CN115632584A - Loss optimization control method for embedded permanent magnet synchronous motor - Google Patents
Loss optimization control method for embedded permanent magnet synchronous motor Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
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Abstract
The invention discloses a loss optimization control method for an embedded permanent magnet synchronous motor. Firstly, a variable parameter equivalent series loss resistance motor model considering the influence of motor current and rotating speed is provided, and the model is simple in form and convenient to calculate; secondly, providing a sample operation condition point selection rule for training a neural network function mapping relation, wherein the motor loss and the torque measured under the operation condition point determined by the rule have less characteristic redundancy, and the optimization of experimental data volume requirements can be realized; then, two gradient descent methods are provided, and parameters of a neural network function mapping relation representing the difference value between the equivalent total loss resistance and the inductance in the variable parameter equivalent series loss resistance model are respectively solved in an iterative manner; finally, a current vector calculation method for motor loss optimization control based on a gradient descent method is provided, and target torque can be output at different rotating speeds with optimal motor loss. The method is suitable for the application field of loss optimization control of the embedded permanent magnet synchronous motor.
Description
Technical Field
The invention relates to a loss optimization control method for an embedded permanent magnet synchronous motor, and belongs to the fields of electrical engineering, motor modeling and motor control.
Background
The embedded permanent magnet synchronous motor has the advantages of high power density, high operation efficiency and the like, so that the embedded permanent magnet synchronous motor is widely applied to the fields of electric automobile driving, air-conditioning compressors and the like. In these fields, the operating speed and torque (current) of the motor vary greatly, which causes the motor parameters to deviate. For a high-performance motor driving system, motor loss optimization is always an important target influencing energy conservation and improving thermal reliability. Therefore, the loss optimization control method of the embedded permanent magnet synchronous motor considering the influence of the running speed and the current of the motor has great engineering value and social significance.
At present, loss optimization control methods of an embedded permanent magnet synchronous motor are roughly divided into two types: an online search method, a loss model method. The online searching method finally finds a current working point with zero motor loss gradient by gradually adjusting a current vector. The current vector adjusting method can be a disturbance searching method with fixed step length or variable step length, and can also be used for integrating the motor loss gradient. However, the existing online searching method generally has the problems of slow dynamic response, large steady-state fluctuation and the like. For application fields such as electric vehicle driving, the operation condition of the motor may change rapidly, and the steady-state time is too short, so that the current vector of motor loss optimization cannot be transited in time, and the motor loss optimization target cannot be realized actually.
Correspondingly, the loss model method can directly calculate the current vector of the motor loss optimization without iteration, so that the method has the advantages of quick response, small steady-state fluctuation and the like, and has a very large application prospect. At present, a commonly used loss model method is calculated based on an equivalent parallel loss resistance motor model. However, the method is complex in calculation formula, and needs to be assisted by off-line numerical calculation, equation simplification and the like. The necessary simplification can affect the setting precision of the model parameters, further affect the motor loss optimization current vector calculation result and is not beneficial to realizing the motor loss optimization target.
In addition, the control performance of the loss model method depends heavily on the accuracy of the model parameters. If a model variable parameter considering the motor running rotating speed and current influence is set, motor loss and output torque under different current vectors and different rotating speeds need to be acquired. This will generate a huge data volume demand, which is accompanied by a very large investment in human, material and time costs, and is not conducive to economic cost management and control of industrial production, and rapid iterative development of control strategies. At present, the problem of large data volume demand is still not effectively solved.
Disclosure of Invention
The invention aims to simplify the complexity of a loss optimization control method of an embedded permanent magnet synchronous motor based on a loss model, reduce the requirement of experimental data quantity required by setting model parameters, and provide the loss optimization control method of the embedded permanent magnet synchronous motor.
In order to solve the problems, the invention adopts the technical scheme that:
a loss optimization control method for an embedded permanent magnet synchronous motor specifically comprises the following steps:
a variable parameter equivalent series loss resistance motor model considering the influence of motor current and rotating speed is provided. The steady state voltage equation for this model is:
in the above equation, u ds And u qs Terminal voltages of d-axis motor and q-axis motor, i ds And i qs D-axis and q-axis motor currents, L, respectively ds And L qs D-axis motor inductance and q-axis motor inductance respectively, and omega is the electrical angular velocity of the motor, psi fs Is a permanent magnet flux linkage, R a Is the motor copper loss resistance, R cs The resistance is the iron loss resistance of the motor, and P is the number of pole pairs of the motor.
Equivalent total loss resistance R of the model Loss Is defined as:
R Loss ＝R a +R cs
the total loss P of the motor of the model Loss The calculation equation is:
P Loss ＝1.5R Loss (i ds 2 +i qs 2 )
equivalent total loss resistance R of the model Loss The variable parameter relation of (2) is defined as:
R Loss ＝f NN1 (i ds ,i qs ,f)
in the above equation, f represents the fundamental frequency of motor supply, f NN1 Relation 1 is mapped for a neural network based function.
Inductance difference L of the model dqs Is defined as:
L dqs ＝L ds -L qs
motor torque T of the model em The calculation equation is:
T em ＝1.5P(ψ fs +L dqs i ds )i qs
inductance difference L of the model dqs The variable parameter relation of (2) is defined as:
L dqs ＝f NN2 (i ds ,i qs )
in the above equation, f NN2 Relation 2 is mapped for the neural network based function.
