Constraint polytope selection method for expanding actual operable area of permanent magnet synchronous motor

Abstract

The invention discloses a constraint polytope selection method for expanding an actual operable area of a permanent magnet synchronous motor. The method comprises the following steps: constructing a voltage constraint polytope with five vertexes; scanning the slope of the line segment Li-G in the full speed range to obtain the minimum absolute value of the slope of the line segment Li-G; according to the minimum absolute value of the slope of the line segment Li-G, the position of a point Wi is determined, and then the position and the shape of the voltage constraint polytope are determined; obtaining a voltage constraint polytope linear equation set; and constructing an explicit model prediction controller by combining a traditional prediction model and a value function according to the voltage constraint polytope linear equation set. According to the method, the explicit model prediction controller is simplified, the limit boundary of the actual operable area of the motor is expanded, the speed regulation range and the torque output capacity of the motor are increased, the external characteristic curve of the motor is widened, and the limit operation capacity is enhanced.

Description

Technical Field

[0001] The invention belongs to the field of explicit model predictive control of permanent magnet synchronous motors, and in particular relates to a constrained polyhedral selection method for expanding an actual operable region of a permanent magnet synchronous motor. Background Art

[0002] Permanent magnet synchronous motor (PMSM) is widely used in advanced servo drive fields such as drones, robots, and electric vehicles due to its simple structure, high power density, and fast response speed. Explicit model predictive control has become an advanced control algorithm favored by PMSM due to its advantages such as being good at handling multi-objective collaborative control problems of multi-input and multi-output systems, strong constraint processing capabilities, and low online computing burden. With explicit model predictive control, one controller can be used to control the d-axis and q-axis currents at the same time to achieve a highly dynamic current response.

[0003] As one of the key elements in the construction of explicit model predictive controller, the voltage constraint polytope is d -u q The specific position and form in the plane directly affect the size of the motor's operating area and determine the motor's speed regulation range and torque output capacity. However, the traditional method selects the inscribed regular hexagon of the voltage limit circle as the voltage polyhedral constraint, which inevitably reduces the reachable area of ​​the voltage vector and the motor's operating area, severely limiting the motor's extreme operating capacity; the existing improved method selects the inscribed irregular hexagon of the voltage limit circle as the voltage polyhedral constraint, which greatly expands the motor's operating area and increases the speed regulation range and load capacity. However, further research has found that the existing improved method still does not maximize the use of the motor's actual operating area, and the motor's speed regulation range and load capacity have room for further improvement. Summary of the invention

[0004] The purpose of the present invention is to provide a constrained polytope selection method for expanding the actual operable area of ​​a permanent magnet synchronous motor, so as to solve the above problems. The present invention can further expand the actual operable area of ​​the motor, increase the speed regulation range, enhance the torque output capacity at each speed, and broaden the speed-torque external characteristic curve.

[0005] The present invention is implemented according to the following technical solutions:

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

[0007] Construct a voltage constraint polytope with five vertices, u d -u q The five vertices in the plane are denoted as point L, point W, point U, point K and point I;

[0008] The current constraint and voltage constraint of the PMSM are plotted on i d -i q In the plane, the current constraint is fixed and the voltage constraint decreases with the increase of the speed; i d -i q The overlapping part of the voltage constraint and the current constraint in the second quadrant of the plane is the operational area of ​​the motor, and the intersection of the voltage limit circle and the current limit circle is denoted as point G;

[0009] will u d -u q The voltage constraint polytope in the plane is mapped to i d -i q After the plane, rotate 90 degrees clockwise and map it to i d -i q After the plane is drawn, points L, W, U, K and I are obtained at i d -i q Mapping point L in the plane i , click W i , point U i , click K i , point I i ;

[0010] The u d and u q are the d-axis component and q-axis component of the motor stator voltage respectively; i d and i q They are the d-axis component and q-axis component of the motor stator current respectively;

[0011] Scan line segment L in the full speed range i -G slope, get line segment L i -G slope absolute minimum value min{|k Li-G |};

[0012] According to line segment L i -G slope absolute minimum and point W i The position selection conditions are as follows: i The position of , thereby determining the position and shape of the voltage-constrained polyhedron;

[0013] Obtain the coordinates of five vertices of the voltage constraint polytope, derive the linear equations of the voltage constraint polytope from the coordinates of the five points using the straight line two-point formula, and convert them into the voltage constraint polytope equations described in matrix form;

[0014] According to the voltage constraint polytope equation described in matrix form, combined with the prediction model and cost function, an explicit model predictive controller is constructed to optimize the operation performance and voltage stability of the power system.

