阅读说明：本技术 一种五相永磁同步电机三相开路故障下的容错控制方法 (Fault-tolerant control method for five-phase permanent magnet synchronous motor under three-phase open circuit fault ) 是由 李桂丹 赵宇霞 李斌 于 2020-03-31 设计创作，主要内容包括：本发明涉及一种五相永磁同步电机三相开路故障下的容错控制方法,其特征在于,先设定三相开路故障下剩余两相容错电流表达式,然后不考虑圆形磁动势约束,基于转矩谐波含量最小原则和故障前后转矩平均值不变原则求容错电流的相位和幅值,容错电流的供应采用全桥逆变器实现,且该方法对于相邻三相和不相邻三相开路故障都适用。(The invention relates to a fault-tolerant control method under a three-phase open-circuit fault of a five-phase permanent magnet synchronous motor, which is characterized in that a residual two-phase fault-tolerant current expression under the three-phase open-circuit fault is set, then circular magnetomotive force constraint is not considered, the phase and amplitude of the fault-tolerant current are obtained based on a principle of minimum torque harmonic content and a principle of unchanged torque average values before and after the fault, the fault-tolerant current is supplied by a full-bridge inverter, and the method is suitable for adjacent three-phase and non-adjacent three-phase open-circuit faults.)

1. A fault-tolerant control method under a three-phase open-circuit fault of a five-phase permanent magnet synchronous motor is characterized in that a residual two-phase fault-tolerant current expression under the three-phase open-circuit fault is set, then circular magnetomotive force constraint is not considered, the phase and amplitude of the fault-tolerant current are obtained based on a principle that torque harmonic content is minimum and a torque average value before and after the fault is constant, the fault-tolerant current is supplied by a full-bridge inverter, and the method is suitable for adjacent three-phase and non-adjacent three-phase open-circuit faults. The fault tolerance control steps are as follows:

(1) the fault phase of the adjacent three-phase open circuit fault of the five-phase permanent magnet synchronous motor is A, B, E phases, and the fault-tolerant current of the residual C, D two phases is set according to the principle of mirror symmetry about the axis of the A-phase winding as follows:

wherein α is the phase position of C, D phase winding current relative to A phase current I_nIs the phase winding current amplitude; m is₁Is the phase winding current amplitude coefficient; theta_eIs the current space vector phase angle;

in order to improve the torque performance under fault tolerance, the circular magnetomotive force constraint is not considered, and the phase and amplitude of fault-tolerant current under adjacent three-phase open-circuit fault are solved by taking the torque performance as a target, wherein the method comprises the following steps:

first, it is assumed that the post-fault current magnitude is constant, i.e., m₁Changing only the phase α to 1, the second harmonic coefficient k of the torque₂Fourth harmonic coefficient k₄And a DC component coefficient k₀With the changes, the following are:

in the formula, #_m1Is the fundamental amplitude of the permanent magnet flux linkage; psi_m3Is the third harmonic amplitude of the permanent magnet flux linkage;

establishing a relation between torque harmonic content THD and α, and determining the optimal phase α of fault-tolerant current based on the torque harmonic content THD minimum principle_THD：

|k₀|≠0

Then, the fault tolerant current phase takes the optimal phase α_THDEnsuring the phase unchanged, and determining the amplitude coefficient m based on the principle that the torque average value before and after the fault is unchanged₁And solving the fault-tolerant current under the adjacent three-phase open circuit fault as follows:

(2) the fault phase of the non-adjacent three-phase open-circuit fault of the five-phase permanent magnet synchronous motor is A, C, D phases, and the residual B, E two-phase fault-tolerant current is set according to the principle of mirror symmetry about the axis of the A-phase winding as follows:

wherein, beta is B, E phase of winding current relative to A phase current; m2 is the phase winding current magnitude coefficient;

the fault-tolerant current calculation process is the same as that of an adjacent three-phase open-circuit fault, firstly, the current amplitude is unchanged after the fault, and only the phase beta is changed; the phase β is related to the torque dc component coefficient, the second harmonic component coefficient, and the fourth harmonic component coefficient as follows:

based on the above formula, the optimal phase β when the torque harmonic content THD is minimum can be determined_THDThen, the guaranteed phase takes the optimum phase β_THDDetermining the amplitude coefficient m based on the principle that the torque average value before and after the fault is unchanged₂(ii) a And solving the fault-tolerant current under the condition of the non-adjacent three-phase open circuit fault as follows:

