A node modeling simulation method of a salient pole permanent magnet synchronous motor

Abstract

The application provides a node simulation modeling method of a salient pole permanent magnet synchronous motor. The method comprehensively considers the asymmetric characteristics of the rotor structure of the salient pole permanent magnet synchronous motor and the difficulty in connecting the motor model with an external network, and establishes a node mathematical model of the salient pole permanent magnet synchronous motor in the form of "resistance voltage + inductance voltage + extended counter electromotive force". The modeling method is simple and effective, the meanings of various physical quantities are clear during the model establishment process, the motor model is externally expressed as a three-phase voltage source, the voltage source is composed of a resistance voltage, an inductance voltage drop and a controlled voltage source, the model structure is simple, the expression is clear, and the model has good accuracy and does not need to additionally add a buffer resistance to solve a node. In the numerical solution process, an explicit-implicit integration method combined with a discretization method is used, so that the motor model avoids an algebraic constraint problem in the solution process, and the operation efficiency of the model is improved on the premise of ensuring the accuracy of the model.

Description

Technical Field

[0001] This invention relates to the field of modeling and simulation technology for salient-pole permanent magnet synchronous motors, and more particularly to a node modeling and simulation method for salient-pole permanent magnet synchronous motors. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are developed based on electrically excited three-phase synchronous motors. They use permanent magnets instead of the electrically excited system, eliminating the need for electromagnetic windings, slip rings, and brushes. The stator structure is essentially the same as that of electrically excited three-phase synchronous motors. Compared to electrically excited synchronous motors, PMSMs have advantages such as simpler structure, smaller size, higher efficiency, and more reliable operation. There are three types of permanent magnet mounting methods for PMSMs: surface-mounted, insert-mounted, and internal-mounted. In surface-mounted PMSMs, the rotor's direct-axis air gap reluctance is equal to the quadrature-axis air gap reluctance, and the direct-axis inductance is equal to the quadrature-axis inductance; this type is a salient-pole synchronous motor. In insert-mounted and internal-mounted PMSMs, the rotor's direct-axis air gap reluctance is greater than the quadrature-axis air gap reluctance, and the direct-axis inductance is less than the quadrature-axis inductance; this type is a salient-pole synchronous motor.

[0003] When performing modeling and analysis, there are generally two ways to connect the motor model with other parts of the network: one is the compensation method, where the other parts of the network are represented using Thevenin equivalent circuits from the perspective of the motor terminals, and then solved simultaneously with the motor's mathematical equations. While this method is computationally accurate, it requires motors to be separated by distributed parameter circuits to ensure the uniqueness of the solution, which limits its application. The other method represents the motor using a parallel circuit of admittance and current sources, requiring the prediction of certain variables; this is also called the prediction method. This method is widely used in simulation software such as MATLAB and EMTP. For example, EMTP simulations are based on the trapezoidal integral rule, using the adjoint model as the dynamic element, establishing equations using the nodal method, replacing various power system components with equivalent current sources and resistors, and then solving the nodal admittance equations of the equivalent loops. Summary of the Invention

[0004] The embodiments of the present invention provide a node modeling and simulation method for a salient pole permanent magnet synchronous motor, which is used to solve the problems existing in the prior art.

[0005] To achieve the above objectives, the present invention adopts the following technical solution.

[0006] A node modeling and simulation method for a salient-pole permanent magnet synchronous motor includes:

[0007] S1 obtains the mathematical model of the salient pole permanent magnet synchronous motor in a two-phase rotating coordinate system by performing coordinate transformation on the mathematical model of the salient pole permanent magnet synchronous motor in a three-phase stationary coordinate system.

[0008] S2 reconstructs the mathematical model of the salient pole permanent magnet synchronous motor in the two-phase rotating coordinate system and establishes the nodal mathematical model of the salient pole permanent magnet synchronous motor.

[0009] S3 is based on the node mathematical model of a salient-pole permanent magnet synchronous motor. The current equation of the node mathematical model of the salient-pole permanent magnet synchronous motor is solved by the backward Euler implicit integration method, and the flux linkage equation of the node mathematical model of the salient-pole permanent magnet synchronous motor is solved by the explicit Adams-Bashforth numerical integration method. The node simulation calculation of the salient-pole permanent magnet synchronous motor is performed based on the explicit and implicit integration methods to obtain the numerical model of the salient-pole permanent magnet synchronous motor.

