Constraint polytope selection method for enlarging the actual operating region of permanent magnet synchronous motor

Abstract

This invention discloses a method for selecting a constrained polytope to expand the actual operable range of a permanent magnet synchronous motor. The method includes: constructing a voltage-constrained polytope with five vertices; scanning the entire speed range, line segment L... i -G slope, to obtain line segment L i -Minimum absolute value of the slope of G; based on line segment L i The minimum absolute value of the slope of -G is used to determine the location of point Wi, and then the location and shape of the voltage-constrained polytope are determined. A system of linear equations for the voltage-constrained polytope is obtained. Based on this system of linear equations, combined with traditional prediction models and value functions, an explicit model predictive controller is constructed. This invention simplifies the explicit model predictive controller, expands the limit boundary of the actual operating range of the motor, increases the speed range and torque output capability of the motor, broadens the external characteristic curve of the motor, and enhances its extreme operating capability.

Description

Constraint Polycellular Selection Method for Expanding the Actual Operating Range of Permanent Magnet Synchronous Motors Technical Field

[0001] This invention belongs to the field of explicit model predictive control of permanent magnet synchronous motors, and particularly relates to a method for selecting constrained polytopes to expand the actual operable region of permanent magnet synchronous motors. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in advanced servo drive fields such as drones, robots, and electric vehicles due to their advantages of simple structure, high power density, and fast response speed. Explicit model predictive control (EMC) has become a preferred advanced control algorithm for PMSMs due to its strengths in handling multi-input, multi-output systems and multi-objective cooperative control problems, strong constraint handling capabilities, and low online computational burden. With EMC, a single controller can simultaneously control the d-axis and q-axis currents, achieving highly dynamic current response.

[0003] As one of the key elements in the construction of explicit model predictive controllers, voltage-constrained multicells in u d -u q The specific location and form within the plane directly affect the size of the motor's operating range, determining its speed regulation range and torque output capability. However, traditional methods, which use an inscribed regular hexagon of the voltage limit circle as the voltage polytopic constraint, inevitably reduce the reachable region of the voltage vector and the motor's operating range, severely limiting the motor's extreme operating capability. Existing improved methods, which use an inscribed irregular hexagon of the voltage limit circle as the voltage polytopic constraint, significantly expand the motor's operating range while increasing the speed regulation range and load capacity. However, further research reveals that existing improved methods still do not fully utilize the motor's actual operating range, and there is room for further improvement in the motor's speed regulation range and load capacity. Summary of the Invention

[0004] The purpose of this invention is to provide a constrained polytopic selection method for expanding the actual operational range of a permanent magnet synchronous motor, thereby solving the aforementioned problems. This invention can further expand the actual operational range of the motor, increase the speed regulation range, enhance the torque output capability at various speeds, and broaden the speed-torque external characteristic curve.

[0005] This invention is implemented according to the following technical solution:

[0006] In a first aspect, the present invention provides a method for selecting a constrained polytope to expand the actual operable region of a permanent magnet synchronous motor, the method comprising:

[0007] Construct a voltage-constrained multicell with five vertices, u d -u qThe five vertices in the plane are denoted as L, W, U, K, and I.

[0008] Plot both the current constraint and voltage constraint of the PMSM on i. d -i q Within a plane, the current constraint remains constant, while the voltage constraint decreases as the rotational speed increases; i d -i q The overlapping area of ​​voltage and current constraints in the second quadrant of the plane is the operating region of the motor. Let point G be the intersection of the voltage limit circle and the current limit circle.

[0009] will u d -u q Voltage-constrained multicells in the plane mapped to i d -i q After planarizing, rotate 90 degrees clockwise to obtain points L, W, U, K, and I at position i. d -i q Mapping point L in the plane i Point W i , point U i Point K i , point I i ;

[0010] The u d and u q These are the d-axis and q-axis components of the motor stator voltage, respectively; i d and i q These are the d-axis and q-axis components of the motor stator current, respectively.

[0011] Scan line segment L across the full speed range i -G slope, to obtain line segment L i -Minimum absolute value of the slope of G (min{|k Li-G |};

[0012] Based on line segment L i -Minimum absolute value of slope G and point W i Location selection criteria, determine point W i The location of the voltage-constrained polytope is determined by this location.

[0013] Obtain the coordinates of the five vertices of the voltage-constrained multicell. Use the two-point equation of a straight line to derive the linear equations of the voltage-constrained multicell and transform them into the voltage-constrained multicell equations described in matrix form.