Technical Field

The invention belongs to the field of multi-phase motor fault-tolerant control, and provides a fault-tolerant control method for a five-phase permanent magnet synchronous motor under a three-phase open-circuit fault.

Background

Compared with the traditional three-phase motor, the multi-phase motor has the advantages of low-voltage high-power output, multiple degrees of freedom, high reliability and the like, so that more and more attention is paid. The fault-tolerant control of the multi-phase motor is the key for improving the reliability, and when the motor fails, the motor can continue to operate well without changing a hardware circuit through the fault-tolerant control, so that the research on the fault-tolerant control has important practical significance.

At present, five-phase motors are mostly used for fault-tolerant control to conduct research. Two main types of methods are proposed: optimal fault tolerant current control and decoupling vector control. The optimal fault-tolerant current control is to establish an objective function according to constraint conditions and solve the optimal solution of the objective function by adopting a Lagrange multiplier method; the decoupling vector control mainly establishes a reduced order transformation matrix to realize decoupling under a fault, and the essence of the reduced order transformation matrix is also the combination of several constraint conditions. The two methods are mainly used for five-phase star-connected motors driven by half-bridge inverters, and can accommodate two-phase open-circuit faults at most. A full-bridge inverter without zero-sequence current constraint is adopted to drive a five-phase motor, so that a three-phase open-circuit fault can be accommodated. One of the existing fault-tolerant current calculation methods for three-phase open-circuit faults is to extend an optimal current control method, but the Lagrange multiplier method used in the method is complex and has the problem of falling into local optimization. The other is to obtain the remaining two-phase current by reconstructing the circular magnetomotive force, and the Chinese invention patent of the current setting method for fault-tolerant control of the open-circuit fault of the five-phase permanent magnet synchronous motor winding (patent number is CN105743398A) obtains the fault-tolerant current under the three-phase open-circuit fault based on the circular magnetomotive force, but the torque fluctuation obtained by the fault-tolerant current is large. In order to solve the problems, a simple variable control method is provided, the amplitude of the fault-tolerant current is controlled to be unchanged, only the current phase is changed, the optimal phase with the minimum torque harmonic content is found, then the optimal phase is ensured to be unchanged, and the amplitude of the fault-tolerant current is determined according to the unchanged torque before and after the fault. Compared with the existing method, the method has simple calculation and is not restricted by the circular magnetomotive force, the magnetomotive force formed by the calculated current is elliptical, and the fluctuation of the torque can be obviously reduced compared with the current obtained according to the circular magnetomotive force.

Disclosure of Invention

The invention aims to provide a simple fault-tolerant current calculation method for a three-phase open-circuit fault of a five-phase permanent magnet synchronous motor, which is not constrained by circular magnetomotive force and effectively reduces torque fluctuation compared with the traditional method of constraining according to the circular magnetomotive force. The technical scheme is as follows:

a fault-tolerant control method under a three-phase open-circuit fault of a five-phase permanent magnet synchronous motor is characterized in that a residual two-phase fault-tolerant current expression under the three-phase open-circuit fault is set, then circular magnetomotive force constraint is not considered, the phase and amplitude of the fault-tolerant current are obtained based on a principle that torque harmonic content is minimum and a torque average value before and after the fault is constant, the fault-tolerant current is supplied by a full-bridge inverter, and the method is suitable for adjacent three-phase and non-adjacent three-phase open-circuit faults. The fault tolerance control steps are as follows:

(1) the fault phase of the adjacent three-phase open circuit fault of the five-phase permanent magnet synchronous motor is A, B, E phases, and the fault-tolerant current of the residual C, D two phases is set according to the principle of mirror symmetry about the axis of the A-phase winding as follows:

wherein α is the phase position of C, D phase winding current relative to A phase current I_nIs the phase winding current amplitude; m is₁Is the phase winding current amplitude coefficient; theta_eIs the current space vector phase angle.