[0010] Preferably, the mathematical model of the salient-pole permanent magnet synchronous motor in the three-phase stationary coordinate system in step S1 includes:

[0011] Voltage equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system

[0012] (1),

[0013] Flux linkage equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system

[0014] (2),

[0015] Torque equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system

[0016] (3);

[0017] In the formula, , , This refers to the three-phase stator phase voltage. , , For three-phase stator current, The resistance per phase of the stator, , , For three-phase winding flux linkage, For differential operators, , , For the self-inductance of the stator phase winding, , , For the mutual inductance between stator phase windings The magnitude of the flux linkage of the permanent magnet to the stator phase winding. The angle between the rotor axis and the axis of the stator phase a winding is denoted as . This represents the number of pole pairs of the motor.

[0018] Step S1 includes:

[0019] Based on the principle of power invariance, coordinate transformation is performed on equations (1) and (2), and the coordinate transformation matrix is ​​combined with the coordinate transformation matrix.

[0020] (4)

[0021] The voltage equations for obtaining the mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system.

[0022] (5)

[0023] Flux linkage equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system

[0024] (6)

[0025] Torque equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system

[0026] (7);

[0027] In the formula, in the formula, The angular frequency of the motor. u d , u q , i d , i q These represent the d-axis and q-axis components of the stator voltage and current in a two-phase rotating coordinate system, respectively. , For right- and quadrature-axis inductors, .

[0028] Preferably, step S2 includes:

[0029] Reconstructing equation (3) yields the stator terminal voltage equation of the node mathematical model of the salient pole permanent magnet synchronous motor.

[0030] (8);

[0031] Transform equation (8) into equation (9)

[0032] (9),

[0033] The nodal mathematical model of the salient-pole permanent magnet synchronous motor is obtained; where, , The expression is

[0034] (10);

[0035] Will u d , u q , i d , i q As input, through formula

[0036] (11)

[0037] calculate and The magnetic flux in; where, It is a virtual d-axis flux linkage, and ;

[0038] Substituting equation (11) into equation (10), we obtain equation (11).

[0039] (12)

[0040] The differential term used to eliminate current;

[0041] Equation (12) is transformed by the inverse coordinate transformation matrix

[0042] (13)

[0043] By performing inverse coordinate transformation, the nodal mathematical model of the salient-pole permanent magnet synchronous motor in the three-phase stationary coordinate system is obtained.

[0044] (14).

[0045] Preferably, step S3 includes:

[0046] Based on the nodal mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system, the inductance characteristic equation of the equivalent three-phase circuit of the nodal mathematical model of the salient-pole permanent magnet synchronous motor in the three-phase stationary coordinate system is obtained.

[0047] (15);

[0048] In the formula, u L Inductor voltage, i L It is the inductor current;

[0049] The discretized expression for the inductor current is obtained by solving equation (15) using the implicit integration method of backward Euler.

[0050] (16);

[0051] In the formula, k express k The sampled value or variable at time 1. k +1 means k The variables in the next moment, h The discretization simulation step size for the salient-pole permanent magnet synchronous motor model is expressed as follows:

[0052] (17);

[0053] Substituting equation (16) into equation (17) and processing it, we obtain the first... k Expression for inductor current at time +1

[0054] (18);

[0055] Solving equation (11) using the explicit integration method of the Adams-Bashforth method yields...

[0056] (19)

[0057] Calculate the flux linkage of the node mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system; where, and They are k Time and k The differential expression for the flux linkage at time -1 is obtained from the flux linkage, voltage, and current at each time point, and the calculation formula is:

[0058] (20)

[0059] (twenty one);

[0060] Substituting the flux linkage calculated using equation (19) and the inductor current and voltage calculated using equation (18) into equation (12), we obtain the following calculation: k The voltage of the controlled voltage source element at time +1 e d ( k +1) and e q ( k +1);

[0061] This k The voltage of the controlled voltage source element at time +1 is subjected to an inverse coordinate transformation to obtain the extended back electromotive force in the three-phase stationary coordinate system. e a ( k +1) e b ( k +1)e c ( k +1).

