CN114826094A - Fault-tolerant operation method under PMSM turn-to-turn short circuit fault state - Google Patents

Abstract

The invention discloses a fault-tolerant operation method under a PMSM turn-to-turn short circuit fault state, which comprises the following steps: establishing a short-circuit circulating current model and an electromagnetic torque model of the PMSM in a turn-to-turn short-circuit fault state in a synchronous rotating coordinate system; based on the short-circuit loop current model and the electromagnetic torque model, a plurality of types of fault-tolerant operating points on the dq current plane are obtained by using the constraint conditions that the short-circuit loop current is controlled not to exceed a preset allowable value and the output torque is maximized under the condition that the output torque does not exceed the pre-fault level; obtaining turn-to-turn short circuit fault based on voltage information, current information and rotating speed information of PMSM under turn-to-turn short circuit fault stateNumber of short circuit turns N in the event of a fault _f And a short-circuit point resistor r _f (ii) a According to the number of short-circuit turns N _f And a short-circuit point resistor r _f And selecting corresponding fault-tolerant operating points from a plurality of classes of fault-tolerant operating points according to the current rotating speed information and the current torque information of the PMSM in the turn-to-turn short circuit fault state and a pre-established motor parameter lookup table.

Description

A fault-tolerant operation method for PMSM under inter-turn short-circuit fault state

technical field

The present specification relates to the technical field of motor control, and in particular, to a fault-tolerant operation method in a PMSM inter-turn short-circuit fault state.

Background technique

Among the many failure modes of PMSM drive systems, the inter-turn short-circuit fault of the stator winding caused by the degradation of the inter-turn insulation is one of the most common failure modes. Turn-to-turn short circuit is a gradual fault, but when proper fault-tolerant control is not applied, the short-circuit circulating current of the fault loop will also increase in a short period of time, thereby damaging the motor and threatening the safety of the system and personnel.

In general motor drive applications, after a short-circuit fault between turns of the stator is detected, the adverse effects of the fault can be eliminated by direct shutdown. However, in the case of high safety requirements, the sudden shutdown of the motor drive system may cause serious accidents. Therefore, even if the motor has a short-circuit fault between the turns of the stator, it must be ensured that the motor can output torque, at least until it can be safely stopped. At present, the research on fault-tolerant control of PMSM stator inter-turn short-circuit fault mainly focuses on multi-phase motors and three-phase motor drive systems with complex inverter structures. The fault-tolerant control methods or fault-tolerant operation methods are not suitable for traditional three-phase PMSM drive systems. . In addition, in the case of high safety requirements, in order to ensure the output torque of the motor as much as possible, the influence of the severity of the inter-turn short-circuit fault on the fault-tolerant operating point should be considered, so as to maximize the maintenance of the operating performance of the motor after the fault and reduce the risk of system accidents.

Therefore, it is necessary to provide a fault-tolerant operation method suitable for the short-circuit fault state of the conventional three-phase PMSM drive system.

SUMMARY OF THE INVENTION

The embodiments of the present specification provide a fault-tolerant operation method in a short-circuit fault state between turns of a PMSM, so as to provide a fault-tolerant operation method in a short-circuit fault state suitable for a conventional three-phase PMSM drive system.

In order to solve the above-mentioned technical problems, the embodiments of this specification are implemented as follows:

A fault-tolerant operation method in a PMSM inter-turn short-circuit fault state provided by the embodiments of this specification includes:

The short-circuit circulating current model and electromagnetic torque model of PMSM under the condition of inter-turn short-circuit fault are established in the synchronous rotating coordinate system;

Based on the short-circuit circulating current model and the electromagnetic torque model, the PMSM inter-turn short circuit is obtained by controlling the short-circuit circulating current not to exceed a predetermined allowable value and maximizing the output torque under the condition that the output torque does not exceed the pre-fault level. Several types of fault-tolerant operating points on the dq current plane after a fault;

Based on the voltage information, current information and rotational speed information of the PMSM under the inter-turn short-circuit fault state, the number of short-circuit turns N _f and the short-circuit point resistance r _f during the inter-turn short-circuit fault are obtained;

According to the number of short-circuit turns N _f and the short-circuit point resistance r _f , as well as the current rotational speed information and current torque information of the PMSM in the inter-turn short-circuit fault state, and the pre-established motor parameter look-up table, from the several types of fault-tolerant operation Select the corresponding fault-tolerant operating point from the point.

Preferably, the method for establishing the short-circuit circulation model specifically includes:

Denote the phase resistance of the PMSM in a healthy state as rs _s , the number of turns per phase is Ns , and the inter-turn short-circuit fault with the number of short-circuit turns N _f occurs in the A phase, denoting Δ=N _f /N _s , the A phase is divided into The healthy part of the winding a _h and the faulty part of the winding a _f , the resistance r _ah of the winding a _h , the resistance r _af of the winding a _f , the b-phase winding resistance r _b , and the _c -phase winding resistance rc are respectively:

Note that the self-inductance of phase a of the PMSM in the healthy state is L _a , the self-inductance of winding a _h in the state of inter-turn short-circuit fault is L _ah , the self-inductance of winding a _f is L _af , the difference between winding a _h and winding a _f The mutual inductance between them is _Mahaf , λ _pm is the flux linkage generated by the permanent magnet, θ _e is the electrical angle between the q-axis and the a phase of the synchronous rotating coordinate system, ω _e is the electrical angular velocity of rotor rotation, and the back electromotive force vector is [e _a ,e _b ,e _c ,e _af ] ^T , then:

According to the inter-turn short circuit loop voltage equation:

Wherein, i _af =i _{a -if is the current flowing through the winding a f ;}

Rearranging the formula (4) according to the short-circuit circulation i _f as the variable, there are:

With the help of the current space vector, it is expressed as:

Among them, I _s and δ represent the amplitude and angle of the current space vector, respectively; bring i _a in formula (6) into formula (5) and solve the linear differential equation in formula (5), the short-circuit circulating current i is obtained. _f is:

in,

The expression of the current space vector on the dq axis is:

Substituting Equation (9) into Equations (7) and (8), the effective value of the short-circuit circulating current can be obtained:

in,

From equation (10), it can be known that the characteristic of the rms value of the constant short-circuit circulating current on the dq current plane is a circle, which is called the short-circuit circulating current circle;

Use the following formula (12) to solve the coordinates of the center of the short-circuit circulation circle:

Preferably, for the surface-mounted PMSM, the method for establishing the electromagnetic torque model specifically includes:

Using the following formula (13) to solve the electromagnetic torque characteristic of the PMSM in the dq current plane in the healthy state is a straight line parallel to the d axis,

Use the following formula (14) to solve the electromagnetic torque formula T _f during inter-turn short circuit:

Among them, n _p is the number of _{pole pairs} ; |if | represents the amplitude of if, which can be obtained from formula (7); the first term on the right side of formula (14) is the electromagnetic torque formula in the healthy state, and the second term is the change of torque DC component caused by inter-turn short-circuit fault and the introduced second harmonic component;

的公式(15)：Taking formula (9) into formulas (8) and (14), the average electromagnetic torque of the PMSM in the fault state is obtained

The formula (15) of:

in,

Formula (15) is a binary linear equation including id and i _q . Therefore, when id is the independent variable and i _q is the dependent variable, the _formula (15) represents a straight line in the _dq current plane. Using the formula (17) Solve for the slope k of the line:

Preferably, after solving the PMSM inter-turn short-circuit fault, several types of fault-tolerant operating points on the dq current plane specifically include:

In the healthy state and the inter-turn short-circuit fault state, the motor operating point needs to be within the current limit circle represented by the formula (18) determined by the maximum phase current _Imax ; at the same time, it operates in the second quadrant of the dq current plane in the electromotive state;

In the dq current plane, the short-circuit circulating current circle determined by the allowable short-circuit circulating current value CC _lim is the CC _lim circle, and the fault-tolerant operating point cannot be outside the CC _lim circle;

The inter-turn short-circuit fault reduces the PMSM output torque, and the fault-tolerant operating point is determined in two cases, the rated torque and below the rated torque, respectively, before the PMSM fault.

Preferably, the fault-tolerant operating point after the fault is determined when the PMSM operates at the rated torque before the fault. At this time, the torque level before the fault cannot be maintained. According to the severity of the inter-turn short-circuit fault, there are three types of fault-tolerant operating points, including:

Solve separately the P point that represents the maximum torque output by the limit of the I _max circle after the fault, the Q point that represents the maximum torque that can be output by the limit of the I _max circle and the CC _lim circle, and represents the limit of the CC _lim The T point of the maximum torque that the circle limit can output; where,

The method for determining the fault-tolerant operating point P specifically includes:

Point P is the maximum torque operating point that the motor can output on the dq current plane after the fault, and is the tangent point between the I _max circle and the torque line under the corresponding fault, and the center of the I _max circle is the origin, so the straight line passing through the point P and the origin Perpendicular to the torque line, there are:

Among them, k ₁ is the slope of the torque straight line;

By combining formula (18) and formula (19), the coordinates of point P are solved as:

Bring the coordinates of point P into formulas (10) and (15) to obtain the RMS short-circuit circulating current CC _P and the average electromagnetic torque generated by PMSM at point P, respectively.

The method for determining the fault-tolerant operating point Q specifically includes:

Simultaneous formulas (10) and (18), where i _frms in formula (10) is replaced by CC _lim , solve the coordinates of point Q:

in,

The effective value of the short-circuit circulating current generated by PMSM at point Q is CC _lim , and the coordinate of point Q is brought into formula (15) to obtain the average electromagnetic torque of PMSM at point Q

The method for determining the fault-tolerant operating point T specifically includes:

The line passing through the point T and the center of the short-circuit circulation circle (i _do , i _qo ) is perpendicular to the corresponding torque line, then:

Simultaneous formulas (10) and (23), where i _frms in formula (10) is replaced by CC _lim , the coordinates of point T are solved as:

in,

The effective value of the short-circuit circulating current generated by PMSM at point T is CC _lim , and the coordinates of point T are brought into formula (15) to obtain the average electromagnetic torque of PMSM at point T

Preferably, the fault-tolerant operating point after the fault is determined when the PMSM operates at a lower torque than the rated torque before the fault. At this time, the torque level before the fault can be maintained. According to the severity of the inter-turn short-circuit fault, there are two types of fault-tolerant operating points, including :

分别求解代表了故障后产生转矩

同时产生最小短路环流有效值的H点，代表了故障后产生转矩

同时由I_max圆的限制的R点；其中，The average electromagnetic torque generated by the PMSM after the fault can be the same as before the fault, denoted as

Solving separately represents the torque generated after the fault

At the same time, the H point that generates the minimum short-circuit circulating current RMS represents the torque generated after the fault.

At the same time the R point bounded by the _Imax circle; where,

The method for determining the fault-tolerant operating point H specifically includes:

垂直，联立公式(15)和下述公式(26)，其中公式(15)中

由

代替，The straight line passing through the point H and the center of the short-circuit circulation circle (i _do , i _qo ) and the average torque straight line

Vertically, formula (15) and the following formula (26) are simultaneously combined, where in formula (15)

Depend on

replace,

The coordinates of the solution point H are:

Bring the coordinates of point H into formula (10) to obtain the effective value of the short-circuit circulating current CC H generated by the PMSM at point _H ;

The method for determining the fault-tolerant operating point R specifically includes:

由

代替，解得下述公式(28)表示的R点的坐标：Simultaneous formula (15) and formula (18), where in formula (15)

Depend on

Instead, solve for the coordinates of point R expressed by the following formula (28):

in,

Bring the coordinates of point R into formula (10) to obtain the effective value CC _R of the short-circuit circulating current generated by the PMSM at point R.

