A method for belt-speed re-switching of permanent magnet synchronous motors based on virtual impedance

Abstract

This invention discloses a method for speed-based re-start of a permanent magnet synchronous motor based on virtual impedance, specifically including the following steps: Step 1, establishing an adaptive control law for the virtual inductor and calculating the adaptive virtual inductor; calculating the stable range of the virtual resistance; Step 2, obtaining the rotor estimation error from the virtual resistance and virtual inductor obtained in Step 1; Step 3, estimating the rotor position and rotor speed of the permanent magnet synchronous motor using the rotor error obtained in Step 2 through a phase-locked loop. This invention fundamentally solves the problems of large position estimation errors, system oscillation, and even speed-based re-start failure caused by the dynamic change of stator inductance with factors such as magnetic saturation in the traditional fixed virtual inductor method; at the same time, for the stable range of the virtual resistance, the maximum value is continuously updated in conjunction with the adaptive virtual inductor, avoiding the problem of system oscillation caused by the virtual resistance exceeding the stability boundary.

Description

Technical Field

[0001] This invention belongs to the field of sensorless control technology for permanent magnet synchronous motors, specifically relating to a method for re-suspension of speed on a permanent magnet synchronous motor based on virtual impedance. Background Technology

[0002] Permanent magnet synchronous motors, with their advantages of high power density, high efficiency, and low torque ripple, have become core power devices in industrial drives, new energy vehicles, and other fields. Meanwhile, sensorless control technology estimates rotor position and speed through algorithms, completely eliminating the problems of increased size and cost associated with position sensors such as photoelectric encoders, and significantly improving system reliability.

[0003] The starting of a motor in a free-rotating state without sensor control is called belt-speed restart (or "fly-start"). For belt-speed restart of permanent magnet synchronous motors, there are currently many methods based on virtual resistance. These methods simulate the characteristics of variable resistors through an inverter, effectively suppressing inrush current and achieving parameter-independent rotor position and speed estimation using estimated current. However, because the influence of stator inductance is not considered, the system's equivalent impedance has an inherent inductive component, causing the current phase to lag behind the back electromotive force. Although some improvement schemes introduce virtual inductance to compensate for stator inductance, the fixed virtual inductance value, while the stator inductance dynamically changes with factors such as magnetic saturation, means that the fixed virtual inductance cannot match in real time. The residual inductive component further increases the position estimation error. Simultaneously, changes in virtual inductance alter the stability range of the virtual resistance. Fixed virtual inductance designs do not consider this coupling relationship, and under extreme conditions, the virtual resistance may exceed the stability boundary, causing system oscillation. Summary of the Invention

[0004] The purpose of this invention is to provide a speed-based re-switching method for permanent magnet synchronous motors based on virtual impedance, which solves the problems in existing methods where the position estimation error is large due to the influence of factors such as stator inductance magnetic saturation, and the inability of fixed virtual inductance to match in real time, and the virtual resistance may exceed the stability boundary, causing system oscillation.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for re-energizing a permanent magnet synchronous motor based on virtual impedance includes the following steps:

[0007] Step 1: Design the virtual resistor and adaptive virtual inductor;

[0008] Step 1.1: Establish the adaptive control law of the virtual inductor and calculate the adaptive virtual inductor;

[0009] Step 1.2: Calculate the stable range of the virtual resistance;

[0010] Step 2: Obtain the rotor estimation error from the virtual resistance and virtual inductance obtained in Step 1;

[0011] Step 3: The rotor estimation error obtained in Step 2 is used to obtain the estimated rotor position and estimated rotor speed through a phase-locked loop.

[0012] Furthermore, the specific steps in step 1.1 are as follows:

[0013] Define a positive definite Lyapunov candidate function containing only a position error term:

[0014] (1)

[0015] in, For rotor estimation error;

[0016] Find the time derivative of V(t):

[0017] (2)

[0018] Because when a sensory component exists, Approximately linear with the magnitude of the sense:

[0019] (3)

[0020] Where k is a constant greater than zero, L v (t) represents the virtual inductance value at time t;

[0021] Substituting equation (3) into equation (2), we get:

[0022] (4)

[0023] To ensure global asymptotic stability, it is necessary to make Take the adaptive law:

[0024] (5)

[0025] Where γ is the adaptive gain, and its value increases with higher sampling frequencies; sign[ [t] ensures correct adaptive direction for both forward and reverse rotation, i inv_d (t) is a weighted average of the introduced current amplitude to avoid excessive adaptive noise at low currents;