[0062] As can be seen from the technical solutions provided by the embodiments of the present invention, the present invention proposes a node simulation modeling method for salient-pole permanent magnet synchronous motors. This method comprehensively considers the asymmetrical characteristics of the rotor structure of the salient-pole permanent magnet synchronous motor and the difficulties in connecting the motor model to the external network, establishing a node mathematical model of the salient-pole permanent magnet synchronous motor expressed in the form of "resistance voltage + inductance voltage + extended back EMF". The modeling method of the present invention is simple and effective. During the model establishment process, the meaning of each physical quantity is clear. The motor model is externally represented as a three-phase voltage source, which is composed of resistance voltage, inductance voltage drop, and a controlled voltage source. The model structure is simple, the expression is clear, and no additional buffer resistor is needed to solve the nodes, resulting in good accuracy. In the numerical solution process, a discretization method combining explicit and implicit integration methods is used, which avoids algebraic constraint problems in the solution process of the motor model, improving the computational efficiency of the model while ensuring its accuracy. The present invention provides an optimized node model and numerical solution method for salient-pole permanent magnet synchronous motors.

[0063] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0064] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0065] Figure 1 A flowchart illustrating the node modeling and simulation method for a salient-pole permanent magnet synchronous motor provided by this invention.

[0066] Figure 2 The overall structure diagram of a salient-pole permanent magnet synchronous motor connected to a DC bus via a three-phase converter is provided by the present invention for a node modeling and simulation method of a salient-pole permanent magnet synchronous motor.

[0067] Figure 3 Vector relationship diagram of permanent magnet synchronous motor for a node modeling and simulation method of salient pole permanent magnet synchronous motor provided by the present invention;

[0068] Figure 4 The equivalent circuit diagram of the node mathematical model of a salient-pole permanent magnet synchronous motor provided by the present invention is shown in the node modeling and simulation method of the present invention.

[0069] Figure 5 (a) Comparison of the stator a-phase current simulation results of the motor model in the MATLAB SimPowerSystem component library for the node modeling and simulation method of a salient pole permanent magnet synchronous motor provided by the present invention and the model constructed by the present invention;

[0070] Figure 5 (b) is Figure 5 (a) A partial enlarged view of the stator phase a current waveform;

[0071] Figure 6 (a) A waveform diagram of the simulation error of the stator a-phase current of the two models when the simulation step size is set to 5e-5s, for the node modeling and simulation method of the salient pole permanent magnet synchronous motor provided by the present invention.

[0072] Figure 6 (b) A waveform diagram of the simulation error of the stator a-phase current of the two models when the simulation step size is set to 1e-6s, for the node modeling and simulation method of the salient pole permanent magnet synchronous motor provided by the present invention. Detailed Implementation

[0073] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0074] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0075] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0076] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0077] This invention provides a node modeling and simulation method for salient-pole permanent magnet synchronous motors, which addresses the following technical problems existing in the prior art:

[0078] In commonly used simulation software, the modeling of salient-pole permanent magnet synchronous motors (SPSMs) involves transforming the mathematical model of the motor from a three-phase coordinate system (abc) to a two-phase rotating coordinate system (dq). This coordinate transformation eliminates the time-varying inductance matrix between the stator and rotor and decouples the flux linkage equations, simplifying the mathematical model of the SPSM, reducing the computational load, and improving simulation efficiency. However, the models of components other than the motor are all modeled using variables in the three-phase coordinate system. Therefore, "nodes" are needed to connect them to the SPSM model. When using predictive methods to solve for these nodes, since the SPSM is represented as a voltage-controlled current source, additional buffer resistors are required when connecting it to a nonlinear external network. Therefore, this modeling method negatively impacts the simulation accuracy and efficiency of the SPSM model.

[0079] Therefore, it is necessary to propose an optimized modeling and simulation method for salient-pole permanent magnet synchronous motors to improve upon the shortcomings of current modeling and simulation methods.

