Harmonic injection-based fault-tolerant control method for six-phase permanent magnet motor

Abstract

The invention discloses a six-phase permanent magnet motor fault-tolerant control method based on harmonic injection, and provides a fault-tolerant control scheme based on harmonic injection for an open-circuit fault of a six-phase permanent magnet motor driving system. The torque output capability of the torque mode during fault-tolerant operation of the motor is improved as much as possible, and the system copper loss of the copper loss mode is further reduced. The method comprises the following steps: firstly, on the premise of ensuring that the output torque is not changed before and after a fault, giving up the constraint of direct-axis magnetomotive force, and assuming a current expression of direct-axis harmonic injection after the fault; secondly, in order to realize decoupling of the harmonic subspace and the fundamental subspace during fault-tolerant operation, a current reference of the harmonic subspace is assumed through simple linear operation; and finally, taking unit copper loss and unit torque output as optimization targets, and solving an optimal direct-axis harmonic current injection coefficient and phase and harmonic subspace current reference expression. The scheme is not only suitable for a single-phase open-circuit fault of a six-phase permanent magnet motor system, but also suitable for a two-phase open-circuit fault of a motor.

Description

Technical Field

[0001] The invention belongs to the field of multi-phase motor fault-tolerant control, and in particular relates to a six-phase permanent magnet motor fault-tolerant control method based on harmonic injection. Background Art

[0002] Six-phase permanent magnet motors are widely used in aerospace, electric vehicles, electric boats and other fields due to their advantages such as small torque pulsation, high control freedom and good fault tolerance. The open circuit fault caused by high temperature and line stray inductance is one of the most common faults in electric drive systems. After fault detection, if the appropriate method cannot be used to tolerate the fault, it will inevitably lead to a rapid decline in its torque output capacity and operating efficiency, seriously affecting the control performance of the motor system.

[0003] Studies have shown that even without introducing additional auxiliary circuits, as long as the rotating magnetic motive force before and after the fault remains unchanged, the torque output before the fault can be maintained under an open circuit fault. Based on this, this type of fault-tolerant control scheme can be divided into two categories: reconstructing the mathematical model and modifying the current reference. However, the fault-tolerant control scheme of reconstructing the mathematical model requires remodeling the motor while considering the dimensionality reduction matrix, which significantly increases the complexity of fault-tolerant control. Therefore, the fault-tolerant control scheme of modifying the current reference has been widely favored by scholars. The existing fault-tolerant current optimization methods of modifying the current reference can be divided into the minimum copper loss strategy, the maximum torque strategy, and the minimum copper loss strategy in the full torque range. The minimum copper loss strategy and the maximum torque strategy can be divided into sinusoidal power supply mode and non-sinusoidal power supply mode, while the minimum copper loss strategy in the full torque range only includes the sinusoidal power supply mode.

[0004] The fault-tolerant control scheme for non-sinusoidal power supply has only verified its feasibility in the minimum copper loss strategy, but has not yet explored the optimal harmonic injection number. The high-order harmonic injection scheme in the maximum torque strategy only considers the amplitude of harmonic injection but not the injection phase angle. In addition, the minimum copper loss strategy and the maximum torque strategy lack a unified injection form, which makes their models complex and difficult to solve. To this end, the present invention proposes a fault-tolerant control method for a six-phase permanent magnet motor based on harmonic injection, in order to further solve the above problems. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention proposes a six-phase permanent magnet motor fault-tolerant control method based on harmonic injection. First, the method derives the general formula of harmonic injection in non-sinusoidal fault-tolerant mode. It only needs to change the injection amplitude and phase angle of the d-axis harmonic current and the current reference of the harmonic plane to achieve smooth switching between the minimum copper loss strategy and the maximum torque strategy. Secondly, the method derives the optimal harmonic injection order, that is, injects 2nd, 4th, and 6th harmonics into the direct axis under the premise of ensuring that the output torque remains unchanged, so as to minimize the loss of the minimum copper loss strategy and maximize the torque output of the maximum torque strategy. The scheme is not only applicable to single-phase open circuit faults, but also to two-phase open circuit faults.

