Modeling and control method of embedded permanent magnet synchronous motor based on vector magnetic circuit coordinate transformation

Abstract

The present invention discloses an embedded permanent magnet synchronous motor modeling and control method based on vector magnetic circuit coordinate transformation. First, the d-axis and q-axis vector magnetic circuit models of the embedded permanent magnet motor are established, and the arctangent value of the ratio of the equivalent magnetic inductive reactance to the magnetic resistance of the d-axis or q-axis magnetic circuit is regarded as the iron loss angle of the d-axis or q-axis magnetic circuit. The d-axis and q-axis iron loss angles are used to consider the influence of iron loss and its salient pole effect on motor performance and its control, and an R-L coordinate transformation considering the salient pole effect and an R-L coordinate system considering the salient pole effect are proposed; then, a magnetic flux equation and a voltage equation are established based on the vector magnetic circuit and the R-L coordinate system considering the salient pole effect, and a position sensorless control method is established based on the proposed analysis model. The method proposed in the present invention can fully consider the influence of iron loss and salient pole effect on motor performance and its control, and is simple and convenient, with clear physical meaning, and improves the rotor position identification accuracy of position sensorless control.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor control, and in particular relates to a modeling and control method of an embedded permanent magnet synchronous motor based on vector magnetic circuit coordinate transformation. Background Art

[0002] Interior permanent magnet synchronous motor (IPMSM) has the advantages of high power density, wide speed regulation range, high working efficiency, etc. It has broad application prospects in the industrial field. In recent years, it has been widely used in rail transportation, household appliances, electric vehicles and other fields. The performance of permanent magnet synchronous motor is not only affected by the structure of the motor body, but also by the control algorithm. Among them, vector control is one of the most common control methods of permanent magnet synchronous motor.

[0003] To achieve high-performance control of permanent magnet synchronous motors, accurate rotor position and speed information is essential. Usually, rotor position and speed information can be obtained through position sensors, such as resolvers, absolute position encoders, etc. However, position sensors also bring some problems to the entire traction drive system, such as increased system cost, reduced system reliability caused by position sensor failure, and increased installation volume of traction motors. In order to solve the problems caused by position sensors, position sensorless control has received more and more attention at home and abroad in recent years. According to the current research status, permanent magnet synchronous motor position sensorless control is mainly divided into methods based on salient pole characteristics applied in the zero-low speed range and methods based on fundamental wave models applied in the medium and high speed range. Usually, methods based on fundamental wave models can obtain satisfactory control performance in the medium and high speed operation range. Methods based on fundamental wave models mainly estimate the rotor position and speed information by estimating the back electromotive force component. Iron loss is inevitable when the motor is running. However, most of the research on position sensorless control of permanent magnet synchronous motors is carried out without considering iron loss. When the motor is running at medium and high speeds, the iron loss is large due to the high speed, and the motor fundamental wave model is required. The use of traditional motor models that do not consider iron loss will affect the performance of the position sensorless control system. Therefore, it is very important to establish a more accurate permanent magnet synchronous motor model that takes iron loss into account.

[0004] The Southeast University team proposed the magnetic induction, magnetic capacitance, vector magnetic circuit theory and magneto-electric power law, which provided a new method for considering the iron loss of permanent magnet synchronous motors, which is different from the equivalent resistance. The active loss caused by the magnetic induction element corresponds to the eddy current loss in the magnetic circuit, and the active loss caused by the magnetic capacitance element corresponds to the hysteresis loss in the magnetic circuit. They introduced magnetic induction into the permanent magnet synchronous motor model to consider the influence of eddy current reaction on the permanent magnet magnetic flux and the stator magnetic flux excited by the armature current, and derived a new permanent magnet synchronous motor model based on the vector magnetic circuit theory.

[0005] For embedded permanent magnet synchronous motors, due to the asymmetry of the d-axis and q-axis inductances, it is not possible to directly use basic mathematical models to estimate the rotor position and speed. Therefore, some scholars have proposed the concept of extended back-EMF, which is used to estimate the rotor position and speed by estimating the extended back-EMF. In the analysis model of embedded permanent magnet synchronous motors based on vector magnetic circuit theory, the introduction of coupling terms makes the extended back-EMF more complicated. The method of constructing observers is used for estimation, such as disturbance observers, full-order observers, sliding mode observers, etc. Among them, the sliding mode observer, as a nonlinear robust control strategy, has good robustness to the uncertainty and disturbance of the system model, has broad application prospects, and has gradually been applied to position sensorless control. Summary of the invention

[0006] The purpose of the present invention is to consider the iron loss of an embedded permanent magnet synchronous motor, use coordinate transformation to reflect the influence of iron loss on the motor, improve the analysis model of the embedded permanent magnet synchronous motor based on the vector magnetic circuit, realize the position sensorless control of the embedded permanent magnet synchronous motor considering the iron loss when the motor is running at medium and high speeds, and improve the position sensorless control accuracy of the embedded permanent magnet synchronous motor.