In order to reduce the requirement of experimental data quantity required by setting model parameters, a method for training a neural network function mapping relation f is provided NN1 And f NN2 The sample operating condition point selection rule. The specific steps of the sample operation condition point selection rule are as follows:
(1) Determining the peak current I of the motor from a motor parameter table provided by a manufacturer max And peak motor speed n max ；
(2) Selecting the number N of current sharing I Number N is equally divided by sum rotation speed n . In general N I Selecting 20 to 30,N n Selecting 5-15;
(3) Determining a current discrete test step S I ＝I max /N I Discrete test step S of rotation speed n ＝n max /N n ；
(4) Initialization parameter j =1;
(4.1) initializing parameter k =1;
(4.2) determining discrete operating mode points (i) dsj ,i qsk ,n mjk ). Wherein i dsj ＝-jS I ，i qsk ＝kS I ，n mjk ＝m jk S n ，m jk Based on the average probability distribution from 1 to N n An integer selected at will; i all right angle dsj For the jth d-axis motor current, i qsk For the kth q-axis motor current, n mjk Is m at jk The rotating speed of each motor;
(4.3) if k is not less than N I Then jump to step (4.4). If k is<N I If k = k +1, jumping to step (4.2);
(4.4) if j is not less than N I Then jump to step (5). If j is<N I If j = j +1, jumping to step (4.1);
(5) Summarizing all discrete current operating condition points (i) with any discrete rotating speed determined in the step (4) dsj ,i qsk ,n mjk ) The desired sample operating condition point is formed.
Then, based on the motor loss P measured under the operation condition point determined by the extracted sample operation condition point selection rule Act A gradient descent method 1 is provided for iteratively solving the characteristic of the equivalent total loss resistance R in the variable parameter equivalent series loss resistance motor model considering the influence of the motor current and the rotating speed Loss Neural network function mapping relation f NN1 The parameter (c) of (c). The specific working steps of the gradient descent method 1 are as follows:
(1) Defining a neural network function mapping relationship f NN1 The parameters of (2), including: the threshold value of the jth neuron of the output layer of the neural network is theta j1 The h neuron of the hidden layer of the neural network has a threshold value of gamma h1 Input of neural networkThe connection weight between the ith neuron of the layer and the h neuron of the hidden layer is v ih1 The connection weight between the h-th neuron of the hidden layer and the j-th neuron of the output layer is w hj1 ；
(2) Generally in the range of 0-1, initializing the neural network function mapping relation f NN1 The parameter (c) of (c). And, selecting a relative error upper limit ε 1 Usually, the value is less than 3%;
(3) Function mapping relation f based on neural network NN1 Calculating an estimated motor loss value P Obs The expression is:
in the above equation, y 11 ～y 41 Respectively 1 st to 4 th output variables, y, of the neural network j1 Is the j output variable, beta, of the output layer of the neural network j1 Input variables for the jth neuron of the output layer of the neural network, b h1 Output variable, alpha, for the h-th neuron of the hidden layer of the neural network h1 Input variable, x, for the h-th neuron of the hidden layer of a neural network i1 The ith input variable of the neural network, f is the motor power supply fundamental frequency, sigma is a Sigmoid function, q is the total number of neurons of an output layer of the neural network, d is the total number of input variables of the neural network, and R Obs Is an estimated value of the equivalent total loss resistance;
(4) Calculating P Obs Actual motor loss P obtained by experiment Act Relative error between E and E 1 ＝|P Obs -P Act |/P Act . If the relative error E 1 <ε 1 Then jump to step (8). If the relative error E 1 ≥ε 1 Jumping to the step (5);
(5) Calculating a neural network function mapping relationship f NN1 Gradient of each parameter of (a):
in the above equation, η is the learning rate, i.e., the iteration step. g j1 And e h1 For mathematical variables used to simplify the form of the equation:
in the equation, l is the total number of output variables of the neural network, and sign is a sign function;
(6) Updating the neural network function mapping relation f based on the gradient calculated in the step (5) NN1 The parameters of (c):
(7) Neural network function mapping relation f based on (6) updating NN1 Skipping to the step (3), thereby continuing the iterative computation;
(8) The iterative solution process is ended and the latest theta j1 、γ h1 、v ih1 、w hj1 I.e. to characterize the equivalent total loss resistance R Loss Neural network function mapping relation f NN1 The parameters of (1);
and, based on the measured motor torque T at the operating point determined by the sample operating point selection rule Act A gradient descent method 2 is provided for iteratively solving the characteristic inductance difference value L in the variable parameter equivalent series loss resistance motor model considering the influence of the motor current and the rotating speed dqs Neural network function mapping relation f NN2 The parameter (c) of (c). The gradient descent method 2 comprises the following specific working steps:
(1) Neural network function mapping relation f for defining inductance difference value NN2 The parameters of (2), including: the threshold value of the 1 st neuron of the output layer of the neural network is theta 12 The h neuron of the hidden layer of the neural network has a threshold value of gamma h2 The connection weight between the ith neuron of the input layer and the h neuron of the hidden layer of the neural network is v ih2 H, hidden layer hThe connection weight between the neuron and the 1 st neuron of the output layer is w h12 ；
(2) Generally in the range of 0-1, initializing the neural network function mapping relation f NN2 The parameter (c) of (c). And, selecting a relative error upper limit ε 2 Usually, the value is less than 3%;
(3) Function mapping relation f based on neural network NN2 Calculating the motor torque estimate T Obs The expression is:
in the above equation, y 12 For the 1 st output variable, beta, of the neural network 12 Input variables for the 1 st neuron of the output layer of the neural network, b h2 Output variable, α, for the h-th neuron of the hidden layer of the neural network h2 Input variable, x, for the h-th neuron of the hidden layer of a neural network i2 The number of the ith input variable of the neural network is Q, the total number of the neurons of an output layer of the neural network is D, and the total number of the input variables of the neural network is D;