[0015] In one embodiment, the coordinates of point L, point W, point U, point K and point I are respectively:

[0016] Voltage Constrained Polytopes and u q The intersection of the positive half axis, that is, the coordinates (0,U max ) is point L;

[0017] Voltage Constrained Polytopes and u q The intersection of the negative half axis, that is, the coordinates are (0, -U max ) is point K;

[0018] Voltage Constrained Polytopes and u d The intersection of the positive half axis, that is, the coordinates are (U max ,0) is point I;

[0019] Voltage Constrained Polytopes and u d The intersection of the negative half axis, that is, the coordinate is (-U max ,0) is point U;

[0020] Voltage constraint polytope 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 |} Solve;

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

[0022] In one embodiment, the line segment L i -W i As a weakening magnetic trajectory, by limiting the actual operating point of the motor to the line segment L i -W i On the , get the d, q axis current reference value i in real time dref and i qref , optimizing and guiding the distribution of current and weak magnetic operation.

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

[0024] 1. In the full speed range, click W i It should approach point G to reduce the wasted operating area and thus obtain a larger speed regulation range and torque output capacity.

[0025] 2. In the full speed range, click W i Do not enter the operating area of ​​the motor.

[0026] In one embodiment, according to line segment L i-G slope absolute minimum and point W i Select the conditional point at the position of point W i The position selection rules are as follows: when the line segment L i -G slope takes min{|k Li-G |}, let point W i Coincident with point G.

[0027] In one embodiment, the linear equations of the edges of the voltage constraint polytope are as follows:

[0028]

[0029] The voltage constraint polytope equation converted into matrix form is:

[0030]

[0031] Among them, u dopt W point u d Axis coordinate, u qopt W point u q Axis coordinates.

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

[0033]

[0034] Among them, x is the state variable, u is the control variable, A and B are system matrices, T s is a discrete time interval, k is a natural number, i d (k) and i q (k) are the d-axis component and q-axis component of the stator current of the permanent magnet synchronous motor at time k, T represents the transposition, and are the observed values ​​of the unknown disturbances in the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, is the observed value of the unknown disturbance in the permanent magnet synchronous motor speed equation at time k, Δu d (k) and Δu q (k) are the voltage increments of the d-axis and q-axis of the permanent magnet synchronous motor at time k, and Δu d (k) = u d (k+1)-u d (k), Δu q (k) = u q (k+1)-u q (k),u d (k) and u d (k+1) are the d-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, u q (k) and uq (k+1) are the q-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, L0 is the nominal value of the motor stator inductance, i dref (k) is the reference value of the d-axis component of the stator current of the permanent magnet synchronous motor at time k.

[0035] In one embodiment, the cost function is:

[0036]

[0037] Among them, J represents the value function, q d and q q i d and i q The weight coefficient, q u is Δu d and Δu q The weight coefficient, J r0 is the moment of inertia, k t0 is the nameplate value of the rotation constant.

[0038] In a second aspect, the present invention provides an explicit model predictive controller, comprising a processor and a memory; wherein, when the processor executes a computer program stored in the memory, the above-mentioned constraint polyhedral selection method for expanding the actual operating area of ​​the permanent magnet synchronous motor is implemented.

[0039] In a third aspect, the present invention provides an explicit model predictive current control system, comprising the explicit model predictive controller as claimed above.

[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 constraint polyhedron constructed in the present invention is a pentagon, which further reduces the number of constraints and simplifies the explicit model predictive controller;

[0043] (2) The voltage-constrained polyhedron and the proposed weak magnetic trajectory constructed by the present invention expand the limit boundary of the actual operating area of ​​the motor, while increasing the speed regulation range and torque output capacity of the motor, broadening the external characteristic curve of the motor, and enhancing the limit operating capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The accompanying drawings are part of the present invention and are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention, but do not constitute an improper limitation of the present invention. Obviously, the accompanying drawings described below are only some embodiments. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0045] Figure 1 A flow chart of a method for selecting a constrained polytope for expanding the actual operable area of ​​a permanent magnet synchronous motor provided by an embodiment of the present invention;

[0046] Figure 2 A schematic diagram of a voltage-constrained polyhedron structure provided in one embodiment of the present invention;

[0047] Figure 3 Schematic diagram of two problems existing in the existing voltage constraints: Figure 3 (a) is a schematic diagram showing the situation where there is waste in the operable area. Figure 3 (b) is a schematic diagram of the situation when point W enters the operable area.