[0007] The present invention proposes a method for establishing a vector magnetic circuit coordinate transformation and an embedded permanent magnet synchronous motor analysis model considering the salient pole effect: establishing the d-axis and q-axis vector magnetic circuit models of the embedded permanent magnet synchronous motor, considering the different d-axis and q-axis magnetic resistances of the embedded permanent magnet synchronous motor, and taking the inverse tangent value of the ratio of the equivalent magnetic reactance to the d-axis magnetic resistance as the d-axis iron loss angle δ d , the inverse tangent of the ratio of the equivalent magnetic inductive reactance to the q-axis magnetic resistance is regarded as the q-axis iron loss angle δ q , the d-axis and q-axis iron loss angles are used to characterize the influence of iron loss and salient pole effect on stator flux and permanent magnet flux;

[0008] A method considering the saliency effect is proposed. Coordinate transformation and consideration of saliency effect Coordinate system, considering the saliency effect Coordinate system Axis and The axis lags behind the d-axis and q-axis of the dq coordinate system by δ d and δq , based on vector magnetic circuit and considering salient pole effect The analysis model of embedded permanent magnet motor is established in the coordinate system, including the vector magnetic circuit and the salient pole effect. Coordinate system flux equation and voltage equation;

[0009] Furthermore, the d-axis and q-axis vector magnetic circuit models of the embedded permanent magnet synchronous motor refer to the introduction of magnetic induction into the d-axis and q-axis magnetic circuit models of the embedded permanent magnet synchronous motor IPMSM. and magnetic capacitance C; using magnetic induction and magnetic capacitance C characterize iron loss; magnetic induction Both the magnetic flux and the magnetic capacitance C lag behind the magnetomotive force or current, so the equivalent magnetic induction parameter Equivalent magnetic induction The active power loss caused by the magnetic induction element corresponds to the eddy current loss in the magnetic circuit, and the active power loss caused by the magnetic capacitance element corresponds to the hysteresis loss in the magnetic circuit.

[0010] Furthermore, the d-axis iron loss angle δ d and q-axis iron loss angle δ q , respectively expressed as follows:

[0011]

[0012] make:

[0013]

[0014] k is called the equivalent magnetic induction coefficient;

[0015] Since the magnetic resistance of the d-axis and q-axis is expressed as and

[0016] Then, the iron loss angle δ of the embedded permanent magnet synchronous motor IPMSMd axis is d and the iron loss angle δ of the q axis q It is expressed as:

[0017] δ d =arctan(ωL d k) (4)

[0018] δ q =arctan(ωL q k) (5)

[0019] is the magnetic induction in the dq coordinate system, C is the magnetic capacitance in the dq coordinate system, is the magnetic reluctance of the d-axis, is the magnetic resistance of the q axis, L d is the inductance of the d-axis, Lq is the inductance of the q axis, δ d is the iron loss angle of the d-axis, δ q is the iron loss angle of the q-axis, ω is the rotor electrical angular velocity, and N is the number of turns of the armature winding.

[0020] Furthermore, the equivalent magnetic induction parameter is introduced into the magnetic circuit of the embedded permanent magnet motor, and the magnetic flux equation of the embedded permanent magnet motor based on the vector magnetic circuit in dq coordinates is obtained:

[0021]

[0022] The voltage equation of the embedded permanent magnet synchronous motor in the dq coordinate system:

[0023]

[0024] Multiply both sides of the above equation by the matrix And because Ignore R s tanδ d , R s tanδ q tan 2 δ d and tan 2 δ q ;

[0025] The voltage equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the dq coordinate system is obtained:

[0026]

[0027] The voltage equation of the embedded permanent magnet motor based on the vector magnetic circuit in the α-β coordinate system is obtained:

[0028]

[0029] Among them, the back electromotive force for:

[0030]

[0031] In the formula, ψ d and ψ q is the magnetic flux in the dq coordinate system, u d and u q is the voltage in the dq coordinate system, i d and i q is the current in the dq coordinate system, u α and u β is the voltage in the α-β coordinate system, i α and i β is the current in the α-β coordinate system, Ld is the inductance of the d-axis, L q is the inductance of the q axis, R s is the armature winding resistance, ψ f is the permanent magnet flux, k is the equivalent magnetic induction coefficient, δ d is the d-axis iron loss angle, δ q is the q-axis iron loss angle, ω is the rotor electrical angular velocity, and p is the differential operator.

[0032] Furthermore, considering the salient pole effect The coordinate transformation satisfies that the amplitude, phase and angular velocity of the synthetic phasor remain unchanged before and after the transformation, which can be expressed as:

[0033]

[0034] in, is the synthetic phase, The synthetic phase Axis component, The synthetic phase Axis component, is the d-axis component of the synthetic phase, is the q-axis component of the synthetic phase, e jωt is the angular velocity of rotation of the phasor;

[0035] The dq coordinate system and the salient pole effect are considered Coordinate transformation relationship of coordinate system:

[0036]

[0037] in, To consider the saliency effect The coordinate transformation matrix is ​​to rotate the d-axis and q-axis in the direction of lag by the iron loss angle δ d and δ q , so that the dq coordinate system is transformed to Coordinate system.