[0014] Based on the voltage-constrained multicellular equations described in matrix form, and combined with the prediction model and value function, an explicit model predictive controller is constructed to optimize the operating performance and voltage stability of the power system.

[0015] In one embodiment, the coordinates of points L, W, U, K, and I are as follows:

[0016] Voltage-constrained multicell and u q The intersection of the positive and negative axes, i.e., the coordinates (0, U). max Let L be the point L.

[0017] Voltage-constrained multicell and u q The intersection of the negative half-axis and the negative half-axis, i.e., the coordinates are (0, -U). max Let point K be the point in the equation.

[0018] Voltage-constrained multicell and u d The intersection of the positive and negative axes, i.e., the coordinates (U... max The point I is the point where (0, 0).

[0019] Voltage-constrained multicell and u d The intersection of the negative half-axis and the negative half-axis, i.e., the coordinates are (-U). max The point U is the point where , 0).

[0020] Voltage-constrained multicell in u d -u q The vertex in the second quadrant of the plane is point W, and the coordinates of point W are determined by the coordinates of point L and min{|k Li-G The solution is found.

[0021] The U max The radius of the voltage limit circle is the voltage constraint value.

[0022] In one implementation, line segment L i -W i As a field weakening trajectory, the actual operating point of the motor is limited to line segment L. i -W i The reference values ​​i of the d-axis and q-axis currents are obtained in real time. dref and i qref Optimize guidance for current distribution and magnetic field weakening operation.

[0023] In one implementation, point W i The location selection must meet two requirements:

[0024] 1. Within the full speed range, point W i The speed should be approached from point G to reduce wasted operating range, thereby achieving a greater speed range and torque output capability.

[0025] II. Within the full speed range, point W i Do not enter the operating area of ​​the motor.

[0026] In one implementation, according to line segment L i-Minimum absolute value of slope G and point W i Location selection criteria point, for point W i The rules for selecting the position are as follows: when line segment L... i -G slope is taken as min{|k Li-G When |}, let point W i It coincides with point G.

[0027] In one embodiment, the linear equations for each side of the voltage-constrained multicell are as follows:

[0028]

[0029] The voltage-constrained multicell equation, described in matrix form, is as follows:

[0030]

[0031] Among them, u dopt Point U is W d Axis coordinates, u qopt Point U is W q Axis coordinates.

[0032] In one implementation, the prediction model is:

[0033]

[0034] in, For state variables, To control variables, and Let T be the system matrix. s For discrete time intervals, For natural numbers, and These are the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, respectively. Indicates transpose. and These are the observed values ​​of the unknown disturbance in the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, respectively. Let k be the observed value of the unknown disturbance in the speed equation of the permanent magnet synchronous motor at time k. and The voltage increments of the permanent magnet synchronous motor along the d-axis and q-axis at time k are respectively. , , and These are the d-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, respectively. and Let L1 and L2 be the q-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, respectively, and L0 be the nominal value of the stator inductance of the motor. The value is the reference value for the d-axis component of the stator current of the permanent magnet synchronous motor at time k.

[0035] In one implementation, the value function is:

[0036]

[0037] Where J represents the value function, and They are respectively and The weighting coefficients, for and The weighting coefficients, For rotational inertia, The rotational constant is the nameplate value.

[0038] Secondly, this invention provides an explicit model predictive controller, including a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the aforementioned constrained polytope selection method for expanding the actual operable region of a permanent magnet synchronous motor.

[0039] Thirdly, the present invention provides an explicit model predictive current control system, including the aforementioned explicit model predictive controller.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0042] (1) The voltage-constrained polycell constructed in this invention is pentagonal, which further reduces the number of constraints and simplifies the explicit model predictive controller;

[0043] (2) The voltage-constrained multicell structure and the proposed field weakening trajectory constructed in this invention expand the limit boundary of the actual operating range of the motor, while increasing the speed regulation range and torque output capability of the motor, widening the external characteristic curve of the motor, and enhancing the extreme operating capability. Attached Figure Description

[0044] The accompanying drawings, as part of this invention, are provided to further illustrate the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation thereof. Clearly, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0045] Figure 1 is a flowchart of a constrained multicell selection method for expanding the actual operable area of ​​a permanent magnet synchronous motor according to an embodiment of the present invention.

[0046] Figure 2 is a schematic diagram of a voltage-constrained multicell structure provided in an embodiment of the present invention;

[0047] Figure 3 shows two problems existing in the current voltage constraint. Figure 3(a) shows the case where there is wasted operating area, and Figure 3(b) shows the case where point W enters the operating area.