(4) Calculating T Obs And the actual motor torque T obtained by the experiment Act Relative error between E and E 2 ＝|T Obs -T Act |/T Act . If relative error E 2 <ε 2 Then jump to step (8). If relative error E 2 ≥ε 2 Jumping to the step (5);
(5) Calculating a neural network function mapping relationship f NN2 Gradient of each parameter of (a):
in the above equation, g 12 And e h2 To simplify the mathematical variables of the equation form:
(6) Updating the neural network function mapping relation f based on the gradient calculated in the step (5) NN2 The parameters of (2):
(7) Neural network function mapping relation f based on (6) updating NN2 Skipping to the step (3), thereby continuing the iterative computation;
(8) The iterative solution process is ended and the latest theta 12 、γ h2 、v ih2 、w h12 I.e. representing the equivalent inductance difference L dqs Neural network function mapping relation f NN2 The parameters of (1);
finally, based on the variable parameter equivalent series loss resistance motor model considering the motor current and rotating speed influence, the presented gradient descent method 1 is adopted to iteratively solve to obtain the characterization equivalent total loss resistance R Loss Neural network function mapping relation f NN1 The characterization inductance difference value L obtained by iterative solution of the gradient descent method 2 dqs Neural network function mapping relation f NN2 The method is based on a current vector calculation method of motor loss optimization control of a gradient descent method 3, and the purpose that the target torque is output with the optimal motor loss at the target rotating speed is achieved. The specific working steps of the current vector calculation method are as follows:
(1) Setting a target rotational speed n Ref And target torque T Ref ；
(2) Determining the peak current I of the motor from a motor parameter table provided by a manufacturer max And selecting the number N of current sharing IME ；
(3) Determining a current discrete test step S IME ＝I max /N IME ；
(4) Initializing p =1;
(4.1) calculating d-axis Current i dsp ＝-pS IME ；
(4.2) in the range of 0 to I max In the range, initializing the q-axis currenti qsp . And, selecting a relative error upper limit ε NN Usually, values are less than 0.1%;
(4.3) characterization-based inductance difference L dqs Neural network function mapping relation f NN2 And parameters thereof, including θ 12 、γ h2 、v ih2 、w h12 Calculating an estimated value T of motor torque Obs The specific calculation formula can be expressed as:
(4.4) calculating T Obs And T Ref Relative error between E and E NN ＝|T Obs -T Ref |/T Ref . If relative error E NN <ε NN Then jump to step (4.8). If the relative error E NN ≥ε NN Jumping to the step (4.5);
(4.5) calculating the gradient of the q-axis current:
(4.6) updating the q-axis current based on the gradient calculated in step (4.5):
i qsp ＝i qsp +Δi qsp
(4.7) jumping to step (4.3) based on the updated q-axis current of (4.6), thereby continuing the iterative calculation;
(4.8) based on the latest i qsp 、i dsp Characterization of the equivalent total loss resistance R Loss Neural network function mapping relation f NN1 Solving the motor loss P under the P operating condition point Obsp ：
(4.9) forming the data set (i) dsp ,i qsp ,P Obsp ) And is stored in the memory of the computer,facilitating the comparison in step (5);
(4.10) if p.gtoreq.N IME Then jump to step (5). If p is<N IME If p = p +1, jumping to step (4.1);
(5) Comparing the motor losses P in all the data sets obtained in the step (4) Obsp Selecting the data set with the minimum loss, which corresponds to (i) dsp ,i qsp ) That is at the target speed n Ref Lower output target torque T Ref The motor losses of (1) optimize the current vector of the control.
The invention principle of the invention is as follows:
firstly, the invention mathematically simplifies the traditional equivalent parallel loss resistance motor model by means of algebraic substitution, coordinate rotation transformation and the like, omits an equivalent parallel loss resistance branch circuit, and reduces the state variable of the model, namely the current of the parallel loss branch circuit, thereby realizing the simplification of the motor model. In addition, the changes of the current and the rotating speed respectively influence the magnetic field distribution and the power supply fundamental wave frequency of the motor, and further influence the output torque, the loss and the corresponding model parameters of the motor. Based on Bertotti theoretical analysis, the influence of the rotating speed on the magnetic field distribution of the motor is small, in other words, the influence of the rotating speed change on the motor torque and corresponding model parameters can be ignored. Finally, a simplified motor model and the influence relation of the current and the rotating speed on the motor model parameters are integrated, and a variable parameter equivalent series loss resistance motor model with simplified complexity and considering the influence of the motor current and the rotating speed can be formed.
Secondly, based on the analysis of the Hough's equation, when the number of samples for training the neural network function mapping relation exceeds 380, and the selected sample operation working condition points are distributed on the whole current working point plane and each current working point and only need one rotating speed working point which meets the average independent same distribution, the average absolute error of the selected sample can approximately represent the generalized fitting capability of the trained neural network to the target object. In other words, the sample obtained by downsampling the operation working condition points determined by the provided sample operation working condition point selection rule contains the main characteristics of the target object, so that the variable parameter behavior pattern and the characteristics of the target object in the sample can be extracted with the help of the neural network, and a better generalized fitting effect is realized. In addition, as each current working point of the sample operation working condition point selection rule is provided with and only needs one rotating speed working point, the characteristic redundancy is less, and the data volume requirement optimization can be realized.