[0048] Figure 4 A structural block diagram of a current control system using an explicit model prediction method of the present invention provided in one embodiment of the present invention;

[0049] Figure 5 It is a simulation result diagram using the method of the present invention;

[0050] Figure 6 In one embodiment of the present invention, the motor is d -i q Comparison of in-plane control trajectories.

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

[0052] In order to deepen the recognition and understanding of the present invention, the technical solution of the present invention is further introduced below in conjunction with the accompanying drawings and specific implementation methods. The following embodiments are explanations of the present invention and the present invention is not limited to the following embodiments.

[0053] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown 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 cannot be interpreted as limiting the present invention.

[0054] Reference Figure 1As shown, the embodiment of the present disclosure provides a method for selecting constrained polytopes to expand the actual operable area of ​​a permanent magnet synchronous motor, the method comprising the following steps:

[0055] Step S100: construct a voltage constraint polytope with five vertices, u d -u q The five vertices in the plane are recorded as point L, point W, point U, point K and point I respectively.

[0056] The present invention constructs a voltage constraint polytope with five vertices, that is, only five linear constraints are needed to describe it. d -u q The five vertices in the plane are respectively recorded as point L, point W, point U, point K and point I, where the voltage constraint polyhedron and u q The intersection of the positive half axis, that is, the coordinates (0,U max ) is point L; the voltage constraint polyhedron and u q The intersection of the negative half axis, that is, the coordinates are (0, -U max ) is point K; the voltage constraint polyhedron and u d The intersection of the positive half axis, that is, the coordinates are (U max ,0) is point I; the voltage constraint polyhedron and u d The intersection of the negative half axis, that is, the coordinate is (-U max ,0) is point U; and the voltage constraint polyhedron is at 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. The voltage constraint polytope can be represented as LWUKI with the help of vertices, such as Figure 2 shown.

[0057] Step S200: Plot the current constraint and voltage constraint of the PMSM on the i d -i q In the plane, the current constraint is fixed and the voltage constraint decreases with the increase of the speed; i d -i q The overlapping part of the voltage constraint and the current constraint in the second quadrant of the plane is the operable area of ​​the motor, and the intersection of the voltage limit circle and the current limit circle is denoted as point G.

[0058] In order to analyze the motor operation, the current constraint and voltage constraint of the PMSM are plotted on i d -i q In the plane, the current constraint remains constant, while the voltage constraint decreases as the speed increases; i d -i qThe overlapped part of the voltage constraint and the current constraint in the second quadrant of the plane is the motor's operable area. As the speed increases, the motor's operable area also gradually shrinks. Point G is the intersection of the voltage limit circle and the current limit circle, and point G moves with the change of speed.

[0059] Step S300: d -u q The voltage constraint polytope in the plane is mapped to i d -i q After the plane, rotate 90 degrees clockwise and map it to i d -i q After the plane is drawn, points L, W, U, K and I are obtained at i d -i q Mapping point L in the plane i , click W i , point U i , click K i , point I i .

[0060] Specifically, d -u q The voltage constraint polytope in the plane is mapped to i d -i q After the plane, rotate it 90 degrees clockwise and map it to i d -i q The plane back voltage constraint polytope is L i -W i -U i -K i -I i , where point L i , click W i , point U i , click K i , point I i Point L, point W, point U, point K and point I are respectively d -i q Mapping points in the plane.

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

[0062] Step S400: Scan line segment L within the full speed range i -G slope, get line segment L i -G slope absolute minimum.

[0063] Scanning the full speed range, line segment L i -G slope, get line segment L i -G is the minimum absolute value of the slope. As the permanent magnet synchronous motor gradually increases its speed from zero to the maximum speed, the intersection point G and point L of the voltage limit circle and the current limit circle i As the speed changes, point G and point L change with the speed. i Connecting line, i.e. line segment L i -G, with i d The angle between the negative semi-axis and the axis has a minimum value. At this time, the line segment L i -G slope has an absolute minimum value, and the minimum value (denoted as min{|k Li-G |}), and the motor speed when the slope takes the minimum value, point L i location.

[0064] Step S500: Based on line segment L i -G slope absolute minimum and point W i The position selection conditions are as follows: i ’s position, thereby determining the position and shape of the voltage-constrained polyhedron.