[0048] Figure 4 is a block diagram of an explicit model predictive current control system provided in an embodiment of the present invention;

[0049] Figure 5 shows the simulation results using the method of the present invention;

[0050] Figure 6 shows the motor in an embodiment of the present invention. d -i q Comparison of control trajectories in the plane.

[0051] It should be noted that these accompanying drawings and textual descriptions are not intended to limit the scope of the invention in any way, but rather to illustrate the concept of the invention to those skilled in the art by referring to specific embodiments. Detailed Implementation

[0052] To enhance understanding of the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following embodiments.

[0053] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. 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.

[0054] Referring to Figure 1, this disclosure provides a method for selecting a constrained polytope to expand the actual operable region of a permanent magnet synchronous motor. The method includes the following steps:

[0055] Step S100: Construct a voltage-constrained multicell with five vertices, u d -u q The five vertices in the plane are denoted as L, W, U, K, and I.

[0056] This invention constructs a voltage-constrained polytope with five vertices, requiring only five linear constraints to describe. The voltage-constrained polytope is then placed in u... d -u qThe five vertices in the plane are denoted as points L, W, U, K, and I, respectively. Among them, the voltage-constrained polytope and u... q The intersection of the positive and negative axes, i.e., the coordinates (0, U). max The point is L; voltage-constrained multicell and u q The intersection of the negative half-axis and the negative half-axis, i.e., the coordinates are (0, -U). max Point K is the point of the voltage-constrained multicell and u. d The intersection of the positive and negative axes, i.e., the coordinates (U... max Point I is the point (0, 0); voltage-constrained multicell and u d The intersection of the negative half-axis and the negative half-axis, i.e., the coordinates are (-U). max The point U is the point where , 0); while the voltage-constrained multicell is in u d -u q The vertex in the second quadrant of the plane is point W, and the coordinates of point W are to be determined. This voltage-constrained polytope can be represented by the vertices as LWUKI, as shown in Figure 2.

[0057] Step S200: Plot both the current constraint and voltage constraint of the PMSM on i d -i q Within a plane, the current constraint remains constant, while the voltage constraint decreases as the rotational speed increases; i d -i q The overlapping area of ​​voltage and current constraints in the second quadrant of the plane is the operating region of the motor. Let point G be the intersection of the voltage limit circle and the current limit circle.

[0058] To analyze the motor's operating status, both the current and voltage constraints of the PMSM are plotted on i. d -i q Within the plane, the current constraint remains constant, while the voltage constraint decreases as the rotational speed increases; i d -i q The overlapping area of ​​voltage and current constraints in the second quadrant of the plane constitutes the operational region of the motor. This operational region gradually shrinks as the rotational speed increases. Point G is designated as the intersection of the voltage and current limit circles, and it moves with changes in speed.

[0059] Step S300: Put u d -u q Voltage-constrained multicells in the plane mapped to i d -i q After planarizing, rotate 90 degrees clockwise to obtain points L, W, U, K, and I at position i. d -i q Mapping point L in the plane i Point W i , point U i Point Ki , point I i .

[0060] Specifically, u d -u q Voltage-constrained multicells in the plane mapped to i d -i q After planarization, rotate 90 degrees clockwise, and let the mapping be i. d -i q Planar voltage-constrained multicell is L i -W i -U i -K i -I i Among them, point L i Point W i , point U i Point K i , point I i Points L, W, U, K, and I are respectively located at i d -i q Mapping points in the plane.

[0061] In the above description, u d and u q These are the d-axis and q-axis components of the motor stator voltage, respectively; i d and i q These are the d-axis and q-axis components of the motor stator current, respectively; U max The radius of the voltage limit circle is the voltage constraint value.

[0062] Step S400: Scan line segment L across the entire speed range i -G slope, to obtain line segment L i -Minimum absolute value of the slope of G.

[0063] Scanning the entire speed range, line segment L i -G slope, to obtain line segment L i -Minimum absolute value of the slope of G. Because the permanent magnet synchronous motor's speed gradually increases from zero to maximum speed, the intersection points G and L of the voltage limit circle and the current limit circle... i Both change continuously with the rotational speed; within the complete speed range, points G and L... i The line segment L i -G, with i d The angle between the negative half-axis and the line segment L has a minimum value. i -G slope has an absolute minimum value. This minimum value is obtained (denoted as min{|k... Li-G |}), and the motor speed and point L when the slope reaches its minimum value. i The location.

