A permanent magnet synchronous motor harmonic self-tuning method based on peak envelope electromagnetic standing value residual and a permanent magnet synchronous motor driver

Abstract

This invention relates to a harmonic self-tuning method for permanent magnet synchronous motors (PMSMs) based on peak envelope electromagnetic stationary value residuals and a PMSM driver. The fundamental and third harmonic synchronous quadrature-axis voltages and currents are averaged over the entire electrical cycle to obtain two electrical residuals. The torque stationary value condition of the phase current peak envelope is directly synthesized with the two electrical residuals to form an electromagnetic stationary value residual. This residual simultaneously characterizes optimality, update direction, and distance to the stationary value root, and k3 is directly recursively derived after slope normalization. The fundamental and third harmonic currents are then given according to the peak envelope F(k3). This eliminates the need for prior identification of the third flux linkage and harmonic inductance, and eliminates the need for external torque comparison or extreme value search. For a three-phase four-arm structure, the fourth arm current constraint is further written into the same coefficient feasible set. This method is suitable for surface-mounted PMSMs where the third permanent magnet back EMF can generate average torque.

Description

Technical Field

[0001] This invention relates to the fields of harmonic current utilization of permanent magnet synchronous motors, peak phase current constraint, online full-cycle voltage residual construction, and three-phase four-bridge inverter control technology, and in particular to a harmonic self-tuning method for permanent magnet synchronous motors based on peak envelope electromagnetic stationary residual and a permanent magnet synchronous motor driver. Background Technology

[0002] Permanent magnet synchronous motors with non-sinusoidal permanent magnet back EMF can generate additional average torque by utilizing current harmonics of the same order as the space magnetic field. For multiphase or three-phase four-wire structures that allow the flow of third-order zero-sequence current, injecting third harmonics can also flatten the phase current peak value when the phase current peak value is limited, making the fundamental amplitude higher than that of pure sinusoidal current.

[0003] Existing public theory already knows that when no available third back EMF exists, a 1 / 6 third harmonic can increase the fundamental current by approximately 15.47% at the same phase current peak value; when the third back EMF itself participates in the average torque, the optimal third harmonic ratio will vary with E3 / E1. Therefore, the optimal ratio depends on the ratio of the third to the fundamental back EMF and should not be considered as the source of inventiveness of this invention.

[0004] On the other hand, existing online solutions typically follow a series chain that identifies flux linkage or inductance, calculates harmonic coefficients, and then corrects for and controls harmonic current using torque or harmonic indices. This chain suffers from problems such as observability of identification, multiple independent convergence criteria, parameter dimensions, and the ease with which different module combinations can be covered by existing technologies. The technical problem addressed by this invention is not to replace the recursive identifier, but to establish a single residual that can be directly obtained from the operating voltage and current, and is simultaneously the optimal condition for peak-limited torque. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method for harmonic self-tuning of a permanent magnet synchronous motor (PMSM) based on the peak envelope electromagnetic stationary residual and a PMSM driver. Specifically, in a surface-mount PMSM that allows for third-order zero-sequence current, the invention addresses how to adjust the third harmonic ratio online as the permanent magnet harmonics change with temperature, load, or magnetic saturation, while avoiding the need to pre-estimate ψ. f3 L d3 L q3 Then calculate the multi-parameter chain of k3; and make the current optimality, the direction of update, and how far away from the optimal point all given by the same verifiable quantity.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a harmonic self-tuning method for permanent magnet synchronous motors based on peak envelope electromagnetic stationary residuals, applied to a surface-mounted permanent magnet synchronous motor drive system having a third permanent magnet back electromotive force component and a drive topology capable of providing a closed current loop for the third zero-sequence current, characterized in that it includes:

[0007] Step 1: Obtain the quadrature-axis voltage and current in the fundamental synchronous coordinates and the third harmonic synchronous coordinates, and construct the fundamental integer-cycle voltage residual and the third harmonic integer-cycle voltage residual respectively within an update window containing an integer number of electrical cycles:

[0008]

[0009] in, The residual voltage (V) of the h-th harmonic is physically the average voltage retained within the update window after deducting the stator resistance voltage drop. τ is the compensated / estimated value of the stator phase resistance (Ω); τ is the integral time variable (s); To update the window length; Let be the quadrature-axis voltage of the h-th harmonic synchronous coordinate system; Let be the quadrature-axis current in the synchronous coordinate system of the h-th harmonic.

[0010] Where h is 1 or 3; when the direct-axis current is controlled to zero or its window average coupling term is negligible and the cross-axis currents at the window endpoints are equal, the total cycle voltage residuals represent the fundamental back electromotive force amplitude E1 and the third back electromotive force amplitude E3, respectively.

[0011] Step 2: Let the ratio of the peak value of the third harmonic current to the peak value of the fundamental current be k3. Without separately identifying the third magnetic flux and the third harmonic inductance, the stationary condition of the phase current peak envelope with respect to k3 is directly combined with the two full-cycle voltage residuals from Step 1 into a single electromagnetic stationary residual:

[0012]

[0013] in, For the online full-cycle voltage residual , The directly constructed electromagnetic stationary residual estimate (V); the symbol “^” indicates the estimate obtained from online observations.