[0026] Substituting equation (5) into equation (4), we get:

[0027] (6)

[0028] Satisfies Lyapunov stability, and θ err When L approaches 0,v It will converge to the optimal compensation value, thereby offsetting the residual insensitivity;

[0029] The continuous-time adaptive law is then discretized to obtain the adaptive virtual inductance value L. v (k):

[0030] (7)

[0031] Among them, T s L is the system sampling period; v (k) represents the adaptive virtual inductance value for the k-th time step; L v (k-1) is the adaptive virtual inductance value for the (k-1)th time step;

[0032] Set the initial value of the virtual inductance to the negative value of the d-axis inductance:

[0033] (8)

[0034] in, The initial value of the virtual inductance, This is the nominal value of the d-axis inductance;

[0035] Configure virtual inductor limiting protection to prevent over-compensation or under-compensation:

[0036] (9)

[0037] Among them, L d_n This is the nominal value of the d-axis stator inductance.

[0038] Furthermore, the specific steps in step 1.2 are as follows:

[0039] The voltage command for SVPWM input is implemented using an algebraic virtual impedance, as shown in formula (10) below:

[0040] (10)

[0041] Where k is the kth sampling period, R v (k) is the virtual resistance of the k-th cycle, L v (k) represents the adaptive virtual inductance at the k-th time step. Estimate the rotor's electric angular velocity for the k-th pulse. , For the two-phase stator current of the k-th phase, , The voltage signal input to the k-th SVPWM is shown.

[0042] The total equivalent impedance of the system is:

[0043] (11)

[0044] Among them, R s L is the stator resistance. d The actual value of the stator inductance along the d-axis is given. To realize the virtual inductance, differential control needs to be introduced. However, differential control is sensitive to noise. Therefore, an algebraic approximation is used to replace the differential term, and the differential term s is replaced with jw.

[0045] By adaptively adjusting L v (k) makes the equivalent inductance L eq (k)=L d +L v (k) approaches 0, thus realizing the pure resistive nature of the system's equivalent impedance:

[0046] (12)

[0047] To suppress inrush current, the initial value of the virtual resistance is set to its maximum value within its stable range; the stable range of the virtual resistance changes in real time with the virtual inductance, and its maximum stable value is:

[0048] (13)

[0049] Where η is the stability margin coefficient;

[0050] Each update L v (k) After that, the limit of the virtual resistance is updated synchronously:

[0051] (14)

[0052] When R v (k) is close to 0.8R v_max When (k), the adaptive gain is reduced to prevent the virtual resistance from exceeding the stable range, thereby achieving coordinated stable control of the virtual resistance and virtual inductance.

[0053] Furthermore, the specific steps for step 2 are as follows:

[0054] Rotor estimation error for:

[0055] (15)

[0056] in, This represents the actual rotor position. To estimate the rotor position;

[0057] Since the virtual resistance and virtual inductance make the stator impedance resistive, and the stator current is regarded as the q-axis component, the estimation of the d-axis current in the synchronous rotating coordinate system can be simplified to:

[0058] (16)

[0059] Among them, i inv_d To estimate the d-axis current in a synchronously rotating coordinate system; i d i q with I s These represent the amplitudes of the d-axis current, q-axis current, and stator current in the actual synchronous rotating coordinate system; sign [i q ] for i q The sign function, whose value is 1 or -1; although i q It cannot be measured directly, but sign [i] can be derived from the direction of rotation. q The result is that, under resistive load, sign[i] q ], sign[E q ], sign[ They are equal;

[0060] The rotor estimation error can be obtained from formula (16):

[0061] (17)

[0062] in, To estimate the current reference value, since this estimated current will generate magnetic braking torque on the motor, if the reference value is set too high, the motor will experience a large braking torque; if it is set too low, the estimated speed and position will fluctuate significantly due to current ripple caused by measurement noise. Therefore, its range is limited as follows:

[0063] (18)

[0064] In the formula, For the maximum back electromotive force, This represents the maximum virtual resistance.