[0064] Step S500: Based on line segment L i -Minimum absolute value of slope G and point W i Location selection criteria, determine point W i The location of the voltage-constrained polycell is determined, thereby identifying its position and shape.

[0065] Considering that the quality of the d-axis and q-axis current distribution directly affects the field weakening performance, as well as the motor's speed range, torque output capability, and other extreme operating capabilities during explicit model prediction of field weakening operation, this invention will use line segment L... i -W i As a field weakening trajectory, the actual operating point of the motor is limited to line segment L. i -W i The reference values ​​i of the d-axis and q-axis currents are obtained in real time. dref and i qref Optimize guidance for current distribution and magnetic field weakening operation.

[0066] Based on the above description of the construction of the voltage-constrained polytope and the setting of the weak magnetic trajectory, for point W i The selection of the location put forward two requirements:

[0067] 1. Within the full speed range, point W i It should be as close as possible to point G to reduce wasted operating area and obtain the largest possible speed range and torque output capability, as shown in Figure 3(a).

[0068] II. Within the full speed range, point W i Do not enter the operating area of ​​the motor.

[0069] Because this invention uses L i -W i The use of clearly known linear equations to guide current distribution and field weakening operations ensures the simplicity and convenience of the field weakening algorithm. However, once point W... i Once inside the motor's operating range, it will no longer be possible to simply rely on L... i -W i Calculate the linear equation for i across the entire velocity range. dref and i qref It is necessary to solve point W in real time. i The coordinates of line segment L are used to determine the line segment L. i -W i The endpoints will greatly increase the computational burden of the algorithm, making the algorithm infeasible, as shown in Figure 3(b).

[0070] Taking into account the above two requirements, the present invention will point W i The rules for selecting the position are as follows: when line segment L... i -G slope is taken as min{|kLi-G When |}, let point W i It coincides with point G.

[0071] The above rules can guarantee the protection of point W. i It is located within the motor's operating range across the entire speed range, while also ensuring point W. i The goal is to approximate point G as closely as possible to obtain the largest possible operational area. Determine point W. i The position of W can then be used to determine the position and shape of the voltage-constrained polytope. At this point, the coordinates of W are denoted as (u...). dopt u qopt ).

[0072] Step S600: Obtain the coordinates of the five vertices of the voltage-constrained polytope. Use the two-point equation of a straight line to derive the linear equation system of the voltage-constrained polytope from the coordinates of the five points, and transform it into the voltage-constrained polytope equation described in matrix form.

[0073] Furthermore, the linear equations for each edge of the voltage-constrained multicell are obtained as follows:

[0074]

[0075] The voltage-constrained multicell equations, described in matrix form, are as follows:

[0076]

[0077] Among them, u dopt Point U is W d Axis coordinates, u qopt Point U is W q Axis coordinates.

[0078] Step S700: Based on the voltage-constrained multicellular equations described in matrix form, and combining the prediction model and the value function, construct an explicit model predictive controller to optimize the operating performance and voltage stability of the power system.

[0079] Furthermore, the prediction model is as follows:

[0080]

[0081] in, For state variables, To control variables, and Let T be the system matrix. s For discrete time intervals, For natural numbers, and These are the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, respectively. Indicates transpose. and These are the observed values ​​of the unknown disturbance in the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, respectively. Let k be the observed value of the unknown disturbance in the speed equation of the permanent magnet synchronous motor at time k. and The voltage increments of the permanent magnet synchronous motor along the d-axis and q-axis at time k are respectively. , , and These are the d-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, respectively. and Let L1 and L2 be the q-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, respectively, and L0 be the nominal value of the stator inductance of the motor. The value is the reference value for the d-axis component of the stator current of the permanent magnet synchronous motor at time k.

[0082] Furthermore, the value function is:

[0083]

[0084] Where J represents the value function, and They are respectively and The weighting coefficients, for and The weighting coefficients, For rotational inertia, The rotational constant is the nameplate value.