[0014] Step 3: Using the same electromagnetic stationary value residual as the update error for the harmonic coefficients, and normalizing it with respect to the slope of k3, update k3 according to the following formula:

[0015]

[0016] Where n is the discrete update window index; γ is the dimensionless update step size, 0 < γ ≤ 1; Π K [·] is the projection operator to the feasible set K, used to simultaneously implement hardware constraints such as harmonic coefficients and fourth arm current; For the electromagnetic stationary residual estimate of the nth update window; The fundamental integer-cycle voltage residual for the nth update window; This represents the residual voltage of the third harmonic integer cycle in the nth update window.

[0017] Step 4: Given I by the updated k3 and the peak phase current pk * Directly generate the given amplitudes of the fundamental and third harmonic currents:

[0018]

[0019] Where F(k3) is the peak envelope of the combined phase current of the fundamental wave and the third harmonic in phase, and the fundamental wave and the third harmonic current are given and applied to the permanent magnet synchronous motor through current tracking and pulse width modulation. pk * The allowable peak value of the phase current or the peak value of the phase current generated by the outer loop is given (A); I1 * I3 * The amplitudes of the fundamental and third harmonic currents are given in A, respectively; the superscript * indicates the given value.

[0020] In a preferred embodiment, the three-phase current input and the three-phase permanent magnet back electromotive force satisfy equations (1) and (2), respectively:

[0021] (1)

[0022] Among them, i a i b i c The instantaneous values ​​(A) of the three-phase stator currents A, B, and C are respectively; I1 and I3 are the peak values ​​(A) of the fundamental and third harmonic currents, respectively; θ e The rotor electrical angle is rad.

[0023] (2)

[0024] Among them, e a e b e c E1 and E3 are the instantaneous values ​​(V) of the three-phase permanent magnet back electromotive force (PMMF) of phases A, B, and C, respectively; E1 and E3 are the peak values ​​(V) of the fundamental and third-phase PMMFs, respectively.

[0025] The average electromagnetic torque is obtained from the conservation of electromagnetic power:

[0026] (3)

[0027] in, The average electromagnetic torque is (N·m). This represents the number of pole pairs of the motor. Electric angular velocity (rad / s); , Let Wb be the fundamental and third harmonic amplitudes of the permanent magnet flux linkage, respectively, and let E1 = ω. e ·ψ f1 E3=3ω e ·ψ f3 .

[0028] In a preferred embodiment, the peak envelope of the phase current is defined as:

[0029] (4)

[0030] (5)

[0031] Wherein, F(k3) is the dimensionless phase current peak envelope function; max indicates that it takes the maximum value within one fundamental electrical cycle; θ is the electrical angle variable used to traverse the synthetic phase current waveform within θ∈[0,2π), and is not a newly added control state variable.

[0032] When k3 is not less than 1 / 9, the normalized average torque target under the condition of limited phase current peak value is:

[0033] (6)

[0034] Where J(k3) is the target average electromagnetic torque corresponding to the peak value of the unit phase current, with dimensions N·m / A; I pk The peak value of the synthesized phase current (A).

[0035] Its stationary condition is simplified from equation (7) to obtain equation (8), and the stationary root shown in equation (9) is obtained:

[0036] By determining the stationary value of the normalized average torque target, the electromagnetic stationary value condition and its stationary value root can be obtained:

[0037] (7)

[0038] Where d lnJ / dk3 represents the logarithmic derivative of the normalized average torque target with respect to the harmonic coefficient k3; its zero value corresponds to the internal stationary condition.

[0039] (8)

[0040] Where, ε KThe theoretical electromagnetic stationary residual (V) is constructed using the actual back electromotive forces E1 and E3; ε K =0 indicates that k3 satisfies the stationary condition of the peak-limited average torque target.

[0041] (9)

[0042] Among them, k3 * Let be the theoretical stationary roots (dimensionless); the superscript * in this formula indicates the optimal stationary solution. To ensure that the denominator is non-zero, 6E1−3E3≠0 is required; the engineering working region further takes the corresponding stationary roots that fall into the feasible set K; It is the ratio of the peak value of the third back EMF to the peak value of the fundamental back EMF, and it is the dimensionless back EMF harmonic ratio.

[0043] In a preferred embodiment, the synchronous quadrature-axis voltage model of the h-th harmonic is:

[0044] (10)

[0045] Among them, u qh Let i be the quadrature-axis voltage (V) in the synchronous coordinate system of the h-th harmonic; qh i dh These are the quadrature-axis and direct-axis currents (A), respectively; R s Stator phase resistance (Ω); L h The equivalent inductance for the h-th harmonic is (H); For i qh The derivative with respect to time (A / s); E h Let be the amplitude (V) of the back electromotive force of the h-th harmonic; h∈{1,3} is the harmonic order.

[0046] The updated window satisfies:

[0047] (11)

[0048] Among them, T w The window length (s) is updated online; t is the window start time (s); N is a positive integer, indicating that the window contains N fundamental frequency cycles; window endpoint i qh Equal terms are used to make the integer-cycle integral of the inductance differential term zero.