Finally, the gradient descent method commonly adopted by the invention has the core idea that the gradient of the cost function to the optimization parameter is calculated, and the obtained gradient is multiplied by the step length and then subtracted from the original optimization parameter to obtain the updated optimization parameter, thereby realizing the iterative descent of the cost function. In the invention, the characteristic equivalent total loss resistance R is aimed at Loss The model parameter training target of the neural network function mapping relation adopts the mean square error of the motor loss as a cost function to realize high-precision fitting of the motor loss and corresponding parameters; for characterizing the inductance difference L dqs The method comprises the following steps of training a target by using model parameters of a neural network function mapping relation, calculating a q-axis current target based on a given torque and a d-axis current, and adopting the mean square error of the motor torque as a cost function to realize high-precision fitting of the motor torque and corresponding parameters and high-precision calculation of the q-axis current of an output target torque. Finally, comparing the motor losses of the current working points under the same output target torque and different d-axis currents, and finding out the current vector which accords with the motor loss optimization control.
The invention has the beneficial effects that:
1. a variable parameter equivalent series loss resistance motor model considering the influence of motor current and rotating speed is provided, compared with the traditional equivalent parallel loss resistance motor model, the model is simpler in mathematical formula, a complex approximation method is not needed, and the model is very convenient to apply. In addition, the parameters of the model are separated from each other, so that parameter setting calculation is very convenient, and the precision of the model parameters is ensured.
2. The method has the advantages that a sample operation working condition point selection rule for training the neural network function mapping relation is provided, and the motor loss or torque obtained under the operation working condition point determined by the selection rule has less characteristic redundancy, so that the requirement on experimental data quantity required by setting the model parameters can be reduced, the time cost and the resource investment can be greatly reduced, the rapid iteration of a control strategy can be realized, and the method has a very large engineering application value.
3. Providing a motor model for iteratively solving equivalent series loss resistance to characterize equivalent total loss resistance R Loss Difference L from inductance dqs The gradient descent method of the model parameters of the neural network function mapping relation can realize effective extraction of variable parameter characteristic values in experimental data, and assist the extracted sample operation condition point selection rule to reduce the requirement of experimental data quantity required by setting the model parameters;
4. the current vector calculation method for the motor loss optimization control based on the gradient descent method is provided, so that the target torque can be output at different rotating speeds by the optimal motor loss, and the targets of saving energy, improving thermal reliability and the like are realized;
drawings
FIG. 1 is a schematic diagram of an equivalent series-loss resistance motor model;
FIG. 2 is a schematic diagram of a training sample operation condition point selection rule for data volume demand optimization;
FIG. 3 represents the equivalent total loss resistance R Loss The mapping relation schematic diagram of the neural network function;
FIG. 4 represents the inductance difference L dqs The mapping relation of the neural network function is shown schematically.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
Fig. 1 is a schematic diagram of an equivalent series-loss resistance motor model. Wherein u is ds And u qs Terminal voltages of d-axis motor and q-axis motor, i ds And i qs D-axis and q-axis motor currents, L, respectively ds And L qs D-axis motor inductance and q-axis motor inductance respectively, and omega is the electrical angular velocity of the motor, psi fs Is a permanent magnet flux linkage, R a Is a motor copper loss resistor, R cs F is the motor iron loss resistance, f is the motor power supply fundamental frequency, and n represents the motor rotating speed. When the influence of the current and the rotating speed of the motor is considered, the model parameters are deviatedMoving:
R Loss ＝f NN1 (i ds ,i qs ,f),L dqs ＝f NN2 (i ds ,i qs )
in the above equation, f NN1 And f NN2 Respectively, to characterize the equivalent total loss resistance R Loss The neural network function mapping relation and the characterization inductance difference value L dqs The neural network function mapping relationship. Equivalent total loss resistance R Loss Difference L from inductance dqs The specific definition is as follows:
R Loss ＝R a +R cs ,L dqs ＝L ds -L qs
total motor loss P of the equivalent series loss resistance motor model Loss With motor torque T em The calculation formulas are respectively as follows:
P Loss ＝1.5R Loss (i ds 2 +i qs 2 ),T em ＝1.5P(ψ fs +L dqs i ds )i qs
characterization of equivalent total loss resistance R in equivalent series loss resistance motor model provided for training Loss Neural network function mapping relation f NN1 Difference value L from the characteristic inductance dqs Neural network function mapping relation f NN2 The parameters in (1) need to be tested to obtain training samples, namely, the motor loss and the torque under different currents and rotating speeds are measured.