The above-mentioned at least one technical solution adopted in the embodiments of this specification can achieve the following beneficial effects:

The fault-tolerant operating point determination method proposed by the invention is suitable for a three-phase PMSM motor system driven by a three-phase inverter, and can also be extended to a multi-phase motor and a three-phase motor drive system with a complex inverter structure. The fault-tolerant operating point determined by the present invention, based on the short-circuit circulating current model under the synchronous rotating coordinate system and the electromagnetic torque model under the fault state, can control the short-circuit circulating current not to exceed a predetermined limit value while maximizing the output torque (not exceeding the pre-fault value). Torque level), the influence of different operating torque levels of the motor before the fault and the different insulation degradation levels between turns after the fault are fully considered, which improves the reliability and safety of the motor drive system.

Description of drawings

FIG. 1 is a flowchart of a fault-tolerant operation method in a PMSM inter-turn short-circuit fault state provided by an embodiment of the present specification;

2 is a schematic diagram of an equivalent circuit diagram of a PMSM stator inter-turn short-circuit fault in the fault-tolerant operation method under the PMSM inter-turn short-circuit fault state provided by the embodiment of the present specification;

3 is a schematic diagram of a current space vector of a synchronously rotating coordinate system in a fault-tolerant operation method under a PMSM inter-turn short-circuit fault state provided by an embodiment of the present specification;

4 is a schematic diagram of a short-circuit circulation circle in a dq current plane in a fault-tolerant operation method under a PMSM inter-turn short-circuit fault state provided by an embodiment of the present specification;

5 is a schematic diagram of the PMSM torque straight line in the fault-tolerant operation method under the PMSM inter-turn short-circuit fault state provided by the embodiment of the present specification;

FIG. 6 is the fault-tolerant operating point P when r _f =1.5Ω inter-turn short-circuit fault (Δ=0.2) occurs in the PMSM when _Th =T _N in the fault-tolerant operation method of the PMSM in the state of inter-turn short-circuit fault provided by the embodiment of the present specification Schematic diagram;

FIG. 7 shows the fault-tolerant operating point Q of the PMSM when r _f =1.2Ω inter-turn short-circuit fault (Δ=0.2) occurs when _Th =T _N in the fault-tolerant operation method of the PMSM provided by the embodiment of the present specification. Schematic diagram;

FIG. 8 shows the fault-tolerant operating point T of the PMSM when r _f =0.79Ω inter-turn short-circuit fault (Δ=0.2) occurs when _Th =T _N in the fault-tolerant operation method of the PMSM under the fault condition of inter-turn short-circuit fault provided by the embodiment of the present specification Schematic diagram;

FIG. 9 is the fault-tolerant operating point H when the PMSM has r _f =10Ω inter-turn short-circuit fault (Δ=0.2) when Th = _{0.95T N} in the fault-tolerant operation method of the PMSM under the fault condition of inter-turn short-circuit fault provided by the embodiment of the present specification Schematic diagram;

FIG. 10 shows the fault-tolerant operating point of PMSM when r _f =1.98Ω inter-turn short-circuit fault (Δ=0.2) occurs when Th = _{0.95T N} in the fault-tolerant operation method of PMSM under inter-turn short-circuit fault state provided by the embodiment of the present specification Schematic of R.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present application clearer, the technical solutions of the present application will be clearly and completely described below with reference to the specific embodiments of the present application and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

As stated above, among many failure modes of a permanent magnet synchronous motor (Permanent Magnet Synchronous Motor, PMSM) drive system, the inter-turn short-circuit fault of the stator winding caused by the degradation of the inter-turn insulation is one of the most common failure modes. Turn-to-turn short circuit is a gradual fault, but when proper fault-tolerant control is not applied, the short-circuit circulating current of the fault loop will also increase in a short period of time, thereby damaging the motor and threatening the safety of the system and personnel.

In general motor drive applications, after a short-circuit fault between turns of the stator is detected, the adverse effects of the fault can be eliminated by direct shutdown. However, in the case of high safety requirements, the sudden shutdown of the motor drive system may cause serious accidents. Therefore, even if the motor has a short-circuit fault between the turns of the stator, it must be ensured that the motor can output torque, at least until it can be safely stopped. At present, the research on fault-tolerant control of PMSM stator inter-turn short-circuit fault mainly focuses on multi-phase motors and three-phase motor drive systems with complex inverter structures. The fault-tolerant control methods or fault-tolerant operation methods are not suitable for traditional three-phase PMSM drive systems. . In addition, in the case of high safety requirements, in order to ensure the output torque of the motor as much as possible, the influence of the severity of the inter-turn short-circuit fault on the fault-tolerant operating point should be considered, so as to maximize the maintenance of the operating performance of the motor after the fault and reduce the risk of system accidents.

The present invention provides a fault-tolerant operation method of PMSM under inter-turn short-circuit fault state. As shown in FIG. 1 , the method includes: firstly, establishing a short-circuit circulation model and electromagnetic rotation model of PMSM in inter-turn short-circuit fault state in a synchronous rotating coordinate system Based on the short-circuit circulating current model and the electromagnetic torque model, the PMSM is obtained by controlling the short-circuit circulating current not to exceed a predetermined allowable value and maximizing the output torque when the output torque does not exceed the pre-fault level. Several classes of fault-tolerant operating points on the dq current plane after a turn-to-turn short-circuit fault.

In the actual situation, when the PMSM has an inter-turn short-circuit fault, the number of short-circuit turns N _f of the PMSM in the inter-turn short-circuit fault state is obtained based on the voltage information, current information and speed information of the PMSM in the inter-turn short-circuit fault state. and short-circuit point resistance r _f ;

According to the number of short-circuit turns N _f and the short-circuit point resistance r _f , as well as the current rotational speed information, the current torque information and the pre-established motor parameter look-up table of the PMSM in the inter-turn short-circuit fault state, from the several types of fault tolerance Select the corresponding fault-tolerant operating point from the operating point;

The d-axis current and q-axis current corresponding to the selected fault-tolerant operating point are assigned to the current regulator as reference currents, and the PMSM in the inter-turn short-circuit fault state is controlled to operate at the corresponding fault-tolerant operating point.