[0006] The technical solution adopted by the present invention is a six-phase permanent magnet motor fault-tolerant control method based on harmonic injection. The specific contents are as follows:

[0007] Step 1): Through the vector space decomposition (VSD) matrix, the physical quantities of the six-phase permanent magnet motor system can be decoupled into three mutually orthogonal subspaces, namely, αβ, xy and o1o2 subspaces.

[0008] [f ɑ f β f x f y f o1 t o2 ] T

[0009] =T 6s [f A f B f C f U f V f W ] T

[0010]

[0011] In the formula, the VSD transformation matrix T 6s The physical quantity f of the six-phase permanent magnet motor in the six-phase stationary coordinate system is A 、f B 、f C 、f U 、f V and f W Transform to α-β coordinate system (f ɑ and f β )、xy coordinate system (f x and f y ) and o1-o2 coordinate system (f o1 and f o2). Through Park transformation, the physical quantities of the six-phase permanent magnet motor in the stationary coordinate system can be transformed into the rotating coordinate system.

[0012] [f d f q f x f y ] T =T 2r [f α f β f x f y ] T

[0013]

[0014] Where, Park transformation matrix T 2r The physical quantity f in the αβ coordinate system α and f β Transform to the rotating coordinate system (f d and f q ) and keep the physical quantity value in the xy coordinate system unchanged, P 2r (θ) represents the second-order park transformation matrix, I represents the second-order identity matrix, and θ represents the electrical angle of the motor.

[0015] in i d = 0 control, the electromagnetic torque equation of the six-phase permanent magnet motor can be expressed as

[0016] T e =3P n [i q ψ f -i d i q (L d -L q )]

[0017] Where P n , f 、i d 、i q and L d , L q They respectively represent the pole pair number, flux amplitude, dq axis current and dq axis inductance of the six-phase permanent magnet motor.

[0018] Step 2) Design of basic fault-tolerant control framework. Since the six-phase permanent magnet motor has more control freedom, it is only necessary to modify the current reference of the corresponding harmonic plane to achieve undisturbed operation after an open-circuit fault. For a six-phase permanent magnet motor system with an isolated neutral point, the current constraint to be considered after an open-circuit fault is

[0019]

[0020] In the formula, i A 、i B 、i C 、i U 、i V 、i W Represents the six-phase stator current of the six-phase permanent magnet motor, I rt Indicates the rated current of the motor, i fp Indicates the fault phase. Since the current in the α-β plane participates in energy conversion, its current reference needs to remain unchanged, and the current reference in the xy subspace is corrected by the ɑ-β current, which can be expressed as

[0021]

[0022] In the formula, i α 、i β 、i x 、i y They represent the motor's α-axis, β-axis, x-axis, and y-axis currents respectively, and the variable k xα , k xβ , k yɑ and k yβ Respectively represent i x The α-axis current correction factor, i x The β-axis current correction factor, i y The α-axis current correction factor and i y The β-axis current correction coefficients are usually solved using two common optimization objectives.

[0023] 1) Minimum copper loss strategy: The optimization goal is to minimize the copper loss J ML .

[0024]

[0025] 2) Maximum torque strategy: The optimization goal is to maximize the torque output J MT , that is, to maximize the amplitude of the α-β phase.

[0026] J MT =max(|I αβ |)

[0027] In the formula, |·| represents the modulus of the α-β phase. The variable k is solved by different optimization objectives. xα , k xβ , k yα , k yβ By adjusting the specific value of , smooth switching between the minimum copper loss strategy and the maximum torque strategy can be achieved.