Fig. 2 is a schematic diagram of a training sample operation condition point selection rule. The solid points are training samples corresponding to the extracted operating condition point selection rule, and the hollow points are other samples which do not need to be sampled and only play a role in auxiliary display in the figure. The specific steps of the training sample operation condition point selection rule are as follows:
(1) Determining the peak current I of the motor from a motor parameter table provided by a manufacturer max And the peak rotation speed n of the motor max . For example in fig. 2: i is max Is 6A, n max At 14krpm;
(2) Selecting the number N of current sharing I Number N is equally divided by sum rotation speed n . For example in fig. 2: n is a radical of I Is 6,N n Is 7;
(3) Determining a current discrete test step S I ＝I max /N I Discrete test step S of rotation speed n ＝n max /N n ；
(4) Initialization parameter j =1;
(4.1) initializing parameter k =1;
(4.2) determining discrete operating mode points (i) dsj ,i qsk ,n mjk ) (ii) a Wherein i dsj ＝-jS I ，i qsk ＝kS I ，n mjk ＝m jk S n ，m jk Based on an average probability distribution from 1 to N n An integer selected at will; i.e. i dsj For the j-th d-axis motor current, i qsk For the kth q-axis motor current, n mjk Is m at the m jk The rotating speed of each motor;
(4.3) if k is not less than N I Jumping to the step (4.4); if k is<N I If k = k +1, jumping to step (4.2);
(4.4) if j is not less than N I Jumping to the step (5); if j<N I If j = j +1, jumping to step (4.1);
(5) Summarizing all discrete current operating condition points (i) with any discrete rotating speed determined in the step (4) dsj ,i qsk ,n mjk ) And obtaining the required sample operation condition point.
FIG. 3 is a graph representing the equivalent total loss resistance R Loss Neural network function mapping relation f NN1 Schematic representation. Wherein x is 11 And x 21 For the 1 st, 2 nd input variables, y, of the neural network 11 ～y 41 Respectively 1 st to 4 th output variables of the neural network, b 11 、b 21 、b h1 、b q1 Output variables of 1 st, 2 nd, h th and q neurons of a hidden layer of the neural network are respectively, and q is the total number of the neurons of the output layer of the neural network. The input variables, the input and output variables of the neurons of the hidden layer and the output variables meet the following conditions:
in the above equation, y j1 Is the jth output variable, beta, of the output layer of the neural network j1 Is the input variable of the j-th neuron of the output layer, b h1 Output variable, alpha, for the h-th neuron of the hidden layer of the neural network h1 Input variable, x, for the h-th neuron of the hidden layer i1 Is the ith input variable of the neural network, sigma is Sigmoid function, d is the total number of input variables of the neural network, theta j1 Threshold value of j-th neuron of output layer, gamma h1 Threshold value for h neuron of hidden layer, v ih1 Is the connection weight between the ith neuron of the input layer and the h-th neuron of the hidden layer, w hj1 The connection weight between the h-th neuron of the hidden layer and the j-th neuron of the output layer is set.
Equivalent total loss resistance R Loss The method can be obtained by calculating the output variable of the neural network, and the specific calculation formula is as follows:
R Obs ＝y 11 +y 21 f+y 31 f 1.5 +y 41 f 2
then, based on the motor loss P measured under the operation condition point determined by the operation condition point selection rule of the provided training sample Act The gradient descent method 1 is adopted for iteratively solving the characteristic equivalent total loss resistance R in the variable parameter equivalent series loss resistance motor model considering the influence of the motor current and the rotating speed Loss Neural network function mapping relation f NN1 The parameter (c) of (c). The specific working steps of the gradient descent method 1 are as follows:
(1) Neural network function mapping relation f for defining equivalent total loss resistance NN1 Parameter (d) of (1) containing theta j1 ，γ h1 ，v ih1 ，w hj1 ；
(2) Generally in the range of 0-1, initializing the neural network function mapping relation f NN1 The parameter (c) of (c). And, selecting a relative error upper limit ε 1 Usually, the value is less than 3%;
(3) Mapping relation based on neural network functionIs f NN1 Calculating an estimated motor loss value P Obs The expression is:
in the above equation, f is the fundamental frequency of the motor supply, R Obs Is an estimated value of the equivalent total loss resistance;
(4) Calculating P Obs And the actual motor loss P obtained by the experiment Act Relative error between E and E 1 ＝|P Obs -P Act |/P Act . If the relative error E 1 <ε 1 Then jump to step (8). If relative error E 1 ≥ε 1 Jumping to the step (5);
(5) Calculating a neural network function mapping relationship f NN1 Gradient of each parameter of (a):
in the above equation, η is the learning rate, i.e., the iteration step. g j1 And e h1 For mathematical variables used to simplify the form of the equation:
in the equation, l is the total number of output variables of the neural network, and sign is a sign function;
(6) Updating the neural network function mapping relation f based on the gradient calculated in the step (5) NN1 The parameters of (c):
(7) Neural network function mapping relation f based on (6) updating NN1 Skipping to the step (3), thereby continuing the iterative computation;
(8) The iterative solution process is ended and the latest theta j1 、γ h1 、v ih1 、w hj1 I.e. to characterize the equivalent total loss resistance R Loss Neural network function mapping relation f NN1 The parameters of (1);
FIG. 4 is a graph representing the inductance difference L dqs Neural network function mapping relation f NN2 Schematic illustration. Wherein, y 12 For the 1 st output variable of the neural network, the inductance difference L dqs I.e. y 12 ，x 12 And x 22 For the 1 st and 2 nd input variables of the neural network, b 12 、b 22 、b h2 、b Q2 Output variables of 1 st, 2 nd, h th and Q neurons of a hidden layer of the neural network are respectively, and Q is the total number of the neurons of the output layer of the neural network. The input variables, the input and output variables of the neurons of the hidden layer and the output variables meet the following conditions:
in the above equation, β 12 Input variables for the 1 st neuron of the output layer, b h2 Output variable, alpha, for the h-th neuron of the hidden layer of the neural network h2 Input variable, x, for the h-th neuron of the hidden layer i2 Is the ith input variable of the neural network, D is the total number of input variables of the neural network, theta 12 Threshold of the 1 st neuron of the output layer, γ h2 Threshold value for h neuron of hidden layer, v ih2 Is the connection weight between the ith neuron of the input layer and the h neuron of the hidden layer, w h12 The connection weight between the h-th neuron of the hidden layer and the 1 st neuron of the output layer is set.