[0085] In one embodiment, an explicit model predictive controller is proposed, including a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it performs the following steps: constructing a voltage-constrained polytope with five vertices, u d -u q The five vertices in the plane are denoted as L, W, U, K, and I, respectively; the current and voltage constraints of the PMSM are plotted on i. d -i q Within a plane, the current constraint remains constant, while the voltage constraint decreases as the rotational speed increases; i d -i q The overlapping region of voltage and current constraints in the second quadrant of the plane constitutes the operational region of the motor. Let point G be the intersection of the voltage limit circle and the current limit circle. d -u qVoltage-constrained multicells in the plane mapped to i d -i q After the plane is formed, rotate it 90 degrees clockwise, and let it be mapped to i. d -i q After plane, points L, W, U, K, and I are obtained in i d -i q Mapping point L in the plane i Point W i , point U i Point K i , point I i ; Scan line segment L across the entire velocity range i -G slope, to obtain line segment L i -Minimum absolute value of the slope of G; based on line segment L i -Minimum absolute value of slope G and point W i Location selection criteria, determine point W i The location of the voltage-constrained polytope is determined by the position of the point, thus determining its position and shape. The coordinates of the five vertices of the voltage-constrained polytope are obtained, and the linear equations of the voltage-constrained polytope are derived from the five point coordinates using the two-point linear equation method. These equations are then transformed into a matrix-form description of the voltage-constrained polytope equations. Based on the matrix-form description of the voltage-constrained polytope equations, combined with the prediction model and the value function, an explicit model predictive controller is constructed to optimize the operating performance and voltage stability of the power system.

[0086] As shown in Figure 4, in one embodiment, an explicit model predictive current control system is proposed, which includes the aforementioned explicit model predictive controller.

[0087] This control system will control the d-axis and q-axis currents i d i q and d-axis current reference value i dref In an explicit model predictive controller, the output d-axis and q-axis voltage reference values ​​u dref and u qref The d-axis and q-axis voltage reference values ​​u are transformed via coordinate transformation. dref and u qref Transform into , Shaft voltage reference value and The inverter generates three-phase power through an SVPWM circuit, which is then input into the permanent magnet synchronous motor. Simultaneously, the A and B phase currents of the three-phase power supply are collected. and i is generated through coordinate transformation d and i q , with u dref u qref and rotational speed acquired by the encoder The data is input into the observer and then output. , and Add to state variables This completes the closed-loop control.

[0088] The description of the explicit model predictive controller is the same as described above, and will not be repeated here.

[0089] To verify the effectiveness and superiority of the constraint polytope selection method for expanding the actual operable range of the permanent magnet synchronous motor in this invention, we conducted simulation verification on the Simulink platform and compared the experimental results of the method of this invention with the reference performance to more intuitively compare and evaluate the control performance.

[0090] First, to verify the control performance of the proposed method, simulation verification was conducted on the Simulink platform. The verification condition was as follows: the rotational speed first jumped from 0 to 500 r / min, then accelerated uniformly to 1550 r / min, followed by the application of load torque, which increased continuously over time. The experimental results of the proposed method are shown in Figure 5, where n ref T is the reference value for rotational speed. e For electromagnetic torque, T load For the load torque, i d i represents the d-axis component of the stator current. dref The d-axis component of the stator current is the reference value. As shown in Figure 5, the method of the present invention can achieve excellent dynamic performance with fast response and virtually no overshoot; at the same time, the experimental curve and the reference value curve basically coincide, achieving good following control performance.

[0091] Next, to compare the actual operating range and limit operating capabilities of motors under traditional regular hexagonal constraints, existing irregular hexagonal constraints, and the improved polycellular constraints proposed in this invention, an explicit model predictive control system using these three constraints will be tested under the aforementioned operating conditions, specifically in i... d -i q The control trajectory in the plane is plotted in Figure 6. d -i q Figure 6 shows that the proposed improved multicellular constraint increases the torque output capability of the motor during field weakening operation, broadens the external characteristic curve of the motor, and enhances its extreme operating capability.

[0092] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This computer program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. The aforementioned storage medium can be a non-volatile storage medium such as a magnetic disk, optical disk, or read-only memory (ROM), or random access memory (RAM).