In order to improve the torque performance under fault tolerance, the circular magnetomotive force constraint is not considered, and the phase and amplitude of fault-tolerant current under adjacent three-phase open-circuit fault are solved by taking the torque performance as a target, wherein the method comprises the following steps:

first, it is assumed that the post-fault current magnitude is constant, i.e., m₁Changing only the phase α to 1, the second harmonic coefficient k of the torque₂Fourth harmonic coefficient k₄And a DC component coefficient k₀With the changes, the following are:

in the formula, #_m1Is the fundamental amplitude of the permanent magnet flux linkage; psi_m3Is the third harmonic amplitude of the permanent magnet flux linkage.

Establishing a relation between torque harmonic content THD and α, and determining the optimal phase α of fault-tolerant current based on the torque harmonic content THD minimum principle_THD：

Then, the fault tolerant current phase takes the optimal phase α_THDEnsuring the phase unchanged, and determining the amplitude coefficient m based on the principle that the torque average value before and after the fault is unchanged₁And solving the fault-tolerant current under the adjacent three-phase open circuit fault as follows:

(2) the fault phase of the non-adjacent three-phase open-circuit fault of the five-phase permanent magnet synchronous motor is A, C, D phases, and the residual B, E two-phase fault-tolerant current is set according to the principle of mirror symmetry about the axis of the A-phase winding as follows:

wherein β is the phase position of B, E phase winding current relative to A phase current, m₂Is the phase winding current magnitude coefficient.

The fault-tolerant current calculation process is the same as that of an adjacent three-phase open circuit fault, firstly, the current amplitude is unchanged after the fault, and only the phase beta is changed. The phase β is related to the torque dc component coefficient, the second harmonic component coefficient, and the fourth harmonic component coefficient as follows:

based on the above formula, the optimal phase β when the torque harmonic content THD is minimum can be determined_THDThen, the guaranteed phase takes the optimum phase β_THDThe temperature of the molten steel is not changed,amplitude coefficient m is determined based on principle that torque average value is unchanged before and after fault₂. And solving the fault-tolerant current under the condition of the non-adjacent three-phase open circuit fault as follows:

compared with the three-phase open-circuit fault-tolerant current obtained by traditional reconstruction of circular magnetomotive force, the fault-tolerant current obtained by the method can obtain smaller torque fluctuation. The invention has the following technical effects:

(1) the fault-tolerant current calculation method under the three-phase open-circuit fault of the five-phase permanent magnet synchronous motor directly aims at torque performance, is not constrained by circular magnetomotive force, increases the degree of freedom of control, and can effectively reduce torque fluctuation compared with the existing method constrained by the circular magnetomotive force.

(2) The magnetomotive force formed by the fault-tolerant current obtained by the invention is elliptical, and the elliptical magnetomotive force is formed by controlling the stator current after indicating the three-phase open-circuit fault of the motor.

Description of the drawings:

FIG. 1: five-phase permanent magnet synchronous motor full-bridge drive circuit topological diagram

FIG. 2: current vector diagram, (a): a current vector diagram under an adjacent three-phase open circuit fault; (b) the method comprises the following steps Current vector diagram under non-adjacent three-phase open circuit fault

Fig. 3 shows a schematic diagram of an adjacent three-phase open circuit fault, (a): a relation graph of torque harmonic content and phase under adjacent three-phase open circuit faults; (b) the method comprises the following steps A relation graph of torque average value and phase under adjacent three-phase open circuit faults; (c) the method comprises the following steps Comparing the elliptical magnetomotive force formed by the method with the traditional circular magnetomotive force under the condition of adjacent three-phase open circuit faults; (d) the method comprises the following steps Comparing torque harmonic content graphs corresponding to the elliptic magnetomotive force and the traditional circular magnetomotive force formed by the method under the adjacent three-phase open circuit fault; (e) the method comprises the following steps Comparison of elliptical magnetomotive force formed by the method under adjacent three-phase open-circuit fault and traditional circular magnetomotive force finite element simulation torque waveform