Thereafter, the motor torque T measured at the operating mode point determined based on the extracted training sample operating mode point selection rule Act The gradient descent method 2 is adopted for iterative solution of the representation inductance difference value L in the variable parameter equivalent series loss resistance motor model considering the influence of the motor current and the rotating speed dqs Neural network function mapping relation f NN2 The parameter (c) of (c). The gradient descent method comprises the following specific working steps:
(1) Neural network function mapping relation f for defining inductance difference value NN2 Parameter (d) of (1) containing theta 12 ，γ h2 ，v ih2 ，w h12 ；
(2) Generally in the range of 0-1, initializing the neural network function mapping relation f NN2 The parameter (c) of (c). And, selecting a relative error upper limit ε 2 Usually, the value is less than 3%;
(3) Function mapping relation f based on neural network NN2 Calculating an estimated value T of motor torque Obs The expression is:
(4) Calculating T Obs And the actual motor torque T obtained by the experiment Act Relative error between E and E 2 ＝|T Obs -T Act |/T Act . If the relative error E 2 <ε 2 Then, it jumps to step (8). If relative error E 2 ≥ε 2 Jumping to the step (5);
(5) Calculating a neural network function mapping relationship f NN2 Gradient of each parameter of (a):
in the above equation, g 12 And e h2 For mathematical variables used to simplify the form of the equation:
(6) Updating the neural network function mapping relation f based on the gradient calculated in the step (5) NN2 The parameters of (2):
(7) Neural network function mapping relation f based on (6) updating NN2 Skipping to the step (3), thereby continuing the iterative computation;
(8) The iterative solution process is ended and the latest theta 12 、γ h2 、v ih2 、w h12 I.e. representing the equivalent inductance difference L dqs Neural network function mapping relation f NN2 The parameters of (1);
finally, based on the variable parameter equivalent series loss resistance motor model considering the motor current and rotating speed influence, the presented gradient descent method 1 is adopted to iteratively solve to obtain the characterization equivalent total loss resistance R Loss Neural network function mapping relation f NN1 The characterization inductance difference value L obtained by iterative solution of the gradient descent method 2 dqs Neural network function mapping relation f NN2 The target torque is output with the optimal motor loss at the target rotating speed by adopting a current vector calculation method of motor loss optimal control based on a gradient descent method 3. The current vector calculation method comprises the following specific steps:
(1) Setting a target rotational speed n Ref And target torque T Ref ；
(2) Determining the peak current I of the motor from the motor parameter table provided by the manufacturer max And selecting the number N of current sharing IME ；
(3) Determining a current discrete test step S IME ＝I max /N IME ；
(4) Initializing p =1;
(4.1) calculating d-axis Current i dsp ＝-pS IME ；
(4.2) in the range of 0 to I max Within range, initializing q-axis current i qsp . And, selecting a relative error upper limit ε NN Usually, the value is less than 0.1%;
(4.3) characterization-based inductance difference L dqs Neural network function mapping relation f NN2 And parameters thereof, including θ 12 、γ h2 、v ih2 、w h12 Calculating an estimated value T of motor torque Obs The specific calculation formula is as follows:
(4.4) calculating T Obs And T Ref Relative error between E and E NN ＝|T Obs -T Ref |/T Ref (ii) a If relative error E NN <ε NN Jumping to the step (4.8); if the relative error E NN ≥ε NN Jumping to the step (4.5);
(4.5) calculating the gradient of the q-axis current:
(4.6) updating the q-axis current based on the gradient calculated in step (4.5):
i qsp ＝i qsp +Δi qsp
(4.7) jumping to step (4.3) based on the updated q-axis current of (4.6), thereby continuing the iterative computation;
(4.8) based on the latest i qsp 、i dsp Characterization of the equivalent total loss resistance R Loss Neural network function mapping relation f NN1 Solving the motor loss P at the P operating condition point Obsp ：
(4.9) forming the data set (i) dsp ,i qsp ,P Obsp ) And storing;
(4.10) if p.gtoreq.N IME Jumping to the step (5); if p is<N IME If p = p +1, jumping to step (4.1);
(5) Comparing the motor losses P in all the data sets obtained in the step (4) Obsp Selecting the least lossy data set corresponding thereto(i dsp ,i qsp ) That is at the target speed n Ref Lower output target torque T Ref The motor losses of (2) optimize the current vector.