[0038] Furthermore, the flux term in the flux equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the dq coordinate system is transformed to In the coordinate system, based on the vector magnetic circuit and considering the salient pole effect, The flux equation of the embedded permanent magnet synchronous motor in the coordinate system is:

[0039]

[0040] Transform the flux term in the voltage equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the dq coordinate system to In the coordinate system, since the iron loss angle is small, sin(δ q -δd )≈tanδ q -tanδ d 、sin(δ q -δ d )(tanδ q -tanδ d )<<1, Based on the vector magnetic circuit and considering the salient pole effect, The voltage equation of the embedded permanent magnet synchronous motor in the coordinate system is:

[0041]

[0042] Ignore L q sin(δ q -δ d )pi q and L d sin(δ q -δ d )pi d , based on the vector magnetic circuit and considering the salient pole effect The simplified form of the voltage equation of the embedded permanent magnet synchronous motor in the coordinate system is:

[0043]

[0044] In the formula, and for Magnetic flux in the coordinate system, and for The voltage in the coordinate system, i d and i q is the current in the dq coordinate system, L d is the inductance of the d-axis, L q is the inductance of the q axis, R s is the armature winding resistance, ψ f is the permanent magnet flux, δ d is the d-axis iron loss angle, δ q is the q-axis iron loss angle, ω is the rotor electrical angular velocity, and p is the differential operator.

[0045] Based on the vector magnetic circuit coordinate transformation considering the salient pole effect and the embedded permanent magnet synchronous motor analysis model of the present invention, the present invention also proposes a position sensorless control method for an embedded permanent magnet motor, and the specific steps are as follows:

[0046] The three-phase current of the motor is sampled to obtain Will The current sampling value in the α-β coordinate system is obtained through the Clark transformation module and Then and The current sampling value in the dq coordinate system is obtained through the Park transformation module and Rotor speed observation With the setting value n ref The error is passed through the PI controller to obtain the d-axis and q-axis current setting values ​​i d and i q , calculate the d-axis and q-axis current sampling values ​​i d * and i q * With the set value i d and i q The error is input into two PI controllers respectively, and we get Voltage in coordinate system and By considering the saliency effect The coordinate transformation module obtains the voltage u in the dq coordinate system d and u q , and then through the Park inverse transformation module, based on the rotor position angle observation value Perform Park inverse transformation to obtain the voltage u in the α-β coordinate system α and u β , use u α and u β The synthesized voltage space vector is input into the voltage space vector modulation module for modulation, and the state coding values ​​of the three half bridges are output to control the MOS tube switches of the three-phase inverter to control the motor.

[0047] Furthermore, the rotor speed observation value is obtained through the rotor position and speed observation module and the rotor position angle observation

[0048] The rotor position and speed observation module includes a sliding mode observer, a low-pass filter and a phase-locked loop;

[0049] Assume the back electromotive force: in:

[0050]

[0051] The sliding mode observer is designed according to formula (12). The input of the sliding mode observer is and The back electromotive force observation value is obtained by low-pass filtering and phase and amplitude compensation. The rotor position information is extracted as follows:

[0052]

[0053] Rotor position angle observation It is expressed as:

[0054]

[0055] The inverse tangent is calculated by the phase-locked loop to obtain the rotor position angle observation value

[0056] Rotor angular velocity observation It is expressed as:

[0057]

[0058] Rotor speed observation It is expressed as:

[0059]

[0060] In formula (20-24), A and B are the motor state measurement values ​​in the dq coordinate system, and is the observed value of the back electromotive force in the two-phase stationary coordinate system, u α and u β is the voltage of the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, L d is the inductance of the d-axis, L q is the inductance of the q axis, R s is the resistance of the armature winding, ψ f is the permanent magnet flux, k is the equivalent magnetic induction coefficient, δ d is the d-axis iron loss angle, ω is the rotor electrical angular velocity, is the observed value of the rotor electrical angular velocity, θ is the electrical angle of the rotor position, is the observed value of the rotor position angle, p is the differential operator, and P is the pole pair number.

[0061] Furthermore, considering the salient pole effect The coordinate transformation module is to transform Axis and The axis voltage is transformed into d-axis and q-axis voltages, and the input-output relationship is expressed as:

[0062] u out =T δ u in (19)

[0063] In formula (19), and To consider the saliency effect The input and output matrices of the coordinate transformation module, T δ To consider the saliency effect Coordinate transformation matrix T δ The inverse matrix of ′.

[0064] Compared with the existing model, the above model has the following technical effects:

[0065] (1) The embedded permanent magnet synchronous motor analysis model considering iron loss proposed in the present invention is closer to the actual embedded permanent magnet synchronous motor than the model ignoring iron loss, and has higher control accuracy;

[0066] (2) Different from the traditional method of using resistance to equate iron loss, the present invention is based on the vector magnetic circuit theory and takes into account the relationship between the magnetic circuit and the circuit, and proposes an analysis model of an embedded permanent magnet synchronous motor based on the vector magnetic circuit and the influence of iron loss.

