magnitude of the current vector, beta is the angle of the current vector with the q-axis.
It can be seen that ε is linearly related to δ, and can be eliminated by adjusting δ. A can be conveniently calculated, the partial derivative term of the motor inductance parameter contained in B is difficult to accurately calculate, and B is estimated by introducing the parameter gamma, so that epsilon can be eliminated by optimizing the upper bound of the error, and the component is expressed as
|ε|＝|Aδ+B|≤|Aδ+γ|+|B-γ|.
The upper bound of the error can be used
Indicating, then the question of error eliminationQuestions can be represented by optimization problems
This is a multivariable optimization problem involving delta and gamma, which we can use coordinate descent method to update delta and gamma alternatively
At a minimum, i.e.
δ (k) ＝root(Aδ (k) +γ (k-1) )，
γ (k) ＝min|B-γ (k) |.
Wherein the number of iterations k =1,2.
Step 2: based on line search, making gamma gradually approach B to realize gamma (k) ＝min|B-γ (k) L. The method comprises the following specific steps:
step 2.1: the direction of the gamma change is explored. When the gamma is close to the B, the gamma is,
will decrease which means that the operating point of the motor will move towards the MTPA point. According to the definition of MTPA, I m Will be reduced accordingly, which will result in a reduction of B according to the formula of B. Therefore, γ and B are chase-to-chase relationships during optimization, and errors between them can affect I m Size of (1), therefore I m Can be used as an index for quantifying whether the current change direction of gamma is reasonable or not, and indicates the change direction of gamma at the next moment. The d gamma/dt at the next time is thus determined by the d gamma/dt and dI at this time m The/dt common decision can be expressed as
Step 2.2: the step size of the gamma change is explored. Since γ and B are alternately updated, we want the step size of γ to be comparable to the change of B, i.e., | d γ |. Varies | dB |. And dB can be expressed as
Wherein
Considering that d τ is much less than dI m We can ignore
And τ is approximated as a constant. Thus, the approximate step size of γ may be
Is shown as
|dγ|∝|I m .dI m |.
In addition, in practical applications, two problems occur due to system delay: 1. too large a leads to system delay; 2. the system enters stabilization early when the motor has not yet reached the MTPA point. To solve these two problems, the update step formula is
Where ↓ is decreasing and ↓ is increasing, the first arrow in the subscript of K denotes I m The change trend, and the second arrow represents the change trend of the current gamma; k ↑↑ ＞K ↑↓ ,K ↓↑ ＜K ↓↓ The reduction ratio of gamma is easy to increase and is not easy to be overlarge, thereby solving the first problem; wherein c is 1 Is a small positive integer, and ensures that the product cannot be caused by
Equaling 0 ahead of time stabilizes the system ahead of time, solving problem two. The specific value can be set up by K i And c 1 In order to optimize the motor system simulation model of the variable, the difference value between the minimized simulation result and the real MTPA point is taken as the optimization targetAnd then Bayesian optimization is carried out to obtain the target.
Step 2.3: and updating gamma. The binding direction and step size, d γ/dt, can be expressed as
After the integrator calculation, gamma can be updated.
And 3, step 3: a virtual square wave signal is generated. The method comprises the following specific steps:
step 3.1: based on the updated γ, δ may be updated according to δ = root (a δ + γ).
Step 3.2: based on the definition of the virtual square wave signal, a virtual square wave signal may be generated
Wherein N represents the Nth period, T s The period of the virtual square wave signal. After one update of δ and γ, a schematic diagram of generating a virtual square wave signal is shown in fig. 2.
And 4, step 4: and controlling the synchronous reluctance motor based on VSIM to realize optimal MTPA control. The method comprises the following specific steps:
step 4.1: extraction of
The electromagnetic torque before and after the injection of the virtual square wave signal (denoted by the superscript h) can be expressed as
Fourier expansion of the electromagnetic torque at beta can be obtained
Since δ is small, o (δ) can be ignored. Therefore, the temperature of the molten metal is controlled,
can pass through->
And T e And (4) calculating.
Step 4.2:
the output of the integrator is a given current phase angle β as input to the integrator. Is different from what a conventional VSIM gets>
Obtained here>
The error is taken into account and as it approaches 0 gradually, it is shown that the error is eliminated step by step. When the system is completely stable, is selected>
The motor can work at the MTPA point by meeting the definition of MTPA. The overall block diagram of the VSIM-based synchronous reluctance motor control system is shown in fig. 3.
And 5: if the MTPA is not realized, repeating the steps 2-4, and continuously updating the iteration (delta, gamma) based on a coordinate descent method until the iteration reaches a global optimal point (delta * ,γ * ) (i.e. gamma.) * = B), the error is completely eliminated and the motor operates at the MTPA point.
The method comprises the steps of obtaining an error expression by re-modeling a virtual square wave injection method, eliminating errors based on a coordinate descent method, and estimating parameter partial derivatives based on line search to form an accurate MTPA control method; the method adopts a coordinate descent method in the process of eliminating the error of the traditional VSIM, and is practicalThe existing parameters are independent of accurate MTPA control, complex parameter calculation is not needed, and motor parameters are not needed to be obtained in advance; estimating parameter partial derivative items step by adopting line search, and eliminating errors step by adjusting the amplitude of the injected virtual square wave; in addition, in the process of estimating the parameter partial derivative, aiming at two problems that the estimated value caused by the system time delay cannot be overlarge and the system enters into stability in advance, K under different conditions is set i And introducing a threshold value c 1 The problem of system time delay generation in practical application is effectively solved.