The technical solution of the present invention will be described in detail below based on FIGS. 2 to 10 , and the short-circuit circulating current model under the inter-turn short-circuit fault of the stator in the technical solution of the present invention will be deduced first, as shown in FIG. 2 . The schematic diagram of the equivalent circuit diagram of the PMSM stator inter-turn short-circuit fault in the fault-tolerant operation method under the inter-turn short-circuit fault state, and the phase resistance in the motor healthy state is rs _s , then the resistance of the winding a _h r _ah , the resistance of the winding a _f r _af And the _b and _c phase winding resistances rb and rc are respectively:

In the healthy state of the motor, the self-inductance of phase a is L _a , then the self-inductance L _ah of winding a _h , the self-inductance L _af of winding a _f , and the mutual inductance between winding a _h and winding a _f in the state of inter-turn short-circuit fault M _ahaf , λ _pm is the flux linkage generated by the permanent magnet, θ _e is the electrical angle between the q-axis of the synchronous rotating coordinate system (dq coordinate system) and phase a, ω _e is the rotor rotational electrical angular velocity, the inductance L _f and the back electromotive force vector They are:

According to the inter-turn short-circuit loop voltage equation in Figure 2, it can be expressed as:

Wherein, i _af =i _a -if _{is the current flowing through the winding a f ;} r _af , L _af , _Mahaf and e _af refer to equations (1), (2), (3). Rearranging the formula (4) according to the short-circuit circulation i _f as the variable, there are:

Under the action of an ideal current regulator or adding a negative sequence current regulator, even under the condition of inter-turn short circuit, the three-phase current can be considered as a three-phase balanced current, and can be expressed as:

Among them, I _s and δ represent the amplitude and angle of the current space vector, respectively, as shown in FIG. 3 , the current space of the synchronously rotating coordinate system in the fault-tolerant operation method under the fault-tolerant operation method of the PMSM inter-turn short-circuit fault state provided by the embodiment of this specification Vector illustration. Taking i _a in formula (6) into formula (5) and solving the linear differential equation, the short-circuit circulation i _f can be solved as:

in,

According to Fig. 3, through the transformation of the synchronous rotation coordinate system, the current space vector on the dq axis can be expressed as:

Substituting formula (9) into formulas (7) and (8), the effective value of the short-circuit circulating current can be obtained:

in,

Therefore, the characteristic of the rms value of the constant short-circuit circulating current on the dq current plane is a circle. Multiplying the radii of these circles by m yields a Circulating current circle (CC circle) in the dq current plane. The short-circuit circulation circles have the same center, and their coordinates are:

From the relevant formulas of _raf , _Lf , _Zf and _eaf , it can be known that the position of the center of the short-circuit circulation circle in the dq current plane is only related to the short-circuit turns ratio Δ, and has nothing to do with the insulation state _rf of the short-circuit point.

Taking the relevant motor parameters shown in Table 1 as an example, the short-circuit circulation circle and its center are shown in Figure 4. The numbers on the circle represent the radius of the circle, and also represent the effective value of the short-circuit circulating current generated when the motor runs at a certain point ( _id , i _q ) on the circle.

Table 1 Co-simulation and test prototype parameters

The derivation of the electromagnetic torque model under the inter-turn short-circuit fault of the stator is described below. After the inter-turn short-circuit fault, the size of the short-circuit circulating current can be controlled by adjusting the motor operating point (id , i _q ) in the _dq current plane. Therefore, in order to obtain the maximum torque at the same operating point, it is necessary to analyze the mathematical relationship between the electromagnetic torque and (id , i _q ) in the fault state, and obtain a model in the _dq current plane.

In the healthy state, the electromagnetic torque characteristic of PMSM in the dq current plane is a straight line parallel to the d axis. The calculation formula is:

In the case of inter-turn short circuit, the literature in the prior art points out that the electromagnetic torque formula at this time is:

和引入的二次谐波脉动

将公式(9)带入到公式(8)和(14)，整理可得PMSM故障状态下的平均电磁转矩公式：Among them, n _p is the number of _{pole pairs} ; |if | represents the amplitude of if, which can be obtained by formula (7). In formula (14), the first term on the right side of the formula is the electromagnetic torque formula in the healthy state, and the second term is the change of the torque DC component caused by the inter-turn short-circuit fault.

and the introduced second harmonic ripple

Bringing formula (9) into formulas (8) and (14), the average electromagnetic torque formula under PMSM fault state can be obtained:

in,

Formula (15) is a binary linear equation including id and i _q . Therefore, when id is the independent variable and i _q is the dependent variable, _formula (15) represents a straight line in the _dq current plane, and the slope k is:

The average electromagnetic torque of the PMSM in the inter-turn short-circuit fault state is a straight line with a non-zero slope. According to formula (14) and formula (15), the PMSM in the healthy state and the inter-turn short-circuit fault state can be plotted in the dq current plane respectively. Torque lines, taking the relevant motor parameters shown in Table 1 as an example, the number of short-circuit turns is 15 turns, the short-circuit resistance is r _f = 0, and the motor speed is 300r/min. The moment line is shown in Figure 5. Among them, the dotted line and the realization represent the torque in the healthy state and the inter-turn short-circuit fault state, respectively, and the value displayed on the straight line is the torque value.

The fault-tolerant operation method on the dq current plane after a turn-to-turn short-circuit fault of the PMSM is described below. The motor is usually operated in a maximum torque-to-current ratio (MTPA) control mode when the motor is in a healthy state. As can be seen from Figure 5, when the motor runs on the MTPA (q-axis), the torque will decrease at the same operating point after the inter-turn short-circuit fault.

The motor operating point should be within the current limit circle (18) determined by the maximum phase current _Imax , whether in a healthy state or in a turn-to-turn short fault state. At the same time, it operates in the second quadrant of the dq current plane in an electrodynamic state.

In addition, in the dq current plane, a short-circuit circulation circle (called the CC _lim circle) is determined with the allowable value of the short-circuit circulation current, and the fault-tolerant operating point should be within the CC _lim circle. The radius of the CC _lim circle in the dq current plane decreases as r _f decreases, and the selectable operating points in the dq current plane also decrease.