[0080] See Figure 1 This invention provides a node modeling and simulation method for a salient-pole permanent magnet synchronous motor, comprising the following steps:

[0081] S1 obtains the mathematical model of the salient pole permanent magnet synchronous motor in a two-phase rotating coordinate system by performing coordinate transformation on the mathematical model of the salient pole permanent magnet synchronous motor in a three-phase stationary coordinate system.

[0082] S2 reconstructs the mathematical model of the salient pole permanent magnet synchronous motor in the two-phase rotating coordinate system and establishes the nodal mathematical model of the salient pole permanent magnet synchronous motor.

[0083] S3 Based on the node mathematical model of the salient-pole permanent magnet synchronous motor, the current equation of the node mathematical model of the salient-pole permanent magnet synchronous motor is solved by the backward Euler implicit integration method, and the flux linkage equation of the node mathematical model of the salient-pole permanent magnet synchronous motor is solved by the explicit Adams-Bashforth numerical integration method; the node simulation calculation of the salient-pole permanent magnet synchronous motor is performed based on the explicit and implicit integration methods to obtain the numerical value of the salient-pole permanent magnet synchronous motor model.

[0084] In the embodiments provided by the present invention, step S1 specifically includes the following process.

[0085] Figure 2 This is a structural diagram of the salient-pole permanent magnet motor of these preferred embodiments connected to a DC bus via a three-phase converter. Figure 3 The vector relationship diagram of the permanent magnet synchronous motors of these preferred embodiments is shown with reference to... Figure 3 To obtain the mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system, the mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system can be expressed as:

[0086] Voltage equations for a mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system:

[0087] (1)

[0088] In the formula, , , This refers to the three-phase stator phase voltage. , , For three-phase stator current, The resistance per phase of the stator, , , For three-phase winding flux linkage, It is a differential operator.

[0089] Flux linkage equations for a mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system:

[0090] (2)

[0091] In the formula, , , For the self-inductance of the stator phase winding, , , For the mutual inductance between stator phase windings The magnitude of the flux linkage of the permanent magnet to the stator phase winding. It is the angle between the rotor axis and the axis of the stator phase a winding.

[0092] Torque equation of mathematical model of salient pole permanent magnet synchronous motor in three-phase stationary coordinate system:

[0093] (3)

[0094] According to the principle of energy conversion, the electromagnetic torque of a permanent magnet synchronous motor is equal to the sum of the products of the stator current and magnetic flux of each phase, where, This represents the number of pole pairs of the motor.

[0095] By transforming the mathematical models (1) and (2) of the permanent magnet synchronous motor in the three-phase stationary coordinate system according to the principle of constant power, we can obtain the mathematical model in the two-phase rotating coordinate system. The coordinate transformation matrix used can be expressed as:

[0096] (4)

[0097] The mathematical model of the salient-pole permanent magnet synchronous motor in the two-phase rotating coordinate system obtained after coordinate transformation can be expressed as follows:

[0098] Voltage equations for the mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system:

[0099] (5)

[0100] In the formula, The angular frequency of the motor. u d , u q , i d , i q These are the d-axis and q-axis components of the stator voltage and current in a two-phase rotating coordinate system, respectively.

[0101] The flux linkage equations of the mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system:

[0102] (6)

[0103] In the formula, , For right- and quadrature-axis inductors, .

[0104] Torque equation of the mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system:

[0105] (7)

[0106] The derivation process of the mathematical model of the salient pole permanent magnet synchronous motor in the two-phase rotating coordinate system shown in equations (5) to (7) is based on existing technology, and the specific derivation steps will not be repeated here.

[0107] In a preferred embodiment provided by the present invention, step S2 specifically includes the following process.

[0108] The voltage equations of the salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system are reconstructed:

[0109] (8).

[0110] The obtained stator terminal voltage equations are expressed in the form of "resistor voltage + inductor voltage + extended back EMF", and the nodal mathematical model of the salient pole permanent magnet synchronous motor is obtained by simplification:

[0111] (9).