[0065] Furthermore, the specific steps for step 3 are as follows:

[0066] The open-loop transfer function of the phase-locked loop is:

[0067] (19)

[0068] Where, k p_pll For the phase-locked loop proportional gain, k i_pll is the integral gain of the phase-locked loop; s is the complex frequency variable of the Laplace transform;

[0069] The closed-loop transfer function is:

[0070] (20)

[0071] The closed-loop transfer function is that of a second-order low-pass filter, and its performance can be estimated by tuning the PI gain; ζ is the damping ratio, ω n Given the natural frequency, the PI gain is:

[0072] (twenty one)

[0073] Rotor position error in the kth step The estimated rotational speed obtained through the PI controller is as follows:

[0074] (twenty two)

[0075] in It is the estimated rotor speed in the k-th cycle;

[0076] The estimated rotor position can be obtained by integrating the estimated rotor speed.

[0077] (twenty three)

[0078] Differentiating both sides of equation (23) and rearranging, we get:

[0079] (twenty four)

[0080] in, It is the estimated rotor position for the kth time step.

[0081] Compared with the prior art, the present invention has the following beneficial effects:

[0082] This invention employs a speed-based re-suspension method for permanent magnet synchronous motors based on virtual impedance. This fundamentally solves the problems of large position estimation errors, system oscillations, and even speed-based re-suspension failures caused by the dynamic changes in stator inductance due to factors such as magnetic saturation in traditional fixed virtual inductance methods. Furthermore, by continuously updating the maximum value of the virtual resistance within its stable range using an adaptive virtual inductance, it avoids the problem of the virtual resistance potentially exceeding the stability boundary, which could lead to system oscillations. Attached Figure Description

[0083] Figure 1 This is a block diagram of the control system used in the present invention, a method for re-switching a permanent magnet synchronous motor based on virtual impedance.

[0084] Figure 2 This is a flowchart of a method for speed-driven re-switching of a permanent magnet synchronous motor based on virtual impedance according to the present invention;

[0085] Figure 3 This is an adaptive virtual inductance control block diagram proposed in the present invention, a method for re-spinning a permanent magnet synchronous motor based on virtual impedance.

[0086] Figure 4This is a block diagram of the phase-locked loop structure used in the method for re-switching a permanent magnet synchronous motor based on virtual impedance according to the present invention. Detailed Implementation

[0087] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0088] like Figure 2 As shown, the present invention provides a method for re-energizing a permanent magnet synchronous motor based on virtual impedance, which is implemented according to the following steps:

[0089] Step 1: Design the virtual resistor and adaptive virtual inductor;

[0090] Step 1.1: Establish the adaptive control law of the virtual inductor and calculate the adaptive virtual inductor;

[0091] The specific steps are as follows:

[0092] Define a positive definite Lyapunov candidate function containing only a position error term:

[0093] (1)

[0094] in, For rotor estimation error;

[0095] Find the time derivative of V(t):

[0096] (2)

[0097] Because when a sensory component exists, Approximately linear with the magnitude of the sense:

[0098] (3)

[0099] Where k is a constant greater than zero, L v (t) represents the virtual inductance value at time t;

[0100] Substituting equation (3) into equation (2), we get:

[0101] (4)

[0102] To ensure global asymptotic stability, it is necessary to make Take the adaptive law:

[0103] (5)

[0104] Where γ is the adaptive gain, and its value increases with higher sampling frequencies; sign[ [t] ensures correct adaptive direction for both forward and reverse rotation, i inv_d(t) is a weighted average of the introduced current amplitude to avoid excessive adaptive noise at low currents;

[0105] Substituting equation (5) into equation (4), we get:

[0106] (6)

[0107] Satisfies Lyapunov stability, and θ err When L approaches 0, v It will converge to the optimal compensation value, thereby offsetting the residual insensitivity;

[0108] The continuous-time adaptive law is then discretized to obtain the adaptive virtual inductance value L. v (k):

[0109] (7)

[0110] Among them, T s L is the system sampling period; v (k) represents the adaptive virtual inductance value for the k-th time step; L v (k-1) is the adaptive virtual inductance value for the (k-1)th time step;

[0111] Set the initial value of the virtual inductance to the negative value of the d-axis inductance:

[0112] (8)

[0113] in, The initial value of the virtual inductance, This is the nominal value of the d-axis inductance;

[0114] Configure virtual inductor limiting protection to prevent over-compensation or under-compensation:

[0115] (9)

[0116] Among them, L d_n This is the nominal value of the d-axis stator inductance.