Fig. 4 is a schematic diagram of a non-adjacent three-phase open circuit fault, (a): a relation graph of torque harmonic content THD and phase under the condition of non-adjacent three-phase open circuit fault; (b) the method comprises the following steps A relation graph of torque average value and phase under non-adjacent three-phase open circuit fault; (c) the method comprises the following steps Comparing the elliptical magnetomotive force formed by the method with the shape of the traditional circular magnetomotive force under the condition of non-adjacent three-phase open circuit faults; (d) the method comprises the following steps The torque harmonic content comparison graph corresponding to the elliptic magnetomotive force and the traditional circular magnetomotive force formed by the method under the condition of non-adjacent three-phase open circuit faults is shown; (e) the method comprises the following steps Comparison of the elliptical magnetomotive force formed by the method under the condition of non-adjacent three-phase open-circuit fault and the simulation torque waveform of the traditional circular magnetomotive force finite element

Detailed description of the invention

The five-phase permanent magnet synchronous motor driving circuit adopts a full-bridge inverter, and the topology of the inverter is shown in figure 1. The full-bridge inverter enables the supply of each phase current of the motor to be independent, has no constraint that zero sequence current is zero, and can accommodate three-phase open circuit faults.

The electromagnetic torque of a known motor is equal to the partial derivative of the magnetic common energy W with a constant current with respect to the mechanical angular displacement. For a surface-mounted permanent magnet synchronous motor, the stator inductance matrix L can be regarded as_sIs a constant matrix, so the torque T_eCan be expressed as:

in the formula, p is the number of pole pairs of the motor; i is_sIs a phase winding current matrix; theta_mIs the rotor mechanical angular position; theta is the rotor electrical angle, theta-p theta_m；ψ_mIs stator winding flux linked with permanent magnet field, and the motor is normally psi_mComprises the following steps:

in the formula, #_m1Is the fundamental amplitude, psi, of the permanent magnet flux linkage_m3Is the third harmonic amplitude of the permanent magnet flux linkage.

The formula (1) shows that under the known parameters of the pole pair number, the flux linkage of the permanent magnet and the like of the motor, the torque is only influenced by the winding current of each phase. Therefore, the fault-tolerant current under the three-phase open-circuit fault of the five-phase permanent magnet synchronous motor is calculated based on the torque performance, and the fault-tolerant current under the three-phase open-circuit fault of the five-phase permanent magnet synchronous motor is characterized in that the three-phase open-circuit fault of the five-phase permanent magnet synchronous motor is divided into an adjacent three-phase open-circuit fault and.

Because the windings of the five-phase permanent magnet synchronous motor are completely symmetrical in space, a fault-tolerant current calculation method under the adjacent three-phase open-circuit fault of the five-phase permanent magnet synchronous motor is described by taking A, B, E-phase open circuit as an example, when A, B, E adjacent three phases have the open-circuit fault, residual C, D two-phase fault-tolerant current is set according to the principle of mirror symmetry about the axis of the a-phase winding, and a current vector diagram of the fault-tolerant current is shown in fig. 2 (a).

Wherein α is the phase position of C, D phase winding current relative to A phase current I_nIs the phase winding current amplitude; m is₁Is the phase winding current amplitude coefficient; theta_eIs the current space vector phase angle, and θ_eTheta +0.5 pi to ensure maximum torque output.

In order to improve the torque performance under the three-phase open-circuit fault, the traditional circular magnetomotive force constraint is not considered, and the phase and amplitude of the fault-tolerant current are directly obtained by taking the torque performance as a target.

First, it is assumed that the post-fault current magnitude is constant, i.e., m₁Only phase α is changed, 1.