The determination of the fault-tolerant operating point of the stator inter-turn short-circuit fault depends on the severity of the fault on the one hand, and should also refer to the torque level before the fault. Therefore, before the fault, the PMSM operates at the rated torque and below the rated torque. Determine the fault tolerance operating point.

The following describes the fault-tolerant operation method when the motor runs at the rated torque before the fault. In the healthy state, the PMSM operates at the maximum current I _max of the q-axis in the MTPA mode, generating the rated torque T _N (that is, T _h =T _N ). After an inter-turn short circuit occurs, the torque decreases due to the fault. Therefore, when _Th = _TN , there is no fault-tolerant operating point within I _max that can maintain _TN after the fault. As r _f decreases, the fault severity increases and the radius of the CC _lim circle decreases. According to the position of the CC _lim circle relative to the I _max circle, the fault-tolerant operating points in the process of reducing r _f to zero can be divided into three categories, denoted as P, Q and T respectively. Among them, the point P represents the maximum torque that can be output due to the limitation of the I _max circle after the fault; the point Q represents the maximum torque that can be output due to the limitations of the I _max circle and the CC _lim circle; point P represents the limit of the CC lim circle. The _lim circle limits the maximum torque that can be output.

在P点的i_frms(记为CC_P)不超过CC_lim(CC_lim＝I_max＝25A)，即切点P在CC_lim圆以内时，故障后电机可以运行在点P上，以获得最大的转矩输出。The method of determining the fault-tolerant operating point P: The inter-turn short circuit usually starts from an early fault with a higher r _f . Compared with the I _max circle, the radius of the CC _lim circle is larger at this time, and the maximum torque that can be output by the PMSM after the fault is limited. I _max circle limit. Therefore, the maximum torque operation point that the motor may output after the fault is the tangent point between the I _max circle and the torque straight line under the corresponding fault, and this point is recorded as P(i _dP , i _qP ), and the corresponding torque is

When the i _frms (denoted as CC _P ) at point P does not exceed CC _lim (CC _lim =I _max = 25A), that is, when the tangent point P is within the circle of CC _lim , the motor can run on the point P after the fault to obtain the maximum torque output.

Since P is the tangent point between the I _max circle and the corresponding torque line, and the center of the I _max circle is the origin, the line passing through the point P and the origin is perpendicular to the torque line, then:

Among them, k is the slope of the torque straight line. With reference to equation (17), and equations (18) and (19), the coordinates of point P can be solved as:

运行点P的容错性能可通过图6说明，其中电机参数参考表1。Bringing the coordinates of point P into equations (10) and (15), we can get CC _P and

The fault-tolerant performance of the operating point P can be illustrated by Figure 6, in which the motor parameters refer to Table 1.

由于Q点位于CC_lim圆上，因此电机运行在Q点时产生的短路环流即为CC_lim。联立式(10)和(18)，其中式(10)中i_frms由CC_lim代替，即可解得Q点的坐标：The method of determining the fault-tolerant operating point Q: the radius of the CC _lim circle decreases with the decrease of r _f . When the CC _P exceeds the CC _lim , the motor cannot continue to run at the fault-tolerant point P, and the maximum torque that can be output at this time Constrained by the CC _lim circle and the I _max circle. In this case, the fault tolerance of the motor can be controlled at the intersection of the CC _lim circle and the I _max circle, denoting this point as Q( _idQ , i _qQ ), and the corresponding torque is

Since the Q point is on the CC _lim circle, the short-circuit circulating current generated when the motor runs at the Q point is CC _lim . Simultaneous equations (10) and (18), where i _frms in equation (10) is replaced by CC _lim , the coordinates of the Q point can be solved:

in,

Put the coordinates of point Q into equation (15), you can get

在Q点产生的短路环流被限制在CC_lim＝25A。The fault tolerance performance of the operating point Q can be illustrated by Figure 7, where the motor parameters refer to Table 1. Under the same motor operating conditions and the same number of short-circuit turns, when r _{f is} reduced to 1.2Ω, point P is outside the circle of CC _lim , that is, CC _P >CC _lim . At this time, the fault tolerance of the faulty motor is controlled at point Q to output the maximum torque

The short-circuit circulating current generated at point Q is limited to CC _lim =25A.

Determination method of fault-tolerant operating point T: When r _f is further reduced, point Q moves down along the I _max circle with the reduction of the radius of CC _lim . During this process, since the current torque component i _q continues to decrease, the output torque of the motor continues to decrease. The radius of the CC _lim circle continues to shrink as r _f decreases. When there is no intersection between the CC _lim circle and the I _max circle, even if the current vector angle is increased to 180°, the short-circuit circulating current will still be larger than CC _lim .

由于T为CC_lim圆和相应转矩直线的切点、CC_lim圆的圆心为(i_do，i_qo)，所以经过点T和(i_do，i_qo)的直线与该转矩直线垂直，则有：The tangent point between the CC _lim circle and the corresponding torque straight line under fault moves downward with the reduction of the CC _lim radius. Therefore, when the tangent point falls within the I _max circle, run the motor at this tangent point, and you can To maximize the torque output under the premise of suppressing the short-circuit circulating current not exceeding CC _lim , the maximum torque that can be output at this time is limited by the CC _lim circle. Let this tangent point be T(i _dT , i _qT ), and the corresponding torque is

Since T is the tangent point of the CC _lim circle and the corresponding torque line, and the center of the CC _lim circle is (i _do , i _qo ), the line passing through the point T and (i _do , i _qo ) is perpendicular to the torque line, Then there are:

Combining equations (10) and (23), where i _frms in equation (10) is replaced by CC _lim , the coordinates of point T can be solved as:

in,

Put the coordinates of point T into formula (15), you can get the sum

同时，在T点产生的短路环流被限制在CC_lim。The fault tolerance performance of the operating point T can be illustrated by Figure 8, in which the motor parameters refer to Table 1. Under the same motor operating conditions and the same number of short-circuit turns, when r _{f is} reduced to 0.79Ω, the fault-tolerant motor is controlled at point T to output the maximum torque

At the same time, the short-circuit circulating current generated at point T is limited to CC _lim .