[0093] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0094] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for selecting a constrained polytope to expand the actual operable region of a permanent magnet synchronous motor, characterized in that, The method includes: constructing a voltage-constrained multicell with five vertices, u d -u q The five vertices in the plane are denoted as L, W, U, K, and I; the current and voltage constraints of the PMSM are plotted on i. d -i q Within a plane, the current constraint remains constant, while the voltage constraint decreases as the rotational speed increases; i d -i q The overlapping region of voltage and current constraints in the second quadrant of the plane constitutes the operational region of the motor. Let point G be the intersection of the voltage limit circle and the current limit circle. d -u q Voltage-constrained multicells in the plane mapped to i d -i q After planarizing, rotate 90 degrees clockwise to obtain points L, W, U, K, and I at position i. d -i q Mapping point L in the plane i Point W i , point U i Point K i , point I i The u d and u q These are the d-axis and q-axis components of the motor stator voltage, respectively; i d and i q These are the d-axis and q-axis components of the motor stator current, respectively; scanning line segment L across the entire speed range. i -G slope, to obtain line segment L i -Minimum absolute value of the slope of G (min{|k Li-G |};Based on line segment L i -Minimum absolute value of slope G and point W i Location selection criteria, determine point W i The position of the line segment L is used to determine the position and shape of the voltage-constrained polytope; i -W i As a field weakening trajectory, the actual operating point of the motor is limited to line segment L. i -W i The reference values ​​i of the d-axis and q-axis currents are obtained in real time. dref and i qref Optimize guidance for current distribution and field weakening operation; point W i The location selection must meet two requirements: First, within the entire speed range, point W... i The speed range should be approached from point G to reduce wasted operating space, thereby achieving a wider speed range and torque output capability; secondly, within the full speed range, point W... i Do not enter the operating area of ​​the motor; according to line segment L i -Minimum absolute value of slope G and point W i Location selection criteria point, for point W i The rules for selecting the position are as follows: when line segment L... i -G slope is taken as min{|k Li-G When |}, let point W i Coincident with point G; obtain the coordinates of the five vertices of the voltage-constrained polytope, derive the linear equations of the voltage-constrained polytope using the two-point linear equation from the five point coordinates, and transform them into voltage-constrained polytope equations described in matrix form; based on the voltage-constrained polytope equations described in matrix form, combine the prediction model and the value function to construct an explicit model predictive controller to optimize the operating performance and voltage stability of the power system.

2. The constrained polytopic selection method for expanding the actual operable region of a permanent magnet synchronous motor according to claim 1, characterized in that, The coordinates of points L, W, U, K, and I are respectively: voltage-constrained multicell and u q The intersection of the positive and negative axes, i.e., the coordinates (0, U). max The point is L; voltage-constrained multicell and u q The intersection of the negative half-axis and the negative half-axis, i.e., the coordinates are (0, -U). max Point K is the point of the voltage-constrained multicell and u. d The intersection of the positive and negative axes, i.e., the coordinates (U... max Point I is the point at (0, 0); voltage-constrained multicell and u d The intersection of the negative half-axis and the negative half-axis, i.e., the coordinates are (-U). max The point U is the point of the voltage-constrained multicell at u. d -u q The vertex in the second quadrant of the plane is point W, and the coordinates of point W are determined by the coordinates of point L and min{|k Li-G |} Solve for the U; max The radius of the voltage limit circle is the voltage constraint value.

3. The constrained polytopic selection method for expanding the actual operable region of a permanent magnet synchronous motor according to claim 2, characterized in that, The linear equations for each edge of the voltage-constrained multicell are as follows: The voltage-constrained multicell equations, transformed into matrix form, are as follows: , where u dopt Point U of W d Axis coordinates, u qopt Point U of W q Axis coordinates.

4. The constrained polytopic selection method for expanding the actual operable region of a permanent magnet synchronous motor according to claim 1, characterized in that, The prediction model is as follows: ,in, For state variables, To control variables, and Let T be the system matrix. s For discrete time intervals, For natural numbers, and These are the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, respectively. Indicates transpose. and These are the observed values ​​of the unknown disturbance in the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, respectively. Let k be the observed value of the unknown disturbance in the speed equation of the permanent magnet synchronous motor at time k. and The voltage increments of the permanent magnet synchronous motor along the d-axis and q-axis at time k are respectively. ， ， and These are the d-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, respectively. and Let L1 and L2 be the q-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, respectively, and L0 be the nominal value of the stator inductance of the motor. The value is the reference value for the d-axis component of the stator current of the permanent magnet synchronous motor at time k.

5. The constrained polytopic selection method for expanding the actual operable region of a permanent magnet synchronous motor according to claim 1, characterized in that, The value function is: Where J represents the value function, and They are respectively and The weighting coefficients, for and The weighting coefficients, For rotational inertia, The rotational constant is the nameplate value.

6. An explicit model predictive controller, characterized in that: It includes a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the constrained polytopic selection method for expanding the actual operable area of ​​a permanent magnet synchronous motor as described in any one of claims 1 to 5.

7. An explicit model predictive current control system, characterized in that: Includes the explicit model prediction controller as described in claim 6.

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