[0067] (3) According to the proposed vector control of the voltage equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit for coordinate transformation, the decoupling effect of the d-axis current loop and the q-axis current loop is better, the step response of the embedded permanent magnet synchronous motor is faster, the current waveform is more stable, and it is more conducive to the vector control of the embedded permanent magnet synchronous motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0069] Figure 1 is a flow chart of the method of the present invention;

[0070] Figure 2 A schematic diagram of a coordinate system established for the present invention;

[0071] Figure 3 The invention is based on the vector magnetic circuit and considers the salient pole effect. Block diagram of the position sensorless control method for an embedded permanent magnet motor in a coordinate system;

[0072] Figure 4 This is a simulation effect diagram of the control method of the present invention;

[0073] Figure 5 This is a simulation effect diagram of the position sensorless control when the rotation speed of the present invention is 500r / min;

[0074] Figure 6 This is a simulation effect diagram of position sensorless control when the rotation speed of the present invention is 1000r / min. DETAILED DESCRIPTION

[0075] Combined with the present invention Figure 1-3 Based on the content of the present invention, a specific embodiment of a vector magnetic circuit coordinate transformation and an embedded permanent magnet synchronous motor analysis and control method considering the salient pole effect is completed. Figure 4-6 The simulation results of the specific embodiments verify the effectiveness of the present invention. The described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0076] The vector magnetic circuit coordinate transformation and embedded permanent magnet synchronous motor analysis and control method considering the salient pole effect of the present invention comprises the following steps:

[0077] Step 1: Establish the d-axis and q-axis vector magnetic circuit models of the embedded permanent magnet motor. Considering the different magnetic resistances of the d-axis and q-axis of the embedded permanent magnet synchronous motor, the inverse tangent of the ratio of the equivalent magnetic reactance to the d-axis magnetic resistance is regarded as the d-axis iron loss angle δ d , the inverse tangent of the ratio of the equivalent magnetic inductive reactance to the q-axis magnetic resistance is regarded as the q-axis iron loss angle δ q , the d-axis and q-axis iron loss angles are used to characterize the influence of iron loss and salient pole effect on stator flux and permanent magnet flux;

[0078] Introducing magnetic induction into the d-axis and q-axis magnetic circuit models of embedded permanent magnet synchronous motors The two vector magnetic circuit parameters of magnetic induction and magnetic capacitance C are used to construct the d-axis and q-axis vector magnetic circuit models. The magnetic induction element and magnetic capacitance C characterize the iron loss. The active power loss caused by the magnetic induction element corresponds to the eddy current loss in the magnetic circuit, and the active power loss caused by the magnetic capacitance element corresponds to the hysteresis loss in the magnetic circuit. Both the magnetic flux and the magnetic capacitance C lag behind the magnetomotive force or current, so the equivalent magnetic induction parameter can be used Equivalent magnetic induction The combined effect of the magnetic capacitance C and the iron loss is taken into account. In the d-axis and q-axis vector magnetic circuit models, the d-axis and q-axis magnetic circuits are different, that is, the magnetic resistance is different, and the iron loss angles generated by the d-axis and q-axis are also different. The angle at which the d-axis magnetic flux lags behind the d-axis magnetomotive force or current is the iron loss angle δ d , iron loss angle δ d It can be expressed as the inverse tangent of the ratio of the equivalent magnetic inductive reactance to the d-axis magnetic resistance; the angle at which the q-axis magnetic flux lags behind the q-axis magnetomotive force or current is the iron loss angle δ q , iron loss angle δ q It can be expressed as the inverse tangent of the ratio of the equivalent magnetic inductive reactance to the q-axis magnetic resistance. The formula is as follows:

[0079]

[0080] make:

[0081]

[0082] k is called the equivalent magnetic induction coefficient, which can be measured experimentally. In the present invention, the change of the equivalent magnetic induction coefficient is not considered, and the equivalent magnetic induction coefficient is considered to be a fixed parameter. Since the d-axis and q-axis magnetic resistance can be expressed as and Furthermore, the iron loss angle δ of the d-axis of the embedded permanent magnet synchronous motor d and the iron loss angle δ of the q axis q It can be expressed as:

[0083] δ d =arctan(ωL d k) (4)

[0084] δ q =arctan(ωL q k) (5)

[0085] In formula (1-5), is the magnetic induction in the dq coordinate system, C is the magnetic capacitance in the dq coordinate system, is the magnetic reluctance of the d-axis, is the magnetic resistance of the q axis, L d is the inductance of the d-axis, L q is the inductance of the q axis, δ d is the iron loss angle of the d-axis, δ q is the iron loss angle of the q-axis, ω is the rotor electrical angular velocity, and N is the number of turns of the armature winding.

[0086] Step 2: Propose a method that takes into account the saliency effect Coordinate transformation and consideration of saliency effect Coordinate system, considering the saliency effect Coordinate system Axis and The axis lags behind the d-axis and q-axis of the dq coordinate system by δ d and δ q , based on vector magnetic circuit and considering salient pole effect The embedded permanent magnet motor analysis model is established in the coordinate system, including the vector magnetic circuit and the salient pole effect. Coordinate system flux equation and voltage equation;

[0087] Introducing equivalent magnetic induction parameters into magnetic circuit equations of embedded permanent magnet synchronous motors Based on the vector magnetic circuit theory, Parker transformation is performed to obtain the magnetic circuit equation based on the vector magnetic circuit in the dq coordinate system.