[0028] Step 3: Design of harmonic injection fault-tolerant strategy framework.d = 0, the electromagnetic torque of the system depends only on the q-axis current. That is, without changing the q-axis current, the injection of harmonics will not affect the torque output performance of the six-phase permanent magnet motor during fault-tolerant operation. q The plane is mapped to the 2nd, 4th, and 6th harmonics, so the d-axis reference current after harmonic injection can be assumed to be

[0029]

[0030] In the formula, λ d2 , d4 , d6 They represent the injection coefficients of the 2nd, 4th, and 6th harmonic currents, respectively, and θ d2 ,θ d4 ,θ d6 Respectively represent the phase shift of the 2nd, 4th, and 6th currents, They represent the d-axis and q-axis reference currents respectively. From the expression of the d-axis reference current, we can see that there are 6 unknowns that need to be solved.

[0031] In order to obtain the current reference of the harmonic plane, the six-phase current expression needs to be converted to the two-phase stationary coordinate system:

[0032]

[0033] Assume that the current reference expression of the harmonic plane after an open circuit fault occurs is:

[0034]

[0035] In the formula, They represent the reference currents of the x-axis, y-axis, α-axis and β-axis respectively. Combining the above two equations, the expression of the six-phase current after an open circuit fault occurs can be expressed as

[0036]

[0037] Combined with the d-axis current expression after harmonic injection, it can be calculated as The specific calculation expression of

[0038]

[0039] According to theoretical analysis, there are 10 unknown quantities (k xα , k xβ , k yα , k yβ , d2 , d4 , d6 ,θ d2 ,θ d4 ,θd6 ) needs to be solved, so it is necessary to introduce additional objective functions to solve the harmonic plane fundamental wave injection coefficient, the optimal harmonic injection coefficient and the optimal harmonic injection phase.

[0040] Step 4): Solve the minimum copper loss mode. In the minimum copper loss mode, the unit copper loss generated by the motor system can be expressed as

[0041]

[0042] Assuming from the above

[0043]

[0044] The unit copper loss expression can be simplified to:

[0045]

[0046] The final solution is the unit loss expression:

[0047] P cu =Λ ɑ Δ α +Λ β Δ β +Λ m Δ m

[0048] In the formula,

[0049] Step 5): Solve the maximum torque mode. In the maximum torque mode, the normalized stator current of the motor system can be expressed as

[0050]

[0051] In the formula, i m (m=A, B, C, U, V, W) represents the six-phase stator current of the motor. Substituting the current expressions of each phase into the above formula, the constraint conditions under the maximum torque mode can be obtained:

[0052]

[0053] Among them, Δ α , Δ β , Δ m Same as the above expression, and the remaining terms can be expressed as follows

[0054]

[0055]

[0056] From the analysis in steps 4) and 5), it can be seen that for the minimum copper loss mode and the maximum torque mode, it is only necessary to solve the constraints of the above fault-tolerant modes through the fmincon and fminmax functions in the Matlab optimization toolbox to obtain the optimal 10 unknowns that meet the constraints after different open-circuit faults, so as to achieve undisturbed operation after open-circuit faults.

[0057] Compared with the existing technical solutions, the technical solutions of the present invention have the following beneficial effects:

[0058] The present invention derives the general formula for harmonic injection in non-sinusoidal fault-tolerant mode. It only needs to change the injection amplitude and phase angle of the d-axis harmonic current and the current reference of the harmonic plane to achieve smooth switching between the minimum copper loss strategy and the maximum torque strategy. Secondly, under the premise of ensuring that the output torque remains unchanged, the optimal harmonic injection number is derived, that is, injecting 2nd, 4th, and 6th harmonics into the d-axis to achieve the loss of the copper loss strategy and the torque output of the maximum torque strategy. This scheme is not only applicable to single-phase open circuit faults, but also to two-phase open circuit faults. Finally, through the adopted fault-tolerant control algorithm, its torque output can theoretically reach 73.4% of normal operation, and its loss is reduced by about 5.7% compared with the traditional sinusoidal mode, which greatly improves the control performance during fault-tolerant operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a driving system diagram of the present invention;