A, B, E is known to correspond to the flux linkage psi when the adjacent three phases have open circuit fault_mComprises the following steps:

at this time, the torque T is obtained by substituting equations (3) and (4) into torque equation (1)_eRelationship to α:

T_e＝pI_n(k₀+k₁cos2θ+k₂cos4θ) (5)

wherein k is₀、k₂、k₄The direct current component coefficient, the 2 nd harmonic component coefficient and the 4 th harmonic component coefficient of the torque are respectively as follows:

analysis shows that the phase α changes, the direct current component, the 2 th harmonic component and the 4 th harmonic component of the torque change along with the change of the phase α, the relation between the torque harmonic content THD and the phase α is established, as shown in formula (7), and the optimal phase α of the fault-tolerant current is determined according to the principle that the torque harmonic content is minimum_THD。

Then, the fault tolerant current phase takes the optimal phase α_THDThe current amplitude coefficient m is invariable adjusted based on the torque average value before and after the fault₁。

The average value of the torque under the normal condition of the motor is known as T_eav＝2.5ψ_m1pI_nA, B, E Torque mean at Adjacent three phase open Fault is T'_eav＝m₁k₀pI_nFrom T'_eav＝T_eavThe following can be obtained:

therefore, A, B, E the fault tolerant current for an adjacent three-phase open fault is:

the relation between the stator magnetomotive force and each phase current of the five-phase permanent magnet synchronous motor is known:

in the formula, F_αThe stator magnetomotive force is positioned in a stator two-phase static coordinate system α - βα axis component under the mark F_βThe stator magnetomotive force is β axis component of the stator magnetomotive force under a stator two-phase static coordinate system α - β, and N is the number of turns of each phase of winding in series.

When | F is satisfied_α|＝|F_βWhen | F, a circular magnetomotive force is formed_α|≠|F_βWhen | l, an elliptical magnetomotive force is formed. F obtained by fault-tolerant current under adjacent three-phase open circuit fault_αAnd F_βComprises the following steps:

to form a circular magnetomotive force according to the above formula, the phase α must be ± 0.3 pi + k pi (k ═ 0, ± 1, ± 2 …), but this is in accordance with the optimal phase α_THDAnd the magnetomotive force of the formula is elliptical, namely the obtained fault-tolerant current of the adjacent three-phase open-circuit fault forms elliptical magnetomotive force.

Because the windings of the five-phase permanent magnet synchronous motor are completely symmetrical in space, A, C, D-phase open circuit is taken as an example to illustrate the fault-tolerant current calculation method under the open circuit fault of the nonadjacent three phases of the five-phase permanent magnet synchronous motor, when the open circuit fault occurs in the A, C, D nonadjacent three phases, the residual B, E two-phase fault-tolerant current is set according to the principle of mirror symmetry about the axis of the a-phase winding, and the current vector diagram is shown in fig. 2 (b).

Wherein β is the phase position of B, E phase winding current relative to A phase current, m₂Is the current magnitude coefficient.

Flux linkage psi corresponding to known A, C, D nonadjacent three-phase open circuit fault_mComprises the following steps:

in the same way, it is first assumed that the current amplitude after a fault is constant, i.e. m₂When β is adjusted for 1, equations (10) and (11) are substituted into torque equation (1),β and the coefficient of each harmonic component of the torque are obtained, and based on the relation between the torque harmonic content and the phase, the phase β, namely the optimal phase β corresponding to the minimum torque harmonic content is found_THD。

B, E compatible fault current phase then takes the optimum phase β_THDThe current amplitude coefficient m is adjusted according to the equal torque average value before and after the fault without changing₂. To obtain m₂：

Therefore, the fault-tolerant current under the open-circuit fault of A, C, D non-adjacent three phases is:

the alpha-axis component and the beta-axis component of the stator magnetomotive force corresponding to the current in the alpha-beta coordinate system of the stator two-phase static coordinate system are as follows:

according to the above formula, a circular magnetomotive force is formed only when the phase β is ± 0.1 pi + k pi (k ═ 0, ± 1, ± 2 …)_THDUnequal, the magnetomotive force of the formula is elliptical, namely the obtained non-adjacent three-phase open-circuit fault-tolerant current forms elliptical magnetomotive force.