[0049] Thus, the inductance differential term disappears during the integral over the entire cycle; when the direct-axis average coupling term is negligible and the stator resistance compensation is accurate, the voltage residual over the entire cycle described in step 1 satisfies:

[0050] (12)

[0051] Among them, when The current at the window endpoints is consistent and When its window-averaged coupling term is negligible. ,therefore and They are used as equivalent observations of the back electromotive force of E1 and E3, respectively.

[0052] In a preferred embodiment, the following is defined:

[0053] (13)

[0054] in, The slope (V) of k3; This is the online estimated stationary root (dimensionless) obtained directly from the residual of the current window.

[0055] The electromagnetic stationary residual not only provides the update direction, but also directly provides the distance certificate from the current harmonic coefficient to the stationary root:

[0056] (14)

[0057] in, From the current harmonic coefficient k3 to the online estimated stationary root A dimensionless distance certificate; this relationship requires |D| to be greater than a preset minimum slope threshold D. min .

[0058] In a preferred embodiment, when the voltage residuals of the two full-cycle circuits remain unchanged in adjacent update windows and the projection does not change, let This indicates the relationship between the current harmonic coefficient k3 and the fixed online estimated stationary root. The difference is:

[0059] (15)

[0060] in, To determine the current k when the residual voltage of the two circuits is fixed and the projection does not change. 3,n Compared to fixed online estimation stationary roots The deviation (dimensionless); its shrinkage proportionally by 1-γ with each update.

[0061] (16)

[0062] Among them, V n V is a nonnegative Lyapunov function used to prove discrete contractility; n These are only mathematical analysis quantities and do not represent the actual energy storage of the motor.

[0063] When the back EMF harmonic ratio changes slowly and there is an estimation error in the whole-cycle voltage residual, the true tracking error is defined. Then it satisfies:

[0064] (17)

[0065] in, The tracking error is relative to the time-varying true stationary root; For the nth window, This represents the corresponding online estimation stationary root. The second term characterizes the residual estimation error, and the third term characterizes the drift of the optimal root caused by changes in operating conditions.

[0066] In a preferred embodiment, the third harmonic is a zero-sequence third harmonic, the motor neutral point is connected to the fourth bridge arm, and the current of the fourth bridge arm satisfies:

[0067] (18)

[0068] Among them, i N The return current (A) through the fourth bridge arm of the motor neutral point; I N,pk The value is the peak current (A) of the fourth bridge arm; the negative sign is determined by the selected neutral point current reference direction.

[0069] Peak phase current command Already by I pk,max Under the premise of limiting the amplitude, a feasible set is constructed based on the upper limit of the peak current of the fourth bridge arm and the upper limit of the harmonic coefficient allowed by the hardware:

[0070] (19)

[0071] Where K is the dimensionless feasible set of harmonic coefficients k3; I N,max For the fourth bridge arm, the allowable peak current (A); k hw,max The maximum allowable third harmonic coefficient for the driver; peak phase current I pk Before entering the set for judgment, it has already been determined by I. pk,max Limit the amplitude.

[0072] The projection operator Π K The harmonic coefficients are directly restricted to the same set of physical feasibility.

[0073] In a preferred embodiment, the phase voltage is reconstructed from the DC bus voltage and the actual switching state or duty cycle of the three-phase four-arm inverter, the stator current is sampled by the phase current sensor, and the rotor electrical angle is provided by the position sensor or position observer; the fundamental and third harmonic full-cycle voltage residuals are summed by the sample values ​​within the window after synchronous coordinate transformation.

[0074] When the outer loop input is the average electromagnetic torque Te*, the peak phase current is generated by the following formula and limited by the upper limit of the peak phase current:

[0075] (20)

[0076] in, The average electromagnetic torque (N·m) given for the outer ring; I pk,max The maximum allowable peak phase current (A); sat[0,I pk,max ][·] indicates that the calculation result within the parentheses is limited to [0, I]. pk,max ] interval.

[0077] The present invention also provides a permanent magnet synchronous motor driver, including a three-phase four-arm inverter, a DC bus voltage sampling unit, a phase current sampling unit, a rotor position acquisition unit, a processor, and a memory. The neutral point of the permanent magnet synchronous motor is connected to the fourth arm. When the program in the memory is executed by the processor, it implements the aforementioned method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residual.

[0078] Compared with the prior art, the present invention has the following beneficial effects:

[0079] (1) The multi-parameter identification, coefficient calculation and mixed torque verification are rewritten as the closure of the single peak envelope electromagnetic stationary value residual, reducing the risk of obvious module combination.

[0080] (2) The voltage residual of the complete circuit is periodically eliminated by using the endpoints to eliminate the inductance differential term; it is no longer necessary to identify ψ from a single cubic cross-axis equation. f3 L d3 L q3 .

[0081] (3) The same ε K It also provides certificates of optimality, update direction, and distance; the normalized update has an explicit contraction rate 1-γ under a steady-state back potential ratio.

[0082] (4) The peak envelope of the phase current F(k3) is directly generated. and This avoids separating the k3 limiting and current peak control.