[0065] Considering that the explicit model predicts that the d-axis and q-axis current distribution will directly affect the weak magnetic performance, as well as the motor's speed range, torque output capacity and other extreme operating capabilities, the present invention divides the line segment L i -W i As a weakening magnetic trajectory, by limiting the actual operating point of the motor to the line segment L i -W i On the , get the d, q axis current reference value i in real time dref and i qref , optimizing and guiding the distribution of current and weak magnetic operation.

[0066] Combined with the construction of the voltage constraint polytope and the setting of the weak magnetic track in the above description, for point W i The location selection makes two requirements:

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

[0068] 2. In the full speed range, click W i Do not enter the operating area of ​​the motor.

[0069] Because the present invention is based on i -Wi The clearly known linear equations are used to guide the current distribution and field weakening operation, ensuring the simplicity and convenience of the field weakening algorithm. i Once you enter the motor's operating area, you will not be able to simply use L i -W i The straight line equation calculates i over the full speed range dref and i qref , point W needs to be solved in real time i The coordinates of line segment L i -W i This will greatly increase the computational burden of the algorithm and make the algorithm infeasible, such as Figure 3 (b) as shown.

[0070] Taking the above two requirements into consideration, the present invention will point W i The position selection rules are as follows: when the line segment L i -G slope takes min{|k Li-G |}, let point W i Coincident with point G.

[0071] The above rules can ensure that point W i Within the full speed range, it is located within the motor's operating area, and point W can be guaranteed i It should be as close to point G as possible to obtain the largest practical operable area. Determine point W i The position and shape of the voltage constraint polytope can be determined by the position of W. At this time, the coordinates of W are marked as (u dopt ,u qopt ).

[0072] Step S600: Obtain the coordinates of the five vertices of the voltage constraint polytope, derive the linear equations of the voltage constraint polytope from the five point coordinates using the straight line two-point formula, and convert them into the voltage constraint polytope equations described in matrix form.

[0073] Furthermore, the linear equations of each edge of the voltage constraint polytope are obtained as follows:

[0074]

[0075] The voltage constraint polytope equation converted into matrix form is:

[0076]

[0077] Among them, u dopt W point u d Axis coordinate, u qopt W point u q Axis coordinates.

[0078] Step S700: constructing an explicit model predictive controller based on the voltage constraint polytope equation described in matrix form, combined with the prediction model and the cost function, to optimize the operating performance and voltage stability of the power system.

[0079] Furthermore, the prediction model is:

[0080]

[0081] Among them, x is the state variable, u is the control variable, A and B are system matrices, T s is a discrete time interval, k is a natural number, i d (k) and i q (k) are the d-axis component and q-axis component of the stator current of the permanent magnet synchronous motor at time k, T represents the transposition, and are the observed values ​​of the unknown disturbances in the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, is the observed value of the unknown disturbance in the permanent magnet synchronous motor speed equation at time k, Δu d (k) and Δu q (k) are the voltage increments of the d-axis and q-axis of the permanent magnet synchronous motor at time k, and Δu d (k) = u d (k+1)-u d (k), Δu q (k) = u q (k+1)-u q (k),u d (k) and u d (k+1) are the d-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, u q (k) and u q (k+1) are the q-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, L0 is the nominal value of the motor stator inductance, i dref (k) is the reference value of 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] Among them, J represents the value function, q d and q q i d and i q The weight coefficient, q u is Δu d and Δu q The weight coefficient, J r0 is the moment of inertia, kt0 is the nameplate value of the rotation constant.

[0085] In one embodiment, an explicit model predictive controller is proposed, comprising a processor and a memory; wherein the processor implements the following steps when executing a computer program stored in the memory: constructing a voltage constraint polytope with five vertices, u d -u q The five vertices in the plane are marked as point L, point W, point U, point K and point I respectively; the current constraint and voltage constraint of the PMSM are drawn on i d -i q In the plane, the current constraint is fixed and the voltage constraint decreases with the increase of the speed; i d -i q The overlapped part of the voltage constraint and the current constraint in the second quadrant of the plane is the operational area of ​​the motor. The intersection of the voltage limit circle and the current limit circle is denoted as point G. d -u q The voltage constraint polytope in the plane is mapped to i d -i q After the plane, rotate 90 degrees clockwise and map it to i d -i q After the plane is drawn, points L, W, U, K and I are obtained at i d -i q Mapping point L in the plane i , click W i , point U i , click K i , point I i ; Scan line segment L within the full speed range i -G slope, get line segment L i -G minimum absolute value of the slope; based on line segment L i -G slope absolute minimum and point W i The position selection conditions are as follows: i The position of the voltage constraint polytope is determined by the position of the voltage constraint polytope. The coordinates of the five vertices of the voltage constraint polytope are obtained, and the linear equations of the voltage constraint polytope are derived from the coordinates of the five points using the straight line two-point formula, and converted into the voltage constraint polytope equation described in matrix form. According to the voltage constraint polytope equation described in matrix form, combined with the prediction model and the cost function, an explicit model predictive controller is constructed to optimize the operating performance and voltage stability of the power system.