[0060] Figure 2 This is a current characterization diagram after the optimal harmonic injection times of the present invention;

[0061] Figure 3 It is a fault-tolerant current characterization diagram after different open circuit faults of the present invention; DETAILED DESCRIPTION

[0062] Step 1): Different from the traditional three-phase motor drive system, the six-phase permanent magnet motor drive system fed by the six-phase voltage source inverter is as follows Figure 1 As shown in the figure, there is a 30° phase shift between the two sets of stator windings of the six-phase permanent magnet motor, and the neutral points are isolated from each other. dc Indicates the DC bus voltage, S m，p and S m，n They respectively represent the switching states of the upper and lower bridge arm IGBTs of the inverter, with "1" representing the on state and "0" representing the off state, where m = (A, B, C, U, V, W).

[0063] Through the vector space decomposition (VSD) matrix, the physical quantities of the six-phase permanent magnet motor system can be decoupled into three mutually orthogonal subspaces, namely, αβ, xy and o1o2 subspaces.

[0064]

[0065] In the formula, the VSD transformation matrix T 6s The physical quantity f of the six-phase permanent magnet motor in the six-phase stationary coordinate system is A 、f B 、f C 、f U 、f V and f W Transform to α-β coordinate system (f α and f β )、xy coordinate system (f x and f y ) and o1-o2 coordinate system (f o1 and f o2 ). Through Park transformation, the physical quantities of the six-phase permanent magnet motor in the stationary coordinate system can be transformed into the rotating coordinate system.

[0066] [f d f q f x f y ] T =T 2r [f α f β f x f y ] T (3)

[0067]

[0068] Where, Park transformation matrix T 2r The physical quantity f in the αβ coordinate system α and f β Transform to the rotating coordinate system (f d and f q ) and keep the physical quantity value in the xy coordinate system unchanged, P 2r (θ) represents the second-order park transformation matrix, I represents the second-order identity matrix, and θ represents the electrical angle of the motor.

[0069] in i d = 0 control, the electromagnetic torque equation of the six-phase permanent magnet motor can be expressed as

[0070] T e =3P n [iq ψ f -i d i q (L d -L q )] (5)

[0071] Where P n , f 、i d 、i q and L d , L q They respectively represent the pole pair number, flux amplitude, dq axis current and dq axis inductance of the six-phase permanent magnet motor.

[0072] Step 2) Design of basic fault-tolerant control framework. Since the six-phase permanent magnet motor has more control freedom, it is only necessary to modify the current reference of the corresponding harmonic plane to achieve undisturbed operation after an open-circuit fault. For a six-phase permanent magnet motor system with an isolated neutral point, the current constraint to be considered after an open-circuit fault is

[0073]

[0074] In the formula, i A 、i B 、i C 、i U 、i V 、i W Represents the six-phase stator current of the six-phase permanent magnet motor, I rt Indicates the rated current of the motor, i fp Indicates the fault phase. Since the current in the α-β plane participates in energy conversion, its current reference needs to remain unchanged, and the current reference in the xy subspace is corrected by the ɑ-β current, which can be expressed as

[0075]

[0076] In the formula, i α 、i β 、i x 、i y They represent the motor's α-axis, β-axis, x-axis, and y-axis currents respectively, and the variable k xa , k xβ , k yɑ and k yβ Respectively represent i x The α-axis current correction factor, i x The β-axis current correction factor, i y The α-axis current correction factor and i y The β-axis current correction coefficients are usually solved using two common optimization objectives.

[0077] 1) Minimum copper loss strategy: The optimization goal is to minimize the copper loss J ML .

[0078]

[0079] 2) Maximum torque strategy: The optimization goal is to maximize the torque output J MT , that is, to maximize the amplitude of the α-β phase.