[0083] (5) The zero-sequence current constraint of the fourth bridge arm can be parsably written into the same k3 feasible set; the topology only provides three zero-sequence current channels and is not packaged into a new algorithm module. Attached Figure Description

[0084] Figure 1 This is a flowchart of a preferred embodiment of the present invention. Detailed Implementation

[0085] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0086] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0087] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0088] A method for harmonic self-tuning of permanent magnet synchronous motors based on peak envelope electromagnetic stationary residuals, referenced Figure 1 This includes the following steps:

[0089] Step 1: Electromagnetic power model and peak envelope of phase current

[0090] Assuming that the three-phase currents and back electromotive forces use the same fundamental and third harmonic phase references, they are written as equations (1) and (2) respectively. The third component is in phase in the three phases, so it belongs to the zero-sequence component; the three phases of the fundamental wave are 120° apart. By using orthogonality to calculate the average electromagnetic power within one electric cycle, equation (3) can be obtained.

[0091] (1)

[0092] In the formula, i a i b i c The instantaneous values ​​(A) of the three-phase stator currents A, B, and C are respectively; I1 and I3 are the peak values ​​(A) of the fundamental and third harmonic currents, respectively; θ e The rotor electrical angle is rad.

[0093] (2)

[0094] In the formula, e a e b e c E1 and E3 are the instantaneous values ​​(V) of the three-phase permanent magnet back electromotive force (PMMF) of phases A, B, and C, respectively; E1 and E3 are the peak values ​​(V) of the fundamental and third-phase PMMFs, respectively.

[0095] (3)

[0096] In the formula, The average electromagnetic torque (N·m); p n ω is the number of pole pairs of the motor; eψ is the electric angular velocity (rad / s). f1 ψ f3 Let Wb be the fundamental and third harmonic amplitudes of the permanent magnet flux linkage, respectively, and let E1 = ω. e ψ f1 E3=3ω e ψ f3 .

[0097] (4)

[0098] In the formula, k3 is the ratio of the peak value of the third harmonic current to the peak value of the fundamental current, and r is the dimensionless harmonic coefficient; e It is the ratio of the peak value of the third back EMF to the peak value of the fundamental back EMF, and it is the dimensionless back EMF harmonic ratio.

[0099] The peak phase current constraint is not I1+I3≤I pk Instead, it is the infinite norm constraint of the synthesized waveform; where θ is only used as the electric angle ergodic variable within θ∈[0,2π). Let F(k3) be Equation (5), using sin3θ=3sinθ-4sin 3 θ can be used to obtain the closed envelope of equation (6).

[0100] (5)

[0101] In the formula, F(k3) is the dimensionless phase current peak envelope function; max indicates that it takes the maximum value within one fundamental electrical cycle; θ is the electrical angle variable used to traverse the synthetic phase current waveform within θ∈[0,2π], and is not a newly added control state variable.

[0102] (6)

[0103] In the formula, k3=1 / 9 is the boundary where the stationary point appears inside the peak envelope; the stationary value optimization working area of ​​this invention takes k3≥1 / 9.

[0104] (7)

[0105] In the formula, The allowable peak value of the phase current or the peak value of the phase current generated by the outer loop is given (A); , The amplitudes of the fundamental and third harmonic currents are given in A, respectively; the superscript * indicates the given value.

[0106] Equation (6) shows that the classical 1 / 6 coefficient only corresponds to a specific objective: to make the peak value of the synthesized current as flat as possible when the third back EMF does not contribute to the average torque. If E3 itself can generate average power with I3, then the peak flattening benefit and the third harmonic electromagnetic benefit must be handled in the same objective.

[0107] Step 2:

[0108] Substitute equation (7) into the average torque and divide by I pk Equation (8) is obtained. In the engineering working area where k3≥1 / 9, taking its logarithmic derivative yields equation (9), and the stationary condition is simplified to equation (10).

[0109] (8)

[0110] In the formula, J(k3) is the target average electromagnetic torque corresponding to the peak value of the unit phase current, with dimensions in N·m / A; I pk The peak value of the synthesized phase current (A).

[0111] (9)

[0112] In the formula, Represents the normalized average torque target with respect to harmonic coefficients The logarithmic derivative of ; its zero value corresponds to the internal stationary condition.

[0113] (10)

[0114] In the formula, ε K The theoretical electromagnetic stationary residual (V) is constructed using the actual back electromotive forces E1 and E3; ε K =0 indicates that k3 satisfies the stationary condition of the peak-limited average torque target.

[0115] (11)

[0116] In the formula, Let be the theoretical stationary roots (dimensionless); the superscript * in this formula indicates the optimal stationary solution. To ensure that the denominator is non-zero, 6E1−3E3≠0 is required; the engineering working region further takes the corresponding stationary roots that fall into the feasible set K.

[0117] Equation (11), which determines the optimal ratio based on the analytical conclusion of E3 / E1, is already supported by published literature. Therefore, this invention does not isolate Equation (11) as an inventive step. The new structure is as follows: instead of first identifying the flux linkage parameters corresponding to E1 and E3 before calling Equation (11), the two-cycle voltage residuals are obtained from the motor operating voltage equation and then directly substituted into Equation (10), compressing the online electrical observations and optimal conditions into a single scalar ε. K .

[0118] Step 3: Residual Voltage During Rectification Cycle: Remove the inductance term from the update chain.