[0117] Step 1.2: Calculate the stable range of the virtual resistance;

[0118] The specific steps are as follows:

[0119] The voltage command for SVPWM input is implemented using an algebraic virtual impedance, as shown in formula (10) below:

[0120] (10)

[0121] Where k is the kth sampling period, R v (k) is the virtual resistance of the k-th cycle, L v(k) represents the adaptive virtual inductance at the k-th time step. Estimate the rotor's electric angular velocity for the k-th pulse. , For the two-phase stator current of the k-th phase, , The voltage signal input to the k-th SVPWM is shown.

[0122] The total equivalent impedance of the system is:

[0123] (11)

[0124] Among them, R s L is the stator resistance. d The actual value of the stator inductance along the d-axis is given. To realize the virtual inductance, differential control needs to be introduced. However, differential control is sensitive to noise. Therefore, an algebraic approximation is used to replace the differential term, and the differential term s is replaced with jw.

[0125] By adaptively adjusting L v (k) makes the equivalent inductance L eq (k)=L d +L v (k) approaches 0, thus realizing the pure resistive nature of the system's equivalent impedance:

[0126] (12)

[0127] To suppress inrush current, the initial value of the virtual resistance is set to its maximum value within its stable range; the stable range of the virtual resistance changes in real time with the virtual inductance, and its maximum stable value is:

[0128] (13)

[0129] Where η is the stability margin coefficient;

[0130] Each update L v (k) After that, the limit of the virtual resistance is updated synchronously:

[0131] (14)

[0132] When R v (k) is close to 0.8R v_max When (k), the adaptive gain is reduced to prevent the virtual resistance from exceeding the stable range, thereby achieving coordinated stable control of the virtual resistance and virtual inductance.

[0133] Step 2: Obtain the rotor estimation error from the virtual resistance and virtual inductance obtained in Step 1;

[0134] The specific steps are as follows:

[0135] Rotor estimation error for:

[0136] (15)

[0137] in, This represents the actual rotor position. To estimate the rotor position;

[0138] Since the virtual resistance and virtual inductance make the stator impedance resistive, and the stator current is regarded as the q-axis component, the estimation of the d-axis current in the synchronous rotating coordinate system can be simplified to:

[0139] (16)

[0140] Among them, i inv_d To estimate the d-axis current in a synchronously rotating coordinate system; i d i q with I s These represent the amplitudes of the d-axis current, q-axis current, and stator current in the actual synchronous rotating coordinate system; sign [i q ] for i q The sign function, whose value is 1 or -1; although i q It cannot be measured directly, but sign [i] can be derived from the direction of rotation. q The result is that, under resistive load, sign[i] q ], sign[E q ], sign[ They are equal;

[0141] The rotor estimation error can be obtained from formula (16):

[0142] (17)

[0143] in, To estimate the current reference value (during the adjustment process, to estimate the initial speed and position, the amplitude of the stator current is controlled at a relatively small value; this relatively small stator current is...), The reference value is determined before the start-up process of the flying car. Since this estimated current will generate magnetic braking torque on the motor, if the reference value is set too high, the motor will bear a large braking torque; if it is too low, the estimated speed and position will fluctuate significantly due to the current ripple caused by measurement noise. Therefore, its range is limited as follows:

[0144] (18)

[0145] In the formula, For the maximum back electromotive force, This represents the maximum virtual resistance.

[0146] Step 3, the rotor estimation error obtained in Step 2 is processed as follows: Figure 4 The phase-locked loop shown obtains the estimated rotor position and estimated rotor speed of the permanent magnet synchronous motor;

[0147] The specific steps are as follows:

[0148] The open-loop transfer function of the phase-locked loop is:

[0149] (19)

[0150] Where, k p_pll For the phase-locked loop proportional gain, k i_pll is the integral gain of the phase-locked loop; s is the complex frequency variable of the Laplace transform;

[0151] The closed-loop transfer function is:

[0152] (20)

[0153] The closed-loop transfer function is that of a second-order low-pass filter, and its performance can be estimated by tuning the PI gain; ζ is the damping ratio, ω n Given the natural frequency, the PI gain is:

[0154] (twenty one)

[0155] Rotor position error in the kth step The estimated rotational speed obtained through the PI controller is as follows:

[0156] (twenty two)

[0157] in It is the estimated rotor speed in the k-th cycle;

[0158] The estimated rotor position can be obtained by integrating the estimated rotor speed.

[0159] (twenty three)

[0160] Differentiating both sides of equation (23) and rearranging, we get:

[0161] (twenty four)

[0162] in, It is the estimated rotor position for the kth time step.