[0080] J MT =max(|I αβ |) (9)

[0081] In the formula, |·| represents the modulus of the α-β phase. The variable k is solved by different optimization objectives. xα ,k xβ ,k yα ,k yβ By adjusting the specific value of , smooth switching between the minimum copper loss strategy and the maximum torque strategy can be achieved.

[0082] However, the existing basic fault-tolerant architecture can only achieve the most traditional sinusoidal fault-tolerant control, and cannot maximize the controller output performance after fault-tolerant control. Therefore, it is necessary to abandon some constraints in order to further improve the controller output performance. Regardless of whether there is a fault or not, after high-order harmonic injection, the phase current expression of the six-phase permanent magnet motor can be expressed as

[0083]

[0084] In the formula, I M represents the amplitude of the fundamental phase current, represents the phase angle of the fundamental current, and k3 represents the third harmonic injection coefficient, The electromagnetic torque expression and copper loss expression of the six-phase permanent magnet motor containing high-order harmonics can be expressed by equations (11) and (13) respectively.

[0085]

[0086] In the formula, ω r represents the electrical angular velocity of the six-phase permanent magnet motor, e m (m=A,B,C,U,V,W) represents the reverse electromotive force of the motor, E1 represents the amplitude of the phase current reverse electromotive force. RMS(·) represents the effective value of the motor phase current, R sRepresents the stator resistance of the motor. From the expression of electromagnetic torque, it can be seen that when the back electromotive force amplitude and the fundamental phase current amplitude of the six-phase permanent magnet motor remain unchanged, the injection of harmonic current can further improve the torque output of the six-phase permanent magnet motor. From the copper loss expression of higher harmonics, it can be seen that if the effective value of the phase current can be reduced by harmonics, the corresponding copper loss will also be further reduced.

[0087] It should be noted that harmonics of different orders have different effects on the torque output capacity, and the injected phase angle will not only affect the tracking performance of the controller, but will also affect the torque output capacity of the six-phase permanent magnet motor and further increase the copper loss of the system. Therefore, it is necessary to solve the optimal harmonic injection order and phase angle to maximize the torque output of the maximum torque mode and reduce the copper loss of the minimum copper loss mode. As can be seen from the foregoing, although there are harmonic injection methods to optimize the optimization objectives separately, there is no unified harmonic injection method to simultaneously achieve the above-mentioned two fault-tolerant modes, that is, the optimal solution for the minimum copper loss and maximum torque modes cannot be obtained at the same time. Therefore, the present invention constructs a unified harmonic injection framework in order to simultaneously obtain the optimal solution in both modes. The optimal harmonic injection order and harmonic effect are as follows. Figure 2 As shown, Figure 2 Where (A) represents the unit of phase current, ampere, and (rad) represents radians.

[0088] Step 3: Design of harmonic injection fault-tolerant strategy framework. d = 0, the electromagnetic torque of the system depends only on the q-axis current. That is, without changing the q-axis current, the injection of harmonics will not affect the torque output performance of the six-phase permanent magnet motor during fault-tolerant operation. Since the 3rd, 5th, and 7th harmonics of the fundamental plane are mapped to the 2nd, 4th, and 6th harmonics on the dq plane, the d-axis reference current after harmonic injection can be assumed to be

[0089]

[0090] In the formula, λ d2 , d4 , d6 They represent the injection coefficients of the 2nd, 4th, and 6th harmonic currents, respectively, and θ d2 ,θ d4 ,θ d6 Respectively represent the phase shift of the 2nd, 4th, and 6th currents, They represent the d-axis and q-axis reference currents respectively. From the expression of the d-axis reference current, we can see that there are 6 unknowns that need to be solved.