[0119] In the h-th harmonic synchronous coordinate system, the general form of the quadrature-axis voltage is written as equation (12). For the maximum torque / peak current operating range of a surface-mounted PMSM, the fundamental and third harmonic direct-axis reference values ​​can be set to zero; within the update window containing integer electrical cycles, k3 and the amplitude setting remain unchanged, so that the quadrature-axis currents at the beginning and end of the window are equal.

[0120] (12)

[0121] In the formula, u qh Let i be the quadrature-axis voltage (V) in the synchronous coordinate system of the h-th harmonic; qh i dh These are the quadrature-axis and direct-axis currents (A), respectively; R s Stator phase resistance (Ω); L h The equivalent inductance for the h-th harmonic is (H); For i qh The derivative with respect to time (A / s); E h Let be the amplitude (V) of the back electromotive force of the h-th harmonic; h∈{1,3} is the harmonic order.

[0122] (13)

[0123] In the formula, T w The window length (s) is updated online; t is the window start time (s); N is a positive integer, indicating that the window contains N fundamental frequency cycles; window endpoint i qh Equal terms are used to make the integer-cycle integral of the inductance differential term zero.

[0124] (14)

[0125] In the formula, The residual voltage (V) of the h-th harmonic is physically the average voltage retained within the update window after deducting the stator resistance voltage drop. τ is the compensated / estimated value of the stator phase resistance (Ω); τ is the integral time variable (s).

[0126] (15)

[0127] In the formula, when The current at the window endpoints is consistent and i dh When ≈0 or its window average coupling term is negligible, ,therefore and They are used as equivalent observations of the back electromotive force of E1 and E3, respectively.

[0128] Thus, L h ·di qh / dt is strictly determined by the endpoint difference and disappears in the window integral, ω e L h i dh in i dh It disappears when ≈0. Therefore, online updates do not require L. d3 L q3 As a state to be identified. In practice, the system only needs to identify R. s Correct for known values ​​or low-speed temperature; R s The error enters the error bounds of ξ1 and ξ3 without changing the stationary residual structure.

[0129] Step 4: The same stationary residual performs three functions simultaneously.

[0130] (16)

[0131] In the formula, For the online full-cycle voltage residual , The directly constructed electromagnetic stationary residual estimate (V); the symbol “^” indicates the estimate / computation obtained from online observations.

[0132] (17)

[0133] In the formula, The slope (V) of k3; This is the online estimated stationary root (dimensionless) obtained directly from the residual of the current window.

[0134] (18)

[0135] In the formula, From the current harmonic coefficient k3 to the online estimated stationary root A dimensionless distance certificate; this relationship requires |D| to be greater than a preset minimum slope threshold D. min .

[0136] Equation (17) is the most crucial unifying relationship in this invention: within an update window, ε K It's not an indicator for judgment, but rather the signed distance from the current k3 to the stationary root multiplied by the slope D. Therefore, its sign gives the update direction, its absolute value, normalized by D, gives the distance, and its zero point gives optimality. There is no other torque error loop or another convergence judgment module.

[0137] The normalized update is constructed using the same residual as in equation (19). When D remains unchanged in adjacent update windows and the projection does not change, equation (19) is equivalent to a first-order contraction mapping of the stationary roots of the fixed online estimate, thus directly obtaining the contractility shown in equations (20) and (21).

[0138] (19)

[0139] In the formula, n is the discrete update window index; γ is the dimensionless update step size, 0 < γ ≤ 1; Π K [·] is the projection operator to the feasible set K, used to simultaneously implement hardware constraints such as harmonic coefficients and fourth arm current.

[0140] (20)

[0141] In the formula, To determine the current k when the residual voltage of the two circuits is fixed and the projection does not change. 3,n Compared to fixed online estimation stationary roots The deviation (dimensionless); its shrinkage proportionally by 1-γ with each update.

[0142] (twenty one)

[0143] In the formula, V n V is a nonnegative Lyapunov function used to prove discrete contractility; n These are only mathematical analysis quantities and do not represent the actual energy storage of the motor.

[0144] (twenty two)

[0145] In the formula, The tracking error is relative to the time-varying true stationary root; For the nth window, This represents the corresponding online estimation stationary root. The second term characterizes the residual estimation error, and the third term characterizes the drift of the optimal root caused by changes in operating conditions.

[0146] Step 5: The physical constraints are not another patch, but a projection onto the same coefficient domain.

[0147] For a three-phase four-arm structure, all three zero-sequence currents return through the fourth arm. Equation (23) can be obtained by summing equation (1). Therefore, the current capacity of the fourth arm can be directly written as the feasible region of k3, instead of adding an over-limit switch afterward.

[0148] (twenty three)

[0149] In the formula, i N The return current (A) through the fourth bridge arm of the motor neutral point; I N,pk The value is the peak current (A) of the fourth bridge arm; the negative sign is determined by the selected neutral point current reference direction.

[0150] (twenty four)

[0151] In the formula, K is the dimensionless feasible set of harmonic coefficients k3; I N,max For the fourth bridge arm, the allowable peak current (A); k hw,max The maximum allowable third harmonic coefficient for the driver; peak phase current I pk Before entering the set for judgment, it has already been determined by I. pk,max Limit the amplitude.