Claims (5)
1. A loss optimization control method for an embedded permanent magnet synchronous motor is characterized in that a variable parameter equivalent series loss resistance motor model considering the influence of motor current and rotating speed is provided, a current vector calculation method for motor loss optimization control based on a gradient descent method is provided to solve the model, and finally target torque can be output with optimal motor loss at a target rotating speed;
the variable parameter equivalent series loss resistance motor model considering the influence of the motor current and the rotating speed specifically comprises the following steps:
the steady state voltage equation for this model is:
in the above equation, u ds And u qs Terminal voltages of d-axis motor and q-axis motor, i ds And i qs D-axis and q-axis motor currents, L, respectively ds And L qs D-axis motor inductance and q-axis motor inductance respectively, and omega is motor electrical angular velocity psi fs Is a permanent magnet flux linkage, R a Is a motor copper loss resistor, R cs The resistance is the iron loss resistance of the motor, and P is the number of pole pairs of the motor;
the total loss P of the motor of the model Loss The calculation equation is:
P Loss ＝1.5(R a +R cs )(i ds 2 +i qs 2 )
motor torque T of the model em The calculation equation is:
T em ＝1.5P[ψ fs +(L ds -L qs )i ds ]i qs
the equivalent total loss resistance R of the model Loss Is defined as follows:
R Loss ＝R a +R cs
the total motor loss P of the model Loss The calculation equation is simplified as:
P Loss ＝1.5R Loss (i ds 2 +i qs 2 )
the equivalent total loss resistance R Loss The variable parameter relation of (2) is defined as:
R Loss ＝f NN1 (i ds ,i qs ,f)
in the above equation, f represents the fundamental frequency of the motor supply, f NN1 Mapping relation 1 for a function based on a neural network;
the inductance difference L of the model is calculated dqs Is defined as:
L dqs ＝L ds -L qs
thenMotor torque T of the model em The calculation equation is simplified as:
T em ＝1.5P(ψ fs +L dqs i ds )i qs
the inductance difference value L dqs The variable parameter relation of (2) is defined as:
L dqs ＝f NN2 (i ds ,i qs )
in the above equation, f NN2 Relation 2 is mapped for the neural network based function.
2. The loss optimization control method of the embedded permanent magnet synchronous motor according to claim 1, wherein a neural network function mapping relation f is obtained by selecting a sample operation condition point for training NN1 And f NN2 (ii) a The selection of the sample operation working condition point comprises the following specific steps:
(1) Determining the peak current I of the motor from a motor parameter table provided by a manufacturer max And the peak rotation speed n of the motor max ；
(2) Selecting the number N of current sharing I Number N is divided equally with the rotating speed n ；
(3) Determining a current discrete test step S I ＝I max /N I Discrete test step S of rotation speed n ＝n max /N n ；
(4) Initializing a parameter j =1;
(4.1) initializing parameter k =1;
(4.2) determining discrete operating mode points (i) dsj ,i qsk ,n mjk ) (ii) a Wherein i dsj ＝-jS I ，i qsk ＝kS I ，n mjk ＝m jk S n ，m jk Based on an average probability distribution from 1 to N n An integer selected at will; i all right angle dsj For the j-th d-axis motor current, i qsk For the kth q-axis motor current, n mjk Is m at the m jk The rotating speed of each motor;
(4.3) if k is not less than N I Jumping to the step (4.4); if k is<N I If k = k +1, jumping to step (4.2);
(4.4) if j is not less than N I Jumping to the step (5); if j<N I If j = j +1, jumping to step (4.1);
(5) Summarizing all discrete current operating condition points (i) with any discrete rotating speed determined in the step (4) dsj ,i qsk ,n mjk ) And obtaining the required sample operation working condition point.
3. The loss optimization control method for the interior permanent magnet synchronous motor according to claim 1, characterized in that a gradient descent method 1 is adopted to iteratively solve a neural network function mapping relation f NN1 The parameters of (a); the gradient descent method 1 comprises the following specific steps:
(1) Defining a neural network function mapping relationship f NN1 The parameters of (2), including: the threshold value of the jth neuron of the output layer of the neural network is theta j1 The h neuron of the hidden layer of the neural network has a threshold value of gamma h1 The connection weight between the ith neuron of the input layer and the h neuron of the hidden layer of the neural network is v ih1 The connection weight between the h-th neuron of the hidden layer and the j-th neuron of the output layer is w hj1 ；
(2) In the range of 0 to 1In-the-wall, initializing neural network function mapping relation f NN1 The parameters of (1); selecting the upper limit of relative error epsilon 1 ；
(3) Function mapping relation f based on neural network NN1 Calculating an estimated motor loss value P Obs The expression is:
in the above equation, y 11 ～y 41 Respectively 1 st to 4 th output variables, y, of the neural network j1 Is the jth output variable, beta, of the output layer of the neural network j1 Input variables for the jth neuron of the output layer of the neural network, b h1 Output variable, alpha, for the h-th neuron of the hidden layer of the neural network h1 Input variable, x, for the h-th neuron of the hidden layer of a neural network i1 The ith input variable of the neural network is f, the fundamental frequency of the motor power supply is σ, the Sigmoid function is q, the total number of the neurons of the output layer of the neural network is d, the total number of the input variables of the neural network is R Obs The value is the estimated value of the equivalent total loss resistance;
(4) Calculating P Obs And the actual motor loss P obtained by the experiment Act Relative error between E and E 1 ＝|P Obs -P Act |/P Act (ii) a If the relative error E 1 <ε 1 Jumping to the step (8); if relative error E 1 ≥ε 1 Jumping to the step (5);
(5) Calculating a neural network function mapping relationship f NN1 Gradient of each parameter of (a):
in the above equation, η is the learning rate, i.e. the iteration step length; g j1 And e h1 For mathematical variables used to simplify the form of the equation:
in the equation, l is the total number of output variables of the neural network, and sign is a sign function;
(6) Updating the neural network function mapping relation f based on the gradient calculated in the step (5) NN1 The parameters of (2):
(7) Neural network function mapping relation f based on (6) updating NN1 Skipping to the step (3), thereby continuing the iterative computation;
(8) The iterative solution process is ended and the latest theta j1 、γ h1 、v ih1 、w hj1 I.e. the neural network function mapping relation f NN1 The parameter (c) of (c).