[0088]

[0089] In formula (6), and is the magnetomotive force in the dq coordinate system, Φ d and Φ q is the magnetic flux in the dq coordinate system, i d and i q is the current in the dq coordinate system, is the equivalent magnetic induction in the dq coordinate system, is the magnetic reluctance of the d-axis, is the magnetic resistance of the q axis, L d is the inductance of the d-axis, L q is the inductance of the q-axis, ψ f is the permanent magnet flux, ω is the rotor electrical angular velocity, N is the number of turns of the armature winding, and p is the differential operator;

[0090] When the motor is running stably, it is considered that the d-axis and q-axis magnetic circuits are in a stable state, and further, it can be obtained that:

[0091]

[0092] Combining equations (4), (5) and (7), we can obtain the flux equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the dq coordinate system:

[0093]

[0094] The voltage equation of the embedded permanent magnet synchronous motor in the dq coordinate system:

[0095]

[0096] Multiply both sides of the above equation by the matrix have to:

[0097]

[0098] In formula (10) R can be ignored s tanδ d , R s tanδ q tan 2 δ d and tan 2 δ q , the voltage equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the dq coordinate system is obtained:

[0099]

[0100] Furthermore, the voltage equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the α-β coordinate system is obtained:

[0101]

[0102] In formula (12), the back electromotive force for:

[0103]

[0104] In formula (7-13), ψ d and ψ q is the magnetic flux in the dq coordinate system, u d and u q is the voltage in the dq coordinate system, i d and i q is the current in the dq coordinate system, u α and u β is the voltage of the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, L d is the inductance of the d-axis, L q is the inductance of the q axis, R s is the armature winding resistance, ψ f is the permanent magnet flux, k is the equivalent magnetic induction coefficient, δ d is the d-axis iron loss angle, δ q is the q-axis iron loss angle, ω is the rotor electrical angular velocity, θ is the rotor position electrical angle, and p is the differential operator.

[0105] Due to the salient pole effect, the d-axis and q-axis magnetic circuits are different, the magnetic resistance is different, and the iron loss angles generated by the d-axis and q-axis are also different, such as Figure 2 As shown in Figure 2, considering the salient pole effect In the coordinate system, Axis hysteresis d axis iron loss angle δ d , Axis hysteresis q-axis iron loss angle δ q ;

[0106] Considering the saliency effect The coordinate transformation needs to ensure that the amplitude, phase and angular velocity of the synthetic phasor remain unchanged before and after the transformation, which can be expressed as:

[0107]

[0108] In formula (14), is the synthetic phase, The synthetic phase Axis component, The synthetic phase Axis component, is the d-axis component of the synthetic phase, is the q-axis component of the synthetic phase, e jωt is the angular velocity of rotation of the phasor;

[0109] The dq coordinate system and the salient pole effect can be obtained Coordinate transformation relationship of coordinate system:

[0110]

[0111] In formula (15), To consider the saliency effect The coordinate transformation matrix is ​​to rotate the d-axis and q-axis in the direction of lag by the iron loss angle δ d and δ q , so that the dq coordinate system is transformed to Coordinate system;

[0112] Combining equations (8) and (15), we can obtain the equation based on the vector magnetic circuit and considering the salient pole effect: The flux equation of the embedded permanent magnet synchronous motor in the coordinate system is:

[0113]

[0114] The voltage term on the left side of equation (11) is transformed by the coordinate system matrix T δ 'Transform to In the coordinate system, due to the small iron loss angle, it can be considered that sin(δ q -δ d )≈tanδ q -tanδ d 、sin(δ q -δ d )(tanδ q -tanδ d )<<1. The voltage equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit and the RL coordinate system considering the salient pole effect can be obtained:

[0115]

[0116] If we ignore L q sin(δ q -δ d )pi q and L d sin(δ q -δ d )pi d , based on the vector magnetic circuit and considering the salient pole effect, The simplified form of the voltage equation of the embedded permanent magnet synchronous motor in the coordinate system is:

[0117]

[0118] In formula (15-18), and for Magnetic flux in the coordinate system, and for Voltage in the coordinate system, u d and u q is the voltage in the dq coordinate system, i d and i q is the current in the dq coordinate system, L d is the inductance of the d-axis, L q is the inductance of the q axis, R s is the armature winding resistance, ψ f is the permanent magnet flux, δ d is the d-axis iron loss angle, δ q is the q-axis iron loss angle, ω is the rotor electrical angular velocity, and p is the differential operator.