[0152] When the desired stationary value is within K, an unconstrained stationary value is obtained; otherwise, it is determined by Π. K The boundary solutions for the same constraint optimization problem are given. Therefore, the phase current peak, the fourth bridge arm peak, and the harmonic ratio hard constraints are still handled under the same k3 state.

[0153] Step 6: Torque setting and current reference generation

[0154] If the upper layer directly gives the peak phase current command, then equation (7) can be used; if the upper layer gives the average torque command, then when the voltage residual of the whole cycle has already characterized E1 and E3, the peak phase current can be solved by equation (3):

[0155] (25)

[0156] In the formula, The average electromagnetic torque (N·m) given for the outer ring; I pk,max The maximum allowable peak phase current (A); sat[0,I pk,max ][·] indicates that the calculation result within the parentheses is limited to [0, I]. pk,max ] interval.

[0157] income Together with k3, it enters equation (7), and then the three-phase current reference is generated by equation (1). The current tracker can be implemented using existing PI, PR, prediction, or other methods; its type is not a condition for the inventive step of this invention.

[0158] Scenario 1: Calculation of synchronous full-cycle voltage residual

[0159] Taking a surface-mount PMSM driven by a three-phase four-arm inverter as an example, the controller samples the three-phase current, DC bus voltage, and rotor position in each PWM cycle; the phase voltage can be reconstructed from the bus voltage and the actual PWM switching state / duty cycle. The controller uses θ... e and 3θ e Complete the synchronous projection of the fundamental and third harmonic waves. Update the window by taking N integer electrical cycles, with k3 and k2 fixed within the window. The fundamental frequency and the third direct-axis current reference are both 0. For u qh -R s i qh Calculate the window average to obtain ξ1 and ξ3.

[0160] In practical engineering, the effective phase voltage or measured terminal voltage after dead-time and device voltage drop compensation should be used. This compensation only changes ξ. h The measurement error does not change the structure of equations (16) to (19). The selection of the update window should make the update of k3 significantly slower than that of the inner current loop, so as to ensure that the current at the window endpoints is approximately periodically consistent.

[0161] Scenario 2: Quantity verification of motor data

[0162] Motor parameters p n =4、R s =0.505 Ω、ψ f1 =0.1325 Wb, and considering ψ f3 The value changes from 0.0166 Wb to 0.0151 Wb. From equation (4), E3 / E1 are 0.37585 and 0.34189 respectively; the stationary value k3 corresponding to equation (11) is 0.20524 and 0.20103 respectively.

[0163] If the peak phase current command =100 A, then from equations (6) and (7), we get: initial state F=0.87244, =114.62 A、 =23.52 A, the peak current of the third phase of the fourth bridge arm is about 70.57 A; after the change, F=0.87121. =114.78A =23.07 A, the peak value of the fourth bridge arm is approximately 69.22 A. Therefore, it can be determined directly during the design phase whether the fourth bridge arm needs to have its current rating increased.

[0164] Scenario 3: Recursive calculation of stationary residuals

[0165] Let the update cycle T w =5 ms, γ=0.35, initial value k3=1 / 6. The simulation normalizes ξ1 to 100 V, and adds about 1% window-averaged noise to ξ1 and ξ3; at 0.15 s, E3 / E1 is changed from 0.37585 to 0.34189 according to the original flux linkage change, and after 0.30 s, E3 / E1 is further set to 0.65 as a wide-range stress condition. The final difference between k3 and the instantaneous stationary root is about 5.4×10. ⁻4 The average loss of the entire sequence relative to the instantaneous theoretical optimal target is approximately 0.0208%.

[0166] Scenario 4: Parsing the envelope and optimizing cross-validation with independent numerical values

[0167] 5000 samples were randomly selected from E3 / E1 in the range of 0.02 to 0.80. For each sample, one method was to calculate the stationary root using equation (11), and the other method was to independently enumerate equation (8) with 4001 points on k3∈[1 / 9,0.32]. The maximum difference in k3 was approximately 2.61×10. ⁻5 The maximum objective function relative difference is less than 0.004 ppm. Furthermore, the phase current peak envelope of equation (6) is verified using 200,001 θ points, with a maximum absolute error of approximately 3.2 × 10⁻⁶. ⁻10 This result indicates that the core closed relation in the implementation is consistent with the direct numerical definition.

[0168] Scenario 5: Low speed and parameter error boundary

[0169] When |ω e If the values ​​are too low, causing E1 and E3 to become indistinguishable relative to the voltage sampling error, or if the absolute value of D = 6ξ1−3ξ3 is less than the design threshold, the most recent k3 can be frozen or the system can be run according to the offline calibration value. This low-speed processing is not part of the stationary value algorithm, and it is not recommended to obtain the harmonic ratio from the back EMF residual at zero speed. For R s As temperature changes, it can be determined by a winding temperature model or existing R... s The estimation method is given The error is expressed in equation (22). The item enters the tracking boundary.