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

[0087] The control system converts the d and q axis currents id 、i q and d-axis current reference value i dref Input explicit model predictive controller, output d, q axis voltage reference value u dref and u qref . Through coordinate transformation, the d and q axis voltage reference values ​​u dref and u qref Converted into α, β axis voltage reference value u αref and u βref , the inverter is controlled by SVPWM link to generate three-phase power, which is input into the permanent magnet synchronous motor. At the same time, the A and B phase currents i a and i b , through coordinate transformation to generate i d and i q , with u dref 、u qref The speed ω collected by the encoder is input into the observer, and then the output and Add it to the state variable x to complete the closed-loop control.

[0088] The description of the explicit model predictive controller refers to the above description and will not be repeated here.

[0089] In order to verify the effectiveness and superiority of the constraint polyhedral selection method for expanding the actual operating area of ​​the permanent magnet synchronous motor of the present invention, we carried out simulation verification on the Simulink platform, and compared the experimental results of the method of the present 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 carried out on the Simulink platform. The verification conditions were: the speed first jumped from 0 to 500r / min, then uniformly accelerated to 1550r / min, and then the load torque was applied, and the load torque increased continuously over time. The experimental results of the proposed method are shown in Figure 2. Figure 5 As shown, where n ref is the speed reference value, T e is the electromagnetic torque, T load is the load torque, i d is the d-axis component of the stator current, i dref is the reference value of the d-axis component of the stator current. Figure 5 It can be seen that the method of the present invention can obtain excellent dynamic performance with fast speed and basically no overshoot; at the same time, the experimental curve and the reference value curve basically coincide with each other, and good following control performance is obtained.

[0091] Next, in order to compare the actual operating area and the limit operating capacity of the motor with the traditional regular hexagon constraint, the existing irregular hexagon constraint and the improved polyhedral constraint proposed by the present invention, the explicit model predictive control system using the three constraints of the traditional regular hexagon constraint, the existing irregular hexagon constraint and the improved polyhedral constraint proposed by the present invention is used. Under the above working conditions, d -i q The control trajectory in the plane is plotted on Figure 6 middle. i d -i q Control trajectory in the plane Figure 6 It is shown that the proposed improved polyhedral constraint increases the torque output capacity of the motor during weak magnetic field operation, broadens the external characteristic curve of the motor, and enhances the limit operation capability.

[0092] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, the aforementioned storage medium can be a non-volatile storage medium such as a disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0093] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, 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 above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A method for selecting constrained polytopes for expanding the actual operable area of ​​a permanent magnet synchronous motor, characterized in that: The method comprises: Construct a voltage constraint polytope with five vertices, u d -u q The five vertices in the plane are denoted as point L, point W, point U, point K and point I; The current constraint and voltage constraint of the PMSM are plotted on i d -i q In the plane, the current constraint is fixed and the voltage constraint decreases with the increase of the speed; i d -i q The overlapping part of the voltage constraint and the current constraint in the second quadrant of the plane is the operational area of ​​the motor, and the intersection of the voltage limit circle and the current limit circle is denoted as point G; will u d -u q The voltage constraint polytope in the plane is mapped to i d -i q After the plane, rotate 90 degrees clockwise and map it to i d -i q After the plane is drawn, points L, W, U, K and I are obtained at i d -i q Mapping point L in the plane i , click W i , point U i , click K i , point I i ; The u d and u q are the d-axis component and q-axis component of the motor stator voltage respectively; i d and i q They are the d-axis component and q-axis component of the motor stator current respectively; Scan line segment L in the full speed range i -G slope, get line segment L i -G slope absolute minimum value min{|k Li-G |}; According to line segment L i -G slope absolute minimum and point W i The position selection conditions are as follows: i The position of , thereby determining the position and shape of the voltage-constrained polyhedron; Obtain the coordinates of five vertices of the voltage constraint polytope, derive the linear equations of the voltage constraint polytope from the coordinates of the five points using the straight line two-point formula, and convert them into the voltage constraint polytope equations described in matrix form; According to the voltage constraint polytope equation described in matrix form, combined with the prediction model and cost function, an explicit model predictive controller is constructed to optimize the operation performance and voltage stability of the power system.