[0119] Step 3: Establish a vector magnetic circuit and consider the salient pole effect Position sensorless control method for embedded permanent magnet motor in coordinate system;

[0120] Based on the vector magnetic circuit and considering the salient pole effect The embedded permanent magnet motor analysis model is established in the coordinate system, and the vector magnetic circuit and salient pole effect are considered. The invention discloses a method for controlling an embedded permanent magnet motor without position sensor in a coordinate system, including a speed loop, a d-axis current loop, and a q-axis current loop; the specific modules include a PI controller (PI), a voltage space vector modulation module (SVPWM), a Clark transformation module (abc / αβ), a Clark inverse transformation module (αβ / abc), a Park transformation module (αβ / dq), a Park inverse transformation module (dq / αβ), and a salient pole effect considering the salient pole effect. Coordinate transformation module and rotor position and speed observation module (SMO);

[0121] The collaborative working process of each module is as follows: Figure 3 As shown, the three-phase current of the motor is sampled to obtain Will The current sampling value in the α-β coordinate system is obtained through the Clark transformation module (abc / αβ) and Then and The current sampling value in the dq coordinate system is obtained through the Park transformation module (αβ / dq) and Rotor speed observation The error with the set value n is passed through the PI controller (PI) to obtain the d-axis and q-axis current set values ​​i dand i q , calculate the d-axis and q-axis current sampling values ​​i d * and i q * With the set value i d and i q The error is input into two PI controllers (PI), and we get Voltage in coordinate system and By considering the saliency effect Coordinate transformation module Get the voltage u in the dq coordinate system d and u q , and then through the Park inverse transformation module (dq / αβ), based on the rotor position angle observation value Perform Park inverse transformation to obtain the voltage u in the α-β coordinate system α and u β , use u α and u β The synthesized voltage space vector is input into the voltage space vector modulation module (SVPWM) for modulation, and the state coding values ​​of the three half-bridges are output to control the MOS tube switches of the three-phase inverter to control the motor. The rotor speed and rotor position angle used are provided by the rotor position and speed observation module (SMO);

[0122] Considering the saliency effect The coordinate transformation module is to transform Axis and The axis voltage is transformed into d-axis and q-axis voltages, and the input-output relationship can be expressed as:

[0123] u out =T δ u in (19)

[0124] In formula (19), and To consider the saliency effect The input and output matrices of the coordinate transformation module, T δ To consider the saliency effect Coordinate transformation matrix T δ ′’s inverse matrix;

[0125] The rotor position and speed observation module in the present invention comprises: a sliding mode observer, a low-pass filter and a phase-locked loop;

[0126] According to formula (13), the back electromotive force is: in:

[0127]

[0128] The sliding mode observer is designed according to formula (12). The input of the sliding mode observer is and The back electromotive force observation value is obtained by low-pass filtering and phase and amplitude compensation. The rotor position information is extracted as follows:

[0129]

[0130] Rotor position angle observation It can be expressed as:

[0131]

[0132] The inverse tangent is calculated by the phase-locked loop to obtain the rotor position angle observation value

[0133] Rotor angular velocity observation It can be expressed as:

[0134]

[0135] Rotor speed observation It is expressed as:

[0136]

[0137] In formula (20-24), A and B are the motor state measurement values ​​in the dq coordinate system, and is the observed value of the back electromotive force in the two-phase stationary coordinate system, u α and u β is the voltage of the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, L d is the inductance of the d-axis, L q is the inductance of the q axis, R s is the resistance of the armature winding, ψ f is the permanent magnet flux, k is the equivalent magnetic induction coefficient, δ d is the d-axis iron loss angle, ω is the rotor electrical angular velocity, is the observed value of the rotor electrical angular velocity, θ is the electrical angle of the rotor position, is the observed value of the rotor position angle, p is the differential operator, and P is the pole pair number.

[0138] The embedded permanent magnet synchronous motor is simulated by position sensorless vector control. The motor speed is first adjusted to 500r / min and the load is 20N·m. Then the speed is adjusted to 1000r / min and the load is reduced to 8N·m. The step response speed and the stability of the current waveform are observed. Figure 4 As shown, the effects of the vector control proposed by the present invention and the traditional vector control are compared;

[0139] like Figure 5 and Figure 6 , respectively control the embedded permanent magnet synchronous motor at 500r / min and 1000r / min to identify the rotor position and speed information, compare the position sensorless control based on the proposed model with the traditional position sensorless control, compare the errors between the observed rotor position and speed information and the actual values, and verify the feasibility and effectiveness of the motor analysis model and control method proposed in the present invention. The parameters of the embedded permanent magnet synchronous motor in the simulation are shown in the following table:

[0140]

[0141]

[0142] like Figure 4 As shown, use i d =0 control, control i d unchanged, in the process of speed regulation and load reduction, the vector control i d The fluctuation is smaller, which improves the speed and stability of vector control in dealing with step response.

[0143] like Figure 5 and Figure 6 As shown in the figure, the position sensorless control based on the proposed model improves the rotor position observation accuracy compared with the traditional position sensorless control. The error is reduced by about 0.25 electrical degrees at 500r / min and by about 0.8 electrical degrees at 1000r / min. Figure 5 and Figure 6 When the speed is high, the iron loss is also greater, which causes the traditional position sensorless control to produce a large identification error. The position sensorless control based on the proposed model is also more effective in improving the error.