Claims

1. A harmonic self-tuning method for permanent magnet synchronous motors based on peak envelope electromagnetic stationary residuals, applied to a surface-mounted permanent magnet synchronous motor drive system having a third-order permanent magnet back electromotive force component and a drive topology capable of providing a closed current loop for the third-order zero-sequence current, characterized in that, include: Step 1: Obtain the cross-axis voltage and current in the fundamental synchronous coordinate and the third harmonic synchronous coordinate, and construct the fundamental integer-cycle voltage residual and the third harmonic integer-cycle voltage residual respectively within an update window containing an integer number of electrical cycles; Step 2: Let the ratio of the peak value of the third harmonic current to the peak value of the fundamental current be k3. Then, combine the stationary condition of the phase current peak envelope with respect to k3 with the two full-cycle voltage residuals from Step 1 into a single electromagnetic stationary residual. Step 3: Use the same electromagnetic stationary value residual as the update error of the harmonic coefficient, and normalize it with respect to the slope of k3 to update k3; Step 4: Given I by the updated k3 and the peak phase current pk * The amplitudes of the fundamental and third harmonic currents are directly generated.

2. The method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residual as described in claim 1, characterized in that, The fundamental frequency full-cycle voltage residual and the third harmonic frequency full-cycle voltage residual are expressed as follows: in, The residual voltage of the h-th harmonic throughout the entire cycle; τ represents the compensated / estimated value of the stator phase resistance; τ is the integration time variable. To update the window length; Let be the quadrature-axis voltage of the h-th harmonic synchronous coordinate system; Let be the quadrature-axis current in the synchronous coordinate system of the h-th harmonic; Where h is 1 or 3; when the direct-axis current is controlled to zero or its window average coupling term is negligible and the cross-axis currents at the window endpoints are equal, the total cycle voltage residuals represent the fundamental back electromotive force amplitude E1 and the third back electromotive force amplitude E3, respectively. The single electromagnetic stationary value residual is: in, For the online full-cycle voltage residual , Directly constructed electromagnetic stationary residual estimator; the symbol "^" indicates an estimator obtained from online observations; Update k3 according to the following formula: Where n is the discrete update window index; γ is the dimensionless update step size, 0 < γ ≤ 1; Π K [·] is the projection operator to the feasible set K, used to simultaneously implement hardware constraints such as harmonic coefficients and fourth arm current; For the electromagnetic stationary residual estimate of the nth update window; The fundamental integer-cycle voltage residual for the nth update window; The third harmonic integer-cycle voltage residual for the nth update window; The given amplitudes of the fundamental and third harmonic currents are expressed as follows: Where F(k3) is the peak envelope of the combined phase current of the fundamental wave and the third harmonic in phase, and the fundamental wave and the third harmonic current are applied to the permanent magnet synchronous motor through current tracking and pulse width modulation; I pk * Given the allowable peak value of the phase current or the peak value of the phase current generated by the outer loop; I1 * I3 * The amplitudes of the fundamental and third harmonic currents are given respectively; the superscript * indicates the given value.

3. The method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residual as described in claim 2, characterized in that, The three-phase current and the three-phase permanent magnet back electromotive force satisfy equations (1) and (2) respectively: （1） Among them, i a i b i c These represent the instantaneous values ​​of the three-phase stator currents A, B, and C, respectively; I1 and I3 represent the peak values ​​of the fundamental and third harmonic currents, respectively; θ e The rotor electrical angle; （2） Among them, e a e b e c E1 and E3 are the instantaneous values ​​of the three-phase permanent magnet back electromotive force (EMF) of phases A, B, and C, respectively; E1 and E3 are the peak values ​​of the fundamental and third-phase permanent magnet back EMF, respectively. The average electromagnetic torque is obtained from the conservation of electromagnetic power: （3） in, The average electromagnetic torque; p n ω is the number of pole pairs of the motor; e ψ is the electric angular velocity. f1 ψ f3 These are the fundamental and third harmonic amplitudes of the permanent magnet flux linkage, respectively, and E1 = ω. e ·ψ f1 E3=3ω e ·ψ f3 .

4. The method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residual as described in claim 3, characterized in that, The peak envelope of the phase current is defined as: （4） （5） Where F(k3) is the dimensionless peak envelope function of the phase current; max represents the maximum value within one fundamental electrical cycle; θ is the electrical angle variable used to traverse the composite phase current waveform within θ∈[0,2π); When k3 is not less than 1 / 9, the normalized average torque target under the condition of limited phase current peak value is: （6） Where J(k3) is the target average electromagnetic torque corresponding to the peak value of the unit phase current; I pk This represents the peak value of the synthesized phase current. Its stationary condition is simplified from equation (7) to equation (8), and the stationary root shown in equation (9) is obtained: By calculating the stationary value of the normalized average torque target, the electromagnetic stationary value condition and its stationary value root are obtained: （7） in, This represents the logarithmic derivative of the normalized average torque target with respect to the harmonic coefficient k3; its zero value corresponds to the internal stationary condition. （8） Where, ε K The theoretical electromagnetic stationary residual is constructed using the actual back electromotive forces E1 and E3; ε K =0 indicates that k3 satisfies the stationary condition of the peak-limited average torque target; （9） Among them, k3 * is the theoretical stationary root, which is dimensionless; the superscript * in equation (9) represents the optimal solution of the stationary value; to ensure that the denominator is non-zero, it is required that 6E1−3E3≠0; the engineering work area further takes the corresponding stationary root that falls into the feasible set K; It is the ratio of the peak value of the third back EMF to the peak value of the fundamental back EMF, and it is the dimensionless back EMF harmonic ratio.