2. The method for selecting constrained polytopes for expanding the actual operable area of ​​a permanent magnet synchronous motor according to claim 1, characterized in that: The coordinates of the points L, W, U, K and I are: Voltage Constrained Polytopes and u q The intersection of the positive half axis, that is, the coordinates (0,U max ) is point L; Voltage Constrained Polytopes and u q The intersection of the negative half axis, that is, the coordinates are (0, -U max ) is point K; Voltage Constrained Polytopes and u d The intersection of the positive half axis, that is, the coordinates are (U max ,0) is point I; Voltage Constrained Polytopes and u d The intersection of the negative half axis, that is, the coordinate is (-U max ,0) is point U; Voltage constraint polytope 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 |} Solve; The U max is the radius of the voltage limit circle, that is, the voltage constraint value.

3. The method for selecting constrained polytopes for expanding the actual operable area of ​​a permanent magnet synchronous motor according to claim 1, characterized in that: Line segment L i -W i As a weakening magnetic trajectory, by limiting the actual operating point of the motor to the line segment L i -W i On the , get the d, q axis current reference value i in real time dref and i qref , optimizing and guiding the distribution of current and weak magnetic operation.

4. The method for selecting constrained polytopes for expanding the actual operable area of ​​a permanent magnet synchronous motor according to claim 3, characterized in that: Point W i The location selection must meet two requirements:

1. In the full speed range, click W i It should approach point G to reduce the wasted operating area, thereby obtaining a larger speed regulation range and torque output capacity; 2. In the full speed range, click W i Do not enter the operating area of ​​the motor.

5. The method for selecting constrained polytopes for expanding the actual operable area of ​​a permanent magnet synchronous motor according to claim 4, characterized in that: According to line segment L i -G slope absolute minimum and point W i Select the conditional point at the position of point W i The position selection rules are as follows: when line segment L i -G slope takes min{|k Li-G |}, let point W i Coincident with point G.

6. The method for selecting constrained polytopes for expanding the actual operable area of ​​a permanent magnet synchronous motor according to claim 5, characterized in that: The linear equations of each edge of the voltage constraint polytope are as follows: The voltage constraint polytope equation converted into matrix form is: Among them, u dopt W point u d Axis coordinate, u qopt W point u q Axis coordinates.

7. The method for selecting constrained polytopes for expanding the actual operable area of ​​a permanent magnet synchronous motor according to claim 1, characterized in that: The prediction model is: Among them, x is the state variable, u is the control variable, A and B are system matrices, T s is a discrete time interval, k is a natural number, i d (k) and i q (k) are the d-axis component and q-axis component of the stator current of the permanent magnet synchronous motor at time k, T represents the transposition, and are the observed values ​​of the unknown disturbances in the d-axis and q-axis components of the stator current of the permanent magnet synchronous motor at time k, is the observed value of the unknown disturbance in the permanent magnet synchronous motor speed equation at time k, Δu d (k) and Δu q (k) are the voltage increments of the d-axis and q-axis of the permanent magnet synchronous motor at time k, and Δu d (k) = u d (k+1)-u d (k), Δu q (k) = u q (k+1)-u q (k),u d (k) and u d (k+1) are the d-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, u q (k) and u q (k+1) are the q-axis components of the stator voltage of the permanent magnet synchronous motor at time k and time k+1, L0 is the nominal value of the motor stator inductance, i dref (k) is the reference value of the d-axis component of the stator current of the permanent magnet synchronous motor at time k.

8. The method for selecting constrained polytopes for expanding the actual operable area of ​​a permanent magnet synchronous motor according to claim 1, characterized in that: The value function is: Among them, J represents the value function, q d and q q i d and i q The weight coefficient, q u is Δu d and Δu q The weight coefficient, J r0 is the moment of inertia, k t0 is the nameplate value of the rotation constant.

9. An explicit model predictive controller, characterized in that: It comprises a processor and a memory; wherein, when the processor executes the computer program stored in the memory, it implements the constrained polyhedral selection method for expanding the actual operable area of ​​a permanent magnet synchronous motor as described in any one of claims 1 to 7.

10. An explicit model predictive current control system, characterized in that: Includes the explicit model predictive controller as described in claim 9.

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