[0144] The above describes the embodiments of the present invention in conjunction with the figures, but does not limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solution of the present invention by ordinary technicians in this field should fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for establishing an analysis model of an embedded permanent magnet synchronous motor based on a vector magnetic circuit, characterized in that: First, the d-axis and q-axis vector magnetic circuit models of the embedded permanent magnet synchronous motor are established. The d-axis and q-axis vector magnetic circuit models of the embedded permanent magnet synchronous motor refer to introducing magnetic induction into the d-axis and q-axis magnetic circuit models of the embedded permanent magnet synchronous motor. and magnetic capacitance C; The angle at which the d-axis magnetic flux lags behind the d-axis magnetomotive force or current is recorded as the d-axis iron loss angle δ d , d-axis iron loss angle δ d Equivalent magnetic inductive reactance and d-axis magnetic resistance R d The inverse tangent of the ratio; where ω is the rotor electrical angular velocity, represents the equivalent magnetic induction parameter; Equivalent magnetic inductive reactance The expression is: d-axis magnetic resistance R d It is expressed as: Where N is the number of turns of the armature winding, L d is the inductance of the d-axis; The angle at which the q-axis magnetic flux lags behind the q-axis magnetomotive force or current is recorded as the q-axis iron loss angle δ q , q-axis iron loss angle δ q Equivalent magnetic inductive reactance and q-axis magnetic resistance R q The inverse tangent of the ratio; q-axis magnetic resistance R q It is expressed as: Among them, L q is the inductance of the q-axis; The saliency effect is considered Coordinate transformation and consideration of saliency effect Coordinate system, the salient pole effect is considered Coordinate system Axis lag dq coordinate system d axis δ d , the consideration of salient pole effect Coordinate system Axis lag dq axis δ q ; Based on vector magnetic circuit and considering salient pole effect The embedded permanent magnet motor analysis model is established in the coordinate system, including the vector magnetic circuit and the salient pole effect. Coordinate system flux equation and voltage equation.

2. The method for establishing an analysis model of an embedded permanent magnet synchronous motor based on a vector magnetic circuit according to claim 1, characterized in that: ； Using magnetic induction and magnetic capacitance C characterize the iron loss; Magnetic induction Both the magnetic flux and the magnetic capacitance C lag behind the magnetomotive force or current, so the equivalent magnetic induction parameter Equivalent magnetic induction and the combined effect of magnetic capacitance C.

3. The method for establishing an analysis model of an embedded permanent magnet synchronous motor based on a vector magnetic circuit according to claim 2, characterized in that: The active power loss caused by the magnetic induction element corresponds to the eddy current loss in the magnetic circuit, and the active power loss caused by the magnetic capacitance element corresponds to the hysteresis loss in the magnetic circuit.

4. The method for establishing an analysis model of an embedded permanent magnet synchronous motor based on a vector magnetic circuit according to claim 2, characterized in that: d-axis iron loss angle δ d and q-axis iron loss angle δ q , respectively expressed as follows: make: k is called the equivalent magnetic induction coefficient; Since the magnetic resistance of the d-axis and q-axis is expressed as and Then, the iron loss angle δ of the embedded permanent magnet synchronous motor IPMSMd axis is d and the iron loss angle δ of the q axis q It is expressed as: δ d =arctan(ωL d k) (4) δ q =arctan(ωL q k) (5) is the magnetic induction in the dq coordinate system, C is the magnetic capacitance in the dq coordinate system, is the magnetic reluctance of the d-axis, is the magnetic resistance of the q axis, L d is the inductance of the d-axis, L q is the inductance of the q axis, δ d is the iron loss angle of the d-axis, δ q is the iron loss angle of the q-axis, ω is the rotor electrical angular velocity, and N is the number of turns of the armature winding.

5. The method for establishing an analysis model of an embedded permanent magnet synchronous motor based on a vector magnetic circuit according to claim 3 is characterized in that: By introducing equivalent magnetic induction parameters into the magnetic circuit of the embedded permanent magnet motor, the magnetic flux equation of the embedded permanent magnet motor based on the vector magnetic circuit in dq coordinates is obtained: The voltage equation of the embedded permanent magnet synchronous motor in the dq coordinate system: Multiply both sides of the above equation by the matrix And because Ignore R s tanδ d , R s tanδ q tan 2 δ d and tan 2 δ q ; The voltage equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the dq coordinate system is obtained: The voltage equation of the embedded permanent magnet motor based on the vector magnetic circuit in the α-β coordinate system is obtained: Among them, the back electromotive force for: In the formula, ψ d and ψ q is the magnetic flux in the dq coordinate system, u d and u q is the voltage in the dq coordinate system, i d and i q is the current in the dq coordinate system, u α and u β is the voltage in the α-β coordinate system, i α and i β is the current in the α-β coordinate system, L d is the inductance of the d-axis, L q is the inductance of the q axis, R s is the armature winding resistance, ψ f is the permanent magnet flux, k is the equivalent magnetic induction coefficient, δ d is the d-axis iron loss angle, δ q is the q-axis iron loss angle, ω is the rotor electrical angular velocity, and p is the differential operator.