In the process of further reducing r _f to zero, the motor is always run at point T by fault-tolerant control to maximize the output torque and ensure the system's post-fault operating performance as much as possible.

The following describes the fault-tolerant operation method when the motor running torque is lower than the rated torque before the fault.

即

由于故障后在相同运行点(i_d，i_q)上输出的转矩减少，且随着r_f的降低转矩减少的量增加，因此，转矩直线

在dq电流平面的位置随着r_f的降低而升高。所以，可以维持转矩

并同时最小化短路环流的运行点也发生改变。在T_h<T_N的情况下，在转矩直线

上存在两类容错运行点，可以维持故障前转矩水平，同时最小化短路环流，分别记为点H和点R。In the healthy state, the PMSM operates in the MTPA mode at a place where the q-axis is lower than I _max , when the motor operating torque is lower than the rated torque (ie, T _h <T _N ), after the inter-turn short circuit occurs, the insulation degradation level does not In severe cases (ie, higher r _f ), maintaining the pre-fault torque level while minimizing short-circuit circulating currents can be achieved by injecting higher currents into the motor within the _Imax circle. The torque straight line with the same torque value after the fault and before the fault is recorded as

which is

Since the torque output at the same operating point (id , i _q ) decreases after the fault, and the amount of torque decrease increases with the decrease of _{r f ,} the torque linear

The position in the dq current plane increases with decreasing _rf . Therefore, the torque can be maintained

At the same time, the operating point that minimizes the short-circuit circulating current also changes. In the case of T _h <T _N , in the torque straight line

There are two types of fault-tolerant operating points on , which can maintain the pre-fault torque level while minimizing the short-circuit circulating current, denoted as point H and point R, respectively.

并未完全上升至I_max圆以外。因此，当电机运行在转矩直线

与相应的短路环流圆相切的切点上时，既可以维持转矩输出故障前水平又可以产生最小的短路环流。若该切点也落在I_max圆内，则其就称为既能维持转矩输出故障前水平又能最小化短路环流的容错运行点，记为点H(i_dH，i_qH)。由于r_f相对较高，在H处产生的短路环流，记为CC_H，小于CC_lim。Fault-tolerant operating point H: In the case of T _h < T _N , for early turn-to-turn short circuits with high r _f , the torque straight line

does not rise completely beyond the I _max circle. Therefore, when the motor runs in a torque line

When the tangent point is tangent to the corresponding short-circuit circulating current circle, the torque output can maintain the pre-fault level and generate the minimum short-circuit circulating current. If the tangent point also falls within the _Imax circle, it is called a fault-tolerant operating point that can maintain the pre-fault level of torque output and minimize short-circuit circulating current, denoted as point H(i _dH , i _qH ). Due to the relatively high r _f , the short-circuit circulating current at H, denoted as CC _H , is smaller than CC _lim .

与相应的短路环流圆的切点、短路环流圆的圆心为(i_do，i_qo)，所以经过点H和(i_do，i_qo)的直线与转矩直线

垂直，则有：Since H is the torque straight line

The tangent point to the corresponding short-circuit circulation circle and the center of the short-circuit circulation circle are (i _do , i _qo ), so the straight line passing through the point H and (i _do , i _qo ) and the torque straight line

Vertically, there are:

由

代替，可解得H点的坐标为：Simultaneous equations (15) and (26), where in equation (15)

Depend on

Instead, the coordinates of point H can be solved as:

Here, A ₁ and A ₂ refer to formula (16). Put the coordinates of the _H point into equation (10), and then CCH can be obtained.

以下)。然而，此时点H在I_max圆内，通过将电机容错控制在H，可以输出与故障前相同的转矩水平，同时最小化短路环流。在H点的短路环流CC_H为4.3A，小于预设CC_lim。The fault-tolerant performance of operating point H can be illustrated by Figure 9, where the motor parameters refer to Table 1. The PMSM operates at point A(0, 23.75A) in a healthy state, the operating torque is _Th =95%×T _N =36.55N·m, and the rotational speed is the rated rotational speed. When a 60-turn short-circuit fault occurs (Δ=0.2) and r _f = 10Ω, the operating torque of the motor at point A decreases (point A in the figure is located on the torque straight line)

the following). However, at this time, the point H is within the _Imax circle, and by controlling the motor fault tolerance at H, the same torque level as before the fault can be output while minimizing the short-circuit circulating current. The short-circuit circulating current CC _{H at point H} is 4.3 A, which is less than the preset CC _lim .

上升，H点开始移出I_max圆，此时，电机将不能继续容错运行在H点。然而，转矩直线

还未完全上升至I_max圆以外，因此，使电机运行在转矩直线

处于I_max圆内上的任一点上仍可输出转矩

而此时，经过转矩直线

与I_max圆的交点的短路环流圆，相比与经过转矩直线

处于I_max圆内其他点的短路环流圆的半径更小，具有更低的短路环流。所以，该交点即为此时的容错运行点，记为点R(i_dR，i_qR)。同样的，由于r_f仍然相对较高，在R处产生的短路环流，记为CC_R，也会小于CC_lim。Determination method of fault-tolerant operating point R: with the decrease of r _f , the torque straight line

Rising, the H point begins to move out of the I _max circle, at this time, the motor will not continue to run at the H point in a fault-tolerant manner. However, the torque linear

has not fully risen beyond the I _max circle, therefore, make the motor run on a torque straight line

Torque can still be output at any point within the circle of I _max

At this time, through the torque straight line

The short-circuit circulation circle at the intersection with the _Imax circle, compared to the straight line passing through the torque

The short-circuit circulation circles at other points within the circle of I _max have smaller radii and lower short-circuit circulation. Therefore, the intersection point is the fault-tolerant operating point at this time, which is denoted as point R( _idR , _iqR ). Likewise, since r _f is still relatively high, the short-circuit circulating current at R, denoted CC _R , will also be smaller than CC _lim .

和I_max圆的交点，联立式(15)和(18)，其中式(15)中

由

代替，可解得R点的坐标为：Since point R is a torque straight line

and the intersection of the I _max circle, formulas (15) and (18) simultaneously, where in formula (15)

Depend on

Instead, the coordinates of point R can be solved as:

in,

Bringing the coordinates of point R into formula (10), C _R can be obtained.