[0163] Specific working principle: The control system block diagram of this invention, based on a method for re-suspension of a permanent magnet synchronous motor with virtual impedance, is shown below. Figure 1As shown. The three-phase stator current i of the built-in permanent magnet synchronous motor in the three-phase stationary coordinate system is detected by a current Hall sensor. a i b i c The detected three-phase stator current is transformed by abc / αβ to obtain i in the two-phase stationary coordinate system. α i β i α i β Multiply by the output values ​​R of the virtual resistance regulator and the virtual inductance regulator respectively. v (The initial value is set to the maximum value within the stable range) and L v (The initial value is set to the negative of the d-axis inductance), the virtual inductance term needs to be multiplied by the estimated rotational speed. (Initial value set to 0), thus obtaining the input voltage signal V of SVPWM. α_svm V β_svm ; Detect the current i obtained by the abc / αβ transformation at this time. α i β Then, after αβ / dq transformation, i is obtained. inv_d i inv_q (Estimate the current along the d-q axis); then estimate the current i along the d-axis. inv_d With stator current reference value (Given value) is divided by the sign function value of the rotational speed to be estimated, sign[ The rotor error θ is obtained. err After Figure 4 The phase-locked loop shown calculates the estimated rotational speed. Then, the estimated rotor position is obtained by integrating the estimated rotational speed. .

[0164] Figure 3 This is the control block diagram for the adaptive virtual inductor. It uses the negative value of the d-axis inductance as a reference value and adjusts the output virtual inductor by combining the position error value with the adaptive controller, so that the load of the entire system is always purely resistive.

[0165] Figure 2 This is a flowchart of a speed-based re-start method for permanent magnet synchronous motors based on virtual impedance. Initially, the motor speed is not zero, and both the speed and rotor position are unknown. First, the value L of the virtual inductance at the k-th pulse is calculated using the adaptive rate of the virtual inductance. v (k), whose initial value is set to the negative of the nominal value of the d-axis inductance: Next, determine the adjustable range of the virtual resistor from 0 to... The initial value of the virtual resistor is set to its maximum allowable value. Then, the input signal of SVPWM is calculated using formula (10). , The estimated dq-axis current values ​​are obtained through the Park transformation. , The initial estimated rotational speed and rotor position are set as follows: Then, the rotor estimation error is calculated using formula (17). Finally, the estimated rotational speed is calculated using a phase-locked loop. and estimate rotor position Determine if the set belt speed re-spinning time has been reached. If not, obtain the estimated rotational speed for the k-th cycle. and estimate rotor position Carry the calculation to the next cycle (i.e., the (k+1)th cycle) and repeat the above calculation process; repeat the above process until the designed belt speed re-spinning time is reached, and finally obtain the belt speed re-spinning time required. , .

[0166] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A method for re-energizing a permanent magnet synchronous motor based on virtual impedance, characterized in that, Specifically, the steps include the following: Step 1: Design the virtual resistor and adaptive virtual inductor; Step 1.1: Establish the adaptive control law of the virtual inductor and calculate the adaptive virtual inductor; Step 1.2: Calculate the stable range of the virtual resistance; Step 2: Obtain the rotor estimation error from the virtual resistance and virtual inductance obtained in Step 1; Step 3: The rotor estimation error obtained in Step 2 is used to obtain the estimated rotor position and estimated rotor speed through a phase-locked loop.

2. The method for re-energizing a permanent magnet synchronous motor based on virtual impedance according to claim 1, characterized in that, The specific steps for step 1.1 are as follows: Define a positive definite Lyapunov candidate function containing only a position error term: (1) in, For rotor estimation error; Find the time derivative of V(t): (2) Because when there is a sensory component, Approximately linear with the magnitude of intuition: (3) where k is a constant greater than zero, L v (t) is the virtual inductance value at time t; Substituting equation (3) into equation (2), we get: (4) To ensure global asymptotic stability, it is necessary to make Take the adaptive law: (5) Where γ is the adaptive gain, its value increases with higher sampling frequencies; sign[ [t] ensures correct adaptive direction for both forward and reverse rotation, i inv_d (t) is a weighted average of the introduced current amplitude to avoid excessive adaptive noise at low currents; Substituting equation (5) into equation (4), we get: (6) Satisfies Lyapunov stability, and θ err When L approaches 0, v It will converge to the optimal compensation value, thereby offsetting the residual insensitivity; The continuous-time adaptive law is then discretized to obtain the adaptive virtual inductance value L. v (k): (7) Among them, T s L is the system sampling period; v (k) represents the adaptive virtual inductance value for the k-th time step; L v (k-1) is the adaptive virtual inductance value for the (k-1)th time step; Set the initial value of the virtual inductance to the negative value of the d-axis inductance: (8) in, The initial value of the virtual inductance, This is the nominal value of the d-axis inductance; Configure virtual inductor limiting protection to prevent over-compensation or under-compensation: (9) Among them, L d_n This is the nominal value of the d-axis stator inductance.