5. The method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residual as described in claim 1, characterized in that, The synchronous quadrature-axis voltage model for the h-th harmonic is: （10） Among them, u qh Let i be the quadrature-axis voltage in the synchronous coordinate system of the h-th harmonic; qh i dh These are the quadrature-axis and direct-axis currents, respectively; R s L is the stator phase resistance; h The equivalent inductance for the h-th harmonic; For i qh The derivative with respect to time; E h Let h be the amplitude of the back electromotive force of the h-th harmonic; h∈{1,3} is the harmonic order. The updated window satisfies: （11） Among them, T w The window length is updated online; t is the window start time; N is a positive integer, indicating that the window contains N fundamental frequency cycles; window endpoint i qh Equal terms are used to make the integer-cycle integral of the inductance differential term zero; Thus, the inductance differential term disappears during the integral over the entire cycle; when the direct-axis average coupling term is negligible and the stator resistance compensation is accurate, the voltage residual over the entire cycle described in step 1 satisfies: （12） Among them, when The current at the window endpoints is consistent and When its window-averaged coupling term is negligible. ,therefore and They are used as equivalent observations of the back electromotive force of E1 and E3, respectively.

6. The method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residual as described in claim 5, characterized in that, definition: （13） in, Regarding the slope of k3; The stationary root is the online estimate obtained directly from the residual of the current window, and is dimensionless; The electromagnetic stationary residual provides the update direction and a certificate of distance from the current harmonic coefficient to the stationary root: （14） in, From the current harmonic coefficient k3 to the online estimated stationary root A dimensionless distance certificate; this relationship requires |D| to be greater than a preset minimum slope threshold D. min .

7. A method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residuals according to claim 6, characterized in that, When the voltage residuals of the two full cycles remain unchanged in adjacent update windows and the projection does not change, let This indicates the relationship between the current harmonic coefficient k3 and the fixed online estimated stationary root. The difference is: （15） in, To determine the current k when the residual voltage of the two circuits is fixed and the projection does not change. 3,n Compared to fixed online estimation stationary roots The deviation; its shrinkage proportionally by 1-γ with each update; （16） Among them, V n V is a nonnegative Lyapunov function used to prove discrete contractility; n These are only mathematical analysis quantities and do not represent the actual energy storage of the motor; When the back EMF harmonic ratio changes slowly and there is an estimation error in the whole-cycle voltage residual, the true tracking error is defined. Then it satisfies: （17） in, The tracking error is relative to the time-varying true stationary root; For the nth window, The first term represents the corresponding online estimated stationary root; the second term represents the residual estimation error; and the third term represents the drift of the optimal root caused by changes in operating conditions.

8. The method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residual as described in claim 7, characterized in that, The third harmonic is a zero-sequence third harmonic. The motor neutral point is connected to the fourth bridge arm, and the current in the fourth bridge arm satisfies: （18） Among them, i N I is the return current from the motor neutral point through the fourth bridge arm. N,pk This represents the peak current of the fourth bridge arm; the negative sign is determined by the selected neutral point current reference direction. Peak phase current command Already by I pk,max Under the premise of limiting, a feasible set is constructed based on the upper limit of the peak current of the fourth bridge arm and the upper limit of the harmonic coefficient allowed by the hardware: （19） Where K is the dimensionless feasible set of harmonic coefficients k3; I N,max For the fourth bridge arm, the allowable peak current; k hw,max The maximum allowable third harmonic coefficient for the driver; peak phase current I pk Before entering the set for judgment, it has already been determined by I. pk,max Limit the amplitude; The projection operator Π K The harmonic coefficients are directly restricted to the same set of physical feasibility.

9. A method for harmonic self-tuning of a permanent magnet synchronous motor based on peak envelope electromagnetic stationary residuals according to claim 1, characterized in that, Phase voltage is reconstructed from DC bus voltage and actual switching state or duty cycle of three-phase four-bridge inverter; stator current is sampled by phase current sensor; rotor electrical angle is provided by position sensor or position observer; the fundamental and third harmonic full-cycle voltage residuals are summed by synchronous coordinate transformation of the sample values ​​in the window. When the outer loop input is the average electromagnetic torque Te*, the peak phase current is generated by the following formula and limited by the upper limit of the peak phase current: （20） in, The average electromagnetic torque given for the outer loop; I pk,max The upper limit of the allowable peak phase current; sat[0,I pk,max ][·] indicates that the calculation result within the parentheses is limited to [0, I]. pk,max ] interval.

10. A permanent magnet synchronous motor driver, comprising a three-phase four-arm inverter, a DC bus voltage sampling unit, a phase current sampling unit, a rotor position acquisition unit, a processor, and a memory, wherein the neutral point of the permanent magnet synchronous motor is connected to the fourth arm, characterized in that, When the program in the memory is executed by the processor, it implements the harmonic self-tuning method for a permanent magnet synchronous motor based on the peak envelope electromagnetic stationary residual as described in any one of claims 1 to 9.

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