的同时，限制注入到电机的相电流不超过I_max。如图所示，点R在CC_lim圆以内，即CC_R<CC_lim。The fault tolerance performance of the operating point R can be illustrated by Figure 10, where the motor parameters refer to Table 1. Under the same motor operating conditions and the same number of short-circuit turns, when r _{f is} reduced to 1.98Ω, point H has moved beyond the circle of I _max . At this time, the fault tolerance of the motor is controlled to point R, and the torque level before the fault is maintained.

At the same time, the phase current injected into the motor is limited to not exceed I _max . As shown, the point R is within the circle of CC _lim , that is, CC _R < CC _lim .

上升至I_max圆外，此时，可以将电机容错运行在P点以输出故障状态下最大转矩，或者进一步容错运行在Q点和T点，以限制短路环流至CC_lim，同时最大化转矩输出。When the running torque of the motor in a healthy state is lower than the rated torque, in the early stage of an inter-turn short-circuit fault, the motor can be operated at the fault-tolerant control points H and R to maintain the pre-fault torque level while minimizing the short-circuit circulating current. As the insulation further degrades and r _f decreases further, the final torque straight line

Rise to the outside of the I _max circle, at this time, the motor can be run fault-tolerant at point P to output the maximum torque in the fault state, or further fault-tolerant running at points Q and T to limit the short-circuit circulating current to CC _lim , while maximizing the torque. torque output.

When the running torque of the motor is the rated torque in the healthy state, due to the limitation of the I _max circle, the same torque as before the fault cannot be output after the fault, and the fault-tolerant operating points are only P, Q and T.

In the actual situation, when the PMSM has an inter-turn short-circuit fault, the number of short-circuit turns N _f of the PMSM in the inter-turn short-circuit fault state is obtained based on the voltage information, current information and speed information of the PMSM in the inter-turn short-circuit fault state. and short-circuit point resistance r _f ;

According to the number of short-circuit turns N _f and the short-circuit point resistance r _f , as well as the current rotational speed information, current torque information and the pre-established motor parameter look-up table of the PMSM in the inter-turn short-circuit fault state, from the several types of fault tolerance Select the corresponding fault-tolerant operating point from the operating point;

The d-axis current and the q-axis current corresponding to the selected fault-tolerant operating point are assigned to the current regulator as reference currents, and the PMSM under the inter-turn short-circuit fault state is controlled to operate at the corresponding fault-tolerant operating point.

The fault-tolerant operating point determination method proposed by the invention is suitable for a three-phase PMSM motor system driven by a three-phase inverter, and can also be extended to a multi-phase motor and a three-phase motor drive system with a complex inverter structure. The fault-tolerant operating point determined by the technical solution of the present invention is based on the model of the short-circuit circulating current in the synchronous rotating coordinate system and the electromagnetic torque model under the fault state, so that the short-circuit circulating current can be controlled not to exceed a predetermined limit value and the output torque can be maximized (no more than Torque level before the fault), thus fully considering the influence of the different operating torque levels of the motor before the fault and the different insulation degradation levels between the turns after the fault, and improving the reliability and safety of the motor drive system.

The above-mentioned embodiments merely illustrate the principles and effects of the present invention, but are not intended to limit the present invention. Anyone skilled in the art can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical idea disclosed in the present invention should still be covered by the claims of the present invention.

Claims (6)

1. a fault-tolerant operation method under a PMSM inter-turn short-circuit fault state, characterized in that the method comprises: The short-circuit circulating current model and electromagnetic torque model of PMSM under the condition of inter-turn short-circuit fault are established in the synchronous rotating coordinate system; Based on the short-circuit circulating current model and the electromagnetic torque model, the PMSM inter-turn short circuit is obtained by controlling the short-circuit circulating current not to exceed a predetermined allowable value and maximizing the output torque under the condition that the output torque does not exceed the pre-fault level. Several types of fault-tolerant operating points on the dq current plane after a fault; Based on the voltage information, current information and rotational speed information of the PMSM under the inter-turn short-circuit fault state, the number of short-circuit turns N _f and the short-circuit point resistance r _f during the inter-turn short-circuit fault are obtained; According to the number of short-circuit turns N _f and the short-circuit point resistance r _f , as well as the current rotational speed information and current torque information of the PMSM in the inter-turn short-circuit fault state, and the pre-established motor parameter look-up table, from the several types of fault-tolerant operation Select the corresponding fault-tolerant operating point from the point. 2. the fault-tolerant operation method under the PMSM inter-turn short-circuit fault state according to claim 1, is characterized in that, the establishment method of described short-circuit circulation model specifically comprises: Denote the phase resistance of the PMSM in a healthy state as rs _s , the number of turns per phase is Ns , and the inter-turn short-circuit fault with the number of short-circuit turns N _f occurs in the A phase, denoting Δ=N _f /N _s , the A phase is divided into The healthy part of the winding a _h and the faulty part of the winding a _f , the resistance r _ah of the winding a _h , the resistance r _af of the winding a _f , the b-phase winding resistance r _b , and the _c -phase winding resistance rc are respectively:

Note that the self-inductance of phase a of the PMSM in the healthy state is L _a , the self-inductance of winding a _h in the state of inter-turn short-circuit fault is L _ah , the self-inductance of winding a _f is L _af , the difference between winding a _h and winding a _f The mutual inductance between

λ _pm is the flux linkage generated by the permanent magnet, θ _e is the electrical angle between the q-axis of the synchronous rotating coordinate system and phase a, ω _e is the electrical angular velocity of rotor rotation, and the back electromotive force vector is [e _a , e _b , e _c ,e _af ] ^T , then:

According to the inter-turn short circuit loop voltage equation:

Wherein, i _af =i _{a -if is the current flowing through the winding a f ;} Rearranging the formula (4) according to the short-circuit circulation i _f as the variable, there are:

With the help of the current space vector, it is expressed as:

Among them, I _s and δ represent the amplitude and angle of the current space vector, respectively; bring i _a in formula (6) into formula (5) and solve the linear differential equation in formula (5), the short-circuit circulating current i is obtained. _f is:

in,

The expression of the current space vector on the dq axis is:

Substituting Equation (9) into Equations (7) and (8), the effective value of the short-circuit circulating current can be obtained:

in,

From equation (10), it can be known that the characteristic of the rms value of the constant short-circuit circulating current on the dq current plane is a circle, which is called the short-circuit circulating current circle; Use the following formula (12) to solve the coordinates of the center of the short-circuit circulation circle:

3. the fault-tolerant operation method under the PMSM inter-turn short-circuit fault state according to claim 2, is characterized in that, for surface-mounted PMSM, the establishment method of described electromagnetic torque model specifically comprises: Using the following formula (13) to solve the electromagnetic torque characteristic of the PMSM in the dq current plane in the healthy state is a straight line parallel to the d axis,

Use the following formula (14) to solve the electromagnetic torque formula T _f during inter-turn short circuit:

Among them, n _p is the number of _{pole pairs} ; |if | represents the amplitude of if, which can be obtained from formula (7); the first term on the right side of formula (14) is the electromagnetic torque formula in the healthy state, and the second term is the change of torque DC component caused by inter-turn short-circuit fault and the introduced second harmonic component; Taking formula (9) into formulas (8) and (14), the average electromagnetic torque of the PMSM in the fault state is obtained

The formula (15) of:

in,

Formula (15) is a binary linear equation including id and i _q . Therefore, when id is the independent variable and i _q is the dependent variable, the _formula (15) represents a straight line in the _dq current plane. Using the formula (17) Solve for the slope k of the line:

4. the fault-tolerant operation method under PMSM inter-turn short-circuit fault state according to claim 3, is characterized in that, after described solving described PMSM inter-turn short-circuit fault, several kinds of fault-tolerant operation points on the dq current plane, specifically comprise : In the healthy state and the inter-turn short-circuit fault state, the operating point of the motor must be within the current limit circle represented by the formula (18) determined by the maximum phase current _Imax ; at the same time, it operates in the second quadrant of the dq current plane in the electromotive state;

In the dq current plane, the short-circuit circulating current circle determined by the allowable short-circuit circulating current value CC _lim is the CC _lim circle, and the fault-tolerant operating point cannot be outside the CC _lim circle; The inter-turn short-circuit fault reduces the PMSM output torque, and the fault-tolerant operating point is determined under the two conditions of running at the rated torque and below the rated torque before the PMSM fault. 5. The fault-tolerant operation method under PMSM inter-turn short-circuit fault state according to claim 4, characterized in that, before the fault, the PMSM operates at rated torque to determine the fault-tolerant operating point after the fault, and the torque level before the fault is at this moment. can not be maintained. According to the severity of the inter-turn short-circuit fault, there are three types of fault-tolerant operating points, including: Solve separately the P point that represents the maximum torque output by the limit of the I _max circle after the fault, the Q point that represents the maximum torque that can be output by the limit of the I _max circle and the CC _lim circle, and represents the limit of the CC _lim The T point of the maximum torque that the circle limit can output; where, The method for determining the fault-tolerant operating point P specifically includes: Point P is the maximum torque operation point that the motor can output on the dq current plane after the fault, and is the tangent point between the I _max circle and the torque line under the corresponding fault, and the center of the I _max circle is the origin, so the straight line passing through the point P and the origin Perpendicular to the torque line, there are:

Among them, k ₁ is the slope of the torque straight line; By combining formula (18) and formula (19), the coordinates of point P are solved as:

Bring the coordinates of point P into formulas (10) and (15) to obtain the RMS short-circuit circulating current CC _P and the average electromagnetic torque generated by PMSM at point P, respectively.

The method for determining the fault-tolerant operating point Q specifically includes: Simultaneous formulas (10) and (18), where i _frms in formula (10) is replaced by CC _lim , solve the coordinates of point Q:

in,

The effective value of the short-circuit circulating current generated by PMSM at point Q is CC _lim , and the coordinate of point Q is brought into formula (15) to obtain the average electromagnetic torque of PMSM at point Q

The method for determining the fault-tolerant operating point T specifically includes: The line passing through the point T and the center of the short-circuit circulation circle (i _do , i _qo ) is perpendicular to the corresponding torque line, then:

Simultaneous formulas (10) and (23), where i _frms in formula (10) is replaced by CC _lim , the coordinates of point T are solved as:

in,

The effective value of the short-circuit circulating current generated by PMSM at point T is CC _lim , and the coordinates of point T are brought into formula (15) to obtain the average electromagnetic torque of PMSM at point T

6. The fault-tolerant operation method under PMSM inter-turn short-circuit fault state according to claim 5, is characterized in that, the fault-tolerant operation point after the fault is determined under the condition that the PMSM is operated before the fault is lower than the rated torque, and the fault is forwarded at this time. The torque level can be maintained. According to the severity of the inter-turn short circuit fault, there are two types of fault-tolerant operating points, including: The average electromagnetic torque generated by the PMSM after the fault can be the same as before the fault, denoted as

Solving separately represents the torque generated after the fault

At the same time, the H point that generates the minimum short-circuit circulating current RMS represents the torque generated after the fault.

At the same time the R point bounded by the _Imax circle; where, The method for determining the fault-tolerant operating point H specifically includes: The straight line passing through the point H and the center of the short-circuit circulation circle (i _do , i _qo ) and the average torque straight line

Vertically, formula (15) and the following formula (26) are simultaneously combined, where in formula (15)

Depend on

replace,

The coordinates of the solution point H are:

Bring the coordinates of point H into formula (10) to obtain the effective value of the short-circuit circulating current CC H generated by the PMSM at point _H ; The method for determining the fault-tolerant operating point R specifically includes: Simultaneous formula (15) and formula (18), where in formula (15)

Depend on

Instead, solve for the coordinates of point R expressed by the following formula (28):

in,

Bring the coordinates of point R into formula (10) to obtain the effective value CC _R of the short-circuit circulating current generated by the PMSM at point R.

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