3. The method for re-energizing a permanent magnet synchronous motor based on virtual impedance according to claim 1, characterized in that, The specific steps for step 1.2 are as follows: The voltage command for SVPWM input is implemented using an algebraic virtual impedance, as shown in formula (10) below: (10) Where k is the kth sampling period, R v (k) is the virtual resistance of the k-th cycle, L v (k) represents the adaptive virtual inductance at the k-th time step. Estimate the rotor electric angular velocity for the k-th pulse. , For the two-phase stator current of the k-th phase, , The voltage signal input to the k-th SVPWM is shown. The total equivalent impedance of the system is: (11) Among them, R s L is the stator resistance. d The actual value of the stator inductance along the d-axis is given. To realize the virtual inductance, differential control needs to be introduced. However, differential control is sensitive to noise. Therefore, an algebraic approximation is used to replace the differential term, and the differential term s is replaced with jw. By adaptively adjusting L v (k), making the equivalent inductance L eq (k)=L d +L v (k) approaches 0, thus realizing the pure resistive nature of the system's equivalent impedance: (12) To suppress inrush current, the initial value of the virtual resistance is set to its maximum value within its stable range; the stable range of the virtual resistance changes in real time with the virtual inductance, and its maximum stable value is: (13) Where η is the stability margin coefficient; Each update L v (k) After that, the limit of the virtual resistance is updated synchronously: (14) When R v (k) is close to 0.8R v_max When (k), the adaptive gain is reduced to prevent the virtual resistance from exceeding the stable range, thereby achieving coordinated stable control of the virtual resistance and virtual inductance.

4. The method for re-energizing a permanent magnet synchronous motor based on virtual impedance according to claim 1, characterized in that, The specific steps for step 2 are as follows: Rotor estimation error for: (15) in, This represents the actual rotor position. To estimate the rotor position; Since the virtual resistance and virtual inductance make the stator impedance resistive, and the stator current is regarded as the q-axis component, the estimation of the d-axis current in the synchronous rotating coordinate system can be simplified to: (16) Among them, i inv_d To estimate the d-axis current in a synchronously rotating coordinate system; i d i q with I s These represent the amplitudes of the d-axis current, q-axis current, and stator current in the actual synchronous rotating coordinate system; sign [i q ] for i q The sign function, whose value is 1 or -1; although i q It cannot be measured directly, but sign [i] can be derived from the direction of rotation. q The result is that, under resistive load, sign[i] q ], sign[E q ], sign[ They are equal; The rotor estimation error can be obtained from formula (16): (17) in, To estimate the current reference value, since this estimated current will generate magnetic braking torque on the motor, if the reference value is set too high, the motor will experience a large braking torque; if it is set too low, the estimated speed and position will fluctuate significantly due to current ripple caused by measurement noise. Therefore, its range is limited as follows: (18) In the formula, For the maximum back electromotive force, This represents the maximum virtual resistance.

5. The method for re-energizing a permanent magnet synchronous motor based on virtual impedance according to claim 1, characterized in that, The specific steps for step 3 are as follows: The open-loop transfer function of the phase-locked loop is: (19) Where, k p_pll For the phase-locked loop proportional gain, k i_pll is the integral gain of the phase-locked loop; s is the complex frequency variable of the Laplace transform; The closed-loop transfer function is: (20) The closed-loop transfer function is that of a second-order low-pass filter, and its performance can be estimated by tuning the PI gain; ζ is the damping ratio, ω n Given the natural frequency, the PI gain is: (21) Rotor position error in the kth step The estimated rotational speed obtained through the PI controller is as follows: (22) in It is the estimated rotor speed in the k-th cycle; The estimated rotor position can be obtained by integrating the estimated rotor speed. (23) Differentiating both sides of equation (23) and rearranging, we get: (24) in, It is the estimated rotor position for the kth cycle.

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