[0112] In the formula, , The expression is:

[0113] (10)

[0114] , The magnetic flux in the middle is based on current and voltage (as mentioned above) u d , u q , i d , i q () is the input quantity, which is calculated from the state variable, and the equation is as follows:

[0115] (11)

[0116] In the formula, It is a virtual d-axis flux linkage. In order to construct a diagonal matrix, it will... Rewritten as In form, .

[0117] Substituting the above equation into... , In the expression, the differential term of the current can be eliminated:

[0118] (12)

[0119] After transforming the obtained nodal mathematical model of the salient-pole permanent magnet synchronous motor to a three-phase stationary coordinate system using inverse coordinates, the resistance and inductance matrices in the equations are converted into diagonal matrices. The first two terms represent the voltages across the stator resistance and direct-axis inductance, respectively, and the third term in the equations is expressed as an extended back EMF. The inverse coordinate transformation matrix used can be represented as follows:

[0120] (13)

[0121] Finally, the nodal mathematical model of the salient-pole permanent magnet synchronous motor in the three-phase stationary coordinate system can be obtained:

[0122] (14).

[0123] In a preferred embodiment provided by the present invention, step S3 includes the following process.

[0124] Based on the node mathematical model of the salient-pole permanent magnet synchronous motor obtained in step S2, it can be equivalent to a three-phase circuit, where each phase consists of a resistive element, an inductive element, and a controlled voltage source element connected in series, such as... Figure 4 As shown. The resistance value of the resistive element is equal to the stator resistance value of the motor. R s The inductance value of the inductor is equal to the direct-axis inductance value of the motor. L d The voltage of the controlled voltage source element e d , e q The phase voltage and phase current of the salient-pole permanent magnet synchronous motor model can be sampled and calculated within each simulation step. The phase current of the salient-pole permanent magnet synchronous motor model is the current flowing through the resistive and inductive components; the phase voltage of the salient-pole permanent magnet synchronous motor is the phase voltage generated by the network-driven motor model outside the motor model interface.

[0125] The characteristic equation of the inductor is:

[0126] (15)

[0127] In the formula, u L Inductor voltage, i L This is the inductor current, which is the phase current of the motor.

[0128] In the numerical solution process, the implicit integration method of backward Euler is used to discretize the inductor current of the salient pole permanent magnet synchronous motor model. Then the... k The inductor current at time +1 is:

[0129] (16)

[0130] In the formula, k express k The sampled value or variable at time 1. k +1 means k The variables in the next moment, h This is the discretization simulation step size for the salient pole permanent magnet synchronous motor model.

[0131] (17)

[0132] Substituting (16) into (17) and rearranging, we can obtain the first... k The expression for the inductor current at time +1:

[0133] (18)

[0134] Solving for the voltage values ​​of the controlled voltage source components requires first calculating the flux linkage values. In the nodal mathematical model of a salient-pole permanent magnet synchronous motor (PMSM), the flux linkage is a differential term. An explicit numerical integration algorithm is used in the simulation to calculate the flux linkage, ensuring both the computational efficiency and accuracy of the PMSM model. Considering the stability of the model calculation, this method employs the second-order explicit Adams-Basforth method for flux linkage calculation.

[0135] (19)

[0136] In the formula, and They are k Time and k The differential expression for the flux linkage at time -1 is obtained from the flux linkage, voltage, and current at each time point, and can be specifically expressed as:

[0137] (20)

[0138] (twenty one)

[0139] k After the flux linkage calculation at time +1 is completed, it is compared with... k Substitute the voltage and current at time +1 into the extended back EMF. e d , e q From the mathematical expression, we can obtain k The voltage of the controlled voltage source element at time +1 can be used to obtain the extended back electromotive force in the three-phase stationary coordinate system after inverse coordinate transformation. e a ( k +1)e b ( k +1) e c ( k +1).

[0140] The present invention also provides an embodiment for demonstrating the effect of performing the method provided by the present invention.