Finally, the method provided herein is verified by taking a 20-slot 18-pole five-phase permanent magnet synchronous fault-tolerant motor as an example. The parameters of the machine are known as listed in table 1:

TABLE 1 Motor parameters

Fig. 3(a) shows that the corresponding torque harmonic content is minimal at α ═ 0.7253 π, about 14.37%, i.e., α @_THD＝0.7253π。

FIG. 3(b) shows that at α_THDThe average torque value corresponding to 0.7253 pi is not very different from the maximum torque value.

Therefore α is selected_THD0.7253 pi can simultaneously take into account the torque fluctuation and the torque magnitude under the adjacent three-phase open-circuit fault.

Ensuring current phase at α_THDObtaining a current amplitude coefficient m according to the electromagnetic torque before and after the fault without changing when 0.7253 pi is not changed₁2.577, the fault tolerant current is:

the invention of Chinese patent for current setting method for fault-tolerant control of five-phase permanent magnet synchronous motor winding open-circuit fault (patent number is CN105743398A) based on circular magnetomotive force obtains fault-tolerant current under adjacent three-phase open-circuit fault as follows:

fig. 3(c) shows that the fault-tolerant current obtained by the method under the adjacent three-phase open-circuit fault forms an elliptical magnetomotive force, and the shape of the fault-tolerant current is obviously compared with that of a circular magnetomotive force.

Fig. 3(d) is a comparison of the torque harmonic contents generated by two fault-tolerant currents, which shows that the torque harmonic content corresponding to the elliptical magnetomotive force obtained by the method is lower than the torque harmonic content corresponding to the circular magnetomotive force.

Fig. 3(e) is a comparison of torque waveforms obtained by two fault-tolerant current finite element simulations, which proves that the torque fluctuation corresponding to the elliptic magnetomotive force obtained by the method is smaller.

Fig. 4(a) shows that the corresponding torque harmonic content is minimal at β ═ 0.1474 π, about 10%, i.e., β_THD＝0.1474π。

FIG. 4(b) shows that at β_THDThe average torque value corresponding to 0.1474 pi is not very different from the maximum torque value.

Therefore β is selected_THD0.1474 pi can simultaneously take account of the torque fluctuation and the torque magnitude under the condition of non-adjacent three-phase open circuit faults.

Ensuring current phase at β_THDThe current amplitude obtained according to the electromagnetic torque before and after the fault is not changed when 0.1474 pi is not changed

Value coefficient m₂3.582, the fault tolerant current is:

the Chinese invention patent current setting method for fault-tolerant control of open-circuit faults of windings of five-phase permanent magnet synchronous motors (with the patent number of CN105743398A) obtains fault-tolerant currents under nonadjacent three-phase open-circuit faults based on circular magnetomotive force as follows:

fig. 4(c) shows that the fault-tolerant current under the nonadjacent three-phase open-circuit fault, which is obtained by the method, forms an elliptical magnetomotive force, and the shape of the fault-tolerant current is obviously compared with that of a circular magnetomotive force.

Fig. 4(d) is a comparison of the torque harmonic contents generated by two fault-tolerant currents, which shows that the torque harmonic content corresponding to the elliptical magnetomotive force obtained by the method is lower than the torque harmonic content corresponding to the circular magnetomotive force.

Fig. 4(e) is a comparison of torque waveforms obtained by two fault-tolerant current finite element simulations, which proves that the torque fluctuation corresponding to the elliptic magnetomotive force obtained by the method is smaller.

In conclusion, when the motor has a three-phase open-circuit fault, compared with the fault-tolerant current obtained by traditional reconstruction of the circular magnetomotive force, the elliptical magnetomotive force formed by the fault-tolerant current obtained by the method generates smaller torque fluctuation, and better fault-tolerant performance can be obtained.