4. The loss optimization control method of the embedded permanent magnet synchronous motor according to claim 3, wherein a gradient descent method 2 is adopted to solve the neural network function mapping relation f in an iteration mode NN2 The parameters of (a); the gradient descent method 2 comprises the following specific steps:
(1) Defining a neural network function mapping relationship f NN2 The parameters of (a), including: the threshold value of the 1 st neuron of the output layer of the neural network is theta 12 The h neuron of the hidden layer of the neural network has a threshold value of gamma h2 The connection weight between the ith neuron of the input layer and the h neuron of the hidden layer of the neural network is v ih2 The connection weight between the h-th neuron of the hidden layer and the 1 st neuron of the output layer is w h12 ；
(2) Initializing a neural network function mapping relation f within the range of 0-1 NN2 The parameters of (1); selecting the upper limit of relative error epsilon 2 ；
(3) Function mapping relation f based on neural network NN2 Calculating the motor torque estimate T Obs The expression is：
In the above equation, y 12 For the 1 st output variable of the neural network, beta 12 Input variables for the 1 st neuron of the output layer of the neural network, b h2 Output variable, alpha, for the h-th neuron of the hidden layer of the neural network h2 Input variable, x, for the h-th neuron of the hidden layer of the neural network i2 The number of the input variables is the ith input variable of the neural network, Q is the total number of the neurons of the output layer of the neural network, and D is the total number of the input variables of the neural network;
(4) Calculating T Obs And the actual motor torque T obtained by the experiment Act Relative error between E and E 2 ＝|T Obs -T Act |/T Act (ii) a If relative error E 2 <ε 2 Jumping to the step (8); if the relative error E 2 ≥ε 2 Jumping to the step (5);
(5) Calculating a neural network function mapping relationship f NN2 Gradient of each parameter of (a):
in the above equation, g 12 And e h2 For mathematical variables used to simplify the form of the equation:
(6) Updating the neural network function mapping relation f based on the gradient calculated in the step (5) NN2 The parameters of (2):
(7) Neural network function mapping relation f based on (6) updating NN2 Skipping to the step (3), thereby continuing the iterative computation;
(8) The iterative solution process is ended and the latest theta 12 、γ h2 、v ih2 、w h12 I.e. the neural network function mapping relation f NN2 The parameter (c) of (c).
5. The loss optimization control method for the interior permanent magnet synchronous motor according to claim 4, wherein the motor loss optimization current vector calculation method based on the gradient descent method 3 is specifically implemented by the following steps:
(1) Setting a target rotational speed n Ref And target torque T Ref ；
(2) Determining the peak current I of the motor from the motor parameter table provided by the manufacturer max And selecting the number N of current sharing IME ；
(3) Determining a current discrete test step S IME ＝I max /N IME ；
(4) Initializing p =1;
(4.1) calculating d-axis Current i dsp ＝-pS IME ；
(4.2) in the range of 0 to I max Within range, initializing q-axis current i qsp (ii) a Selecting the upper limit of relative error epsilon NN ；
(4.3) mapping relation f based on neural network function NN2 Calculating an estimated value T of motor torque Obs The specific calculation formula is as follows:
(4.4) calculating T Obs And T Ref Relative error between E and E NN ＝|T Obs -T Ref |/T Ref (ii) a If the relative error E NN <ε NN Jumping to the step (4.8); if the relative error E NN ≥ε NN Jumping to the step (4.5);
(4.5) calculating the gradient of the q-axis current:
(4.6) updating the q-axis current based on the gradient calculated in step (4.5):
i qsp ＝i qsp +Δi qsp
(4.7) jumping to step (4.3) based on the updated q-axis current of (4.6), thereby continuing the iterative computation;
(4.8) based on the latest i qsp 、i dsp Function mapping relation f with neural network NN1 Solving the motor loss P under the P operating condition point Obsp ：
(4.9) formation of the data set (i) dsp ,i qsp ,P Obsp ) And storing;
(4.10) if p.gtoreq.N IME Jumping to the step (5); if p is<N IME If p = p +1, jumping to step (4.1);
(5) Comparing the motor losses P in all the data sets obtained in the step (4) Obsp Selecting the data set with the minimum loss, which corresponds to (i) dsp ,i qsp ) That is at the target speed n Ref Lower output target torque T Ref The motor losses of (2) optimize the current vector.
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| CN116749786A (en) * | 2023-06-26 | 2023-09-15 | 上海大学 | Modularized axial flux motor system efficiency optimization control method and system |
| CN117970819A (en) * | 2024-04-01 | 2024-05-03 | 北京邮电大学 | Optimal control method and system for nonlinear electromechanical system under state constraint |
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| CN116455288A (en) * | 2023-06-12 | 2023-07-18 | 国网上海能源互联网研究院有限公司 | No-parameter prediction control method, device, equipment and medium for electric locomotive |
| CN116455288B (en) * | 2023-06-12 | 2023-08-29 | 国网上海能源互联网研究院有限公司 | No-parameter prediction control method, device, equipment and medium for electric locomotive |
| CN116749786A (en) * | 2023-06-26 | 2023-09-15 | 上海大学 | Modularized axial flux motor system efficiency optimization control method and system |
| CN116749786B (en) * | 2023-06-26 | 2024-01-23 | 上海大学 | Modularized axial flux motor system efficiency optimization control method and system |
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