Examples of specific applications
To verify the reliability of the method of the invention, relevant experiments were performed. The parameters of the synchronous reluctance machine used in the experiment are shown in table 1 below.
TABLE 1 synchronous reluctance machine parameters
| Rated current (effective value) | 13A |
| Rated speed of rotation | 2000r/min |
| Rated torque | 10Nm |
| Number of pole pairs | 3 |
| Stator resistor | 0.3Ω |
| D-axis inductor | 0.00462～0.01073H |
| q-axis inductor | 0.01115～0.02270H |
In table 2, the motor is controlled by the proposed method under the conditions that the rotation speed is 2000r/min and the load torque is 4, 7 and 10Nm respectively, and the current amplitude of the working point and the current amplitude of the MTPA point of the motor are obtained when the motor enters a steady state. It can be seen that through the elimination of the error by the method, the motor can accurately work at the MTPA point, and the optimal control is realized.
Table 2 presents the current amplitudes of the steady state operating point and MTPA point of the motor under the control of the method
| Load torque (Nm) | I m (method is provided) (A) | I m (MTPA Point) (A) |
| 4 | 11.20 | 11.20 |
| 7 | 14.77 | 14.77 |
| 10 | 17.97 | 17.97 |
Fig. 4 is a waveform diagram of the motor current amplitude with the proposed method for controlling the motor at a speed of 2000r/min and a load torque stepped at 3Nm every 50s, from 4Nm to 10Nm and then stepped back to 3 Nm. It can be seen that the proposed method has good dynamic characteristics, the transient response of the current amplitude waveform is fast, and the waveform remains stable after entering a steady state.
Claims (3)
1. A method for controlling a maximum torque to current ratio (MTPA) of a synchronous machine based on a virtual signal injection method, the method comprising:
based on a reconstructed virtual square wave injection method mathematical model, presenting the relation between MTPA control error and virtual square wave amplitude caused by not considering the nonlinear characteristic of synchronous motor parameters through a linear expression, and converting the error elimination problem into an optimization problem of an upper error bound by considering a partial derivative item of the motor parameters which are contained in the expression and difficult to accurately calculate;
solving by using an optimization method based on a coordinate descent method, and alternately optimizing the amplitude of the virtual square wave signal and the estimation value of the partial derivative term of the motor parameter, so that the error is continuously converged until the error is completely eliminated, and the optimal MTPA control of the motor is realized;
based on the reconstructed virtual square wave injection method mathematical model, the relationship between the MTPA control error and the virtual square wave amplitude caused by not considering the nonlinear characteristic of the synchronous motor parameter is represented by a linear expression as follows: the error ε is expressed as:
ε＝Aδ+B
wherein
Wherein, delta is the amplitude of the injected virtual square wave signal, P represents the pole pair number of the motor, and L d ,L q Are respectively a motor dQ-axis inductance parameter, i d ,i q D, q-axis currents, I, of the motor m Representing the amplitude of the current vector, wherein beta is an included angle between the current vector and the q axis;
the partial derivative of the motor inductance parameter contained in B is difficult to calculate accurately, so introducing the parameter γ to estimate B includes:
|ε|＝|Aδ+B|≤|Aδ+γ|+|B-γ|.
by using
And (3) representing an upper error bound, and converting the error elimination problem into an optimization problem of the upper error bound:
by alternately and iteratively updating delta and gamma using a coordinate descent method
And minimum, updating delta according to gamma updated in each iteration and delta = root (A delta + gamma), generating a virtual square wave signal, controlling the synchronous motor based on a virtual signal injection method, and extracting
And when the error is eliminated to be within the acceptance range, the MTPA control is realized, otherwise, the next iteration is carried out.
2. The method for controlling the maximum torque current ratio of the synchronous motor based on the virtual signal injection method as claimed in claim 1, wherein the iteration process is as follows:
δ (k) ＝root(Aδ (k) +γ (k-1) ),
γ (k) ＝min|B-γ (k) |.
wherein k is the number of iterations in the coordinate descent method;
in each iteration, the basis of a line search method is adopted
Updating gamma to make gamma gradually approach B; wherein:
c 1 、K i two parameters are introduced to overcome the problem of system delay.
3. The method for controlling the maximum torque to current ratio of a synchronous motor based on the virtual signal injection method as claimed in claim 2, wherein K is i Middle subscript i = ↓ ↓, and with K ↑↑ ＞K ↑↓ ,K ↓↑ ＜K ↓↓ The relationship holds all the time, the first arrow in I denotes I m Trend of change, second arrow indicates trend of change of current gamma, c 1 Taking a positive integer as the threshold value.
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| CN110336504A (en) * | 2019-06-18 | 2019-10-15 | 浙江大学 | Method for controlling permanent magnet synchronous motor based on virtual signal injection and gradient descent method |
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