[0091] From formula (7), it can be seen that in order to obtain the current reference of the harmonic plane, the six-phase current expression needs to be converted to the two-phase stationary coordinate system, which can be expressed as follows in combination with formula (1):

[0092]

[0093] Assume that the current reference expression of the harmonic plane after an open circuit fault occurs is:

[0094]

[0095] In the formula, They represent the reference currents of the x-axis, y-axis, α-axis and β-axis respectively. Combining equations (15) and (16), the six-phase current expression after an open circuit fault occurs can be expressed as

[0096]

[0097] Combining equations (1), (2) and (14), we can calculate The specific calculation expression of

[0098]

[0099] According to theoretical analysis, there are 10 unknown quantities (k xα , k xβ , k yα , k yβ , d2 , d4 , d6 ,θ d2 ,θ d4 ,θ d6 ) needs to be solved, so it is necessary to introduce additional objective functions to solve the harmonic plane fundamental wave injection coefficient, the optimal harmonic injection coefficient and the optimal harmonic injection phase.

[0100] Step 4): Solve the minimum copper loss mode. In the minimum copper loss mode, the unit copper loss generated by the motor system can be expressed as

[0101]

[0102] Assuming from formula (18)

[0103]

[0104] Combining equation (16) and equation (20), equation (19) can be simplified to

[0105]

[0106] The final solution is the unit loss expression:

[0107] P cu =Λ α Δ α +Λ β Δ β +Λm Δ m (twenty two)

[0108] in,

[0109]

[0110] Step 5): Solve the maximum torque mode. In the maximum torque mode, the normalized stator current of the motor system can be expressed as

[0111]

[0112] In the formula, i m (m=A, B, C, U, V, W) represents the six-phase stator current of the motor. Substituting the phase current expression (17) into (24), the constraint condition under the maximum torque mode can be obtained:

[0113]

[0114] Among them, Δ α , Δ β , Δ m Same as the above expression, and the remaining terms can be expressed as follows

[0115]

[0116]

[0117] From the analysis in step 4) and step 5), it can be seen that for the minimum copper loss mode and the maximum torque mode, the optimization objectives are to minimize (19) and maximize (25), respectively. It should be noted that the switching of the fault phase is performed by adding the equation constraint (17). Finally, the f mincon and f minmax The function solves the constraints of the above fault-tolerant mode (the minimum copper loss mode constraint is equation (23), the maximum torque mode constraint is equation (25), equation (26), equation (27), equation (28)), and the optimal 10 unknowns that meet the constraints after different open-circuit faults can be obtained, as shown in Table I. After a single-phase open-circuit fault occurs, the optimized ideal current waveform is as follows Figure 3 shown. Figure 3 Among them, m-ML and m-MT (m=A, B, C, U, V, W) respectively represent the current waveforms of minimum copper loss mode and maximum torque mode after an open circuit fault occurs in phase m. Similarly, (A) represents the phase current in ampere, and (rad) represents radians.

[0118] Table I

[0119] Optimal parameter selection table

[0120]

[0121] From the above description, it can be seen that the present invention proposes a six-phase permanent magnet motor fault-tolerant control method based on harmonic injection, which is expected to significantly improve the output performance of the controller after a fault while ensuring the fault-tolerant effect.

[0122] The above description of the functions and working processes of the present invention in combination with the drawings in the specification is only one of the preferred implementation cases, but the present invention is not limited to the above-mentioned specific functions and working processes. The above-mentioned specific implementation methods are only illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all within the protection scope of the present invention.

Claims

1. A six-phase permanent magnet motor fault-tolerant control method based on harmonic injection, characterized in that: The following steps are involved: 1) Under the premise of ensuring that the output torque remains unchanged before and after the fault, the constraint of the direct-axis magnetomotive force is abandoned, and the current expression of the direct-axis harmonic injection after the fault is assumed. 2) To achieve the decoupling of the harmonic subspace and the fundamental subspace during fault-tolerant operation, the current reference of the harmonic subspace is assumed through simple linear operations. 3) Taking unit copper loss and unit torque output as optimization targets, the optimal direct-axis harmonic current injection coefficient and the phase and harmonic subspace current reference expressions are solved to achieve high-performance fault-tolerant operation of the six-phase permanent magnet motor after a fault.

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