[0141] Taking a salient-pole permanent magnet motor with a capacity of 10kW and a rated voltage of 380V as an example. The parameters of this permanent magnet motor are as follows: stator armature winding resistance... =2.85Ω, rotor permanent magnet flux linkage =0.85Wb, equivalent inductance of rotor d-axis =24.75mH, rotor q-axis equivalent inductance =80.75mH, pole pair number p=4, specifically including the following steps:

[0142] Figure 2 This is a schematic diagram of the overall structure of a salient-pole permanent magnet motor connected to a DC bus via a three-phase converter, referencing... Figure 2 A node modeling and simulation method for a salient-pole permanent magnet synchronous motor is proposed. The method is implemented as follows: coordinate transformation is performed on the mathematical model of the salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system to determine the mathematical model of the salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system; based on the mathematical model of the salient-pole permanent magnet synchronous motor in the two-phase rotating coordinate system, the node mathematical model of the salient-pole permanent magnet synchronous motor is established; based on the node mathematical model of the salient-pole permanent magnet synchronous motor, the numerical solution of the salient-pole permanent magnet synchronous motor model is realized.

[0143] Figure 5 (a) Comparison of the a-phase stator current simulation results between the model constructed in this invention and the motor model in the MATLAB / Simulink SimPowerSystem component library under the same simulation environment and using the same control system. The simulation environment settings are as follows: simulation step size 5e-5s, simulation time 1.2s, and the q-axis current setpoint in the motor model control module is 3A in 0s-0.2s, 10A in 0.2s-0.5s, 3A in 0.5s-0.8s, and 6.4A in 0.8s-1.5s. Figure 5 (b) is Figure 5 (a) Local magnification of the current waveform.

[0144] Using the stator a-phase current of the SimPowerSystem motor model as a reference, the difference between its stator a-phase current and the stator a-phase current of the simulation model constructed in this invention is defined as the "error". The waveform of this error is as follows: Figure 6As shown in (a), it can be seen that at a simulation step size of 5e-5s, the peak error accounts for approximately 4% of the peak stator current. Furthermore, the model exhibits good stability even at larger simulation step sizes.

[0145] Figure 6 (b) shows the waveform of the error at a simulation step size of 1e-6s. The maximum error is 4.5‱ of the peak value of the stator a-phase current. It can be concluded that the maximum error of the modeling method proposed in this invention decreases significantly as the simulation step size decreases. The simulation results show that the error of the motor model proposed in this invention is within a very small range. Therefore, the accuracy and effectiveness of the node mathematical model of the salient pole permanent magnet synchronous motor proposed in this invention can be ensured.

[0146] In summary, this invention proposes a node simulation modeling method for salient-pole permanent magnet synchronous motors. This method comprehensively considers the asymmetrical characteristics of the rotor structure of salient-pole permanent magnet synchronous motors and the difficulties in connecting the motor model to the external network, establishing a mathematical model of the salient-pole permanent magnet synchronous motor nodes expressed in the form of "resistance voltage + inductance voltage + extended back EMF". The modeling method of this invention is simple and effective. During the model establishment process, the meaning of each physical quantity is clear. The motor model externally manifests as a three-phase voltage source, which is composed of resistance voltage, inductance voltage drop, and a controlled voltage source. The model structure is simple, the expression is clear, and it does not require additional buffer resistors to solve the nodes, exhibiting good accuracy. In the numerical solution process, a discretization method combining explicit and implicit integration methods is used, which avoids algebraic constraint problems in the solution process, improving the computational efficiency of the model while ensuring its accuracy. This invention provides an optimized node model and numerical solution method for salient-pole permanent magnet synchronous motors.

[0147] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0148] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0149] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0150] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A node modeling and simulation method for a salient-pole permanent magnet synchronous motor, characterized in that, include: S1 obtains the mathematical model of the salient pole permanent magnet synchronous motor in a two-phase rotating coordinate system by performing coordinate transformation on the mathematical model of the salient pole permanent magnet synchronous motor in a three-phase stationary coordinate system. S2 reconstructs the mathematical model of the salient pole permanent magnet synchronous motor in the two-phase rotating coordinate system and establishes the node mathematical model of the salient pole permanent magnet synchronous motor. S3, based on the node mathematical model of the salient-pole permanent magnet synchronous motor, solves the current equation of the node mathematical model of the salient-pole permanent magnet synchronous motor by means of the backward Euler implicit integration method, and solves the flux linkage equation of the node mathematical model of the salient-pole permanent magnet synchronous motor by means of the explicit Adams-Bashforth numerical integration method; and performs simulation calculations of the nodes of the salient-pole permanent magnet synchronous motor based on the explicit and implicit integration methods to obtain the numerical values ​​of the salient-pole permanent magnet synchronous motor model.