6. The method for establishing an analysis model of an embedded permanent magnet synchronous motor based on a vector magnetic circuit according to claim 5, characterized in that: Considering the saliency effect The coordinate transformation satisfies that the amplitude, phase and angular velocity of the synthetic phasor remain unchanged before and after the transformation, which can be expressed as: in, is the synthetic phase, The synthetic phase Axis component, The synthetic phase Axis component, is the d-axis component of the synthetic phase, is the q-axis component of the synthetic phase, e jωt is the angular velocity of rotation of the phasor; The dq coordinate system and the salient pole effect are considered Coordinate transformation relationship of coordinate system: in, To consider the saliency effect The coordinate transformation matrix is ​​to rotate the d-axis and q-axis in the direction of lag by the iron loss angle δ d and δ q , so that the dq coordinate system is transformed to Coordinate system.

7. The method for establishing an analysis model of an embedded permanent magnet synchronous motor based on a vector magnetic circuit according to claim 6, characterized in that: Transform the flux term in the flux equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the dq coordinate system to In the coordinate system, based on the vector magnetic circuit and considering the salient pole effect, The flux equation of the embedded permanent magnet synchronous motor in the coordinate system is: Transform the flux term in the voltage equation of the embedded permanent magnet synchronous motor based on the vector magnetic circuit in the dq coordinate system to In the coordinate system, since the iron loss angle is small, sin(δ q -δ d )≈tanδ q -tanδ d 、sin(δ q -δ d )(tanδ q -tanδ d )<<1, Based on the vector magnetic circuit and considering the salient pole effect, The voltage equation of the embedded permanent magnet synchronous motor in the coordinate system is: Ignore L q sin(δ q -δ d )pi q and L d sin(δ q -δ d )pi d , based on the vector magnetic circuit and considering the salient pole effect The simplified form of the voltage equation of the embedded permanent magnet synchronous motor in the coordinate system is: In the formula, and for Magnetic flux in the coordinate system, and for The voltage in the coordinate system, i d and i q is the current in the dq coordinate system, L d is the inductance of the d-axis, L q is the inductance of the q axis, R s is the armature winding resistance, ψ f is the permanent magnet flux, δ d is the d-axis iron loss angle, δ q is the q-axis iron loss angle, ω is the rotor electrical angular velocity, and p is the differential operator.

8. A method for controlling an embedded permanent magnet synchronous motor, characterized in that: The analysis model of the embedded permanent magnet synchronous motor is established based on the establishment method as claimed in claim 7; The control method comprises the following steps: The three-phase current of the motor is sampled to obtain Will The current sampling value in the α-β coordinate system is obtained through the Clark transformation module and Then and The current sampling value in the dq coordinate system is obtained through the Park transformation module and Rotor speed observation With the setting value n ref The error is passed through the PI controller to obtain the d-axis and q-axis current setting values ​​i d and i q , calculate the d-axis and q-axis current sampling values ​​i d * and i q * With the setting value i d and i q The error is input into two PI controllers respectively, and we get Voltage in coordinate system and By considering the saliency effect The coordinate transformation module obtains the voltage u in the dq coordinate system d and u q , and then through the Park inverse transformation module, based on the rotor position angle observation value Perform Park inverse transformation to obtain the voltage u in the α-β coordinate system α and u β , use u α and u β The synthesized voltage space vector is input into the voltage space vector modulation module for modulation, and the state coding values ​​of the three half bridges are output to control the MOS tube switches of the three-phase inverter to control the motor.

9. The motor control method according to claim 8, characterized in that: Obtain rotor speed observation value through rotor position and speed observation module and the rotor position angle observation The rotor position and speed observation module includes a sliding mode observer, a low-pass filter and a phase-locked loop; Assume the back electromotive force: in: The sliding mode observer is designed according to formula (12). The input of the sliding mode observer is and The back electromotive force observation value is obtained by low-pass filtering and phase and amplitude compensation. The rotor position information is extracted as follows: Rotor position angle observation It is expressed as: The inverse tangent is calculated by the phase-locked loop to obtain the rotor position angle observation value Rotor angular velocity observation It is expressed as: Rotor speed observation It is expressed as: In formula (20-24), A and B are the motor state measurement values ​​in the dq coordinate system, and is the observed value of the back electromotive force in the two-phase stationary coordinate system, u α and u β is the voltage of the two-phase stationary coordinate system, i α and i β is the current in the two-phase stationary coordinate system, L d is the inductance of the d-axis, L q is the inductance of the q axis, R s is the resistance of the armature winding, ψ f is the permanent magnet flux, k is the equivalent magnetic induction coefficient, δ d is the d-axis iron loss angle, ω is the rotor electrical angular velocity, is the observed value of the rotor electrical angular velocity, θ is the electrical angle of the rotor position, is the observed value of the rotor position angle, p is the differential operator, and P is the pole pair number.

10. The motor control method according to claim 8, characterized in that: The consideration of the saliency effect The coordinate transformation module is to transform Axis and The axis voltage is transformed into d-axis and q-axis voltages, and the input-output relationship is expressed as: u out =T δ u in (19) In formula (19), and To consider the saliency effect The input and output matrices of the coordinate transformation module, T δ To consider the saliency effect Coordinate transformation matrix T δ The inverse matrix of ′.

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