2. The method according to claim 1, characterized in that, The mathematical model of the salient-pole permanent magnet synchronous motor in the three-phase stationary coordinate system mentioned in step S1 includes: Voltage equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system （1）， Flux linkage equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system （2）， Torque equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a three-phase stationary coordinate system （3）； In the formula, , , This refers to the three-phase stator phase voltage. , , For three-phase stator current, The resistance per phase of the stator, , , For three-phase winding flux linkage, For differential operators, , , For the self-inductance of the stator phase winding, , , For the mutual inductance between stator phase windings The magnitude of the flux linkage of the permanent magnet to the stator phase winding. The angle between the rotor axis and the axis of the stator phase a winding is denoted as . This represents the number of pole pairs of the motor. Step S1 includes: Based on the principle of power invariance, coordinate transformation is performed on equations (1) and (2), and the coordinate transformation matrix is ​​combined with the coordinate transformation matrix. （4） The voltage equations for obtaining the mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system. （5）、 Flux linkage equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system （6） Torque equations of a mathematical model of a salient-pole permanent magnet synchronous motor in a two-phase rotating coordinate system （7）； In the formula, The angular frequency of the motor. u d , u q , i d , i q These represent the d-axis and q-axis components of the stator voltage and current in a two-phase rotating coordinate system, respectively. , For right- and quadrature-axis inductors, .

3. The method according to claim 2, characterized in that, Step S2 includes: Reconstructing equation (3) yields the stator terminal voltage equation of the node mathematical model of the salient pole permanent magnet synchronous motor. （8）； Transform equation (8) into equation (9) （9）， The nodal mathematical model of the salient pole permanent magnet synchronous motor is obtained; where, , The expression is （10）； Will u d , u q , i d , i q As input, through formula （11） calculate and The magnetic flux in; where, It is a virtual d-axis flux linkage, and ; Substituting equation (11) into equation (10), we obtain equation (11). （12）， The differential term used to eliminate current; Equation (12) is transformed by the inverse coordinate transformation matrix （13） By performing inverse coordinate transformation, the nodal mathematical model of the salient-pole permanent magnet synchronous motor in the three-phase stationary coordinate system is obtained. （14）。 4. The method according to claim 3, characterized in that, Step S3 includes: Based on the nodal mathematical model of the salient-pole permanent magnet synchronous motor in the three-phase stationary coordinate system, the inductance characteristic equation of the equivalent three-phase circuit of the nodal mathematical model of the salient-pole permanent magnet synchronous motor in the three-phase stationary coordinate system is obtained. （15）； In the formula, u L Inductor voltage, i L It is the inductor current; The discretized expression for the inductor current is obtained by solving equation (15) using the implicit integration method of backward Euler. （16）； In the formula, k express k The sampled value or variable at time 10:

00. k +1 means k The variables in the next moment, h The discretization simulation step size for the salient-pole permanent magnet synchronous motor model is expressed as follows: （17）； Substituting equation (16) into equation (17) and processing it, we obtain the first... k Expression for inductor current at time +1 （18）； Solving equation (11) using the explicit integration method of the Adams-Bashforth method yields... （19） Calculate the flux linkage of the node mathematical model of the salient pole permanent magnet synchronous motor in the two-phase rotating coordinate system; where, and They are k Time and k The differential expression for the flux linkage at time -1 is obtained from the flux linkage, voltage, and current at each time point, and the calculation formula is: （20） （21）； Substituting the flux linkage calculated using equation (19) and the inductor current and voltage calculated using equation (18) into equation (12), we obtain the following calculation: k The voltage of the controlled voltage source element at time +1 e d ( k +1) and e q ( k +1); This k The voltage of the controlled voltage source element at time +1 is subjected to an inverse coordinate transformation to obtain the extended back electromotive force in the three-phase stationary coordinate system. e a ( k +1) e b ( k +1) e c ( k +1).

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